The 32 elements you will meet in this book, out of the 118 known today.
A letter to Kym
Dear Kym,
I should tell you something first: I am not a chemist. I don’t know much chemistry at all. What I have tried to do is make the book I would have loved to read when I was your age: one that tells you who found each idea and how, that lets you try things in the kitchen, and that never just hands you a fact to learn by heart. Much of what is in here was new to me too. I also had help: I made this book with the help of AI, which searched out the research, wrote the chapters to my design, and then checked them. The explanations draw on the free courses and books that MIT and OpenStax share with the world, and on what researchers have learned about the ideas students most often get wrong. Every fact, date and number was checked against reliable sources, more than once, by checkers whose only job was to find mistakes, and every number was worked out again from scratch. Even so, a few mistakes may have slipped through. If something here doesn’t match what you find somewhere else, don’t simply trust the book: tell me, and we will find out together which is right. And where the people who really know chemistry still argue about something, the book says so.
Pick up a pencil and look at the grey tip. Now think of a diamond on a ring, flashing in the light. The pencil tip is so soft that it rubs off onto paper every time you draw. The diamond is hard enough to scratch glass. Yet they are made of the same stuff. The grey part of a pencil is mostly graphite, with a little clay mixed in to make it firmer, and graphite and diamond are both made of carbon atoms and nothing else. What makes them different is not what the atoms are but how they are joined. In graphite the atoms sit in flat sheets that slide over each other, so layers flake off onto the page as you draw. In diamond every atom is locked to four neighbours in a rigid three-dimensional frame, with no layers to slide.
That is the kind of surprise this book is full of. Chemistry is the study of what things are made of and how they change into other things. It explains why salt disappears in water and comes back as tiny cubes when the water dries up, why a cut apple goes brown, why a kettle of water can boil away without turning into anything new, why nimbu pani tastes sour, and how a battery pushes electricity through a wire. It explains you, too. The hydrogen in the water you drink was made in the first few minutes after the universe began. Most of the carbon, oxygen and iron in your body was made inside stars that lived and died before the Sun was born.
The things that do all this are far too small to see. If you could shrink yourself ten billion times, you would be about the size of a single atom. No microscope that uses light will ever show you one clearly, because atoms are thousands of times smaller than the waves of light themselves. So how do we know anything about them? That question, how do we know?, is the most important one in this book, and you will see it again and again. Every chapter tells you about real experiments: a beam of particles fired at gold foil, X-rays bounced off a salt crystal, gases weighed before and after they react. Each one taught people something about a world they could not see.
Because we cannot see atoms, every picture of them is a model: a careful drawing that shows some things truthfully and leaves other things out on purpose. A map of Mumbai is useful precisely because it is not as big as Mumbai. The diagrams in this book are maps like that. They are good for counting particles and thinking about what pushes and pulls on them. They are wrong about sizes, colours and distances, and I will tell you where each one stops being trustworthy. When a better experiment shows that a model is too simple, we do not throw it away in embarrassment. We improve it. That is how science works.
You will sometimes hear people say things like “sodium wants to lose an electron so it can have a full shell.” Be suspicious of sentences like that. Atoms do not want anything. They have no wishes and no plans. Particles move the way they do because of forces (mostly electric attraction and repulsion), because they are always jiggling with heat, and because, in any ordinary chemical change, every atom is kept. This book tries to explain everything in those terms, and I think you will find the real explanations are more interesting than the made-up ones.
This is not a book of facts to memorise. It is an adventure story, and the heroes are real people: a French tax collector who weighed everything and lost his head in the Revolution, a Russian professor who left gaps in his table for elements nobody had found, a young man from a New Zealand farm who fired particles at gold and was astonished when some bounced back. Every idea in chemistry was found by someone who was puzzled, tried things, got them wrong, and tried again. When you see a word with a little book beside it, tap it, and you will get the whole story.
One more thing. Many sections ask you to make a prediction before you find out the answer. Please actually do it, in your head or on paper. A prediction that turns out wrong is not a failure. It is the most useful moment in learning, because it shows you exactly where your picture of the world needs to change. Nobody is grading you here. Take your time, go back whenever you like, and keep asking how we know.
With love,
Amar
P.S. The book goes with the chemistry lab app. Whenever you see a dashed box marked Try it, the matching investigation in the app has the same number, so you can build, change and test the thing you have just read about.
How this book works
This book is one long adventure. It follows people across two and a half thousand years, from Greek thinkers arguing about whether you can cut a pebble forever, to a schoolteacher in Manchester weighing the invisible, to a young scientist firing particles at gold in a darkened room, to the people who built the battery in your pocket. Each of them was trying to answer the same question you are about to ask: what is everything made of, and how do we know?
There are three volumes and twelve chapters, numbered from 0 because Chapter 0 is the warm-up. Each chapter is an episode: it opens with a puzzle, follows the people who cracked it, and then explains the idea plainly, one numbered section at a time. You can read straight through, or jump to anything that makes you curious. The numbers of the sections match the investigations in the lab app.
As you read, you will meet a few kinds of boxes. Each one has one job.
Story links
Some words in the text are marked like this. Each one opens a longer story beside the page: the full adventure of how that idea was found, with the idea explained slowly, step by step. They are all collected in Stories behind the ideas, and The adventure in time puts them in the order they happened.
The cast
Chemistry was made by people: shy schoolteachers, a bookbinder, a tax collector, alchemists, a girl who studied in a secret university. Their names are story links too, and tapping one opens their life story. The cast, near the front, introduces them all.
Scenes
A small pin and a place and date, like Manchester, 1909, means the story is taking you somewhere real.
Margin notes
When a new word matters, it is marked like this in the text and explained in the margin beside it (or just below, on a narrow screen). All of them are collected in Words worth knowing at the back.
How do we know?
The experiment or measurement behind an idea. Science is not a list of facts; it is a list of facts together with the reasons we believe them.
Careful
A tempting idea that is wrong, and why it is wrong. Most of these are ideas that lots of clever people have had, so if you have had them too, you are in good company.
Try it
Something to predict, sketch or do, usually with the matching investigation in the lab app.
Try it at home
A real experiment with things from the kitchen. Everything in these boxes is safe to do, but ask an adult first, and never taste anything unless the box says it is ordinary food.
Watch and turn
Many pictures come alive: a button under them starts an animation or a 3D model you can turn with your finger. They only move when you ask.
Check yourself
One question at the end of a section. The answers, with the reasoning, are at the back of the book.
Case file
A mystery at the end of each chapter. You get the clues; you work out what is going on. The solution is hidden until you ask for it.
Numbers in this book are real measured values unless the text says they are made up for a model. A few useful habits for reading them: 10⁶ means a million (a 1 followed by six zeros), and 10⁻⁶ means one millionth. The small number written low in H₂O counts atoms: two hydrogen atoms and one oxygen atom in each molecule. A small sign written high, as in Na⁺, shows an electric charge.
Four ideas that run through everything
Chemistry can look like an enormous pile of separate facts. It is not. Almost every explanation in this book is built from four ideas, used again and again in different combinations. When something puzzles you, it is worth asking which of the four is at work.
Count everything.An atom’s number of protons decides which element it is. In ordinary chemical changes, atoms are never created or destroyed, and electric charge is never created or destroyed either. So you can always keep an account, like a shopkeeper’s ledger, of where every atom and every charge went.
Opposite charges attract.Positive and negative charges pull on each other; like charges push apart; both effects get weaker with distance. This electric attraction is what holds atoms together, holds atoms to each other, and holds molecules near their neighbours.
Jiggling against sticking.Every particle is always moving, and the hotter something is, the harder its particles jiggle. Whether a substance is solid, liquid or gas, and whether a reaction gets going, depends on a contest between that jiggling and the attractions or barriers holding things back.
Huge numbers make steady averages.Even a drop of water holds more molecules than there are grains of sand on all of Earth’s beaches. With numbers that big, the random behaviour of single particles averages out into the steady, measurable things we see: a mass on a balance, the strength of a solution, a reaction that seems to have stopped but is secretly still going both ways.
And underneath all four is a fifth habit: keep what you observe separate from the model you use to explain it. The observation is what any careful person would measure. The model is our best explanation so far, and it can always be improved by a better experiment.
Every adventure has its characters. These are some of the people you will meet in this book: secret alchemists, a weaver’s son, a blacksmith’s son who bound books, a tax collector, a nobleman’s son, an accountant who did physics at night, women who had to fight to be allowed to study, and a boy from a New Zealand farm. Tap anyone to read their life story.
The periodic table is the most useful picture in chemistry, and hardly anyone is shown how to read it. Start with five plain questions, then scroll slowly: the table builds itself beside the words.
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The adventure map
Every scene in this book happened somewhere real. Here they all are, from Abdera to Mauna Loa. Slide through time, or tap a pin to jump into the story.
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IVolume I
Particles and structure
What everything is made of, how we know, and how the same few kinds of atom build water, salt, diamond and air.
The big questionA drop of water looks perfectly smooth. Chemists say it is made of about 1.7 × 10²¹ separate, jostling molecules. How can anyone know that about something nobody can see?
Abdera, a port town in northern Greece, about 420 BCE
Our adventure begins nearly two and a half thousand years ago, with a man and a question. The man was Democritus, and he is said to have laughed so much at the foolishness of the world that people called him the laughing philosopher. The question was one you can ask about anything around you: what happens if you keep cutting it?
Take a raindrop. Cut it in half (in your imagination) and you have two smaller drops. Cut those, and again, and again. Is there an end to the cutting? Democritus, and his teacher Leucippus before him, thought there must be. Somewhere, they said, you reach pieces so small they cannot be cut any further. They called them atomos, Greek for “uncuttable”. Nobody could see these pieces, and nobody could test the idea. Aristotle, the most admired thinker of the ancient world, rejected it, and for nearly two thousand years most people agreed with him.
Trinity College, Cambridge, the 1690s
Instead, for most of those two thousand years, the people who worked hardest on what things are made of were the alchemists. In workshops from Cairo to Prague they heated, dissolved, distilled and mixed, chasing one great dream: to turn “base” metals such as lead or mercury into gold. They never managed it, but they invented much of the equipment chemists still use, and they kept careful notes on how substances behave.
One of the most devoted alchemists of all is a surprise. Isaac Newton, the Cambridge professor who worked out the laws of motion and gravity, spent years at the furnace of a small laboratory in the garden beside his rooms at Trinity College, and secretly wrote about a million words about alchemy. He published almost none of it. In 1936 a large collection of his private papers was sold at auction at Sotheby’s in London, and the economist John Maynard Keynes bought many of them. After reading them, Keynes wrote that Newton was not the first of the age of reason but “the last of the magicians”.
The alchemists’ dream will come back, with a twist, in Chapter 1. It took until the twentieth century to settle the argument beyond doubt, and the people who settled it had to learn two habits first. The first habit is keeping what you see separate from what you think is going on underneath. The second is learning to think with numbers far bigger and far smaller than anything in daily life. This short chapter is about those two habits. You will use them on every page that follows.
0.1What we see and what we think
Fill a glass with water and be a scientist for a minute. What can you find out just by looking and measuring? It is clear and colourless. It takes the shape of the glass. A 100-millilitre glassful has a mass of about 100 grams. Put it in the freezer and it turns solid at 0 °C; heat it in a pan near sea level and it boils at 100 °C. These are observations: anyone with the right equipment can check them, anywhere in the world, and they will get the same results.
Now here is a very different kind of sentence: water is made of tiny molecules, each one an oxygen atom joined to two hydrogen atoms, H₂O. Democritus would have loved it. But notice: nobody has ever looked into a glass of water and seen that. It is an inference: an explanation worked out from many observations and tested against many more. It is an extremely good inference, supported by dozens of completely different kinds of experiment, which you will meet in this book. But it belongs in a different column from “boils at 100 °C”.
Figure 0.1Two columns that a chemist keeps separate. On the left, things anyone can observe about water. On the right, the particle model that explains them. The model is drawn far larger than life and coloured for clarity; real molecules have no colour at all.
This is what makes chemistry such a detective game. A detective sees footprints, a broken window and an empty jewellery box: those are observations. “The thief came in through the window” is an inference. A good detective, like a good chemist, keeps the two apart and is always ready to change the inference when a new clue turns up.
Chemists move back and forth between three ways of describing the same thing, all the time. There is the bench view: what you see and measure in the lab or the kitchen. There is the particle view: the atoms and molecules that we think are doing the work. And there is the symbol view: the shorthand we write down, such as H₂O. A big part of learning chemistry is learning to move smoothly between the three, and to remember which one you are in.
Careful
“If you looked at water through a powerful enough magnifying glass, you would see the bent shape of the H₂O molecules, like in the diagrams.”
You would not, and not only because magnifying glasses are not strong enough. Light itself is the problem. Visible light is a wave, and its waves are between about 400 and 700 nanometres long. A water molecule is about 0.3 nanometres across: more than a thousand times smaller than the shortest wave of visible light. Light simply cannot pick out details that small. We know the shape of a water molecule from other kinds of evidence, which you will meet later. The diagrams are models drawn from that evidence, not photographs.
Understand itObservation and inference
What is it?
An observation is something anyone can see or measure for themselves, such as “water boils at 100 °C”. An inference is an explanation reasoned out from observations, such as “water is made of H₂O molecules”.
Why is it called this?
“Observe” comes from Latin observare, to watch over. “Infer” comes from Latin inferre, to carry in: you carry a conclusion in from the evidence.
What problem did it solve?
For centuries people argued about things nobody could see, with no way to settle the argument. Keeping the two columns apart shows which claims anyone can check and which still need more evidence.
Why does it work?
Anyone, anywhere, can repeat an observation, so it is hard to fool yourself about. An inference is kept only while it explains every observation and survives new tests; one stubborn new fact can overturn it.
How does it help?
It lets you build confident knowledge about things far too small to see, such as atoms, and it tells you what to test next when a clue does not fit.
Go deeper how do we know, what it isn’t, where does it stop working
How do we know?
We trust the H₂O inference because many completely different kinds of experiment, from splitting water with electricity to watching specks jiggle under a microscope, all point the same way.
What it isn’t
An inference is not a wild guess or “just an opinion”. The best inferences, like atoms, rest on so much evidence that scientists rely on them every day.
Where does it stop working?
The line can blur: even reading a thermometer relies on ideas about how thermometers work. Scientists still keep the two as separate as they can.
Your turn
Explain Observation and inference to a friend in one sentence, in your own words. Then compare it with the book’s.
An observation is something anyone can see or measure for themselves, such as “water boils at 100 °C”. An inference is an explanation reasoned out from observations, such as “water is made of H₂O molecules”.
One drop, two glasses
You need two clear glasses of still water, one warm (from a hot tap, or mixed by an adult with a little water from the kettle: warm, not scalding) and one with ice water, and food colouring. Predict first: if you let one drop fall gently into each glass and do not stir, which will spread faster, or will they be the same? Write your prediction down. Then drop them in together and watch for ten minutes. Write down what you observe (colours, shapes, how long it took in each glass). Then write one inference about what might be happening, too small to see, that lets the colour spread out without anyone stirring it, and faster in one glass than the other. Keep the two lists separate: that is exactly what scientists do. (You will find out whether your inference was right in Chapter 3.)
The mystery box
Scientists spend their lives working out what is inside things they cannot open. Practise on a box. Ask someone to tape one or two objects to the inside of a shoebox (a cork, a small cup, a ruler laid across: anything, without telling you), drop in a marble, and tape the lid shut. Now tilt the box, roll the marble, listen to it and feel it stop. Draw your best map of what is inside, and write down which observation told you each thing. Only when you have made your best inference may you open the box. You have just done, with a marble, what the scientists in this book did with atoms. One of them, in Chapter 1, will do it by firing tiny particles at a sheet of gold.
Investigation 0.1
In the app, switch between the four samples: hydrogen gas, oxygen gas, a mixture of the two, and water. For each one, write down one thing you could observe about a real sample and one thing the particle picture claims. Which of your sentences could someone check with a thermometer or a balance?
Check yourself
Which of these is an observation and which is an inference? (a) “This liquid boils at 100 °C.” (b) “This liquid is made of H₂O molecules.”
(a) is an observation: anyone with a thermometer can check it. (b) is an inference: a very well-tested explanation, but one built from evidence rather than seen directly.
0.2Powers of ten: from a flask to an atom
If atoms exist, they must be unimaginably small, and there must be unimaginably many of them. To talk about numbers like that without filling the page with zeros, scientists use powers of ten. 10³ means 10 × 10 × 10 = 1,000. 10⁻³ means one thousandth, 0.001. A millimetre is 10⁻³ metres; a nanometre is 10⁻⁹ metres, a billionth of a metre.
Take a journey down Figure 0.2. Each step is ten times smaller than the one before. Ten steps take you from something you can hold, past a grain of salt, a red blood cell and a virus, all the way to a single molecule.
Figure 0.2Ten powers of ten. Each mark is ten times smaller than the one to its left. A water molecule, about 3 × 10⁻¹⁰ m across, is as much smaller than a grain of salt as a grain of salt is smaller than a skyscraper 300 metres tall.
Masses are just as extreme. One water molecule has a mass of about 3 × 10⁻²³ grams. Even an extremely sensitive laboratory balance can only detect about a ten-millionth of a gram, 10⁻⁷ g, which is still more than a thousand million million times the mass of one molecule. So you could never weigh molecules one at a time. Chemists solved that problem the way a rice seller does: they count by weighing, using a counting unit made for the job, called the mole. A mole is 6.022 × 10²³ things, a number called Avogadro’s constant. It was chosen so that a mole of any substance has a mass in grams equal to the relative mass of its particles: 12 g for carbon-12 atoms, about 18 g for water molecules, roughly one big gulp.
A drop of water. A typical raindrop-sized drop has a mass of about 0.05 g.
Number of moles = 0.05 g ÷ 18 g per mole ≈ 0.0028 moles.
Number of molecules ≈ 0.0028 × 6.022 × 10²³ ≈ 1.7 × 10²¹.
That is 1,700,000,000,000,000,000,000 molecules in one drop.
When you have twice as many moles, you have twice the mass and twice the number of molecules. What you do not get is bigger molecules. A spoonful and a bucketful of water are made of exactly the same molecules; the bucket simply has more of them.
How many molecules in one drop?
You need a medicine dropper (or a straw you can pinch at the top), a 5 mL measuring spoon and a little water. Count how many drops it takes to fill the spoon. A spoonful of 5 mL of water has a mass of about 5 g, so divide 5 g by your number of drops to get the mass of one drop. Then follow the steps in the box above to work out how many molecules are in one of your drops. (With a typical dropper it takes about 100 drops, which gives about 0.05 g a drop.)
Paris, 1908
Back to Democritus. By 1900 most chemists used atoms every day, but some famous scientists in Europe, such as the German chemist Wilhelm Ostwald, still argued that atoms were only a handy way of talking, not real things. The person who changed their minds was Jean Perrin, a French physicist at the Sorbonne in Paris, patient and stubborn in equal measure. He looked through a microscope at tiny grains of resin, each about a thousandth of a millimetre across, floating in water. The grains never kept still. They jiggled and wandered, this way and that, for as long as he watched. The Scottish botanist Robert Brown, peering through his microscope at tiny specks released from pollen grains in water, had noticed this restless motion in 1827, and it is called Brownian motion after him.
Figure 0.3Brownian motion. A grain of resin about a thousandth of a millimetre across, floating in water, never stops wandering. Perrin tracked grains like this and recorded their zig-zag paths. The cause is invisible: water molecules striking the grain from every side, a few more on one side than the other at each instant.
In 1905 a young Albert Einstein, then working as a clerk in the patent office in Bern, Switzerland, had explained the jiggling: each grain is being battered by invisible water molecules from every side, and at each instant a few more hit one side than the other. He even worked out how far a grain should wander, depending on how many molecules there are. Perrin measured the wandering with enormous patience, marking each grain’s position again and again, and from it worked out the number of molecules in a mole. Then he measured that number in several other, completely different ways, and the answers agreed. Ostwald and most of the other doubters gave in. Perrin won the Nobel Prize in Physics in 1926.
A century later, scientists measured the number again, far more precisely, by counting the atoms in an almost perfect sphere of pure silicon, using X-rays to measure the spacing between them. The results were so good that in 2019 the number was fixed exactly: 6.022 140 76 × 10²³. Democritus’s uncuttable pieces had been counted.
Understand itAtom
What is it?
The smallest piece of an element that is still that element. Everything you can touch is built from atoms, joined together in different ways.
Why is it called this?
From the Greek atomos, “uncuttable”, the name Leucippus and Democritus gave their imagined smallest pieces. The name turned out to be wrong: in Chapter 1 you will see atoms opened up.
What problem did it solve?
It explained why substances combine in fixed amounts, and why melting, boiling and dissolving never make matter vanish: the same pieces are only being rearranged.
Why does it work?
Matter really is made of separate particles, far too small to see, and chemical changes rearrange them instead of creating or destroying them.
How does it help?
It lets chemists count by weighing, using the mole, and predict how much of each substance a change will need and make.
Go deeper how do we know, what it isn’t, where does it stop working
How do we know?
Perrin’s measurements of Brownian motion, and several other completely different methods, all gave the same number of molecules in a mole. That agreement convinced even the doubters.
What it isn’t
Not a tiny coloured ball like the drawings. Atoms have no colour, and as Chapter 1 shows, an atom is mostly empty space.
Where does it stop working?
“Uncuttable” fails: atoms have a nucleus and electrons inside, and nuclear processes can even turn one element into another.
Your turn
Explain Atom to a friend in one sentence, in your own words. Then compare it with the book’s.
The smallest piece of an element that is still that element. Everything you can touch is built from atoms, joined together in different ways.
Investigation 0.2
Keep the molar mass at 18 g per mole and change the amount from 0.25 mol to 2 mol. Before you look, predict what happens to the mass and to the number of molecules when you double the amount. Then predict what happens to the size of each molecule.
Check yourself
One mole of water has a mass of about 18 g and contains 6.022 × 10²³ molecules. Each molecule contains three atoms. How many atoms are in that 18 g of water?
3 × 6.022 × 10²³ ≈ 1.8 × 10²⁴ atoms: two hydrogen atoms and one oxygen atom in each of the 6.022 × 10²³ molecules. Always say what you are counting.
Case file 0
The case of the vanishing water
A student puts 0.90 g of water into a strong, empty 2-litre glass flask, seals it, and weighs it: 250.90 g. She heats the flask to 120 °C until every drop has disappeared. Her friend says: “The water has broken up into hydrogen and oxygen gas, and the flask must be lighter now that the liquid has gone.”
Weighed while still hot and sealed, the flask is 250.90 g.
As the flask cools, droplets of colourless liquid form on the inside of the glass. The liquid boils at 100 °C, just like water.
0.90 g of water is 0.050 mol, which is about 3.0 × 10²² molecules.
What happened to the water? Which clue rules out each half of the friend’s claim?
Show the solution
The water turned to invisible water vapour: the same H₂O molecules, now spread through the whole flask instead of sitting in a puddle at the bottom. Clue 1 rules out “lighter”: nothing left the sealed flask, so the mass did not change. Clue 2 rules out “broken up”: the liquid that came back behaves exactly like water, because it is water. A mixture of hydrogen and oxygen would not condense on cooling. The molecules never changed; only their spacing did. Clue 3 reminds you how many molecules were wandering around the flask while you couldn’t see them.
What this chapter can’t explain yet
So Democritus was right: there are uncuttable pieces, and we can even count them. But picturing water as a crowd of tiny balls treats each atom as featureless. It cannot tell us what makes an oxygen atom different from a hydrogen atom, or where electric charge comes from. In the next chapter the adventure moves to a laboratory in Cambridge in 1897, where someone is about to discover that atoms are not uncuttable after all.
1
Chapter 1
What makes an atom?
The big questionTable salt contains sodium ions, Na⁺, which have exactly as many electrons as an atom of neon. So why doesn’t salt contain neon?
At the end of Chapter 0, Democritus’s uncuttable pieces had been counted. But the people who counted them already knew a secret that would have astonished him: atoms can be cut. They have insides.
Here is a puzzle to carry through this chapter. Gold and mercury sit side by side in the periodic table. Gold is a heavy yellow metal that stays bright for thousands of years. Mercury is a silvery liquid at room temperature that runs about like quicksilver, which is its old name. And yet, deep inside, a mercury nucleus has exactly one more proton than a gold nucleus: 80 instead of 79. One tiny particle separates a wedding ring from a puddle of liquid metal. This chapter opens the atom up, counts what is inside, and finds out which of those counts decides what an atom is.
1.1Inside an atom
Cambridge, 1897
The first crack in the uncuttable atom appeared in a glass tube. At the Cavendish Laboratory in Cambridge, J. J. Thomson, a Manchester bookseller’s son who had become head of the laboratory at just 28, pumped nearly all the air out of a tube, sealed a metal plate into each end, and connected them to a high voltage. A ghostly beam streamed from one plate, making the glass glow where it struck. Thomson bent the beam with magnets and with electric charges, and from how much it bent he worked out that it was made of tiny particles with negative charge, far lighter than any atom. It did not matter which metal he used for the plates or which gas was left in the tube: the particles were always the same. So every atom must contain them. These were electrons, and the atom had just been shown to have parts.
Today we know every atom is built from three kinds of smaller particle. Protons carry a positive electric charge. Neutrons carry no charge at all. Electrons carry a negative charge, exactly as strong as a proton’s positive one but opposite in sign. Protons and neutrons are packed together in a tiny, dense centre called the nucleus. Electrons occupy the much larger space around it.
But Thomson did not know about the nucleus. He imagined the electrons dotted through a soft ball of positive charge, like currants in a pudding. Finding out how wrong that picture was took a darkened room in Manchester.
Manchester, 1909
Picture a small room with the blinds down. Hans Geiger, a German physicist, and Ernest Marsden, a twenty-year-old student, sit in the dark for half an hour until their eyes adjust. In front of them is a source of alpha particles: small, fast, positively charged bullets shot out by radioactive radium. The bullets are aimed at a sheet of gold foil only about a thousand atoms thick. Beyond the foil is a screen that gives off a tiny flash of light each time an alpha particle hits it, and the two men count the flashes through a microscope, one by one.
Predict first. Remember the mystery box from Chapter 0: this is the same game, with gold atoms in the box and alpha particles for marbles. If each gold atom really were a soft pudding, with its positive charge spread thinly all through it, what would you expect the fast alpha particles to do when they hit the foil? Decide before you read on.
Their professor, Ernest Rutherford, a farmer’s son from New Zealand with a booming voice and a habit of singing hymns, loudly and off-key, as he walked round the lab, expected the bullets to pass through the soft “pudding” atoms of gold with hardly a wobble, and almost all of them did. But about one in several thousand was turned aside by a large angle, and a very few came almost straight back towards the source. Rutherford said it was as surprising as firing a heavy shell at a sheet of tissue paper and having it bounce back at you. He thought about it for nearly two years. In 1911 he gave the only explanation that worked: each gold atom’s positive charge and almost all its mass are crammed into a minute centre, with mostly empty space around it. The pudding was gone. The nucleus had arrived. (If you predicted that nearly all would sail straight through, you were right about the many, as Rutherford was. The surprise was in the few: a soft pudding has nothing hard enough to send anything back.)
Figure 1.1The gold-foil experiment, in outline. Most alpha particles pass straight through the foil. A few are deflected sharply, and a very few bounce back. Only a tiny, heavy, positively charged nucleus can explain those rebounds.
So almost all of an atom’s mass is in its nucleus, because a proton or a neutron has nearly 2,000 times the mass of an electron. But almost all of an atom’s size comes from its electrons. If an atom were blown up to the size of a cricket stadium, its nucleus would be about the size of a pea on the pitch, and the rest of the stadium would be the region where its electrons are found.
A grain of salt and a very big atom
Ask an adult to come outside with you to a park or a long, safe pavement. Put one grain of salt on the ground: that is your nucleus. Now walk away from it, counting your steps. For a carbon atom built to this scale, the edge of the atom would be somewhere between about 5 and 15 metres away (roughly seven to twenty big steps), depending on how you measure an atom’s edge. Turn round and look back at the grain you can hardly see. Almost all of the atom’s mass is in that grain. Everything between you and it is the space where the atom’s six electrons are found. That is why most of Geiger and Marsden’s alpha particles flew straight through.
Drawing an atom on a page is a problem, then: draw the nucleus big enough to see and the atom would not fit in the room. So chemists use a different kind of picture.
Figure 1.2A counting model of a carbon-12 atom: six protons (+) and six neutrons packed into the nucleus, and six electrons (−) in the region around it. The drawing is good for counting. It is badly wrong about size: drawn to scale, the nucleus would be far too small to see on this page.
The electrons in that drawing are dots scattered around the nucleus. They are not on tracks, and the dots are not where real electrons “are” at some moment. Electrons do not behave like tiny planets, and we will improve this part of the picture as the book goes on. For now, this is a counting model: it is drawn to help you count how many of each particle there are, and nothing more.
Understand itThe nucleus
What is it?
The tiny centre of an atom, made of protons and neutrons. It holds almost all of the atom’s mass but takes up almost none of its space.
Why is it called this?
From Latin nucleus, “kernel”, which comes from a word for a little nut: the hard centre inside a fruit. Rutherford was using the word for the atom’s core by 1912.
What problem did it solve?
Thomson’s “plum pudding” atom could not explain why a few alpha particles bounced back from gold foil. Something small, heavy and positively charged had to be there.
Why does it work?
All of the atom’s positive charge is packed into that minute centre, so an alpha particle that comes very close to it feels a fierce push, strong enough to turn it right round. The rest pass through the empty space.
How does it help?
It explains why atoms are mostly empty space and where their mass comes from, and it gives the picture used for the rest of this book: a nucleus, with electrons around it.
Go deeper how do we know, what it isn’t, where does it stop working
How do we know?
Geiger and Marsden counted flashes from alpha particles fired at gold foil in Manchester in 1909. About one in several thousand was turned aside sharply, which only a tiny, heavy, charged centre can explain.
What it isn’t
Not a sun with electrons going round it like planets. Electrons do not follow tracks at all.
Where does it stop working?
A small solid ball is itself only a model. The nucleus has its own inner structure, which takes nuclear physics to describe.
Your turn
Explain The nucleus to a friend in one sentence, in your own words. Then compare it with the book’s.
The tiny centre of an atom, made of protons and neutrons. It holds almost all of the atom’s mass but takes up almost none of its space.
Investigation 1.1
Compare the three particle counts for helium-4, carbon-12 and neon-20. Then write two lists: three things the diagram tells you truthfully, and one thing it cannot show you.
Check yourself
A counting diagram shows 6 red tokens marked + in the centre, 6 brown tokens, and 6 blue tokens marked − around the outside. Name one thing this diagram reliably tells you, and one thing it does not.
It reliably tells you the numbers: 6 protons, 6 neutrons and 6 electrons (so this is a carbon atom, and it is neutral). It does not tell you the real size of the nucleus compared with the atom, where the electrons actually are, or what anything looks like; atoms have no colour.
1.2What identifies an element?
An element is a substance made of only one kind of atom. Hydrogen, carbon, oxygen, gold and mercury are all elements, and there are 118 known so far. But what makes two atoms “the same kind”? For a long time nobody could say. Chemists arranged the elements in order of how heavy their atoms were, and a few of them stubbornly seemed to sit in the wrong places.
Manchester, 1913
The answer came from one of Rutherford’s young researchers, Henry Moseley, who was twenty-five. He fired electrons at targets made of different elements, one after another, and measured the X-rays that came off. Each element gave out its own X-ray “note”. When Moseley plotted the square root of each note’s frequency, the points rose in a perfectly even staircase, one step per element, with no wobbles at all. The steps were counting something inside the atom: the positive charge of its nucleus, in other words the number of protons. Moseley’s staircase put every element in its correct place, and where a step was missing, it showed exactly where an undiscovered element must fit.
That number is called the atomic number, and it has the symbolZ. It is the answer to the question, and it is simple and absolute: two atoms are the same element if, and only if, they have the same number of protons.
Moseley did not live to see what his staircase became. In 1915, during the First World War, he was killed by a sniper at Gallipoli, aged 27. Many scientists have said that his death was one of the war’s great losses to science.
Every atom with 6 protons is carbon, whether it is in a pencil, a diamond, a sugar crystal or the carbon dioxide you breathe out. Every atom with 7 protons is nitrogen. Change the number of neutrons, and you still have the same element. Change the number of electrons, and you still have the same element. Change the number of protons, and you have a different element. Add one proton to gold, and you have mercury.
Figure 1.3Three changes to a carbon atom. Taking away an electron leaves it carbon (with a charge). Adding a neutron leaves it carbon (a heavier version). Adding a proton makes it nitrogen.
So could you turn mercury into gold, the dream of the alchemists and of Isaac Newton at his furnace, by taking one proton away? In the lab app you can do it with one tap. In the real world, that is not something chemistry can do, and this is why every alchemist failed. Chemical changes, like burning or rusting or cooking, move electrons around and rearrange atoms, but they never change the number of protons in a nucleus. However hot the furnace, however clever the recipe, the nucleus is untouched. Changing that number takes a nuclear process, such as the reactions in the core of a star or in a nuclear reactor. So when you tap that button, you are editing a model, not doing an experiment.
Nuclear physics, though, can do it, and in our own time it has. At CERN, the giant laboratory near Geneva, the Large Hadron Collider smashes lead nuclei together at nearly the speed of light. In May 2025 the team running its ALICE experiment reported that when two lead nuclei only just miss each other, the electric jolt can knock three protons out of one of them. Lead has 82 protons; take away three and you have 79, which is gold. Over the years 2015 to 2018 the collider made gold nuclei this way, about 29 picograms in all (a picogram is a millionth of a millionth of a gram), and each one lasted only a split second before hitting the machine’s walls and breaking apart. Then, in October 2026, a US start-up called Marathon Fusion announced that it had made gold from mercury, using neutrons from fusion reactions: a neutron knocks a neutron out of mercury-198, making mercury-197, which then decays by itself into gold-197. That is a company’s claim, and when this book was written its data had not yet been published or checked by other scientists. Either way, notice what did the work. Not a chemical recipe, but a change to the nucleus.
Careful
“Na⁺ has 10 electrons, the same as neon. So it has turned into neon.”
Count the protons instead. A sodium ion still has 11 protons, so it is still sodium, just with a positive charge. Neon has 10 protons. Having the same number of electrons as another element makes two particles similar in some ways, but it never makes them the same element. That is the answer to this chapter’s big question.
Understand itElement
What is it?
A substance made of only one kind of atom: atoms that all have the same number of protons. Carbon, oxygen and gold are elements, and 118 are known so far.
Why is it called this?
From Latin elementum, a first principle or basic part. Where the Latin word itself came from, nobody knows.
What problem did it solve?
For two thousand years people argued about what the basic ingredients of everything were. Elements are the ingredients chemistry cannot split any further, and Moseley’s proton count finally gave an exact test of which is which.
Why does it work?
The number of protons fixes the charge of the nucleus. That fixes how many electrons a neutral atom holds, and the electrons decide how the atom behaves.
How does it help?
Every substance in the world is made of elements joined in different ways, so a list of 118 ingredients describes everything you will ever touch.
Go deeper how do we know, what it isn’t, where does it stop working
How do we know?
Moseley’s X-ray staircase of 1913 rose by one equal step per element, with no wobbles: it was counting the protons.
What it isn’t
Not “an atom with a certain mass” or “an atom with a certain number of electrons”. Isotopes and ions change those, and the element stays the same. Only the protons count.
Where does it stop working?
Chemistry can never turn one element into another, but nuclear processes can, in stars, in reactors, and in machines like the Large Hadron Collider.
Your turn
Explain Element to a friend in one sentence, in your own words. Then compare it with the book’s.
A substance made of only one kind of atom: atoms that all have the same number of protons. Carbon, oxygen and gold are elements, and 118 are known so far.
Investigation 1.2
Start with carbon (6 protons, 6 neutrons, 6 electrons). Change the electrons first, then the neutrons, then the protons. Watch the element’s name. Save one pair that is the same element and one pair that is not.
Check yourself
A particle has 8 protons, 8 neutrons and 10 electrons. Which element is it?
Oxygen, because it has 8 protons. The 10 electrons only tell you about its charge (it is an oxide ion, O²⁻), and the 8 neutrons only tell you which isotope it is.
Check yourself
When a candle burns, its wax (made of carbon and hydrogen) seems to disappear. Do any of its carbon atoms turn into atoms of a different element?
No. Burning is a chemical change, and chemical changes only move electrons and rearrange atoms; they never touch the nucleus. Every carbon atom keeps its 6 protons and ends up, still carbon, in carbon dioxide gas that drifts away into the air.
1.3Same element, different isotope
Cambridge, 1919
Back in Cambridge, J. J. Thomson had noticed something odd as early as 1913. When he sent a beam of charged neon atoms through magnetic and electric fields, it split into two faint streaks instead of one, as if neon came in two weights. His former assistant Francis Aston returned from war work and built a much sharper machine to settle it, one of the first mass spectrometers. It gives atoms an electric charge, then sends them flying through a magnetic field. The field bends heavier particles less than lighter ones, so the beam splits into separate streams, one for each mass. In 1919 Aston confirmed that neon really is a mixture of two kinds of atom, and went on to show the same for chlorine and many other elements.
How can one element come in different weights? The protons cannot differ, or it would be a different element. The extra weight belongs to the neutrons. Atoms of the same element can have different numbers of neutrons. Carbon atoms, for example, can have 6, 7 or 8 neutrons, and all of them are carbon. These versions are called isotopes. We name an isotope by its mass number, the total number of protons and neutrons: carbon-12 has 6 + 6 = 12, carbon-13 has 6 + 7 = 13, and carbon-14 has 6 + 8 = 14.
Isotopes behave almost identically in chemistry, because chemistry is mostly about electrons, and isotopes of an element have the same number of electrons. But their nuclei can be very different. Carbon-12 and carbon-13 last forever. Carbon-14 is radioactive: its nuclei slowly break down, so that half of any sample is gone after about 5,700 years. That is how archaeologists date ancient wood and bone. Adding a neutron in the app does not tell you whether the new nucleus would be stable; that depends on nuclear physics, not on counting.
Most elements found in nature are a mixture of isotopes. Chlorine, for example, is about three-quarters chlorine-35 and one-quarter chlorine-37. So the average atomic mass of chlorine is somewhere between 35 and 37. Here is the arithmetic, using the real measured fractions:
0.758 × 35.0 + 0.242 × 37.0 ≈ 26.5 + 9.0 = 35.5
(With the isotopes’ exact masses, 34.969 and 36.966, the answer is 35.45.)
That is why periodic tables give chlorine as 35.45. But notice something odd: no single chlorine atom has a mass of 35.45. Every chlorine atom is either about 35 or about 37. The average describes the crowd, not any member of it, in the same way that the average number of children in a family can be 2.4 even though no family has 0.4 of a child.
Figure 1.4The mass spectrum of chlorine. Each peak is a group of atoms with the same mass; its height shows how common that isotope is. The average, 35.45, falls between the peaks, where there are no atoms at all.
This is exactly the kind of picture Aston’s machine drew: one peak for each isotope, with the height of each peak showing how common it is.
An element made of beans
Make your own “element” with two isotopes: mix 75 rajma beans and 25 small brown chickpeas, kala chana (any two clearly different sizes of bean or dal will do; big white chickpeas can weigh about as much as rajma) in a bowl. Predict first: will the average mass of a bean in the bowl be nearer a rajma’s mass or a chickpea’s? A kitchen scale only reads to about a gram, so weigh beans in twenties: weigh 20 rajma and divide by 20; weigh 20 chickpeas and divide by 20. Work out the average just as for chlorine: 0.75 × (one rajma) + 0.25 × (one chickpea). Check it by weighing all 100 and dividing by 100. Then look in the bowl: is any bean an “average bean”? Each one is a rajma or a chickpea, just as each chlorine atom is chlorine-35 or chlorine-37.
Understand itIsotope
What is it?
One of the different versions of the same element. Isotopes have the same number of protons but different numbers of neutrons, so their atoms have different masses.
Why is it called this?
From Greek isos, “equal”, and topos, “place”: isotopes of an element sit in the same place in the periodic table. The word was suggested to Frederick Soddy in 1913 by Margaret Todd, a Scottish doctor and writer and a friend of his family.
What problem did it solve?
Thomson’s neon beam split in two, and many elements had average masses that were not whole numbers. Isotopes explained both: an element can be a mixture of atoms of different masses.
Why does it work?
Neutrons add mass but no charge, so they change the weight of the nucleus without changing the electrons. Chemistry is mostly about electrons, so isotopes of an element behave almost the same.
How does it help?
It explains averages such as chlorine’s 35.45, and gives tools such as carbon-14 dating of ancient wood and bone.
Go deeper how do we know, what it isn’t, where does it stop working
How do we know?
Aston’s mass spectrometer of 1919 split neon, and then chlorine and many other elements, into one stream for each mass.
What it isn’t
Not a different element, and not necessarily radioactive. Carbon-12 and carbon-13 last forever; only some isotopes, such as carbon-14, break down.
Where does it stop working?
“Almost the same” is only almost. Hydrogen is the big exception: its heavy isotope, deuterium, doubles the atom’s mass, and “heavy water” made from it freezes at about 3.8 °C instead of 0 °C.
Your turn
Explain Isotope to a friend in one sentence, in your own words. Then compare it with the book’s.
One of the different versions of the same element. Isotopes have the same number of protons but different numbers of neutrons, so their atoms have different masses.
Investigation 1.3
Predict the average mass of a mixture that is half 12 u and half 13 u. Then move the percentage slider. Explain why the average always stays between the two masses, and why no particle ever has the average mass.
Check yourself
A made-up element is a mixture of two isotopes: 75% have mass 10 and 25% have mass 14. What is its average atomic mass? Does any atom have that mass?
0.75 × 10 + 0.25 × 14 = 7.5 + 3.5 = 11. No atom has mass 11: each atom is either 10 or 14. The 11 describes the mixture.
1.4Where does charge come from?
Try a little magic before the explanation.
The balloon that sorts salt from pepper
On a dry day, sprinkle a teaspoon of salt and a pinch of ground black pepper on a plate and mix them. Blow up a balloon, tie it, and rub it hard on your hair or a wool jumper for ten seconds. Now hold the balloon a couple of centimetres above the plate and slowly lower it. The pepper jumps up and sticks to the balloon first; bring it lower and some salt follows. Rubbing moved electrons from your hair onto the balloon, giving it a negative charge, and that charge pulls on the specks below. The lighter pepper flakes are lifted first. Now rub a second balloon, hang both from threads so that they dangle side by side, and let them go: they swing apart. Both carry the same kind of charge, and like charges push each other away. Only electrons moved in all this. Your hair, having lost some, is left with a positive charge, which is why it may lift towards the balloon.
Nothing was created when you rubbed that balloon. Electrons were simply moved from one place to another. Each proton has a charge of +1 and each electron a charge of −1, measured in a unit called the elementary charge. Neutrons have no charge. So the overall charge of any particle is just a subtraction:
charge = number of protons − number of electrons
A sodium atom has 11 protons and 11 electrons, so its charge is 11 − 11 = 0: it is neutral. If it loses one electron, it has 11 protons and 10 electrons, and its charge is +1. A particle with an overall charge is called an ion. This one is written Na⁺, “sodium plus”. An oxygen atom with 8 protons that has gained two extra electrons has 8 − 10 = −2, and is written O²⁻.
Figure 1.5Charge is a count. A sodium atom (left) has 11 positive and 11 negative charges, which cancel. A sodium ion (right) has one electron fewer, so one positive charge is left over. The nucleus has not changed at all.
Notice what does not change when an ion forms: the nucleus. The protons and neutrons stay exactly where they were. That is why an ion is still the same element.
London, the 1830s
The word “ion” is older than the electron. At the Royal Institution in London, Michael Faraday, who had started life as a bookbinder’s apprentice, was passing electric currents through all sorts of substances. Solid salt would not carry a current. But when salt was melted, or dissolved in water, a current flowed through it, and new substances appeared at the metal plates where the current went in and out. Something in the liquid was carrying charge from one plate to the other. In 1834 Faraday named these charge-carriers ions, from the Greek for “going”. Sixty years before anyone knew about electrons, he had found their footprints. We now know that in salt water they are Na⁺ ions drifting one way and Cl⁻ ions drifting the other.
Arithmetic lets you write down any charge you like: carbon with 5 electrons, oxygen with 12. But being able to write a particle down does not mean it can exist for long in the real world. Whether an ion survives depends on its surroundings. Na⁺ ions last indefinitely in salt crystals and in seawater; a C⁺ ion can be made in a vacuum chamber but would not last a moment in water. The subtraction tells you the charge. It does not tell you whether the particle is real.
Careful
“The charge of an atom is the number of protons minus the number of neutrons.”
Neutrons have no charge, so they cannot affect the subtraction at all. They change the mass of an atom, not its charge. Charge is always protons minus electrons.
Understand itIon
What is it?
An atom, or a group of atoms, with an electric charge, because it has more or fewer electrons than protons. Na⁺ has lost one electron; O²⁻ has gained two.
Why is it called this?
From the Greek for “going”. Michael Faraday named ions in 1834, on the suggestion of his friend William Whewell, because they travel through a liquid towards the plates where a current goes in and out.
What problem did it solve?
Faraday could not explain how melted or dissolved salt carried an electric current when solid salt could not. Charged particles moving through the liquid were the answer.
Why does it work?
Charge is a simple count: protons minus electrons. Move electrons on or off and the count changes, while the nucleus, and so the element, stays exactly the same.
How does it help?
It explains why salt water carries electricity, why salt is safe to eat although sodium and chlorine are dangerous, and much of what happens inside batteries.
Go deeper how do we know, what it isn’t, where does it stop working
How do we know?
Pass a current through melted or dissolved salt and new substances appear at each plate, just as moving charged particles would make them.
What it isn’t
Not a different element. Na⁺ still has 11 protons, so it is still sodium, even though it has the same number of electrons as neon.
Where does it stop working?
The arithmetic can describe ions that cannot last. A C⁺ ion can be made in a vacuum chamber, but it would not survive a moment in water.
Your turn
Explain Ion to a friend in one sentence, in your own words. Then compare it with the book’s.
An atom, or a group of atoms, with an electric charge, because it has more or fewer electrons than protons. Na⁺ has lost one electron; O²⁻ has gained two.
Investigation 1.4
Keep the protons and neutrons fixed. Remove one electron and save; then add two electrons and compare. What happened to the charge each time, and what happened to the nucleus?
Check yourself
A sulfide ion has 16 protons, 16 neutrons and 18 electrons. What is its charge?
16 − 18 = −2, so it is written S²⁻. The 16 neutrons do not count towards the charge at all.
1.5Reading an atom’s identity
You have now met everything the explorers of this chapter found: Thomson’s electrons, Rutherford’s nucleus, Moseley’s proton count, Aston’s isotopes, Faraday’s ions. Chemists have a compact way of writing all of it down at once. Take the element’s symbol, for example O for oxygen, and put three numbers around it, each in its own corner.
Figure 1.6The three corners of a nuclear symbol. Bottom left: protons. Top left: protons plus neutrons. Top right: the charge. This particle has 8 protons, 9 neutrons and 10 electrons.
The bottom-left number is the atomic number, Z. It is the number of protons, and it is really the same information as the symbol: an O always has 8. The top-left number is the mass number, A, protons plus neutrons. The top-right number is the charge, protons minus electrons, with its sign written after the number. Leave it off when the charge is zero.
So 178O2− means: 8 protons; 17 − 8 = 9 neutrons; and a charge of −2, so 8 + 2 = 10 electrons.
To find the neutrons, subtract the bottom number from the top: N = A − Z. To find the electrons, start from the protons and use the charge: a charge of 2− means two more electrons than protons; a charge of 3+ means three fewer.
The positions of these numbers are an international agreement, kept up to date by the International Union of Pure and Applied Chemistry (IUPAC), so that a chemist in Mumbai, Moscow or Montreal reads the symbol in exactly the same way. Getting the corners mixed up is one of the commonest mistakes in chemistry exams, so the labels in Figure 1.5 are worth learning.
Careful
“The periodic table says oxygen is 15.999, so the top-left number for oxygen should be 15.999.”
These are two different kinds of number. The top-left number in a nuclear symbol describes one nucleus, and it is always a whole number because you cannot have part of a proton or neutron. The 15.999 on the periodic table is the average atomic mass for natural oxygen: an average over a mixture of isotopes, measured in units in which the individual masses are not quite whole numbers either.
Investigation 1.5
Make a particle with 8 protons, 9 neutrons and 10 electrons. Before you look at the app’s symbol, write the full nuclear symbol yourself, and explain each number.
Check yourself
An atom has Z = 7 and A = 15. How many neutrons does it have, and which element is it?
15 − 7 = 8 neutrons. With 7 protons it is nitrogen: this is nitrogen-15, a rare but stable isotope.
1.6What might explain patterns?
London, 1807
Go back a century, to the basement laboratory of the Royal Institution, where Faraday would later work. Humphry Davy, a woodcarver’s son from Penzance in Cornwall who had become the most famous lecturer in London, passed a powerful electric current through a lump of slightly damp potash. Tiny silvery globules appeared, like drops of mercury; some burst into flame as they broke through the crust. Davy had discovered potassium. His cousin Edmund, who was helping him, later recalled that Davy danced about the room with delight. A few days later he made sodium the same way.
Lithium, sodium and potassium are soft, shiny metals that react with water (sodium and potassium fiercely) and are stored under oil. Chemists noticed long ago that they belong together as a family, and that the same family pattern repeats across the elements. That repeating pattern is what Dmitri Mendeleev, a chemist born in Siberia and teaching in St Petersburg, built his periodic table around in 1869. Something about these atoms must be alike. Their nuclei are very different (3, 11 and 19 protons), so it must be something about their electrons.
The clue comes from measuring how much energy it takes to pull one electron off an atom. This is called the ionisation energy. Figure 1.6 shows it for the first 18 elements.
Figure 1.7First ionisation energies of elements 1 to 18. The tallest peaks are helium, neon and argon, whose electrons are held most tightly. Straight after each peak comes a deep drop: lithium, then sodium, which lose one electron easily. The pattern repeats.
The pattern is not a smooth climb. It rises, crashes, rises again, crashes again. The best explanation is that electrons are arranged in groups, called shells, at different energies. The first shell holds up to 2 electrons; the next holds up to 8; for the first 18 elements, the third also fills at 8. Lithium has 2 electrons in the first shell and 1 in the second (written 2, 1). Sodium has 2, 8, 1. Both have a single electron in their outermost shell, farther from the nucleus and more shielded from its pull by the electrons inside it. That lone outer electron is easy to remove, and it explains why the two metals behave so much alike.
Figure 1.8Shell counts for lithium (2, 1) and sodium (2, 8, 1). Both have one electron in their outermost shell. The rings show groupings by energy, not paths that electrons travel along.
Predict first. The rings in the figure above look like tracks, with electrons running round them like trains on a circle line. If you could photograph an electron in a neon atom again and again, would the dots all land on a neat circle?
They would not. Electrons don’t follow paths at all. What we can know is where an electron is likely to be found, and that likelihood makes a cloud: thick in some places, thin in others, fading away with no edge. Each shell is made of one or more of these clouds, and each cloud holds at most two electrons. The first shell is a single round cloud (called 1s). The second shell is a bigger round cloud (2s) plus three dumbbell-shaped clouds (2p) at right angles to each other: 1 + 3 = 4 clouds × 2 electrons = 8, the second shell’s eight. Turn the atom below and see for yourself.
Figure 1.9Two ways to picture an atom’s electrons. Left: shells as rings, a handy way to count. Right: what electrons really do, shown as clouds of likely positions: 1s, 2s (with its hollow layer) and one of the three 2p clouds. Each cloud holds at most two electrons. Dots are sampled from the real hydrogen-like shapes.
The rings are not wrong: they are a model that keeps the counting right and leaves out the shapes. You will meet the clouds again in the story of why the periodic table has its strange shape: the 2p clouds are why the second row has six columns on the right, and the five d clouds are why the middle of the table is ten columns wide.
What, then, makes a full shell special? You will often hear the answer “atoms want a full shell”. It is time to look at that word properly.
Careful
“Sodium wants to lose its electron to get a full shell, and chlorine wants to gain one.”
The word. “Want” is shorthand. Scientists use it when talking quickly, and your school book may say that atoms gain, lose or share electrons “to get a full outer shell”. It is a handy way to predict what happens. But an atom has no wishes, so the word hides the real reason. Here is the reason.
The real principle. Put a marble in a bowl and it ends up at the bottom and stays there. Not because it wants to be at the bottom, but because getting it out again costs energy that something has to supply. On its way down it gave energy away, as a little heat, which spread out into the bowl and the air. Arrangements of atoms work the same way: the ones that last are the ones lower in energy, because leaving them costs energy. And once the energy has gone out as heat, it spreads through the surroundings and does not come back by itself, for the same reason that a shuffled pack of cards never sorts itself back into order: there are overwhelmingly more spread-out ways than gathered-up ones.
The sodium paradox. If sodium really “wanted” to lose its electron, taking it off would give out energy. It does the opposite. Look at the graph: removing sodium’s outer electron costs about 496 kJ per mole. When chlorine catches that electron it gives back only about 349 kJ. So the swap on its own is uphill: the pair ends up 147 kJ worse off, and if nothing else happened, salt would never form. What makes the whole journey run downhill is what comes next: the new ions pull together into a crystal and release about 787 kJ per mole. You will see that energy account in full in Section 2.5. (In Chapter 2 you can follow this energy account step by step in a moving figure.)
Why full shells look “stable”. A full shell is not magic; it is where the next step gets expensive. Take one electron from sodium (2, 8, 1) and you remove the lonely outer one, which is far out and shielded. Try to take a second, and it must come out of the full shell underneath, much closer to the nucleus: that costs about 4,560 kJ per mole, more than nine times as much. Neon (2, 8) is the mirror image. An extra electron would have to go into a brand-new shell much farther out, where the 10 electrons inside shield it from almost all of the nucleus’s pull, so it would not be held at all: a neon atom cannot keep an extra electron. Full shells mark the places where adding or removing one more electron suddenly costs a great deal of energy. That is all “a full shell is stable” really means.
Careful
“Shells are the circles that electrons travel around on, like planets around the Sun.”
Shell diagrams are a way of counting electrons by energy, and they are useful. But electrons do not follow tracks at all. The truth, which needs quantum physics to describe properly, is that we can only say how likely an electron is to be found in different places. Shell diagrams are a simplified model, and later chapters will show where it needs improving.
Investigation 1.6
Compare neutral lithium and sodium. Write down the pattern they share. Then write one question about them that a counting diagram cannot answer.
Check yourself
Neutral fluorine has 9 electrons and neutral chlorine has 17. Work out their shell counts. What do they have in common?
Fluorine is 2, 7 and chlorine is 2, 8, 7. Both have 7 electrons in their outermost shell, and indeed they are members of the same chemical family (the halogens). Notice we can say this without claiming that either one “wants” an extra electron.
Case file 1
The three mystery beams
A particle detector picks up three kinds of particle, called X, Y and Z.
X has 8 protons, 8 neutrons and 10 electrons.
Y has 8 protons, 10 neutrons and 8 electrons.
Z has 10 protons, 10 neutrons and 10 electrons.
A lab assistant notices that X and Z have the same number of electrons, and that Y and Z have the same mass number. She concludes that at least two of them must be the same element.
Which of X, Y and Z are the same element? Write a full nuclear symbol for each, and explain where the assistant went wrong.
Show the solution
Only the protons decide the element. X and Y both have 8 protons, so both are oxygen. Z has 10 protons, so it is neon.
X is 168O2−: oxygen-16 with two extra electrons, an oxide ion.
Y is 188O: oxygen-18, a neutral atom of a heavier isotope.
Z is 2010Ne: neon-20, a neutral atom.
The assistant matched the wrong counts. Sharing an electron count (X and Z) or a mass number (Y and Z) does not make two particles the same element. Sharing a proton count (X and Y) does.
What this chapter can’t explain yet
You can now take any atom or ion and count everything in it. But a single atom on its own is a lonely thing, and almost nothing in the world around you is made of lonely atoms. Water is made of molecules, salt of a crystal of ions, diamond of carbon atoms locked together by the trillion. What holds atoms to each other? In Chapter 2 we go back to Davy’s basement, and to a silvery metal and a poisonous green gas that together make something you sprinkle on your dinner.
2
Chapter 2
How atoms form substances
The big questionSodium is a soft metal that fizzes violently in water. Chlorine is a choking green gas. Together they make the salt you sprinkle on your food. How can two dangerous elements turn into something you eat every day?
We left Chapter 1 in the basement of the Royal Institution, with Humphry Davy dancing round his laboratory over a few silvery globules of potassium. A few days later he made sodium the same way: a metal so soft you can cut it with a knife, which tarnishes in seconds in air and skates fizzing across water. A few years after that, in 1810, Davy showed that a choking yellow-green gas, first made by the Swedish apothecary Carl Wilhelm Scheele in 1774, was an element too. He named it chlorine, from the Greek for “pale green”.
Put those two together and something extraordinary happens. Sodium burns in chlorine with a fierce yellow flame, and what is left behind is a white powder you could sprinkle on your chips: table salt. Two dangerous elements become something you eat every day. That is a clue that when atoms join, they become something new.
Look around the room you are in. The walls, the air, a glass of water, the screen or page in front of you: almost nothing is made of single, separate atoms. Atoms are nearly always attached to other atoms. Sometimes a few of them join into a small group; sometimes trillions lock together into a crystal. This chapter is about what holds them together, and why the same handful of elements can make substances as different as water, salt, pencil lead and diamond.
2.1Element, compound or mixture?
Spain, the 1790s
In the 1790s a French chemist called Joseph Proust was working in Spain, where the king paid for a fine laboratory. Proust analysed copper carbonate, a green substance, again and again: some he made himself, some was dug out of the ground. However it had been made, it contained the same elements in exactly the same proportions by mass. He argued that every pure compound has a fixed recipe. The most famous chemist in France, Claude-Louis Berthollet, disagreed, and for several years the two argued politely in print. Proust won. His idea, now called the law of definite proportions, became one of the main clues that matter is made of atoms that join in whole-number ratios.
Chemists now sort every material into three kinds. An element you met in Chapter 1: it contains only one kind of atom. Oxygen gas is an element, even though its atoms travel in pairs, O₂, because both atoms in each pair are oxygen.
A compound contains two or more elements joined together, always in the same fixed proportions, just as Proust found. Water is a compound: every water molecule has exactly two hydrogen atoms joined to one oxygen atom. Water from the Arabian Sea, from a monsoon puddle or from a laboratory bottle has the same 2 : 1 ratio, and that is why it can be given one formula, H₂O.
A mixture contains two or more substances that are simply mingled, not joined. Salt water is a mixture: you can stir in a little salt or a lot, and you can get the salt back by letting the water evaporate. A mixture has no single formula, because its proportions can vary.
Figure 2.1Four samples, drawn as particle models. Hydrogen and oxygen are elements: each holds only one kind of atom. Water is a compound: every molecule has the same 2 : 1 ratio of hydrogen to oxygen. A mixture of hydrogen and oxygen holds two separate substances in whatever proportions you put in.
Here is a subtle point. A mixture of hydrogen and oxygen gas contains exactly the same kinds of atoms as water. But it is not water, and it behaves completely differently: it is an invisible gas, and with a spark it explodes. What matters is not just which atoms are present, but how they are joined.
The reverse surprise is just as striking: a compound can be utterly unlike the elements it is made from. Sugar is a sweet white powder, yet it is made of carbon (black, like soot), hydrogen and oxygen (two invisible gases).
Find the carbon in sugar (an adult does this one)
This needs the stove, so an adult does the heating while you watch from a safe distance. Melted sugar sticks to skin and burns very badly, so only the adult handles anything, holding the spoon with tongs or an oven glove. The adult puts half a teaspoon of sugar in an old steel spoon and holds it over a low flame, with a window open. Over a minute or two it melts, turns golden, then brown, and finally black and bubbling, with a sharp burnt smell. The adult holds a cold, dry steel plate above it for a moment and the plate mists over. (A gas flame makes a little water of its own, so for a fair test the adult can first hold the plate over an empty spoon and compare.) Predict first: where do the black stuff and the mist come from? The black solid is mostly carbon and the mist is water: both were locked inside the sugar all along, joined into one compound that looked like neither. (Let the spoon and the black crust cool completely, for at least ten minutes, before anyone touches them.)
Get the salt back
Stir two teaspoons of salt into half a glass of warm tap water until it disappears. The water looks just like plain water, but it is a mixture. Pour a thin layer into a saucer or a dark plate and leave it somewhere warm and still, like a sunny windowsill, for a few days. As the water evaporates, white crusts of salt appear, often as tiny cubes. You have separated a mixture without any chemistry at all. Try the same thing with sugar water and compare what is left.
Understand itCompound
What is it?
A substance made of two or more elements joined together in a fixed ratio. Water, H₂O, is always two hydrogen atoms to one oxygen atom.
Why is it called this?
From Latin componere, “to put together”: a compound is elements put together.
What problem did it solve?
Chemists argued over whether a substance could hold its elements in any proportions. Proust showed that a pure compound always has the same recipe, a key clue that atoms join in whole numbers.
Why does it work?
Atoms join in particular whole-number patterns, so every molecule or crystal of the compound has the same ratio of atoms.
How does it help?
A compound can be given one formula and has fixed properties, so you can predict what a recipe will make, every time.
Go deeper how do we know, what it isn’t, where does it stop working
How do we know?
Proust analysed copper carbonate again and again in the 1790s. Made in the lab or dug from the ground, it held the same elements in exactly the same proportions by mass.
What it isn’t
Not a mixture. A mixture of hydrogen and oxygen gas contains the same atoms as water, but it is not water: it explodes with a spark.
Where does it stop working?
Some solid compounds, such as certain minerals and metal oxides, have slightly variable ratios. Chemists call them berthollides, after Proust’s rival, who was partly right after all.
Your turn
Explain Compound to a friend in one sentence, in your own words. Then compare it with the book’s.
A substance made of two or more elements joined together in a fixed ratio. Water, H₂O, is always two hydrogen atoms to one oxygen atom.
Investigation 2.1
Compare all four samples in the app. For each one, decide: element, compound or mixture? Then explain why oxygen, O₂, is an element even though it is made of molecules.
Check yourself
Is air an element, a compound or a mixture? Give a reason.
A mixture. Air contains several separate substances, mainly nitrogen (N₂), oxygen (O₂) and argon, not joined to each other. Their proportions can vary (for example, humid air has more water vapour than dry air), which a compound’s proportions never do.
2.2How do charges interact?
Remember the balloon that lifted pepper off a plate in Chapter 1? Everything that holds atoms together comes down to the same rule, one of the four ideas at the start of the book: opposite charges attract, and like charges repel. A proton and an electron pull towards each other. Two electrons push each other apart. So do two protons.
Paris, 1785
How strong is the pull? The first person to measure it was Charles-Augustin de Coulomb, a French army engineer who had spent years building a fort on the Caribbean island of Martinique before turning to physics. He hung a light rod from a very thin wire, with a small charged ball on one end. When he brought another charged ball near it, the rod turned and twisted the wire. The more the wire twisted, the bigger the force, so the twist was a way of weighing a force too small to feel.
By changing the distance between the balls, Coulomb found the rule, now called Coulomb’s law. The pull depends on two things: how big the charges are, and how far apart they are. Bigger charges pull harder. And the force gets weaker very quickly with distance. If you double the distance between two charges, the force does not halve. It drops to a quarter. Triple the distance, and it drops to a ninth. Scientists call this an inverse-square law.
Figure 2.2Two pairs of opposite charges. Moving them twice as far apart cuts the attraction to one quarter. Like charges (bottom) push apart instead of pulling together.
Coulomb’s law is about tiny charged points, and atoms are not points. When two atoms come very close, their electron clouds start to overlap and a powerful push-back sets in, which is why atoms do not collapse into each other. To describe that properly you need quantum physics. But almost every attraction in this book, between ions, between atoms in a molecule, between neighbouring molecules, is at heart this electric pull.
Careful
“If you double the distance, the force halves.”
It is much more dramatic than that. Twice the distance means one quarter of the force, because the distance is squared: 2 × 2 = 4. This is why electric forces between atoms matter enormously at close range and fade quickly further away.
See why the distance is squared
Cut a small square hole, about 1 cm across, in a piece of card. In a dark room, hold the torch of a phone (its light is a tiny point, which is what you want) 5 cm behind the hole, and shine it onto a sheet of squared paper 10 cm from the light. Measure every distance from the light itself, not from the card. Count how many squares the patch of light covers. Now move the paper to 20 cm from the light, keeping the card where it was. Predict first: twice the distance, so twice as many squares? Count them: about four times as many, because the patch has grown twice as wide and twice as tall. The same light is spread over four times the area, so each square gets a quarter as much. Electric pull spreads out from a charge in a similar way, which is why it falls off with the square of the distance.
Investigation 2.2
Hold the distance fixed and change the sign of one charge. What happens to the direction of the force? Then double the distance and predict the new size of the force before you look.
Check yourself
Two opposite charges are 1 unit apart. They are moved to 3 units apart. What fraction of the original attraction is left?
One ninth. The distance has tripled, and 3 × 3 = 9, so the force is 1/9 as strong. It is still an attraction, because the charges are still opposite.
2.3How can atoms share electrons?
Berkeley, California, 1916
Salt’s ions hold together because they have opposite charges. But what about a hydrogen molecule, H₂, where two identical atoms cling together and neither has a charge? This puzzled chemists until the American chemist Gilbert NewtonLewis, head of chemistry at the University of California in Berkeley, suggested a simple answer in 1916: the two atoms share a pair of electrons. Lewis had been doodling atoms as little cubes with electrons at the corners in his notebooks since 1902. His dots-for-electrons drawings are still used in every chemistry class in the world.
Picture two hydrogen atoms floating towards each other. Each has one proton and one electron. As they get close, each electron starts to feel the pull of both protons. The electrons spend much of their time in the space between the two nuclei, and both nuclei are attracted to that shared negative region. This joins the atoms into a molecule of hydrogen, H₂. A link like this, made by shared electrons, is called a covalent bond.
A bond is not a stick or a hook. It is a balance. Pull the two nuclei closer, and the two positive nuclei repel each other more strongly. Pull them further apart, and they lose the shared attraction. In between there is a best distance, where the energy is lowest. For H₂, that distance is 74 picometres (0.074 nanometres).
Predict first. Two hydrogen atoms drift towards each other. Will they keep getting closer until they touch, stop somewhere, or bounce away? Make your guess, then move them with the slider below.
Figure 2.3Energy of two hydrogen atoms as they move closer together. Far apart, nothing happens. Closer in, sharing electrons lowers the energy. Too close, the nuclei repel. The bond sits at the bottom of the dip, 74 pm apart. (Shape of curve drawn schematically; the two marked values are measured.)
Because bonded atoms sit in an energy dip, pulling them apart always takes energy. To split one mole of H₂ molecules into separate hydrogen atoms takes 436 kilojoules: about enough to bring a litre of water from room temperature to the boil, and then some. This is worth fixing firmly in your head, because everyday life suggests the opposite (snap a stick, and it seems to let something out): breaking a bond never gives out energy; it always costs energy. Energy comes out when bonds form, as the atoms drop into the dip.
Try Let them come together in the figure. The atoms roll down into the dip and rock back and forth, and they only settle at the bottom if the extra energy is carried away, as heat passed to other molecules. That is the whole secret of a bond: it is the bottom of an energy valley. Nothing holds the atoms with a hook. They stay because climbing out would cost 436 kJ for every mole, and nobody is paying.
How can anyone measure a distance of 74 picometres? With light. Molecules vibrate and spin, and they absorb and give out light only at particular colours that match those movements. From those colours, physicists work out how far apart the nuclei are and how much energy it takes to pull them apart. The same measurements have been made for thousands of other bonds, and X-ray maps of crystals show that, in many of them, electrons really do pile up in the regions between bonded atoms, just where Lewis drew his shared pairs.
Careful
“Hydrogen atoms bond because each one wants two electrons to be stable.”
Atoms do not want anything. The bond forms because the arrangement with shared electrons has lower energy than two separate atoms: each electron is attracted to two protons instead of one. Energy has to be put in to break that arrangement. That is the whole story, without any wishing.
Understand itCovalent bond
What is it?
A link between two atoms that share a pair of electrons. Both nuclei are pulled towards the shared electrons between them, and that holds the atoms together.
Why is it called this?
“Co-” means together, and “valence” is chemists’ word for an atom’s power to combine, from Latin valentia, strength. The American chemist Irving Langmuir introduced “covalence” in 1919 for electrons shared between atoms.
What problem did it solve?
Ions explained salt, but not molecules such as H₂, where two identical atoms with no charge cling together. Lewis’s shared pair of 1916 explained how.
Why does it work?
Each shared electron is attracted by two nuclei instead of one, which lowers the energy. Too close and the nuclei repel; too far and the sharing is lost. The bond sits at the distance where the energy is lowest.
How does it help?
It explains how molecules hold together, why breaking a bond always costs energy, and where the energy of a reaction comes from when new bonds form.
Go deeper how do we know, what it isn’t, where does it stop working
How do we know?
The colours of light that molecules absorb reveal how long and how strong their bonds are: 74 pm and 436 kJ per mole for H₂. X-ray maps of crystals show electrons piled up between bonded atoms.
What it isn’t
Not a stick or a hook, and not two atoms “wanting” to fill their shells. It is a balance of attractions and repulsions.
Where does it stop working?
Real bonds lie on a scale, from equal sharing, through unequal sharing (Section 2.7), to the complete hand-over of electrons that makes ions. The neat sharing picture is one end of that scale.
Your turn
Explain Covalent bond to a friend in one sentence, in your own words. Then compare it with the book’s.
A link between two atoms that share a pair of electrons. Both nuclei are pulled towards the shared electrons between them, and that holds the atoms together.
Investigation 2.3
Compare H₂, O₂ and H₂O in the app. Sketch which atoms belong to each molecule. Then write down something the formula H₂O does not tell you about a water molecule.
Check yourself
Rewrite this sentence so it is scientifically accurate: “Atoms bond because they want to fill their shells.”
One good version: “Atoms bond when sharing or transferring electrons leads to an arrangement with lower energy, because of the electric attraction between nuclei and electrons.” Any answer that talks about attraction and energy, and not about atoms wanting, is right.
2.4What is a molecule?
Turin, 1811
A hundred years before Lewis, chemists had a puzzle about gases. The French chemist Joseph Gay-Lussac, who once rode a hydrogen balloon seven kilometres up into the sky to sample the air, noticed that gases react in simple volume ratios. Two litres of hydrogen react with one litre of oxygen to make two litres of steam (all measured at the same temperature and pressure). If each atom acted alone, you would expect only one litre of steam.
In northern Italy, a quiet professor from Turin called Amedeo Avogadro, then teaching in the nearby town of Vercelli, who had trained as a lawyer before falling in love with physics, explained it in 1811. Equal volumes of gas contain equal numbers of particles, he said, and hydrogen and oxygen gas are made not of single atoms but of pairs, H₂ and O₂. Then 2 H₂ + O₂ → 2 H₂O fits the volumes exactly. Almost nobody listened. It took about fifty years before most chemists accepted his idea, and by then Avogadro had died.
What Avogadro had seen was the molecule: a small group of atoms held together by covalent bonds, which travels around as one unit. A water molecule is three atoms; an oxygen molecule is two; a sugar molecule is 45. Every molecule of a given substance is the same.
A formula tells you which atoms are in one molecule, and how many. The small number written low after a symbol, called a subscript, counts atoms of that element in one molecule: CO₂ has 1 carbon atom and 2 oxygen atoms. A big number written in front counts whole molecules: 3 CO₂ means three separate carbon dioxide molecules, with 3 carbon atoms and 6 oxygen atoms between them.
Figure 2.4Three CO₂ molecules: 3 carbon atoms and 6 oxygen atoms in total, but packaged as three separate molecules. That is not the same as one big C₃O₆ molecule.
The grouping matters. “3 C and 6 O” lists the atoms, but loses the most important fact: they come as three separate CO₂ molecules, each one a straight line of O=C=O.
Investigation 2.4
Build three water molecules and then three carbon dioxide molecules. Count the atoms in each, but draw them in their groups rather than as one pile.
Eight. Each CO₂ molecule has 2 oxygen atoms, and there are 4 molecules: 4 × 2 = 8. (There are also 4 carbon atoms.)
2.5A formula without a molecule
Now back to Davy’s two elements, sodium and chlorine. When sodium metal burns in chlorine gas, each sodium atom passes one electron to a chlorine atom. That makes Na⁺ ions and Cl⁻ ions. Opposite charges attract, so the ions pack together. But the attraction works in every direction at once, so each Na⁺ pulls in Cl⁻ ions on all sides, and each Cl⁻ pulls in Na⁺ ions on all sides. The result is not a set of little pairs but a huge, repeating three-dimensional grid of alternating ions: an ionic lattice. A single grain of salt contains roughly 10¹⁸ of them.
Salt is made of cubes
Sprinkle a few grains of ordinary table salt onto a dark plate and look at them through a magnifying glass, or through a phone camera zoomed right in. Many grains are tiny cubes, or broken pieces of cubes, with flat faces and square corners. Now do the same with sugar: its grains are a different, more slanted shape. The square shape of a salt grain is the ionic lattice in the figure below, repeated millions of times in every direction until it is big enough to see.
Figure 2.5A small piece of the sodium chloride lattice. Each Na⁺ (purple) has six Cl⁻ (green) neighbours, and each Cl⁻ has six Na⁺. No ion belongs to any one partner. The real crystal continues in every direction for billions of ions.
Leeds and Cambridge, 1913
How do we know the grid is really there? In 1912 the German physicist Max von Laue showed that X-rays passing through a crystal scatter into a pattern of spots. Within months, a father and son in England turned that pattern into a way of seeing atoms. William Henry Bragg was a professor at Leeds; his son William Lawrence Bragg was a young researcher at Cambridge. Together they shone X-rays through crystals of rock salt and worked out the only arrangement that could make the pattern: a regular grid of alternating ions, with every sodium surrounded by six chlorides and every chloride by six sodiums. No sodium was paired with one particular chloride. Some chemists found this very hard to accept: what had happened to the salt molecule? The father and son shared the Nobel Prize in Physics in 1915. Lawrence was 25, and he is still the youngest physics laureate.
So in solid salt there is no such thing as “a NaCl molecule”, and no pairs either.
Careful
“Each sodium ion is bonded to the chloride ion that took its electron, so salt is really made of Na–Cl pairs.”
It is a very natural picture, because the story of salt usually begins with one sodium handing one electron to one chlorine. But look at the lattice: each Na⁺ is surrounded by six Cl⁻ ions, all exactly the same distance away, all pulling equally. Which one is “its” partner? None of them. An ion is held by its charge, not by its history. Here is proof you have already made with your own hands: the salt cubes that grew on your saucer in Section 2.1 formed from ions that were already ions, floating in water. Not one of those sodium ions gave an electron to the chloride beside it, and yet the crystal holds together exactly as well as any other.
The formula NaCl tells you the ratio: one sodium ion for every chloride ion, which makes the whole crystal neutral. Chemists call that smallest ratio a formula unit.
Here is the answer Chapter 1 promised. Pulling an electron off a sodium atom costs energy: 496 kJ for every mole of atoms. A chlorine atom capturing that electron gives some energy back, 349 kJ per mole. That still leaves the pair 147 kJ worse off. If ions just floated apart, salt would never form. But when the ions come together into a lattice, all those opposite charges pulling on each other release a great deal of energy: about 787 kJ per mole. So the lattice ends up far lower in energy than the separate atoms. Sodium does not “want” to lose an electron. Losing it costs energy, and the attraction in the crystal pays that cost back several times over.
Predict first. Sodium “wants” to lose an electron, school books often say. If that were true, would pulling the electron off sodium give out energy or cost energy? Decide, then follow the energy one step at a time below.
Figure 2.6An energy account for making solid salt from sodium and chlorine atoms, per mole. Removing electrons from sodium costs 496 kJ; chlorine capturing them gives back 349 kJ; the ions packing into a lattice releases 787 kJ. Overall: 640 kJ lower than where it started. (All values for gas-phase atoms and ions.)
Watch the ball. It climbs 496 kJ when sodium loses its electron, comes only part of the way back down (349 kJ) when chlorine catches it, and is still 147 kJ uphill. Only the last step, the ions packing together into a crystal, carries it far below where it started: 787 kJ down, 640 kJ below the start overall. Salt forms not because any atom wants anything, but because the finished crystal sits at the bottom of a deep energy valley.
And that also answers the big question about why salt is safe to eat. The ions in salt are not sodium metal or chlorine gas. Na⁺ ions have different numbers of electrons from sodium atoms, so they behave completely differently: they do not react with water at all. Same nuclei, different electrons, different chemistry.
Understand itIonic lattice
What is it?
A giant, regular, repeating grid of positive and negative ions, each held by its neighbours in every direction. In salt, each Na⁺ is surrounded by six Cl⁻, and each Cl⁻ by six Na⁺.
Why is it called this?
A lattice is a criss-cross framework of thin strips with gaps between them, like a garden trellis; the word comes from an old French word for a strip of wood. “Ionic” because it is built from ions.
What problem did it solve?
Chemists expected salt to be made of NaCl molecules, and could not explain why it melts only at a very high temperature, grows as cubes, and carries electricity only when melted or dissolved. A grid of ions explains all three.
Why does it work?
Opposite charges attract and like charges repel. In alternating rows, every ion is surrounded by opposite charges, so the attractions win in every direction and release a great deal of energy: about 787 kJ per mole for salt.
How does it help?
It explains why the formula NaCl gives a ratio and not a molecule, why salt grains are cubes, and why the energy account for salt runs downhill.
Go deeper how do we know, what it isn’t, where does it stop working
How do we know?
In 1913 the Braggs shone X-rays through rock salt and showed that only a grid of alternating ions, each with six neighbours, could make the pattern of spots.
What it isn’t
Not a collection of Na–Cl pairs. No ion belongs to any one partner.
Where does it stop working?
Real crystals have flaws: missing ions, cracks and rough surfaces. The perfect grid describes the inside of a crystal, not every corner of it.
Your turn
Explain Ionic lattice to a friend in one sentence, in your own words. Then compare it with the book’s.
A giant, regular, repeating grid of positive and negative ions, each held by its neighbours in every direction. In salt, each Na⁺ is surrounded by six Cl⁻, and each Cl⁻ by six Na⁺.
Investigation 2.5
Compare sodium chloride with water in the app. Sketch a small repeating patch of the ionic lattice next to a single water molecule, and label what makes them different.
Check yourself
Magnesium chloride is an ionic solid with formula MgCl₂. Magnesium ions have a charge of 2+. What does the 2 in MgCl₂ tell you?
That there are two chloride ions (Cl⁻) for every magnesium ion (Mg²⁺) in the crystal. Two charges of −1 balance one charge of +2, so the crystal is neutral. It does not mean there are MgCl₂ molecules.
2.6Why composition is not enough
Paris, 1772
On a sunny day in Paris, a group of chemists gathered round a giant magnifying glass. Among them was Antoine Lavoisier, a wealthy young tax official who spent every spare hour, and much of his fortune, on chemistry. They focused the sunlight onto a diamond sealed inside a glass jar. The diamond grew hot, then simply vanished, and the air in the jar now contained “fixed air”, what we call carbon dioxide. Twenty-five years later, in 1797, the English chemist Smithson Tennant burned weighed amounts of diamond and of charcoal, and showed that equal masses give equal amounts of carbon dioxide. The most precious stone in the world was nothing but carbon, the same stuff as soot.
Diamond and graphite, the grey material in a pencil, are both pure carbon. (Pencil “lead” has no lead in it at all: it is graphite mixed with clay.) Burn a gram of either one in oxygen and you get exactly the same amount of carbon dioxide. So their formula is the same: just C. And yet diamond is the hardest natural material known, while graphite is so soft that it leaves a trail on paper. Graphite even conducts electricity; diamond does not.
The difference is entirely in how the atoms are connected. In diamond, every carbon atom is joined by covalent bonds to four others, pointing to the corners of a pyramid-like shape called a tetrahedron. The bonds continue in every direction through the whole crystal, making one enormous, rigid covalent network. In graphite, each carbon atom is joined to only three others, in flat sheets of hexagons like chicken wire. The sheets are stacked in layers, and the attraction between layers is weak, so they slide past each other easily. That sliding is what you see when a pencil leaves a mark: thousands of sheets peeling off onto the paper. Much later, X-rays like the Braggs’ showed exactly how differently the carbon atoms are arranged in the two.
Figure 2.7Two ways of joining carbon atoms. Diamond (left): every atom bonded to four neighbours, in a network that runs through the whole crystal. Graphite (right): flat hexagonal sheets, weakly attracted to the sheets above and below.
You can test the strangest of these differences yourself.
Draw a wire
Do this with an adult nearby. You need a very soft pencil (6B to 8B; an ordinary HB pencil will not work), a 9-volt battery, a small LED (red works best) and some sticky tape. On paper, shade a short, wide strip, about 4 cm long and 1 cm wide, pressing hard and going over it again and again until it is dark and shiny. Hold one terminal of the battery on one end of the strip. Press one leg of the LED firmly onto the other end of the strip, and touch the LED’s other leg to the battery’s other terminal, so that the electricity has to travel along the pencil line. (If it does not light, turn the LED round: it only works one way, with its longer leg towards the battery’s + terminal.) Predict first: can a pencil line carry electricity? It can: the LED glows, faintly, so dim the room to see it, because electrons can travel along graphite’s sheets. Make the strip longer or thinner and the LED dims, or goes out. A diamond line, if you could draw one, would carry nothing, though it is the same element. Never touch the LED’s legs straight onto both battery terminals: without the pencil line to hold the current back, it will burn the LED out. Use only a small battery like this, never the mains.
Different forms of the same element are called allotropes. Oxygen has them too: ordinary oxygen, O₂, which you breathe, and ozone, O₃, a sharp-smelling gas that high in the atmosphere absorbs much of the Sun’s harmful ultraviolet light.
Lavoisier did not live to see any of this. During the French Revolution, tax officials were hated, and in 1794 he was sent to the guillotine. The mathematician Joseph-Louis Lagrange is reported to have said that it took only a moment to cut off that head, and a hundred years might not produce another like it.
Investigation 2.6
Select diamond, and compare it with graphite. Write a question about these two materials that the formula C cannot answer.
Check yourself
Can the formula C tell you whether a sample is graphite or diamond? What extra information do you need?
No. Both are pure carbon, so their formula is the same. You need to know the structure: how each atom is bonded to its neighbours (four neighbours in a 3D network for diamond; three, in flat sheets, for graphite).
2.7Unequal sharing and molecular dipoles
In a hydrogen molecule, both atoms are the same, so the shared electrons are shared equally. But in a water molecule, the oxygen nucleus, with 8 protons, pulls on the shared electrons much more strongly than a hydrogen nucleus with only 1 (even after oxygen’s inner electrons screen off part of that pull). So the shared electrons spend more time near the oxygen. The oxygen end becomes slightly negative, written δ⁻ (“delta minus”), and the hydrogen ends slightly positive, δ⁺. These are partial charges: much smaller than the full charge of an ion.
Pasadena, California, 1932
How hard does each atom pull? In 1932 Linus Pauling, a young chemist at the California Institute of Technology who would later win two Nobel Prizes, one for chemistry and one for peace, worked out a scale by comparing the energies of many different bonds. How strongly an atom pulls shared electrons is called its electronegativity. On the scale that grew from Pauling’s, hydrogen scores 2.20, carbon 2.55, nitrogen 3.04 and oxygen 3.44. The bigger the difference between two bonded atoms, the more unequal the sharing. A bond with unequal sharing is called a polar bond.
Now the interesting part. Carbon dioxide has two polar bonds too: oxygen (3.44) pulls harder than carbon (2.55). But a CO₂ molecule is perfectly straight, O=C=O, so the two oxygen ends pull in exactly opposite directions and cancel out, like two equally strong children in a tug of war. The molecule as a whole has no positive end and no negative end. Water is bent, with an angle of 104.5° between its bonds, so its two pulls do not cancel. Water has a negative oxygen side and a positive hydrogen side: it is a polar molecule, with a dipole.
Figure 2.8Bond pulls (thin arrows, pointing towards the atom that pulls the electrons harder) and the molecule’s overall pull (thick arrow). In straight CO₂ the two bond pulls cancel. In bent H₂O they add up, so the molecule has a positive side and a negative side.
So a molecule’s polarity depends on two things at once: its bonds, and its shape. Methane, CH₄, also comes out non-polar: its four slightly polar bonds point to the corners of a tetrahedron and cancel. Ammonia, NH₃, is a squat pyramid, and its bonds do not cancel.
How do we know? Measuring a molecule’s lopsidedness 20th century
Polar molecules twist to line up in an electric field, and this changes how a substance responds to the field and how its molecules absorb microwaves. The Dutch-born physicist Peter Debye worked out how to turn such measurements into each molecule’s dipole moment, a measure of how lopsided its charge is; the unit is named the debye after him. Water’s is 1.85 debye, ammonia’s 1.47 and hydrogen chloride’s 1.08. Carbon dioxide and methane come out at zero, just as the shapes predict. These same measurements also confirmed the shapes themselves.
Careful
“A thin stream of water bends towards a charged comb, so that proves water molecules are polar.”
It is a lovely demonstration, and you may see it in a textbook. But careful experiments in 2000 showed that the stream bends mainly because the charged comb pulls extra charge onto the water as it flows from the tap, and then attracts that charge. How much a liquid bends depends mostly on how easily charge can flow onto it, not simply on whether its molecules are polar. So the bending stream is not good evidence that water molecules are polar. The real evidence is the dipole-moment measurements described above. It is a good example of why scientists keep re-checking even familiar experiments.
So what can you see at home? Not dipoles themselves, but one of their most important consequences: polar substances mix with polar substances, and non-polar with non-polar.
Fireworks in a glass
Fill a tall glass nearly to the top with water. In a cup, stir three or four drops of food colouring into two tablespoons of cooking oil (the drops will not mix in; they break into little beads). Pour the oil gently onto the water. Predict first: what will the coloured beads do? They sink slowly through the oil. Some rest on top of the water for a little while (give them a few minutes), but when each one breaks through it bursts into a streaming cloud of colour. Food colouring is dye dissolved in water. It mixes into water, whose molecules are polar, but not into oil, whose molecules are almost non-polar. This shows “like mixes with like”; it does not measure a dipole, but it is a real effect of one.
Understand itPolar molecule
What is it?
A molecule with a slightly positive end and a slightly negative end, because its electrons are shared unequally and its shape does not let the pulls cancel. Water is polar; carbon dioxide is not.
Why is it called this?
From “pole”, the name for each end of a magnet, which comes from the Greek polos, a pivot or axis. A polar molecule has two ends with opposite charges, so it is also called a dipole, “two poles”.
What problem did it solve?
It explained why some substances mix and others refuse, and why molecules with the same kinds of bond can behave so differently: CO₂ and H₂O both have polar bonds, but only water is a polar molecule.
Why does it work?
A more electronegative atom, such as oxygen, pulls shared electrons towards itself, making small partial charges. If the molecule is lopsided, like bent water, the pulls add up; if it is straight or evenly balanced, they cancel.
How does it help?
It predicts what dissolves in what (“like mixes with like”), and helps explain how strongly molecules stick to each other, which Chapter 3 uses to explain boiling points.
Go deeper how do we know, what it isn’t, where does it stop working
How do we know?
Measured dipole moments: water 1.85 debye, ammonia 1.47, carbon dioxide and methane zero, just as their shapes predict.
What it isn’t
Not an ion. The charges are only partial, small fractions of a full charge, and the molecule as a whole is neutral.
Where does it stop working?
Electronegativity is a handy scale, not a single measured thing, and different scales give slightly different numbers. It tells you roughly how unequal the sharing is, not exactly.
Your turn
Explain Polar molecule to a friend in one sentence, in your own words. Then compare it with the book’s.
A molecule with a slightly positive end and a slightly negative end, because its electrons are shared unequally and its shape does not let the pulls cancel. Water is polar; carbon dioxide is not.
Investigation 2.7
Compare H₂O (bent), CO₂ (straight) and CH₄ (tetrahedral). For each, decide whether the bonds are polar, and then whether the whole molecule is polar. Explain how CO₂ can have polar bonds and still be non-polar.
Check yourself
Ammonia (NH₃) is a pyramid, with the nitrogen at the top. Boron trifluoride (BF₃) is flat, with its three fluorines spread 120° apart. Both have three polar bonds. Which molecule is polar overall, and why?
Ammonia is polar; boron trifluoride is not. In flat, evenly spread BF₃, the three bond pulls cancel exactly, like three equal ropes pulling a ring from three evenly spaced directions. In pyramid-shaped NH₃, all three N–H pulls point partly the same way, so they add up instead of cancelling.
Case file 2
The case of the three unlabelled jars
A laboratory has three jars whose labels have fallen off. The labels on the floor say water, carbon dioxide and sodium chloride. Here is what the technician finds.
Jar A holds a colourless liquid that boils at 100 °C. Measurements show its molecules have a dipole moment of 1.85 debye.
Jar B holds a white solid at −80 °C, which turns straight into a colourless gas at −78 °C without melting first. Its molecules have polar bonds, but a dipole moment of zero.
Jar C holds hard, white, cube-shaped crystals that melt only at 801 °C. As a solid it does not conduct electricity; dissolved in water, it does.
Which label belongs on each jar? For each one, say what kind of particles it is made of and which clue settles it.
Show the solution
Jar A is water. It is made of bent H₂O molecules. The bent shape means the two polar O–H bonds do not cancel, giving a dipole moment (clue 1); and water boils at 100 °C.
Jar B is carbon dioxide, frozen (“dry ice”). It is made of straight O=C=O molecules: polar bonds whose pulls cancel exactly, so the dipole moment is zero (clue 2).
Jar C is sodium chloride. It is an ionic lattice, not molecules. The very high melting point (clue 3) shows how strong the attractions in the lattice are. It cannot conduct as a solid because the ions are locked in place; dissolved, they are free to move.
What this chapter can’t explain yet
You now know what holds atoms together inside a molecule or a crystal. But one big puzzle remains. When you heat ice, it melts, and then boils, and steam is still water. The bonds inside the H₂O molecules never break. So what does change when a substance melts or boils? Chapter 3 is about the forces between molecules, and the jiggling of heat that fights against them.
3
Chapter 3
Why matter has different states
The big questionWhen water boils in a kettle, bubbles of invisible gas rise through it and escape as steam. What is inside those bubbles, and what actually breaks when water boils?
On a cold winter’s day a young professor called Joseph Black set a pan of ice and a pan of ice-cold water side by side in a warm room, and watched two thermometers. The water warmed up steadily, as you would expect. The ice did something strange. Its thermometer sat stuck at the freezing point, hour after hour, while the ice slowly turned to water. Heat was pouring into it from the room, and yet it was getting no warmer. Where was all that heat going?
Black had been born in Bordeaux, in France, the son of a wine merchant from Belfast, and trained as a doctor. He was a quiet, cautious man who hated to publish anything until he was sure, and he lectured to packed rooms of medical students rather than write books. But he trusted his thermometers more than the ideas of his day, and that is what let him see the puzzle at all.
Black’s answer was that melting itself swallows heat: the ice needed energy just to stop being ice. He did not know about molecules, and nor did anyone else in Glasgow. But he had caught the first clue to the question this chapter answers. Ask a few people what is inside the bubbles in boiling water, and some will say “air”, some “oxygen”, and some “hydrogen and oxygen, because the water is splitting up”. Predict first: before you read on, decide what you think is in those bubbles, and keep your answer in mind. By the end of Section 3.3 you will have seen the evidence for yourself. Follow the particles of a substance as it melts, boils and spreads out, and you find that the particles themselves never change. What changes is how far apart they are, how fast they move, and whether the pulls between them can hold them together.
3.1One substance, three states
Water is the only substance most of us see every day as a solid, a liquid and a gas: ice in the freezer, water in the tap, steam from the kettle. These are the three common states of matter. You can tell them apart without any equipment. A solid keeps its own shape. A liquid flows and takes the shape of its container, but keeps the same volume: a litre of water is a litre whether it is in a bottle or a bowl. A gas spreads out to fill whatever space it is given, and can be squashed into a smaller space.
The particle model explains all three with one picture. In a solid, the particles are packed closely together and each one vibrates about a fixed spot, held there by the attractions of its neighbours. In a liquid, they are still close together, which is why a liquid is hard to squash, but they move around and slide past each other, which is why it flows. In a gas, the particles are far apart compared with their own size and fly about freely, colliding with each other and with the walls.
Two things in that picture are invisible, and both are easy to get wrong. The first is the space between the particles. It is not filled with air, or with anything else: air is itself made of particles, and between those there is nothing at all. The second is the motion in a solid. The molecules in an ice cube are not frozen still; they shiver in place all the time, and the colder the ice, the smaller the shiver.
Figure 3.1The same twelve molecules as a solid, a liquid and a gas. Only their arrangement and motion change. The molecules themselves are identical in all three boxes. (In a real gas the molecules would be much further apart than the box allows.)
How much further apart are they in a gas? When water boils at 100 °C and normal pressure, the steam takes up about 1,700 times as much space as the liquid water it came from. A 250 mL cup of water makes roughly 400 litres of steam: enough to fill a bathtub. That enormous swelling is what James Watt and the engineers after him harnessed in steam engines, a few years after Black’s ice experiment and in the same university town.
Careful
“When ice melts, the water molecules melt too, and when water boils, the molecules expand.”
The molecules do not melt, swell or soften, and they do not stop moving when water freezes. Every H₂O molecule in steam is exactly the same size and shape as one in ice. What changes is the space between molecules and how freely they move. Water even shows that a solid is not always more tightly packed than its liquid: ice is slightly less dense than liquid water, because its molecules are held in an open, hexagonal pattern. That is why ice floats.
Watch heat vanish into ice
Put a few ice cubes and a little cold water in a glass, stir, and put a kitchen thermometer in it (or just feel the glass). Keep stirring now and then. As long as there is still ice in the glass, the temperature stays at about 0 °C, even though the room is pouring heat into it. Only when the last of the ice has melted does the water start to warm up. You are watching Joseph Black’s puzzle: the heat is going into pulling the molecules out of their ice pattern, not into making them move faster.
Understand itThe particle model
What is it?
The idea that every substance is made of tiny particles that are always moving and that attract each other. Solid, liquid and gas are the same particles, arranged and moving differently.
Why is it called this?
“Particle” comes from Latin particula, “a little part”. It is called a model because it is a simplified picture built to explain what we observe, not a photograph.
What problem did it solve?
Why does a solid keep its shape, a liquid flow but keep its volume, and a gas fill any space and squash easily? One picture explains all three.
Why does it work?
In a solid, the attractions hold particles in place while they vibrate. In a liquid, they stay close but slide past each other. In a gas, they are far apart and fly freely. Heating or cooling changes which wins: the motion or the pull.
How does it help?
It predicts what happens when you heat, cool or squeeze things: why ice melts at a fixed temperature, why gases can be squashed, and why steam takes up about 1,700 times the space of the water it came from.
Go deeper how do we know, what it isn’t, where does it stop working
How do we know?
Brownian motion shows the particles jostling (Chapter 0), and the heat that vanishes into melting ice, Joseph Black’s puzzle, is just what pulling particles out of their pattern would need.
What it isn’t
The space between the particles is not filled with air, or with anything else: it is empty. And the particles themselves do not melt, swell or stop moving.
Where does it stop working?
Some materials do not fit three neat states, such as glass, gels and toothpaste, and at very high temperatures matter becomes a fourth state, plasma, as in lightning and the Sun.
Your turn
Explain The particle model to a friend in one sentence, in your own words. Then compare it with the book’s.
The idea that every substance is made of tiny particles that are always moving and that attract each other. Solid, liquid and gas are the same particles, arranged and moving differently.
Investigation 3.1
Heat the ice slowly from −30 °C to steam, watching the graph. Predict first: where will the temperature stop rising, and which flat part will be longer? Then explain, without saying that the particles got bigger, why the gas takes up more room.
Check yourself
Why is it easy to squash the air in a bicycle pump, but almost impossible to squash a syringe full of water?
In a gas the particles are far apart, with lots of empty space between them, so pushing them closer is easy. In a liquid they are already touching their neighbours, so there is almost no empty space left to squeeze out.
3.2Temperature and particle motion
Paris, 1 December 1783
Half of Paris had come to the gardens of the Tuileries Palace. Ten days earlier, two men had floated over the city under a huge paper-and-cloth balloon filled with hot air from a fire, built by the Montgolfier brothers: the first people ever to fly. Now a physicist named Jacques Charles was about to go one better. His balloon was filled not with hot air but with hydrogen, a gas much lighter than air, and he rose into the sky with his engineer Nicolas-Louis Robert, a thermometer and a barometer on board to take measurements. Charles flew for about two hours and came down safely, 36 kilometres away.
Charles spent the following years asking a quieter question: what does heat do to a gas? Warm a gas, he found, and it swells; and every gas he tried swelled by the same fraction for the same warming. To understand why, you need to picture the particles.
The particles in everything around you are always moving. In a gas they are fast. The nitrogen and oxygen molecules in the air of your room are zooming about at an average of roughly 500 metres per second, faster than a passenger jet. They do not get far: each one collides with another molecule billions of times a second.
What we feel as temperature is connected to this motion. The hotter a gas is, the faster its particles move, on average. Not every particle moves at the same speed; some are always faster and some slower. But warm the gas and the whole crowd speeds up.
Remember the two glasses from Chapter 0, with a drop of food colouring in each? Here is the inference you were reaching for. The water molecules are always moving and jostling the colour’s molecules about, and in the warm glass they move faster, so the colour is shoved outwards sooner. Nobody stirs it: the molecules do the stirring.
Picture a gas sealed in a strong box. Its particles keep slamming into the walls, and all those tiny collisions add up to a steady push on the walls: the pressure of the gas. Heat the box, and the particles move faster. They hit the walls more often and harder. So the pressure rises, even though the number of particles and the size of the box have not changed. (Let the walls move, as the skin of a balloon can, and instead of the pressure rising, the gas swells: Charles’s discovery.)
Figure 3.2One mole of gas in a sealed 10-litre box, at 200 K and at 400 K. Doubling the kelvin temperature makes the molecules move faster (longer arrows) and doubles the pressure, from 166 kPa to 333 kPa. The number of molecules does not change.
To make this rule work, temperature has to be measured from the right starting point, and finding that starting point was its own small adventure. In about 1702 the French physicist Guillaume Amontons noticed that air in a sealed container pushes harder when it is heated. A century later Charles and Joseph Gay-Lussac measured carefully how the volume (and, later, the pressure) of many gases changes with temperature. Plot either one against temperature, and every gas gives a straight line. Follow the lines backwards, and they all point to zero at the same temperature: about −273 °C. In 1848 William Thomson, later Lord Kelvin, proposed a temperature scale that starts right there. Real gases turn to liquid before they get that cold, but the lines still point the way.
The kelvin scale starts at absolute zero, −273.15 °C, the coldest anything can possibly be, where particle motion is as small as nature allows. A kelvin step is the same size as a degree Celsius, so to convert, you add 273.15. Water freezes at 273.15 K and boils at 373.15 K. Doubling the temperature in kelvin doubles the pressure of a gas in a sealed box. Doubling it in Celsius does not: going from 10 °C to 20 °C is only going from 283 K to 293 K.
A balloon that breathes
Stretch a balloon over the neck of an empty plastic bottle. Stand the bottle in a bowl of hot tap water, or water an adult has mixed from the kettle (hot, but not boiling), for a few minutes, and the balloon slowly lifts and stands up as the air inside warms and swells. Move the bottle into a bowl of ice water, and the balloon sags again. Nothing has gone in or out: the same air molecules are simply moving faster, then slower. If you have a kitchen scale, weigh the bottle and balloon cold and again when warm, wiping the bottle dry each time. Predict first: will the warm one be heavier? (It weighs the same. Faster molecules take up more room, but there are no more of them, and none of them got heavier.)
Understand itTemperature
What does it measure?
How hot something is. In a gas, it measures the average energy of the particles’ motion: the hotter the gas, the faster its particles move on average.
Why is it called this?
From Latin temperatura, “a mixing in the right proportion”, from temperare, to mix or moderate. Galileo and later Boyle used the word for the degree of heat.
What problem did it solve?
“Hot” and “cold” are feelings that differ from person to person. A temperature scale turns them into numbers anyone can check, and the kelvin scale gives a true starting point, absolute zero.
Why does it work?
When a hot thing touches a cold one, energy passes from the faster-moving particles to the slower ones until both are at the same temperature. A thermometer settles at the temperature of whatever it touches, and reads its own.
How does it help?
It lets you predict how gases behave: double the kelvin temperature of a sealed gas and its pressure doubles.
Go deeper how do we know, what it isn’t, where does it stop working
How do we know?
Plot the volume or pressure of a gas against temperature and every gas gives a straight line, all pointing to zero at about −273 °C, the start of the kelvin scale.
What it isn’t
Not the same as heat. A bucket of warm water holds far more energy than a cup of hot tea, enough to melt much more ice, even though the tea is at a higher temperature.
Where does it stop working?
Temperature describes a crowd. A single molecule has a speed, not a temperature, and in any gas some molecules are always faster and some slower.
Your turn
Explain Temperature to a friend in one sentence, in your own words. Then compare it with the book’s.
How hot something is. In a gas, it measures the average energy of the particles’ motion: the hotter the gas, the faster its particles move on average.
Investigation 3.2
Hold the volume at 10 L. Compare 200 K and 400 K. Explain the pressure change without saying that the particles got bigger.
Check yourself
A sealed, rigid container of gas is warmed from 27 °C to 327 °C. By what factor does its pressure change?
Convert to kelvin first: 27 °C = 300 K and 327 °C = 600 K. The kelvin temperature has doubled, so the pressure doubles. (If you had used Celsius, you would wrongly have said it went up more than twelve times.)
3.3Changing state is not changing identity
London, May 1800
News had just arrived from Italy that Alessandro Volta had built the first battery, a tall pile of metal discs and salty cardboard that pushed a steady electric current. Within weeks, two Londoners, William Nicholson and Anthony Carlisle, had built their own. They dipped its two wires into water, and bubbles of gas streamed off both of them: hydrogen at one wire, oxygen at the other, with twice as much hydrogen as oxygen. Electricity had torn water apart into two elements.
So could boiling do the same? Is that what is inside the bubbles in a kettle? The answer is no. Inside the bubbles in boiling water is water: water vapour, made of the same H₂O molecules as the liquid. When water boils, the molecules break away from their neighbours and spread out, but each molecule stays whole. Boiling, melting, freezing and condensing are changes of state. They change how molecules are arranged, not what the molecules are.
One small thing about the word “steam”. Look closely at a boiling kettle: right at the spout there is a clear gap, and the white cloud starts a little further out. The clear gap is the real water vapour, and it is invisible, like air. The white cloud is made of tiny droplets of liquid water that have already cooled and condensed. So the bubbles in boiling water are full of something you cannot see at all: water as a gas.
The proof is in any kitchen. When steam from a pan meets a cold lid, drops of liquid form on it. They are water: they look and behave exactly like water. If boiling had split the molecules into hydrogen and oxygen, the steam would be a mixture of two gases that would not turn back into liquid on a cold plate, and that would explode if it met a flame. No amount of ordinary boiling does what Nicholson and Carlisle’s battery did.
Boil water without a flame (an adult does this one)
Hot water can scald, so this one is for an adult to do while you watch. You need a plastic syringe from the chemist (20 mL is ideal, no needle) and a blob of Blu-Tack. The adult pours some water that has just boiled into a cup, sucks up about 10 mL into the syringe, pushes out any air with the nozzle pointing down into the cup, and seals the nozzle firmly with the Blu-Tack. Then, holding the syringe in a cloth, they pull the plunger back hard and hold it. Predict first: with no flame, and water that is cooling down, can it boil?
It can. The water fills with bubbles and froths, as if it were on the stove. (It works best while the water is still very hot, so do it straight away; as it cools you have to pull harder.) Now let the plunger go: the bubbles vanish, back into liquid. At most a tiny bead of air may be left, which was dissolved in the water. Think about what that rules out. Nothing could get in through the sealed nozzle, and the big bubbles disappeared when squeezed, so they were not air. They turned straight back into liquid when squeezed, so they are not hydrogen and oxygen. And no heat was added, so heat did not “break” anything. Pulling the plunger gave the molecules room, and the fastest ones escaped into it, just as in a kettle. Bubbles in boiling water are water.
So what does break when water boils? The pulls between molecules. Inside each molecule there are strong covalent bonds. Between neighbouring molecules there are much weaker attractions, called intermolecular forces. Boiling needs only enough energy to overcome the weak ones. This is what Joseph Black’s vanishing heat was doing: pulling molecules away from their neighbours.
Figure 3.3Boiling and splitting are different changes. Boiling (left) separates whole H₂O molecules from each other, at a cost of about 41 kJ per mole: a bubble holds only whole H₂O molecules, with empty space between them. Splitting water into hydrogen and oxygen (right) breaks the bonds inside the molecules and makes new substances, and takes about seven times as much energy, about 286 kJ per mole.
The numbers show how different the two changes are. Boiling a mole of water (18 grams) at 100 °C takes about 41 kJ of energy. Breaking all the O–H bonds in that same mole, two per molecule, would take about 926 kJ, more than 20 times as much. (Splitting water into hydrogen and oxygen costs less than that, about 286 kJ, because new H–H and O=O bonds form and pay some of it back.) Steam at 100 °C is nowhere near hot enough to do that.
Investigation 3.3
Sketch twelve water molecules before and after boiling. Then write one thing that the app’s state switch cannot tell you about a real sample (hint: at what temperature does it change?).
Check yourself
What observation in a kitchen shows that the steam from a kettle is still water?
When steam touches something cold, such as a window or a pan lid, it condenses back into drops of liquid water. Hydrogen and oxygen gas would not do that at kitchen temperatures.
3.4Squeezing a gas
Oxford, England, 1662
A century before Charles’s balloon, in a house on the High Street in Oxford, Robert Boyle and his brilliant young assistant Robert Hooke were at work. Boyle was the fourteenth child of the Earl of Cork, one of the richest men in Ireland, and he could have lived an idle life. Instead he spent his money on glassware, furnaces and assistants, and argued, against most scholars of his day, that you learn how nature works by doing experiments and writing down exactly what happens, failures included. He and Hooke were busy with the most exciting machine in England: an air pump, which could suck the air out of a glass globe. Boyle was fascinated by what he called “the spring of the air”: squeeze air, and it pushes back, like a spring.
To measure the spring, Boyle used a glass tube bent into the shape of a J, with the short end sealed. He poured mercury into the long open end, trapping a pocket of air in the short end. The more mercury he poured in, the harder it pressed on the trapped air, and the smaller the air pocket became. When he doubled the pressure, the air’s volume halved. When he tripled it, the volume fell to a third. The rule is still called Boyle’s law.
Push the handle of a bicycle pump while blocking the end with your thumb, and you can feel Boyle’s spring of the air. Why does the air push back harder and harder?
Before going on, notice something easy to forget: the air in the pump has mass, like any other matter.
Weigh some air
Find a football or basketball that is soft and needs pumping. Weigh it on a kitchen scale. Predict first: after you pump it up hard, will the scale read more, less or the same? Pump it up and weigh it again. A football pumped up from nearly flat gains about 3 to 5 g; one that was only a little soft gains less, perhaps a gram or two, so you need a scale that shows single grams. All of the extra is air you have squeezed in. Squashing a gas does not make it lighter or heavier; adding more of it does.
The temperature has not changed much, so the molecules are moving at about the same speed as before. But now the same number of molecules is crowded into less space. Each bit of wall gets hit more often. Halve the volume, and the molecules hit the walls twice as often, so the pressure doubles. Double the volume, and the pressure halves. As long as the temperature and the amount of gas stay the same, pressure × volume stays the same.
Figure 3.4One mole of gas at 300 K. Halving the volume from 10 L to 5 L doubles the pressure; doubling it to 20 L halves the pressure. Pressure × volume stays the same along the whole curve. (Calculated with the ideal-gas rule, which real gases follow closely at these conditions.)
Boyle’s squeezing rule and Charles’s warming rule can be combined into one statement, called the ideal gas law: P × V = n × R × T. Here P is pressure, V volume, n the number of moles, T the kelvin temperature, and R is a fixed number, 8.314. You do not need to memorise it now. What matters is what it says: pressure goes up with more particles and higher temperature, and down with more space.
1 mole of gas at 300 K in a 10-litre box: P = nRT ÷ V = 1 × 8.314 × 300 ÷ 10 = 249 kPa (with V in litres, P comes out in kPa).
In 5 litres: 1 × 8.314 × 300 ÷ 5 = 499 kPa, twice as much.
In 20 litres: 125 kPa, half as much.
The ideal gas law treats molecules as dots that never attract each other. That works because gas molecules are usually far apart. Squeeze a gas hard enough, or cool it enough, and the molecules get close enough for their attractions to matter. Then the gas stops following the rule, and eventually it turns into a liquid. That is how the butane in a lighter is stored as a liquid: squeezed under pressure in its little tank.
Understand itGas pressure
What is it?
The push of a gas on each square metre of the walls around it, made by countless particles hitting the walls. Normal air pressure is about 101 kPa.
Why is it called this?
From Latin pressura, “pressing”, from premere, to press. Scientists began using the word for a push spread over an area in the 1650s, around the time of Boyle’s experiments.
What problem did it solve?
Boyle wanted to explain “the spring of the air”: why squeezed air pushes back harder and harder. Pressure, pictured as particles hitting the walls, explains it.
Why does it work?
Squeeze the same particles into half the space and each bit of wall is hit twice as often, so the pressure doubles. Heat them and they hit harder and more often, so the pressure rises again.
How does it help?
With the ideal gas law, PV = nRT, you can predict the pressure in a tyre, a pressure cooker or a gas cylinder from its volume, the amount of gas and the temperature.
Go deeper how do we know, what it isn’t, where does it stop working
How do we know?
Boyle’s J-shaped tube of 1662: double the pressure of the mercury on a trapped pocket of air, and its volume halves.
What it isn’t
Not something a single particle has. One molecule hitting a wall is a tiny tap; pressure is the steady total of billions upon billions of taps.
Where does it stop working?
Squeeze or cool a gas enough and its particles get close enough to attract each other. Then the simple rule fails and the gas turns into a liquid, like the butane in a lighter.
Your turn
Explain Gas pressure to a friend in one sentence, in your own words. Then compare it with the book’s.
The push of a gas on each square metre of the walls around it, made by countless particles hitting the walls. Normal air pressure is about 101 kPa.
Investigation 3.4
Hold the temperature at 300 K. Compare 5 L, 10 L and 20 L, and save two results. Multiply pressure by volume for each one. What do you notice?
Check yourself
A gas at constant temperature is squeezed from 12 litres to 4 litres. What happens to its pressure?
The volume becomes one third as big, so the pressure becomes three times as big. (Pressure × volume stays the same: 12 × P = 4 × 3P.)
3.5Where did the solute go?
Dandi, Gujarat, 6 April 1930
Early in the morning, after a march of 24 days and nearly 390 kilometres from his ashram at Sabarmati, Mahatma Gandhi walked down to the shore at Dandi and picked up a lump of natural salt left by evaporating seawater. It was a small act that shook an empire: the British government of India taxed salt and forbade Indians to make their own. Gandhi chose salt because everyone needed it, and because anyone could see where it came from. The sea is full of it, though you cannot see a single grain.
Stir a spoonful of salt into a glass of water, and in a minute or so the crystals vanish. The water looks exactly as clear as before. Has the salt gone?
Predict first: put a glass of water and a spoonful of salt (in its own little cup) on a kitchen scale together; then stir the salt in and put the empty cup back beside the glass. Will the reading be lighter, heavier or the same?
Taste it and you know the salt has not gone. It has dissolved: its ions have separated and spread out among the water molecules, too small and too evenly mixed to see. The salt is the solute; the water it dissolves in is the solvent; together they make a solution.
Try it, and the scale reads the same before and after: not one particle has left. The salt is still all there, just spread out too finely to see.
Careful
“The sugar melted in the tea.”
It dissolved; it did not melt. Melting needs heat and involves one substance: sugar melts on its own in a hot pan at about 186 °C and turns into a sticky liquid, which soon starts to brown as it breaks down. Dissolving needs a second substance, and happens even in cold water: the sugar molecules come away from their crystal and spread out among the water molecules. Nor is dissolving a chemical reaction. Every sugar molecule is still a sugar molecule; let the water evaporate slowly and you get your sugar back.
Dissolved particles are so small that they pass straight through filter paper, which easily stops grains of sand. But they are still there, and they can be counted. Dissolve 5.00 g of salt in water, pour it through filter paper, and nothing is caught. Heat the solution gently in a weighed dish until all the water has gone, and 5.00 g of white crystals are left behind: exactly the mass you put in. The salt pans of Gujarat’s coast and the Rann of Kutch do the same thing on a vast scale, with the sun as the heater.
How much solute is in each bit of a solution is called its concentration. Chemists usually measure it in moles of solute per litre of solution (mol/L). One mole of salt dissolved to make 2 litres of solution has a concentration of 0.50 mol/L. Add water to make 4 litres, and the same one mole is spread through twice the volume, so the concentration halves to 0.25 mol/L. This is called dilution. Every sip is weaker, but the total amount of salt has not changed. You do this every time you make nimbu pani or Rooh Afza: a little concentrated syrup from the bottle goes into a big glass of water. All the syrup is still there, but spread through more water, so each sip is less sweet.
Figure 3.5The same eight solute particles in 1 litre and in 2 litres of solution. Adding water does not remove any solute, but spreads it out, so each litre (and each sip) holds half as much.
concentration = amount of solute ÷ volume of solution
One small detail: the volume that counts is the final volume of the whole solution, not the volume of water you poured in. When you dissolve things, volumes do not always add up exactly, which is why chemists make solutions in special flasks with a single line marking an exact final volume.
Understand itDissolving
What happens?
The particles of a solid such as salt or sugar come away from their crystal and spread out evenly among the water molecules, too small to see. The salt is the solute, the water is the solvent, and together they make a solution.
Why is it called this?
From Latin dissolvere, “to loosen apart”, from solvere, to loosen or untie. The crystal is loosened apart, not destroyed.
What problem did it solve?
Where does salt go when it disappears into water? The answer, that every bit of it is still there, explains how the sea can hold salt you cannot see, and how salt pans get it back.
Why does it work?
Water molecules are polar, so they pull on the charged ions of salt (and on sugar’s slightly charged molecules), surround them and tug them away from the crystal. Their constant motion then spreads them through the whole solution.
How does it help?
It lets you make solutions of any strength and work out their concentration, from a glass of nimbu pani to a hospital drip.
Go deeper how do we know, what it isn’t, where does it stop working
How do we know?
Weigh a glass of water and a spoonful of salt before and after stirring: the scale reads the same. Let the water evaporate and the salt comes back.
What it isn’t
Not melting, which needs heat and only one substance, and not a chemical reaction: every sugar molecule is still a sugar molecule.
Where does it stop working?
Water can hold only so much. Keep adding salt and eventually no more dissolves: about 36 g in 100 g of water at room temperature.
Your turn
Explain Dissolving to a friend in one sentence, in your own words. Then compare it with the book’s.
The particles of a solid such as salt or sugar come away from their crystal and spread out evenly among the water molecules, too small to see. The salt is the solute, the water is the solvent, and together they make a solution.
Investigation 3.5
Keep the amount of dissolved solute fixed and increase the final volume. Explain what changes and what stays the same.
Check yourself
Bottle A holds 1 litre of salt solution at 0.50 mol/L. Bottle B holds 4 litres at 0.25 mol/L. Which tastes saltier? Which holds more salt altogether?
Bottle A tastes saltier, because each litre (and each sip) contains more salt: 0.50 mol/L against 0.25 mol/L. But Bottle B holds more salt altogether: 4 × 0.25 = 1.0 mol, compared with 1 × 0.50 = 0.50 mol in Bottle A.
3.6Intermolecular forces against thermal motion
Here is a puzzle that bothered chemists for a long time. Methane (CH₄), ammonia (NH₃) and water (H₂O) are all small molecules with almost the same mass: 16, 17 and 18 grams per mole. Each molecule even has exactly 10 electrons. Yet methane boils at −161.5 °C, ammonia at −33.3 °C, and water at +100 °C. Why such huge differences?
Water was the oddest of all. In most families of similar compounds, boiling point rises steadily with molecular size. The compounds of hydrogen with the elements in oxygen’s column of the periodic table boil at about −60 °C (H₂S), −41 °C (H₂Se) and −2 °C (H₂Te). Follow that trend down to the smallest member, water, and you would expect it to boil far below zero. Instead it boils at +100 °C. If water followed the pattern, there would be no rivers, no oceans, no monsoon and no you.
Every state of matter is a contest. On one side are the attractions between molecules, pulling them together. On the other side is thermal motion, the jiggling of heat, shaking them apart. A substance boils at the temperature where the jiggling becomes strong enough to tear molecules away from their neighbours. Strong attractions mean a high boiling point.
There are three main kinds of attraction between molecules, from weakest to strongest (for small molecules like these):
Dispersion forces: the electrons in any molecule slosh around, making brief, flickering positive and negative patches that attract the patches on neighbouring molecules. Every molecule has these. Molecules with more electrons and more surface have stronger ones.
Dipole attractions: in polar molecules (Section 2.7) the permanent positive end of one molecule attracts the negative end of the next.
Hydrogen bonds: an especially strong dipole attraction. A hydrogen atom bonded to nitrogen, oxygen or fluorine is left very positive, and it is pulled towards a lone pair of electrons on an N, O or F atom of a neighbouring molecule.
The idea of the hydrogen bond grew up in the laboratory of G. N. Lewis at Berkeley, in California, where in 1920 two young chemists, Wendell Latimer and Worth Rodebush, suggested that a hydrogen atom could be shared, weakly, between two neighbouring molecules. Water’s strange boiling point, and ammonia’s and hydrogen fluoride’s, were among the strongest clues that they were right.
Figure 3.6Three molecules with 10 electrons each and almost the same mass, but very different boiling points. Methane has only dispersion forces. Ammonia and water form hydrogen bonds (dotted lines, right), and water, with two hydrogens and two lone pairs on each oxygen, forms the most.
Methane is non-polar and has no hydrogen attached to N, O or F, so only weak dispersion forces hold its molecules together: it boils at a very low temperature. Ammonia can form hydrogen bonds, so it boils much higher. Water forms them most of all: each molecule can make up to four, with its two hydrogens and the two lone pairs on its oxygen. So water stays liquid right up to 100 °C. Life on Earth depends on that.
Hydrogen bonds sound strong, but remember the scale. Breaking an O–H bond inside a water molecule takes about 463 kJ per mole; a hydrogen bond between molecules is roughly 20 times weaker. That is why boiling separates whole molecules and never breaks them apart.
Predict first: almost every substance shrinks when it freezes, because the particles settle closer together. Water does the opposite: ice floats. Before you turn the model, decide what you think the molecules in ice must be doing to take up more room than the same molecules in liquid water.
Figure 3.7The same 72 water molecules as a liquid and as ice. In the liquid, hydrogen bonds keep breaking and re-forming, and molecules crowd close. In ice, each molecule is held by exactly four hydrogen bonds, at the corners of a tetrahedron, in open six-sided rings with empty channels through them, so the same molecules fill more space.
Turn the ice until you are looking straight down the channels. Each oxygen is joined to four others, never more, and the four links point to the corners of a tetrahedron, like the legs of a camera tripod with one more leg pointing up. Four links that stiff cannot fold up tightly: they build a honeycomb with holes in it. In the liquid, the links break and re-form all the time (in real water, a hydrogen bond lasts only a few million-millionths of a second), so the honeycomb keeps collapsing and molecules slip into the holes. The same molecules end up closer together. That is why liquid water is denser than ice (about 1.00 g per mL against 0.917), and why ice floats with about nine-tenths of itself under the surface.
This one odd fact matters enormously. Lakes and ponds freeze from the top down, and the floating ice blanket keeps the water underneath liquid all winter, so fish and plants survive. If ice sank, cold lakes would fill up with ice from the bottom.
Careful
“When water boils, the heat breaks the bonds inside the water molecules.”
Boiling overcomes the attractions between molecules: mostly hydrogen bonds in water. The covalent O–H bonds inside each molecule stay intact. Steam is made of whole H₂O molecules.
Investigation 3.6
Select water and raise the temperature from 250 K to 420 K. Then compare methane and carbon dioxide at 300 K. Which attraction is being overcome at each change, and which bonds never break?
Check yourself
Carbon dioxide (CO₂, 22 electrons per molecule) and hydrogen (H₂, 2 electrons) are both non-polar gases at room temperature. Solid CO₂ turns to gas at −78.5 °C, but hydrogen boils at −252.9 °C. Why the difference?
Neither has dipole attractions or hydrogen bonds, so only dispersion forces hold their molecules together. Dispersion forces are much stronger for bigger molecules with more electrons. CO₂, with 22 electrons, attracts its neighbours far more strongly than H₂ with 2, so it needs a much higher temperature to break free.
Case file 3
The case of the quadrupled pressure
An engineer seals 1.0 mol of methane gas in a steel cylinder closed by a piston, holding 10 litres at 200 K. The pressure gauge reads 166 kPa. Later, the gauge reads 665 kPa: four times as much. A worried colleague says: “The amount of gas must have quadrupled. Either something leaked in, or the methane has broken up into more, smaller molecules.”
The sealed cylinder, piston and all, is weighed before and after. Its mass has not changed at all.
The log shows that the gas was warmed from 200 K to 400 K, and then the piston was pushed in until the gas filled only 5 litres.
A sample of the gas, cooled and analysed afterwards, is still pure methane, CH₄. Methane boils at 112 K, so at 200 K and 400 K it is a gas throughout.
Explain the fourfold rise in pressure without any new molecules. Which clue rules out each of the colleague’s ideas?
Show the solution
Two changes each doubled the pressure. Doubling the kelvin temperature (200 K to 400 K) makes the molecules move faster, so they hit the walls harder and more often: pressure × 2 (Charles’s and Amontons’s discovery). Halving the volume (10 L to 5 L) crowds the same molecules into half the space: pressure × 2 again (Boyle’s). Altogether, 166 × 2 × 2 ≈ 665 kPa, exactly what the gauge shows. Clue 1 rules out a leak: nothing was added. Clue 3 rules out breaking up: the molecules are unchanged. The number of molecules stayed at 1.0 mol the whole time.
What this chapter can’t explain yet
In this chapter, molecules moved apart, came together, spread through water and bounced off walls, but they never changed. Every H₂O stayed an H₂O. Real chemistry begins when that stops being true: when bonds break and atoms rearrange into substances that were not there before. For that part of the adventure we go to Paris in the 1770s, to a rich young man with a laboratory full of the finest balances in Europe, who decided to weigh everything.
IIVolume II
Change and quantity
What happens when substances turn into new ones: where the atoms go, where the energy goes, how fast it happens, and how chemists count what they cannot see.
The big questionA big log burns down to a small heap of ash, so it looks as if matter has vanished. An iron nail left in the rain turns to rust and gets heavier. Where did the wood go, and where did the extra mass on the nail come from?
In his private laboratory in Paris, Antoine Lavoisier and his wife, Marie-Anne Paulze Lavoisier, were weighing a glass vessel with a piece of tin sealed inside it. Lavoisier was thirty, trained as a lawyer, and earned his fortune as a partner in the company that collected the king’s taxes; chemistry was what he did before breakfast and after work, and on one whole day each week. He was rich, careful and slightly obsessed. He owned some of the most accurate balances in Europe, and he had come to believe that if you wanted to understand a change, you had to weigh everything, before and after, including the parts you could not see. Marie-Anne kept the notes, and later drew the engravings of his apparatus that chemists still reproduce today.
A hundred years earlier, Robert Boyle (the same Boyle who squeezed air in Chapter 3) had heated tin in a sealed flask, opened it, and found that the tin had become heavier. He thought particles of fire had soaked through the glass and stuck to the metal. Lavoisier repeated the experiment with one small change, and the change was everything. He did not open the vessel before weighing it.
So far, every change in this book has left the particles themselves alone. Ice melted, water boiled, salt dissolved, and the same molecules or ions were there at the end as at the start. Now something new happens. When wood burns, or iron rusts, or a cake bakes, the substances at the end are different substances from the ones you started with. This chapter is about what changes in a chemical reaction, and, just as important, what never does. It is also the chapter where chemistry, thanks largely to Lavoisier, became a science of measuring.
4.1What counts as a chemical change?
Put an ice cube in a glass and wait. It melts into water, which still freezes at 0 °C, still boils at 100 °C, and is still H₂O. Nothing new has been made: the molecules have only moved further apart and started sliding past each other. That is a physical change.
Now leave an iron nail outside through a Mumbai monsoon. A flaky, reddish-brown crust grows on it. The crust is not iron: it is brittle where iron bends, it is not attracted to a magnet the way iron is, and it does not shine. It is rust, a compound of iron, oxygen and hydrogen (mostly a form of iron oxide with water built into it). New substances have appeared, so this is a chemical change, also called a chemical reaction.
At the particle level, the difference is sharp. In a physical change the same molecules end up in a different arrangement. In a chemical change the bonds inside the starting substances break and new bonds form, so the atoms regroup into different particles.
Figure 4.1Left: melting. The same H₂O molecules, just more loosely arranged. Right: hydrogen burning in oxygen. The bonds in H₂ and O₂ break and the atoms regroup into H₂O, a new substance. In both panels every atom is still there.
How would you know which kind of change you are looking at, in a real kitchen? Clues like fizzing, a colour change, a smell, or heat given out are hints, but not proof. Sugar dissolving in chai disappears, yet it is still sugar (the tea tastes sweet). A pan of water bubbling on the stove is not making a gas from nothing; it is boiling. The real test is whether the substances at the end have different properties from the ones at the start: a different melting point, a different colour, different behaviour with a magnet or with water. If they do, something new was made.
How do we know? Test the stuff, not the drama 18th century onwards
Chemists decide that a reaction has happened by testing what is there afterwards. Melted ice, refrozen, behaves exactly like the ice you started with: same melting point, same density, same everything. Rust does not: dissolve it in acid and you get a yellow-brown solution of iron ions; heat it strongly with carbon and you can get iron back, but only by another chemical reaction. When the properties are new, the substance is new.
Careful
“The picture changed from H₂ and O₂ to H₂O, so a reaction has happened.”
In the app, choosing a different diagram just shows you a different picture. It is not an experiment. In the real world, a mixture of hydrogen and oxygen can sit in a sealed bottle for years without turning into water (you will see why in Chapter 5). A claim that a reaction happened needs evidence that a new substance was formed.
Investigation 4.1
Compare the H₂ and O₂ mixture with water in the app. Count the hydrogen and oxygen atoms in each picture. What is the same? What is different? Then write one real measurement you could make to show that water is a different substance from the mixture.
Understand itChemical reaction
What is it?
A change in which the atoms of the starting substances let go of their old partners and join up in new ways, making new substances with new properties. Rust is not iron; water is not hydrogen and oxygen.
Why is it called this?
From re- (“back, again”) and action: the substances act on each other. English chemists were using “reaction” in this sense by the 1830s.
What problem did it solve?
It separated two very different kinds of change. Melting, dissolving and mixing leave the substances what they were; burning, rusting and cooking make something new. Without that line, nobody could say what had really happened in a pot or a furnace.
Why does it work?
Atoms are held together by bonds. In a reaction some bonds break and new ones form, so the same atoms end up in different particles. The atoms themselves are never changed.
How does it help?
It tells you what to look for. To prove a reaction, test whether a new substance is there afterwards: a new melting point, a new colour that stays, a gas that turns limewater milky.
Go deeper how do we know, what it isn’t, where does it stop working
How do we know?
Testing what is there afterwards. Refrozen ice behaves exactly like the ice you started with; rust does not behave like iron, however you treat it.
What it isn’t
It is not the same as drama. Fizzing, a colour change or warmth are clues, not proof: sugar vanishes into chai and is still sugar, and boiling water bubbles without becoming anything new.
Where does it stop working?
The border can be blurry. When salt dissolves, its ions come apart and get wrapped in water, which is a bit of both. And changes that alter the atoms themselves, inside the nucleus, are nuclear reactions, not chemical ones.
Your turn
Explain Chemical reaction to a friend in one sentence, in your own words. Then compare it with the book’s.
A change in which the atoms of the starting substances let go of their old partners and join up in new ways, making new substances with new properties. Rust is not iron; water is not hydrogen and oxygen.
Check yourself
When a fizzy tablet is dropped into water, bubbles appear and the water cools slightly. Is that enough to prove a chemical reaction has happened? What would you need to test?
Not on its own. Bubbles could be air that was trapped in the tablet, and cooling can happen when some things simply dissolve. You would need to show that a new substance was made: for example, collect the gas and test it (carbon dioxide turns limewater milky; air does not), or show that the dissolved substances left behind are different from what was in the tablet.
4.2Reading a chemical formula
Stockholm, 1813
By the early 1800s chemists had a problem of handwriting. John Dalton in Manchester drew each element as a little circle with a pattern inside: a dot for hydrogen, a plain ring for oxygen, a ring with a cross for sulfur. That worked for twenty elements, and became impossible for fifty, and nobody could print it easily. In Stockholm, the Swedish chemist Jöns Jacob Berzelius, who spent years measuring the masses of elements with fierce precision, proposed something far simpler: use the first letter of each element’s Latin name, adding a second letter when two names begin the same way. H for hydrogen, O for oxygen, C for carbon, Cu for copper (cuprum), Na for sodium (natrium), Fe for iron (ferrum). Two hundred years later, every chemist on Earth writes his letters.
A chemical formula is a recipe for one particle. H₂O says: two hydrogen atoms and one oxygen atom, joined. The small number written low, the subscript, belongs to the atom just before it. No number means one. (Berzelius himself wrote the numbers high, like H²O; the low position became standard later.)
If you want to talk about more than one particle, you put a big number in front, called a coefficient. 3 H₂O means three separate water molecules. Count the atoms by multiplying: 3 × 2 = 6 hydrogen atoms and 3 × 1 = 3 oxygen atoms.
The two numbers do very different jobs. A coefficient changes how much you have. A subscript changes what you have. H₂O is water, which you drink. H₂O₂ is hydrogen peroxide, a pale liquid that bleaches hair and is used to clean wounds in dilute form; concentrated, it is dangerous. One extra oxygen atom in the recipe, and it is a different substance.
Figure 4.2Three water molecules (3 H₂O) and one molecule of hydrogen peroxide (H₂O₂). The coefficient 3 multiplies whole molecules. The subscript 2 after the O changes the molecule itself.
For ionic compounds (Chapter 2), the subscripts give the ratio of ions, and that ratio comes straight from the charges. A crystal as a whole has no overall charge, so the positive and negative charges must cancel. A magnesium ion is Mg²⁺ and a chloride ion is Cl⁻, so you need two chlorides for every magnesium: MgCl₂. Aluminium oxide needs a bit more thought. Al³⁺ and O²⁻ balance when there are two aluminiums (+6) for every three oxides (−6): Al₂O₃.
Careful
“2 H₂O and H₄O₂ are the same thing. They both have four hydrogens and two oxygens.”
They have the same number of atoms, but they say different things about how the atoms are grouped. 2 H₂O is two separate water molecules. H₄O₂ would claim a single molecule with all six atoms joined together, which is not water (and is not a real substance you can buy). The grouping is the chemistry.
Investigation 4.2
Change the number of water molecules from 1 to 3. Watch how the atom counts change. Then try the ion combiner with Mg²⁺ and Cl⁻, and with Al³⁺ and O²⁻. Before you look, predict the formula from the charges.
Check yourself
How many hydrogen atoms are there in 4 NH₃? And what is the formula of the compound made from calcium ions, Ca²⁺, and chloride ions, Cl⁻?
4 × 3 = 12 hydrogen atoms (and 4 nitrogen atoms). Calcium chloride is CaCl₂: one Ca²⁺ (+2) needs two Cl⁻ (−1 each) for the charges to cancel.
4.3Where did every atom go?
Back to Paris, and to Lavoisier’s sealed vessel. He heated the tin inside it until a dull grey crust had formed on the metal, let it cool, and weighed the whole sealed vessel, glass, tin, crust, air and all. The mass had not changed. Then he broke the seal. Air rushed in with a hiss, and only now did the vessel get heavier. The crust had used up part of the air inside, leaving a partial emptiness that fresh air flowed in to fill. Boyle’s “particles of fire” had never existed. Boyle had simply weighed his flask after the outside air had got in.
Lavoisier drew a conclusion that has held for every ordinary reaction ever measured: matter is neither created nor destroyed in a chemical change. Burning, rusting, cooking and digestion all rearrange atoms. None of them makes or destroys a single one. So if you count the atoms of each element before a reaction and after it, the counts must match. A chemical equation that shows this is called balanced.
Take hydrogen burning in oxygen to make water. A first try might be
H₂ + O₂ → H₂O
Count. Hydrogen: 2 on the left, 2 on the right. Fine. Oxygen: 2 on the left, 1 on the right. One oxygen atom has vanished, which is impossible, so this equation is not balanced. You may not fix it by changing H₂O into H₂O₂, because that is a different substance. You may only change the coefficients, the numbers of whole molecules. Two water molecules use both oxygen atoms; then they need four hydrogen atoms, so two hydrogen molecules:
2 H₂ + O₂ → 2 H₂O
Now there are 4 H and 2 O on each side. Methane, the main gas in a cooking-gas pipeline, burns the same way:
Figure 4.3Balancing the burning of methane, CH₄ + 2 O₂ → CO₂ + 2 H₂O. Every atom on the left turns up on the right: 1 carbon, 4 hydrogen and 4 oxygen on each side. The bonds are different; the atoms are the same ones.
So where does a burning log go? Mostly into the air. Wood is made largely of carbon, hydrogen and oxygen, and when it burns those atoms join with oxygen from the air to make carbon dioxide and water vapour, which drift away as invisible gases. Only the small amount of mineral matter is left behind as ash. The rusting nail works the other way round: oxygen and water from the air join onto the iron and stay there as solid rust, so the nail gains their mass. Lavoisier’s lesson in one line: if the mass seems to change, look for a gas you forgot to weigh.
Lavoisier’s experiment in a fizzy-drink bottle
Part 1, open. Put a glass on a kitchen scale, pour in about 100 mL of vinegar, and set one level teaspoon of baking soda on a piece of paper beside it, on the scale too. Note the total. Tip the soda into the vinegar (use a big glass: it fizzes hard), and when the fizzing stops, read the scale again with the paper still on it. The total has dropped by about 2 grams.
Part 2, sealed. Now do what Lavoisier did. You need an adult, an empty 1.5 or 2 litre plastic fizzy-drink bottle (made to hold pressure; never a glass bottle or a thin water bottle) and its cap. Pour in 100 mL of vinegar. Wrap half a teaspoon of baking soda in a twist of tissue, drop it in, and screw the cap on tight at once. Stand the bottle on the scale.
Predict first: while it fizzes, will the reading go down, go up, or stay the same? Write your guess.
Watch the reading as the fizzing runs its course. Then, with the bottle pointing away from everyone’s face, unscrew the cap slowly. Listen to the hiss, and read the scale again.
The sealed bottle does not change at all while it fizzes: every atom of the gas is still inside, pressing on the plastic. Only when the cap comes off, and the gas leaves, does the reading fall, by about a gram for half a teaspoon of soda. That hiss is the sound of Lavoisier’s broken seal, two and a half centuries later.
Careful
“Gases don’t weigh anything. They’re just air.”
Every gas is made of molecules, and every molecule has mass. A litre of the air around you has a mass of about 1.2 grams; the air in a small bedroom has a mass of about 30 kilograms, not far off your own. The bottle proves it: the scale only dropped when the gas was allowed out.
Careful
“You can balance an equation by changing the little numbers until the counts match.”
Changing a subscript changes the substance, so the equation stops describing the reaction you meant. CH₄ + O₂ → CO₂ + H₂O₂ might look easier, but hydrogen peroxide is not what comes out of a gas flame. Only the coefficients are yours to choose.
Investigation 4.3
Start with 1 H₂ + 1 O₂ → 1 H₂O and adjust the coefficients until both elements balance. Save one unbalanced and one balanced version. Then balance the formation of ammonia from nitrogen and hydrogen yourself before you check.
Understand itConservation of mass
What is it?
In a chemical reaction, nothing is gained and nothing is lost: the total mass at the end equals the total mass at the start, because every atom is still there.
Why is it called this?
To conserve something (from Latin conservare, “to keep safe”) is to keep it. Mass is kept.
What problem did it solve?
For centuries burning looked like destruction and rusting looked like creation: ash is lighter than wood, rust is heavier than iron. Nobody could keep an honest account of a reaction until Lavoisier weighed everything, gases included, in sealed vessels.
Why does it work?
A reaction only rearranges atoms; it never makes or destroys one. Count the atoms of each element before and after and the counts match, so the masses must match too.
How does it help?
It lets chemists balance equations, find a gas they cannot see by weighing what is missing, and work out exactly how much of each ingredient a reaction needs.
Go deeper how do we know, what it isn’t, where does it stop working
How do we know?
Lavoisier’s sealed tin weighed the same before and after; the mass only changed when he broke the seal and air rushed in. Your sealed fizzy-drink bottle does the same thing.
What it isn’t
It is not “mass never seems to change”. Open containers do lose or gain mass, because gases escape or join in. The law is about everything, gases included.
Where does it stop working?
In nuclear reactions a little mass really does turn into energy. In chemical reactions the same thing happens, but far too little to weigh: burning methane changes the mass by about one ten-billionth.
Your turn
Explain Conservation of mass to a friend in one sentence, in your own words. Then compare it with the book’s.
In a chemical reaction, nothing is gained and nothing is lost: the total mass at the end equals the total mass at the start, because every atom is still there.
Check yourself
Nitrogen and hydrogen react to make ammonia. Why is 1 N₂ + 1 H₂ → 1 NH₃ unbalanced, and what coefficients balance it?
Left: 2 N and 2 H. Right: 1 N and 3 H. Neither element matches. Put 2 in front of NH₃ to fix nitrogen (2 N, 6 H on the right), then 3 in front of H₂ to supply 6 H: N₂ + 3 H₂ → 2 NH₃. Check: 2 N and 6 H on each side.
4.4What a balanced equation cannot tell us
London, 1781
Henry Cavendish was so shy that he left notes for his housekeeper rather than speak to her, and he ordered his dinner the same way. He was also one of the most careful experimenters who ever lived. In 1781 he filled a sealed glass vessel with a mixture of hydrogen (which he called “inflammable air”) and ordinary air, and set it off with an electric spark. There was a flash, and the inside of the glass misted with dew. Cavendish collected the dew and tested it. It was pure water. Two years later, Lavoisier repeated the work and gave hydrogen its name, from the Greek for “water-maker”.
You can write 2 H₂ + O₂ → 2 H₂O in a few seconds, and it is perfectly balanced. Does that mean hydrogen and oxygen turn into water whenever they meet? No. Cavendish’s gases sat quietly in their vessel until the spark. Mix the two gases in a bottle at room temperature, keep it dark and still, and you could wait years without finding a drop of water. Bring a spark near, and the whole mixture reacts in a fraction of a second, with a loud bang.
Figure 4.4The same balanced equation, two very different outcomes. Left: hydrogen and oxygen mixed at room temperature; nothing measurable happens. Right: a small spark, and the mixture reacts almost instantly. The equation describes the atoms, not the speed or the trigger.
A balanced equation is an accounting statement. It says: if these substances react to give these products, then the atoms are used in this ratio. It does not say whether the reaction actually happens, how fast it goes, whether it needs a spark or heat or a catalyst, or whether it gives out or takes in energy. Those questions need experiments, and they are what Chapter 5 is about.
The ratio, at least, is fixed. 2 H₂ + O₂ → 2 H₂O, 4 H₂ + 2 O₂ → 4 H₂O and 6 H₂ + 3 O₂ → 6 H₂O all say the same thing: hydrogen molecules and oxygen molecules are used up two to one. We normally write the smallest whole numbers, which is the first version.
You can even write perfectly balanced equations for reactions that do not happen by themselves at all. Water does not split back into hydrogen and oxygen on its own, even though 2 H₂O → 2 H₂ + O₂ balances. To make that happen you have to push electricity through the water, as Nicholson and Carlisle did in Chapter 3 (and as you will see again in Chapter 8), supplying energy all the time. Whether a reaction goes is decided by energy and by speed, not by whether you can make the numbers match.
Careful
“Someone wrote 2 CO₂ → 2 CO + O₂, and it’s balanced. So the carbon dioxide in our classroom must be turning into poisonous carbon monoxide.”
Balancing only proves that the atoms could be accounted for. Carbon dioxide in ordinary air does not break down into carbon monoxide; it would need a great deal of energy to do that. Measuring the air (carbon monoxide detectors exist) is how you would check, not writing equations.
A rusting nail that eats air
Predict first: if iron really takes oxygen out of the air, how far will the water climb: not at all, all the way, or somewhere in between? Then push a small pad of plain steel wool (soap-free, from a hardware or paint shop; the shiny stainless-steel scrubbers in most Indian kitchens are made not to rust, so they will not work) into the bottom of a narrow glass, dampen it with a little vinegar (which strips its thin protective coating so it rusts faster), and stand the glass upside down in a saucer of water, so that air is trapped above the water. Mark the water level inside the glass with tape. Over the next few days the steel wool turns rusty brown, and the water slowly climbs up inside the glass, by about a fifth of the trapped air. The iron has joined with the oxygen, about a fifth of air, and taken it out of the gas. (Ask an adult before using steel wool: it can splinter, so handle it with gloves.) It takes days, not seconds: the balanced equation for rusting would never have told you that.
Investigation 4.4
Find two different sets of coefficients that both balance the water equation. Explain why chemists write the smallest one. Then write down one question about this reaction that no balanced equation can answer.
Check yourself
What does the balanced equation N₂ + 3 H₂ → 2 NH₃ tell you, and what does it not tell you?
It tells you that if nitrogen and hydrogen react to make ammonia, they are used up in a 1 : 3 ratio of molecules and make 2 ammonia molecules for every nitrogen molecule, with every atom accounted for. It does not tell you whether the reaction happens at room temperature, how fast it is, whether it needs a catalyst (it does, and high pressure, in industry), or whether it gives out or takes in energy.
Case file 4
The case of the clever shortcut
Three students are asked to balance the burning of methane, CH₄ + O₂ → CO₂ + H₂O. Each hands in an answer where the atoms match.
Asha writes: CH₄ + O₃ → CO₂ + H₄O
Bilal writes: CH₄ + 2 O₂ → CO₂ + 2 H₂O
Chitra writes: 2 CH₄ + 4 O₂ → 2 CO₂ + 4 H₂O
Clues:
Oxygen in the air is O₂ molecules. O₃ is ozone, a different gas.
The product you can collect from a gas flame condenses into ordinary water, H₂O.
Count the atoms on both sides of each answer.
Which answers are correct? Which is best, and what exactly is wrong with the other one?
Show the solution
Count first. All three answers balance: Asha has 1 C, 4 H, 3 O on each side; Bilal has 1 C, 4 H, 4 O; Chitra has 2 C, 8 H, 8 O.
But Asha changed subscripts. She turned the oxygen into ozone (O₃) and the water into “H₄O”, which is not water and not anything you would find in a flame (clues 1 and 2). Her equation balances, but it describes a reaction that is not the one happening. It is wrong.
Bilal and Chitra both describe the real reaction. Chitra’s is just Bilal’s doubled, so the ratio is the same. Bilal’s is the best answer because chemists write the smallest whole numbers: CH₄ + 2 O₂ → CO₂ + 2 H₂O.
What this chapter can’t explain yet
A balanced equation keeps a perfect account of the atoms, and stays silent about everything else. Why did Cavendish’s gases wait for a spark? Why does burning methane give out heat, while some reactions make things cold? And why do some reactions seem to stop half-way? To answer those, the adventure follows the energy, into the hands of a Swedish chemist with a new idea about heat, and a glowstick that behaves very differently in a cup of hot water. That is Chapter 5.
5
Chapter 5
Energy, speed and balance
The big questionPaper burns in oxygen and gives out a lot of heat. This book is surrounded by oxygen all the time. Why doesn’t it burst into flame?
Start with a little magic. Take two glowsticks, snap them both so they light, and drop one into a mug of hot tap water and the other into a glass of iced water. Within a minute the one in hot water is blazing brightly, and the one in iced water has dimmed to a ghostly glow. Swap them over and the brightness swaps too. Nothing has been added or taken away. The same chemicals are reacting inside each plastic tube, giving out their energy as light. The only difference is the temperature, and it changes how fast they react.
Chapter 4 kept count of atoms. This chapter keeps count of something just as strictly conserved, energy, and then asks two new questions that atom-counting cannot answer. How fast does a reaction go? And when does it stop? The answers explain the glowsticks, why a matchstick needs striking, why cooking speeds up when the flame is turned up, why enzymes in your body matter so much, and why some reactions never quite finish.
5.1Where does the energy go?
Light a gas burner and hold your hand above it (not too close). The reaction between methane and oxygen is warming the air around it. Now squeeze an instant cold pack from a first-aid kit: inside, a solid dissolves in water, and the pack gets cold enough to sting your fingers. Some changes give energy out; others take energy in.
To keep track, chemists split the world into two parts. The system is the chemicals you are studying. The surroundings are everything else: the water around them, the beaker, the air, your hand. Energy is never created or destroyed, so any energy the system loses, the surroundings gain, and the other way round.
A change that gives energy to the surroundings is exothermic: the surroundings warm up. A change that takes energy from the surroundings is endothermic: the surroundings cool down. In an energy diagram, exothermic means the products sit lower than the starting substances, and the difference has gone out into the surroundings. (Where does that energy actually come from? Not, as most people guess, from bonds breaking. Section 5.6 shows it is the other way round.)
Figure 5.1Two energy diagrams. Left: an exothermic change. The products are lower in energy, and the difference warms the surroundings. Right: an endothermic change, like a cold pack. The products are higher, and the energy is taken from the surroundings, which get colder.
How do we know? You can’t put a thermometer in a bond
We cannot measure the energy of a molecule directly, so we measure what happens around it. In a calorimeter, a reaction happens inside a container surrounded by a known amount of water, with a thermometer in the water. Warming 1 gram of water by 1 °C takes about 4.2 joules. So if 100 g of water warms by 10 °C, about 100 × 10 × 4.2 = 4,200 joules came out of the reaction. A cold pack works in reverse: its temperature drop tells you how much energy the dissolving took in. The first ice calorimeter was built in Paris in the winter of 1782–83 by Lavoisier, the man who weighed everything in Chapter 4, and the mathematician Pierre-Simon Laplace: they measured heat by how much ice it melted, using Joseph Black’s discovery from Chapter 3.
A reaction that feels cold
Predict first: most people expect a fierce, fizzing reaction to get hot. Write down what you think will happen to the temperature.
Pour about half a cup of vinegar into a glass and wrap your hand around it for a moment to feel its temperature. Stir in a heaped teaspoon of baking soda (stand the glass in a bowl or the sink: it fizzes up). While it fizzes, hold the glass again, or put a kitchen thermometer in it. The mixture gets a few degrees cooler. This reaction is endothermic: to make its products it takes energy from its surroundings, and the nearest surroundings are the vinegar, the glass and your hand.
For a twin that does the opposite, dampen a pad of plain steel wool with vinegar, squeeze it out, and seal it in a zip bag with a thermometer if you have one. Over a few minutes the bag grows slightly warm as the iron quietly rusts. One reaction fizzes and cools; the other sits still and warms. Drama tells you nothing about which way the energy flows.
You may have read at school that when an acid and a base neutralise each other, heat is given out. That is true for many of them; this one is an exception, because breaking up the baking soda into carbon dioxide gas costs more energy than the rest of the reaction gives back.
Careful
“In an exothermic reaction the energy is used up, so afterwards there’s less energy in the universe.”
The energy has moved, not vanished. It left the chemicals and went into the surroundings, mostly as faster-jiggling particles of air and water (which is what “warmer” means). Count system and surroundings together and the total never changes.
Investigation 5.1
Set the products below the reactants, then above them. For each case, say which way energy flows between the system and the surroundings, and whether a thermometer in the surroundings would go up or down.
Check yourself
When the solid in a cold pack dissolves, the pack gets cold. Is dissolving it exothermic or endothermic? Which is higher in energy, the start or the end?
Endothermic. The surroundings (the water, the pack, your hand) lose energy and get colder, because the system took energy in. So the end (dissolved) is higher in energy than the start.
5.2Why is there an energy barrier?
Sweden, 1889
Svante Arrhenius was not supposed to be a success. Five years earlier, his doctoral thesis at Uppsala, which claimed that salts break up into charged particles when they dissolve, had been given nearly the lowest passing grade: his examiners thought it was probably nonsense. Arrhenius, a big, cheerful, stubborn young Swede, sent it to the best chemists in Europe anyway, and some of them, especially Wilhelm Ostwald in Riga, thought it was brilliant. (He was right about the ions, and won a Nobel Prize for them in 1903. In 1896 he also became the first person to calculate how much carbon dioxide in the air could warm the Earth.)
In 1889 he turned to a different puzzle. Chemists had long noticed that many reactions speed up dramatically with only a small rise in temperature, often roughly doubling for every 10 °C (this is only a rule of thumb). Why should a small warming make such a large difference?
Start with the bigger puzzle. Burning paper gives out plenty of energy, so the products, carbon dioxide and water, are lower in energy than paper and oxygen. Downhill, you might think, so it should just happen. And yet the book in your hands has been sitting in air for its whole life without catching fire. Why?
Because to get from the start to the finish, the particles have to pass through an awkward in-between stage: old bonds stretched and partly broken, new ones not yet formed. That in-between arrangement is higher in energy than either the start or the end. To get over it, colliding particles must bring enough energy with them. The height of that hump, measured from the starting level, is called the activation energy. The idea is Arrhenius’s.
Figure 5.2An energy profile (schematic, in made-up units). The reactants start at 50, the products end at 20, so 30 units are released overall. But first the reaction must climb to the peak at 100: a barrier of 50 going forward, and 80 going backward. The horizontal axis is progress of the reaction, not time.
Think of a ball in a dip on a hillside, with a deeper valley on the other side of a ridge. The valley is lower, but the ball stays put until something kicks it over the ridge. A struck match is the kick for paper: the flame heats a small patch until its molecules are colliding hard enough to get over the barrier. The energy given out then heats the next patch, and the fire spreads by itself.
Now Arrhenius’s answer about temperature. At any temperature, particles have a spread of energies: most are moving at middling speeds, and a few are moving very fast. Only the few that collide with more than the activation energy can react. Warm the mixture slightly, and the whole crowd speeds up a little, but the number of those rare, very fast particles goes up a lot. So the rate jumps. That is why the glowstick in hot water blazes, why food spoils faster in heat and keeps longer in a fridge, and why Cavendish’s hydrogen and oxygen in Chapter 4 waited for a spark: at room temperature, almost no collisions were hard enough.
Notice two separate numbers in Figure 5.2. The overall energy change (30 units released) depends only on where the reaction starts and ends. The barrier (50 units forward) depends on the peak. Raise or lower the peak, and the overall change stays exactly the same.
Careful
“A reaction that releases lots of energy must happen quickly.”
How much energy a reaction releases and how fast it goes are separate questions. Paper burning releases a lot, yet it does not start at room temperature, because its barrier is high. Some reactions release almost nothing and are very fast. And warming speeds up every reaction, whichever way its energy flows: the glowstick gives energy out, and it still blazes faster in hot water.
Investigation 5.2
Keep the reactants and products where they are, and raise the peak. What happens to the forward barrier, the reverse barrier, and the overall energy change? Predict first.
Understand itActivation energy
What is it?
The extra energy that colliding particles need to get over the “hump” between the start and the end of a reaction. It is why paper can sit in air for years without catching fire.
Why is it called this?
It is the energy needed to activate a reaction, to get it going, like the push that starts a swing.
What problem did it solve?
It explained two puzzles at once: why reactions that would give out lots of energy can still refuse to start, and why a small rise in temperature can make a reaction much faster. Arrhenius tackled the second in 1889.
Why does it work?
To change partners, atoms must pass through an awkward in-between stage, with old bonds stretched and new ones only half-made, which is higher in energy than either the start or the end. Only collisions with enough energy get over it, and warming makes those energetic collisions much more common.
How does it help?
It tells you how to start or stop a reaction: heat it, strike a match, or find a catalyst to lower the hump; cool it to slow it down, which is how a fridge keeps food fresh.
Go deeper how do we know, what it isn’t, where does it stop working
How do we know?
Reaction speeds rise steeply with temperature, as a glowstick in hot and cold water shows, and they rise far more than the small increase in average speed could explain on its own.
What it isn’t
It is not the energy a reaction gives out. How high the hump is and how far downhill the reaction goes are separate questions.
Where does it stop working?
A single hump is a simplified picture. Real reactions often go through several steps, each with its own hump.
Your turn
Explain Activation energy to a friend in one sentence, in your own words. Then compare it with the book’s.
The extra energy that colliding particles need to get over the “hump” between the start and the end of a reaction. It is why paper can sit in air for years without catching fire.
Check yourself
In a schematic profile, the reactants are at 40 units, the products at 10, and the peak at 100. What are the forward barrier, the reverse barrier and the overall energy change?
Forward barrier = 100 − 40 = 60. Reverse barrier = 100 − 10 = 90. Overall change = 10 − 40 = −30 (30 units released). The reverse barrier is bigger because the products sit lower, so they have further to climb.
5.3How quickly does change happen?
A rate is a change per unit of time. Your heartbeat is a rate (beats per minute); so is the speed of a car (kilometres per hour). The rate of a reaction is how much of a substance is used up, or made, per second or per minute. A glowstick’s brightness is a rate you can see: the brighter it shines, the more molecules are reacting each second.
Rates depend on how often particles collide, and how hard. You can speed a reaction up by heating it (harder, more frequent collisions), making the solutions more concentrated (more particles to hit), or cutting a solid into smaller pieces (more surface where collisions can happen). An iron nail in a flame just glows; steel wool, which is iron in very thin strands, burns with sparks.
Glowsticks, fast and slow
Snap two identical glowsticks and leave them whole (never cut one open). Put one in a mug of hot tap water and one in a glass of water with plenty of ice, and turn the lights off. Which is brighter? Next morning, which is still glowing? The warm one reacts faster, so it shines more brightly but uses up its chemicals sooner. The cold one is dimmer but lasts much longer. (A glowstick kept in the freezer can still glow faintly the next day.) Same reaction, same amount of chemicals, different rate.
To see rates clearly, the app uses a simple made-up reaction in which a substance A turns into B, and B can also turn back into A:
A ⇌ B
The double arrow means the change goes both ways. In this model, A turns into B at a rate of 2 × (the amount of A) per second, so in each hundredth of a second about 2% of the A changes; we say its forward rate constant is 2 per second. B turns back at 1 × (the amount of B) per second, about 1% of the B in each hundredth of a second (reverse constant 1 per second). We start with 10 units of A and no B.
Figure 5.3The made-up A ⇌ B reaction, starting with 10 units of A. At first A turns into B quickly, because there is lots of A and no B to turn back. The change slows down and the amounts level off at about 3.33 units of A and 6.67 of B. The dashed lines show the same reaction with both rate constants doubled: same end point, reached twice as fast.
At the start, A is turning into B at 2 × 10 = 20 units per second and nothing is turning back. After one second the amounts are about 3.67 of A and 6.33 of B. A is now changing into B at 2 × 3.67 ≈ 7.3 units per second, while B is turning back at 1 × 6.33 ≈ 6.3 per second. The overall change has slowed to about 1 unit per second. After a few seconds the amounts barely move at all.
Here is the important thing: how fast it gets there and where it ends up are different questions. Double both rate constants (dashed lines) and the reaction reaches the same 3.33 : 6.67 mixture in half the time.
How do chemists draw curves like these for real reactions? They follow something that changes as the reaction goes: the colour of a solution (with a meter that measures how much light gets through), the pressure of a gas, or the mass of a flask as a gas escapes, just like your vinegar on the kitchen scale in Chapter 4. Reading it every few seconds gives a curve steep at first and flattening out. The steepness of the curve at any moment is the rate.
Investigation 5.3
Move the time slider from 0 to 1 second to 20 seconds and note the amounts and the two rates. Then double both rate constants. Predict before you look: will the final amounts change?
Check yourself
In the A ⇌ B model with forward constant 2 and reverse constant 1, what are the forward and reverse rates at the very start, when there are 10 units of A and none of B?
Forward rate = 2 × 10 = 20 units per second. Reverse rate = 1 × 0 = 0, because there is no B yet to turn back. That is why the change is fastest at the start.
5.4A different pathway
London, 1817
Humphry Davy, who had danced round his laboratory over potassium in Chapter 1, was by now the most famous scientist in Britain. In 1815 he had invented a safety lamp for coal miners, who were being killed by explosions of methane gas underground. Two years later, still experimenting with methane, he noticed something strange. A coil of warm platinum wire, held in a mixture of methane and air, began to glow red hot, and stayed glowing, with no flame at all. The gas was reacting on the surface of the metal, quietly and steadily, and the platinum was not used up.
In 1835 Berzelius, the inventor of chemical symbols from Chapter 4, gave such effects a name: catalysis. A catalyst is a substance that makes a reaction faster without being used up. It works by giving the reaction a different route, one with a lower hump to climb. The start and the finish are exactly the same as before; only the path between them changes.
Figure 5.4A catalyst opens a lower route (dashed) between the same start and finish. In this made-up example the peak drops from 130 to 90 units, so the forward barrier drops from 80 to 40 and the reverse barrier from 110 to 70: both by the same 40 units. The overall energy change stays at −30.
Because the start and finish do not move, lowering the peak lowers the barrier in both directions by the same amount. So a catalyst speeds up the forward and the reverse reactions together. It makes a reaction reach its end point sooner, but it cannot change where that end point is.
Catalysts are everywhere. The catalytic converter in a car’s exhaust uses metals like platinum, Davy’s metal, to turn poisonous carbon monoxide into carbon dioxide before it leaves the exhaust pipe. Your body runs on catalysts called enzymes: without them, the reactions that digest your food and keep your cells alive would be far too slow to keep you alive.
Here is one at work right now. Your blood carries carbon dioxide from your muscles to your lungs, and part of the trip involves carbon dioxide reacting with water. On its own, that reaction is too slow for the job. An enzyme in your red blood cells, carbonic anhydrase, speeds it up by more than a million times, in both directions. In the muscles, where carbon dioxide is plentiful, the reaction runs forward; in the lungs, where carbon dioxide is breathed away, it runs backward. One catalyst, both directions, exactly as Figure 5.4 predicts.
A helper that is never used up
You need an adult, a small bottle of 3% hydrogen peroxide from a chemist’s shop (sold for cleaning cuts; if the label says 6% or “20 volume”, the adult should mix one part with three parts water instead of half and half below), a packet of dried yeast and a raw potato. Peroxide slowly breaks down by itself into water and oxygen, far too slowly to see: 2 H₂O₂ → 2 H₂O + O₂. Living things carry an enzyme that speeds this up enormously.
Mix a little peroxide half and half with water in two glasses. Into one, sprinkle a pinch of yeast; into the other, drop a slice of raw potato. Both froth with bubbles of oxygen, and the glass may feel faintly warm. When the frothing dies down, pour fresh diluted peroxide onto the same yeast. It froths again: the catalyst was not used up.
Predict first: what will a slice of boiled potato do? Then try it. (Almost nothing happens: cooking wrecks the enzyme’s shape, and with it the lower route.) Keep the peroxide away from eyes, taste nothing, and pour everything down the sink afterwards.
Careful
“A catalyst makes a reaction give out more energy, or makes more product.”
A catalyst does not change the start or the finish, so it cannot change the overall energy change or the final mixture. It only changes how fast you get there.
Investigation 5.4
Lower the peak without moving either end. Write down the forward and reverse barriers before and after. Then go back to the A ⇌ B model and double both constants. How is that like adding a catalyst?
Understand itCatalyst
What is it?
A substance that makes a reaction faster without being used up. The enzymes in your body are catalysts; so is the platinum in a car’s exhaust system.
Why is it called this?
Berzelius named the effect catalysis in 1835, from a Greek word meaning “a loosening” or “a dissolving”. He chose it to match analysis, chemists’ word for taking substances apart.
What problem did it solve?
Chemists had seen strange cases, like a platinum wire glowing in a gas mixture without changing itself, and could not explain them. The idea of a catalyst made sense of them, and later made reactions such as making ammonia for fertiliser fast enough to be practical.
Why does it work?
It gives the reaction a different route with a lower hump. More collisions now have enough energy to get over, so the reaction runs faster, and the catalyst is given back at the end.
How does it help?
It lets chemists, and living cells, make the reactions they need happen quickly at ordinary temperatures. Without enzymes, your body would digest a meal far, far too slowly to keep you alive.
Go deeper how do we know, what it isn’t, where does it stop working
How do we know?
The catalyst can be weighed or collected afterwards, unchanged. Yeast or raw potato keeps making hydrogen peroxide froth every time you add fresh peroxide.
What it isn’t
It does not make a reaction give out more energy or make more product in the end. It only gets you to the same finish sooner.
Where does it stop working?
“Never used up” is true overall, but real catalysts can be worn out or poisoned. Lead, for example, ruins the catalysts in car exhausts, which is one reason leaded petrol was banned.
Your turn
Explain Catalyst to a friend in one sentence, in your own words. Then compare it with the book’s.
A substance that makes a reaction faster without being used up. The enzymes in your body are catalysts; so is the platinum in a car’s exhaust system.
Check yourself
At a fixed temperature, could a catalyst lower the forward barrier by 30 units while lowering the reverse barrier by only 10? Why or why not?
No. Both barriers are measured up to the same peak. The reactants and products stay where they were, so if the peak drops by 30, both barriers drop by 30.
5.5A balance that keeps moving
The salt lakes of Egypt, 1799
Claude-Louis Berthollet was one of the scientists Napoleon took with him when he invaded Egypt, a chemist who had worked alongside Lavoisier in Paris. Exploring the Natron Lakes in the desert west of the Nile, he saw crusts of soda (sodium carbonate) forming along the shores. In the laboratory, everyone knew the reaction went the other way: soda and calcium chloride react to make limestone and salt, and that was that. Yet here, in lakes thick with salt and lined with limestone, the reaction was running backwards. Berthollet’s conclusion, published a few years later, was bold: reactions are not one-way streets. With enough of the “products” crowded together, a reaction can run in reverse.
Look at the end of Figure 5.3 again. After a few seconds, the amounts of A and B stop changing. Has the reaction stopped? No. A is still turning into B, and B is still turning into A. They are simply happening at the same rate, so the amounts no longer change. This is called dynamic equilibrium: “equilibrium” because nothing seems to change, “dynamic” because underneath, everything is still moving.
Think of a crowded platform at a Mumbai local station in the rush hour. Every minute, people pour in from the stairs and people squeeze onto trains. If they arrive as fast as they leave, the number of people on the platform stays the same, even though it is never the same people for long.
In the A ⇌ B model, the end point is 3.33 units of A and 6.67 units of B. Check the rates: forward is 2 × 3.33 = 6.67 units per second, and reverse is 1 × 6.67 = 6.67 units per second. Equal rates. But notice that the amounts are not equal at all: there is twice as much B as A. Equilibrium means equal rates, not equal amounts.
Figure 5.5The two rates in the A ⇌ B model. The forward rate falls as A is used up; the reverse rate rises as B builds up. Where they meet, the amounts stop changing: dynamic equilibrium. Both reactions are still going at 6.67 units per second.
How do we know a reaction at equilibrium is still running both ways, if nothing seems to change? Chemists use atoms that can be told apart. Make two identical mixtures of nitrogen, hydrogen and ammonia, and let both settle at equilibrium (at high temperature, with a catalyst). In one, use ordinary hydrogen; in the other, use deuterium, a heavier isotope of hydrogen that behaves almost exactly the same. Then mix the two. The total amounts of nitrogen, hydrogen and ammonia stay just as they were. But soon ammonia molecules turn up carrying a mixture of ordinary and heavy hydrogen atoms. The only way that can happen is if ammonia was still being broken apart and made again, all the time.
Two glasses, two straws
You need two identical glasses, one wide straw (a bubble-tea or milkshake straw) and one ordinary thin straw. Fill one glass about three-quarters full of water with a drop of food colouring; leave the other empty. Call them A and B.
Now take turns. Dip the wide straw to the bottom of glass A, close the top with your thumb, lift out the water trapped inside and let it go into B. Then dip the thin straw to the bottom of B, carry its water back to A. Repeat, one scoop each way, over and over.
Predict first: when the levels stop changing, will A and B be level?
Keep going until they stop changing. Each scoop is small, so this takes patience: fifty rounds or more, which is easier with a friend holding the second straw. They do not end level: B, which started empty, ends up fuller than A. Yet every round you are still moving water both ways. The levels settle where the wide straw’s scoop from the shallower glass carries exactly as much as the thin straw’s scoop from the deeper one. Equal flows, unequal amounts: that is a dynamic equilibrium, and you just made one with your thumbs.
Careful
“At equilibrium, there must be equal amounts of reactants and products.”
Equal rates, not equal amounts. With a forward constant of 2 and a reverse constant of 1, B ends up twice as plentiful as A. The amounts only come out equal if the two constants happen to be equal.
Investigation 5.5
Set the forward constant to 2 and the reverse constant to 1, and jump to a late time. Compare the amounts and the rates. Then try forward 1 and reverse 4. Which substance is favoured now?
Understand itDynamic equilibrium
What is it?
The state a reversible reaction reaches when the forward and backward reactions run at the same speed, so the amounts stop changing even though both reactions keep going.
Why is it called this?
Equilibrium is Latin for “equal balance”, from aequus (equal) and libra (a pair of scales). Dynamic comes from the Greek for “power” or “force”: the balance is full of movement, not still.
What problem did it solve?
Many reactions seemed to stop halfway, with some starting material always left over. Berthollet, at the Natron Lakes in Egypt, saw a reaction running backwards, and the idea of two-way reactions in balance explained both.
Why does it work?
As the forward reaction uses up its starting material, it slows; as the product builds up, the backward reaction speeds up. At some point the two speeds meet, and from then on every change in one direction is cancelled by a change in the other.
How does it help?
It tells you how to push a reaction the way you want, by adding more of a starting material, removing the product, or changing the temperature or pressure. That is how industry makes ammonia efficiently.
Go deeper how do we know, what it isn’t, where does it stop working
How do we know?
Make two identical mixtures, one built with ordinary hydrogen and one with heavy hydrogen (deuterium), and mix them. Soon ammonia molecules turn up carrying both ordinary and heavy hydrogen atoms, so the reactions must still be running both ways.
What it isn’t
It does not mean equal amounts. It means equal speeds. The amounts can be very lopsided.
Where does it stop working?
It needs a closed container. Open a bottle of soda and the gas escapes, so the balance is never reached; and some reactions are so one-sided that, in practice, they simply go to completion.
Your turn
Explain Dynamic equilibrium to a friend in one sentence, in your own words. Then compare it with the book’s.
The state a reversible reaction reaches when the forward and backward reactions run at the same speed, so the amounts stop changing even though both reactions keep going.
Check yourself
Set the forward constant to 1 and the reverse constant to 3, starting with 10 units of A. At equilibrium, A = 7.5 and B = 2.5. Show that the rates are equal, and explain why A ends up three times as plentiful as B.
Forward rate = 1 × 7.5 = 7.5 per second. Reverse rate = 3 × 2.5 = 7.5 per second. Equal. B turns back into A three times as readily as A turns into B, so the rates can only balance when there is three times as much A as B.
5.6Breaking bonds costs; making bonds pays
Here is one of the most important ideas in the book, and one that many adults get wrong. Breaking a bond always takes energy. Making a bond always gives energy out.
It follows from Chapter 2. A bond is an attraction between atoms. Pulling two attracted things apart is like stretching a rubber band or lifting a magnet off a fridge: you have to put energy in. Letting them snap together gives energy out. (The figure in section 2.3 lets you try it: pull two hydrogen atoms apart and watch the energy you must supply climb to 436 kJ per mole.)
So where does the energy of burning come from? A reaction is a two-step account. First, bonds in the reactants break, which costs energy. Then new bonds form in the products, which pays energy back. If the new bonds are stronger, more is paid back than was spent, and the reaction is exothermic.
How do we know how strong a bond is? It can be measured by shining light or other radiation on molecules and finding the lowest energy that splits them, or worked out from many calorimeter measurements. Average values for each kind of bond are collected in data tables. Using average bond enthalpies in kilojoules per mole (H–H 436, O=O 498, O–H 463), hydrogen burning works out like this:
2 H₂ + O₂ → 2 H₂O (all as gases)
Break 2 H–H and 1 O=O: 2 × 436 + 498 = 1,370 kJ in
Make 4 O–H: 4 × 463 = 1,852 kJ out
Overall: 1,370 − 1,852 = −482 kJ, so 482 kJ is released.
Measured value: −484 kJ. Close, because average bond enthalpies are estimates.
Figure 5.6The energy account for 2 H₂ + O₂ → 2 H₂O. Climbing to separate atoms costs 1,370 kJ; forming four O–H bonds gives back 1,852 kJ. The difference, about 482 kJ, comes out as heat. (Real reactions don’t actually pull everything into separate atoms first; the account works because energy depends only on where you start and finish.)
Landing within a few per cent of the measured answer, as here, is a good test that the “break, then make” account is right. Now a reaction that goes the other way. In lightning and in hot car engines, nitrogen and oxygen from the air join to make nitrogen monoxide, NO:
N₂ + O₂ → 2 NO
Break 1 N≡N and 1 O=O: 945 + 498 = 1,443 kJ in
Make 2 N=O (631 kJ each in NO): 2 × 631 = 1,262 kJ out
Overall: 1,443 − 1,262 = +181 kJ, so energy is taken in. Measured value: +181 kJ.
This one is endothermic. The triple bond in N₂ is one of the strongest bonds there is, and the bonds in NO do not pay back enough. That is part of why the nitrogen in the air (78% of it) is so unreactive, and why it takes something as fierce as lightning or a hot engine to make NO.
Careful
“Energy is stored in bonds, and released when the bonds break.”
This is the wrong way round, though you will hear it often. Breaking any bond takes energy in. The energy released by burning fuel comes from making the new, stronger bonds in carbon dioxide and water. Fuels are useful because their bonds, together with oxygen’s, are weaker than the bonds in the products.
Investigation 5.6
Step through the three stages for 2 H₂ + O₂ → 2 H₂O: reactants, separated atoms, products. Then do the same for N₂ + O₂ → 2 NO. In which reaction is more paid back than spent?
Check yourself
Methane burns: CH₄ + 2 O₂ → CO₂ + 2 H₂O. Using average bond enthalpies (C–H 413, O=O 498, C=O in CO₂ 799, O–H 463 kJ per mole), estimate the overall energy change. Is it exothermic or endothermic?
Break 4 C–H and 2 O=O: 4 × 413 + 2 × 498 = 2,648 kJ in. Make 2 C=O and 4 O–H: 2 × 799 + 4 × 463 = 3,450 kJ out. Overall 2,648 − 3,450 = −802 kJ: exothermic, which is why methane makes a good cooking gas. (The measured value, with the water as a gas, is also about −802 kJ.)
5.7Disturbing an equilibrium
Paris, 1884
Henry Le Châtelier came from a family of engineers: his father helped build France’s railways, and the family had long worked with lime and cement. He trained at the École Polytechnique and the School of Mines, and much of his work was practical and urgent: why coal dust and methane explode in mines, how cement sets, how to measure the fierce temperatures inside furnaces. In 1884, thinking about how chemical balances respond when conditions change, he wrote down a rule that chemistry students have used ever since.
What happens if you change a mixture that has already settled at equilibrium? Suppose the A ⇌ B mixture has reached 3.33 units of A and 6.67 of B, and you suddenly add 4 more units of A.
Think about the rates. There is now much more A, 7.33 units, so the forward rate jumps to 2 × 7.33 ≈ 14.7 per second. The amount of B has not changed yet, so the reverse rate is still 6.67. Forward is faster than reverse, so overall A turns into B. As it does, the forward rate falls and the reverse rate rises, until they are equal again. This is Berthollet’s salt lakes in miniature: crowd in more of one side, and the reaction is pushed the other way.
Figure 5.7Adding 4 units of A to the settled A ⇌ B mixture at 2 seconds. The forward reaction briefly outruns the reverse one, so some of the added A turns into B. The mixture settles again at about 4.67 of A and 9.33 of B: the total is 14, and B is once more twice A.
Where does it end? The total is now 10 + 4 = 14 units, and the rates balance when B is twice A again. So A settles at 14 ÷ 3 ≈ 4.67 and B at 28 ÷ 3 ≈ 9.33. Some of the added A has turned into B, but not all of it.
Taking B away works the same way in reverse. Remove half the B, and the reverse rate drops, so the forward reaction wins until the 2 : 1 balance is restored. Le Châtelier’s rule, called Le Châtelier’s principle, says: if you disturb a reaction at equilibrium, the mixture shifts in the direction that partly undoes the disturbance. That sounds as if the mixture is fighting back on purpose. It is not. The shift is just the rates becoming unequal for a while, then equal again.
You can watch it happen in a bottle of soda water. Sealed, it shows no bubbles at all: carbon dioxide is escaping from the liquid into the gas at the top exactly as fast as it dissolves back in. Open the cap and the gas above rushes out. Now the dissolving-back direction has almost nothing to work with, so escaping wins, and bubbles stream up. Screw the cap back on and the bubbling soon stops, as the gas above builds up until the two rates match again. (Keep it in the fridge and it stays fizzy longer: carbon dioxide dissolves better in cold water.)
Your own body does it too. Climb high in the mountains, in Ladakh say, and there is less oxygen in each breath, so less oxygen joins onto the haemoglobin in your blood: the balance has shifted. You feel breathless. You breathe faster at once, and over the following weeks your body makes extra red blood cells, packed with haemoglobin, which pushes the balance back. Trekkers call it getting used to the height; a chemist sees an equilibrium being nudged.
Two honest limits. First, our A ⇌ B model is the simplest possible reaction; real reactions often involve several steps and more complicated rate rules, though the idea of balancing rates still holds. Second, changing the temperature is different. It changes the rate constants themselves, unequally, so it moves the balance point. Adding a catalyst does not: it speeds both directions equally, so the mixture stays where it was.
Careful
“Adding more A changes the balance point for good. The equilibrium constant goes up to make room for the extra A.”
The rate constants, 2 and 1, have not changed (the temperature is the same), so the balance point is still B : A = 2 : 1. Adding A only changes the amounts; the mixture moves until it reaches that same ratio again.
Investigation 5.7
Let the A ⇌ B mixture settle, then try each disturbance: add 4 units of A, remove half of B, or add a catalyst (double both constants). For each one, predict which rate is bigger just afterwards, and where the mixture will settle.
Check yourself
The A ⇌ B mixture (forward 2, reverse 1) has settled at 3.33 of A and 6.67 of B. You remove half of B. Which rate is bigger immediately afterwards, and where does the mixture settle?
After removing half the B: A = 3.33, B = 3.33. Forward rate = 2 × 3.33 ≈ 6.7, reverse = 1 × 3.33 ≈ 3.3, so the forward reaction is faster and A turns into B. The total is now 6.67, and it settles when B is twice A: A ≈ 2.22, B ≈ 4.44.
Case file 5
The case of the expensive catalyst
A (made-up) chemical factory turns a substance A into a useful product B, in a reversible reaction A ⇌ B that gives out heat. At the factory’s working temperature, the mixture always settles at 2 parts B to 1 part A, so only about 67% ends up as B. The manager buys an expensive catalyst, hoping to push the yield up to 95%.
The catalyst lowers the peak of the energy profile without moving the start or the finish.
With the catalyst, the forward and reverse rate constants both double, from 2 and 1 to 4 and 2.
A chemist on the staff points out that the reaction is exothermic, and that its balance shifts towards B at lower temperatures, where it is unfortunately very slow.
Will the catalyst raise the yield to 95%? If not, what does it do, and what could the factory actually change to get more B?
Show the solution
The catalyst will not change the yield. Doubling both rate constants keeps their ratio at 4 : 2 = 2 : 1, so the mixture settles at the same 67% B, just faster (clues 1 and 2).
Two things could help. The factory could keep removing B as it forms: the reverse rate then stays low, so the forward reaction keeps winning and A keeps turning into B. Or it could run the reaction at a lower temperature, where the balance favours B more (clue 3). On its own, a lower temperature would make the reaction painfully slow, and that is where the catalyst earns its price: it lets a cooler reactor still reach its balance in a sensible time. Real chemical plants, such as the ones that make ammonia for fertiliser, use exactly this combination of catalyst, temperature and removing product.
What this chapter can’t explain yet
You can now follow energy through a reaction, and you know the difference between how much, how fast and how far. But in a real lab nobody counts molecules one at a time. To make a medicine or a fertiliser, you need to know how many grams of each substance to weigh out, and how much product to expect. The next part of the adventure goes back to 1811, to an Italian lawyer-turned-physicist named Amedeo Avogadro with an idea almost nobody believed for fifty years, and builds the counting tools chemists use every day: the mole, molar mass and concentration. That is Chapter 6.
6
Chapter 6
A quantitative language
The big questionNobody can count molecules one by one, yet a pharmacist making a saline drip, or a chemist running a reaction, needs exactly the right number of them. How do you count things you cannot see, using only a balance and a measuring flask?
In the autumn of 1860, about 140 chemists from all over Europe crowded into a hall in the German town of Karlsruhe. It was the first international meeting of chemists ever held, and it had been called because chemistry was in a muddle. Everyone agreed that substances were made of atoms. Almost nobody agreed on how many atoms were in anything. Was water HO or H₂O? One textbook published the next year listed nineteen different formulas that chemists had proposed for acetic acid, the acid in vinegar. If you cannot agree on the recipe, you cannot cook.
For three days they argued and got nowhere. Then, as people were leaving, a friend of the Italian chemist Stanislao Cannizzaro handed out copies of a little booklet Cannizzaro had written. Cannizzaro was no ordinary professor: as a young man he had fought in the Sicilian revolution of 1848 and had to flee into exile, and he wrote his booklet to help his own students make sense of a subject he thought was being taught as a jumble. It showed how an idea almost everyone had forgotten, published half a century earlier by Amedeo Avogadro, a lawyer from Turin who had given up the law for physics and spent his life teaching quietly, largely ignored, could sort the whole mess out. One young German chemist, Lothar Meyer, read it on the journey home and later wrote that it was as if the scales fell from his eyes. Another person in that hall was a young Russian called Dmitri Mendeleev, the youngest child of a big family from Siberia, whose widowed mother had travelled across Russia with him so that he could study. He would use the same clear atomic weights a few years later to build the periodic table.
This chapter is about the problem those chemists solved: how much. Chapters 4 and 5 were about what happens in a reaction. But if you want to make 10 grams of something, how much of each ingredient should you weigh out? A cook can measure cups and spoons, because flour and sugar are big enough to see. A chemist’s real ingredients are molecules, and the recipe in a balanced equation counts molecules. So the whole chapter is one translation: from counting particles, which is what nature does, to weighing grams and measuring litres, which is what we can do.
6.1Ratios tell a story
London, May 1800
Weeks after Alessandro Volta in Italy announced the first battery, two Englishmen, William Nicholson and Anthony Carlisle, made one of their own and dipped its two wires into water. Bubbles streamed up from both wires. When they collected the gases, there was always about twice as much gas from one wire as from the other. The bigger bubble of gas burned with a pop: hydrogen. The smaller one was oxygen, the gas that makes a glowing splint burst into flame. Water, the most ordinary thing in the world, had come apart into two gases, and always in the same proportion.
That 2 : 1 is not an accident. A few years later Joseph Gay-Lussac in Paris found that gases always combine in simple whole-number volumes, and in 1811 Avogadro guessed why: equal volumes of gas, at the same temperature and pressure, hold equal numbers of molecules. So twice the volume of hydrogen means twice the number of molecules. The formula H₂O says it in letters: two hydrogen atoms for every one oxygen atom. One molecule has 2 H and 1 O. Five molecules have 10 H and 5 O. A glassful has an enormous number of each, but always exactly twice as many hydrogens as oxygens. Chemists call this an atom ratio.
Now for the trap that caught chemists for decades. If water has twice as many hydrogen atoms, surely most of its mass is hydrogen? It is the other way round. An oxygen atom has about 16 times the mass of a hydrogen atom. In each water molecule, the two hydrogens together weigh about 2 units and the one oxygen about 16. By mass, water is roughly 1 part hydrogen to 8 parts oxygen. Weigh the two gases that Nicholson and Carlisle collected, and the small bubble of oxygen is about eight times heavier than the big bubble of hydrogen. Almost nine-tenths of the mass of every glass of water you drink is oxygen.
Figure 6.1Five water molecules counted two ways. By number, there are twice as many hydrogen atoms as oxygen atoms. By mass, the oxygen atoms outweigh the hydrogen atoms about eight to one, because each oxygen atom is about 16 times heavier.
Both numbers are right. They answer different questions: how many? and how heavy? A ratio only means something once you say what you are counting: atoms, molecules, or grams. Most mistakes in this chapter, and most of the muddle at Karlsruhe, come from mixing them up.
Investigation 6.1
Compare one water molecule with five. Which numbers in the app grow, and which ratio stays fixed? Predict the hydrogen-to-oxygen ratio for a million molecules before you check.
Check yourself
Carbon dioxide is CO₂. A carbon atom has a mass of about 12 units and an oxygen atom about 16. What is the atom ratio of carbon to oxygen, and roughly what is the mass ratio?
The atom ratio is 1 : 2 (one carbon, two oxygens). The mass ratio is 12 : 32, which simplifies to 3 : 8. So although carbon dioxide is “one-third carbon” by atoms, it is only about 27% carbon by mass.
6.2Counting beyond what we can see
In Chapter 0 you met the mole: a counting unit, like a dozen, but holding 6.022 × 10²³ things. This is where it earns its keep, so let us take it slowly.
The point of a dozen is that it is the same number whatever you are counting. A dozen eggs and a dozen watermelons are both twelve things, even though the watermelons are far heavier. A mole works in exactly the same way. A mole of carbon atoms and a mole of water molecules contain the same number of particles, 6.022 × 10²³ each. But a carbon atom and a water molecule have different masses, so the two piles weigh different amounts: about 12 grams for the carbon, about 18 grams for the water.
Figure 6.2One mole each of three substances. Each pile holds the same number of particles, 6.022 × 10²³. The masses differ because the particles themselves have different masses.
Predict first: a tablespoon and a bit of water (18 grams) is one mole of water molecules. If you could line those molecules up side by side across the width of the spoon, roughly how many would fit: a thousand? a million? a thousand million? Write your guess, then zoom in.
Figure 6.3Zooming into a spoonful of water, ten times at a step, past a raindrop, a grain of salt, a hair, a blood cell, a bacterium, a virus and the width of DNA, until single water molecules appear, about 0.3 nanometres apart.
Every view is drawn at its true size, and the box in the corner counts how many water molecules would fit side by side across it. Across the spoon it is roughly two hundred million. Shrink the view to the width of a hair and it is still a quarter of a million. Only at the very bottom, a few nanometres across, can you count them on your fingers.
Now the real surprise. Two hundred million across sounds enormous, but the spoon is three-dimensional. Pour the water into a cube 2.6 centimetres wide and about 84 million molecules sit along each edge, so the whole cube holds 84 million × 84 million × 84 million: about 6 × 10²³, one mole. Multiplying the same big number by itself three times is what makes a mole so unimaginably large. And yet it is only a tablespoon and a bit of water. That is how small molecules are.
Here is the clever part, the trick that made the whole of quantitative chemistry possible. Because a carbon atom is 12 units and an oxygen atom 16, then 12 grams of carbon and 16 grams of oxygen must contain the same number of atoms, whatever that number is. Weigh out any element’s relative mass in grams and you always get the same count. Chemists used this trick for decades before anyone knew what the count actually was. It was a bit like buying eggs by the dozen without knowing that a dozen is twelve, and it worked, because what matters in a recipe is that the number is the same for everything.
The number itself was finally pinned down in the early 1900s by the French physicist Jean Perrin, who measured it in several completely different ways and got the same answer each time. He suggested naming it after Avogadro, and today it is Avogadro’s constant, fixed since 2019 at exactly 6.022 140 76 × 10²³.
This is why chemists use moles rather than grams when they think about reactions. Reactions happen particle by particle: one carbon atom meets one oxygen molecule. If you want equal numbers of particles, you want equal numbers of moles, not equal numbers of grams.
There is one rule you must never skip: always say what the “things” are. One mole of water molecules contains three moles of atoms, because every molecule has three atoms. One mole of oxygen gas, O₂, contains two moles of oxygen atoms. Saying “a mole of oxygen” without saying which is like saying “a dozen shoes” when you mean a dozen pairs.
Careful
“One mole of water contains more molecules than one mole of carbon contains atoms, because water is heavier.”
The mole is a number, so one mole of anything contains exactly the same number of particles: 6.022 × 10²³. Water’s extra mass comes from each molecule being heavier (about 18 units against carbon’s 12), not from there being more of them.
Count dal without counting
You need a kitchen scale, a bowl, and a packet of dry dal or lentils. Count out exactly 100 grains and weigh them (if your scale only shows whole grams, count 200 or 500). Work out the mass of one grain. Now fill a cup with dal, weigh it, and divide by the mass of one grain: that is how many grains are in the cup. Check by counting a small spoonful. You have just counted thousands of things by weighing them, exactly as chemists count atoms with moles.
Then build a mole display on the kitchen counter. Measure out 18 g of water (about a tablespoon and a bit), 58 g of salt (a little over three level tablespoons) and 342 g of sugar (about one and three-quarter cups). Three very different heaps, and each holds exactly the same number of particles: one mole, six hundred thousand million million million.
Investigation 6.2
Keep the amount fixed at 1 mol and change the molar mass from carbon (12.011 g per mole) to water (18.015 g per mole). Which number changes, and which stays exactly the same?
Understand itThe mole
What is it?
A counting unit for very small things, like a dozen, but much bigger: one mole is 6.022 × 10²³ particles. Its magic is that one mole of any substance has a mass in grams equal to its formula’s mass.
Why is it called this?
From the German Mol, which Wilhelm Ostwald coined in the 1890s as a short form of Molekül, molecule. It has nothing to do with the animal.
What problem did it solve?
Reactions happen particle by particle, but chemists can only weigh things, never count atoms. The mole turns a kitchen-scale reading into a count of particles.
Why does it work?
Atoms of different elements have different masses in fixed ratios: carbon 12, oxygen 16. So 12 grams of carbon and 16 grams of oxygen hold the same number of atoms. Pick that number as your unit, and weighing becomes counting.
How does it help?
It tells you exactly how much of each ingredient a reaction needs and how much product you will get, from a medicine factory to a rocket’s fuel tanks.
Go deeper how do we know, what it isn’t, where does it stop working
How do we know?
Jean Perrin, in the early 1900s, measured the number in several completely different ways, including watching tiny grains jiggle in water, and they all agreed.
What it isn’t
It is not a mass. A mole is a number of things, and a mole of gold weighs far more than a mole of hydrogen.
Where does it stop working?
It is only useful for huge numbers of tiny things. For a handful of molecules, or anything you can count by eye, just count.
Your turn
Explain The mole to a friend in one sentence, in your own words. Then compare it with the book’s.
A counting unit for very small things, like a dozen, but much bigger: one mole is 6.022 × 10²³ particles. Its magic is that one mole of any substance has a mass in grams equal to its formula’s mass.
Check yourself
You have 1 mole of oxygen gas, O₂. How many O₂ molecules is that, and how many oxygen atoms?
6.022 × 10²³ molecules of O₂. Each molecule has two atoms, so there are 2 × 6.022 × 10²³ ≈ 1.2 × 10²⁴ oxygen atoms.
6.3From moles to mass
Stockholm, around 1810 to 1818
In a small, cramped laboratory in Stockholm, Jöns Jacob Berzelius, the symbol-maker you met in Chapter 4, spent years doing something heroically patient. He took compound after compound, around two thousand of them, purified each one, and weighed exactly how much of each element it contained. From those numbers he worked out how heavy the atoms of dozens of elements are compared with each other, and many of his values were remarkably close to the ones we use today. Every molar mass in this chapter rests on work like his.
Here is why it matters. You cannot set a balance to “count out half a mole”. A balance measures grams. So you need a conversion factor between moles and grams, and it is different for every substance. It is called the molar mass: the mass of one mole, in grams per mole (g/mol). For water it is about 18.0 g/mol; for carbon dioxide, about 44.0 g/mol; for table salt, sodium chloride, about 58.4 g/mol.
Working one out is just adding up the atoms in the formula, using the average atomic masses on the periodic table (Section 1.3). Let us do water slowly:
Water is H₂O: two hydrogen atoms and one oxygen atom.
Hydrogen: 2 × 1.008 = 2.016
Oxygen: 1 × 15.999 = 15.999
Add them: 2.016 + 15.999 = 18.015 g/mol
Then the conversion is one multiplication, or one division:
mass (g) = moles (mol) × molar mass (g/mol)
Figure 6.4The bridge between what you can weigh and what you want to count. Divide grams by the molar mass to get moles; multiply moles by Avogadro’s constant to get the number of particles. Go the other way by doing the opposite.
Here is a habit that will save you over and over: write the units on every number and watch them cancel, like fractions. How much carbon dioxide is in half a mole of it?
0.50 mol × 44.0 g/mol = 22 g
(mol × g/mol: the “mol” on top cancels the “mol” underneath, leaving grams.)
And the other way round: how many moles are in 36 g of water?
36.0 g ÷ 18.0 g/mol = 2.0 mol
(g ÷ g/mol: the grams cancel, leaving moles.)
If the units do not cancel to what you want, you have multiplied when you should have divided. Units are a free check on your arithmetic, and good chemists never leave them off.
Careful
“The equation says 2 H₂O, so I use a molar mass of 36 for water.”
The molar mass belongs to the substance, not to the equation. Water is 18.0 g/mol whether an equation says 2 H₂O or 10 H₂O. The number in front tells you how many moles you have; each of those moles still has a mass of 18.0 g.
Careful
“18.015 is the mass number of water.”
Mass numbers belong to single nuclei and are always whole numbers (Section 1.5). The 18.015 g/mol is an average: it comes from the average atomic masses of hydrogen and oxygen, which already blend in their natural mixtures of isotopes. That is why it has decimals.
Investigation 6.3
Use 18.015 g/mol and compare 1 mol with 2 mol. Before you look, say what the mass will be. Then try a substance with a molar mass of 44 g/mol: what mass is half a mole?
Check yourself
A chemist weighs out 36.03 g of pure water. How many moles is that, and how many molecules?
36.03 g ÷ 18.015 g/mol = 2.000 mol. That is 2 × 6.022 × 10²³ ≈ 1.204 × 10²⁴ molecules. The grams cancel, leaving moles: g ÷ (g/mol) = mol.
6.4Which reactant runs out first?
Launch pad 39A, Florida, 1981 to 2011
For thirty years, the Space Shuttle’s three main engines burned liquid hydrogen with liquid oxygen, the same reaction Nicholson and Carlisle had run backwards in 1800: 2 H₂ + O₂ → 2 H₂O. The perfect recipe, by mass, is about 8 kilograms of oxygen for every 1 kilogram of hydrogen. But the engineers deliberately loaded the engines to burn only about 6 kilograms of oxygen per kilogram of hydrogen. That meant the oxygen always ran out first, and roughly a quarter of the hydrogen shot out of the nozzle unburnt. It was not waste: a hydrogen-rich exhaust is lighter, so it rushes out faster and pushes the rocket harder. The engineers had chosen which reactant would run out.
In chemistry, the ingredient that runs out first is called the limiting reactant. Whatever is left over is in excess.
Here is the idea with something easier to picture than a rocket. A bicycle needs one frame and two wheels. A workshop has 5 frames and 6 wheels. How many bicycles can it build? Not five: it runs out of wheels after three bicycles, with two frames left over. The wheels are limiting; the frames are in excess.
Reactions work exactly like this, because a balanced equation is a recipe in whole particles. For hydrogen burning in oxygen:
2 H₂ + O₂ → 2 H₂O
each “set” needs two hydrogen molecules and one oxygen molecule, and makes two water molecules. Suppose you start with 5 H₂ and 2 O₂. The two oxygen molecules can make two complete sets, using 4 of the H₂. That makes 4 H₂O and leaves 1 H₂ with no oxygen to react with. Oxygen is the limiting reactant.
Figure 6.5Five hydrogen molecules and two oxygen molecules, grouped into complete sets of the recipe 2 H₂ + O₂. Two full sets fit, making four water molecules; one hydrogen molecule is left over.
Now add one more O₂, so you have 5 H₂ and 3 O₂. You might expect more water. But a third set needs two more H₂, and only one is left. So you still make 4 H₂O, and now one H₂and one O₂ are left over. The limiting reactant has switched to hydrogen, even though there are more hydrogen molecules (5) than oxygen molecules (3). The reactant you have fewer of is not always the one that runs out. What matters is how many complete sets each one can make.
Sets possible from each reactant (for 5 H₂ and 3 O₂)
From H₂: 5 ÷ 2 = 2.5, so only 2 complete sets.
From O₂: 3 ÷ 1 = 3 sets.
The smaller number wins: 2 sets, making 2 × 2 = 4 H₂O.
The lab app counts whole molecules, so the sets come out neat. In a real flask, or a rocket’s fuel tanks, with billions of billions of molecules, the same rule applies to moles.
Balloons that stop growing
You need four small bottles, four balloons, vinegar, baking soda and a funnel (a rolled-up piece of paper will do). Pour the same 50 mL of vinegar into each bottle. Using the funnel, put ¼ teaspoon of baking soda into the first balloon, ½ teaspoon into the second, 1 teaspoon into the third and 2 teaspoons into the fourth. Stretch each balloon over a bottle’s neck without letting the powder fall in, then lift them all up together so the soda drops into the vinegar.
Predict first: how big will each balloon get? Draw your guess.
The first two grow in step with the soda you gave them. But the third and fourth end up about the same size, and the fourth has white powder left over at the bottom. Fifty millilitres of ordinary 5% vinegar (check the label; weaker vinegar runs out sooner) can only use up about three-quarters of a teaspoon of soda. After that, the vinegar has run out: it has become the limiting reactant, and the extra soda is in excess, with nothing left to react with.
Investigation 6.4
Start with 5 H₂ and 2 O₂. Count the products and leftovers. Then add one O₂ and predict, before you look, whether another full set of the recipe can happen.
Understand itLimiting reactant
What is it?
The ingredient that runs out first in a reaction, and so decides how much product you can make. Whatever is left over is “in excess”.
Why is it called this?
It sets the limit on how much product can form, just as the number of wheels limits how many bicycles a workshop can build.
What problem did it solve?
It explains why adding more of one ingredient sometimes makes no difference at all, and lets chemists and engineers stop wasting the ingredient they have too much of.
Why does it work?
A balanced equation is a recipe in whole particles. Once one ingredient has been used up, no more complete “sets” of the recipe can be made, however much of the others is left.
How does it help?
You can predict the most product a reaction can give, and choose which ingredient to put in extra on purpose, as the Space Shuttle’s engineers did with hydrogen.
Go deeper how do we know, what it isn’t, where does it stop working
How do we know?
Add more and more baking soda to the same vinegar: the balloons grow, then stop growing, and powder is left over at the bottom.
What it isn’t
It is not always the ingredient you have the least of. It is the one that runs out first for that recipe, so you have to compare against the equation.
Where does it stop working?
Real reactions do not always go all the way to the end, and some ingredients get used in side reactions, so the actual amount of product is often less than this prediction.
Your turn
Explain Limiting reactant to a friend in one sentence, in your own words. Then compare it with the book’s.
The ingredient that runs out first in a reaction, and so decides how much product you can make. Whatever is left over is “in excess”.
Check yourself
For 2 H₂ + O₂ → 2 H₂O, you start with 6 H₂ and 2 O₂. How many water molecules can form, and what is left over?
Each O₂ needs two H₂, so 2 O₂ use 4 H₂ and make 4 H₂O. Oxygen runs out first; 2 H₂ are left over.
6.5How much in each litre?
Leith, Scotland, 1832
Cholera swept through Britain in 1832. Its victims lost so much water and salt from their bodies that their blood grew thick and dark, and most of the very sick died. A Scottish doctor called Thomas Latta tried something astonishing for the time: he dissolved ordinary salt in warm water and let it run straight into a patient’s vein. Some of his dying patients sat up within hours. It took the rest of the medical world many decades to follow him, partly because nobody yet understood exactly how much salt the water should hold. Too little or too much does harm. What mattered was not how much salt was in the whole bag, but how salty each drop was.
That “how salty is each drop” is what chemists call concentration: the number of moles of a dissolved substance in each litre of the finished solution.
concentration (mol/L) = moles dissolved ÷ volume of solution (L)
One mole of salt made up to 2 litres of solution has a concentration of 0.50 mol/L. The same mole made up to 4 litres is 0.25 mol/L: the particles are spread twice as thinly. And 2 moles in 4 litres is back to 0.50 mol/L, the same strength as the first, just more of it.
Figure 6.6Three solutions. The first and third are equally concentrated, 0.50 mol/L, because the amount of salt and the volume have both doubled. The middle one has the same amount of salt as the first, spread through twice the volume.
Concentration is like how crowded a room is, not how many people are in the building. Pour a cup from a big jug of nimbu pani and the cup tastes exactly as sour and sweet as the jug, even though it holds far less sugar. That is why a modern hospital saline drip, the great-grandchild of Latta’s experiment, is labelled with its concentration: 0.9% salt, which is 9 grams of sodium chloride in every litre, or about 0.154 mol/L. The bag might be large or small; every drop has the same concentration, close to the saltiness of the fluid in your blood.
Same sweetness, different amounts
Make two glasses of sugar water (or sharbat). In the first, stir 1 level teaspoon of sugar into half a cup of water. In the second, stir 2 level teaspoons into a full cup. Taste them both. They should taste equally sweet, even though the second glass holds twice as much sugar: the concentration is the same. Now pour half of the first glass away and taste what is left. Still the same. Concentration does not care how much you have, only how crowded it is.
Careful
“To make 1 litre of a 1 mol/L solution, add 1 mole of salt to 1 litre of water.”
Not quite. The solid takes up some room, so you would end up with a little more than 1 litre of solution, and a slightly weaker concentration. Chemists dissolve the solid in less water first, then add water until the total volume of solution reaches exactly 1 litre, using a flask with a line marked on its neck.
Investigation 6.5
Compare 1 mol in 2 L with 1 mol in 4 L. Then find two different mixtures that have exactly the same concentration.
Understand itConcentration
What is it?
How much of a dissolved substance is in each litre of solution, usually counted in moles per litre (mol/L). It is how crowded the solution is.
Why is it called this?
From Latin com- (“together”) and centrum (“centre”): to concentrate is to gather together. A concentrated solution has its dissolved particles packed close.
What problem did it solve?
Doctors and chemists needed to know not just how much salt or medicine they had, but how strong each drop was. Thomas Latta’s salt-water drip in 1832 had to be the right strength to save lives.
Why does it work?
The effect of a dissolved substance depends on how many of its particles are near you, in each sip or each drop of blood, not on how much is in the whole jug.
How does it help?
It lets you make a solution of exactly the right strength, from oral rehydration salts to a lab reagent, and work out how much is in any amount of it.
Go deeper how do we know, what it isn’t, where does it stop working
How do we know?
A cup poured from a jug of nimbu pani tastes just as strong as the jug: same concentration, smaller amount.
What it isn’t
It is not the total amount. A bucket and a spoonful of the same sea water have the same concentration.
Where does it stop working?
It is “per litre of solution”, not per litre of water, and volumes shift slightly with temperature, so very careful work measures and calculates with that in mind.
Your turn
Explain Concentration to a friend in one sentence, in your own words. Then compare it with the book’s.
How much of a dissolved substance is in each litre of solution, usually counted in moles per litre (mol/L). It is how crowded the solution is.
Check yourself
Bottle A holds 1.0 L of salt solution at 0.50 mol/L. Bottle B holds 4.0 L at 0.25 mol/L. Which tastes saltier? Which contains more salt in total?
Bottle A tastes saltier, because its concentration is higher. But bottle B contains more salt in total: 4.0 L × 0.25 mol/L = 1.0 mol, against 1.0 L × 0.50 mol/L = 0.50 mol in A.
6.6From laboratory grams to product grams
You now have every piece the chemists at Karlsruhe were missing. So try a real chemist’s question, the one every medicine factory, fertiliser plant and school laboratory asks every day: if I start with this many grams, how many grams of product can I make?
The secret is that a balanced equation’s numbers count particles, or moles. They are never grams. So the route always goes through moles, in three steps:
grams of reactant → moles of reactant → moles of product → grams of product
Take hydrogen burning again, 2 H₂ + O₂ → 2 H₂O. The equation says 2 moles of hydrogen react with 1 mole of oxygen to make 2 moles of water. In grams, using molar masses of about 2.0, 32.0 and 18.0 g/mol, that is 4.0 g of hydrogen with 32.0 g of oxygen, making 36.0 g of water.
Figure 6.7The same reaction read in moles and in grams. The mole numbers follow the equation, 2 : 1 : 2. The gram numbers do not, but they still add up: 4.0 g + 32.0 g = 36.0 g, because no atom is lost.
Notice two things. First, the gram numbers (4 : 32 : 36) look nothing like the equation’s 2 : 1 : 2. Second, the grams still add up perfectly, 4.0 + 32.0 = 36.0, because atoms are never lost (Lavoisier’s great discovery in Chapter 4). Moles follow the equation; grams follow conservation of mass. Both are true at once.
Here is the three-step route with your hand held all the way:
How much carbon dioxide comes from burning 8.0 g of methane? CH₄ + 2 O₂ → CO₂ + 2 H₂O
Step 1, grams to moles: methane is 16.0 g/mol, so 8.0 g ÷ 16.0 g/mol = 0.50 mol.
Step 2, moles to moles: the equation says 1 CH₄ makes 1 CO₂, so 0.50 mol of CO₂ forms.
Step 3, moles to grams: carbon dioxide is 44.0 g/mol, so 0.50 mol × 44.0 g/mol = 22 g.
The answer you get this way is the most you could possibly make, if every molecule of the limiting reactant reacts and nothing is spilt. Real reactions usually give a little less, and chemists call the comparison between what they got and what they could have got the yield.
Careful
“2 H₂ + O₂ → 2 H₂O means 2 grams of hydrogen react with 1 gram of oxygen.”
The numbers in an equation count particles, not grams. An oxygen molecule has about 16 times the mass of a hydrogen molecule, so the 1 mole of oxygen weighs far more (32 g) than the 2 moles of hydrogen (4 g).
Investigation 6.6
Compare 1.00 mol of O₂ (32 g/mol) with 2.00 mol of H₂O (18 g/mol). Explain why a 1 : 2 mole ratio does not give a 1 : 2 gram ratio.
Check yourself
In CH₄ + 2 O₂ → CO₂ + 2 H₂O, how many grams of water form from burning 8.0 g of methane (16.0 g/mol)? Water is 18.0 g/mol.
8.0 g ÷ 16.0 g/mol = 0.50 mol of methane. The equation gives 2 H₂O for every 1 CH₄, so 1.0 mol of water forms: 1.0 mol × 18.0 g/mol = 18 g.
Case file 6
The missing four grams
A technician puts 12.0 g of hydrogen gas and 64.0 g of oxygen gas into a strong sealed chamber and sets off a spark. The reaction is 2 H₂ + O₂ → 2 H₂O. She expects 12.0 g + 64.0 g = 76.0 g of water. When she collects and weighs the water, there is only 72.0 g.
The chamber stayed sealed, and weighed the same before and after.
After the reaction, a colourless gas is still left in the chamber. It burns with a squeaky pop when lit.
Where did the “missing” 4.0 g go? Which reactant was limiting, and how should she have predicted 72.0 g?
Show the solution
Nothing went missing: 4.0 g of hydrogen never reacted. Convert to moles first: 12.0 g ÷ 2.0 g/mol = 6.0 mol of H₂, and 64.0 g ÷ 32.0 g/mol = 2.0 mol of O₂. The recipe needs 2 mol of H₂ for each mol of O₂, so 2.0 mol of O₂ can use only 4.0 mol of H₂. Oxygen is the limiting reactant. It makes 4.0 mol of water, 4.0 × 18.0 = 72.0 g, and leaves 2.0 mol of hydrogen, 2.0 × 2.0 = 4.0 g, still in the chamber as gas (clue 3: hydrogen burns with a pop). Clue 2 confirms that no mass was lost: 72.0 g + 4.0 g = 76.0 g. Her mistake was adding grams instead of comparing moles, exactly the kind of muddle the chemists at Karlsruhe set out to end.
What this chapter can’t explain yet
Counting moles per litre treats every dissolved substance alike. But two solutions of the same concentration can behave completely differently: one stings, one does not; one dissolves metal, one goes on your salad. To see why, the adventure moves to a brewery in Copenhagen, a purple cabbage, and the most important trade in chemistry: the passing of a single proton from one molecule to another.
IIIVolume III
Chemistry at work
Acids and batteries, the shape of the periodic table, the carbon molecules of life, and the chemistry of a changing planet.
The big questionKitchen vinegar contains about 0.8 moles of acetic acid in every litre. Hydrochloric acid diluted to a tenth of that concentration is still far more acidic. How can the weaker-looking solution be the stronger acid?
Start with a trick. Chop a few leaves of red cabbage, soak them in warm water for ten minutes, and strain off the juice. It is a deep purple. Pour a little into three glasses. Into the first, squeeze some lemon: the purple turns a bright pink-red. Into the second, stir a pinch of baking soda: it turns blue, then green. The third you leave alone, and it stays purple. Nothing was heated, nothing was mixed except kitchen food, and yet the colours changed as if by magic.
If you have ever seen a yellow haldi stain on a white kurta turn red-brown when it was scrubbed with soap, you have already met a detector like this. The cabbage is not magic; it is a detector. Its purple colour comes from molecules called anthocyanins, and their colour depends on how many hydrogen nuclei they are carrying. Lemon juice pushes extra ones onto them; baking soda pulls them off. By the end of this chapter you will know exactly what is being pushed and pulled, and you will be able to read the cabbage like an instrument.
Oxford, 1664
People have used colour detectors like this for a long time. In 1664 the Irish-born scientist Robert Boyle, the fourteenth child of one of the richest men in Ireland, who spent his fortune on laboratories and insisted that every idea be tested by experiment, wrote a book about colours in which he noticed that syrup of violets turns red with sour substances and green with substances such as potash. He used it to sort substances into groups. Later chemists settled on litmus, a purple dye made from lichens, which turns red in acid and blue in its opposite. Your cabbage does the same job with a fuller rainbow.
Lemon juice, vinegar, tamarind and the acid in your stomach all taste sour, turn blue litmus red, fizz with baking soda and slowly eat into some metals. Chemists call substances like these acids. Their opposites, which feel slippery and taste bitter, like soap or baking soda, are bases. Your own blood sits on a knife edge between the two: its acidity has to stay within a very narrow range (a pH of 7.35 to 7.45, as you will learn to say in Section 7.3), even when your muscles pour acid into it during a sprint. This chapter explains what acids and bases actually are, why some are far fiercer than others, and how a solution can resist being made more acidic.
Do not let “acid” make you think “danger” and “base” make you think “safe”. The fiercest chemicals in most homes are bases: drain cleaner, caustic soda, and the chuna that goes into paan can all burn skin and eyes. Strong bases are every bit as dangerous as strong acids.
7.1What makes a solution acidic?
For a long time nobody knew what all acids had in common. Lavoisier, whom you met weighing everything in Chapter 4, guessed it was oxygen. He even named the gas for it: oxygène comes from Greek words meaning “acid-maker”. It was a reasonable guess, and it was wrong. Around 1810 Humphry Davy, the discoverer of potassium from Chapter 1, showed that the acid in hydrochloric acid, then called muriatic acid, contains hydrogen and chlorine and no oxygen at all. The common ingredient was hydrogen. But plenty of substances contain hydrogen and are not acids (sugar is full of it), so what was special?
Here is the clue. Hydrogen chloride, HCl, is a gas. Dry, it is made of separate HCl molecules, and liquid HCl hardly conducts electricity at all. But bubble the gas into water and something dramatic happens: the solution, now called hydrochloric acid, conducts electricity very well. Charged particles have appeared that were not there before.
What happened is a transfer. Each HCl molecule hands its hydrogen nucleus, a bare proton, over to a water molecule. The electrons that used to hold the H to the Cl stay behind on the chlorine. So the chlorine becomes a chloride ion, Cl⁻, and the water molecule, now with an extra proton, becomes H₃O⁺, a hydronium ion.
HCl + H₂O → H₃O⁺ + Cl⁻
Figure 7.1A proton passes from hydrogen chloride to a water molecule. The electrons that held it stay with the chlorine, which becomes a chloride ion. The water molecule becomes a hydronium ion. Every atom and every charge is accounted for.
Copenhagen and Cambridge, 1923
In 1923, two chemists who were working separately, Johannes Brønsted in Copenhagen and Thomas Lowry in Cambridge, published the same idea within months of each other. An acid is a proton donor, and a base is a proton acceptor. That one sentence is the whole definition. In the reaction above, HCl is the acid and water is the base. The extra hydronium ions are what make a solution acidic: what turns litmus red, reacts with baking soda, and stings a cut. And it is what your cabbage detects: an acid passes protons to the anthocyanin molecules, a base takes them away, and each form of the molecule has a different colour.
The idea also explained something older theories could not: why ammonia, NH₃, which contains no OH, still behaves as a base. In water it takes a proton from a water molecule, making NH₄⁺ and leaving OH⁻ behind. Brønsted and Lowry’s idea is still the one chemists use most every day.
Notice that “proton” here does not mean a proton torn out of a nucleus. A hydrogen atom is just one proton and one electron. Take away the electron and a bare proton is all that is left. The chlorine nucleus, with its 17 protons, does not change at all; nor does any other nucleus. Chapter 1’s rule still holds.
Careful
“A bottle of hydrochloric acid is full of HCl molecules floating in water.”
In ordinary dilute hydrochloric acid, almost none are left. Every HCl molecule has handed its proton to water, so the bottle is full of H₃O⁺ and Cl⁻ ions instead. Many people draw whole HCl molecules in the water; it is one of the commonest mistakes in chemistry, and Section 7.2 shows why it matters.
Careful
“An acid loses a proton from inside one of its atoms’ nuclei.”
The proton that moves is the nucleus of a hydrogen atom, which is just a single proton. No nucleus is broken open, and no atom changes element. That would take a nuclear reaction, not an acid in a beaker.
Investigation 7.1
Compare pure water, 0.10 mol/L hydrochloric acid and 0.10 mol/L sodium hydroxide. Which particle becomes more common in the acid? Which becomes more common in the base?
Understand itAcids and bases
What is it?
An acid is a substance that hands protons (bare hydrogen nuclei) to other particles, usually water. A base is a substance that takes them. Lemon juice and vinegar are acids; baking soda, soap and chuna are bases.
Why is it called this?
Acid comes from Latin acidus, “sour”, because the ones people met first tasted sour (never test one by tasting). Base was used by the French chemist Rouelle in 1754 for the substance that gave a salt its solid “base”. Alkali, the old word for a strong base, comes from the Arabic al-qalī, the ashes of saltwort, a plant of salty soils.
What problem did it solve?
For centuries acids were known only by their effects: sour taste, colour changes, metals fizzing. Nobody knew what they had in common; Lavoisier guessed oxygen and was wrong. The proton idea of Brønsted and Lowry in 1923 finally explained them all, and bases with them.
Why does it work?
A hydrogen atom stripped of its electron is a single proton, small and easily passed on. Acids let go of such protons; bases have a spare pair of electrons that one can bond to. Every acid–base reaction is a proton changing hands.
How does it help?
It explains why acids and bases cancel each other out, why your stomach, your blood and the sea care so much about acidity, and how to make, test and handle them safely.
Go deeper how do we know, what it isn’t, where does it stop working
How do we know?
Dry hydrogen chloride hardly conducts electricity, but dissolved in water it conducts well: the protons have moved to the water, making ions.
What it isn’t
It is not “acids are dangerous and bases are mild”. Strong bases such as drain cleaner and caustic soda are just as dangerous as strong acids.
Where does it stop working?
Proton-passing covers almost everything in this book, but chemists also use a wider idea, built on electron pairs, for reactions with no protons at all.
Your turn
Explain Acids and bases to a friend in one sentence, in your own words. Then compare it with the book’s.
An acid is a substance that hands protons (bare hydrogen nuclei) to other particles, usually water. A base is a substance that takes them. Lemon juice and vinegar are acids; baking soda, soap and chuna are bases.
Check yourself
When ammonia dissolves in water, NH₃ + H₂O ⇌ NH₄⁺ + OH⁻. Which molecule is the acid (proton donor), and which is the base (proton acceptor)?
Water is the acid: it gives a proton to ammonia, leaving OH⁻. Ammonia is the base: it accepts the proton and becomes NH₄⁺. Water can act as an acid or as a base, depending on its partner.
7.2Strong or concentrated?
Uppsala, Sweden, 1884
Five years before his energybarrier of Chapter 5, the young Svante Arrhenius spent months passing electric currents through solutions and measuring how well they conducted. He found that, at the same concentration, hydrochloric acid conducted electricity far better than acetic acid, the acid in vinegar. His explanation was bold: in water, some substances split into charged ions, and some split much more than others. This was the thesis his examiners nearly failed, and the idea that won him the Nobel Prize in 1903.
Here is the answer to this chapter’s big question. Hydrochloric acid and acetic acid both give protons to water, but they do it to very different extents.
In hydrochloric acid, essentially every HCl molecule gives up its proton. Chemists call it a strong acid. Acetic acid, CH₃COOH, is a weak acid: in vinegar, only a few molecules in every thousand have handed over a proton at any moment. The rest stay whole. The transfer goes both ways, molecules giving and taking protons back all the time, and it settles into a balance (the dynamic equilibrium of Chapter 5) in which most acetic acid molecules are intact.
So “strong” and “concentrated” are answers to two different questions. Concentration asks how much acid was dissolved in each litre (Section 6.5). Strength asks how readily the acid’s molecules give up their protons, and that is fixed for each acid: at the same concentration, a strong acid hands over all of them and a weak acid only a small fraction. Think of a classroom: concentration is how many children are in the room; strength is how eager each of them is to put a hand up.
Here is another way to hold it, which will pay off in the case at the end of the chapter. A weak acid keeps most of its protons in the bank, locked up in whole molecules. The hydronium ions are the cash in hand. A pH meter (Section 7.3) counts only the cash. A titration (Section 7.4) counts the whole fortune, bank and all.
Figure 7.2Two acids, seen as particles. In dilute hydrochloric acid every molecule has passed its proton to water. In concentrated acetic acid there are far more acid molecules, but nearly all of them are still whole. The counts are illustrative: in real 1 mol/L acetic acid only about 4 molecules in every 1,000 have given up a proton.
Put numbers on it, using measured values. Hydrochloric acid at 0.010 mol/L gives 0.010 mol/L of hydronium ions, because every molecule takes part. Acetic acid at 1.00 mol/L, a hundred times more concentrated, gives only about 0.0042 mol/L of hydronium ions, because only about 0.42% of its molecules take part. The dilute strong acid has more than twice as many hydronium ions per litre as the concentrated weak one. Arrhenius’s meter was really counting those ions; today a pH meter (Section 7.3) measures the hydronium concentration directly, and for 1.00 mol/L acetic acid it reads that same 0.0042 mol/L.
Strong acids are among the most useful chemicals in the world, for making fertilisers, dyes, medicines and metals, and for a long time India had to import them.
Calcutta, 1901
Prafulla Chandra Ray, a chemistry professor at Presidency College in Calcutta (now Kolkata), wanted that to change. He had studied in Edinburgh, came home determined that Indian science should serve India, and lived so simply that he is said to have given much of his salary away. In 1892, with a few hundred rupees, he started a small chemical works, and in 1901 it became the company Bengal Chemical and Pharmaceutical Works, which grew into one of the first big Indian companies to make medicines and laboratory chemicals, acids among them, in India itself. He is often called the father of Indian chemistry.
Back to the kitchen. That is why vinegar is safe on your salad. Kitchen vinegar is roughly 0.8 mol/L acetic acid, but it has only about 0.004 mol/L of hydronium ions. Hydrochloric acid at a tenth of vinegar’s concentration would have about 0.08 mol/L, twenty times more, and would be dangerous to drink.
Careful
“If you add enough water to a strong acid it becomes a weak acid.”
Adding water makes an acid more dilute, never weaker. Every HCl molecule still gives up its proton; there are just fewer of them per litre. Strength belongs to the acid itself, so concentrated acetic acid is still a weak acid, and diluted acetic acid is still a weak acid too. (Diluting a weak acid actually lets a slightly bigger fraction of its molecules give up their protons, because the balance shifts, but the solution still ends up less acidic than before.)
Investigation 7.2
Compare 0.010 mol/L hydrochloric acid with 1.00 mol/L acetic acid. Save both, and compare the fraction of molecules that gave up a proton and the concentration of hydronium ions in each.
Check yourself
Sketch or describe two beakers of particles: (A) a concentrated weak acid and (B) a dilute strong acid. How does your drawing show concentration, and how does it show strength?
Concentration is shown by how many acid particles there are in total in each beaker: lots in A, few in B. Strength is shown by what fraction of them have split into H₃O⁺ and the negative ion: almost none in A (mostly whole HA molecules), all of them in B (no whole HCl left).
7.3Every step on the pH scale is tenfold
Copenhagen, 1909
At the Carlsberg Laboratory, run by the famous beer company, the Danish chemist Søren Sørensen was studying how proteins and enzymes behave during brewing. He found that they were exquisitely sensitive to acidity, and he needed a simple way to write it down. The trouble was the numbers. Strong acid might have 1 mole of hydronium per litre; pure water has one ten-millionth of a mole per litre, 0.000 000 1 mol/L; a strong base might have a ten-millionth of that, 10⁻¹⁴ mol/L. Writing those out is clumsy, so in 1909 Sørensen invented a shortcut: the pH scale. In the same year, Fritz Haber and Zygmunt Klemensiewicz described the glass electrode, the heart of the pH meters still used today.
The idea is to count powers of ten. Write the hydronium concentration as a power of ten, then take the number on top and drop the minus sign:
0.1 mol/L = 10⁻¹ mol/L → pH 1
0.01 mol/L = 10⁻² mol/L → pH 2
0.001 mol/L = 10⁻³ mol/L → pH 3
0.000 000 1 mol/L = 10⁻⁷ mol/L → pH 7 (pure water at 25 °C)
Three things follow, and all three surprise people.
Lower pH means more acidic. Because of that dropped minus sign, pH 1 has more hydronium than pH 3.
Each step of 1 is a factor of ten. pH 2 has ten times more hydronium than pH 3, and pH 1 has a hundred times more than pH 3. The pH scale is not like a ruler where each centimetre is the same size; it is like the powers-of-ten scale in Chapter 0.
In-between numbers are allowed. Acetic acid at 1.00 mol/L has 0.0042 mol/L of hydronium, which lies between 10⁻³ and 10⁻², so its pH lies between 3 and 2. A calculator gives 2.37. (Mathematicians call this power-counting a logarithm; you do not need the word yet.)
Figure 7.3The pH scale with some everyday solutions, and the colours red cabbage juice turns along it. Every step to the left multiplies the hydronium concentration by ten: the dots below count the hydronium ions at pH 7, 6, 5 and 4 against pure water’s one. Values are typical and vary from sample to sample.
Pure water is neutral, pH 7, because water molecules pass protons to each other very slightly: a tiny number become H₃O⁺ and an equal number become OH⁻. Acids push the hydronium concentration up and the pH below 7. Bases mop up hydronium, so the pH rises above 7. Your red cabbage juice is a rough pH meter. It is red around pH 2, pink-purple around pH 4, purple near neutral, blue around pH 8, green by pH 10 and greenish-yellow by pH 12. Notice what it reads: pH, not strength. Lemon juice and vinegar are both weak acids, yet both turn it red, because both have plenty of hydronium for the cabbage to see.
A red cabbage rainbow
Ask an adult to help you make red cabbage juice: chop a quarter of a red cabbage, cover it with warm tap water, leave it for 10 minutes, then strain the purple liquid into a jug. Set out five clear glasses with a little juice in each. Add, one to each glass: a squeeze of lemon juice, a spoonful of white vinegar, nothing (plain juice), a pinch of baking soda, and a bigger spoonful of baking soda. (More baking soda deepens the blue-green but cannot push the pH much past 8, so do not expect yellow. If an adult has washing soda, the laundry powder, they can add a pinch to a sixth glass for a clear green; it stings eyes and skin, so it is theirs to handle.) Before each one goes in, say out loud what colour you expect. Line them up from most acidic to most basic and you have a pH rainbow. Can you guess where milk, sugar water or salt water will land before you test them?
Careful
“pH 2 is twice as acidic as pH 4.”
pH 2 has 10⁻² mol/L of hydronium and pH 4 has 10⁻⁴ mol/L. That is a difference of two powers of ten: 10 × 10 = 100 times more hydronium, not twice as much.
Investigation 7.3
Start with 0.10 mol/L hydrochloric acid and dilute it tenfold, then tenfold again, then again. Before each step, predict the new pH. What happens to the hydronium concentration each time?
Understand itpH
What is it?
A single number that says how acidic or basic a solution is: 7 is neutral, lower is more acidic, higher is more basic. Each step of one means ten times more or less hydronium, the particle that makes a solution acidic.
Why is it called this?
Søren Sørensen invented it in 1909. The H stands for hydrogen. What the p stood for, he never explained, and people still argue: perhaps “power” (Potenz in German, puissance in French), perhaps “potential”, perhaps nothing at all.
What problem did it solve?
Acidity was written as clumsy numbers like 0.000 000 1 moles per litre. Sørensen, studying brewing, needed a quick, easy way to record it. Counting the powers of ten gave one.
Why does it work?
It counts the powers of ten in the hydronium concentration: 10⁻³ mol/L becomes pH 3. A huge range of numbers shrinks to a short, friendly scale.
How does it help?
Gardeners, doctors, swimming-pool cleaners and chemists all use it to keep things in the right range: soil, blood, pool water, a reaction in a flask.
Go deeper how do we know, what it isn’t, where does it stop working
How do we know?
A pH meter, built on the glass electrode of 1909, measures it directly; indicators like red cabbage juice change colour along the scale.
What it isn’t
It is not an ordinary ruler. pH 2 is not twice as acidic as pH 4; it has a hundred times more hydronium.
Where does it stop working?
The scale is not fenced in at 0 and 14: very concentrated acids can go below 0. And “7 is neutral” is exact only at 25 °C; neutral pure water is a little below 7 when it is warmer.
Your turn
Explain pH to a friend in one sentence, in your own words. Then compare it with the book’s.
A single number that says how acidic or basic a solution is: 7 is neutral, lower is more acidic, higher is more basic. Each step of one means ten times more or less hydronium, the particle that makes a solution acidic.
Check yourself
You have 1.0 L of a strong acid at pH 2. How much water must you add to raise its pH to 4?
Going from pH 2 to pH 4 means a hundred times less hydronium per litre, so the acid must be spread through 100 times the volume: a total of 100 L. You need to add 99 L of water. (This works for a strong acid, where every molecule has already given up its proton.)
7.4Titration curves and buffers
How do you find out how much acid is in an unlabelled bottle? French chemists worked out the answer in the decades around 1800, when bleach and soda makers needed to know exactly how strong their solutions were. Around 1791 François Descroizilles built an early graduated tube for adding a liquid little by little, and in 1824 Joseph Gay-Lussac, whom you met in Chapter 6 measuring gas volumes, refined it and gave it its name: the burette. You let the unknown acid react with a base whose concentration you already know, adding the base drop by drop from the burette and measuring the pH as you go. This is a titration. The base used is usually sodium hydroxide, NaOH, which gives OH⁻ ions; each OH⁻ grabs one proton from the acid to make a water molecule.
Figure 7.4 shows two titrations, calculated from measured constants. Each flask holds 25 mL of acid at 0.10 mol/L, which is 2.5 thousandths of a mole (2.5 mmol). The burette holds 0.10 mol/L sodium hydroxide, so it takes exactly 25 mL of base to match the acid proton for proton. That point is called the equivalence point.
Predict first: before you look at Figure 7.4, take a pencil and sketch what you think the pH does as the base goes in, from 0 mL to 40 mL. A straight line climbing steadily? Something else? Most people draw a straight line.
Figure 7.4Calculated titration curves: 25 mL of 0.10 mol/L acid with 0.10 mol/L sodium hydroxide. Both acids need 25 mL to reach the equivalence point. Near it, a single drop sends the pH leaping upwards. The weak acid’s curve has a long, gently sloping stretch, its buffer region, shaded.
It is not a straight line. Both curves stay low at first and then shoot up almost vertically near 25 mL. The flat start does not mean nothing is happening: every drop of base is reacting, but there is so much acid left that each drop’s OH⁻ is grabbed at once and the hydronium hardly changes. Only the last few drops find no acid left to react with, so the OH⁻ piles up. But look at the middle of the weak acid’s curve. For a long stretch, adding base barely changes the pH. That stretch is a buffer.
Here is why. Halfway through, half the acetic acid has been turned into acetate ions, CH₃COO⁻, so the flask contains plenty of both. Any OH⁻ you add is grabbed by a whole acetic acid molecule (CH₃COOH + OH⁻ → CH₃COO⁻ + H₂O) before it can pile up. Any extra acid you add is grabbed by an acetate ion. The pH depends on the ratio of acetic acid to acetate, and adding a little of either only nudges that ratio. At exactly halfway, when the two amounts are equal, the pH is 4.74, a number that is fixed by how strong acetic acid is.
The same base, two different destinations. Start with 50 mL of an acetate buffer containing 2.5 mmol of acetic acid and 2.5 mmol of acetate (pH 4.74). Add 10 mL of 0.10 mol/L sodium hydroxide, which is 1.0 mmol of OH⁻.
In the buffer: acetic acid falls to 1.5 mmol and acetate rises to 3.5 mmol. The pH rises from 4.74 to about 5.11, a change of about 0.37.
In 50 mL of pure water instead: the 1.0 mmol of OH⁻ has nothing to react with. The pH jumps from 7.0 to about 12.2.
Boston, 1908
The American physician and chemist Lawrence Henderson wanted to know how blood keeps its acidity so steady. In 1908 he showed that it is a buffer of exactly this kind, built from carbonic acid and hydrogencarbonate ions (the same hydrogencarbonate that is in baking soda), and he wrote down the rule linking the pH to the ratio of the two. It is why a hard sprint, which pours acid into your blood, changes its pH by so little.
A buffer race
You can feel Henderson’s buffer at work with the very same pair of particles. Pour a little red cabbage juice into two glasses and top each up with half a cup of water. Into glass B only, stir a small pinch of baking soda (it turns blue). Now add lemon juice to both glasses, one drop at a time, counting the drops.
Predict first: which glass will turn pink first, and by how much?
Glass A turns pink within a handful of drops. Glass B drifts from blue to purple and then holds its colour stubbornly for dozens more drops, because each drop of acid is being mopped up by hydrogencarbonate. Only when that runs out does it give way and turn pink. A buffer, its capacity, and the end of its capacity, all in one glass.
Careful
“A buffer stops the pH from changing at all.”
A buffer slows the change; it does not stop it. Every bit of base you add uses up some of the weak acid. Once the weak acid runs out, the pH climbs as fast as in plain water. That is exactly what happens near the equivalence point in Figure 7.4. How much a buffer can absorb before it gives way is called its capacity.
A kitchen titration
Put a quarter of a cup of red cabbage juice in a glass and stir in half a teaspoon of baking soda: it turns blue-green. Now add white vinegar one teaspoon at a time, stirring and counting. (It will fizz: that is carbon dioxide.) Write down the colour after each spoonful. For the first few spoonfuls the colour hardly moves, but look at the fizz: every spoonful is reacting, using up some of the soda. Then, when the soda is nearly gone, the colour swings through purple to pink. Repeat with a whole teaspoon of baking soda. Does it take about twice as many spoonfuls? You have just done a titration, with a spoon for a burette and a cabbage for a pH meter.
Investigation 7.4
Step the sodium hydroxide from 0 mL to 12 mL, 24 mL, 26 mL and 40 mL, first for hydrochloric acid and then for acetic acid. Where is the pH most stubborn, and where does one drop change everything?
Understand itBuffer
What is it?
A mixture of a weak acid and the particle it forms when it gives up a proton. It soaks up small amounts of added acid or base, so the pH hardly changes.
Why is it called this?
After the cushioning pads, like the buffers at the end of a railway line, that soften a knock. The French chemists Fernbach and Hubert described the effect as a tampon (a cushion or pad) in 1900; it became Puffer in German and buffer in English.
What problem did it solve?
Living things only work in a narrow range of acidity. Henderson, in 1908, wanted to know how blood stays so steady when the body keeps making acid. Buffers were the answer.
Why does it work?
The weak acid mops up any base that arrives, and its partner particle mops up any acid. Both stay in the solution, ready for the next drop.
How does it help?
It keeps your blood, the oceans and many medicines and foods at a safe, steady pH, and lets chemists hold a reaction at the acidity they need.
Go deeper how do we know, what it isn’t, where does it stop working
How do we know?
Add the same drops of acid to plain cabbage juice and to cabbage juice with a pinch of baking soda: the plain one changes colour almost at once, the buffered one holds out.
What it isn’t
It does not stop the pH from changing at all. It only slows the change.
Where does it stop working?
Every buffer has a limit. Once its weak acid or its partner particle is used up, the pH changes as fast as in plain water. Each buffer also works best near its own particular pH.
Your turn
Explain Buffer to a friend in one sentence, in your own words. Then compare it with the book’s.
A mixture of a weak acid and the particle it forms when it gives up a proton. It soaks up small amounts of added acid or base, so the pH hardly changes.
Check yourself
Why does a mixture of acetic acid and acetate resist a change in pH when a small amount of sodium hydroxide is added?
The added OH⁻ ions react with intact acetic acid molecules, CH₃COOH + OH⁻ → CH₃COO⁻ + H₂O, instead of staying free in the solution. The amounts of acetic acid and acetate only change a little, so their ratio, and hence the pH, changes only a little. It works until the acetic acid runs out.
Case file 7
The two bottles at pH 3
Two unlabelled flasks both read exactly pH 3.00 on a pH meter. One contains hydrochloric acid and the other acetic acid. You take 25 mL from each and titrate it with 0.10 mol/L sodium hydroxide.
Flask A reaches its equivalence point after only 0.25 mL of sodium hydroxide, a few drops.
Flask B needs 14.1 mL of sodium hydroxide to reach its equivalence point.
After 5.0 mL of sodium hydroxide, Flask A reads about pH 12.2 and Flask B about pH 4.5.
Which flask holds which acid? Both have the same pH, so how can one contain about 57 times more acid than the other?
Show the solution
Flask A is hydrochloric acid and Flask B is acetic acid.
Equal pH means equal concentrations of hydronium ions, 10⁻³ = 0.0010 mol/L. It does not mean equal amounts of acid. Hydrochloric acid gives up every proton, so it only needs 0.0010 mol/L of acid to reach pH 3: 25 mL holds 0.025 mmol, matched by 0.25 mL of the base (clue 1). Acetic acid gives up only a small fraction of its protons, so to reach the same hydronium concentration it must be about 0.057 mol/L: 25 mL holds about 1.41 mmol, which needs 14.1 mL of base (clue 2). That is about 57 times more acid, almost all of it hiding as whole molecules that the pH meter cannot see.
Clue 3 shows the difference in action. After 5.0 mL, Flask A’s tiny amount of acid is long gone and the extra OH⁻ sends the pH soaring. In Flask B the base has turned some acetic acid into acetate, making a buffer, so the pH has only crept up to about 4.5.
What this chapter can’t explain yet
In this chapter the thing being passed from particle to particle was a proton. In the next, it is an electron. Back in Chapter 6 you saw Nicholson and Carlisle split water with Volta’s brand-new battery. Next you find out how that battery worked: when zinc metal meets copper ions, electrons jump from one to the other, and if you can make them travel through a wire on the way, you have built a battery.
8
Chapter 8
Electron transfer and electrochemistry
The big questionPut a strip of zinc into blue copper sulfate solution and it gets coated with copper while the liquid warms up. Split the very same chemicals between two beakers joined by a wire, and they can light a bulb. How does a chemical reaction push electricity through a wire?
Luigi Galvani was a doctor who taught anatomy at the University of Bologna, a careful, devout man more at home with nerves and muscles than with machines. In his laboratory, often working alongside his wife Lucia, he was dissecting frogs. One day, so the story goes, a frog’s leg twitched when a metal scalpel touched a nerve while an electrical machine was sparking nearby. Galvani spent years on it, and he found that a leg would twitch even with no machine at all, if it was touched by two different metals at once. He published in 1791 and concluded that living things make their own “animal electricity”.
A few hundred kilometres away in Pavia, the physicist Alessandro Volta read Galvani’s work and disagreed. Volta was a restless experimenter who had already discovered methane by poking at the mud of marshes and catching the bubbles, and he trusted instruments more than theories. The electricity, he thought, did not come from the frog. It came from the two metals; the wet frog leg was only a damp path between them. To prove it he left out the frog altogether. He piled up discs of zinc and copper, with cardboard soaked in salt water between each pair, and in 1800 he announced the result: a steady flow of electricity from a stack of metal and wet card. It was the first battery, and in 1801 he was demonstrating it to Napoleon in Paris.
Neither man knew what was really moving. That took another century, and the discovery of the electron. In Chapter 7, acids and bases passed protons from one particle to another. This chapter is about the second great family of reactions, in which the thing passed along is an electron. These reactions rust iron, tarnish silver, burn fuel and release the energy from your food. And because electrons moving through a wire are an electric current, they are how every battery works, from Volta’s pile to the one in a phone.
8.1When metals and ions trade electrons
Here is a piece of chemistry that looks like a magic trick. Take a strip of dull grey zinc and lower it into a beaker of clear blue copper(II) sulfate solution. Within minutes the grey strip starts to blush: a crumbly reddish-brown coat of copper grows over it, as if the metal were turning into a different one before your eyes. The blue colour of the liquid slowly fades. The beaker gets slightly warm. Test the liquid afterwards and you find zinc dissolved in it that was not there before.
Predict first. Where did that copper come from? (a) Some of the zinc turned into copper. (b) It came out of the air. (c) It was in the blue liquid all along. Choose before you read on, and notice the clue you have been given: the blue colour faded.
Nothing magic has happened, and nothing has turned into anything else. The answer is (c). The particle story is a swap. The blue colour comes from copper ions, Cu²⁺, in the water. Each Cu²⁺ ion has 29 protons and only 27 electrons. When one bumps into the surface of the zinc, a zinc atom (30 protons, 30 electrons) hands over two electrons. The zinc atom becomes a Zn²⁺ ion (30 protons, 28 electrons) and drifts off into the water. The copper ion becomes a neutral copper atom (29 protons, 29 electrons) and stays stuck to the strip as metal.
Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s)
The letters in brackets say what state each thing is in: (s) for solid, (aq) for dissolved in water, from aqua.
Figure 8.1Zinc meets copper ions. Before: zinc atoms in the strip, Cu²⁺ ions in the solution. Each zinc atom that reacts passes two electrons to one copper ion. After: zinc has gone into solution as Zn²⁺, and copper atoms sit on the strip as metal. Sulfate ions take no part.
The words chemists use for this have a history. In Lavoisier’s day, to “oxidise” something meant to combine it with oxygen, as iron does when it rusts. Once the electron was discovered in 1897, chemists saw that what really matters in rusting, burning and this zinc-and-copper swap is the same thing: electrons leaving one substance for another. So the words were widened. Losing electrons is now called oxidation. Gaining electrons is called reduction. They always happen together, because an electron that leaves one particle must go to another; there are no spare electrons floating loose in the water. A reaction like this is a redox reaction: reduction plus oxidation. A memory trick many chemists use is OIL RIG: Oxidation Is Loss, Reduction Is Gain.
If you meet oxidation described as gaining oxygen, that is the same event seen from outside: when magnesium burns, 2 Mg + O₂ → 2 MgO, each magnesium atom gains oxygen by handing it two electrons; the electron version is simply wider, because it also covers swaps like zinc and copper, where no oxygen takes part at all.
Notice what stays the same. Every nucleus is untouched: zinc stays zinc and copper stays copper, because their proton numbers never change. The alchemists who dreamed of turning cheap metals into precious ones would have been delighted by the copper coat on the zinc, and disappointed to learn that the copper was in the beaker all along. The beaker also contains sulfate ions, SO₄²⁻, but they come out exactly as they went in. Ions that are present but take no part are called spectator ions, and chemists usually leave them out of the equation.
Careful
“The zinc gives the copper two protons, and that turns it into copper.”
Chemical reactions never move protons out of a nucleus. Copper ions are already copper (29 protons); they only lack two electrons. What moves is electrons, from the outside of the zinc atoms to the copper ions. Count the protons before and after and you will find 30 and 29 both times.
Understand itRedox
What is it?
A reaction in which electrons pass from one substance to another. The one that loses electrons is oxidised; the one that gains them is reduced. The two always happen together.
Why is it called this?
Reduction plus oxidation. “Oxidation” comes from oxygen, a name Lavoisier made up in 1777 from Greek words meaning “acid-maker” (he wrongly thought every acid contained it). “Reduction” is from the Latin for “leading back”: heating an ore led the metal back out of it, and the ore got lighter as oxygen left as a gas. Both names are older than the electron, so they mislead a little: oxidation needs no oxygen at all, as zinc and copper show.
What problem did it solve?
Rusting, burning, tarnishing, one metal coating another, and batteries all looked like separate puzzles. Once the electron was found in 1897, chemists saw they are one event: electrons moving from one substance to another.
Why does it work?
When an exchange of electrons gives out energy overall, as zinc meeting copper ions does, the electrons move in that direction and not the other. Every electron one particle loses, another must gain, because there are no spare electrons floating loose in the water.
How does it help?
You can predict which metal will coat which (the reactivity series), balance equations by counting electrons as well as atoms, and understand batteries, rust and how metals are got out of their ores.
Go deeper how do we know, what it isn’t, where does it stop working
How do we know?
Watch and weigh: the zinc wastes away, copper appears and the blue of the copper ions fades. Put the two halves in separate beakers joined by a wire and a salt bridge, and a meter shows the electrons flowing through it, exactly as the half-equations say.
What it isn’t
Not one element turning into another. Every nucleus is untouched: the copper was in the liquid all along as ions, and only electrons moved.
Where does it stop working?
In many reactions electrons are shared rather than handed over completely, as in the covalent bonds of Chapter 2. Chemists still keep redox accounts there, using “oxidation numbers”, but then it is careful bookkeeping, not a picture of whole electrons jumping across.
Your turn
Explain Redox to a friend in one sentence, in your own words. Then compare it with the book’s.
A reaction in which electrons pass from one substance to another. The one that loses electrons is oxidised; the one that gains them is reduced. The two always happen together.
Copper out of a blue liquid
You need plenty of old, dull copper, a good handful: tarnished scraps from an old copper vessel, or old wire gone brown (Indian coins are no longer copper). Bright new wire works poorly, because it is the dull coating that dissolves first. Put the copper in a small glass jar with as little white vinegar as will cover it, stir in a teaspoon of salt, and leave it for a day or two with the lid off, swirling now and then. Often you cannot see any colour, but copper ions have gone into the liquid. Now scrub an iron nail clean and bright and stand it in the liquid overnight. Predict first: what will its surface look like?
It comes out with a thin, patchy pinkish-copper coat. (If you see only a dark smudge, the liquid did not get enough copper: add more dull copper and wait another day.) Iron atoms have handed electrons to the copper ions, exactly as the zinc did. For a second race, stand another clean nail in plain salty water beside it: that one rusts instead. Both nails are losing electrons, to copper ions in one jar and to oxygen from the air in the other. (Pour the liquids away afterwards, and wash your hands. Nothing here is for eating.)
Investigation 8.1
Step the reaction forward one group at a time, up to four. For each step, write how many zinc atoms have been oxidised, how many copper ions reduced, and how many electrons have moved. What is the rule linking the three numbers?
Check yourself
In Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s), which particle is oxidised and which is reduced? How many electrons move for every zinc atom that reacts?
Zinc is oxidised (it loses electrons, Zn → Zn²⁺). Copper ions are reduced (they gain electrons, Cu²⁺ → Cu). Two electrons move for every zinc atom, because zinc goes from a charge of 0 to +2.
8.2Balancing electrons as well as atoms
The Royal Institution, London, 1833
Michael Faraday was a blacksmith’s son who left school early and became a bookbinder’s apprentice, reading the science books he was binding. In 1812 a customer gave him tickets to hear Humphry Davy lecture at the Royal Institution. Faraday wrote up his notes, bound them beautifully, sent them to Davy, and soon afterwards got a job as his assistant, washing bottles. By the 1830s he was the most famous experimenter in Britain, and he wanted to know how much chemistry a given amount of electricity could do. He passed electric currents through solutions of different metals’ salts and weighed the metal that formed on the plates.
He found a rule so clean that it surprised everyone. Before you read it, predict: suppose a certain amount of electricity deposits 108 grams of silver. Pass exactly the same amount through a copper solution instead. Will you get more copper, the same, or less?
The answer: the same amount of electricity always produced the same number of “chemical portions” (what he called equivalents) of each substance, but not the same mass, and not the same number of atoms for every metal. In today’s numbers, the charge that deposits about 108 grams of silver deposits only about 32 grams of copper. That is half as many copper atoms as silver atoms. Faraday never knew why. We do: each copper ion needs two electrons to become an atom, while each silver ion needs only one. Faraday’s balance was counting electrons sixty years before anyone discovered them.
Here is the same idea in a beaker. Put a ribbon of magnesium into a solution of silver nitrate, and needles of shiny silver crystals grow on it while the magnesium dissolves. A magnesium atom loses two electrons to become Mg²⁺. But a silver ion, Ag⁺, has a charge of only +1, so it can take only one electron to become a silver atom. Where does the second electron go?
To a second silver ion. For every magnesium atom that reacts, two silver atoms appear:
Mg(s) + 2 Ag⁺(aq) → Mg²⁺(aq) + 2 Ag(s)
A handy way to see this is to split the reaction into two half-equations, one for each side of the swap, with the electrons written in:
oxidation: Mg → Mg²⁺ + 2 e⁻
reduction: Ag⁺ + e⁻ → Ag (needed twice: 2 Ag⁺ + 2 e⁻ → 2 Ag)
electrons given = 2, electrons taken = 2, so they cancel when you add the two halves
The rule is the one from the front of the book, count everything, with one extra thing to count. A balanced redox equation must have the same number of atoms of each element on both sides and the same total electric charge on both sides. Check it: on the left, Mg has charge 0 and two Ag⁺ ions have +2; on the right, Mg²⁺ has +2 and two silver atoms have 0. Both sides total +2.
Figure 8.2Matching electrons given with electrons taken. One magnesium atom gives two electrons, so it needs two silver ions. Two aluminium atoms give six electrons, which three copper ions can take. The smallest numbers that make the electrons match are the numbers in the equation.
Try writing it the lazy way, Mg + Ag⁺ → Mg²⁺ + Ag. The atoms balance, one of each. But the charge does not: +1 on the left, +2 on the right. One electron has appeared from nowhere, and electrons, like atoms, are never created or destroyed in a chemical reaction.
The same idea works for harder pairs. Aluminium forms Al³⁺ (losing three electrons), and each copper ion takes two. The smallest number that both 3 and 2 go into is 6, so two aluminium atoms give six electrons to three copper ions:
2 Al(s) + 3 Cu²⁺(aq) → 2 Al³⁺(aq) + 3 Cu(s)
Careful
“One magnesium atom splits into two silver atoms.”
Atoms of one element never turn into another in a chemical reaction. Each silver atom was a silver ion in the solution all along; it was waiting for one electron. The magnesium atom supplies two electrons, and so two silver ions become silver metal. (Silver atoms are also more than four times heavier than magnesium atoms, so a magnesium atom could not possibly “split” into two of them.)
Investigation 8.2
Choose Mg + 2 Ag⁺ and step the reaction forward. Compare the number of Mg²⁺ ions made with the number of silver atoms plated. Then switch to 2 Al + 3 Cu²⁺ and predict the numbers before you look.
Check yourself
Aluminium forms Al³⁺ and silver ions are Ag⁺. Write the balanced equation for aluminium metal reacting with silver ions, and check that the charge is the same on both sides.
Al(s) + 3 Ag⁺(aq) → Al³⁺(aq) + 3 Ag(s). One aluminium atom gives three electrons, and each silver ion takes one, so three silver ions are needed. Charge on the left: 0 + 3 × (+1) = +3. On the right: +3 + 0 = +3. Balanced.
8.3Why doesn’t copper dissolve in zinc sulfate?
Alchemists loved to grow glittering crystal “trees” of silver in their flasks, and gave them names like the Tree of Diana. You can grow one with no mystery at all: hang a coil of copper wire in colourless silver nitrate solution, and over an hour a sparkling tree of silver crystals grows on it while the liquid slowly turns blue. Copper is giving electrons to silver ions, and going into solution as blue Cu²⁺.
So try the obvious next experiment. Zinc dropped into copper ions gets coated in copper. What about a piece of copper dropped into colourless zinc sulfate solution? You can write the equation perfectly well:
Cu(s) + Zn²⁺(aq) → Cu²⁺(aq) + Zn(s)
It balances for atoms (one copper, one zinc on each side) and for charge (+2 on each side). And yet, if you try it, nothing happens. Leave the copper there for a day, a week, a month: it stays shiny and the liquid stays colourless. Put the silver from your tree into copper sulfate, and nothing happens either.
This is the lesson of section 4.4 again, now with electrons: a balanced equation tells you what would be conserved if a reaction happened. It does not tell you that the reaction happens. Electron transfer has a direction. Electrons move readily from zinc to copper ions, but not from copper to zinc ions, like water that runs down a staircase but never climbs back up on its own. The reason is the total energy change, which includes pulling atoms out of the solid metal and water molecules gathering round the new ions, not just how tightly a lone atom holds its outer electrons. The forward reaction gives out energy (that is why the beaker warmed up), and running it backwards would need that energy to be put back in.
By testing metals against each other’s ions, every pairing, chemists in the 1800s found one consistent order, with zinc above copper above silver. They lined the metals up in order of how readily they give away electrons, and called it the reactivity series. A metal higher in the series pushes the ions of a lower metal out of solution and coats itself with that metal; a lower metal does nothing to the ions of a higher one. The same order shows up again as the voltage when the metals are made into cells, as you will see next.
Figure 8.3Nine experiments, three metals, three solutions. A reaction happens only when a metal meets the ions of a metal below it in the series. Putting a metal into its own ions changes nothing.
Careful
“Copper doesn’t react with zinc sulfate because the equation can’t be balanced.”
It balances perfectly, for atoms and for charge. The reason is energy, not bookkeeping: electrons do not pass from copper to zinc ions on their own, because that would be an uphill move. Balance is necessary for any real reaction, but it never proves one will happen.
Clean silver with aluminium foil (with an adult)
Find a silver spoon, puja item or anklet gone black with tarnish. The black is silver sulfide: silver that has given electrons to sulfur from the air. Aluminium, higher in the series, can push those electrons back. Line a bowl with aluminium foil, shiny side up. Ask an adult to pour in hot water from the kettle, then stir in a tablespoon each of baking soda and salt. Using a wooden spoon or tongs, not fingers (the water is hot), lay the tarnished silver in the water so it touches the foil. Predict first: what will happen to the black, and does it matter whether the silver touches the foil?
Within minutes the black fades and the silver shines: aluminium atoms give up electrons and silver ions take them back. With the silver not touching the foil, very little happens, because the electrons need a path. Keep a window open for the faint smell of rotten eggs (hydrogen sulfide). Don’t use it on “oxidised” jewellery, which is blackened on purpose, or on valuable antiques.
Investigation 8.3
Compare zinc in Cu²⁺ with copper in Zn²⁺. Predict what the model will show for the second before you switch to it. Then explain why a balanced equation was not enough to decide.
Check yourself
Magnesium is above zinc in the reactivity series. What happens if you put magnesium ribbon into zinc sulfate solution? What happens if you put zinc into magnesium sulfate solution?
Magnesium in zinc sulfate: magnesium gives electrons to Zn²⁺ ions, so zinc metal forms on the ribbon and Mg²⁺ goes into solution. Zinc in magnesium sulfate: nothing happens, because zinc is below magnesium and cannot push electrons onto Mg²⁺.
8.4Galvanic cells and recharging
King’s College London, 1836
Volta’s pile made electricity, but it was a frustrating thing to use. Within minutes its current faded, because bubbles of hydrogen gas collected on the metal plates and smothered the reaction. John Frederic Daniell, the first professor of chemistry at the new King’s College, was a practical man who had already invented an instrument for measuring the moisture in the air. He wanted a battery that would keep going.
Think about what happens when zinc sits in copper sulfate. The electrons jump straight from zinc atoms to copper ions at the surface of the strip. The energy comes out as a little warmth and then it is gone. Daniell’s idea was to make those same electrons travel somewhere useful on the way.
He separated the two halves of the reaction. A zinc plate stands in a beaker of zinc sulfate; a copper plate stands in a beaker of copper sulfate. Now the zinc atoms cannot reach any copper ions. Connect the two plates with a wire, though, and the electrons have a road. Zinc atoms give up electrons, which travel through the wire to the copper plate, where copper ions from the solution collect them and become copper metal. Electrons flowing through a wire are an electric current, so a bulb or a small motor in the wire will run. A cell that turns a chemical reaction into electricity like this is called a galvanic cell, after Galvani and his frogs.
Figure 8.4A Daniell cell. Electrons leave the zinc (where oxidation happens) and travel through the wire to the copper (where reduction happens). In the salt bridge, ions move to keep both beakers electrically balanced: negative ions towards the zinc side, positive ions towards the copper side. With standard solutions the cell gives 1.10 volts.
There is one more part, and it is easy to overlook. As zinc dissolves, the left beaker fills up with extra Zn²⁺ ions, more positive charge than negative. As copper plates out, the right beaker loses Cu²⁺ ions and is left with extra negative sulfate ions. Within a fraction of a second, the build-up of charge would stop the current completely. The fix is a salt bridge: a tube or a strip of paper soaked in a salt solution, such as potassium nitrate, dipped into both beakers. (Daniell’s first cells used a barrier of animal membrane, and later ones a porous clay pot, which do the same job.) Its ions drift to cancel the build-up: nitrate ions (negative) move towards the zinc beaker, potassium ions (positive) towards the copper beaker. Electrons carry the current through the wire; ions carry it through the liquids. Only together do they make a complete loop.
The two plates have names. The anode is where oxidation happens (here, zinc), and the cathode is where reduction happens (here, copper). As the cell runs, the zinc plate gets thinner and the copper plate gets thicker. In a cell like this one, the anode is the negative terminal, which surprises many people: isn’t the zinc losing electrons? Each zinc atom that reacts leaves as a Zn²⁺ ion but leaves its two electrons behind in the metal. Electrons collect in the zinc plate faster than anywhere else, which is exactly why they pour out of it along the wire.
Daniell’s two-liquid design gave a steady current for hours, and it went to work at once: Daniell cells powered many of the early electric telegraphs of the 1840s and 1850s, carrying messages along wires across countries. Measured carefully, a Daniell cell with standard solutions gives 1.10 volts: the size of the push the zinc-to-copper electron transfer can give.
Can you run a cell backwards? Yes, if you push. Connect a power supply that pushes harder than the cell does (more than 1.10 V, the other way round) and you can force electrons onto zinc ions to make zinc metal again, and pull them off copper. Using electricity to drive a reaction that would not go on its own is called electrolysis. It was electrolysis that made Humphry Davy famous. Davy was a woodcarver’s son from Penzance in Cornwall who had taught himself chemistry, tried breathing laughing gas in the name of science, and become the most dazzling lecturer in London. In 1807, using a giant version of Volta’s pile, he passed a current through melted potash and watched tiny globules of a new metal burst out and catch fire: potassium. Days later he made sodium the same way. Both had been locked in their compounds so tightly that no ordinary chemistry could free them.
And recharging a phone battery is exactly this idea: the charger pushes the battery’s reaction backwards, storing energy that the battery gives out again later. (The chemistry inside a phone is different from Daniell’s cell, and Chapter 11 looks at it.)
Understand itElectrolysis
What is it?
Using electricity from outside to drive a chemical reaction that would not happen on its own: pushing electrons where they would not go by themselves.
Why is it called this?
Michael Faraday introduced the word in 1834, prompted by the scholar William Whewell. It means “loosening by electricity”, from the Greek lysis, a loosening, because the current pulls a compound apart. The same pair gave us anode and cathode (Greek for “way up” and “way down”) and ion, “one that goes”.
What problem did it solve?
Some elements are locked into their compounds so tightly that no ordinary reaction can free them. Electrolysis prised them out: Humphry Davy made potassium and sodium this way in 1807, and it is still how aluminium, sodium and chlorine are made today.
Why does it work?
A power supply pushes electrons onto one electrode and pulls them off the other, harder than the reaction can push back. Ions drift to the electrode of opposite charge, where they gain or lose electrons and become atoms or molecules again.
How does it help?
It makes metals and gases we could not otherwise get, coats objects with a thin layer of metal (electroplating), and it is exactly what a charger does to a rechargeable battery.
Go deeper how do we know, what it isn’t, where does it stop working
How do we know?
Faraday weighed what the current deposited. In today’s numbers, the same amount of electricity that deposits about 108 g of silver deposits only about 32 g of copper: half as many atoms, because each copper ion needs two electrons and each silver ion one.
What it isn’t
Not the current smashing the compound like a hammer. It delivers electrons one at a time, and the energy goes into moving them uphill.
Where does it stop working?
It costs a great deal of energy: making one kilogram of aluminium takes about 15 units (kilowatt-hours) of electricity, as much as a ceiling fan uses running day and night for more than a week. And what forms at each electrode depends on everything in the beaker; in salty water you get hydrogen, not sodium, because water molecules take the electrons more easily.
Your turn
Explain Electrolysis to a friend in one sentence, in your own words. Then compare it with the book’s.
Using electricity from outside to drive a chemical reaction that would not happen on its own: pushing electrons where they would not go by themselves.
Careful
“The electrons travel through the salt bridge to get back to the zinc.”
Free electrons do not travel through water or salt solution. In the wire and the metal plates, current is carried by electrons. In the solutions and the salt bridge, it is carried by ions drifting in opposite directions. The loop is complete, but it is made of two different kinds of traffic.
A lemon battery (with an adult)
You can repeat Volta’s argument with Galvani on the kitchen table. You need three lemons, four pieces of thick copper wire (stripped electrical wire is fine; Indian coins are not copper), three galvanised (zinc-coated) iron nails or screws, four short wires with crocodile clips, and a small red LED. If anyone has a cheap multimeter, borrow it too. Roll each lemon on the table to loosen the juice inside.
Predict first. Push two copper pieces into one lemon, a few centimetres apart, and connect them to the LED or the meter. Will anything happen? Then swap one copper piece for the zinc-coated nail. What changes?
With two coppers, nothing worth measuring (a meter reads close to zero): the same metal on both sides gives no push, however juicy the lemon. With copper and zinc, the meter shows a bit under one volt. The lemon is only the damp path, as Volta said of the frog; the push comes from the two different metals. One lemon is not quite enough for most LEDs, so make two or three lemon cells and join them in a chain, the copper of one to the zinc of the next, and look closely in a dim room (if the LED stays dark, turn it round: it only works one way). Plain iron nails work too, but you need five or six lemons, because iron sits lower than zinc in the reactivity series and gives a smaller push.
Now a harder question. Leave the LED glowing for an hour. What has been used up: the electrons, the lemon, or the zinc? Throw the lemons away afterwards rather than eating them, because some zinc will have dissolved into the juice.
Careful
“A battery is full of electrons, and it goes flat when they are used up.”
Electrons are never used up. Every electron that leaves the zinc goes round the wire, through the LED, and into the copper; the same number come out of one end as go in the other. What gets used up in the lemon is zinc atoms, which go into the juice as Zn²⁺ ions, and hydrogen ions in the juice, which take the electrons at the copper and become hydrogen gas. A battery is a store of chemicals that will react as soon as they are given a path; the electrons are only the go-between. When the chemicals run out, the push stops.
Understand itThe battery
What does it do?
A battery is a store of chemicals that are ready to react, arranged so that the electrons they exchange must travel through a wire, doing useful work on the way.
Why is it called this?
Around 1749 Benjamin Franklin called a row of linked electrical jars a “battery”, probably because it looked like a battery of cannon lined up to fire together. The word fitted Volta’s pile of 1800, a stack of many cells. A single cell like Daniell’s is called galvanic, after Galvani and his frogs, even though Volta showed Galvani was wrong about where the electricity came from.
What problem did it solve?
Before 1800, electricity came only in sudden sparks from friction machines and charged jars. Volta’s pile gave the first steady current, and Daniell’s cell of 1836 kept it steady for hours, enough to run the electric telegraph.
Why does it work?
Two different materials pass electrons on with different ease. Keep them apart, give the electrons a wire and the ions a salt bridge, and the electrons run downhill through the wire, from the material that lets them go to the one that takes them.
How does it help?
Every torch, phone and electric car runs on one. And a cell’s voltage measures how hard one metal pushes electrons onto another: the reactivity series, read off a meter.
Go deeper how do we know, what it isn’t, where does it stop working
How do we know?
Two copper pieces in a lemon give almost no voltage; copper and zinc give nearly a volt. The push comes from the difference between two materials, not from the lemon, just as Volta argued against Galvani.
What it isn’t
Not a tank of electrons that empties. Every electron that leaves goes round the circuit and back in; it is the chemicals, such as zinc atoms and hydrogen ions, that run out.
Where does it stop working?
When a reacting chemical runs out, the push stops. Most cells can’t be reversed. Rechargeable ones can be pushed backwards by a charger, but even they slowly wear out as side reactions trap some of their chemicals.
Your turn
Explain The battery to a friend in one sentence, in your own words. Then compare it with the book’s.
A battery is a store of chemicals that are ready to react, arranged so that the electrons they exchange must travel through a wire, doing useful work on the way.
Investigation 8.4
Run the Zn | Cu cell for two groups. Track which plate loses atoms, which gains them, how many electrons go through the wire, and which way the bridge ions move. Then switch to the reverse direction: what has to be added to make it go?
Check yourself
As a Daniell cell runs, which plate gets heavier and which gets lighter? Explain using the half-equations.
The copper plate (cathode) gets heavier, because Cu²⁺ + 2 e⁻ → Cu adds copper atoms to it. The zinc plate (anode) gets lighter, because Zn → Zn²⁺ + 2 e⁻ sends zinc atoms off into the solution as ions.
Case file 8
The cell that would not light
Riya builds a cell from a magnesium strip in magnesium sulfate solution and a silver strip in silver nitrate solution, in two separate beakers. She joins the strips with wires through a small bulb and an ammeter (a meter that measures current). To keep her solutions pure, she does not join the beakers with anything else.
The bulb never lights. The ammeter reads 0 the whole time.
The metal strips are clean and the solutions are fresh. The wires and the bulb work when tested with a torch battery.
Magnesium is far above silver in the reactivity series: a magnesium ribbon dropped straight into silver nitrate grows silver crystals within a minute or so.
When she dips a strip of filter paper soaked in potassium nitrate solution into both beakers, the bulb glows at once. After an hour, she finds that 0.020 mol of magnesium has dissolved.
Why did nothing happen at first? And how many moles of silver should have formed on the silver strip by the end of the hour?
Show the solution
At first the circuit was not a complete loop. Electrons could travel through the wire, but nothing could carry charge between the two beakers. If even a few magnesium atoms had given up electrons, the magnesium beaker would have gained positive charge and the silver beaker would have been left with extra negative nitrate ions, and that imbalance would instantly have stopped any more electrons from moving. In practice, no measurable current flows at all. Clue 3 shows that the reaction itself is ready to go; clue 2 rules out a broken bulb; clue 4 shows the missing piece was the salt bridge.
Silver: each magnesium atom gives 2 electrons and each silver ion takes 1 (Mg + 2 Ag⁺ → Mg²⁺ + 2 Ag), so 0.020 mol of magnesium makes 2 × 0.020 = 0.040 mol of silver, about 4.3 g.
What this chapter can’t explain yet
Zinc gives its electrons away more readily than copper, and copper more readily than silver; magnesium more readily still. For metals in water, the full reason is an energy account with several entries. But one entry runs through all of chemistry: how tightly an atom holds its outer electrons. That is written into the shape of the periodic table itself, a table that a Russian chemist laid out like a game of patience, half a century before anyone knew what an electron shell was. Chapter 9 reads it.
9
Chapter 9
The shape of the periodic table
The big questionGoing across a row of the periodic table, each atom has one more proton and one more electron than the last. So why do the atoms get smaller, not bigger?
Rockets climb into the dark and burst: crimson, then emerald green, then a gold that crackles, then a deep blue that is the hardest colour of all to make. Every one of those colours was chosen by a chemist. The crimson comes from strontium compounds packed into the shell, the green from barium, the yellow-gold from sodium, the blue from copper. Heat a compound of any one of these metals hot enough and it glows with its own colour, as reliably as a signature.
In the 1850s two friends in Heidelberg turned that signature into an instrument. Robert Bunsen was a tough, kindly chemist who had lost the sight of one eye in a laboratory explosion and carried on regardless; Gustav Kirchhoff was a younger physicist who had worked out the rules of electric circuits while still a student. Bunsen had a burner with an almost colourless flame (the one still named after him), and Kirchhoff passed the light from it through a glass prism. Each element’s glow split into its own pattern of sharp, bright coloured lines, different from every other element’s. In 1860 they found a pair of sky-blue lines that belonged to no known element, and named the new metal caesium, from the Latin for sky-blue. A year later deep red lines gave them rubidium, from the Latin for dark red. Light from a flame had become a way of discovering elements nobody had seen.
Light would keep giving up secrets for the rest of the story. In 1921 an Indian physicist, C. V. Raman, sailing home from England, stared at the deep blue of the Mediterranean and refused to accept the usual explanation that the sea simply reflects the sky. Back in Calcutta he and his students spent years shining light through liquids, and in 1928 they found that a tiny fraction of the scattered light comes out with a slightly different colour, changed by the vibrating molecules it has met. Each kind of molecule changes it in its own way. Raman won the 1930 Nobel Prize in Physics for it, the first Asian scientist to win a Nobel Prize in science, and chemists still use his effect to identify substances by the light they scatter.
By the 1860s chemists knew about sixty elements, and they were drowning in facts about them. Which belonged together, and why?
St Petersburg, 1869
Dmitri Mendeleev was the youngest child of a large family in Tobolsk, in Siberia. His father, a headmaster, went blind; his mother kept the family going by running a glass factory, and when it burned down she took her teenage son thousands of kilometres to St Petersburg so that he could study science. She died soon after he got in. By 1869 he was a professor there, wild-haired and famously impatient, and he was writing a chemistry textbook for his students and needed a sensible order to describe the elements in. He wrote each element’s properties on cards and arranged them, in order of the masses of their atoms, so that elements that behaved alike fell into the same columns. (A famous story says the final arrangement came to him in a dream after days of shuffling the cards like a game of patience. It comes from a friend’s recollection years later, so treat it as a legend.) He did all this without knowing about protons, neutrons or electrons, purely from the way the elements reacted.
His boldest move was to leave gaps. Where the pattern demanded an element nobody had found, he left a space and described what would fill it. Below aluminium, he said, there should be a metal with atoms about 68 times as heavy as hydrogen, a density of about 5.9 grams per cubic centimetre, and a low melting point. In 1875 Paul-Émile Lecoq de Boisbaudran, a largely self-taught French chemist from a family of brandy merchants in Cognac, looking at a zinc ore through exactly the kind of spectroscope Bunsen and Kirchhoff had built, saw two violet lines nobody had seen before. He named the new metal gallium. His first measurement of its density was 4.7. Mendeleev wrote to tell him it should be closer to 5.9; Lecoq purified his sample, measured again, and got 5.9.
A table that predicts things nobody has yet seen must be catching something real. But what? Mendeleev could not say. The answer came in the next fifty years, from the inside of the atom, and you already know the beginning of it: the gold foil of Chapter 1, the nucleus, and the electrons arranged in shells around it. This chapter uses that to explain two of the table’s patterns: the sizes of atoms, and how tightly they hold their electrons.
Rainbows from a CD
You can split light into its colours the way Kirchhoff did, using an old CD or DVD instead of a prism. In a darkened room, hold the shiny side of the disc so that it reflects light from a lamp into your eye, and tilt it until you see a band of colours. Try different lights around the house: an old-style bulb, a white LED, a fluorescent tube, a phone screen. Some give a smooth rainbow; others give separate bright stripes of colour with dark gaps between them. If you can, try an orange sodium street lamp at night: older ones give almost nothing but a single strong yellow-orange band, the same yellow that salt gives a flame. (Never look at the Sun, directly or in the disc.) Then, with an adult at the gas stove, ask them to sprinkle a few grains of table salt onto the blue flame while you stand back (the grains crackle and can jump), and look at the flash through your disc: the same yellow as the street lamp. The flash is brief, so it may take a few tries to catch it. That is Bunsen and Kirchhoff’s discovery, in your kitchen.
9.1Why atoms shrink across a row
Manchester, 1913
Mendeleev had ordered the elements by mass, and in a few places that order was wrong. Tellurium atoms are heavier than iodine atoms, yet tellurium clearly belongs in front of iodine. Mendeleev simply swapped them, trusting the chemistry over the masses. In 1913 Henry Moseley, a young physicist working in Rutherford’s laboratory in Manchester, found out why. He fired electrons at targets made of different elements and measured the X-rays that came off. The X-ray frequency rose in a perfectly regular staircase, one step per element, and the steps counted the positive charge on the nucleus: the number of protons. That number, the atomic number, is the true order of the table, and tellurium (52) comes before iodine (53). Moseley was killed two years later, at Gallipoli in the First World War, at the age of 27.
So the table is built one proton at a time. Across the second row, from lithium to fluorine, every step adds one proton to the nucleus and one electron around it. You might expect each atom to be a little bigger than the one before. Measurements say the opposite. A lithium atom is the largest in the row; a fluorine atom is less than half its width.
How can anyone measure something so small? You cannot put a ruler on an atom, but you can measure the distance between two atoms joined by a bond, by bouncing X-rays off crystals or by studying the light that gases absorb. Half the distance between two bonded atoms of the same element gives a rough size for one atom. The distance changes a little from one compound to another, so chemists average thousands of measurements from many different molecules and crystals. Those averages are the sizes in the next figure.
Figure 9.1Atom sizes, measured as the distance from the centre of an atom to the edge of its share of a bond (in picometres, pm: millionths of a millionth of a metre). Across row 2 the atoms shrink; going down column 1 they grow. Circles are drawn to scale with each other.
To see why, think about the electrons as two teams. Lithium has 3 protons and 3 electrons: 2 electrons in the inner shell and 1 in the outer shell. Fluorine has 9 protons and 9 electrons: the same 2 inner electrons, and 7 outer ones. In every atom of row 2 the outer electrons are in the same shell, and the inner shell is the same two electrons.
The outer electrons are pulled inwards by the protons, and pushed outwards by the other electrons (remember from Chapter 2: like charges repel). The two inner electrons sit between the nucleus and the outer shell, so they cancel out a large part of the nucleus’s pull. This is called shielding. Think of the nucleus as a bright lamp and the inner electrons as a screen around it: an outer electron sees the lamp dimmed. (The screen is not a solid wall; it is made of electrons that are themselves moving. But on average it sits between.) Electrons in the same shell are no better placed than each other, so they shield one another only a little.
Now take one step across the row, from lithium to beryllium. Every proton pulls on every electron, so the extra proton pulls on each outer electron, not just on “its own”. And the extra electron does not share out the nucleus’s pull more thinly, as if the nucleus had a fixed amount of pull to divide up; it only adds a small push from a neighbour that is no closer to the nucleus. More pull on each outer electron, hardly any more screening: so with every step the outer shell is held in more tightly, and the atoms get smaller.
Figure 9.2Lithium and fluorine, as simple shell models. Both have the same two inner electrons screening the nucleus. Fluorine has six more protons pulling on its outer shell, but its extra outer electrons barely screen each other, so its outer shell is held closer.
Going down a column is different. Sodium has one more full shell than lithium, and potassium one more than sodium. Each new shell sits farther out, and has more inner electrons screening it. Electric attraction gets weaker with distance, so the outer electron is held more loosely and the atom is bigger.
Careful
“More electrons always take up more room, so atoms must grow across a row.”
Electrons are not marbles, each needing its own space. The size of an atom is set by how strongly its outer electrons are pulled in. Across a row, the pull wins: the protons added are not cancelled by the electrons added to the same shell.
Predict first: before you open the landscape, guess. If every element’s atom size were a tower standing on its square of the periodic table, where would the tallest towers be: on the left, in the middle, or on the right? And would the towers in the bottom rows be taller or shorter than the ones at the top?
Figure 9.3Atom size against atomic number, from hydrogen (1) to barium (56). Every row after the first starts with a peak, an alkali metal, and slopes down to the right. Open the 3D version to stand each element on its own square of the table. (These radii come from a slightly different published set than Figure 9.1, so a few numbers differ by a few picometres.)
Turn the landscape and you can see the whole of this section at once. Each row after the first begins with a skyscraper on the left, an alkali metal, and the towers step down towards the right, with a few bumps along the way. Every step adds one proton, which pulls the same shells in a little tighter. Then the next row begins with a new, taller skyscraper, because it has a whole new shell. Press Look along the rows and all seven rows line up behind each other: the same downhill slope, again and again. (Row 1, with only hydrogen and helium, is too short to join in.) That repeating shape is what “periodic” means.
Understand itShielding
What is it?
The way an atom’s inner electrons stand between the nucleus and the outer electrons and cancel part of its pull, so an outer electron feels a much weaker tug than the full charge of the nucleus.
Why is it called this?
Because the inner electrons act like a shield, or like a screen in front of a lamp; chemists also call it screening. These are plain everyday words, chosen because the picture works, not technical names with a hidden meaning.
What problem did it solve?
Across a row, atoms gain protons and electrons, so you might expect them to grow; down a column they gain many more protons, so you might expect them to shrink. Measurements say the opposite both times. Shielding explains why.
Why does it work?
Electrons repel each other. Inner electrons spend most of their time between the nucleus and the outer shell, so they push outwards on the outer electrons and cancel much of the protons’ pull. Electrons in the same shell are no closer to the nucleus than each other, so they shield one another only a little.
How does it help?
It explains the sizes of atoms, why ionisation energies rise across a row and fall down a column, and so why metals on the left give electrons away readily while non-metals on the right hold on to them.
Go deeper how do we know, what it isn’t, where does it stop working
How do we know?
Remove lithium’s electrons one by one. The outer one, behind its two-electron shield, costs 520 kJ/mol; the next, with no shield in front of it, costs 7,298.
What it isn’t
Not a fixed amount of pull shared out among the electrons. Every proton pulls on every electron; shielding is the push of the other electrons partly cancelling that pull.
Where does it stop working?
The inner electrons are not a solid wall: they move, and outer electrons spend some of their time close to the nucleus. Exact numbers need quantum mechanics, and the simple picture can’t explain small details such as the dips at boron and oxygen.
Your turn
Explain Shielding to a friend in one sentence, in your own words. Then compare it with the book’s.
The way an atom’s inner electrons stand between the nucleus and the outer electrons and cancel part of its pull, so an outer electron feels a much weaker tug than the full charge of the nucleus.
The shell model has done well here. But it is not the end of the story, and you can already see why in Chapter 1’s graph of ionisation energies (Figure 1.7). Across row 2 the line climbs, but with two small dips, at boron and at oxygen. Shells alone cannot explain those. Nor can they explain the sharp coloured lines from Bunsen’s flame: why should sodium glow at one exact yellow and not at every colour? In the 1920s, physicists such as Erwin Schrödinger and Wolfgang Pauli worked out a new kind of mechanics for electrons, quantum mechanics, which answered both questions. Electrons in an atom can have only certain energies, so when they drop from a higher energy to a lower one they give out light of only certain colours. And the electrons in a shell are arranged in smaller groups, described by orbitals. An orbital is not a track: it describes the region where an electron is likely to be found, more like a fuzzy cloud with a particular shape. Some orbitals are round; others have two lobes, like a figure of eight. The dips appear where an electron starts a new kind of orbital (boron) or has to share an orbital with another electron (oxygen). You will meet orbitals properly when you study chemistry further; for now, it is enough to know that shells are a simplified first map.
Investigation 9.1
In the force model, hold the distance fixed and increase the positive charge from +1 to +2. What happens to the pull? Then make the distance smaller. How does this explain why the outer shell moves inwards across a row?
Check yourself
Sodium (2, 8, 1) is much bigger than lithium (2, 1), even though it has 8 more protons. Why?
Sodium’s outer electron is in a third shell, farther from the nucleus, and it is screened by ten inner electrons instead of two. Being farther away and more screened, it is held more weakly, so the atom is bigger.
9.2Why removing an electron always costs energy
How tightly does an atom hold its outermost electron? The answer is its ionisation energy, which you met in Chapter 1: the energy needed to pull one electron right away from an atom. For every element that has ever been measured, the answer is positive. No neutral atom gives up an electron for free. Even lithium and sodium, the easiest in the first 18 elements, need 520 and 496 kilojoules per mole of atoms.
The trends follow from section 9.1. Across a row, the outer electrons are pulled harder and sit closer, so they are harder to remove: lithium needs 520 kJ/mol, neon needs 2,081. Down a column, the outer electron is farther away and better screened, so it is easier to remove: lithium 520, sodium 496, potassium 419. The pattern in the reactivity series of Chapter 8 has the same roots: metals whose outer electrons are held loosely tend to be the ones that give electrons away readily, although in water other energy changes matter too. It is also why most of the metals in the firework colours come from the left-hand side of the table. A flame is hot enough to lift one of their outer electrons to a higher energy level without tearing it away, and the atom gives out its coloured light as the electron falls back. The colour is set by the size of that drop, which is different for every element.
Predict first: sodium in a flame glows yellow, and nothing else. If an electron can fall from many different heights, why does salt not give a whole rainbow? Make a guess, then press Give it energy a few times and watch where each colour lands.
Figure 9.4An atom’s energy levels drawn as a ladder. An electron lifted up by the heat of a flame falls back down, and gives out light whose colour is set by the size of the fall: a big fall gives blue or violet, a small fall red. Because only certain levels exist, only certain colours appear.
Think of the levels as the rungs of a ladder with fixed, uneven gaps. An electron can stand on a rung, never between rungs, so it can only fall by the exact height of one gap or another. Each gap gives light of one exact colour. Sodium’s ladder has one gap that gives far brighter visible light than any other, from its 3p level down to its 3s level, and that light is yellow, at 589 nanometres. Most of its other falls give infrared or ultraviolet light, which is real light that our eyes cannot see, and the few that are visible are very faint. That is why salt in a flame glows an almost pure yellow (so do the low-pressure sodium lamps once used on some roads).
Switch to hydrogen and you will see four visible lines, red, blue-green, blue and violet, all from falls that end on hydrogen’s second rung. Switch to A rainbow and you will see the difference that Bunsen and Kirchhoff used. A hot solid, like a bulb’s filament, gives every colour at once. A hot gas of separate atoms gives only its own few colours, as personal as a fingerprint.
Now try removing a second electron from lithium. Lithium’s first electron was alone in the outer shell. Once it has gone, the next one must come from the inner shell, which is much closer to the nucleus and has almost nothing screening it. The energy needed jumps from 520 to 7,298 kJ/mol, about 14 times as much.
Predict first. Sodium’s electrons are arranged 2, 8, 1. Sketch bars for the energy needed to remove its first three electrons, one after another. Where should the big jump come? Then check your idea against lithium (2, 1) below.
Figure 9.5The energy needed to take lithium’s three electrons away one by one. Removing the first, outer electron is easy. The second and third come from the inner shell and cost far more. A big jump in this kind of graph marks the edge of a shell.
These successive ionisation energies are some of the strongest evidence that shells are real. For any element, plot the energy needed to remove each electron in turn, and a big jump appears exactly where you run out of outer-shell electrons.
How do we know? Knocking electrons out with light from the 1960s
Ionisation energies are measured by shining very energetic light (ultraviolet or X-rays) on atoms of a gas and measuring how fast the electrons fly out. The light’s energy, minus the electron’s leftover energy of motion, is the energy it took to free that electron. This method, called photoelectron spectroscopy, shows separate groups of electrons with different energies inside every atom: direct evidence for shells, and for the orbitals inside them.
The exact set of colours of light that an element gives out when it is heated, or soaks up when light shines through it. Spread out by a prism, it shows as sharp coloured lines that belong to that element alone.
Why is it called this?
Spectrum is Latin for “an appearance” or “an image”. Isaac Newton brought the word into the study of light in the 1670s for the band of colours from a prism. Bunsen and Kirchhoff named two new elements after their spectra: caesium, from the Latin for sky-blue, and rubidium, from the Latin for dark red.
What problem did it solve?
How to tell which elements are present without weighing or reacting anything: in a flame, in a mineral, even in the Sun. Bunsen and Kirchhoff used it to discover two new elements in 1860 and 1861.
Why does it work?
An electron in an atom can have only certain energies. Heat lifts an outer electron to a higher level; when it falls back, the atom gives out exactly the energy of that drop as light of one colour. Each element has its own ladder of levels, so its own set of colours.
How does it help?
Firework makers choose metals for their colours, chemists detect tiny traces of elements, and astronomers read what stars are made of from their light.
Go deeper how do we know, what it isn’t, where does it stop working
How do we know?
The lines are the same every time, in every laboratory and in starlight: the two yellow lines that salt gives a gas flame sit exactly where two dark lines cross the Sun’s spectrum.
What it isn’t
Not the element burning or being used up. Its electrons are lifted and fall back, again and again, for as long as the atom stays hot.
Where does it stop working?
Shells alone can’t predict the exact colours of most elements: that needed quantum mechanics in the 1920s. And molecules and solids give broad, blurred bands rather than sharp lines, which are much harder to read.
Your turn
Explain An element’s colour signature (its spectrum) to a friend in one sentence, in your own words. Then compare it with the book’s.
The exact set of colours of light that an element gives out when it is heated, or soaks up when light shines through it. Spread out by a prism, it shows as sharp coloured lines that belong to that element alone.
Careful
“Sodium gives off energy when it loses its electron, because it wants a full shell.”
Removing sodium’s outer electron costs 496 kJ/mol; nothing about it gives energy out. Sodium does end up as Na⁺ in salt because of what happens afterwards: the oppositely charged ions pull together into a crystal, which gives out more energy than the ionisation cost (Chapter 2). The energy accounting is what decides, not any wish of the atom.
Predict first: atom size had skyscrapers on the left. If you made the towers show how hard it is to pull an electron away instead, where would the tallest ones go now?
Figure 9.6The same landscape idea, now showing first ionisation energy: the energy needed to pull one electron away from each atom in a mole of them. Open it in 3D and compare it with atom size.
It is the mirror image. Now the noble gases on the far right are the mountain peaks: helium highest of all, at about 2,372 kJ/mol. The alkali metals on the left are the deepest valleys: caesium needs only about 376. Big atoms hold their outer electron loosely, far from the nucleus and behind many shielding electrons; small atoms hold it tightly. Two different measurements, one pattern, and one reason behind both. That is why chemists trust the table.
Understand itIonisation energy
What is it?
The energy needed to pull one electron right away from an atom, usually given per mole of atoms. It measures how tightly an atom holds its outermost electron.
Why is it called this?
An atom that has lost or gained electrons is an ion, a word Michael Faraday introduced in 1834, on William Whewell’s suggestion, from the Greek for “going”, because ions travel towards an electrode. Ionisation is turning an atom into an ion, and the ionisation energy is what that costs.
What problem did it solve?
It turned “how readily does this element give electrons away?” into a number you can measure, and it gave some of the strongest evidence that electrons are arranged in shells.
Why does it work?
The outer electron is pulled in by the protons and pushed out by the other electrons. The closer it sits and the less it is shielded, the more energy it takes to tear it away.
How does it help?
It predicts which atoms let electrons go (metals on the left, with low values) and which hold on (non-metals on the right), and a big jump in successive ionisation energies tells you how many outer electrons an atom has, as in the element with a cliff.
Go deeper how do we know, what it isn’t, where does it stop working
How do we know?
Shine very energetic light on atoms of a gas and measure how fast the electrons fly out. The light’s energy, minus the electron’s leftover energy of motion, is the ionisation energy (photoelectron spectroscopy).
What it isn’t
Not energy given out when an atom gets rid of an electron. It is always a cost: no neutral atom gives up an electron for free, not even sodium.
Where does it stop working?
It describes a lone atom in a gas. For a metal in water or in a crystal, other energy changes join in, which is why the reactivity series is not simply the order of ionisation energies.
Your turn
Explain Ionisation energy to a friend in one sentence, in your own words. Then compare it with the book’s.
The energy needed to pull one electron right away from an atom, usually given per mole of atoms. It measures how tightly an atom holds its outermost electron.
Be Mendeleev
Make your own “cards” the way Mendeleev did. On small pieces of paper, write the name and atomic number of the first twenty elements, from hydrogen (1) to calcium (20), and on each one note one fact you can look up: metal or non-metal, gas or solid at room temperature, and whether it forms ions with a charge of +1, +2, −1 or none. Shuffle them, then lay them out in order of atomic number, starting a new row each time you reach an element that behaves like one you have already placed. When your columns line up (lithium, sodium and potassium together; fluorine and chlorine together; helium, neon and argon together), you have rebuilt the shape of the periodic table from its chemistry alone.
Investigation 9.2
Draw ionisation as an uphill energy step. Compare a small step (an alkali metal such as lithium) with a big one (a noble gas such as neon). Explain the difference using distance and screening, without using the word “want”.
Check yourself
Lithium’s first ionisation energy is 520 kJ/mol and its second is 7,298 kJ/mol. Explain why the second is so much larger.
The first electron comes from the outer shell (n = 2), where it is farther from the nucleus and screened by the two inner electrons. The second must come from the inner shell, close to the nucleus with nothing screening it, and from an ion that is already positive. (Not because the pull is now shared among fewer electrons: every proton pulls on every electron regardless.) So it is held far more tightly: about 14 times more energy is needed.
Case file 9
The element with a cliff
A sample of an unknown element X, from row 3 of the periodic table, is turned into a gas and its electrons are removed one at a time. The energies needed are:
Electron removed
1st
2nd
3rd
4th
Energy (kJ/mol)
738
1,451
7,733
10,543
The suspects are sodium (2, 8, 1), magnesium (2, 8, 2) and aluminium (2, 8, 3).
Every value is positive.
The 2nd value is about twice the 1st. The 3rd is more than five times the 2nd.
Which element is X? Which clue decides it, and what does the other clue tell you?
Show the solution
X is magnesium. The cliff comes between the 2nd and 3rd electrons, so X has exactly two electrons in its outer shell before the inner shell is reached: that is 2, 8, 2. Sodium would show its cliff after the 1st electron; aluminium after the 3rd. Clue 1 tells you nothing about which element it is, but it is worth noticing: removing any electron, from any atom or ion, always takes energy.
What this chapter can’t explain yet
Right in the middle of row 2 sits carbon: four outer electrons, held neither very loosely nor very tightly, so that it neither gives them away nor takes extra ones easily. Instead, carbon shares. It shares with hydrogen, oxygen and nitrogen, and above all with other carbon atoms, building chains, rings and frameworks of almost endless variety. Chapter 10 is about the chemistry that carbon makes possible, including the chemistry of life.
10
Chapter 10
Carbon chains and the chemistry of life
The big questionPetrol and sugar are both built mostly from carbon and hydrogen. So why does sugar vanish into your chai, while petrol floats on a monsoon puddle in a rainbow film?
A 27-year-old chemist named Friedrich Wöhler is heating a white salt called ammonium cyanate, made from nothing more mysterious than minerals and the gases of a laboratory. When he looks at the crystals that form, he finds something that should not be there. They are urea: the same substance that living bodies make and get rid of in urine. Wöhler had trained as a doctor before chemistry pulled him away, and he had spent a year in Stockholm learning from the most famous chemist in Europe. Now he writes, delighted, to that old teacher in Stockholm, Jöns Jacob Berzelius, that he can make urea without needing a kidney, “either of man or dog”.
Why was that exciting? For centuries people had believed that the substances of living things, sugar, oil, urea, the stuff of flesh and wood, could only be made by life itself, by some special “vital force” that ordinary chemistry could never copy. Wöhler’s crystals did not end that belief overnight (the story is slower and messier than that, and you can read it in full), but they were one of the first cracks. Slowly chemists came to see that the molecules of life obey exactly the same rules as everything else in this book. They are special for a different reason: almost all of them are built on a skeleton of carbon.
Look at the label on almost anything in a kitchen: sugar, cooking oil, ghee, vinegar, rice, the plastic of the bottle, the soap by the sink. Different as they are, nearly all of them are made of molecules built around carbon. So are the fibres of your clothes, the DNA in your cells and the fuel in a scooter. Of the many millions of compounds that chemists have described, the great majority contain carbon. This episode of our adventure is about why one element can build so much, and about the small groups of atoms that decide what each carbon molecule actually does.
10.1Chains, branches and rings
Utrecht, the Netherlands, 1874
In 1874 a 22-year-old chemist called Jacobus van ‘t Hoff, not yet even a doctor of science, published a little pamphlet with a bold idea. He was a doctor’s son from Rotterdam who read poetry and philosophy as eagerly as chemistry, and he believed that a scientist needed imagination as much as a good balance. Some carbon compounds were known to come in two forms that were mirror images of each other, like your left and right hands. That made no sense if a carbon atom’s bonds lay flat on a page, as chemists usually drew them. But it made perfect sense, van ‘t Hoff argued, if the four bonds of a carbon atom pointed to the four corners of a tetrahedron, a little pyramid with a triangle for a base. In Paris, Joseph Le Bel had reached the same idea independently, within months. A famous German chemist, Hermann Kolbe, mocked van ‘t Hoff in print for his flights of fancy. The young man turned out to be right. Decades later X-ray measurements showed the angle between the bonds of such a carbon atom: about 109.5°, exactly a tetrahedron’s angle. And in 1931 the American chemist Linus Pauling, a pharmacist’s son from Oregon who had lost his father at nine and worked his way through college, chopping wood and teaching younger students, used the new quantum physics to explain why carbon’s four bonds point that way. In 1901 van ‘t Hoff received the very first Nobel Prize in Chemistry (for different work), and molecules have been three-dimensional ever since.
Why four bonds? A carbon atom has 6 electrons: 2 in its inner shell and 4 in its outer one. Those 4 outer electrons let it form four covalent bonds, four shared pairs of electrons (Chapter 2). Count the lines meeting at any carbon atom in a structure, and you will almost always find four.
What makes carbon special is that its bonds to other carbon atoms are strong, roughly as strong as its bonds to hydrogen. So carbon atoms can join to each other again and again, forming long chains, chains with branches, and closed rings, with hydrogen atoms (and sometimes oxygen or nitrogen) filling the remaining bonds. Silicon, the element just below carbon in the periodic table, also forms four bonds, but a silicon–silicon bond is only about two-thirds as strong as a carbon–carbon bond, and long silicon chains fall apart easily in air and water. Carbon’s chains don’t.
The simplest family is the alkanes: chains of carbon with only hydrogen attached and only single bonds. Methane, CH₄, has one carbon; ethane, C₂H₆, has two; propane has three; butane has four. Each extra carbon brings two more hydrogens, so an alkane with n carbons has 2n + 2 hydrogens.
Figure 10.1Three ways to arrange carbon. A straight chain, a branched chain and a ring. The chains are drawn as zig-zags because real chains are zig-zag shaped: the four bonds around each carbon point to the corners of a tetrahedron.
Turn the 3D model and you will see van ‘t Hoff’s tetrahedra everywhere: at every carbon, the four bonds splay out into space, which is why a “straight” chain is really a zig-zag.
Drawing every hydrogen gets tiring, so chemists often use a shorthand called a skeletal formula: just the zig-zag lines of the carbon skeleton, with a carbon understood at every corner and every end, and enough hydrogens understood to give each carbon four bonds. Butane becomes a little zig-zag of three lines. You will see these drawings in any chemistry book; now you know how to read them.
Understand itOrganic chemistry
What is it?
The chemistry of compounds built on a skeleton of carbon atoms, usually with hydrogen attached: sugars, oils, plastics, fuels, medicines and the molecules of life.
Why is it called this?
Berzelius named it around 1807 for substances that came from living organisms, because people then believed only life could make them. The name outlived the belief. In chemistry, “organic” does not mean natural or pesticide-free: petrol and plastic are organic compounds.
What problem did it solve?
Millions of different substances seemed to follow no shared rules. Seeing them as carbon skeletons with groups attached turned a jungle into a handful of patterns.
Why does it work?
A carbon atom has four outer electrons, so it forms four bonds, and its bonds to other carbon atoms are strong. So carbon can link to itself again and again in chains, branches and rings, with bonds left over for hydrogen, oxygen and nitrogen.
How does it help?
Know a molecule’s skeleton and its functional groups, and you can predict how it behaves: whether it mixes with water, how high it boils, whether it is an acid or a base.
Go deeper how do we know, what it isn’t, where does it stop working
How do we know?
In 1828 Wöhler made urea, a substance of living bodies, from lifeless starting materials, and in 1901 Fischer joined the building blocks of proteins by hand. The molecules of life obey the same rules as everything else.
What it isn’t
Not “made only by living things” any more, and not “healthy” or “natural”. The word describes carbon chemistry, nothing more.
Where does it stop working?
The border is blurry. Carbon dioxide, carbonates and diamond all contain carbon but are usually counted as inorganic, by tradition rather than by any deep rule.
Your turn
Explain Organic chemistry to a friend in one sentence, in your own words. Then compare it with the book’s.
The chemistry of compounds built on a skeleton of carbon atoms, usually with hydrogen attached: sugars, oils, plastics, fuels, medicines and the molecules of life.
Investigation 10.1
Compare diamond, water and salt in the app, then look at the 3D carbon structures. In each, which particles are joined by bonds that go on and on, and which are separate little groups?
Check yourself
A straight-chain alkane has 5 carbon atoms. How many hydrogen atoms does it have? Check by counting the bonds each carbon needs.
The two end carbons each have one carbon neighbour, so each needs 3 hydrogens (6 in total); the three middle carbons each have two carbon neighbours, so each needs 2 hydrogens (6 more). That is pentane, C₅H₁₂, matching 2 × 5 + 2 = 12.
10.2The part that does the chemistry
Your kitchen, with an orange and a balloon
Here is a trick that looks like magic. Blow up a balloon and tie it. Peel an orange, then hold a piece of peel close to the balloon and squeeze it hard, so that a fine spray of oil from the peel lands on the rubber. Very often, within a few seconds, the balloon bursts. Nothing sharp touched it.
The trick works because of a rule chemists sum up as like dissolves like. The oil in orange peel is mostly a molecule called limonene: a carbon skeleton covered in hydrogen, with no charged ends at all. Balloon rubber is also a long carbon-and-hydrogen molecule. The limonene soaks into the stretched rubber, softens and weakens it, and the balloon pops. Water, whose molecules have slightly charged ends, would do nothing to the balloon at all.
The orange-peel balloon
You need a balloon and an orange (or a lemon). Blow up the balloon, then squeeze a piece of peel, coloured side towards the balloon, so its oil sprays onto the rubber. Try it on a few spots. Then try dripping plain water on another balloon. What does the difference tell you about which molecules dissolve which? (Keep the peel away from your eyes.)
Alkanes and molecules like limonene are rather dull chemically. Their C–C and C–H bonds share electrons almost equally, so the molecules have no positive or negative ends, and they don’t mix with water. That is the answer to half of this chapter’s big question: petrol is a mixture of hydrocarbons, mostly alkanes, and water molecules stick to each other far more strongly than they stick to petrol, so the two stay apart and the lighter petrol floats on top. (The rainbow colours on a monsoon puddle come from light bouncing off the top and bottom of that very thin film of petrol.)
Now swap one hydrogen on ethane for an oxygen with a hydrogen attached, an –OH group. You get ethanol. The two molecules are almost the same size, yet ethane is a gas that boils at −88.6 °C and ethanol is a liquid that boils at 78.4 °C and mixes with water in any amount.
Figure 10.2Ethane and ethanol. Replacing one hydrogen with an –OH group turns a gas that ignores water into a liquid that mixes with it completely.
The difference comes from the O–H bond. Oxygen attracts the shared electrons much more strongly than hydrogen does, so the oxygen end carries a slight negative charge and the hydrogen a slight positive one. That hydrogen can be attracted to an oxygen on a neighbouring molecule: a hydrogen bond, the same kind of attraction that holds water molecules together (Chapter 3). It was Linus Pauling, again, who gave chemists a number scale for how strongly each element pulls on shared electrons, and who made hydrogen bonds a central idea in chemistry; later he used them to work out how protein chains coil and fold. Ethanol molecules hold on to each other, which raises the boiling point, and they hold on to water molecules too, which lets them mix.
A small group of atoms like –OH, which gives a molecule its particular behaviour, is called a functional group. It is the part that does the chemistry. The carbon skeleton is the frame; the functional groups are the handles, hooks and switches fixed onto it.
Group
Name
Example
What it does
–OH
hydroxyl (alcohols)
ethanol
hydrogen bonds; mixes with water
–COOH
carboxyl (carboxylic acids)
ethanoic acid, in vinegar
gives away H⁺: a weak acid
–NH₂
amino (amines)
in almost every amino acid
picks up H⁺: a weak base
C=C
double bond (alkenes)
ethene
holds the molecule flat; can open up to join other molecules
Sugar answers the other half of the big question. A sugar molecule has a carbon skeleton studded with –OH groups, five of them on a glucose molecule, so it forms hydrogen bonds with water all over its surface and dissolves easily into your chai.
Soap is a molecule with a split personality, and that is exactly why it works. One end is a long carbon tail with no charged ends, which mixes with grease; the other end is charged and loves water. The tails bury themselves in a spot of oil, the heads face outwards into the water, and the oil is carried away in tiny wrapped-up droplets.
Oil, water and soap
Half-fill a clear glass jar with water and add a spoonful of cooking oil. Put the lid on and shake hard. Watch: within a minute the oil gathers back into a layer on top. Now add a few drops of washing-up liquid, shake again, and compare. Which molecules are holding on to which?
Then a second test. Drop one sugar-coated sweet (a Gems or similar) into a glass of water and another into a glass of cooking oil. Predict first: which one will lose its colour? The sugar coat, studded with –OH groups, dissolves in the water and the colour runs; in the oil, it hardly changes. (The sweet from the oil glass is still fine to eat once wiped.)
Careful
“Adding an –OH group makes the molecule boil higher just because it makes it heavier.”
Check the masses. Ethane (30 grams per mole) and methanol, CH₃OH (32 grams per mole), weigh almost the same, yet ethane boils at −88.6 °C and methanol at 64.7 °C. The extra mass is tiny; the hydrogen bonding between methanol molecules is what holds them together.
Understand itFunctional group
What is it?
A small group of atoms on a carbon skeleton, such as –OH or –COOH, that gives the molecule its typical behaviour. The skeleton is the frame; the functional group is the part that does the chemistry.
Why is it called this?
Because it decides the molecule’s function: how it reacts and what it mixes with. Molecules with the same group behave alike, whatever the length of their skeleton.
What problem did it solve?
With millions of carbon compounds, learning each one separately is impossible. Learn a dozen groups and you can predict the behaviour of most of them.
Why does it work?
Carbon–carbon and carbon–hydrogen bonds share electrons almost evenly and do little. Groups containing oxygen or nitrogen share them unevenly, making slightly charged ends that form hydrogen bonds, give away H⁺ or pick it up.
How does it help?
It explains why sugar dissolves in chai but petrol floats on a puddle, why vinegar is sour, why soap lifts grease, and how amino acids link into proteins.
Go deeper how do we know, what it isn’t, where does it stop working
How do we know?
Swap one hydrogen on ethane for –OH: a gas that boils at −88.6 °C becomes ethanol, a liquid that boils at 78.4 °C and mixes with water. Almost the same size; one group changed everything.
What it isn’t
Not just extra weight. Methanol is only slightly heavier than ethane, yet it boils more than 150 °C higher, because of the hydrogen bonds its –OH group makes.
Where does it stop working?
Groups affect their neighbours. The –OH inside vinegar’s –COOH gives up H⁺, while the –OH in ethanol essentially doesn’t, because the C=O next door changes it. A group’s behaviour depends on what it is attached to.
Your turn
Explain Functional group to a friend in one sentence, in your own words. Then compare it with the book’s.
A small group of atoms on a carbon skeleton, such as –OH or –COOH, that gives the molecule its typical behaviour. The skeleton is the frame; the functional group is the part that does the chemistry.
Investigation 10.2
Compare methane with ammonia and water at the same temperature. All three molecules are about the same size. Predict which will be gases and which liquids, then check, and say which bonds are making the difference.
Check yourself
Methane does not dissolve in water. Methanol, CH₃OH, mixes with water completely. Explain the difference in terms of what the molecules attract.
Methane’s electrons are shared almost evenly, so it has no charged ends to attract water molecules; water molecules stay stuck to each other instead. Methanol’s –OH group has a slightly negative oxygen and a slightly positive hydrogen, so it forms hydrogen bonds with water molecules, and the two mix.
10.3Longer chains, higher boiling points
Titusville, Pennsylvania, August 1859
On a farm in western Pennsylvania, a man named Edwin Drake and a hired well-driller had spent months boring a hole into the ground, while the locals laughed at “Drake’s folly”. At about 21 metres down, the drill hit oil. It was not the first oil anyone had ever seen, but Drake’s well started an industry. Within a few years refineries were heating crude oil to sort it into its parts, at first for one thing above all: kerosene, a clean-burning fuel for lamps that could replace whale oil.
What the refiners were exploiting is one of the neatest patterns in chemistry. Crude oil is a jumble of alkanes, from tiny ones to long ones. They have no –OH groups, no charged ends, nothing to grab with. You might expect them all to behave alike. Yet the gas in a camping stove is a gas, the petrol in a car is a liquid, and a candle is a solid, and all three are alkanes. What changes is the length of the chain.
Figure 10.3Boiling points of the first eight straight-chain alkanes (measured values at normal air pressure). Each extra carbon raises the boiling point. Methane to butane are gases in a warm room; pentane onwards are liquids.
Even molecules with no permanent charged ends attract each other a little. The electrons in a molecule are always moving, and at any instant they may be slightly bunched on one side, making a fleeting charged end that tugs on the electrons of the next molecule. These flickering attractions are called dispersion forces. Each one is weak, but they add up along the whole length of the molecule. A long chain has more electrons and more surface touching its neighbours than a short one, so long chains cling together more, and it takes a higher temperature to pull them apart into a gas. These are the same flickering attractions, added up over millions of tiny hairs on its toes, that let a gecko hang upside down from your ceiling.
That is how a refinery sorts crude oil. The oil is heated until most of it boils, and the vapour rises up a tall tower that gets cooler towards the top. Each kind of molecule condenses back into liquid at the height where the temperature falls below its boiling point: the long, heavy chains low down, and the short ones higher up. Short chains become gas for cooking, middle ones petrol and kerosene, long ones diesel, lubricating oil and wax. If boiling points did not climb steadily with chain length, as Figure 10.3 shows, the mixture could not be sorted this way.
Careful
“When butane boils, its molecules break apart into carbon and hydrogen.”
No C–C or C–H bond breaks when an alkane boils. Boiling only pulls whole molecules away from their neighbours, overcoming the weak dispersion forces between them; the strong bonds inside each molecule are untouched. The molecules in butane gas are exactly the molecules that were in the liquid, and if you cool the gas they become liquid butane again. Breaking the bonds inside the molecule is a different and far bigger job: that is burning, or what a refinery’s “crackers” do at much higher temperatures with a catalyst.
Understand itDispersion forces
What are they?
Weak attractions between all molecules, even ones with no charged ends, caused by electrons bunching up for an instant on one side of a molecule and tugging on the electrons of the next.
Why are they called this?
The physicist Fritz London named them in 1930, because his quantum theory of them closely resembled the theory of the dispersion of light, the way light spreads into colours. Chemists often call them London forces after him. The name comes from the mathematics, not from anything spreading out.
What problem did they solve?
Why should molecules with no charged ends, like the alkanes or the noble gases, stick together at all? Without some attraction, they could never become liquids or solids.
Why do they work?
Electrons are always moving. At any instant one side of a molecule may have a few more, making a fleeting charged end that pulls the electrons of its neighbour into step. Each tug is tiny, but they add up along the whole length of a molecule.
How do they help?
They explain why longer chains boil higher (so a refinery can sort crude oil), why branched molecules boil lower, why straight-chained ghee is solid while kinked olive oil is runny, and how a gecko walks on a ceiling.
Go deeper how do we know, what they aren’t, where do they stop working
How do we know?
Boiling points climb steadily as each carbon is added to an alkane chain, from methane, a gas, to octane, a liquid, with nothing changing except the length of the chain.
What they aren’t
Not bonds inside the molecule. When butane boils, no bond breaks; whole molecules pull away from their neighbours.
Where do they stop working?
They are the weakest attractions between molecules. Where molecules have permanent charged ends, and above all where they can hydrogen-bond, those stronger forces usually decide the boiling point instead.
Your turn
Explain Dispersion forces to a friend in one sentence, in your own words. Then compare it with the book’s.
Weak attractions between all molecules, even ones with no charged ends, caused by electrons bunching up for an instant on one side of a molecule and tugging on the electrons of the next.
The alkane ladder
This one is for looking, not for heating. Many homes hold a ladder of alkanes of different lengths. The LPG cylinder in the kitchen holds mostly propane and butane, 3 and 4 carbons long (just look at it; don’t touch the valve). Baby oil (liquid paraffin) is chains of roughly 15 to 30 or more carbons, many of them branched or bent into rings, so they pack together badly. A paraffin candle is mostly straight chains of roughly 20 to 40. Predict first: which is a gas, which a runny liquid, which a solid, and why in that order? Petroleum jelly (Vaseline) sits in between, because it is a mixture: long waxy chains with oily ones trapped among them. Rub a drop of baby oil and a dab of Vaseline between your fingers and feel the difference that chain length makes.
Investigation 10.3
Step the carbon skeleton from methane up to butane, keeping only hydrogens attached. Watch the dispersion attraction and the boiling point. Predict pentane before you look it up.
Check yourself
Propane boils at −42.1 °C and octane at 125.6 °C. One is sold as a liquid fuel for cars; the other is squeezed into gas cylinders for cooking. Which is which, and why?
Octane, with eight carbons, has much stronger dispersion forces, so it is a liquid at room temperature: that is petrol. Propane, with only three carbons, is a gas at room temperature; it is stored as a liquid only by squeezing it under pressure in a cylinder, and turns back into gas when you open the valve.
10.4Same formula, different molecule
Germany, the 1820s
Two young chemists who had never met were puzzling over two silver compounds. In Paris and then Giessen, Justus von Liebig studied silver fulminate, a substance so dangerous that it exploded at a touch. Friedrich Wöhler, the man who would later make urea, studied silver cyanate, which was perfectly calm. When their analyses were published side by side, something looked badly wrong: both compounds were made of exactly the same elements, in exactly the same proportions. Each chemist suspected the other of a mistake. They checked, and checked again, and found that both were right. Instead of becoming enemies, they became lifelong friends and partners. In 1830 Berzelius gave the puzzle its name: these were isomers, from Greek words meaning “equal parts”.
The answer to the puzzle is that a formula lists the parts, but not how they are put together, any more than the list “four wheels, two seats, one engine” tells you whether you have a car or a rickshaw. Here are two substances with exactly the same formula, C₄H₁₀. Each molecule contains 4 carbons and 10 hydrogens, the same atoms, the same mass. One boils at −0.5 °C, the other at −11.7 °C. In butane the four carbons make a straight chain. In isobutane three carbons hang off a central one.
Figure 10.4Two pairs of isomers. Branching makes isobutane more compact than butane, so less of each molecule touches its neighbours and it boils lower. Moving one oxygen turns ethanol, which can hydrogen-bond, into dimethyl ether, which cannot.
The butane pair differ for the reason you met in 10.3: a compact, branched molecule has less surface in contact with its neighbours than a stretched-out chain, so its dispersion forces are weaker and it boils lower.
The second pair differ far more. C₂H₆O can be ethanol, with its –OH group, or dimethyl ether, with the oxygen in the middle of the chain and every hydrogen attached to carbon. Ethanol boils at 78.4 °C; dimethyl ether at −24.8 °C, more than 100 °C lower. Without a hydrogen attached to the oxygen, dimethyl ether molecules can’t form hydrogen bonds with each other. Same atoms, different arrangement: a liquid you could pour versus a gas.
Careful
“Butane and isobutane boil at different temperatures, so one of them must be heavier.”
They contain exactly the same atoms, so their molecules have exactly the same mass. Any difference in how they behave must come from their shape and their connections, not their mass.
Understand itIsomers
What are they?
Different substances whose molecules contain exactly the same atoms, joined in a different order or arrangement. Same formula, different molecule.
Why are they called this?
Berzelius named them in 1830 from the Greek isos, “equal”, and meros, “part”: made of equal parts.
What problem did they solve?
Liebig’s explosive silver fulminate and Wöhler’s calm silver cyanate had exactly the same composition, and each chemist assumed the other had made a mistake. Isomers showed both were right: what a molecule is made of is not the whole story.
Why does it work?
A molecule’s behaviour depends on how its atoms are connected and on its shape. Rearranging the same atoms can hide or expose a group that forms hydrogen bonds, or make a molecule more compact so its neighbours grip it less.
How do they help?
They warn you that a formula names only the parts, and they explain why ethanol is a liquid while dimethyl ether, with the same atoms, is a gas. Shape matters just as much in medicines and inside your body.
Go deeper how do we know, what they aren’t, where does the idea stop working
How do we know?
Butane and isobutane, both C₄H₁₀, boil at −0.5 °C and −11.7 °C, and can be separated and bottled as two pure substances.
What they aren’t
Not one molecule heavier than the other. Isomers have exactly the same mass; the differences come from shape and connections.
Where does the idea stop working?
Some arrangements turn into each other all the time, for example by spinning around a single bond, so they can’t be bottled separately, and chemists don’t usually count them as different substances. Only when an arrangement is locked, for example by different connections or by a double bond, do you get two separate substances.
Your turn
Explain Isomers to a friend in one sentence, in your own words. Then compare it with the book’s.
Different substances whose molecules contain exactly the same atoms, joined in a different order or arrangement. Same formula, different molecule.
Investigation 10.4
Compare butane with isobutane, then ethanol with dimethyl ether. Before each switch, predict which one boils higher and give your reason.
Check yourself
Pentane, C₅H₁₂, has three isomers: a straight chain; a chain of four with one branch; and a “cross” shape with four carbons around a central one, almost a ball. Put them in order of boiling point, highest first, and explain.
Straight chain (36.1 °C), then the singly branched one (27.7 °C), then the ball-shaped one (9.5 °C). The more compact the molecule, the less surface touches its neighbours, the weaker the dispersion forces, and the lower the boiling point.
10.5Double bonds and locked shapes
A kitchen shelf on a winter morning
Look along a kitchen shelf on a cool morning and you will find a puzzle. The ghee in its jar is solid. The coconut oil may be solid too, if the room is cold enough. But the olive oil and the sunflower oil are runny liquids. All of them are fats, made of the same kinds of atoms in the same kinds of long chains. Why are some solid and some liquid at the same temperature? The answer is a tiny, rigid kink.
Carbon atoms can share two pairs of electrons with each other: a double bond, written C=C. Ethene, C₂H₄, is the simplest example. It has two fewer hydrogens than ethane, because each carbon is now using two of its four bonds on its partner. Molecules with C=C bonds are said to be unsaturated: they hold fewer hydrogens than they could.
Figure 10.5Single and double bonds compared. The ends of ethane spin around the single bond all the time. Ethene’s double bond is shorter and keeps the whole molecule flat; twisting it would mean breaking part of the bond.
A single bond is like an axle: the two ends of ethane spin round it freely, billions of times a second at room temperature. A double bond is different. Its second shared pair sits above and below the line between the two carbons, and it only works while the two ends stay lined up, so twisting one end would break part of the bond. At ordinary temperatures, that doesn’t happen. All six atoms of ethene stay in one flat plane, with the bonds around each carbon about 120° apart.
How do we know a double bond really can’t twist? Because some molecules come in two versions that would turn into each other if it could. But-2-ene is a chain of four carbons with a double bond in the middle. It comes as two separate substances: one with the two end groups on the same side of the double bond, which boils at about 4 °C, and one with them on opposite sides, which boils at about 1 °C. Chemists can bottle them separately. If the double bond could spin, there would be only one substance.
Now back to the shelf. The long chains in fats are mostly alkane-like. In ghee and butter, many of the chains are fully saturated and straight, so they pack together neatly, like pencils in a box, and the fat is solid at room temperature. In olive oil, many chains have a double bond with the two halves of the chain on the same side, which puts a fixed kink in the middle. Kinked chains can’t pack neatly, their dispersion forces are weaker, and the oil stays liquid. Stearic acid, a straight 18-carbon chain, melts at about 69 °C; oleic acid, the same length with one kinked double bond, melts at about 13 °C.
The fridge test
Put a spoonful each of ghee or butter, coconut oil (if you have it) and olive or sunflower oil into three small clean bowls and leave them in the fridge for an hour. Which ones turn hard, which go cloudy, and which stay runny? The more straight, saturated chains a fat has, the more easily its molecules pack together into a solid.
Investigation 10.5
Switch between ethane and ethene in both the flat and the 3D views. Count the hydrogens, measure the angles, and try to rotate one end of each.
Check yourself
Why is a fat whose chains are all straight and saturated more likely to be solid at room temperature than an oil whose chains each have a kinked double bond?
Straight chains pack closely side by side, so a lot of surface touches and the dispersion forces add up; it takes a higher temperature to separate them, so the fat is solid. Kinked chains can’t pack closely, so they attract each other less and the oil melts at a lower temperature.
10.6Acids, amines and the links of life
Berlin, 1901
Seventy-three years after Wöhler’s urea, in the same city, the great German chemist Emil Fischer and his colleague Ernest Fourneau did something that would have astonished the believers in a vital force. They took two molecules of glycine, the simplest of the building blocks of proteins, and joined them by hand into a single molecule. It was the first time anyone had deliberately made the kind of link that holds every protein in every living thing together. Fischer went on to build chains of up to eighteen of these building blocks, and showed that they behaved like the fragments you get by breaking real proteins apart. Fischer was a timber merchant’s son whose father, the family story goes, gave up trying to make a businessman of him and sent him off to study instead. He became the most famous organic chemist of his age: he had already worked out the shapes of the sugars, and won the Nobel Prize in 1902. To understand what he joined, and how, we need two more functional groups.
Vinegar is sour because of ethanoic acid (also called acetic acid), CH₃COOH. Its working part is the carboxyl group, –COOH: a carbon with a double-bonded oxygen and an –OH. That hydrogen on the end can be passed to a water molecule as H⁺, so ethanoic acid is an acid, though a weak one: in vinegar, only a small fraction of its molecules give up their H⁺ at any moment (Chapter 7). The neighbouring C=O pulls on the electrons nearby, and once the H⁺ has gone, the leftover negative charge is spread over both oxygens rather than sitting on one. That is why the –OH in a carboxyl group gives up H⁺ while the –OH in ethanol essentially does not.
The amino group, –NH₂, does the opposite. Its nitrogen has a pair of electrons not used in bonding, which can pick up an H⁺. So amines are weak bases. You can smell this one. The fishy smell of fish is mostly a small amine, trimethylamine, drifting into the air. Squeeze lemon on the fish and the smell fades: the lemon’s acid hands H⁺ to the amine’s spare pair of electrons, turning it into a charged ion that stays dissolved in the juice instead of floating up your nose.
When a carboxyl group meets an –OH or an –NH₂ on another molecule, the two can join together, and in doing so they release a molecule of water. This is called a condensation reaction. An acid joined to an alcohol makes an ester; many esters smell of fruit, and they are part of what makes a ripe banana or pineapple smell the way it does.
Figure 10.6Making an ester. The –OH from the acid and the H from the alcohol leave together as water, and the two molecules join through the oxygen that is left. The atom count is the same on both sides.
Now the big one, the link Fischer made. An amino acid has a carboxyl group and an amino group on the same molecule. So amino acids can join head to tail: the –COOH of one with the –NH₂ of the next, releasing water each time. The new link, –CO–NH–, is called a peptide bond, and the result can join to another amino acid, and another, and another. A protein is a chain of hundreds or thousands of amino acids made exactly this way, folded into a particular shape. Every enzyme in your body, the keratin in your hair and the haemoglobin in your blood were built like this, one water molecule at a time.
Joining amino acids is one thing; seeing the shape of the finished molecule is another. In Oxford, Dorothy Hodgkin, who had fallen in love with crystals as a ten-year-old growing them at home, spent decades photographing how X-rays scatter off crystals of the molecules of life. She worked out the structure of penicillin in 1945, of vitamin B₁₂ in the 1950s, and in 1969, after thirty-four years of trying, of the protein insulin, much of it while living with painful arthritis in her hands. She won the Nobel Prize in Chemistry in 1964.
The chemists who followed Wöhler and Fischer turned these ideas into medicines. In Kolkata in the mid-twentieth century, Asima Chatterjee, one of the first women in India to earn a doctorate in science, who had chosen chemistry against the expectations of her time, spent her working life finding out the structures of molecules from plants used in traditional medicine, and helped develop medicines from them. Every one of those molecules was a carbon skeleton with functional groups attached, obeying exactly the rules in this chapter.
Careful
“When two molecules join to make an ester, some atoms are destroyed, which is why the ester is lighter.”
Every atom is accounted for: C₂H₄O₂ + CH₄O → C₃H₆O₂ + H₂O. In grams per mole, 60.05 + 32.04 = 74.08 + 18.02. The ester is lighter than the two starting molecules combined only because one water molecule’s worth of atoms left as water.
Investigation 10.6
Compare the carboxyl, amino and ester options on a short carbon skeleton. For the condensation, count the C, H and O atoms before and after, and find the water.
Check yourself
Glycine, C₂H₅NO₂, has a mass of 75.07 grams per mole. Two glycine molecules join by a peptide bond. What is the formula of the new molecule, and what is its mass per mole? (Water is 18.02 grams per mole.)
Two glycines contain C₄H₁₀N₂O₄. One water, H₂O, leaves, so the new molecule is C₄H₈N₂O₃. Its mass is 2 × 75.07 − 18.02 = 132.12 grams per mole.
Case file 10
The case of the two clear liquids
Two unlabelled bottles each hold a few millilitres of a colourless liquid. The label that fell off says only “C₂H₆O”. A chemist runs three tests.
Bottle A boils at 78 °C. Bottle B is barely liquid: it is in a sealed, chilled pressure bottle, and when it is opened at room temperature it hisses away as a gas.
Each sample has exactly the same mass per molecule: 46 grams per mole.
A drop of A mixes completely into water. A drop of liquid B, chilled first, mixes with water only partly.
A friend says the labels must be wrong, because one substance can’t have two boiling points. Who is right? Draw both molecules, and explain all three clues.
Show the solution
Both bottles are correctly labelled C₂H₆O. They are isomers: the same atoms joined differently, just as Liebig’s and Wöhler’s silver salts were.
Bottle A is ethanol, CH₃–CH₂–OH. Its oxygen carries a hydrogen, so ethanol molecules hydrogen-bond to each other (high boiling point, 78.4 °C) and to water (mixes completely).
Bottle B is dimethyl ether, CH₃–O–CH₃. All six hydrogens are on carbon, so its molecules cannot hydrogen-bond to each other; only weaker attractions hold them, and it boils at −24.8 °C. Its oxygen can still accept a hydrogen bond from water, which is why it mixes partly.
Clue 2 rules out the idea that one is heavier: same formula, same mass. The friend’s mistake is assuming a formula names a single substance. It names only the parts.
What this chapter can’t explain yet
Wöhler’s crystals, van ‘t Hoff’s tetrahedra and Fischer’s peptide bond showed that the molecules of life are built from carbon by ordinary chemistry. But the world is bigger than one molecule at a time. When fuel burns, its carbon ends up in the air and the sea; when you charge a phone, electrons and ions are pushed around inside a battery. The last episode of our adventure brings every idea in this book together on the scale of a whole planet.
11
Chapter 11
Earth, materials and energy
The big questionWhen we burn fuel, where does all the carbon go? And can we store energy for later without burning anything at all?
Open a cold bottle of soda water and listen. That hiss is carbon dioxide escaping: the gas was squeezed into the water at the factory, and the moment you release the pressure, some of it bubbles out. Taste the water and it is faintly sharp, a little sour, even though nobody added lemon. Something in that water is a weak acid, and it came from the gas.
Hold on to that bottle, because it is a small model of something enormous. The whole ocean is slowly doing what your soda water did at the factory: taking in carbon dioxide from the air above it.
All through this adventure, ideas have lived in separate episodes: atoms in one, acids in another, batteries in a third. The real world doesn’t sort itself like that. A single flame on a gas stove involves counting atoms, breaking and making bonds, energy barriers, moles, the air and, years later, the sea. This last episode follows two of the biggest pieces of chemistry on our planet, the carbon dioxide we add to the air and the batteries we hope will replace much of our burning, and shows that you already have every idea you need to understand them.
11.1The ocean and the carbon dioxide we add
Mauna Loa, Hawaii, March 1958
High on the side of a volcano in the middle of the Pacific Ocean, more than three thousand metres up and thousands of kilometres from the nearest continent, a young American scientist, not yet thirty, named Charles David Keeling set up an instrument to measure one thing: how much carbon dioxide there is in the air. Other people had measured it before, but their numbers jumped about wildly, because air near towns, fields and forests is always being changed by whatever is nearby. Keeling was a keen hiker and camper who had first taken up measuring carbon dioxide almost by accident, as a young researcher in California, carrying glass flasks into forests and up mountains. He was fussy, in the best way. He built careful instruments, checked them against standard gases again and again, and chose a place where the air had blown across thousands of kilometres of open sea.
His first readings were about 315 parts per million: out of every million molecules of air, about 315 were carbon dioxide. Within a couple of years he noticed two things. The number went up and down with the seasons, a few parts per million each year, as the forests of the northern half of the world drew carbon dioxide in each summer and let it out again each winter: the planet breathing. And underneath the breathing, the number climbed, every single year. The measurements have continued ever since, and the line, now called the Keeling curve, has passed 420 parts per million.
Where is all that carbon dioxide coming from? When methane, petrol or coal burns, its carbon atoms join with oxygen from the air to make carbon dioxide. None of those atoms disappears (Chapter 4), so all of that carbon ends up somewhere. Some stays in the air, where carbon dioxide traps heat and warms the planet. (The warm ground gives off invisible infrared light. Carbon dioxide molecules absorb some of it and send it off again in every direction, some of it back down, so less heat escapes to space.) Some is taken up by plants. And a large share dissolves into the sea: over the past two centuries, the oceans have absorbed roughly a quarter to a third of the carbon dioxide released by burning fuel.
That sounds like good news, and in one way it is: without the oceans, the air would hold even more carbon dioxide. But dissolving carbon dioxide changes the sea, exactly as it changed your soda water. When CO₂ dissolves, a little of it reacts with water to make carbonic acid, H₂CO₃, a weak acid that can pass an H⁺ to water:
CO₂ + H₂O ⇌ H₂CO₃ ⇌ H⁺ + HCO₃⁻
More H⁺ means a lower pH. But seawater has a defence, and you met it in Chapter 7: a buffer. Seawater contains carbonate ions, CO₃²⁻, and most of the new H⁺ ions are picked up by them, turning them into bicarbonate ions, HCO₃⁻:
H⁺ + CO₃²⁻ → HCO₃⁻
Put the two steps together and count everything. For every molecule of carbon dioxide that dissolves and reacts, one carbonate ion is used up and two bicarbonate ions are made:
CO₂ + H₂O + CO₃²⁻ → 2 HCO₃⁻
The buffer race
Ask an adult to help you make red cabbage indicator: chop a few leaves of red cabbage, cover them with warm tap water, leave them for half an hour, then strain off the purple liquid. Pour equal amounts into two glasses and top each up with the same amount of water (filtered RO drinking water, if you have it, gives the clearest result). Into one glass only, stir the tiniest pinch of baking soda, just enough to turn it blue-green: this is your pretend sea, slightly basic and buffered. The other glass is plain water with no buffer.
Predict first. You are going to blow ten slow breaths through a straw into each glass (blow out only; never suck up the liquid). Which glass will change colour first?
Your breath carries carbon dioxide, made when your body “burns” its food, and in water it makes carbonic acid. The plain glass shifts towards pinkish purple quite quickly; the change is gentle, so judge it against white paper. The pretend sea holds its colour much longer, because its bicarbonate soaks up the H⁺. Keep blowing into it, ten breaths at a time, and slowly it drifts towards purple too: the buffer is being worn down, breath by breath, just as the sea’s carbonate is. For one more link in the chain, an adult can hold an upturned glass a hand’s width above a lit tealight for ten seconds, slide a saucer over its mouth while turning it the right way up, then pour in a little indicator and swirl: burning, too, makes carbon dioxide. That change is small, so look against white paper. (Drink none of it.)
Figure 11.1What happens to carbon dioxide in the sea. Most of the H⁺ it releases is taken up by carbonate ions. The pH drops only a little, but the carbonate that shell-building animals need is used up. (The proportions in the bar are rough values for surface seawater today.)
So the buffer works: the sea’s pH has not plunged towards the pH of lemon juice. But a buffer is not free. Every H⁺ it soaks up uses up a carbonate ion, and corals, oysters, sea snails and many tiny plankton build their shells and skeletons out of exactly those ions:
Ca²⁺ + CO₃²⁻ ⇌ CaCO₃ (shell)
With fewer carbonate ions around, it becomes harder for them to build shells, and in places where the water is already low in carbonate, existing shells can start to dissolve. This whole process is called ocean acidification.
A shell in vinegar
Put a clean piece of eggshell (or a small seashell) in a glass and cover it with white vinegar. Watch closely: tiny bubbles form on the shell. Leave it overnight and see how much of the shell is left. Eggshell and seashell are both mostly calcium carbonate, CaCO₃; the acid in vinegar takes away its carbonate as carbon dioxide gas. Vinegar is far, far more acidic than seawater, so this is a dramatic, sped-up picture, not what is happening in the ocean. But the chemistry pulling on the carbonate is the same.
The pH of the surface ocean has fallen from about 8.2 before industry began to about 8.1 today. A tenth of a pH unit sounds tiny. But remember that each step on the pH scale is a factor of ten (Chapter 7):
Change of 0.1 in pH → H⁺concentration multiplied by 10⁰·¹
10⁰·¹ = 1.26
So there are about 26% more hydrogen ions in surface seawater than before industry. (You will often see “about 30%” quoted, because estimates of the starting pH vary a little.)
Careful
“Ocean acidification means the sea is turning into acid.”
Seawater is still slightly basic: its pH of about 8.1 is above 7, the neutral point. “Acidification” means moving towards acid, not becoming acidic. The worry is not that the sea will burn your skin. It is that the carbonate balance that marine life depends on is shifting faster than it has for a very long time. Nor is it caused by factory waste or acid rain: it is the same carbon dioxide that is in your soda water, simply far more of it.
How do we know the sea is really changing, and not just the air? Keeling’s curve tells us about the air. For the water, scientists needed a second patient watcher. Since 1988, researchers have sailed regularly to a spot in the open ocean north of Hawaii, a station called ALOHA, and sampled the seawater there, month after month. As the carbon dioxide in the air has risen, the dissolved carbon dioxide in the water has risen with it, and the pH has fallen steadily: by a few hundredths of a unit in thirty years. Two long, careful records, one of the air and one of the sea, tell the same story.
Understand itOcean acidification
What is it?
The slow fall in the pH of seawater as the ocean absorbs carbon dioxide from the air. The sea is still slightly basic, at about pH 8.1; it is moving towards acid, not becoming acid.
Why is it called this?
To acidify is to make more acidic, from the Latin acidus, “sour”. The name describes the direction of change, which is exactly why it can mislead: it does not mean the sea is turning into acid.
What problem does the idea explain?
Scientists knew the sea was soaking up a large share of the carbon dioxide from burning fuel, which sounded like good news. This idea names the hidden cost: the water’s chemistry changes, and shell-building animals find it harder to build.
Why does it happen?
Carbon dioxide reacts with water to make carbonic acid, which releases H⁺. Carbonate ions in seawater mop up most of that H⁺, so the pH falls only a little, but every carbonate that does so is used up: CO₂ + H₂O + CO₃²⁻ → 2 HCO₃⁻.
How does it help?
It explains why corals, oysters and plankton are at risk even though the pH has changed by only about a tenth, and why the carbon dioxide we add to the air matters for the sea as well as for the climate.
Go deeper how do we know, what it isn’t, where does the simple picture stop working
How do we know?
Two long records agree: Keeling’s measurements of carbon dioxide in the air since 1958, and monthly samples of seawater at Station ALOHA since 1988, where dissolved carbon dioxide has risen and the pH has fallen steadily.
What it isn’t
Not caused by factory waste or acid rain, and not the sea becoming sour or harmful to swim in. It is the same carbon dioxide that is in soda water, simply far more of it.
Where does the simple picture stop working?
The sea is not one beaker. Cold water takes up more carbon dioxide, some regions are already low in carbonate, and currents mix the water slowly, so the change is uneven from place to place.
Your turn
Explain Ocean acidification to a friend in one sentence, in your own words. Then compare it with the book’s.
The slow fall in the pH of seawater as the ocean absorbs carbon dioxide from the air. The sea is still slightly basic, at about pH 8.1; it is moving towards acid, not becoming acid.
Investigation 11.1
Use the buffer model in the app. Add base or acid in small steps and watch how little the pH moves while both partners of the buffer are present; then keep going until one partner runs out. How is the sea’s carbonate like the partner that gets used up?
Check yourself
If the surface ocean’s pH fell from 8.1 to 7.8, by what factor would the concentration of H⁺ ions increase?
The pH falls by 0.3, so H⁺ is multiplied by 10⁰·³ ≈ 2.0. The concentration of hydrogen ions would roughly double.
11.2A battery you can refill
Oxford, England, 1980
In a laboratory at the University of Oxford, a professor named John Goodenough was hunting for a better material to hold lithium. He was already in his late fifties, an age at which many scientists slow down. As a boy he had struggled badly to learn to read (he was probably dyslexic), and he had served as a weather forecaster in the Second World War before coming to science. He never stopped working: he was still going to his laboratory in his nineties. A few years earlier, Stanley Whittingham, working for the oil company Exxon in the United States, had shown that lithium ions could slip in and out between the layers of a solid and make a working rechargeable cell. But Whittingham’s cells used pure lithium metal, which could catch fire, and they gave only a little over 2 volts. Goodenough reasoned that a metal oxide, built in layers, should hold onto incoming electrons more strongly and so give a higher voltage. His team tried lithium cobalt oxide. It gave about 4 volts.
Five years later in Japan, Akira Yoshino, working for the chemical company Asahi Kasei, took the last dangerous piece away. Instead of lithium metal on the other side, he used a form of carbon that could hold lithium atoms tucked between its layers. The cell no longer contained any bare lithium metal at all, and it was far safer. The first lithium-ion batteries went on sale, made by Sony, in 1991. In 2019 the three men shared the Nobel Prize in Chemistry; Goodenough was 97, the oldest person ever to win a Nobel Prize.
What did they build? Burning releases energy by moving electrons into lower-energy arrangements, as fuel and oxygen turn into carbon dioxide and water. A battery does something similar with electrons, but without fire and without making carbon dioxide, and a rechargeable battery can do it backwards too. The phone in your hand most likely runs on a lithium-ion cell.
Inside, there are two layered materials, separated by a liquid or gel that lets ions through but not electrons (Chapter 8). On one side is graphite, the same flat sheets of carbon as in a pencil, the very pencil this adventure began with. When the cell is charged, lithium atoms are tucked between those sheets. On the other side is a metal oxide, for example Goodenough’s cobalt oxide, also built in layers with gaps between them.
Picture two books. The graphite is one book, and its sheets are the pages; the lithium atoms are slips of paper tucked between the pages. The metal oxide is a second book. Using the battery slides the slips out of the first book, across, and in between the pages of the second. Charging pushes them back. No page is torn and no slip is lost, which is why it can be done hundreds of times.
When you switch on the phone, the cell discharges. Each lithium atom between the graphite sheets gives up one electron and becomes a lithium ion, Li⁺. The electron cannot cross the separator, so it takes the long way round: out through the wire, through the phone, doing useful work, and in at the other side. Meanwhile the Li⁺ ion travels the short way, straight through the electrolyte, and slips in between the layers of the metal oxide, where it meets the electron again.
Figure 11.2A lithium-ion cell discharging. Lithium ions take the short path through the electrolyte; electrons take the long path through the phone. To charge the cell, a charger pushes both back to the graphite.
Count the charges and you will see why the two paths must go together. Every time an electron leaves one side through the wire, a positive ion leaves the same side through the electrolyte, so neither side builds up a charge. Stop either flow (cut the wire, or block the ions) and the other stops too.
When you charge the phone, the charger does work: it pushes electrons back through the wire to the graphite, and the lithium ions follow them back across the electrolyte into the graphite layers. This is the uphill direction (an electrolytic process, Chapter 8), which is why it needs a power supply. No atoms are made or lost in either direction. The same lithium atoms shuttle back and forth, which is why these cells are sometimes called “rocking-chair” batteries.
Why lithium? Three reasons, all from earlier episodes. It is the lightest metal: a mole of lithium has a mass of only 6.94 g. Each atom gives up exactly one electron, so each 6.94 g of lithium can deliver a whole mole of electrons. And lithium gives up that electron very readily, which makes the voltage of a lithium cell high, about 3.6 to 3.7 volts, compared with about 1.1 volts for the zinc–copper cell in Chapter 8.
Moles of electrons per kilogram of metal:
Lithium: 1000 g ÷ 6.94 g per mole × 1 electron = about 144 moles of electrons
Lead (in a car battery, each atom gives 2 electrons): 1000 g ÷ 207.2 g per mole × 2 = about 9.7 moles of electrons
Lithium can deliver about 15 times as many electrons per kilogram.
A whole cell is much heavier than the lithium inside it (there is graphite, metal oxide, electrolyte, casing and wiring too), so a real lithium-ion battery stores several times more energy per kilogram than a lead–acid battery, not fifteen times. That is still why phones and electric cars use lithium.
Careful
“Charging fills a battery up with electrons from the wall socket, so a full battery is heavier.”
The number of electrons in the cell never changes. For every electron the charger pushes into the graphite side, it pulls one out of the metal oxide side. What charging stores is energy: the lithium and its electrons are pushed back into a higher-energy arrangement, ready to run downhill again. (Batteries do slowly wear out, but not because anything is used up by electrons leaving. Side reactions slowly trap some of the lithium in a thin crust on the graphite, so there is less to shuttle.)
Understand itThe lithium-ion battery
What is it?
A rechargeable cell in which lithium ions shuttle between layers of graphite and layers of a metal oxide, while electrons travel round the outside circuit, through your phone.
Why is it called this?
After the ions that do the shuttling. Lithium was named in 1817 by Berzelius, after his student Arfwedson found it, from the Greek lithos, “stone”, because it was discovered in a mineral, unlike potassium, first found in plant ashes, and sodium, known partly from animal blood.
What problem did it solve?
Earlier rechargeable batteries were heavy for the energy they held, and the first lithium cells used bare lithium metal, which could catch fire. Goodenough’s oxide gave a high voltage, and Yoshino’s carbon removed the bare metal: light, safe, rechargeable power.
Why does it work?
Lithium gives up its single outer electron very readily, and its small ion fits neatly between the layers of both materials. Discharging lets lithium and its electrons run downhill into the metal oxide; charging pushes them back up into the graphite. No atoms are made or lost, so it can be repeated hundreds of times.
How does it help?
It powers phones, laptops and electric cars, and it can store electricity from sunshine and wind for later: energy without burning anything.
Go deeper how do we know, what it isn’t, where does it stop working
How do we know?
Lithium is the lightest metal: a kilogram can deliver about 144 moles of electrons, against about 9.7 for lead. And a lithium-ion cell gives about 3.6 to 3.7 volts, against about 1.1 for the zinc–copper cell.
What it isn’t
Not a tank that fills up with electrons from the wall socket. The number of electrons inside never changes; charging stores energy by pushing the lithium into a higher-energy arrangement.
Where does it stop working?
Side reactions slowly trap some lithium, so capacity fades over the years. Damaged or overheated cells can catch fire. And the lithium and cobalt must be mined, which has costs of its own.
Your turn
Explain The lithium-ion battery to a friend in one sentence, in your own words. Then compare it with the book’s.
A rechargeable cell in which lithium ions shuttle between layers of graphite and layers of a metal oxide, while electrons travel round the outside circuit, through your phone.
Investigation 11.2
Step the electron transfers in the cell model forward and count what is conserved at each step: atoms of each kind, total charge, electrons. Then compare the spontaneous direction with the uphill, charging direction.
Check yourself
Why must lithium ions move through the electrolyte at the same time as electrons move through the wire? What would happen if they could not?
Each electron that leaves the graphite side through the wire takes away a negative charge; the Li⁺ ion leaving the same side through the electrolyte takes away a matching positive charge. Together they keep both sides neutral. If the ions could not move, negative charge would pile up on one side and positive on the other, the build-up would push back against the electrons, and the current would stop almost at once.
Case file 11
The kilogram of gas
The piped gas in many Mumbai kitchens is mostly methane, CH₄. Suppose a family’s stove burns exactly 1.00 kg of it over a few weeks. This last case needs everything you have learned on the whole journey. Here is what the clues say.
One mole of methane has a mass of 16.04 g. Burning it: CH₄ + 2 O₂ → CO₂ + 2 H₂O.
Careful measurement shows that the flames produced 2.74 kg of carbon dioxide and 2.25 kg of water vapour: almost 5 kg of products from 1 kg of fuel.
Average bond energies, in kilojoules per mole of bonds: C–H 413, O=O 498, C=O 799, O–H 463.
A sealed bottle of methane and air can sit on a shelf for years without burning, yet a single spark lights it.
Over the following years, a share of that carbon dioxide dissolves in the sea.
Answer these, and for each one say which of the book’s four big ideas (count everything; opposite charges attract; jiggling against sticking; huge numbers make steady averages) you used.
(a) Where did the extra mass of the products come from?
(b) Burning breaks every bond in the methane and oxygen, and breaking bonds always costs energy. So why does the flame give out heat? How much, for the whole kilogram?
(c) Why doesn’t the gas burn on its own, and why does one spark set it going?
(d) What happens to the sea’s carbonate when the CO₂ dissolves?
Show the solution
(a) From the air. 1.00 kg of methane is 1000 ÷ 16.04 = 62.3 moles. The equation needs 2 moles of O₂ for each mole of CH₄, so the flame took 124.7 moles of oxygen, 3.99 kg, out of the kitchen air. Mass in: 1.00 + 3.99 = 4.99 kg. Mass out: 2.74 + 2.25 = 4.99 kg. Every atom is accounted for. Count everything, using moles: huge numbers.
(b) Making bonds pays back more than breaking them costs. For one mole of methane:
Break 4 C–H and 2 O=O: 4 × 413 + 2 × 498 = 2,648 kJ taken in.
Make 2 C=O and 4 O–H: 2 × 799 + 4 × 463 = 3,450 kJ given out.
Net: 2,648 − 3,450 = −802 kJ per mole, which matches the measured value for methane burning to carbon dioxide and water vapour.
For the whole kilogram: 62.3 × 802 ≈ 50,000 kJ, or 50 megajoules. The new bonds hold their atoms more tightly than the old ones did: opposite charges attract, and the electrons end up in lower-energy positions, closer to the nuclei that pull on them.
(c) An energy barrier. At room temperature, only a tiny fraction of collisions between methane and oxygen molecules are energetic enough to get over the barrier and start breaking bonds. A spark makes a small spot so hot that many collisions there do get over it; the heat they release then keeps the next layer of gas hot enough, and the flame keeps going. Jiggling against sticking.
(d) It gets used up. The CO₂ forms carbonic acid, and most of the H⁺ it releases is taken up by carbonate ions, turning them into bicarbonate. The pH falls only a little, but there is less carbonate left for shell-building animals. Equilibria and buffers: huge numbers make steady averages, together with count everything, since every carbon atom from the gas ends up somewhere.
One last story before the end. The alchemists of the Middle Ages, the people who first set up furnaces and flasks and began the long road to chemistry, dreamed above all of turning lead into gold. Chemistry could never do it: as you now know, a reaction only rearranges electrons, and an element is fixed by the number of protons in its nucleus. Only nuclear physics can change that number. In 2025 scientists at CERN’s ALICE experiment reported that lead nuclei, smashed past each other at almost the speed of light, had sometimes lost three protons and become gold: billions of nuclei in all, adding up to only a tiny fraction of a billionth of a gram. In October 2026 a start-up company, Marathon Fusion, claimed to have made gold from mercury using neutrons from fusion; at the time of writing, no one else has yet checked that claim. The old dream came true, in a way nobody in the Middle Ages could have imagined, and it turned out not to matter much. Chemistry’s real treasure was never gold. It was understanding.
Where you go from here
You started this adventure with a pencil and a diamond, and a question about how anyone can know what is inside things too small to see. Look how far you have travelled since. You stood with Greek thinkers arguing about whether a pebble could be cut forever. You watched a Manchester schoolteacher weigh things nobody could see, and a young team fire particles at gold foil in a darkened room and find almost all of an atom is empty. You counted protons, weighed molecules by the mole, watched energy run downhill and be pushed uphill, saw Wöhler’s crystals and van ‘t Hoff’s tetrahedra, and followed carbon from a gas flame in a Mumbai kitchen, through Keeling’s air, into the sea. And the graphite in that first pencil turned out to be the same carbon that holds the lithium in the phone in your pocket.
Every person you met in this book began exactly where you are now: with a question, some careful measurements, and a willingness to be wrong for a while. None of them knew all the answers. Many got things wrong before they got them right. What they had was the habit you now have too: asking how do we know?, and not stopping until the evidence answers.
There is so much more still to find. Beyond this book, electrons stop looking like dots and become clouds of probability, described by quantum mechanics. Chemists design new molecules step by step, from medicines to materials for better batteries. And some of the most important open questions in the world, how to capture carbon dioxide, how to store sunlight, how life began, are chemistry questions that nobody has fully answered yet. The adventure does not end here. It just stops being a book and starts being yours.
Stories behind the ideas
Every big idea in chemistry was found by someone, somewhere, often after years of getting it wrong. These are their stories, told slowly, with the idea explained step by step. Any word in the book that has a story is marked like this; tap it and the story opens beside the page.
1817 to today
The families of the table
Johann Döbereiner, Humphry Davy, William Ramsay, Homi Bhabha
Crawford Market, Mumbai, any afternoon
Walk through a big Mumbai market and the periodic table is all around you, though nobody has labelled it. The salt in the spice stalls is sodium and chlorine. The steel tiffin boxes are iron with chromium and nickel. The copper handi in the pot shop, the aluminium pressure cooker, the neon-red shop sign, the paan seller’s tin of chuna, the phone in your pocket with its lithium battery and its tiny speaker magnet: every one of them is a member of a family.
Chemists first noticed the families two hundred years ago. In 1817 Johann Döbereiner, in Jena, saw that some elements came in threes with matching habits. You can read that story in the periodic-table story. Here is the cast list as we know it now, column by column, with where to meet each family yourself.
The alkali metals (column 1)
Lithium, sodium, potassium, rubidium, caesium, francium. Every one has a single electron alone in its outer shell, and it is held loosely, so these metals hand it over at the slightest chance. They are soft enough to cut with a knife, so reactive that they are stored under oil, and they react with water more fiercely the further down you go: lithium fizzes, sodium skates about, potassium bursts into lilac flame. You will never see the metals themselves at home, but their ions are everywhere: sodium in salt, potassium in bananas and coconut water, lithium in the battery of every phone.
The alkaline earth metals (column 2)
Beryllium, magnesium, calcium, strontium, barium, radium. Two outer electrons, a little more firmly held, so they are tougher and less wild than their neighbours. Calcium is in your bones and teeth, in milk, in the marble of old buildings and in chuna, the slaked lime the paan seller spreads on a leaf (it is strongly alkaline, which is why it must never go near eyes). Magnesium sits at the heart of every chlorophyll molecule, so every green leaf of palak contains it. Strontium makes the crimson of Diwali rockets, and barium the green.
The transition metals (the sunken middle)
Iron, copper, zinc, chromium, nickel, silver, gold, platinum and their neighbours. These are the hard, shiny, useful metals of everyday life. Their newest electrons go into an inner d room, so their outer surfaces look much alike and they mix happily into alloys. Most steel kitchen vessels in India are stainless steel, iron mixed with chromium and usually some nickel (the best grade, often stamped 18/8, has about 18 percent chromium and 8 percent nickel), the chromium forming an invisible skin that stops rust. Copper carries electricity through the wires in your walls. Zinc coats nails and buckets to protect them. Many transition metals make coloured compounds: the blue of copper sulfate, the green of a copper statue, the reds and yellows of iron in the soil.
The boron group and the carbon group (columns 13 and 14)
Here the family characters start to change as you go down a column, from non-metal at the top to metal at the bottom. In column 13, aluminium is the metal of foil and pressure cookers; indium, below it, is in the clear electrical coating on your phone’s touchscreen. Column 14 begins with carbon, the backbone of every living thing (the whole of Chapter 10), then silicon, which as silicon dioxide makes up the quartz in most sand and glass, and which is the heart of the chips in every computer, then tin and lead, which are plainly metals.
The nitrogen and oxygen families (columns 15 and 16)
Nitrogen makes up 78 percent of the air you breathe; phosphorus, below it, is on the striking strip of every matchbox and in the backbone of your DNA. Oxygen is the most abundant element in your body by mass; sulfur, just below, is behind the sharp smell of cut onions and of hing in the tadka. Same outer electrons, very different looks: a reminder that families share chemistry, not appearance.
The halogens (column 17)
Fluorine, chlorine, bromine, iodine, astatine. Each is one electron short of a full outer shell, and taking an electron from another atom releases energy, so they are fierce, poisonous and colourful: pale yellow fluorine, yellow-green chlorine, red-brown liquid bromine, nearly black iodine with a purple vapour. Tamed as ions, they are everywhere. Chlorine disinfects city tap water and is the “chlor” in bleach. Fluoride in toothpaste hardens teeth. Most salt sold in India has a little iodine added, because a lack of iodine harms growing children.
The noble gases (column 18)
Helium, neon, argon, krypton, xenon, radon. Full outer shells, so they almost never react: for a century chemists barely noticed them, until William Ramsay’s work in the 1890s (his life story tells it). Neon glows orange-red in signs; argon fills welding torches and old-style light bulbs; helium lifts party balloons.
The lanthanides and actinides (the floating strip)
The lanthanides, once called the rare earths, are fifteen near-twins that chemists took a century to separate. They are hidden inside modern life: neodymium makes the tiny powerful magnets in phone speakers and earphones; a coating containing cerium helps turn the blue light of a white LED bulb into white. The actinides are all radioactive. Uranium fuels nuclear power stations, including India’s first, at Tarapur, about a hundred kilometres north of Mumbai, which started up in 1969. Thorium matters especially to India, which has large reserves of it in the monazite sands of Kerala; Homi Bhabha planned India’s nuclear programme around using it one day.
Careful
“Elements in the same family look the same.”
They share outer electrons, so they share chemical habits: what they combine with and in what ratios. They can look completely different. Fluorine is a gas and iodine is a solid; carbon is a black powder or a diamond while lead is a soft grey metal. Look for the family resemblance in how they react, not in how they look.
A family hunt in the kitchen
With an adult, go through the kitchen and the bathroom and read labels. Make a chart with a column for each family and add every element you can find a sign of: sodium and chlorine in salt, iodine in iodised salt, sodium in baking soda (sodium hydrogencarbonate), calcium in chuna or calcium tablets, aluminium in foil, iron, chromium and nickel in steel vessels, copper in a copper vessel or wire, fluorine in toothpaste, carbon in sugar. Read and look only: do not open or taste anything that is not ordinary food, and leave chuna and cleaning products closed. Which family turns up most? Which can you not find at all?
When you meet a new element, ask first: which family is it in? That one question tells you more about how it will behave than any other fact you could learn about it.
How to remember the periodic table
Hermann Ebbinghaus, Henry Roediger, Jeffrey Karpicke
A study table at home, the night before a test
It is late, the chapter is open, and the periodic table stares back: 118 boxes, every one with a symbol, a name and a number. The temptation is to read it over and over until it sticks. That is the method most people use, and research on learning suggests it is one of the least effective there is. This story is about better ways, and about something even more useful: how to understand the table so well that you hardly need to memorise it at all.
Step 1: understand before you memorise
A chemist who has forgotten where molybdenum goes can still draw the periodic table, because the shape is not arbitrary. It is the 2, 8, 8, 18, 18, 32, 32 pattern of electron rooms (the table-shape story explains why). If you can draw the skeleton from memory, you already know where every block is and roughly where every element must sit.
So learn the skeleton first, as a drawing, not as a list:
Row 1: one box on the far left, one on the far right (hydrogen and helium).
Rows 2 and 3: two boxes on the left, six on the right, a gap between.
Rows 4 and 5: two on the left, a block of ten in the middle, six on the right: 18.
Rows 6 and 7: the same, plus a strip of fourteen floated underneath: 32.
Then learn the families, because a family tells you more than a name ever will. Column 1 is the soft, violent alkali metals; column 17 the fierce halogens; column 18 the calm noble gases (the families story introduces them all). Once you know that sodium is in column 1, you know a dozen things about it without memorising any of them.
Step 2: memorise strategically
Not all 118 boxes deserve equal effort. Most of the chemistry in this book uses the first twenty elements, plus a handful of famous metals (iron, copper, zinc, silver, gold, mercury, lead) and the halogens bromine and iodine. Learn those well and you can read almost any chemistry you will meet for years. The rest you can always look up, and you will find you remember more of them each time you do.
The first twenty, in order, are hydrogen, helium, lithium, beryllium, boron, carbon, nitrogen, oxygen, fluorine, neon, sodium, magnesium, aluminium, silicon, phosphorus, sulfur, chlorine, argon, potassium and calcium.
Step 3: use methods that actually work
Psychologists have studied memory for more than a century, since Hermann Ebbinghaus in Germany in the 1880s memorised long lists of nonsense syllables and measured how fast he forgot them. Three findings matter most for you.
Test yourself instead of rereading. In a well-known 2006 experiment, Henry Roediger and Jeffrey Karpicke in the United States had students study a passage, then either study it again or take a practice test. A week later, the students who had tested themselves remembered much more. The struggle to pull something out of your memory is what makes it stick. Reading the table again feels productive; covering it and trying to write it down actually is.
Space it out. A large review of hundreds of experiments, published in 2006 by Nicholas Cepeda and colleagues, found that the same amount of practice spread over several days beats cramming it into one session, often by a lot. Ten minutes a day for a week works better than seventy minutes the night before. Each time you are about to forget something and you pull it back, the memory becomes stronger. This idea is called spaced repetition.
Chunk it. In 1956 the psychologist George Miller pointed out that we hold only a few separate items in mind at once, but each item can be a big “chunk”. Do not learn twenty separate elements; learn four rows of the table, or the families, as chunks.
Step 4: tricks that help the hard parts
For lists that have no logic, like the order of the first twenty, memory tricks really do help.
A mnemonic is a sentence whose words start with the same letters as the things you need to remember. The best ones are the ones you make yourself, because making one is itself a kind of practice, and silly or vivid ones stick best. Here is one we made up for this book, with a Mumbai flavour:
Hungry Hens Like Bel But Can’t Nibble Our Fried Neems; Naughty Monkeys Always Silently Pinch Samosas, Clever Arjun Keeps Calm.
(Bel is the wood-apple fruit; neem leaves are bitter, so a fried neem would indeed be hard to nibble.) Now make a better one of your own.
A memory palace is an older trick. According to a story told by the Roman writer Cicero, the Greek poet Simonides survived the collapse of a banquet hall and could name the dead by remembering where each guest had been sitting. Whether or not that happened, the method works: imagine walking through a place you know well, such as your home, and leave each element at a spot along the way. Hydrogen in a balloon at the front door, helium floating beside it, lithium in the phone on the shoe rack, and so on. To recall them, walk the route again in your mind.
There are also songs. The most famous is “The Elements” by the American musician Tom Lehrer, from 1959, which rattles through the names to a tune by Gilbert and Sullivan. If a tune helps you, make your own: a familiar melody with element names fitted to it can be remarkably sticky.
Careful
“Learning the periodic table means memorising all 118 boxes.”
Chemists do not carry 118 boxes in their heads. They carry the shape, the families and the trends, plus the elements they use most, and they look up the rest. Understanding the pattern is worth far more than reciting it, because the pattern lets you predict, and reciting does not.
Practise here
On the book’s page “The periodic table, inside out” you will find a Practise tab, a memory trainer that quizzes you on symbols, names and positions and brings back the ones you got wrong more often: spaced repetition, done for you. Use it a little every day rather than a lot at once.
A week with the skeleton
Every day for seven days, before you look at anything, take a blank sheet and draw the skeleton of the periodic table from memory: the towers, the sunken middle, the right-hand block, the floating strip. Then fill in as many of the first twenty elements as you can. Only then check against the real table and mark what you got wrong. Keep all seven sheets. On day seven, lay them side by side: you will see your memory grow, and you will have used testing, spacing and chunking all at once.
The aim was never to become a walking list. It is to know the table the way you know your own neighbourhood: not every house number, but where everything is, and how to find the rest.
1871 to today
A map that predicts
Dmitri Mendeleev, Marguerite Perey, Emilio Segrè
A map is useful because it tells you about places you have never been. Look at a map of Maharashtra and, even if you have never visited Nashik, you can guess it is inland, north-east of Mumbai, and higher up. The periodic table is a map of that kind. Its greatest power is not that it lists what we know; it is that it lets you work out what you don’t know.
Mendeleev was the first to play this game. In 1871 he described an undiscovered element he called eka-silicon, the gap below silicon. He predicted atoms about 72 times as heavy as hydrogen and a density of about 5.5 grams per cubic centimetre. When germanium was found in Germany in 1886, its atoms came out at about 72.6 and its density at about 5.3. (His life story, and the story of the periodic table, tell the whole adventure.) Now it is your turn.
How to play
There are three rules, and you already know them all.
Find the family. Elements in the same column have the same outer electrons, so they have the same chemical habits.
Follow the trend down the column. Going down, atoms get bigger, the outer electrons sit further out and are held less tightly, so metals get more reactive and non-metals less so. Melting points, colours and densities usually change step by step.
Expect surprises at the extremes. Very heavy atoms have so many protons that their inner electrons move at a large fraction of the speed of light, and that changes things. (This is why gold is yellow instead of silvery, an effect of Einstein’s relativity on its electrons.)
Atom size across the table. Every row after the first starts with a peak and slopes down; almost every column grows as you go down.
Predict first: francium sits at the very bottom of column 1, below caesium. Before you tap its tower, decide: taller than caesium’s, or shorter? Then tap it.
It is slightly shorter: 223 picometres against caesium’s 232. Rule 2 says it should be bigger, so this is rule 3 at work. Calculations suggest that in an atom this heavy, relativity pulls the outer electron in a little closer than the simple trend predicts. Nobody has ever had enough francium to measure its size, so this number comes from those calculations, not from a ruler.
Round one: francium
Paris, 1939
Marguerite Perey had joined Marie Curie’s laboratory as an assistant at nineteen. In 1939, carefully purifying a radioactive substance, she noticed radiation that did not fit any known element. She had found element 87, at the bottom of column 1, and named it francium after her country. In 1962 she became the first woman elected to the French Academy of Sciences, as a corresponding member.
Here is the puzzle: almost nobody has ever seen francium. Its longest-lived form falls apart with a half-life of about 22 minutes, so there is never more than a trace of it anywhere, and nobody has ever gathered enough to see a lump. So what is it like? Use the map.
Column 1 going down: lithium, sodium, potassium, rubidium, caesium, then francium.
Each is softer than the one above, melts at a lower temperature and reacts more violently with water.
Caesium melts at about 28 °C, a warm day in Mumbai. Prediction: francium is a very soft, silvery metal that would melt on a warm day, and would react explosively with water.
That prediction is almost certainly close to the truth, but no one can test it directly, because a visible piece of francium would heat itself, and break apart, from its own radioactivity. The map is the best description we have.
Round two: astatine
Berkeley, 1940
Emilio Segrè and his colleagues made element 85 in 1940 by firing particles at bismuth, and called it astatine, from the Greek for “unstable”. It sits at the bottom of the halogens, under iodine. Like francium, it is so radioactive that only tiny amounts ever exist.
Column 17 going down: fluorine (pale yellow gas), chlorine (yellow-green gas), bromine (red-brown liquid), iodine (nearly black solid with a purple vapour), then astatine.
The colour gets darker and the element goes from gas to liquid to solid. Prediction: astatine is a black solid, and it behaves like a weaker version of iodine.
Good chemistry, and mostly right. But this is where rule 3 comes in. Some calculations suggest that if you could ever gather enough astatine to look at, it might behave like a metal, shiny and conducting, not like the other halogens. The bottom of the table is where the simple trends start to bend. Nobody has been able to check.
Careful
“If an element is in the table, someone must have seen it.”
Several elements near the bottom have only ever existed a few atoms at a time, for seconds or less. For those, everything we “know” about how a lump of them would look and behave comes from position in the table and from calculations, not from seeing it. That is not cheating: it is the table doing exactly what Mendeleev built it to do.
Round three: elements that do not exist yet
The table ends at element 118, oganesson, which completes row 7. What would element 119 be?
Use the map. A new row starts with a new s room, so element 119 would sit at the top of a new row 8, in column 1, under francium. It should be an alkali metal with one outer electron. The simple trend says it would be the most violent alkali metal of all. But calculations that include relativity suggest the opposite: its outer electron is pulled in closer than the trend predicts, so it may be less reactive than caesium and francium, more like potassium. That is a prediction about an element no one has made. As this book was written, in 2026, teams in Japan and Russia were trying, or preparing, to make it by smashing nuclei together, so far without success.
Is there an island out there?
Most of the heaviest elements fall apart in seconds or less. But physicists have long predicted that certain combinations of protons and neutrons should be unusually stable, the way full electron shells are. Somewhere beyond the elements we have made, there may be an island of stability, where superheavy nuclei last much longer: minutes, days, perhaps much more. Nobody has reached it yet. The heaviest atoms made so far have too few neutrons to land on it, and whether the island exists, and how long its atoms would last, is still an open question.
Will the table ever end?
Nobody knows. Each new element is harder to make than the last, and the nuclei get less stable. Some calculations suggest that beyond about 170 protons the atom itself would behave very strangely, because the nucleus pulls so hard on its innermost electrons. But no one is close to testing that, and it is quite possible the practical end will come long before. One of the most famous charts in science still has an unwritten edge.
Play the prediction game
Cover the bottom of a printed periodic table with a sheet of paper so you can see only the top three rows. Choose any column. Write down two facts about each element you can see (gas, liquid or solid; metal or not; reactive or calm) and look for the trend. Then predict the next element down: its state at room temperature, whether it is a metal, and whether it is more or less reactive. Uncover it and look it up. Score yourself a point for each prediction that was right. Mendeleev would have scored very well.
The periodic table is not a finished list to learn by heart. It is a tool for thinking, and its most exciting boxes are the ones where you have to reason your way to the answer.
13.8 billion years ago to 2017
Where the elements come from
Cecilia Payne, Margaret Burbidge, Geoffrey Burbidge, William Fowler, Fred Hoyle, Jennifer Johnson
Cambridge, Massachusetts, 1925
Cecilia Payne was twenty-five, an English student who had crossed the Atlantic because women in Cambridge, England, could study science but could not be awarded degrees. At Harvard College Observatory she was given thousands of glass photographs of starlight, each one spread into a spectrum crossed by dark lines: the fingerprints of elements, the same kind Bunsen and Kirchhoff had found in flames (the spectra story tells that part).
Using the new physics of the atom, Payne worked out not just which elements were in the stars, but how much of each. Her answer was astonishing. The stars were not made of roughly the same stuff as the Earth, as everyone assumed. They were overwhelmingly hydrogen and helium, with everything else a light sprinkling. The most senior astronomer in America, Henry Norris Russell, told her the result was “clearly impossible”, and in her thesis she wrote that the huge amount of hydrogen was “almost certainly not real”. A few years later Russell himself reached the same conclusion by another route. Her thesis has since been called one of the most brilliant ever written in astronomy.
She was right. By mass, the ordinary matter of the universe is about three-quarters hydrogen and about a quarter helium. Everything else, all the carbon and oxygen and iron and gold, adds up to around two percent. So where did that come from?
Chapter one of the story: the Big Bang
About 13.8 billion years ago the universe was unimaginably hot and dense, and it was expanding fast. In the first few minutes it was hot enough for protons and neutrons to fuse, but it cooled too quickly to get far. It made hydrogen, helium and a tiny trace of lithium, and then the window closed.
That means something remarkable about you. Most of the atoms in your body are hydrogen (you are mostly water, and each water molecule has two hydrogen atoms). Nearly every one of those hydrogen atoms was made in the first minutes of the universe. The hydrogen in a glass of water from your kitchen tap is about 13.8 billion years old.
Chapter two: the kitchens inside stars
For everything heavier, the universe needed stars. A star is a vast ball of gas squeezing itself under its own weight until the centre is hot enough for nuclei to fuse. Our Sun turns hydrogen into helium and will keep doing so for billions of years.
Bigger stars go further. When their hydrogen runs low, their cores squeeze harder and heat up more, and they fuse helium into carbon and oxygen, then those into neon, magnesium, silicon and sulfur, and finally into iron. Each step releases energy, which keeps the star shining. But iron is the end of the line. Fusing iron into anything heavier costs energy instead of releasing it, so a star cannot live on it.
Pasadena, 1957
How all this works was set out in a single huge paper in 1957, “Synthesis of the Elements in Stars”, by Margaret Burbidge, Geoffrey Burbidge, William Fowler and Fred Hoyle. It is still known by their initials, B²FH. Margaret Burbidge had to fight for her place in astronomy: she once had to pretend to be her husband’s assistant to be allowed to use a famous telescope. The paper explained, step by step, how stars could build almost every element, and Fowler later shared the 1983 Nobel Prize in Physics for this kind of work.
Chapter three: explosions
When a very big star’s iron core can no longer hold itself up, it collapses in a fraction of a second and the star blows itself apart in a supernova, briefly outshining a whole galaxy. The explosion flings the carbon, oxygen, silicon and iron the star has made out into space, and in the violent blast it makes some heavier elements too. Another kind of explosion, when a small dead star called a white dwarf is pushed over the edge, makes a great deal of the iron in the universe.
The flung-out gas mixes with the clouds between the stars. New stars, and the planets around them, form from that enriched gas. Our Sun and the Earth formed about 4.6 billion years ago from a cloud that had already been seeded by generations of earlier stars. The calcium in your bones and the iron in your blood were made inside stars that died before the Sun was born.
Hanford and Livingston, 17 August 2017
The heaviest elements, like gold, platinum and uranium, need a flood of neutrons to build, far more than ordinary stars can supply. For a long time nobody was sure where that flood happened. Then, on 17 August 2017, the gravitational-wave detectors of LIGO in the United States and Virgo in Italy felt a faint ripple in space itself. It came from two neutron stars, the collapsed cores of dead stars, so dense that a teaspoon would weigh as much as a mountain, spiralling into each other about 130 million light years away. Telescopes around the world turned to the spot and watched a new kind of glow, called a kilonova. Its light carried the signatures of freshly made heavy elements. LIGO’s own summary estimates the collision threw out somewhere between a thousandth and a hundredth of the mass of our Sun.
So the universe has its own gold factory: colliding dead stars. Remember the transmutation story, where people spent fortunes making a few atoms of gold? Nature makes it in quantities the size of planets, in explosions we can now hear across space. Astronomers still debate how much of the universe’s gold comes from mergers like this and how much from rare kinds of supernova; the honest answer is that both seem to contribute, and nobody yet knows the exact share.
Chapter four: cosmic rays and laboratories
Three light elements, lithium, beryllium and boron, are made largely a stranger way (lithium also comes from the Big Bang and from some dying stars): fast particles called cosmic rays smash into heavier nuclei drifting in space and chip pieces off them. And the newest elements of all were made by people. Almost everything heavier than uranium is made in laboratories, a few atoms at a time, by smashing nuclei together; only tiny natural traces of neptunium and plutonium exist.
The astronomer Jennifer Johnson, at Ohio State University, drew a periodic table in which every box is coloured by where that element comes from: the Big Bang, dying small stars, exploding big stars, exploding white dwarfs, colliding neutron stars, cosmic rays. It is one of the most beautiful versions of the table ever made, and worth looking up.
Careful
“Elements are made in factories and chemistry labs.”
Factories and labs only rearrange atoms into new substances. They do not make new atoms of an element; a chemical reaction never changes a nucleus. Almost every atom on Earth, apart from a few made in nuclear reactors and particle accelerators, was made in the Big Bang or in stars long before the Earth existed, and has been recycled ever since.
Your body’s star map
Write down the four elements that make up most of your body by mass: oxygen (about 65 percent), carbon (about 18), hydrogen (about 10) and nitrogen (about 3). Beside each, write where it was made: hydrogen in the Big Bang; carbon, oxygen and nitrogen inside stars. Then add calcium (bones) and iron (blood): both from stars and their explosions. Finally, if anyone in the family has a gold ring, hold it and say where its atoms were most probably made. You are, quite literally, made of stars.
When you look at the periodic table now, you can see a history in it. The first two boxes are the Big Bang. Most of the rest are the work of stars. The heavy metals at the bottom are the ashes of the most violent events in the universe. And the very last boxes were made by people, in laboratories, a few atoms at a time.
1913 to today
Why the table has that strange shape
Niels Bohr, Charles Janet, Theodor Benfey, Eric Scerri
A classroom wall in Mumbai, any school day
Look at the periodic table on any classroom wall and it is a very odd shape for a chart. It is not a neat rectangle. There are two tall towers on the left, a lower block sunk into the middle, a set of six columns on the right with one lonely box perched at the top corner, and then, strangest of all, two long rows floating underneath the whole thing, as if someone had cut them out and forgotten to glue them back.
None of that is decoration. Every bump and gap is a picture of something real: the way electrons arrange themselves around a nucleus. Once you can read the shape, you can say a surprising amount about any element without having memorised anything.
Step 1: shells have rooms inside them
In Chapter 1 you met electron shells: groups of electrons at roughly the same energy, the first holding up to 2, the second up to 8. By the 1920s physicists, Niels Bohr among them, had found that each shell is itself divided into smaller groups, called sub-shells. They are named with letters left over from the early study of spectra: s, p, d and f.
Think of a shell as a floor of a hotel, and the sub-shells as the rooms on that floor. The rooms come in fixed sizes:
an s room has 2 seats
a p room has 6 seats
a d room has 10 seats
an f room has 14 seats
Here is what those rooms actually look like. Each “seat pair” is a cloud where an electron is likely to be found: s rooms are round, p rooms are dumbbells pointing three ways.
Shells as usually drawn, and the clouds electrons really make. Each cloud holds at most two electrons.
The first floor has only an s room (2 seats). The second floor has an s room and a p room (2 + 6 = 8). The third floor has s, p and d (2 + 6 + 10 = 18). The fourth has all four kinds (2 + 6 + 10 + 14 = 32). Electrons fill the cheapest seats first, the ones with the lowest energy, just as water fills the bottom of a jug first.
Step 2: the order of filling builds the rows
Here is the twist that gives the table its shape. The rooms are not filled strictly floor by floor. The 3d room, on the third floor, turns out to be slightly more expensive than the 4s room on the floor above, so electrons fill 4s first and only then go back to 3d. (That simple rule is the one that builds the table, but the full story is subtler: once electrons are actually sitting in 3d, the 3d room ends up slightly lower than 4s, which is why an iron atom loses its 4s electrons first when it becomes an ion. You will meet that later.) In the same way, the 4f room waits until after 6s.
Each new row of the table begins when electrons start a new s room. Count what gets filled before the next s room opens, and you get the length of each row:
That is the famous sequence 2, 8, 8, 18, 18, 32, 32, and it adds up to 118, exactly the number of elements known today. The rows are not long or short by accident. They are as long as the rooms that get filled.
Step 3: the four blocks
Now the shape makes sense. Colour each element by the kind of room its newest electron went into, and the table splits into four regions, called blocks:
the s-block: the two tall towers on the left (2 columns, because s rooms have 2 seats), plus helium
the p-block: the six columns on the right (p rooms have 6 seats)
the d-block: the ten columns sunk into the middle, starting only in row 4, because that is when the first d room fills
the f-block: fourteen elements in each of rows 6 and 7
And the floating strip? If you put the f-block where it really belongs, inside rows 6 and 7, the table would be 32 columns wide: so long and thin that it would not fit on a classroom wall, and every box would be tiny. So printers cut the f-block out and lay it underneath. It is a convenience, not a separate kind of table. Some books do print the long, 32-column version, and it is worth looking at once: it shows the true shape, without the cut.
Step 4: reading the position
This is where the shape pays off. An element’s position tells you how its outermost electrons are arranged, and those outer electrons decide most of its chemistry.
Take sulfur. It is in row 3, so its outer electrons are on the third floor. It is the fourth column of the p-block, so it has 2 electrons in its 3s room and 4 in its 3p room: 6 outer electrons in all. Oxygen sits directly above it, also with 6 outer electrons, and that is why sulfur and oxygen behave like cousins.
A printed box usually carries four things: the atomic number (the proton count), the symbol, the name, and the relative atomic mass (an average over the element’s isotopes, which is why it is rarely a whole number). The atomic number fixes the position, the position tells you the outer electrons, and the outer electrons tell you the chemistry.
Careful
“The table is just a list of elements sorted by weight.”
It is sorted by atomic number, the number of protons, which is why tellurium (heavier) comes before iodine (lighter). And it is not just a list: it is folded. Each fold, each new row, happens where a new shell of electrons begins. The columns line up elements whose outer electrons match.
Careful
“Elements next to each other in a row are similar.”
Usually the opposite. Neighbours in a row can be wildly different: sodium is a soft metal that fizzes in water, while chlorine, a few places along the same row, is a poisonous green gas. It is the columns that hold families. The exception is the f-block, where the newest electrons tuck into a deep inner room and barely change how the outside of the atom looks, so the fifteen elements from lanthanum to lutetium are so alike that chemists struggled for a century to tell them apart.
A few honest wrinkles
The filling order is a very good rule, not a perfect law. A handful of elements bend it slightly; chromium and copper are the famous ones, each moving one electron from the 4s room into 3d. You do not need the details. What matters is that the rule explains the shape of the whole table, and the exceptions are small.
And there are questions about the table that chemists still argue about today.
Where does hydrogen go? It has one electron, like lithium and sodium, so it usually sits on top of the first column. But it is a gas, not a metal, and in some ways it acts like the halogens, which are one electron short of a full shell. Some tables float it above the middle, belonging to no family.
Where does helium go? Chemically it is a noble gas, so it sits above neon. But its two electrons fill an s room, which would put it above beryllium.
Which elements belong in group 3? Under scandium and yttrium, some tables put lanthanum and actinium, and others put lutetium and lawrencium. A task group set up by IUPAC, the international body that looks after chemical names, published a progress report in 2021. It leaned towards lutetium and lawrencium as a possible compromise but did not settle the matter, and tables still differ.
Beauvais, France, the late 1920s
Some people have redrawn the table to show the electron rooms more honestly. Charles Janet, a French engineer and naturalist, drew a “left-step” table in the late 1920s in which every row ends with a filled s room, so helium sits above beryllium and the blocks line up as perfect steps. In 1964 the chemist Theodor Benfey drew the elements as one continuous spiral, with the d- and f-blocks as bulges. People have also drawn the table as pyramids, flowers and towers. They all hold the same information; the classroom version wins because it is the easiest to print and read.
Build the shape from seats
Take a sheet of squared paper. Starting at the top left, colour 2 squares for row 1 (put the second one far over at the right, where helium goes). For row 2, colour 2 on the left and 6 on the right. Row 3: the same. For row 4, add a block of 10 between them. Row 5: the same. For rows 6 and 7, add 14 more, drawn as a separate strip underneath. Count your squares: you should have 118. You have just drawn the periodic table from nothing but the sizes of the electron rooms.
So the next time you see the table on a wall, read its outline like a map. The towers are s rooms, the sunken middle is d rooms, the right-hand block is p rooms, and the floating strip is the f rooms that would not fit. The shape is the atom’s own floor plan.
NB
Niels Bohr
The goalkeeper who drew the atom's staircase
1885 to 1962The Danish physicist who explained why atoms give out light of only certain colours
Copenhagen, 1885
Niels Bohr was born on 7 October 1885 in Copenhagen, the capital of Denmark. His father was a professor of physiology, and his mother came from a family of bankers and teachers. The house was full of scientists and arguments, and Niels and his younger brother Harald grew up listening to both.
The two brothers were inseparable, and both were very good footballers. Niels played in goal for a Copenhagen university club. Harald was even better: he played for Denmark at the 1908 Olympic Games, and the Danish team won the silver medal. For a while, Harald was the more famous of the two Bohrs. That changed.
Niels was not a fast talker or a quick writer. He thought slowly, out loud, turning a problem over and over, and he rewrote his papers again and again. His mother sometimes wrote out his work as he dictated it. But when he had understood something, he had understood it all the way down.
A problem nobody could solve
In 1912 Bohr went to Manchester to work with Ernest Rutherford, who had just discovered that atoms have a tiny nucleus with electrons around it. But there was a serious problem with that picture. According to the physics of the time, an electron circling a nucleus should give out light continuously, lose energy and spiral into the nucleus in a tiny fraction of a second. Every atom in the universe should collapse. They obviously do not.
There was a second puzzle too. When you heat hydrogen gas until it glows and split its light with a prism, you do not see a rainbow. You see a few sharp coloured lines, always at exactly the same places. Why only those colours?
The staircase
Copenhagen, 1913
Back in Copenhagen in 1913, Bohr made a bold suggestion. Suppose, he said, an electron in an atom cannot have any amount of energy, only certain fixed amounts, like the steps of a staircase. You can stand on step 2 or step 3, but not on step two-and-a-half. While the electron stays on one step, it gives out no light and does not spiral in. It simply stays.
But when an electron drops from a higher step to a lower one, the energy it loses comes out as a single packet of light. A big drop gives a packet with lots of energy (blue or violet light); a small drop gives less (red light). Because the steps are fixed, the drops are fixed, and so only certain colours can ever come out. Those are hydrogen’s lines.
Bohr calculated the heights of the steps for hydrogen, and the colours his staircase predicted matched the measured lines almost perfectly. He could not fully explain why the staircase existed. That came later, with the new quantum mechanics of the 1920s, which replaced his neat circular orbits with fuzzier clouds. But the central idea, fixed energy levels and light coming out when electrons drop between them, is still at the heart of chemistry. It is why the electron shells of Chapter 2 exist, and why every element has its own fingerprint of colours.
The institute
In 1921 Bohr opened his own institute in Copenhagen, and for the next twenty years it was one of the most exciting places in the world to do physics. Young scientists came from Germany, Russia, Britain, America, Japan and India. They argued, played table tennis, went to the cinema together, and in the space of a few years built quantum mechanics. Bohr won the Nobel Prize in Physics in 1922.
Two medals in a jar
Copenhagen, April 1940
In April 1940, German soldiers occupied Denmark. In Bohr’s institute were two gold Nobel medals that did not belong to Bohr. The German physicists Max von Laue and James Franck had sent them to Copenhagen for safe keeping, because both men opposed the Nazis, and sending gold out of Germany was forbidden. If the soldiers found the medals, with the names engraved on them, von Laue and Franck could be in serious danger.
A Hungarian chemist at the institute, George de Hevesy, had an idea. Burying them might not work; the soldiers could search. So he dissolved them. He put the medals in aqua regia, “royal water”, a fierce mixture of nitric acid and hydrochloric acid that is one of the few things that can dissolve gold. It took a while, but the medals vanished, leaving an orange-coloured liquid in a jar. De Hevesy put the jar on a shelf among all the other bottles of chemicals, and there it stayed, in plain sight, through the whole war. Nobody looked twice at it.
When the war ended, the jar was still there. The gold was taken out of the solution, and the Nobel Foundation used it to make new medals for von Laue and Franck.
That is a perfect piece of chemistry. Dissolving the gold did not destroy a single gold atom. The atoms were simply spread out through the liquid as tiny charged gold particles (ions), invisible but all still there, and a chemist could gather them up again. You can change what gold looks like, or where it is, but by chemistry alone you can never make it stop being gold.
Escape
Bohr’s mother came from a Jewish family, and by 1943 he was in danger himself. In September that year, warned that he was about to be arrested, he and his wife escaped by small boat across the narrow sea to Sweden. Within days he was talking to the Swedish government about helping Denmark’s Jewish people, thousands of whom were ferried across the same stretch of water to safety by ordinary Danes. Soon after, Bohr was flown to Britain, crammed into the bomb bay of an aeroplane.
After the war he worked hard, with mixed success, to persuade world leaders to share knowledge about nuclear energy openly rather than race each other to build weapons. He died in Copenhagen in 1962. Element 107 is called bohrium.
Dissolve it, and get it back
You can repeat de Hevesy’s trick with something much safer than gold. Stir a teaspoon of salt into half a glass of water until it disappears completely. Is the salt gone? Taste a drop on your fingertip: it is still there. Now pour a little of the salt water onto a saucer and leave it on a sunny windowsill for a few days. As the water evaporates, the salt comes back as tiny square crystals. Dissolving hides things; it does not destroy them.
Every time this book talks about energy levels, shells, or why a flame turns a particular colour, it is climbing Bohr’s staircase.
RB
Robert Boyle
The sceptical chymist
1627 to 1691A rich nobleman's son who made chemistry an experimental science
Lismore Castle, Ireland, 1627
Robert Boyle was born into enormous wealth. His father, Richard Boyle, the first Earl of Cork, was one of the richest men in the British Isles, and Robert was the fourteenth of his fifteen children. He grew up in a castle above a river in the south of Ireland, and at the age of eight he was sent to Eton, the famous English school.
You might expect a boy like that to grow up to do nothing much. Instead, Boyle became one of the founders of modern science, and the man who did more than anyone to turn chemistry from a secret craft into an open, experimental subject.
A storm and a promise
At twelve, Boyle was sent on a long tour of Europe with a tutor. In Florence, in 1642, he read about Galileo, who had just died there, and he was fascinated by the new science that tested ideas against the world. Earlier, in Geneva, according to his own later account, a violent thunderstorm in the night terrified him so much that he vowed to live a deeply religious life. He kept that promise. All his life he was devout, and he saw science as a way of understanding God’s creation.
When he came home, his father had died and Ireland and England were at war. Boyle inherited land and money, which meant he never needed a job. He spent his life, and his fortune, on experiments.
Doubt everything, test everything
In the 1600s, most people still learned about matter from very old books. Some followed Aristotle’s four elements: earth, water, air and fire. Others followed the alchemists’ three “principles”: salt, sulfur and mercury. Both groups mostly argued from authority: the great teacher said so, so it must be true.
Boyle thought this was the wrong way round. In 1661 he published a book with a wonderful title: The Sceptical Chymist. It is written as a conversation between friends, and in it Boyle asks awkward questions. How do you know fire breaks things into their “elements”? When you burn wood, what comes out depends on how you burn it. Shouldn’t an element be something you can actually find by experiment, rather than something an ancient author declared?
He did not discover the modern elements. But he insisted that chemistry must rest on experiments, done carefully, described exactly, and repeatable by anyone. He wrote down his methods in such detail that other people could check them, which was unusual at the time. This is the habit at the very heart of science.
The air pump
Oxford, 1659
Boyle hired a brilliant young assistant called Robert Hooke, a clergyman’s son from the Isle of Wight, who was a superb builder of instruments. Together they built an improved air pump: a glass globe from which most of the air could be pumped out.
With it, they could do things no one had seen before. A ringing bell inside the globe grew fainter and fainter as the air was removed, showing that sound needs air to travel. A candle went out. A feather and a coin fell together. And Boyle measured how the pressure of trapped air changes when you squeeze it, finding that if you halve its volume, its pressure doubles. That rule is now called Boyle’s law, and you will meet it in Chapter 3. (Hooke deserves much of the credit for the apparatus; Boyle was always generous in saying so.)
Some of the experiments are hard for us to read about. Like many experimenters of his time, Boyle put small animals in the globe to see what happened when the air was taken away. It helped show that animals need air, but it is not something scientists would do today.
A Royal Society
Boyle belonged to a group of curious people who met to discuss experiments, sometimes called the “Invisible College”. In 1660 it became the Royal Society of London, one of the oldest scientific societies in the world. Its motto, Nullius in verba, roughly means “take nobody’s word for it”. That is Boyle’s whole philosophy in three words.
The other Boyle: still an alchemist
Here is the surprise. The sceptical chymist was also a believer in alchemy.
Boyle was certain, like his younger friend Isaac Newton, that metals could in principle be transformed. He spent years on alchemical experiments, traded secret recipes, and in 1676 published a paper about a special kind of mercury that he thought might “heat up” when mixed with gold. He seems to have believed, near the end of his life, that he had once witnessed lead being turned into gold.
England had an old law, from 1404 in the reign of Henry IV, which made “multiplying” gold and silver by alchemy a crime, because the king feared fake gold would wreck the currency. Historians generally credit Boyle with helping to get that law repealed in 1689. He did not want alchemists punished for trying.
Was this hypocrisy? Not really. Boyle was a man of his time, standing on the line between two worlds. He doubted ancient authorities, but he could not yet know that gold is an element whose atoms no chemical process can change. That knowledge was still more than two hundred years away.
What became of him
Boyle never married. He lived for many years in London with his beloved older sister Katherine, Lady Ranelagh, who was herself a keen thinker, and he built a laboratory in her house. He wrote dozens of books on science and religion and died in 1691, just a week after her.
Squeeze the air
Boyle’s law at your desk. Take a plastic syringe from a medicine kit (no needle). Pull the plunger out halfway, then put your finger firmly over the tip. Push the plunger in. Feel how the air pushes back harder the more you squeeze it. Let go, and the plunger springs back. You have just felt what Boyle and Hooke measured: squash a gas into less space and its pressure rises.
When you read about pressure in Chapter 3, and about Boyle’s colourful violet syrup in Chapter 7, remember the rich man’s son who spent his fortune on teaching the world to doubt, and to check.
MC
Marie Skłodowska Curie
The girl from the secret university
1867 to 1934Discovered polonium and radium; the first person to win two Nobel Prizes
Warsaw, 1870s
Maria Skłodowska was born in Warsaw in 1867, the youngest of five children. Her parents were both teachers. But Poland at that time did not exist as a free country: Warsaw was ruled by Russia, and Polish children had to be taught in Russian. Polish history and language were forbidden in schools. Maria’s father lost his good teaching job, partly because the Russian authorities distrusted him, and the family became poor.
Maria was brilliant. She finished school at fifteen with a gold medal. But universities in Warsaw did not accept women.
The Flying University
So she and her sister studied in secret. In Warsaw there was a hidden, illegal school known as the Flying University. Its classes met in different people’s homes and kept moving so the authorities would not find them. Teachers taught science, history and Polish to young people, many of them women, who could not study anywhere else.
A deal between sisters
Maria and her older sister Bronisława (Bronya) both dreamed of studying in Paris, where women could go to university. They could not afford it. So they made a deal. Maria would work and send money to Bronya while she studied medicine. Then, once Bronya was a doctor, she would help Maria.
For several years Maria worked as a governess, teaching the children of a rich family in the countryside, sending her money to Paris and studying chemistry and physics from books at night.
A garret in Paris
Paris, 1891
In 1891, aged twenty-four, Maria arrived in Paris and enrolled at the Sorbonne, the University of Paris. She now called herself Marie. She lived in a tiny attic room, so cold in winter that she wore all her clothes to bed, and she sometimes forgot to eat. She came top of her class in physics in 1893 and second in mathematics a year later.
In 1894 she met Pierre Curie, a quiet physicist who had already made important discoveries about crystals and magnets. They talked about science, then about everything. They married in 1895, and for their honeymoon they went touring the countryside by bicycle.
Rays from a rock
In 1896 Henri Becquerel had found that uranium gives off invisible rays all by itself (that story is told in radioactivity). Marie chose these rays for her doctoral research. Using a very sensitive instrument that Pierre and his brother had invented, she measured how strongly different substances gave off rays.
She made a key discovery: the strength of the rays depended only on how much uranium was there, not on what it was combined with. That meant the rays came from inside the atoms themselves. She invented a word for this: radioactivity.
Then something odd. A uranium ore called pitchblende gave off more rays than its uranium could explain. Marie reasoned that it must contain something else, something far more radioactive, in tiny amounts.
The shed
A shed at the School of Physics and Chemistry, Paris, 1898 to 1902
Pierre dropped his own work to join her. In 1898 they announced two new elements. The first they called polonium, after Marie’s homeland, which was not on the map. The second they called radium, from the Latin for “ray”.
But other chemists wanted to see the new elements, not just their rays. So the Curies set out to collect pure radium. They had no proper laboratory, only an old shed with a leaking glass roof, freezing in winter and stifling in summer. Marie stirred boiling vats of pitchblende residue with an iron rod nearly as tall as herself.
It took about four years and tonnes of residue (the exact amount is told differently in different accounts) to produce about a tenth of a gram of radium compound: less than a pinch of salt. At night, Marie later wrote, the little glass tubes of radium glowed faintly in the dark.
Two Nobel Prizes, and a terrible day
In 1903 Marie, Pierre and Becquerel shared the Nobel Prize in Physics. Marie was the first woman ever to win a Nobel Prize.
In 1906 Pierre was killed in a street accident in Paris: he slipped in the rain and was struck by a horse-drawn cart. Marie was left with two daughters, Irène and Ève. She took over Pierre’s teaching post and became the first woman professor at the Sorbonne. In 1911 she won a second Nobel Prize, this time in Chemistry, for discovering polonium and radium. She is still the only person to have won Nobel Prizes in two different sciences.
The little Curies
When the First World War began in 1914, Marie saw that X-rays could help surgeons find bullets and broken bones in wounded soldiers. She fitted cars with X-ray equipment and helped set up many more X-ray posts, learned to drive, and went to the front lines herself, often with her teenage daughter Irène. Soldiers called the vans petites Curies, “little Curies”.
The cost
Nobody at the time understood how dangerous radiation is. Marie carried radium in her pockets and kept it in her desk. Over the years her health suffered, and in 1934 she died of a blood illness that was almost certainly caused by long exposure to radiation.
Her laboratory notebooks are still radioactive today. They are reported to be kept in lead-lined boxes in a French library, and people who wish to read them must take safety precautions.
In 1935 her daughter Irène and Irène’s husband, Frédéric Joliot-Curie, won the Nobel Prize in Chemistry for making new radioactive elements in the laboratory. The Curie family has won more Nobel Prizes than any other.
When you read about the nucleus and radioactivity in Chapter 1, remember the girl who studied in secret, and the glowing tubes in the leaking shed.
JD
John Dalton
The schoolteacher who weighed the invisible
1766 to 1844A Quaker teacher in Manchester who brought atoms back into science
Eaglesfield, Cumberland, 1766
John Dalton was born in a small thatched cottage in a village in the north of England. His father was a handloom weaver, and the family were Quakers, a Christian group who dressed plainly, refused to swear oaths, and believed in education and simple living. They were poor.
Dalton was a quiet, serious boy who loved numbers. A wealthy Quaker neighbour taught him mathematics and let him read his books. And then, at the age of twelve, Dalton did something that seems astonishing today: he opened his own school and began teaching other children, some of them older than he was. It did not last long, but teaching became his life’s work. For the rest of his life, even when he was famous, he earned his living by teaching.
The weather diary
At fifteen he moved to Kendal to teach at a Quaker school with his brother. There he met John Gough, a blind philosopher who taught him science, and Dalton began a habit that he kept until the day before he died: he wrote down the weather. Every day, for 57 years, he recorded the temperature, the air pressure, the rain and the wind. Historians estimate the diary holds around 200,000 observations.
All that watching of the air led him to wonder what air actually is. Why do oxygen and nitrogen and water vapour stay mixed instead of settling into layers? Why does water vapour behave as if the other gases were not there? These questions about gases led him, slowly, to atoms.
Seeing colours differently
Manchester, 1794
In 1793 Dalton moved to Manchester, a booming city of cotton mills, to teach at a new college. In his first paper to the city’s scientific society, he described something odd about his own eyes.
He had noticed it when he bought his mother a pair of stockings he thought were a sober dark blue, suitable for a Quaker woman. She was startled: they were bright scarlet. (This story is told in several versions, and may have been improved in the retelling.) Dalton tested himself and his brother and found that they both saw colours differently from most people. Pink geranium flowers looked sky-blue to him by day.
He wrote one of the first scientific descriptions of colour blindness. For a long time, the condition was even called “Daltonism”. Dalton guessed that the liquid inside his eyes must be tinted blue, and asked that his eyes be examined after his death. They were, and the liquid was perfectly clear: his guess was wrong. But one eye was kept in a jar. In 1995, scientists extracted DNA from it and found that he lacked the gene for one of the three colour-sensing cells in the eye. Two hundred years after he described himself, his own eye told the rest of the story.
Atoms, with weights
Dalton’s great idea came together between about 1803 and 1808. Philosophers had talked about atoms since ancient Greece, but only as an idea. Dalton made atoms into something chemists could use.
All the atoms of one element are identical, and they are different from the atoms of every other element. Above all, they have different weights.
Atoms cannot be created, destroyed or split in a chemical reaction. They are only rearranged.
Compounds form when atoms of different elements join in small whole numbers: one and one, one and two, two and three.
Point 4 explained something chemists had noticed but could not understand: why substances always combine in fixed proportions. And point 2 meant you could compare atoms by weighing. In 1803 Dalton drew up the first table of relative atomic weights, with hydrogen as 1. Many of his numbers were wrong, because he guessed the wrong formulas (he thought water was HO, one hydrogen and one oxygen), but his method was right, and later chemists corrected the numbers.
He drew each atom as a little circle with a pattern inside: a dot for hydrogen, a plain ring for oxygen. Those symbols were soon replaced by letters, but the idea behind them lasted.
A modest celebrity
Dalton became famous across Europe. He was elected to scientific academies, given a royal medal and a government pension. When he was presented to King William IV, there was a problem: Quakers did not wear the colourful court dress the occasion required. Dalton wore the scarlet robe of an Oxford doctor instead. Since he was colour-blind, it is said, it looked a respectable grey to him.
He never married and lived simply, lodging for decades with a friend’s family, playing bowls every Thursday, and teaching right to the end. When he died in Manchester in 1844, the city gave him a huge public funeral, and tens of thousands of people filed past his coffin. A shy weaver’s son had become the man who made atoms real.
Test colour vision the gentle way
Dalton was colour-blind and never knew it until he was in his twenties. You can explore how colours are seen. Collect objects that are red, green, brown and orange, and ask family members to sort them by colour without saying the names out loud. Then try under a dim lamp, where everyone’s colour vision gets worse. About 1 in 12 boys and men, and far fewer girls and women, see some reds and greens differently: if anyone in your family sorts them differently, they are in good company with Dalton.
When you meet Dalton in Chapter 4, picture a quiet Quaker teacher writing in his weather diary, who turned the ancient guess of atoms into a tool every chemist would use.
HD
Humphry Davy
The boy from Penzance who lit up London
1778 to 1829Poet, showman and discoverer of potassium and sodium
Penzance, Cornwall, the 1780s
At the very bottom tip of England, where the land runs out into the Atlantic, there is a small fishing town called Penzance. Humphry Davy was born there in 1778. His father was a woodcarver who never made much money, and when he died the family was left poor. Humphry was the eldest of five children, and at sixteen he had to earn a living.
He was apprenticed to a local surgeon-apothecary: a kind of village doctor who also mixed medicines. It was not a grand job. But the shop had bottles, scales and books, and Humphry read everything. He taught himself chemistry from Lavoisier’s new book, in French. He also wrote poetry, fished, and wandered the cliffs. All his life he would be two things at once: a poet and a scientist.
The gas that made people laugh
Bristol, 1799
At nineteen Davy got a job at a strange new place in Bristol: the Pneumatic Institution, run by a doctor called Thomas Beddoes. “Pneumatic” means to do with air. Beddoes hoped that breathing newly discovered gases might cure diseases.
Davy’s job was to make the gases and test them. Often he tested them on himself, which was brave and also quite reckless. One of them was nitrous oxide. When Davy breathed it, he felt light-headed and giggly, and the world seemed wonderful. Soon his friends were trying it too, including poets. It got the nickname laughing gas.
Davy also noticed something important: it seemed to take away pain. He wrote in 1800 that it might be used during surgery. Almost nobody followed this up for more than forty years, and in the meantime surgery went on without anything to stop the pain. Today nitrous oxide is still used by dentists and in hospitals.
Careful
“Davy was being sensible about safety.”
He was not, by today’s standards. He breathed several gases that could have killed him, and once nearly did. Modern chemists never test unknown gases on themselves. Davy was lucky, and his luck is not a method.
The most famous lecturer in London
The Royal Institution, London, 1801
In 1801 Davy moved to the Royal Institution in London, a new place built to bring science to the public. He was twenty-two, good-looking and a brilliant speaker, and his lectures became the place to be seen. Carriages blocked the street outside. People who knew no chemistry at all came to watch him make things flash, bang, fizz and change colour, while he explained, in beautiful sentences, what was happening.
Tearing metals out of rocks
The Royal Institution basement, October 1807
In 1800, Alessandro Volta had invented the battery (you meet it in Chapter 8). Davy saw at once what it could do. Electricity could pull compounds apart. If you pass a current through water, it splits into hydrogen and oxygen. What else could it split?
For years, chemists had suspected that potash (a substance made from wood ashes) and soda contained metals, but nothing could break them apart. Davy built enormous batteries in the basement of the Royal Institution, melted some potash, and passed a powerful current through it.
At one wire, tiny shining globules appeared, like quicksilver. Some of them burst into flame the moment they appeared. Davy had discovered potassium, a metal so reactive that it catches fire in water. His cousin Edmund, who was helping him, later wrote that Humphry danced about the room with delight. A few days later he made sodium from soda in the same way.
The next year he used the same trick to find calcium, magnesium, barium and strontium. In about two years, one man had added six new elements to the list.
Why did potash resist every chemist before him? Because potassium gives its electrons away more readily than almost any other metal. Ordinary chemicals cannot force those electrons back onto it, so the metal stays locked up in its compounds. A strong enough battery can push the electrons back by brute force. That is why the most reactive metals were the last to be found, and why they were all found with electricity.
A lamp that saved lives
The coal mines of northern England, 1815
Coal mines were filled with a dangerous gas called firedamp (mostly methane). Miners needed light to work, but a candle flame could set the gas off in a terrible explosion. In 1815 the mine owners asked Davy for help.
He worked out that a flame cannot pass through a fine metal gauze, because the metal draws away heat so fast that the gas on the other side never gets hot enough to catch fire. So he wrapped the flame of a miner’s lamp in a cylinder of wire gauze. The gas could get in and burn harmlessly inside, but the flame could not get out.
Davy refused to patent the lamp. He wanted it to be free for every mine. (An engineer called George Stephenson designed a similar lamp at almost the same time, and there was a bitter argument about who came first.)
His greatest discovery
Davy once hired a young bookbinder as an assistant, a young man called Michael Faraday. It is often said, though nobody knows if Davy himself said it, that “Davy’s greatest discovery was Michael Faraday”. Faraday became an even greater scientist than his teacher.
That was not always easy for Davy. As he grew older and more famous (he was made a knight, then president of the Royal Society), he became prouder and touchier. When Faraday was proposed for the Royal Society in 1823, Davy, as president, is reported to have opposed it. Great people can be generous and jealous at once.
Davy’s health failed in his late forties, perhaps in part because of all the chemicals he had breathed and handled, though nobody can be sure. He died in Geneva in 1829, aged fifty.
Split water with a battery
Ask an adult to help. You need a 9-volt battery, two pencils sharpened at both ends, a glass of warm water and a teaspoon of salt. Stir the salt into the water. Hold one end of each pencil against a battery terminal (the adult can tape them on), and dip the other ends into the water, not touching each other. Watch the pencil tips: tiny bubbles stream off them. Electricity is pulling the water apart, the same trick Davy used on potash. Do not touch the wet ends to your skin, do not use anything bigger than a 9-volt battery, and pour the water away afterwards.
When you read about electrolysis and the reactivity series in Chapter 8, remember the poor boy from Penzance who first used a battery to tear metals out of the rocks that had hidden them for ever.
MF
Michael Faraday
The bookbinder's apprentice
1791 to 1867Bookbinder who became the greatest experimenter of his age
A bookbinder’s shop, Blandford Street, London, 1805
Michael Faraday was born in 1791 in a poor part of London. His father was a blacksmith who was often too ill to work, and there were days when Michael’s share of food for a whole week was a single loaf of bread. He went to a simple day school long enough to learn reading, writing and arithmetic, and that was the end of his schooling.
At about fourteen he was apprenticed to a bookbinder, a kind man called George Riebau. A bookbinder sews and glues the pages of books into their covers. Faraday did something most apprentices did not: he read the books he was binding. One was an encyclopaedia with a long article on electricity. Another was a chemistry book written for beginners by Jane Marcet, Conversations on Chemistry. He tried the experiments he read about, with whatever bits of glass and wire he could afford.
Four tickets that changed a life
The Royal Institution, London, 1812
In 1812 a customer of the shop gave Faraday tickets to four lectures by the most famous chemist in London, Humphry Davy. Faraday sat high up in the gallery and wrote down everything. Afterwards he copied his notes out neatly, added drawings, and bound them into a book.
His apprenticeship was ending and he dreaded spending his life in trade. So he did something bold: he sent the bound notes to Davy and asked for any job at all in science. Davy was impressed, but had nothing to offer. Then, in early 1813, Davy’s laboratory assistant was dismissed after a fight, and Faraday got the job. He was twenty-one. His work included washing bottles and cleaning the apparatus.
A hard journey
Paris, Florence, Rome, 1813 to 1815
Later in 1813 Davy set off on a long tour of Europe, even though Britain and France were at war (Napoleon gave him special permission). He took Faraday as his assistant. Faraday met famous scientists, saw a volcano, and watched Davy use a great burning lens in Florence to burn a diamond and prove it was made of carbon.
But there was a bitter side. Davy’s valet refused to come, so Faraday was asked to act as a servant too. Davy’s wife, Lady Davy, treated him as one. In letters home he wrote how unhappy this made him. He nearly gave up science and went home. He did not, and the tour gave him an education no university could have.
Naming the words you use
Back in London, Faraday became a brilliant chemist in his own right. In 1825 he discovered benzene, a liquid that turned out to be one of the most important compounds in all of carbon chemistry (Chapter 10).
He was even more famous for his work on electricity. He built the first electric motor (1821) and found how to make electricity from magnets (1831), the idea behind every power station today. And he worked out the rules of what happens when electricity passes through a solution and splits it, which he called electrolysis.
He needed words for the new ideas, and he asked a scholar friend, William Whewell, to help him make them up from Greek. Together, in 1834, they gave us:
electrode: the metal or carbon rod where the current goes in or out (from Greek for “electricity” and “road”);
anode and cathode: the two electrodes (“the way up” and “the way down”);
ion: the charged particle that travels through the liquid (from Greek for “going”, because ions move).
Every time you read ion in this book, you are using a word Faraday and Whewell invented.
The Christmas Lectures
The Royal Institution lecture theatre, Christmas, 1860
Faraday never forgot the boy in the gallery. In 1825 he started lectures at the Royal Institution for young people at Christmas. They still happen every year, and are shown on television in Britain.
His most famous set, given in 1860, was called The Chemical History of a Candle. For six lectures he talked about nothing but a candle, and through it explained almost all of chemistry: melting, burning, the gases in air, the water and carbon dioxide made by a flame, even breathing. He said, roughly, that there was no better door into science than studying a candle.
Watch a candle like Faraday
An adult must light the candle and stay with you; this is for looking only. Put a plain candle in a holder on a plate, away from anything that can burn. Look closely: the little cup of melted wax at the top, the wick drawing liquid wax up, the dark zone near the wick and the bright yellow part above it. Hold a cold metal spoon briefly above the flame (the adult can do this): it gets a black coating of soot, which is unburnt carbon. Then hold a cold dry glass upside down well above the flame for a few seconds: mist forms inside. That is water, made by burning. A candle is a small chemistry factory.
Humble to the end
Faraday became world-famous, but stayed simple and modest. He belonged to a small, strict Christian church and lived quietly with his wife, Sarah, above the Royal Institution. It is often said that he turned down a knighthood and, later, the presidency of the Royal Society, wanting to remain “plain Michael Faraday” to the end. The story about the presidency is well recorded: he was offered it twice. The knighthood story is less certain: he said more than once that he would never accept one, but no record has been found that he was ever offered it.
He worked on almost every great question of his day, but his own teachers had never been professors: they were the books he bound and the man whose lectures he copied. He died in 1867.
When you meet ions and electrolysis in Chapters 2 and 8, remember the apprentice who read the books he was meant to be sewing, and who named the very words you are reading.
RF
Rosalind Franklin
Photo 51
1920 to 1958The X-ray expert whose photograph revealed the shape of DNA
London, 1920
Rosalind Elsie Franklin was born on 25 July 1920 in London, into a well-off Jewish family of bankers and publishers. She was clever, determined and very direct. By fifteen she had decided she wanted to be a scientist. Her father, the family story goes, was not keen at first, but she went to Newnham College, Cambridge, to study chemistry.
During the Second World War she worked on something that sounds ordinary but mattered a great deal: coal. She studied the tiny holes inside coal and charcoal, which affect how well they burn and how well they work in gas masks. That work earned her a doctorate.
Paris and the X-rays
Paris, 1947
After the war she went to work in a government laboratory in Paris, and later said those were some of the happiest years of her life. She learned to speak French, went walking in the mountains, and became an expert in X-ray diffraction: shining X-rays through a material and studying the pattern they make, to work out how its atoms are arranged. (The Dorothy Hodgkin story explains the idea.)
DNA
King’s College London, 1951
In 1951 she moved to King’s College London to study DNA, the molecule that carries genetic instructions in every living cell. Everyone knew it was important, but no one knew its shape.
Things went badly at King’s from the start. Another scientist there, Maurice Wilkins, was already working on DNA, and the two were not told clearly who was in charge of what. They did not get on.
Franklin was extremely careful. Working with her PhD student Raymond Gosling, she found that DNA comes in two forms, depending on how wet it is, and she learned to keep the two apart, which had been confusing everyone. In May 1952 she and Gosling took an X-ray photograph of the wetter form, which was later labelled Photo 51. It shows a striking X-shaped cross of dark smudges. To someone who knew how to read it, that cross shouted one word: helix. From her measurements she could also work out the spacings inside the molecule, and she concluded that the phosphate backbone lay on the outside.
Without her knowledge
In Cambridge, two other scientists, James Watson and Francis Crick, were trying to build a model of DNA from wire and metal plates. In January 1953 Wilkins showed Watson Photo 51, without asking Franklin. Around the same time, a report containing her measurements, written for a committee, was passed to Crick. Franklin did not know that her results were being used.
With her data, Watson and Crick built their famous double helix: two twisted strands with pairs of bases joining them like the rungs of a ladder. It was right, and it is one of the greatest discoveries in the history of science. Their paper was published in April 1953, alongside a paper by Franklin and Gosling with their X-ray evidence. But for many years, few people realised how much the model had depended on her work.
It is fair to add that Watson and Crick did something Franklin had not yet done: they put all the pieces together into a model that explained how DNA can copy itself. And Franklin herself was very close. Her notebooks show she was moving towards the answer. Science is often like that: several people, each holding part of the truth.
What came after
In 1953 Franklin left King’s for Birkbeck College, also in London, and began studying viruses, including the tobacco mosaic virus that attacks plants. With her colleague Aaron Klug she produced some of the most important early pictures of how a virus is built. She was respected and productive, and she was happy in her work.
In 1956 she became seriously ill with cancer. She kept working as long as she could. She died on 16 April 1958. She was 37.
In 1962 Watson, Crick and Wilkins shared the Nobel Prize. Nobel Prizes are not awarded to people who have died, so Franklin could not have been included. Aaron Klug, carrying on the virus work they had started together, won the Nobel Prize in Chemistry in 1982, and many people, Klug among them, have felt that if she had lived she might well have shared it.
Today, her part in the story is told properly. Schools, research centres and a Mars rover have been named after her.
See a diffraction pattern
On a dark evening, look at a distant street light or a small bright torch through a piece of very fine fabric, such as a thin net curtain, a fine mesh sieve, or the fabric of an umbrella held up close to your eye. Instead of a single point of light you will see a cross or a grid of spots. The regular pattern of threads spreads the light into a regular pattern of spots. Photo 51 was made in the same way: the regular pattern of atoms in DNA spread the X-rays into its famous X.
When this book talks about the giant molecules of life, remember the woman whose photograph showed the world the shape of DNA.
DH
Dorothy Crowfoot Hodgkin
Seeing the shapes of molecules
1910 to 1994The crystal-reader who worked out the shapes of penicillin, vitamin B12 and insulin
Cairo, 1910
Dorothy Crowfoot was born on 12 May 1910 in Cairo, Egypt. Her father worked for the education service there and later in Sudan, and both her parents were passionate about archaeology. For much of her childhood, though, Dorothy and her sisters lived in England, looked after by relatives and a nanny, while their parents worked abroad. She saw them for only part of each year.
When she was ten, at a small class in her town, she grew crystals for the first time: alum and copper sulfate, slowly forming in a dish. She loved them. She went home and set up a little laboratory in the attic.
At thirteen she visited her parents in Khartoum, in Sudan, and was shown round a laboratory there that analysed soils and minerals. A chemist gave her a kit for testing minerals, and she brought it home with her.
Asking to join the boys
At her school in Beccles, in the east of England, girls were expected to study domestic science, not chemistry. Dorothy and one other girl asked to be allowed into the boys’ chemistry class, and the school agreed. She went on to study chemistry at Somerville College, Oxford, one of the colleges for women at a time when Oxford’s colleges were separate for men and women.
Reading the dots
Cambridge and Oxford, 1930s
At Oxford, and then at Cambridge with a brilliant and unconventional scientist called J. D. Bernal, she learned a technique called X-ray crystallography. The idea is simple to say and very hard to do. You shine a beam of X-rays through a crystal. The X-rays bounce off the regularly arranged atoms inside and come out as a pattern of dots on a photographic film. The pattern of dots depends on exactly where the atoms are. So if you are clever enough, you can work backwards from the dots to the positions of the atoms, and see the shape of the molecule.
For a small, simple crystal like table salt, this was already being done. For the big, complicated molecules of living things, it seemed almost impossible: thousands of dots, each needing pages of calculations by hand, long before computers.
In 1934, working with Bernal, she took the first X-ray photograph of a crystal of a protein, pepsin, a digestive enzyme. Then she went back to Oxford, where she spent the rest of her career.
Penicillin
Oxford, 1945
During the Second World War, penicillin, the first antibiotic, was saving thousands of lives, but nobody knew the exact structure of its molecule, so nobody could be sure how to make it in a factory. Chemists argued about it. Hodgkin and her team worked it out from the X-ray patterns, finishing in 1945. Part of the molecule was a small, strained ring of four atoms that many chemists had thought unlikely. The X-rays showed it was there.
Next came vitamin B12, which the body needs to make healthy blood. Its molecule is far bigger, with more than ninety atoms (not counting hydrogens) and a single cobalt atom at its heart. With the help of some of the first computers, she solved it in 1956. In 1964 she was awarded the Nobel Prize in Chemistry, only the third woman to win it, after Marie Curie and her daughter Irène Joliot-Curie.
Thirty-four years of insulin
Her longest puzzle was insulin, the hormone that controls the sugar in your blood, which people with type 1 diabetes need as a medicine. She took her first X-ray photographs of insulin crystals in 1935. It was far too complicated for the methods of the time. She kept at it, improving the methods, training students, waiting for computers to become powerful enough. In 1969, thirty-four years after she started, she and her team finally published its structure.
She did all of this with hands that were often painful. In her late twenties she developed rheumatoid arthritis, which made her joints swollen and stiff, especially her hands and feet. She simply found ways to keep working.
A scientist of the whole world
Hodgkin believed that science belonged to everyone. She travelled widely and helped train crystallographers in many countries, including India and China, where scientists were also working on insulin. She worked for peace, and for scientists on different sides of political divides to keep talking to one another.
She married Thomas Hodgkin, a historian, and they had three children. She died in 1994.
Grow your own crystals
You need salt, warm water from the tap, a clean jar and a saucer. Stir salt into half a glass of warm tap water, a spoonful at a time, until no more will dissolve and a little stays at the bottom. Pour some of the clear liquid onto a saucer (leave the undissolved salt behind) and put the saucer somewhere it will not be disturbed. Over a few days, as the water evaporates, small crystals appear. Look at them with a magnifying glass: many are almost perfect little cubes. Their shape comes from the way sodium and chloride ions stack inside, which is exactly the kind of thing Dorothy Hodgkin learned to read from X-rays.
Whenever this book shows you the shape of a molecule, remember that someone had to see it first, and that for some of the most important molecules in medicine, that someone was Dorothy Hodgkin.
LM
Lise Meitner
A walk in the snow
1878 to 1968The physicist who explained how a uranium nucleus splits in two
Vienna, 1878
Lise Meitner was born in Vienna in November 1878, the third of eight children in a Jewish family (as an adult Lise was baptised a Protestant). Her father was a lawyer who loved chess. As a girl she was fascinated by the colours in a puddle of oil and the way light behaved, and she wanted to understand them.
There was a problem. In Austria at that time, girls were not allowed to go to the kind of school that led to university, and universities did not admit women at all. In 1897 the rules changed, and women were allowed to study. But Lise had missed years of the schooling she needed. So she studied privately, cramming eight years of mathematics, physics, Latin and Greek into two, and in 1901 she passed the university entrance exam. In 1906 she became only the second woman ever to earn a doctorate in physics at the University of Vienna.
The basement
Berlin, 1907
In 1907 she went to Berlin, meaning to stay a short while. She stayed for more than thirty years. She began to work with a young chemist, Otto Hahn, on radioactivity. She was the physicist; he was the chemist. They made an excellent team.
But the head of the chemistry institute did not allow women in his laboratories. So Meitner and Hahn set up their equipment in a former carpentry workshop in the basement, which had its own entrance from the street. She was not supposed to go upstairs where the students worked. When the rule was lifted a couple of years later, she simply carried on.
Slowly, things changed. Together with Hahn she discovered a new element, protactinium, in 1917 and 1918. In 1926 she became a full professor of physics in Berlin, one of the first women in Germany to do so. Physicists in the 1920s talked of her as one of the leading experts on radioactivity in the world. Einstein reportedly called her “the German Marie Curie”.
Escape
In 1933 the Nazis came to power in Germany and began driving Jewish people out of their jobs. Because Meitner was an Austrian citizen, she was protected for a while. But in March 1938 Germany took over Austria, and that protection vanished. She was not allowed to leave the country legally, and it was becoming dangerous to stay.
In July 1938, helped by friends, she slipped across the border into the Netherlands by train, with a small suitcase and very little money. Hahn had given her a diamond ring that had belonged to his mother, to sell if she needed to. She went on to Sweden, where she found a place to work but few colleagues and almost no equipment. She was nearly sixty, and she had lost her home, her laboratory and her work.
The puzzle in the letter
Hahn and his assistant Fritz Strassmann carried on in Berlin. They were firing neutrons at uranium, the heaviest natural element, expecting to make elements slightly heavier or slightly lighter than uranium. But in December 1938 they found something they could not believe: barium. Barium is barely more than half as heavy as uranium. How could you get it by tapping uranium with a neutron? It was like throwing a pebble at a boulder and seeing it break cleanly into two big rocks. Hahn wrote to Meitner: what could it mean?
Kungälv, Sweden, Christmas 1938
Meitner was spending Christmas in a small town on the west coast of Sweden, and her nephew, the physicist Otto Frisch, came to visit. She showed him Hahn’s letter. They went for a walk through the snowy woods to think, Frisch on skis and Meitner on foot (she insisted she could walk just as fast). Somewhere along the way they sat down on a tree trunk and began to calculate on scraps of paper.
They imagined the uranium nucleus not as a hard ball but as a wobbling drop of liquid. Add one more neutron, and the drop starts to wobble and stretch, like a water drop pulled into a peanut shape. If it stretches far enough, the electric push between the two ends, both full of positive protons, drives them apart, and the drop snaps into two smaller drops. One of them could be barium.
Then Meitner worked out how much energy would be released. She remembered that the two pieces together weigh slightly less than the uranium nucleus did. Using Einstein’s famous rule, E = mc², that a tiny amount of mass can turn into a huge amount of energy, she calculated the energy from that missing mass. It matched the energy the flying pieces should have. A single uranium nucleus splitting releases millions of times more energy than a single molecule in any chemical reaction.
Frisch borrowed a word from biology, where a living cell splits in two, and called it fission.
Left out
Within months, scientists everywhere understood that fission could release enormous energy, for power stations, and also for weapons. Meitner was invited to join the British and American project to build an atomic bomb. She refused. She wanted, she said, nothing to do with a bomb.
In 1945, Otto Hahn alone was awarded the Nobel Prize in Chemistry (the prize for 1944) for the discovery of fission. Meitner was left out. Historians who have since studied the Nobel committee’s papers believe this was a serious mistake, partly because the committee did not properly understand her contribution as a physicist. She stayed friends with Hahn, but it hurt.
What became of her
Meitner lived to be nearly ninety, and spent her last years in Cambridge, near family. Her nephew wrote the words for her gravestone: “a physicist who never lost her humanity”. In 1997 element 109 was named meitnerium. Only two elements are named after real women: curium, which honours Marie and Pierre Curie together, and meitnerium, the only one named for a woman alone.
Split a drop
Put a few drops of water on a smooth plate or a sheet of baking paper so they form a round bead. Gently drag the bead with the tip of a toothpick and watch it stretch. Pull it into a long peanut shape, then draw the toothpick through the narrow middle. The drop snaps into two rounder drops. This is the picture Meitner and Frisch had in their heads as they walked in the snow: a liquid drop stretching until it splits. (A real nucleus is pushed apart by electric charge, not pulled by a toothpick, but the shape of the idea is the same.)
When this book talks about the nucleus, and about whether one element can really become another, remember the woman on the tree trunk in the snow, doing sums on scraps of paper.
DM
Dmitri Mendeleev
The Siberian who left gaps
1834 to 1907Built the periodic table and dared to predict the missing elements
Tobolsk, Siberia, the 1840s
Dmitri Mendeleev was born in 1834 in Tobolsk, a town in western Siberia. He was the youngest child of a very big family: sources disagree on how many children there were (numbers from fourteen to seventeen are given), but everyone agrees he was the last.
His father, Ivan, was the headmaster of the local school, until he went blind and had to stop working. The family was suddenly poor. His mother, Maria, did something remarkable: she took over a glass factory that belonged to her family, and ran it to keep the children fed. Dmitri grew up around furnaces, sand and molten glass. When he was about thirteen his father died, and not long afterwards the glass factory burned down.
A mother’s journey
Maria was sure her youngest son was gifted. In 1849, when he was fifteen, she set off with him across Russia to find him a university place. They travelled thousands of kilometres, mostly by horse-drawn transport. Moscow University would not take him, because he came from Siberia. So they went on to St Petersburg, where in 1850 he got into a college for training teachers, partly because an old friend of his father worked there.
A few months later his mother died. Dmitri was sixteen, alone and often ill (for a while doctors believed he had a lung disease and not long to live). He kept working. Many years later he dedicated a great book to her, and wrote that she had taught him to seek truth patiently, through work rather than words.
Sixty-three elements and a problem
St Petersburg, February 1869
By the 1860s Mendeleev was a chemistry professor in St Petersburg. He was writing a textbook for his students, and he had a problem: how to organise the chapters. About sixty-three elements were known. In what order should he teach them?
Other chemists had noticed patterns. Some elements came in families, such as lithium, sodium and potassium, which all behave alike. But nobody had found one arrangement that included everything.
Mendeleev wrote each element on a card, with its atomic weight and its main properties, and laid the cards out on a table, moving them about to find the pattern. Lining them up in order of weight, he saw that similar properties came round again and again, like the days of the week. He arranged the cards so that families sat together in columns. This was his periodic table, first published in 1869. (A German chemist, Lothar Meyer, found a very similar arrangement at about the same time.)
Careful
“Mendeleev saw the periodic table in a dream.”
This is a famous story, but it is a legend. It comes from an account written decades later by someone who said Mendeleev had told him so. There is no evidence from 1869 itself. What we do know is that he worked hard on it, with cards, notes and many rough drafts.
The daring part: gaps
Here is what made Mendeleev different. Sometimes the next element by weight did not fit the family pattern. Instead of forcing it in, he left a gap, and said: an element belongs here that nobody has discovered yet.
He went further. From the neighbours of each gap he predicted what the missing element would be like: its atomic weight, how dense it would be, what compounds it would make. He gave them temporary names, such as eka-aluminium (“one below aluminium”).
Paris, 1875
In 1875 a French chemist, Paul-Émile Lecoq de Boisbaudran, found a new metal using a spectroscope and called it gallium. Mendeleev read the report and said: that is my eka-aluminium. But Lecoq’s measured density, about 4.7 grams per cubic centimetre, did not match Mendeleev’s prediction of about 5.9. Mendeleev wrote to say the measurement must be wrong. Lecoq purified his sample and measured again, and got about 5.9. The man who had never seen gallium knew it better than the man holding it.
Then came scandium (1879) and germanium (1886), both matching his predictions closely. After that, nobody laughed at the periodic table.
Mendeleev’s predictions for eka-aluminium, set beside gallium’s real values.
Build a table with gaps
Take an ordinary pack of cards. Secretly remove two or three cards, say the 7 of hearts and the queen of clubs, and give the rest to a friend. Ask them to lay out the cards in a grid: one row for each suit, numbers in order. Gaps will appear exactly where the missing cards belong, and your friend can tell you what the missing cards must be without ever seeing them. That is exactly what Mendeleev did with elements.
A fiery man
Mendeleev was famous for his temper, his wild hair and beard (he is said to have had it cut only once a year), and his energy. He worked on oil, on agriculture, on weights and measures (he later ran Russia’s office of weights and measures), and much else.
In 1887 he went up alone in a balloon filled with hydrogen to watch a solar eclipse from above the clouds, although he had never flown one by himself before. He landed safely.
He never won a Nobel Prize, though he was nominated and came very close in 1906. Historians think he had made enemies, including a powerful Swedish chemist, Svante Arrhenius, whose ideas Mendeleev had criticised. Nobody can be completely sure. He died in 1907. In 1955 a newly made element, number 101, was named mendelevium in his honour.
When you open the periodic table in Chapters 1 and 9, look for the places where he left gaps, and think of the boy from Siberia whose mother would not give up on him.
HM
Henry Moseley
The young man who counted the elements
1887 to 1915The young physicist who found each element's true number
Weymouth, England, 1887
Henry Gwyn Jeffreys Moseley was born on 23 November 1887, into a family of scientists. His father was a naturalist who had sailed round the world on a famous survey ship, HMS Challenger, collecting sea creatures; his grandfather on his mother’s side was an expert on shells. His father died before Henry was four, and he grew up with his mother and sisters, collecting birds’ eggs, studying animals, and doing very well at school. He won a scholarship to Eton, and then went to Trinity College, Oxford, to study physics.
He was quiet, intense, and extremely hard-working. People who worked with him remembered that he would carry on an experiment through the night, and that he was impatient with anyone who wasted his time.
A puzzle in the periodic table
Manchester, 1913
In 1910 Moseley went to Manchester to work with Ernest Rutherford, who had just discovered the atomic nucleus. By then, the periodic table had been in use for forty years. Mendeleev had arranged the elements roughly in order of their atomic weight, and it worked beautifully. But there were a few awkward places where it did not. Tellurium is heavier than iodine, yet iodine plainly belongs in the column after tellurium, alongside chlorine and bromine. Mendeleev had swapped them, trusting their chemistry over their weight. Nobody could explain why that was allowed.
Some scientists had begun to suspect that the true order was not about weight at all, but about the charge on the nucleus: how many units of positive charge sat at the centre of the atom. But nobody could measure that charge.
Moseley found a way. He knew that when you fire fast electrons at a metal, it gives off X-rays, which are light of extremely high energy, far beyond violet. Each metal gives off X-rays of its own particular energies. Using a crystal to split the X-rays (the trick the Braggs had just invented, see the crystals story), Moseley measured them for one element after another: calcium, titanium, vanadium, chromium, manganese, iron, cobalt, nickel, copper, zinc.
The staircase
When he plotted his results in the right way (using the square root of the X-ray frequency), the elements lined up like the steps of a perfectly even staircase. Every step was the same height. Going from one element to the next always added exactly the same amount.
It meant that each element has exactly one more unit of charge on its nucleus than the one before. Hydrogen has 1, helium 2, lithium 3, and so on, all the way up. That number is the atomic number, and Moseley had found a way to measure it directly. It is the true order of the periodic table. It explained the tellurium and iodine puzzle at once: tellurium is number 52 and iodine is number 53, whatever their weights say. (The weights are muddled because of neutrons, which add weight but no charge. That was discovered later.)
Gaps you can count
There was an even more exciting consequence. If every step on the staircase is one element, then you can see exactly where steps are missing. Moseley, and others using his method, could say: between molybdenum (42) and ruthenium (44) there should be an element number 43, and nobody has found it. The same for 61, 72 and 75. No more guessing about how many elements might be hiding. You could count the gaps.
All of them were later filled. Element 72, hafnium, was found in 1923 by scientists in Bohr’s institute in Copenhagen, who searched for it in zirconium ores because the staircase told them where to look. Element 75, rhenium, followed in 1925. Element 43, technetium, turned out not to exist naturally on Earth in any useful amount; it was made artificially in 1937. Element 61, promethium, was finally identified in the 1940s.
The war
Moseley did all of this in about two years. He moved back to Oxford in 1914 to continue, and many people expected that he would one day win a Nobel Prize.
In the summer of 1914 he travelled to Australia for a scientific meeting. While he was there, the First World War began. He came home and, against the advice of people who knew how valuable his work was, joined the army as a signals officer, setting up telephone and telegraph lines. In 1915 he was sent to Gallipoli, in what is now Turkey. On 10 August 1915, during the fighting there, he was killed. He was 27 years old.
Many scientists felt his loss very deeply, Rutherford among them. It is often said that his death made the British government more careful about sending its scientists into battle in later wars, though it is hard to know how much difference it really made.
Find the missing step
Here is Moseley’s idea with coins. Ask someone to make a row of stacks of coins: a stack of 1, then 2, then 3, and so on up to 12, but to secretly leave out one stack and push the others together so there is no gap. Now look at the row. You cannot easily see which is missing just by glancing at the heights. But count the coins in each stack in order (1, 2, 3, 4, 6 …) and the missing number jumps out. Moseley found the “coin count” of every element, and the missing elements jumped out in the same way.
Every time you see an element’s atomic number in this book, the small whole number in the corner of its box in the periodic table, you are using what Henry Moseley found in two years in Manchester.
IN
Isaac Newton
The last of the magicians
1642 to 1727The greatest physicist of his age, who spent thirty years secretly trying to make gold
Woolsthorpe Manor, Lincolnshire, Christmas Day 1642
The baby was so small that, as he later said himself, he could have fitted into a quart pot. Nobody expected him to live. His father, a farmer who could not write his own name, had died three months before he was born. When the boy was three, his mother married again, a much older clergyman, and moved to the next village, leaving her son behind with his grandmother. He did not forgive her for years.
That boy was Isaac Newton, and he grew into one of the strangest and most brilliant people who ever lived. Most people know him for gravity and the falling apple. Very few know that he spent more time on alchemy than on gravity.
A lonely, clever boy
Young Isaac was not a friendly child. He built things instead: a working model of a windmill turned by a mouse running on a wheel, sundials carved into the walls of the house, kites carrying paper lanterns that frightened the neighbours at night. At school in Grantham he lodged with an apothecary, a man who mixed medicines, and it was probably there that he first saw jars of salts and powders and the art of turning one substance into another.
His mother tried to make him a farmer. It was hopeless. Sent to watch the sheep, he read books, and the sheep wandered into the neighbours’ corn. In 1661 he went to Trinity College, Cambridge, at first as a poor student who paid his way partly by working as a servant to richer ones.
Woolsthorpe again, 1665 and 1666
Then the plague came. Cambridge closed, and Newton went home to the farm for nearly two years. Alone, in his early twenties, he worked out the beginnings of calculus, showed that white light is a mixture of all the colours, and began to think that the force pulling an apple down might be the same force holding the Moon in its orbit. (Whether an apple actually fell near him is a story he told in old age. It may be true; it is certainly a good story.)
The secret laboratory
Back in Cambridge, Newton became a professor at 26. And from around 1669, he started something he told almost nobody about. He bought furnaces, glassware, chemicals and old books. He built a small laboratory, with a furnace, beside his rooms at Trinity, and for nearly thirty years he worked there, sometimes for weeks on end with the fire burning day and night.
He was doing alchemy. The alchemists believed metals could be transformed: lead or mercury, purified and “ripened” in the right way, might become gold. Above all they hunted for the philosopher’s stone, a substance said to turn base metals into gold. Newton copied out old alchemical texts by hand, compared them, and wrote his own notes in a secret language of symbols. He even signed some papers with a hidden name: Jeova sanctus unus, “Jehovah the holy one”, which is a Latin anagram of Isaacus Neuutonus.
How much did he write? Historians who have studied his papers estimate about a million words on alchemy: more than he wrote on gravity and light. Almost none of it was published.
Why would the cleverest scientist in Europe spend so long on something that now sounds like magic? Because in the 1600s, nobody yet knew it was impossible. Chemistry and alchemy were not yet separate subjects. Newton was not looking for easy riches. He believed that metals might “grow” and change inside the Earth, and that hidden forces worked inside matter, just as gravity worked between planets. He wanted to find them. In that sense he was asking the right question, what are things made of, and what holds them together?, with the wrong tools.
The dark year
In 1693, Newton became seriously unwell. He could not sleep, he wrote wild, angry letters to friends accusing them of plotting against him, and then he wrote again to apologise. Nobody knows for certain why. He was exhausted, he had worked brutally hard for years, and he had been badly upset by personal troubles.
There is another possibility. Newton heated mercury and lead for hours in his laboratory, and sometimes tasted the substances he made, as chemists of his time often did. In 1979, scientists analysed strands of hair said to be his and reported very high levels of mercury. Some historians think mercury poisoning may have played a part in his illness; others point out that his symptoms do not fit neatly, and that we cannot be completely sure the hair was his. It remains an open question. What is not in doubt is that his laboratory was a dangerous place.
Why the gold never came
Here is the part you can understand better than Newton could.
Gold is an element. Every gold atom has exactly 79 protons in its nucleus; that number is what makes it gold. Mercury has 80, and lead has 82. A chemical reaction, however clever, only rearranges atoms and the electrons on their outside. It never touches the nucleus. Heat, acids, distillation, years of patient furnace work: none of it can take a proton out of a mercury atom. So no chemical recipe could ever turn mercury into gold. Newton was searching for a door that chemistry does not have.
That door does exist. But it took nuclear physics, more than two hundred years later, to open it, and the gold it makes is fantastically expensive. That story is told in the transmutation story, and it reaches all the way to the news of this year.
The Master of the Mint
In 1696 Newton left Cambridge for London to become Warden of the Royal Mint, where England’s coins were made, and later its Master. Many people expected him to treat it as an easy job. Instead he threw himself into it: he oversaw the recoining of the nation’s money, and he chased down forgers with the same fierce persistence he brought to everything else. There is a pleasing twist here. The man who had tried for decades to make gold ended up in charge of the country’s real gold and silver.
He became President of the Royal Society, was knighted, and died in 1727 at the age of 84. He was buried in Westminster Abbey.
Sotheby’s auction room, London, 1936
For two centuries his alchemy papers stayed mostly hidden, an embarrassment to people who wanted Newton to be a pure, modern scientist. In 1936 a huge collection of his papers was sold at auction. The economist John Maynard Keynes bought many of the alchemy papers and read them. Afterwards he wrote that Newton “was not the first of the age of reason. He was the last of the magicians.”
Both halves of Newton are real. He was the man who gave us the laws of motion. And he was the last great alchemist, standing at the exact moment when the old magic was turning into modern science.
Split sunlight into a rainbow
Newton’s most famous experiment at home used a glass prism. You can do a version with a glass of water. On a sunny day, fill a clear, straight-sided glass to the brim and stand it on a windowsill in full sun, with a sheet of white paper on the floor below. Move the paper about until you catch a small band of colours. Newton showed that white light is all of those colours mixed, and that the glass bends each colour by a slightly different amount. No alchemy needed.
When you meet Newton in the opening chapters of this book, remember both of him: the scientist who saw the hidden order in the heavens, and the alchemist who could not see that gold was beyond his reach.
LP
Linus Pauling
The boy who never stopped asking why
1901 to 1994The chemist who explained the chemical bond, and won two Nobel Prizes on his own
Portland, Oregon, 1910
Linus Pauling was born on 28 February 1901 in Portland, Oregon, in the United States. His father, Herman, was a pharmacist who mixed medicines in his own shop. When Linus was nine, his father died suddenly. The family was left with very little money, and Linus grew up quickly. He read everything: the encyclopaedia, books on insects, books on minerals.
When he was about thirteen, a friend showed him a simple chemistry set and did a few experiments with it. Linus was hooked. He borrowed equipment and chemicals from an abandoned smelter near his grandfather’s home and set up a laboratory in his basement. He later said he decided then that he wanted to be a chemist.
He left high school without a diploma, after an argument over a missing history credit, and went straight to Oregon Agricultural College. To pay his way he did whatever work he could find: chopping wood, mopping floors, working in a shipyard and checking the materials for new roads. Because the college was so short of teachers, he was even asked to teach chemistry to younger students while still a student himself. In one of those classes was a young woman called Ava Helen Miller. They married in 1923 and stayed together for fifty-eight years. (His high school finally gave him his diploma in 1962, by which time he had already won a Nobel Prize.)
How do atoms hold together?
Pasadena, California, 1920s
Pauling went to Caltech, in California, to study how atoms are arranged inside crystals by firing X-rays through them. Then he travelled to Europe, to Munich, Copenhagen and Zurich, just as the new quantum mechanics was being invented, and he saw immediately what it could do for chemistry.
Chemists had a simple idea, from Gilbert Lewis, that atoms in a molecule are held together by sharing pairs of electrons. Pauling used quantum mechanics to explain why that works, and to predict the shapes it gives. One of his ideas explains why carbon’s four bonds point to the corners of a tetrahedron, the shape you meet in Chapter 10. In 1939 he put it all together in a book called The Nature of the Chemical Bond. It became one of the most important chemistry books of the century, and it shaped how chemists thought for decades.
He also gave chemists a number for each element called its electronegativity: how strongly its atoms pull on the electrons in a bond. Fluorine pulls hardest; elements like sodium pull weakly. When two atoms with very different pulls share electrons, the sharing is lopsided, and the bond is polar. That idea is behind the polar water molecule in this book, and behind the hydrogen bonds that hold water molecules to each other, which Pauling also helped explain.
A helix on a sheet of paper
Oxford, England, 1948
Pauling next turned to the giant molecules of life: proteins, the long chains that make up hair, muscle and enzymes. Nobody knew how those chains were folded.
There is a well-known story, which Pauling himself told, about how he found the answer. In 1948, while visiting Oxford, he was stuck in bed with a bad cold. Bored, he took a sheet of paper, drew a protein chain on it with the correct bond lengths and angles, and began folding the paper to see how the chain could twist so that its parts held onto each other with hydrogen bonds. He found a spiral, like a spring or a spiral staircase. It took another three years of checking with his colleagues before they published it in 1951, as the alpha helix. It turned out to be right: it is one of the most common shapes in proteins in your body.
In 1954 he won the Nobel Prize in Chemistry for his work on the chemical bond.
The second prize
Linus and Ava Helen were both deeply worried about nuclear weapons. In the 1950s, countries were testing atomic bombs in the open air, and radioactive dust was spreading round the world. Pauling gathered the signatures of thousands of scientists on a petition calling for the tests to end, gave talks everywhere, and was attacked for it: for a while the American government would not let him have a passport. In 1963 a treaty banning nuclear tests in the air came into force, and Pauling was awarded the Nobel Peace Prize for 1962. He is still the only person to have won two Nobel Prizes on his own, without sharing either.
Getting it wrong
Pauling was brilliant, but he was not always right, and the honest story includes his mistakes.
In early 1953 he was racing to work out the structure of DNA. He published a model with three twisted strands, a triple helix. It was wrong: it even had a basic chemical error, putting acid groups in a place where they could not have held together. A few weeks later, James Watson and Francis Crick in Cambridge published the correct double helix, built partly on Rosalind Franklin’s X-ray photographs, which Pauling had never seen.
Later in life, Pauling became convinced that very large doses of vitamin C could prevent colds and help treat cancer. He wrote best-selling books about it. Careful medical trials since then have not supported his biggest claims. Being a great scientist in one area did not make him right in another, and doctors who tested his ideas properly found that the evidence was not there.
That is worth remembering. In science, it does not matter how famous you are. What matters is what the evidence shows.
Fold a helix
Take a long strip of paper, about 3 cm wide (cut along the long side of a sheet). Draw a zigzag line along it, like a chain of bonds. Now wind the strip loosely round a pencil or a marker, at a slant, so it makes a spiral, then slide the pencil out. Notice how, in a helix, each turn sits just above the one before. In a real alpha helix, each turn is held to the next by hydrogen bonds, which is what Pauling was looking for as he folded his paper in bed.
When you read about why water’s molecules stick together, or why carbon’s bonds point the way they do, you are reading Linus Pauling’s chemistry.
PR
Prafulla Chandra Ray
The chemist who wanted India to make its own
1861 to 1944The teacher who founded modern chemistry in India, and its first chemical company
Raruli, Bengal, 1861
Prafulla Chandra Ray was born on 2 August 1861 in the village of Raruli-Katipara in Bengal (today in Bangladesh). His father was a landowner who loved books and had a large library. Prafulla read history, science and the lives of great people, and he decided early that he wanted to be useful to his country.
He studied in Calcutta, and in 1882 he won a scholarship to the University of Edinburgh in Scotland. He studied chemistry there for six years and earned a doctorate in 1887. Even then he was thinking about India. As a student in Edinburgh he wrote an essay criticising British rule in India, which was a bold thing to do.
A teacher on less pay
Presidency College, Calcutta, 1889
When he came home, Ray found it hard to get a job. Eventually, in 1889, he became a lecturer in chemistry at Presidency College in Calcutta. He was paid much less than British teachers doing the same work, simply because he was Indian. He objected, but he did the job anyway, and he did it brilliantly.
His students loved him. He taught chemistry with stories, jokes and demonstrations, and he expected his students to think for themselves. He was called Acharya, “teacher”, a title of great respect. Among the people he taught or trained were some of India’s greatest scientists, including the physicists Meghnad Saha and Satyendra Nath Bose (the “boson” is named after Bose).
A new compound
In 1896, working with mercury and nitric acid in his laboratory, Ray made a yellow crystalline compound that nobody had described before: mercurous nitrite. Chemists had thought such compounds would be too unstable to make. He went on to study many other nitrites, publishing paper after paper, and became so well known for them that the English chemist Henry Armstrong is said to have called him “the Master of Nitrites”.
A company in his rooms
Ray noticed something that troubled him. India had plenty of raw materials, but almost every medicine and laboratory chemical in the country had to be bought from Europe. Indians were trained as clerks and officials, not as makers. He wanted India to make things for itself.
So, in 1892, with very little money (a few hundred rupees; accounts differ on the exact sum), he started making medicines and chemicals in his own rented house in Calcutta, working in the evenings. It was hard going, and for a while it nearly failed. But it grew, and in 1901 it became a proper company: Bengal Chemical and Pharmaceutical Works, one of the first modern chemical companies in India. It made medicines, laboratory chemicals and household products, and it still exists today.
The history of chemistry in India
Ray was also fascinated by the past. He studied ancient Sanskrit texts about metals, medicines and alchemy, and in 1902 he published the first volume of A History of Hindu Chemistry. It showed that people in ancient and medieval India had known a great deal of practical chemistry: how to extract and purify metals, make alloys, prepare medicines from minerals, and distil liquids. Some of these texts, like European alchemy, chased the dream of turning base metals into gold. Others recorded careful, real chemistry.
A simple life
Ray never married. He lived in a single room at the university’s science college, wore plain clothes, and spent very little on himself. It is widely said that he gave most of his salary away, to the university, to students who could not afford their fees, and to good causes, though exact amounts are hard to pin down. When floods and famines struck Bengal, as they did in 1921 and 1922, he organised relief work, collecting money and supplies and sending volunteers, many of them students.
He kept teaching into his late seventies, and died in Calcutta on 16 June 1944.
Ray believed that science was not just something to admire in other countries, but something every country could do for itself, with its own people, in its own laboratories. When this book talks about acids, and the chemistry that turns raw materials into useful things, remember the Acharya who started a chemical company in his own rooms.
JP
Joseph Priestley
The minister who invented fizzy water
1733 to 1804A preacher and teacher who discovered oxygen but never believed in it
Birstall, Yorkshire, 1733
Joseph Priestley was the son of a cloth-maker in the north of England. His mother died when he was six, and he was brought up partly by an aunt. He was a sickly boy with a bad stammer, and he could not go to Oxford or Cambridge, because those universities only admitted members of the Church of England, and his family were “Dissenters”, Protestants who would not join it.
So Priestley taught himself. By his twenties he could read Latin, Greek, French, Italian, German and Hebrew, and he became a minister and a teacher. He wrote about grammar, history, religion, politics, electricity and education. Science was, at first, something he did in his spare time.
The brewery next door
Leeds, 1767
In Leeds, Priestley lived next to a brewery. Above the great vats of fermenting beer hung a layer of invisible gas, the same “fixed air” we now call carbon dioxide. It was heavier than air, it put out candles, and mice could not live in it.
Priestley began to play with it. He found that if he held a bowl of water above a vat for a while, some of the gas dissolved in the water, giving it a pleasant sharp, fizzy taste. Later he worked out a neater method, making the gas from chalk and acid and bubbling it through water. In 1772 he published a little pamphlet on how to do it.
He had invented soda water. He thought it might be a cure for scurvy on long sea voyages (it was not), and he never made money from it. A few years later a jeweller called Johann Jacob Schweppe built a business on carbonated water, and the name Schweppes is still on bottles today.
A gas that made a candle blaze
Priestley became fascinated by “airs”, as gases were then called. He discovered or studied around ten new ones, among them the gas we call ammonia and the one that later became laughing gas. He made great use of a clever trick: collecting gases over mercury instead of water, so that gases that dissolve in water could be caught too.
Calne, Wiltshire, 1 August 1774
Using a large lens, Priestley focused sunlight onto a red powder, the “calx” of mercury. A gas came out. He put a candle in it, and the candle burned with an astonishingly bright flame. He put a mouse in a sealed jar of it, and the mouse lived much longer than it would have in the same amount of ordinary air. He even breathed a little of it himself and wrote that his chest felt “peculiarly light and easy” for some time afterwards.
He had found oxygen. But he did not call it that. Priestley believed in the old theory of phlogiston: the idea that things burn by giving off an invisible substance. He reasoned that this new air must contain no phlogiston at all, so it could soak up a great deal of it, and things burned fiercely in it. He called it “dephlogisticated air”.
Later that year, in Paris, he described his experiment over dinner to Antoine Lavoisier. Lavoisier repeated it, measured everything, and realised what Priestley had missed: burning is not losing phlogiston but joining with this gas. Lavoisier named it oxygen. Priestley never accepted the new explanation, defending phlogiston for the rest of his life.
Mint and a mouse
Priestley also made a beautiful discovery about plants. He found that if a candle burned out in a closed jar, the air in it was “injured”: a mouse could not live in it. But if he put a sprig of mint in that jar and waited some days, the air was “restored”, and a candle could burn in it again. Plants, he realised, repair the air that burning and breathing use up. Later scientists, especially the Dutch doctor Jan Ingenhousz, showed that plants only do this in light. Priestley had glimpsed photosynthesis.
The riots
Priestley was an honest, kind and stubborn man, and his opinions made enemies. He supported the American and French revolutions and argued for religious freedom and for people’s right to disagree with the government.
Birmingham, 14 July 1791
On the second anniversary of the storming of the Bastille, a mob in Birmingham, stirred up partly by Priestley’s political enemies, attacked the homes and chapels of Dissenters. Priestley’s house was burned, together with his laboratory, his library and years of notes. He and his family escaped, warned just in time.
He never felt safe in England again. In 1794, aged sixty-one, he sailed to America and settled in Northumberland, Pennsylvania, where he built a new laboratory and kept experimenting until he died in 1804. He knew some of the American founders, including Thomas Jefferson and Benjamin Franklin.
Watch fizz being made
Priestley’s “fixed air” is carbon dioxide, and you can make some in the kitchen. Put a teaspoon of baking soda into a glass and pour in a little vinegar. The bubbles are carbon dioxide. Now light nothing, and taste nothing: just watch, and listen to the fizz. If an adult opens a bottle of soda water beside it, you are seeing the same gas, dissolved under pressure and escaping. That is Priestley’s invention, in every fizzy drink on Earth.
When you read about Lavoisier and the discovery of oxygen in Chapter 4, remember the stammering minister who found the gas first, and was generous enough to describe his experiment to the man who would prove his theory wrong.
CR
C. V. Raman
Why is the sea blue?
1888 to 1970The accountant who did physics at night, and found a new secret in scattered light
Tiruchirappalli, South India, 1888
Chandrasekhara Venkata Raman was born on 7 November 1888 near Tiruchirappalli, in what is now Tamil Nadu. His father taught mathematics and physics, and the house was full of books. Raman was a remarkable student. He finished school at eleven, went to Presidency College in Madras (now Chennai), and graduated at sixteen, top of his class, with a gold medal in physics. While still a student he published a research paper about light in a British scientific journal.
In those days there were very few jobs for scientists in India. So Raman took a competitive exam for the government’s finance service, came first, and in 1907 became an assistant accountant-general in Calcutta (now Kolkata). He was eighteen.
Physics after office hours
Calcutta, 1907
Not long after he arrived, Raman noticed a sign on a building on Bowbazar Street: the Indian Association for the Cultivation of Science. It had laboratory equipment but very few people using it. He walked in and asked if he could do experiments there.
For the next ten years, Raman lived two lives. By day he was a government accountant. In the early mornings and in the evenings, he was a physicist, working in the Association’s laboratory, studying sound and vibration: why violins and Indian drums like the tabla and mridangam make the beautiful sounds they do. He published paper after paper. In 1917 he finally left the finance service, taking a large cut in pay, to become a professor of physics at the University of Calcutta.
A question on a ship
The Mediterranean Sea, 1921
In 1921 Raman sailed to Britain for a conference. On the voyage he looked down at the deep blue Mediterranean Sea and asked himself a question. Why is it blue?
The usual answer was that the sea is blue because it reflects the blue sky. Raman was not satisfied. He had a small Nicol prism with him, a crystal that can block light reflected off a surface at a slant, and he used it on deck to cut out the reflected skylight. The sea still looked blue. So the colour had to come from the water itself. He suggested that light is scattered by the water molecules, just as sunlight is scattered by air molecules to make the sky blue. (We now know that water’s colour also comes from the way it soaks up a little red light, but Raman’s question started him on a long journey.)
Back in Calcutta, he and his students began to study how light is scattered by all kinds of liquids and gases.
A new colour
Calcutta, February 1928
When light hits molecules and bounces off in a new direction, it almost always keeps exactly the same colour. Blue light comes out blue; green comes out green. But Raman and his colleague K. S. Krishnan noticed that a tiny fraction of the scattered light, perhaps one part in a million or less, came out a slightly different colour.
They used sunlight focused through a telescope lens, and coloured filters, and later a mercury lamp, and looked very carefully. The extra colours were real. On 28 February 1928 Raman announced the discovery. Today, 28 February is celebrated in India as National Science Day.
What was happening? Think of a ball bouncing off a drum. Usually it bounces back with the same energy. But occasionally it sets the drum vibrating, and comes back with a little less energy, having given some away. Light does the same with molecules. Every molecule vibrates in its own particular ways, so it takes away its own particular amounts of energy, and the scattered light comes out shifted by exactly those amounts. The shifted colours are a fingerprint of the molecule.
This is the Raman effect. Today, Raman instruments are used everywhere: to identify chemicals without touching them, to check medicines for fakes, to study paintings without damaging them, and even on Mars rovers to study rocks.
The prize
In 1930 Raman was awarded the Nobel Prize in Physics, the first Asian scientist to win a Nobel Prize in a science. There is a well-known story that he was so sure he would win that he booked his ship tickets to Sweden months before the announcement. It is often told, but it is hard to know whether it is quite true.
He went on to lead the Indian Institute of Science in Bangalore (now Bengaluru), and in 1948 he founded his own research institute there, the Raman Research Institute, where he worked until he died in 1970. He spent much of his later life studying the colours of flowers, gemstones and crystals. He loved diamonds, and built up a large collection to study.
Make a sunset in a glass
You need a clear glass of water, a few drops of milk and a torch, and a dark room. Stir three or four drops of milk into the water. Shine the torch through the side of the glass and look at the glass from the side: the water has a faint bluish glow. Now look through the glass straight towards the torch: the light coming through looks yellowish or orange. The tiny drops of fat in the milk scatter blue light sideways more than red, just as air scatters sunlight to make the blue sky and the orange sunset. Raman spent his life studying scattered light like this, and he found something hidden in it that no one had noticed before.
When this book talks about light and the colours that molecules and atoms give out, remember the young accountant who walked into a laboratory on Bowbazar Street and asked if he could do some experiments.
WR
William Ramsay
The man who found a missing column
1852 to 1916Discovered the noble gases, an entire family of elements hiding in the air
Glasgow, 1850s and 1860s
William Ramsay was born in Glasgow in 1852. His family were engineers and scientists: his father was a civil engineer, one uncle was a famous geologist, and his grandfather had been a chemical manufacturer. William loved languages, music and mathematics as a boy, and it is said that he first became interested in chemistry while reading about how gunpowder is made. By his mid-teens he was studying at the University of Glasgow, and he went on to study chemistry in Germany.
He became a professor in Bristol, then at University College London. He was known as a superb experimenter with glass: he could blow and shape fine glass apparatus himself.
A puzzle about nitrogen
Cambridge and London, 1892 to 1894
The story begins with somebody else. Lord Rayleigh was a physicist who was measuring the densities of gases very, very precisely. He made nitrogen in two different ways. One way was to take air and remove the oxygen, water and carbon dioxide. The other was to make nitrogen from chemicals such as ammonia.
The two samples should have been identical. They were not. The nitrogen from air was heavier, by about half a percent. A litre of it weighed about 1.257 grams; a litre of the chemical nitrogen about 1.251 grams. A tiny difference, but Rayleigh was a careful man and it never went away.
Rayleigh published a letter asking if anybody could explain it. Ramsay offered to help. Each worked on it separately, in close touch. Their guess: the nitrogen from air was not pure nitrogen. Something else, something heavier, was hiding in it.
Argon, the lazy one
Ramsay passed nitrogen from air over hot magnesium, again and again, which slowly removes nitrogen by turning it into a solid. At the end, a small amount of gas remained that would not react with anything. Its spectrum (the pattern of coloured lines it gives off when electricity passes through it; see spectra) matched no known element.
In 1894 Rayleigh and Ramsay announced a new element. They called it argon, from the Greek for “lazy” or “idle”, because it refused to react. It makes up nearly 1% of air. People had been breathing it for ever, and chemists had been weighing it along with their nitrogen for over a century without knowing it was there. (In fact Henry Cavendish, in 1785, had noticed a small bubble of air that would not react, but nobody followed it up.)
Helium, from the Sun to Earth
In 1868 astronomers had seen a yellow line in the spectrum of the Sun that matched no element on Earth, and named the unknown element helium, after the Greek for “Sun”. In 1895 Ramsay dissolved a uranium mineral in acid and collected the gas it released. He found in it the very same yellow line. Helium was not only in the Sun: it was here, trapped in rocks.
A whole new family
Now Ramsay had two unreactive gases that did not fit anywhere in Mendeleev’s periodic table. He made a bold guess: they belonged to a whole new family, a new column, and there should be more members to find.
University College London, 1898
With his young assistant Morris Travers, Ramsay cooled air until it turned into a liquid, then let it boil off slowly, collecting each gas as it came away. In 1898, in just a few weeks, they found three more:
neon (“new”), which glows a brilliant red-orange in a tube with electricity (the first “neon signs”);
krypton (“hidden”);
xenon (“stranger”).
Travers later recalled the moment they first saw neon’s crimson glow. The whole column of what we now call the noble gases was complete, except for radon, which others found among radioactive elements and which Ramsay helped to study.
In 1904 Ramsay won the Nobel Prize in Chemistry and Rayleigh the Nobel Prize in Physics, in the same year. Ramsay is one of very few scientists to have discovered a whole group of the periodic table.
Mendeleev had at first doubted argon. In the end he accepted the new column, and it fitted his table beautifully: it slotted in between the halogens and the alkali metals.
India
Ramsay also has a link to India. In about 1900 he travelled there to advise on plans for a new research institute that the industrialist Jamsetji Tata hoped to found. His advice helped decide where it should go: Bangalore. The Indian Institute of Science opened there in 1909. (Accounts differ about how much influence his report had, but his visit is well recorded.)
Find the lazy gas in your room
You cannot see argon, smell it or taste it, but it is all around you. Air is about 78% nitrogen, 21% oxygen and nearly 1% argon (0.93%, to be more exact). Measure the room you are sitting in with a tape measure, or estimate it. Multiply length × width × height in metres to get cubic metres, and multiply by 1,000 to get litres. Then find 0.93% of that. For a classroom 10 m by 8 m by 3 m: 240 cubic metres is 240,000 litres of air, and about 2,200 litres of it is argon, enough to fill more than ten bathtubs. Every breath you take is nearly one hundredth argon, and it comes out again unchanged.
He died in 1916. When you look at the last column of the periodic table in Chapter 9, the lazy gases that hardly react with anything, remember the half percent of extra weight that a careful man refused to ignore.
ER
Ernest Rutherford
The boy from the potato field
1871 to 1937The farm boy from New Zealand who found the nucleus and turned one element into another
Brightwater, New Zealand, 1871
Ernest Rutherford was born on 30 August 1871 near Nelson, at the top of New Zealand’s South Island, the fourth of twelve children. His father was a wheelwright and flax-miller; his mother was a schoolteacher. There was not much money, but there were a lot of books, and young Ernest was the kind of boy who took clocks apart to see how they worked and built model water wheels in the creek.
He won scholarships at every step: to Nelson College, then to Canterbury College in Christchurch, where he did his first real experiments in a cold, draughty basement, building detectors for radio waves only a few years after they had been discovered. In 1895 he won a scholarship to study at Cambridge, on the other side of the world.
There is a famous story about that moment. The telegram arrived while he was digging potatoes in his family’s garden, and he threw down his spade and said, “That’s the last potato I’ll ever dig.” It is a lovely story, and it is told everywhere, but nobody wrote it down at the time, so treat it as a family legend rather than a fact.
The colonial in Cambridge
At the Cavendish Laboratory in Cambridge, Rutherford worked under J. J. Thomson, the man who would discover the electron. Some of the English students looked down on the loud young man from the colonies. It did not last. Within a few years Rutherford was famous for one thing above all: he could design simple, clever experiments that went straight to the heart of a question.
Radioactivity had just been discovered, and Rutherford threw himself into it. He found that the rays coming out of uranium were of at least two kinds, and he gave them the names we still use: alpha and beta.
Montreal, and the shock of transmutation
Montreal, Canada, 1901
In 1898 Rutherford became a professor at McGill University in Montreal. There he teamed up with a young English chemist, Frederick Soddy. Together they studied thorium, a radioactive element, and noticed something that seemed impossible: as it gave off radiation, a small amount of thorium was slowly becoming a different element.
For more than two thousand years, alchemists had dreamed of changing one element into another. Serious scientists had decided it could not be done. Now here it was, happening on its own, inside a lump of rock. Soddy later remembered blurting out, “Rutherford, this is transmutation!” and Rutherford snapping back, “For Mike’s sake, Soddy, don’t call it transmutation. They’ll have our heads off as alchemists.” (This is Soddy’s own memory, told many years later, so the exact words may have drifted.)
In 1908 Rutherford won the Nobel Prize. He was a physicist through and through, and he rather looked down on chemistry, so he was amused to find it was the Nobel Prize in Chemistry. He joked that he had seen many transformations in his work, but none as quick as his own, from physicist to chemist.
Manchester and the gold foil
Manchester, 1909
By then he had moved to Manchester. He asked his assistant Hans Geiger and a twenty-year-old student, Ernest Marsden, to fire alpha particles at a sheet of gold foil thinner than a leaf, and to count where they went by watching for tiny flashes of light in a darkened room. Almost all of them flew straight through. But about one in every eight thousand bounced back.
Rutherford said it was as if you fired a large shell at a piece of tissue paper and it came back and hit you. In 1911 he worked out what it meant: almost all the mass of an atom is packed into a tiny, positively charged centre, the nucleus, with the electrons spread out around it, far away. An atom is mostly empty space. Chapter 1 tells this story in full, and you can fire the alpha particles yourself in its figure.
The first person to change an element on purpose
In 1919, just before he went back to Cambridge to run the Cavendish Laboratory, Rutherford did something no alchemist had ever managed. He fired alpha particles into nitrogen gas and found hydrogen nuclei (protons) flying out. A few of the nitrogen nuclei had been hit so hard that they changed. Later work by his colleague Patrick Blackett showed exactly what happened: the alpha particle sticks to the nitrogen nucleus, a proton is knocked out, and what is left is a nucleus of oxygen.
So the first deliberate transmutation in history did not turn lead into gold. It turned nitrogen into oxygen, a handful of atoms at a time. It was worth nothing in money and everything in understanding.
The Crocodile
Rutherford was a big man with a big voice. His students said he sang “Onward, Christian Soldiers” loudly and badly as he walked round the laboratory, and there are stories (perhaps exaggerated) that his booming voice disturbed the delicate instruments. The Russian physicist Pyotr Kapitsa, who worked for him in Cambridge, nicknamed him “the Crocodile”. A crocodile was carved on the wall of the laboratory Kapitsa built there, and you can still see it.
He could be gruff, but he was generous with his students, and he had a gift for picking good people and good problems. A remarkable number of the people who trained or worked with him went on to win Nobel Prizes of their own, among them Niels Bohr, Frederick Soddy, James Chadwick (who found the neutron), and John Cockcroft and Ernest Walton (who split the atom with a machine in 1932).
What became of him
Rutherford became Lord Rutherford of Nelson, named after the town near where he grew up. He died in 1937 and was buried in Westminster Abbey in London, close to Isaac Newton. Element 104 is called rutherfordium in his honour, and his face is on New Zealand’s hundred-dollar note.
Find a hidden shape without looking
This is how Rutherford “saw” the nucleus: by throwing things at it and watching how they bounced. Ask someone to put a small object (a book, a lunchbox, a box of tea) under a large tray or a sheet of cardboard, so you cannot see it. Kneel at the edge and roll marbles under the tray from different directions. Watch where they come out. Some roll straight through; some bounce off at angles. After twenty or thirty rolls, try to sketch the hidden object’s shape and size. Then lift the tray and check. You were doing a scattering experiment.
Whenever you read about the nucleus, or about one element turning into another, you are standing on the potato field in Brightwater, with the boy who threw down his spade.
CS
Carl Wilhelm Scheele
The pharmacist who found everything first
1742 to 1786A Swedish apothecary who discovered oxygen, chlorine and many other substances
Stralsund, on the Baltic coast, 1742
Carl Wilhelm Scheele was the seventh of eleven children of a merchant in Stralsund, a town that then belonged to Sweden. At fourteen he was apprenticed to a pharmacist in Gothenburg. A pharmacy, or apothecary shop, was where medicines were made by hand from plants, minerals, acids and salts. To a boy who loved chemistry, it was a treasure house.
Scheele read every chemistry book in the shop, and at night, after work, he repeated the experiments in them. He never went to university. All his life he worked in pharmacies, and in the back rooms, with simple equipment and very little money, he became one of the greatest discoverers in the history of chemistry.
A list of discoveries
Scheele’s list is astonishing. He was the first to identify or prepare many substances, including:
the gas we now call chlorine, a greenish-yellow gas (he did not realise it was an element; Humphry Davy showed that later);
acids from fruit and from milk, among them the acid of lemons (citric acid), of sour milk (lactic acid) and of apples (malic acid);
glycerol, which is in soap and many foods;
and important early work on manganese, barium, molybdenum and tungsten.
He also found that silver salts darken in light, especially violet light, a discovery that photography would later depend on. And a bright green pigment he invented, “Scheele’s green”, became fashionable for wallpaper and paint. Sadly, it contained arsenic, and in damp rooms it could make people ill. Scheele did not know that would happen.
Fire air
Uppsala, around 1771 to 1772
Scheele wanted to know what air is made of. He heated several different substances, among them a red powder made from mercury and a black mineral of manganese, and collected the gas that came off. A candle burned in it with dazzling brightness. He called it “fire air”, because fire loved it. He also found that ordinary air contains some of this fire air and some “foul air” in which nothing will burn: oxygen and nitrogen, in today’s words.
His notebooks suggest he did these experiments around 1771 or 1772, two or three years before Joseph Priestley found the same gas in England in 1774. But Scheele’s book, Chemical Observations and Experiments on Air and Fire, was held up at the printer, and did not appear until 1777. By then Priestley had published, and Lavoisier had named the gas oxygen and explained burning.
So who discovered oxygen? Historians usually say Scheele found it first, Priestley published first, and Lavoisier understood it first. Science is often like that: a discovery is made by several people, each adding a piece.
A dangerous habit
Scheele had one habit that every chemist since has learned not to copy. In his day, chemists described substances by their colour, their smell, and their taste, and Scheele recorded the taste of many of the chemicals he made, including some that we now know are poisonous. He also worked for years with arsenic, mercury and lead, and breathed fumes in a small, poorly ventilated room.
He died in 1786, at only 43. Nobody knows the exact cause. Many historians think years of exposure to toxic chemicals damaged his health; others think he also had an illness unrelated to his work. Either way, it is a lesson that every chemistry lab in the world now teaches on the first day: you never taste a chemical in a laboratory, and you never sniff one directly. In this book the only things you ever taste are ordinary food.
A quiet, happy life
Scheele was offered jobs as a professor in Berlin and in England, but he turned them down. He preferred his own pharmacy in the small Swedish town of Köping, where he could work in peace. He was elected to the Royal Swedish Academy of Sciences while still a pharmacist’s assistant, which was a very unusual honour. Just days before he died, he married the widow of the pharmacist whose shop he had taken over, so that she would inherit his business.
The acids in your fruit bowl
Scheele was the first to pull citric acid out of lemons and malic acid out of apples. You can taste the difference between them, because these are ordinary foods. Taste a tiny piece of lemon, then a slice of sour green apple, then a sweet ripe apple. The sharpness you notice comes mostly from the acids Scheele discovered. Now notice that a ripe apple tastes less sharp: as fruit ripens, the amount of acid falls and the amount of sugar rises.
When you read in Chapter 2 about how the elements were found one by one, remember the young apprentice reading by candlelight in a Swedish pharmacy, who found more of chemistry’s secrets than almost anyone, and did it all from a shop.
1839 to 1974
Lucky accidents, and the people who noticed
Charles Goodyear, Alexander Fleming, Roy Plunkett, Spencer Silver, Art Fry
There is a saying, usually credited to the French scientist Louis Pasteur: “chance favours only the prepared mind.” Here are five discoveries that began as accidents, and the people who were prepared enough to notice.
Massachusetts, 1839
Rubber that behaves
Natural rubber, from the sap of rubber trees, was a nuisance in the 1830s. In summer it went soft and sticky; in winter it cracked. Charles Goodyear, an American inventor who was often deeply in debt, spent years mixing rubber with everything he could think of.
According to his own account, in 1839 he dropped some rubber mixed with sulfur onto a hot stove. Instead of melting, it charred like leather and stayed firm and springy. (The details come from Goodyear himself and may have been tidied up in the telling.) Heat had made sulfur atoms form bridges between the long rubber molecules, tying them together like the rungs of a ladder. The process was later called vulcanisation, after Vulcan, the Roman god of fire. Every car tyre depends on it.
London, 1928
The mould that killed germs
Alexander Fleming, a Scottish doctor, came back from a holiday to find that a dish of bacteria he had left on his bench had grown a fuzzy patch of mould. Around the mould there was a clear ring where the bacteria had died. Something from the mould was killing them.
Fleming called the substance penicillin. He could not make enough of it to use as a medicine, and for about ten years not much happened. Then, around 1940, a team at Oxford led by Howard Florey and Ernst Chain worked out how to purify it, and the first patients were treated. Penicillin has since saved an enormous number of lives.
New Jersey, 1938
The gas cylinder that went quiet
Roy Plunkett, a young chemist at the DuPont company, was working with a gas for refrigerators. One morning a cylinder that should have been full of gas would not let any out, though it still weighed as much as a full one. Instead of throwing it away, Plunkett had it sawn open. Inside was a white, waxy, slippery powder. The gas molecules had joined together into long chains, all by themselves.
The new material was incredibly slippery and almost nothing reacted with it. It was named Teflon, and today it coats non-stick frying pans.
Minnesota, 1968 and 1974
The glue that did not stick properly
Spencer Silver, a chemist at the company 3M, was trying to make a very strong glue. He made a very weak one instead: it stuck, but peeled off easily and could be stuck again. For years nobody knew what to do with it. Then his colleague Art Fry, who sang in a church choir, was annoyed that his paper bookmarks kept falling out of his hymn book. He remembered Silver’s glue. The result, after more years of work, was the sticky note.
Careful
“Saccharin was found by a chemist licking his fingers, so tasting things is how discoveries get made.”
It is true that in 1879 a chemist named Constantin Fahlberg noticed his bread tasted sweet after a day in the laboratory, traced it to a chemical on his hands, and so found the sweetener saccharin. But many chemists in history poisoned themselves by tasting and smelling unknown substances. Never taste anything from an experiment. Fahlberg was lucky, and lucky is not a method.
What they had in common
None of these people was simply lucky. Goodyear had spent years on rubber. Fleming knew exactly what a clear ring around a mould meant. Plunkett weighed his cylinder instead of assuming it was empty. Each had a prepared mind: they knew enough to recognise that something strange was also something important.
Make a slime that changes
Mix two tablespoons of cornflour with about one tablespoon of water in a bowl. Poke it hard and fast: it feels solid. Let your finger sink in slowly: it flows like a liquid. Nobody planned this; it is just how the starch grains in water behave. Write down what you notice, like a scientist, before reading about it.
about 300 to 1700
Two thousand years of trying to make gold
Zosimos of Panopolis, Jabir ibn Hayyan, Abu Bakr al-Razi, Paracelsus, Hennig Brand
Alexandria, Egypt, about the year 300
Picture a workshop in the great city of Alexandria, on the coast of Egypt. Furnaces glow. Clay pots bubble. A man called Zosimos, from the town of Panopolis, is writing down everything he knows about how to change one metal into another. He describes stills for boiling liquids and catching their vapour, and he writes about a woman he calls Mary the Jewess, who seems to have invented some of this equipment before him. Very little is known about Mary for certain, but a cooking method is still named after her: the bain-marie, a bowl set over hot water.
This was the beginning of alchemy, and for about the next fourteen hundred years some of the cleverest people in the world tried to do the same thing: turn cheap metals such as lead into gold.
Why it seemed possible
The idea was not silly at the time. Metals look alike: shiny, heavy, able to melt and be hammered. Copper mixed with zinc turns a golden colour. Ores dug from the ground change completely in a furnace. If dull rock can become bright metal, why shouldn’t one metal become another? Many alchemists believed metals slowly “ripened” underground, the way fruit ripens, and that gold was the ripest of all. Perhaps, with the right substance, you could speed the ripening up. They called that imagined substance the philosopher’s stone.
The Arabic chemists
When the Roman world faded, the work moved to Baghdad and the other great cities of the Islamic world. A large collection of books is credited to Jabir ibn Hayyan, who may have lived in the 700s. Historians argue about who really wrote them: some of the books were probably written by many different people over a long time and put under his famous name. Whoever wrote them, they describe careful laboratory work: purifying substances, crystallising them, and sorting them into groups.
A little later, in the late 800s and early 900s, the Persian doctor Abu Bakr al-Razi sorted substances into families, such as minerals, salts and spirits, and described his apparatus so clearly that you could rebuild it. He used distillation, the trick of boiling a liquid and cooling its vapour to collect something purer.
You still speak a little of their language every day. Alchemy comes from the Arabic al-kīmiyā, and chemistry comes from that. Alcohol and alkali are Arabic words too.
Paracelsus and the medicine-makers
In the 1500s a loud, quarrelsome Swiss doctor who called himself Paracelsus told alchemists to stop chasing gold and make medicines instead. He was rude to almost everyone, and some of his ideas were badly wrong, but he pushed alchemy towards chemistry: making useful substances and testing what they did.
Hamburg, 1669
Now for one of the strangest discoveries ever made. Hennig Brand, a merchant in Hamburg, was sure the secret of gold was hidden in human urine. It is yellow, after all. So he collected a great deal of it (stories say dozens of buckets, though nobody knows the exact amount), left it to stand for days, and boiled it down.
He did not get gold. At the bottom of his apparatus he got a white, waxy substance that glowed in the dark with a ghostly green light. It caught fire by itself in air. Brand had discovered phosphorus, from the Greek for “light-bringer”. It is usually called the first element whose discoverer we know by name. The elements known before it, such as gold, iron, copper and sulfur, had been in use since ancient times, and nobody knows who first found them.
The secret alchemists
Alchemy did not end when modern science began. Robert Boyle, one of the founders of modern chemistry, practised alchemy all his life and hoped to see a metal transformed. Isaac Newton, the greatest scientist of his age, wrote more than a million words about alchemy, much of it in secret notebooks. Both men are in this book, and both have their own stories.
Why it could never work
Here is the answer the alchemists could not have known. Gold is an element: every gold atom has exactly 79 protons in its nucleus, and that number is what makes it gold. Lead has 82, and mercury has 80.
Chemistry, everything you do with fire, acids, stills and furnaces, only moves the electrons on the outside of atoms. It rearranges atoms into new partners. It never touches the nucleus in the middle. So no chemical reaction, however clever, can turn lead into gold. To change the number of protons, you have to break into the nucleus itself, and that takes energies millions of times greater than any furnace.
Careful
“So the alchemists were just foolish.”
They were not. They had no way of knowing atoms existed, let alone nuclei. And while chasing gold they invented the tools of the laboratory: stills, flasks, furnaces, water baths, and the habit of writing down exactly what they did. They discovered acids, purified salts and found new elements. Modern chemistry grew out of their workshops.
Watch distillation happen
Ask an adult to pour a mug of very hot tap water. Hold a cold plate (straight from the fridge is best) a few centimetres above the mug for half a minute, then look underneath. Water vapour rising from the mug has cooled on the plate and turned back into drops of liquid. That is the heart of distillation, the trick al-Razi and the alchemists used to purify liquids. Don’t use boiling water from a kettle, and keep your hand away from the steam.
The alchemists’ dream did eventually come true, in a way none of them could have imagined, inside particle accelerators and nuclear reactors. That is the story of transmutation.
1865
The snake that bit its own tail
August Kekulé, Michael Faraday, Kathleen Lonsdale
London, 1825
The puzzle began with Michael Faraday. In 1825 he found a new liquid in the oily leftovers of a lighting gas made by heating whale and fish oil, which a London company delivered in metal cylinders. It smelled sweet and caught fire easily. He measured carefully what it was made of, and his numbers, read with what we know today, mean it has equal numbers of carbon and hydrogen atoms. We now write it C₆H₆ and call it benzene.
Here was the trouble. By the 1850s chemists had learned that every carbon atom forms four bonds and every hydrogen atom forms one. A chain of six carbons, like the ones in petrol, needs fourteen hydrogens to use up all those bonds. Benzene had only six. How could six carbons and six hydrogens fit together so that every carbon had its four bonds? And why was benzene so stable, when other molecules short of hydrogen reacted eagerly?
Ghent, Belgium, 1865
August Kekulé, a German chemist teaching in Ghent, had already helped work out that carbon makes four bonds and that carbon atoms can link into chains. In 1865 he proposed something new: the six carbons of benzene join into a ring, a closed hexagon, each carbon holding one hydrogen. To give each carbon four bonds, he suggested the ring had double and single bonds alternating around it.
It was a brilliant idea, and it explained a huge number of facts about benzene and the many substances made from it, including Perkin’s dyes.
The daydream
Twenty-five years later, in 1890, chemists held a great celebration in Berlin for the anniversary of Kekulé’s ring. In his speech, Kekulé told a story. He said he had been dozing by the fire, and saw rows of atoms dancing and twisting like snakes. Then one snake seized its own tail and whirled before his eyes, and he woke with the idea of a ring.
It is a wonderful story, and it is famous all over the world. But it is Kekulé’s own account, told a quarter of a century later at a party in his honour. Some historians think he embellished it, or invented it to make a point about imagination. We cannot know for sure.
Careful
“So the discovery came from a dream.”
Even if the dream happened exactly as he said, it came after years of hard thinking about how carbon atoms join. A dream does not hand you an answer you have not prepared for. Kekulé himself is reported to have ended his speech by telling chemists to dream, but to test their dreams before publishing them.
Seeing the ring
For decades the ring was a brilliant guess that fitted the facts. Then, in 1929, the Irish-born crystallographer Kathleen Lonsdale used X-rays on a crystal of a benzene compound and showed that the ring really is flat and hexagonal. She also found that all six bonds around the ring are the same length. That doesn’t fit Kekulé’s picture of alternating single and double bonds exactly. The modern picture is that the shared electrons are spread evenly around the whole ring, which is why chemists often draw benzene as a hexagon with a circle inside. That evenly spread cloud of electrons is also what makes benzene so stable.
Build a benzene ring
Take six paper clips (the carbons) and link them into a closed ring. Hook one small elastic band or a scrap of paper (a hydrogen) onto the outside of each. Now try to make a straight chain of six clips with only six “hydrogens” so that every clip has four connections: you will find you cannot do it without closing the loop or doubling up connections. That was Kekulé’s puzzle.
1856
The boy who made the world purple
William Henry Perkin, August Wilhelm von Hofmann
East London, Easter holiday, 1856
William Perkin was eighteen, and he had turned part of his family’s house in East London into a laboratory. In term time he was the assistant of a famous German chemist, August Wilhelm von Hofmann, at the Royal College of Chemistry. Over the Easter holiday he carried on experimenting at home.
Hofmann had set him a dream of a problem. Malaria was killing huge numbers of people across the British Empire, including in India. The only medicine, quinine, came from the bark of the cinchona tree, which grew in South America and was expensive and scarce. Could a chemist make quinine in a flask, from something cheap?
The cheap starting point
The cheapest raw material around was coal tar, the black, smelly waste left over when coal was heated to make gas for street lamps. Chemists had found that coal tar contained useful substances. Perkin took one of them, aniline, and treated it with a strong chemical that pulls hydrogen away, hoping to build quinine.
He did not get quinine. Nobody could have, with what was known in 1856: quinine’s structure was far too complicated, and it was not made in a laboratory until 1944. What Perkin got was a black, tarry sludge at the bottom of his flask.
Looking twice
Most people would have thrown it away. Perkin washed the flask out with alcohol, and the alcohol turned a brilliant purple.
He tested the purple on silk. It stuck. It did not wash out, and it did not fade quickly in sunlight. Purple had always been the colour of emperors, because the old purple dye came from sea snails, thousands of them for a scrap of cloth. Perkin had made purple from coal waste.
The gamble
His teacher thought he was throwing away a scientific career. Perkin patented his dye anyway, left college, and, with money from his father and help from his brother, built a factory near London. He was still a teenager. Making it work was hard: they had to work out how to produce aniline by the barrel rather than by the spoonful, and how to fix the dye onto cotton as well as silk.
The colour became known by the French name mauve, and in the late 1850s mauve became the most fashionable colour in Europe. Queen Victoria wore mauve to her daughter’s wedding in 1858. Magazines joked about “mauve measles” because the colour was everywhere.
What came next
Perkin’s dye, later called mauveine, was the first of the coal-tar dyes, and the first artificial dye to become a worldwide success. Within a few years chemists had made magenta, new blues, greens and blacks, all from coal tar. The great chemical companies of Germany and Switzerland began as dye makers. And the skills they learned, building complicated molecules step by step, led straight to synthetic medicines. So in a roundabout way Perkin did help the fight against disease: just not the way he planned.
Perkin made his fortune, sold the factory at 36 and went back to pure research for the rest of his life. He was knighted in 1906, fifty years after that Easter holiday.
Dye with turmeric
You need a spoonful of turmeric powder, a cup of hot tap water (ask an adult), and a strip of white cotton cloth, such as an old handkerchief. Stir the turmeric into the water, drop in the cloth for ten minutes, then rinse it in cold water. It stays bright yellow. Now dab one corner with a little baking soda dissolved in water: turmeric is also an indicator, and it turns red-brown where it meets something basic. Turmeric stains hands and clothes, so wear old clothes and work on a plate.
The lesson to take from Perkin is not “accidents make you rich”. It is that he noticed. Lots of people had made black sludge. He looked at it twice.
1901 to today
Mercury into gold, at last
Ernest Rutherford, Frederick Soddy, Glenn Seaborg, the ALICE team at CERN
Montreal, Canada, 1901
In a basement laboratory at McGill University, two young scientists were puzzling over a radioactive substance called thorium. One was Ernest Rutherford, a farmer’s son from New Zealand. The other was Frederick Soddy, a chemist from England. Thorium kept giving off a gas, and when Soddy tested the gas he realised it was not thorium at all. It was a different element. The thorium atoms were turning, all by themselves, into atoms of something else.
Soddy said many years later that he burst out, “Rutherford, this is transmutation!”, and that Rutherford answered something like, “For goodness’ sake, Soddy, don’t call it transmutation. They’ll have our heads off as alchemists.” We only have Soddy’s memory of the exact words, but the worry was real. Transmutation, changing one element into another, was the alchemists’ word, and serious scientists had spent two hundred years laughing at it.
Yet here it was, happening on their bench.
What makes gold gold
To understand the rest of this story you need one fact. What decides which element an atom is? Not its colour, not its weight, not its electrons. It is the number of protons in its nucleus.
Gold: 79 protons. Mercury: 80 protons. Lead: 82 protons.
To turn mercury into gold, you must take away exactly one proton from each nucleus.
Chemistry cannot do this, because chemistry only rearranges the electrons on the outside. To change the proton number you have to break into the nucleus, which is tiny, extremely tightly held together, and guarded by a powerful electric push against anything with a charge.
The first deliberate transmutation
Manchester, 1919
Radioactive atoms transmute themselves. Could a person make it happen on purpose? In 1919 Rutherford fired fast alpha particles, from a radioactive source, through nitrogen gas. Once in a long while an alpha particle hit a nitrogen nucleus squarely and stuck, and a proton flew out. The nitrogen nucleus became an oxygen nucleus. For the first time, a human being had deliberately turned one element into another. It was not gold, and it was only a handful of atoms, but the door was open.
Gold from mercury, 1941
Then came the neutron (found in 1932), a particle with no electric charge. Because it has no charge, nothing pushes it away, and it can slip into a nucleus easily. In 1941, at Harvard, the physicists Rubby Sherr, Kenneth Bainbridge and Herbert Anderson fired neutrons at mercury and made gold. There was a catch: the gold atoms they made were radioactive kinds that broke down within days. Nobody could have worn it as a ring.
In 1980 the American chemist Glenn Seaborg, who discovered several of the heaviest elements, used a particle accelerator in California to knock protons and neutrons off bismuth (83 protons) and leave gold behind. He made only a tiny number of atoms, and the electricity and machinery cost vastly more than the gold was worth.
The biggest machine in the world
CERN, near Geneva, 2025
The Large Hadron Collider is a ring 27 kilometres round, buried under the border between France and Switzerland. It smashes together nuclei of lead travelling at almost the speed of light. In May 2025 the scientists of its ALICE experiment announced something surprising (published in the journal Physical Review C).
Sometimes two lead nuclei do not hit each other at all. They whizz past very close. Each carries such an intense electric field that, as they pass, a burst of light energy can knock a few particles out of the other nucleus. If exactly three protons are knocked out, lead (82) becomes gold (79).
The ALICE team worked out that in the years 2015 to 2018 the collider had made about 86 billion gold nuclei this way. That sounds like a lot. Add them up, though, and they weigh about 29 picograms: 29 millionths of a millionth of a gram. A single grain of rice is roughly 700 million times heavier. And each gold nucleus lasted only a tiny fraction of a second before it hit the machine’s walls and broke apart.
A claim from a fusion company
Now we come to the news. A company in the United States called Marathon Fusion works on nuclear fusion, the process that powers the Sun. In 2025 its scientists published a proposal based on computer calculations. Future fusion power plants will release enormous numbers of fast neutrons. If those neutrons struck a kind of mercury called mercury-198, they could knock a neutron out, leaving mercury-197. Mercury-197 is unstable. Over a couple of days its nucleus captures one of its own inner electrons; inside the nucleus that electron and a proton turn into a neutron, so 80 protons become 79. The result is gold-197, the ordinary, stable gold of rings and coins. Their calculations suggested a big fusion plant might make a few tonnes of gold a year as a by-product. That was a model on a computer, not a working machine.
On 21 October 2026 the company announced online that it had actually made gold from mercury, beating CERN’s record “by a factor of 10”. As this book was written, that claim had not been checked by other scientists. That does not mean it is false. It means we do not know yet.
Careful
“If a company says it did something, it did it.”
In science a claim becomes knowledge only when others can check it. Scientists would want to see a detailed paper, reviewed by experts who did not do the work, showing exactly how much gold was made and how it was measured, and ideally an independent laboratory confirming it. Until then, a sensible scientist says: “Interesting, and unconfirmed.”
The real treasure
Isaac Newton spent years of secret work trying to transmute metals. He would have been astonished to learn that it can be done, and perhaps more astonished to learn why it was impossible for him: the change happens deep in the nucleus, at energies no furnace could reach.
Even if fusion gold becomes real, the gold is not the most precious thing in this story. Rutherford and Soddy learned what an element is. That understanding gave us nuclear medicine, carbon dating, smoke detectors and power from the atom. The alchemists were searching for gold. What they and their successors actually found was knowledge, and that turned out to be worth far more.
about 450 BCE to 1908
Can you cut forever? The long argument about atoms
Leucippus, Democritus, Kanada, John Dalton
Abdera, a Greek town on the coast of Thrace, about 450 BCE
Imagine you have a piece of cheese and a very sharp knife. Cut it in half. Cut one half in half again. Keep going. The pieces get smaller and smaller, until they are too small to see. Can you keep going for ever, or is there a smallest piece of cheese that cannot be cut?
About two and a half thousand years ago, a Greek thinker called Leucippus and his student Democritus gave an answer. You cannot cut for ever, they said. In the end you reach tiny pieces that are solid all the way through and cannot be divided. They called them atomos, which means “uncuttable”, and that is where our word atom comes from. Everything, they said, is made of atoms moving through empty space. Sweet things are made of smooth round atoms, sour things of sharp, jagged ones. Water flows because its atoms are slippery.
This was a remarkable guess. But it was only a guess. Democritus had no way to test it, and the most famous philosopher of the next generation, Aristotle, did not believe it. Aristotle taught that matter is continuous, like an endless smooth jelly, and that everything is made of four elements: earth, water, air and fire. Aristotle’s ideas were taught in schools for nearly two thousand years. Atoms were mostly forgotten.
Far away, the same idea
Greece was not the only place where people wondered about this. In India, the philosopher Kanada, founder of the Vaisheshika school, also taught that matter is made of tiny, eternal, indivisible particles, which he called paramanu. Nobody knows exactly when Kanada lived; scholars’ guesses range over several centuries before the Common Era. His particles combined in pairs and threes to make bigger things, an idea that sounds surprisingly modern. Like Democritus, though, Kanada was reasoning, not measuring.
Step 1: why a guess is not enough
Here is the important difference between philosophy and science. A philosopher can say “matter is made of atoms” and argue for it beautifully. A scientist has to ask: if that is true, what should I be able to measure? Only when an idea predicts something you can check does it start to become science.
For atoms, that took until about 1800, and it came from weighing.
Manchester, England, 1803
John Dalton was the son of a poor weaver. He started teaching at a village school when he was twelve years old, the same age you are now. Later he taught mathematics and science in Manchester, and in his spare time he studied the weather, kept a daily weather diary for 57 years, and discovered that he and his brother were colour-blind (it is still sometimes called Daltonism).
Dalton was puzzling over gases, and over a strange regularity that chemists had found when substances combine.
Step 2: the clue in the numbers
When elements combine to make compounds, they always do so in fixed proportions by mass. Water is always about 1 gram of hydrogen for every 8 grams of oxygen, no matter where the water comes from. And when two elements can make more than one compound, the amounts come in simple whole-number ratios. Carbon makes two gases with oxygen: in one, 12 grams of carbon combine with 16 grams of oxygen; in the other, the same 12 grams of carbon combine with 32 grams of oxygen. Exactly twice as much. Never 1.7 times, never 2.3 times.
Why whole numbers? Dalton saw the answer. If each element is made of identical atoms, all with the same mass, and compounds form when atoms join in small whole numbers, then the masses must come in simple ratios. One carbon atom with one oxygen atom makes one gas (we now call it carbon monoxide); one carbon atom with two oxygen atoms makes the other (carbon dioxide). Twice the oxygen atoms, twice the mass of oxygen.
Step 3: Dalton’s atomic theory
In 1808 Dalton published his ideas in a book called A New System of Chemical Philosophy. In simple words:
Every element is made of tiny atoms.
All the atoms of one element are identical, with the same mass. Atoms of different elements have different masses.
Atoms are not created or destroyed in chemical reactions; they just rearrange.
Compounds form when atoms of different elements join in small whole numbers.
He drew each kind of atom as a little circle with its own mark, and made the first table of relative atomic masses, with hydrogen as 1. Some of his numbers were wrong, because he guessed some formulas wrong (he thought water was HO, one hydrogen to one oxygen), but the idea was right, and it gave chemists a way to reason about things they could not see.
Careful
“Dalton proved that atoms exist.”
Not quite. Dalton showed that atoms were a very good way to explain the numbers chemists measured. Many scientists used atoms as a handy bookkeeping idea but doubted they were real objects. Some famous chemists, such as Wilhelm Ostwald, argued against real atoms until the early 1900s. They changed their minds only after Jean Perrin’s measurements of Brownian motion, around 1908, showed that atoms behave exactly like real, countable particles.
Step 4: what we know now
Two of Dalton’s ideas needed improving later, which is exactly how science is supposed to work. Atoms can be cut: they are made of protons, neutrons and electrons, as you will see in Chapter 1. And atoms of the same element are not all identical in mass: they come as isotopes. But his central idea, that chemistry is atoms rearranging in whole numbers, is the foundation of everything in this book.
Cut it as small as you can
Take a sugar cube and crush it with the back of a spoon into the finest powder you can. Look at a pinch of it under a magnifying glass, or with your phone camera zoomed in. Every grain is still a sugar crystal with flat faces. Now stir a spoonful of the powder into warm water until it disappears. Taste a drop: the sugar is still there, in pieces far too small to see. Where would Democritus say the cutting stops? (The answer, in this case, is a single sugar molecule, about a millionth of a millimetre across.)
Democritus asked the right question; Dalton found a way to test it. It took two thousand years to get from one to the other, and another hundred years before the last doubters were convinced.
1897
The particle in the glowing tube
William Crookes, J. J. Thomson
The Cavendish Laboratory, Cambridge, 1897
In the late 1800s, one of the most fashionable toys in science was a glass tube with almost all the air pumped out of it. Push a metal wire into each end, connect them to a high voltage, and something eerie happens. A glow appears. Rays seem to stream from the negative wire, which was called the cathode, and where they hit the glass at the far end, the glass shines a ghostly green. Nobody could see the rays themselves, so they were simply called cathode rays.
The English scientist William Crookes built beautiful versions of these tubes. He put a little metal cross in the path of the rays, and it cast a sharp shadow on the glowing glass, so the rays travelled in straight lines. He put a tiny paddle wheel inside, and the rays made it turn, as if they were pushing on it. But what were they? German scientists mostly thought they were a kind of light, a wave. British scientists mostly thought they were a stream of tiny particles. The argument went on for years.
Step 1: a question you can test
Joseph John Thomson, known to everyone as J. J., was the head of the Cavendish Laboratory in Cambridge. He decided to settle it with a simple test. Light is not pushed sideways by electric charges or by magnets. Charged particles are. So: can you bend cathode rays?
Magnets bent them easily; that was already known. Electric charges were harder, because earlier experimenters had failed to make the rays bend near charged metal plates. Thomson guessed why: there was still too much gas in their tubes, and the gas was spoiling the experiment. With better pumps, he got a much emptier tube, put two metal plates inside, charged one positive and one negative, and watched. The glowing spot on the end of the tube moved, towards the positive plate.
Things that are pulled towards positive charge must be negative. Cathode rays, Thomson concluded, are streams of tiny, negatively charged particles.
Step 2: weighing something you cannot see
Then Thomson did something brilliant. By bending the rays with a magnet one way and an electric field the other way, and adjusting the two until they cancelled out, he could work out the ratio of the particles’ charge to their mass. He could not find either one separately, but he could find how much charge each particle carried for its weight.
The answer was astonishing. For its mass, each particle carried an enormous charge: over a thousand times more charge for its mass than a charged hydrogen atom in a solution (the lightest charged thing anyone knew). If the charge was about the same size, then these particles were more than a thousand times lighter than the lightest atom. Today we know the exact figure: a hydrogen atom has about 1,836 times the mass of one of these particles.
And here is the most important part. Thomson got exactly the same particles whatever metal he used for the wires and whatever gas was left in the tube. Aluminium, iron, platinum; air, hydrogen, carbon dioxide: the particles were always identical. So they must be a part of every atom.
Step 3: the atom is not uncuttable after all
For two thousand years, “atom” had meant “the thing that cannot be cut”. Thomson had just found a piece of one. The particle was soon given a name that another physicist, George Johnstone Stoney, had suggested years earlier for the smallest unit of electric charge: the electron.
On 30 April 1897, Thomson announced his results at the Royal Institution in London. Some of the audience thought he was joking. He was not. He had found the first subatomic particle, and he won the Nobel Prize in Physics in 1906.
Step 4: a first model, and why it was wrong
If atoms contain tiny negative electrons, but atoms themselves are neutral, there must be positive charge in there somewhere to balance them. Thomson suggested the atom was a ball of spread-out positive charge with electrons dotted through it, like raisins in a pudding. It became known as the plum pudding model.
It was a sensible guess, and it was wrong. Twelve years later, one of Thomson’s former students, Ernest Rutherford, would fire particles at gold foil and find that the positive charge is not spread out at all. But that is the next story.
Careful
“Electrons are tiny balls that orbit the atom.”
Thomson’s experiment showed that electrons have charge and mass, so in that experiment they behave like particles. But later work showed they also behave like waves, and inside atoms they do not follow tracks at all. The best description we have says where an electron is likely to be found, not where it is. “Particle” is a useful word for electrons, as long as you do not picture a tiny marble.
Pile up some electrons
Rub a balloon on your hair or a wool jumper, then hold it near some small torn bits of tissue paper, or near a friend’s hair. The rubbing moves electrons from one thing to the other, so the balloon ends up with extra electrons: a negative charge. That is the same particle Thomson found, piled up by the trillion on a balloon’s surface.
Every time you switch on a light, electrons are moving through the wire. Every chemical reaction in this book is, at heart, electrons rearranging. They were found because a scientist asked a simple question about a mysterious glow, and then designed an experiment clever enough to answer it.
1913 to 1932
Same element, different weight
Frederick Soddy, Margaret Todd, Francis Aston, James Chadwick, Irène Joliot-Curie
Glasgow, Scotland, 1913
By 1913, chemists studying radioactive substances had a problem. They had found dozens of “new” radioactive substances, far more than there were spaces for in the periodic table. Stranger still, some of them could not be separated from each other by any chemical method at all. One substance from thorium behaved exactly like lead: same reactions, same compounds, same everything. Yet it had a different mass from ordinary lead.
Frederick Soddy, a chemist in Glasgow, decided to stop fighting the facts. Perhaps, he said, these really are the same element. They sit in the same place in the periodic table, but their atoms have different masses. He needed a name for atoms like that. At a dinner party at his father-in-law’s house, he explained the idea to a family friend, Margaret Todd, a Scottish doctor and writer. She suggested a word from Greek: isos, “equal”, and topos, “place”. Same place: isotope.
Step 1: the puzzle in a simple form
If two atoms are the same element, they have the same number of protons (you will meet that idea properly in Chapter 1). But in 1913 nobody knew about protons as separate particles yet, let alone what else might be in a nucleus. So the question was: what can make two atoms of the same element weigh different amounts?
Step 2: sorting atoms by weight
At about the same time, J. J. Thomson in Cambridge sent a beam of charged neon atoms through electric and magnetic fields, and saw two traces on his photographic plate instead of one: most of the neon landed at mass 20, but a little landed at 22. Neon, it seemed, was a mixture.
His assistant Francis Aston took up the idea after the First World War and built a much more precise instrument, the first mass spectrometer (he called it a mass spectrograph), in 1919. It sorts atoms by mass the way a strong wind sorts a handful of thrown objects: light ones are blown further off course than heavy ones. Aston found isotopes in one element after another. Chlorine, for example, turned out to be about three-quarters chlorine-35 and one-quarter chlorine-37. He won the Nobel Prize in Chemistry in 1922.
What a mass spectrometer shows for chlorine: two kinds of atom, at mass 35 and mass 37. The average, 35.45, sits between them, where there are no atoms at all.
Step 3: the missing particle
There was still a gap in the explanation. A helium nucleus has twice the charge of a hydrogen nucleus, but about four times the mass. Carbon has six times the charge but twelve times the mass. Something in the nucleus was adding mass without adding charge.
As early as 1920, Rutherford guessed that the nucleus might contain a neutral particle, about as heavy as a proton. But how do you catch something with no charge? Charged particles leave tracks, bend in magnets, and make flashes on screens. A neutral particle does none of that. It slips through everything without a trace.
Step 4: the race of 1932
In 1930 two German physicists, Walther Bothe and Herbert Becker, found that the metal beryllium, when hit by alpha particles, gave off a strange, very penetrating radiation. In Paris, Irène Joliot-Curie (Marie Curie’s daughter) and her husband Frédéric Joliot showed in January 1932 that this radiation could knock protons out of paraffin wax at high speed. They thought it was a powerful kind of light, gamma rays.
In Cambridge, Rutherford’s colleague James Chadwick read their paper and did not believe the explanation. Light hitting a proton should not be able to knock it out that fast. But a particle as heavy as the proton could, just as one snooker ball can send another flying. Chadwick worked almost day and night for about two weeks, measuring how the mystery radiation knocked atoms of different masses. In February 1932 he announced it: the radiation was a stream of neutral particles with almost exactly the mass of a proton. The neutron had been found. Chadwick won the Nobel Prize in Physics in 1935.
Step 5: everything fits
Now the puzzle of isotopes has a simple answer:
The number of protons decides the element. Chlorine always has 17.
The number of neutrons can vary. Chlorine-35 has 17 protons and 18 neutrons; chlorine-37 has 17 protons and 20 neutrons.
Neutrons have no charge, so they do not change how the atom behaves chemically (that is mostly about electrons). They only change its mass, and sometimes how stable its nucleus is.
That is why Soddy could not separate his “lead” from ordinary lead: chemically they were the same element, just with different numbers of neutrons.
Careful
“Heavier isotopes are a different element.”
No: an isotope is the same element with a different number of neutrons. Heavy water, made with the hydrogen isotope deuterium (one proton and one neutron), is still water: it looks the same and freezes and boils at almost the same temperatures. It is about 11% denser, which is why an ice cube of heavy water sinks in ordinary water.
A mixture you can average
Put 3 large spoons and 1 small spoon into a bag. Weigh each kind on a kitchen scale, then weigh all four together and divide by 4. That average is like chlorine’s 35.45: a real, useful number, even though not one spoon in the bag has that mass.
Isotopes turned out to be useful everywhere: carbon-14 for dating ancient bones, uranium-235 for nuclear power, and harmless heavy isotopes for tracing where atoms go inside living things.
1909 to 1911
The shell that bounced back
Ernest Rutherford, Hans Geiger, Ernest Marsden
The University of Manchester, 1909
Ernest Rutherford grew up on a farm in New Zealand, one of twelve children. By 1909 he was a famous physicist in Manchester, and he already had a Nobel Prize for his work on radioactivity. His favourite tool was the alpha particle: a tiny, fast, positively charged bullet shot out by radioactive substances such as radium. (We now know an alpha particle is the nucleus of a heliumatom.) Rutherford liked to fire alpha particles at things and see what happened.
His assistant, Hans Geiger, had a promising young student, Ernest Marsden, who was twenty years old and needed a project. Rutherford suggested one, more or less to keep him busy: fire alpha particles at a thin sheet of gold foil, and see whether any of them bounce off at a big angle.
Nobody expected him to find any. According to the best idea of the time, Thomson’s “plum pudding” atom, the positive charge in an atom was spread out thinly, like dough. A fast alpha particle should punch straight through, perhaps wobbling slightly. It was like firing bullets at a cloud of mist.
Step 1: counting flashes in the dark
There were no electronic detectors yet. To see an alpha particle, you let it hit a small screen coated with zinc sulfide. Where it hits, there is a tiny flash of light, a scintillation, too faint to see in daylight. So Geiger and Marsden sat in a completely dark room for half an hour to let their eyes adjust, then peered through a microscope at the screen and counted flashes, one by one, for minutes at a time. It was slow, tiring work, and you could only do it accurately for a short time before your eyes tired.
Most of the flashes came where they expected: almost straight through the foil. But then Marsden moved the screen round to the same side as the source, and kept seeing flashes. Some alpha particles were coming back.
Step 2: “as if you fired a shell at tissue paper”
Only a very few bounced back: for thin gold foil, roughly one in many thousands. But that they bounced back at all was shocking. Rutherford said later that it was the most incredible thing that had ever happened to him, “almost as incredible as if you fired a fifteen-inch shell at a piece of tissue paper and it came back and hit you.”
A heavy, fast alpha particle can only be turned right round by something even heavier and very strongly charged. A thinly spread cloud of charge could never do it. So the positive charge, and most of the mass, must be packed into something tiny.
The gold-foil experiment in outline: most alpha particles pass straight through, a few are deflected, and a very few bounce back.
Step 3: Rutherford’s new atom
Rutherford spent nearly two years working out the mathematics. If all the positive charge sat in a minute point at the centre of each atom, he calculated how many alpha particles should be turned through each angle. Geiger and Marsden then checked his predictions with more painstaking counting, publishing their results in 1913. They matched.
In 1911 Rutherford published his new picture of the atom:
Almost all the mass of an atom, and all its positive charge, are concentrated in a tiny centre. By 1912 he was calling it the nucleus, from the Latin word for a small nut or kernel.
The electrons are spread out around it, far away.
Between them is mostly empty space.
How tiny is tiny? A gold atom is about 0.29 nanometres across. Its nucleus is about 20,000 times smaller across. If a gold atom were the size of a cricket ground, its nucleus would be about the size of a small pea on the centre of the pitch, yet it would hold more than 99.9% of the atom’s mass.
Step 4: why most particles go straight through
Now the result makes sense. An alpha particle flying through the foil passes through thousands of atoms, but each atom is almost all empty space with a tiny nucleus in the middle. Most of the time the alpha particle never comes anywhere near a nucleus, so it sails straight through. Only on the rare occasions when it heads almost straight at one does the enormous push between two positive charges turn it sharply, or send it back.
Careful
“If atoms are mostly empty space, why can’t I push my hand through the table?”
Because “empty” here means “empty of nuclei”, not “empty of everything”. The space is filled by the atoms’ electrons, and when the electrons of your hand come close to the electrons of the table, they push each other apart very strongly. An alpha particle is a tiny, fast nucleus; your hand is a crowd of atoms with their own electrons on the outside.
Find the hidden nail
This is a model of Rutherford’s idea, not of the real sizes. Prop a large tray or a sheet of stiff cardboard on four books, so marbles can roll underneath. Ask someone to hide a few heavy objects (a mug, a small jar) under it, without telling you where. Roll marbles under the tray from one side, many times, along different lines, and watch where they come out. Most roll straight through. A few hit something and bounce off at an angle. From the bounces alone, try to work out where the hidden objects are. You have just done, in a small way, what Geiger and Marsden did with gold.
The nucleus explained the mass of atoms. It also raised a new puzzle: if the electrons are spread out around a positive nucleus, why don’t they fall straight into it? Answering that took a young Danish physicist, Niels Bohr, and a whole new kind of physics.
1913 to 1926
Why electrons don't fall in
Johann Balmer, Niels Bohr, Erwin Schrödinger
Manchester and Copenhagen, 1912 to 1913
When Rutherford found the nucleus, he created a terrible problem. According to the physics everyone trusted, a negative electron moving around a positive nucleus should give off light continuously, lose energy, and spiral inwards. Calculations said it should crash into the nucleus in far less than a millionth of a second. Every atom in the universe should have collapsed long ago. Yet here we are, made of atoms that have lasted billions of years.
In 1912 a young Danish physicist, Niels Bohr, came to work with Rutherford in Manchester. He was twenty-six, softly spoken, and known for thinking aloud in long, careful sentences. He was not willing to throw away the nucleus, because the gold-foil evidence was too strong. So he did something braver: he decided that the old physics must be wrong for things as small as atoms.
Step 1: a clue hidden in light
Bohr found his clue in a pattern that had puzzled people for decades. If you make hydrogen gas glow with electricity and pass its light through a prism, you do not get a smooth rainbow. You get just a few sharp, bright coloured lines: a red one, a blue-green one, and two violet ones, at exactly the same places every time.
Each element, made to glow, gives off light of only certain colours. Hydrogen’s four visible lines are at 656, 486, 434 and 410 nanometres. Bohr realised these lines are a message from inside the atom.
In 1885 a Swiss schoolteacher, Johann Balmer, had found a simple formula that gave the positions of hydrogen’s lines exactly, though nobody knew why it worked. When Bohr saw Balmer’s formula, he later said, everything became clear to him.
Step 2: the staircase idea
Bohr’s idea, published in 1913, was this. An electron in an atom cannot have just any energy. It can only have certain fixed amounts, like standing on the steps of a staircase but never between steps. These allowed energies are called energy levels. While an electron stays on one step, it gives off no light at all, so it does not spiral in. That rescued Rutherford’s atom.
But an electron can jump between steps. When it drops from a higher step to a lower one, the difference in energy comes out as a tiny flash of light of one exact colour. Big drop: more energy, bluer light. Small drop: less energy, redder light. Because the steps are always at the same heights, the colours are always the same. Hydrogen’s red line is an electron dropping from the third step to the second; the blue-green line is a drop from the fourth step to the second.
Using his staircase, Bohr calculated the positions of hydrogen’s lines from scratch, and they matched Balmer’s measurements almost perfectly. The word quantum, meaning a fixed amount, became the name for this new kind of physics. Bohr won the Nobel Prize in Physics in 1922.
Step 3: from steps to shells
Chemists soon used Bohr’s idea to explain the periodic table. Electrons in bigger atoms fill the steps from the bottom up, in groups called shells: the first shell holds up to 2 electrons, the next up to 8, and so on. This is the shell picture you meet in Chapter 1, and it explains why lithium and sodium, each with one electron alone in its outermost shell, behave so alike.
Shell counts for lithium and sodium. The rings show groups of electrons with similar energy. They are not tracks that electrons run along.
Step 4: the model improves again
Bohr’s atom worked beautifully for hydrogen but struggled with bigger atoms, and it still pictured electrons circling like little planets. In the 1920s, physicists including Louis de Broglie and Erwin Schrödinger found that electrons also behave like waves. In 1926 Schrödinger wrote an equation that describes them, and its answers are not tracks at all. They are clouds: maps of where an electron is likely to be found. These clouds are called orbitals. Some are round, some are shaped like dumb-bells, and some are more complicated still.
Bohr’s steps survived this upgrade: electrons still have only certain allowed energies. What changed was the picture of where they are. That is a perfect example of how science improves its models: the useful part stays, and the part that was wrong is replaced by something better.
Careful
“Electrons orbit the nucleus like planets around the Sun.”
This is the most famous picture of the atom, and it is wrong in an important way. Electrons do not follow paths. The rings in shell diagrams are a way of grouping electrons by energy. The best picture we have, the orbital, says where an electron is likely to be, not where it is going.
See the lines yourself
Look at the reflection of a light in the shiny underside of an old CD or DVD (the tiny grooves split light into colours). An ordinary old-style bulb or daylight gives a smooth rainbow. A fluorescent tube or a street lamp with an orange glow often gives separate bright lines instead, because the light comes from glowing atoms of particular elements, each with its own staircase.
So the reason you are not collapsing right now is a quantum one: the electrons in your atoms are standing on the lowest steps they can reach, and there is no lower step to fall to.
1896 to 1949
Atoms that change
Henri Becquerel, Marie Curie, Pierre Curie, Ernest Rutherford, Frederick Soddy, Harriet Brooks, Willard Libby
Paris, February 1896
Henri Becquerel came from a family of physicists who studied things that glow. Early in 1896, the whole scientific world was excited about X-rays, discovered a few weeks before, and Becquerel wondered whether glowing minerals might give off X-rays too. His idea was to put crystals of a uranium salt in sunlight, so that they would glow, then lay them on a photographic plate wrapped in thick black paper. If the plate darkened, something had passed through the paper.
It did darken. But then Paris had a run of cloudy days. Becquerel put his wrapped plates and uranium crystals away in a drawer to wait for sunshine. On 1 March, for reasons of his own, he developed the plates anyway, expecting nothing. They were strongly fogged, with the shapes of the crystals clearly visible. The uranium had not needed sunlight at all. It was giving off some invisible radiation all by itself, all the time, in the dark.
Step 1: a young scientist picks up the trail
Marie Skłodowska had grown up in Warsaw, in a Poland ruled by Russia, where women could not go to university. She studied in secret, worked as a governess to save money, and moved to Paris, where she studied physics and mathematics and married the physicist Pierre Curie. For her doctoral research she chose Becquerel’s mysterious rays.
She measured the rays with an electrical instrument Pierre and his brother had invented, and found two crucial things. First, the strength of the rays depended only on how much uranium was present, not on what it was combined with or whether it was hot or cold. So the rays came from inside the uranium atoms themselves. Second, a uranium ore called pitchblende gave off more radiation than its uranium could explain. Something even more powerful was hidden in it. She invented a word for this property: radioactivity.
Step 2: hunting in a shed
Marie and Pierre set out to find the hidden substances. They worked in a leaky, freezing shed, grinding, dissolving and boiling down tonnes of pitchblende waste, a bit at a time, following the radioactivity wherever it went. In July 1898 they announced a new element and named it polonium, after Marie’s homeland, which did not then exist as a country on the map. In December 1898 they announced a second, radium, which glows faintly in the dark. It took Marie years more work to collect a tenth of a gram of pure radium compound.
Marie Curie shared the Nobel Prize in Physics in 1903 with Pierre and Becquerel, and won the Nobel Prize in Chemistry in 1911 on her own. She is still the only person to have won Nobel Prizes in two different sciences.
Step 3: the atom transforms
In Montreal, Ernest Rutherford and the chemist Frederick Soddy studied radioactive thorium in 1901 and 1902. Working with them, Rutherford’s student Harriet Brooks, one of Canada’s first women nuclear physicists, helped show that the “emanation” thorium and radium gave off was a radioactive gas. Rutherford and Soddy found that radioactive atoms were turning into atoms of different elements. Soddy later remembered saying, in amazement, “Rutherford, this is transmutation!”: the old alchemists’ dream of changing one element into another, happening by itself.
For more than a century chemistry had rested on the idea that elements never change. In chemical reactions, that is still true. But inside an unstable nucleus, a radioactive atom can throw out particles and become a different element.
Step 4: the half-life, step by step
Radioactive atoms do not all break down at once. Each one has a fixed chance of breaking down in any given time, a bit like a coin toss. For a large crowd of atoms, that gives a beautifully steady rule: after a certain time, half of them have broken down. That time is the half-life.
Carbon-14 has a half-life of about 5,730 years. Whatever amount you start with, half is left after 5,730 years, a quarter after 11,460 years, an eighth after 17,190 years, and so on.
Half-life with carbon-14 (half-life about 5,730 years)
Start: 100% of the carbon-14.
After 5,730 years: 50%.
After 2 × 5,730 = 11,460 years: half of 50% = 25%.
After 3 × 5,730 = 17,190 years: 12.5%.
It never quite reaches zero; it keeps halving.
Step 5: a clock in every living thing
In 1949 the American chemist Willard Libby turned this into a clock. A little of the carbon in the air is radioactive carbon-14, made high in the atmosphere. Plants take it in, animals eat plants, and so every living thing has the same small share of carbon-14. When it dies, it stops taking in new carbon, and its carbon-14 starts to halve every 5,730 years. Measure how much is left, and you know how long ago it died. If a piece of ancient wood has a quarter of the carbon-14 of living wood, it died about 11,460 years ago. Libby won the Nobel Prize in Chemistry in 1960, and his method is used to date everything from Egyptian mummies to cave paintings.
Careful
“After two half-lives, everything is gone.”
Half and half again is a quarter, not zero. After two half-lives, a quarter is left. Radioactive substances fade away more and more slowly, never quite vanishing.
The coin half-life
Take 32 coins and put them all in a box. Shake, then tip them out: remove every coin that lands heads up. Count what is left, write it down, and put the rest back. Repeat. Each shake is one “half-life”. Roughly half disappear each time: 32, about 16, about 8, about 4… With real atoms there are so many that the halving is almost perfectly smooth.
Radioactivity came at a cost. Nobody yet knew how dangerous it was. Marie Curie carried tubes of radium in her pockets and died in 1934 of a blood disease almost certainly caused by her years of exposure; her notebooks are still radioactive today and are kept in lead-lined boxes. Yet her work also saved lives: radium became one of the first treatments for cancer, and during the First World War she set up mobile X-ray units to help surgeons find bullets and broken bones, and drove them to the front herself.
1859 to 1895
Fingerprints of light
Robert Bunsen, Gustav Kirchhoff, Jules Janssen, Norman Lockyer, William Ramsay
Heidelberg, Germany, 1859
Think of Diwali night. A rocket bursts into deep red, then a shower of green, then a sparkle of brilliant gold. Those colours are not paint. Each one is made by a different element, glowing with its own particular light: strontium for red, barium for green, copper compounds for blue, sodium for that bright yellow-orange. The people who make fireworks learned this by trial and error. The reason it works was discovered by two friends in a German university town.
Robert Bunsen was a chemist who had helped design a new gas burner with a clean, almost invisible blue flame (you may meet a Bunsen burner in a school laboratory). Bunsen liked to hold a bit of a substance in the flame on a wire and watch its colour. Lithium gives crimson, potassium a soft lilac, sodium a strong yellow. This is called a flame test. But colours can be confusing to the eye: a little sodium drowns out almost anything else.
Hydrogen’s energy ladder and its four visible colours: each comes from an electron falling to the second rung.
His friend Gustav Kirchhoff, a physicist, suggested a better way to look. Pass the coloured light through a prism, which spreads light out into its separate colours. Together they built an instrument for it, the spectroscope.
Step 1: light in lines
What they saw changed science. A hot glowing solid, like the filament in an old bulb, gives a smooth rainbow with every colour. But a glowing gas or vapour of an element gives only a few sharp, bright lines of particular colours, always in the same places for the same element. Sodium gives a close pair of yellow lines. Lithium gives a red line. Every element has its own pattern, as unique as a fingerprint.
Each element’s own pattern of bright lines, spread out by a prism. Hydrogen, sodium and helium are shown; the numbers are wavelengths of light in nanometres.
(Why the lines? Nobody knew for another fifty years. The answer, from Niels Bohr in 1913, is that electrons in each kind of atom can only jump between certain energy steps, and each jump gives out light of one exact colour.)
Step 2: finding elements nobody had seen
Bunsen and Kirchhoff realised they now had a detective’s tool. If a sample glowed with a line that matched no known element, it must contain a new one.
In 1860 they boiled down an enormous amount of mineral water from a spa town, tens of thousands of litres of it, and looked at the glow of what was left. There were two bright blue lines that belonged to no known element. They named the new element caesium, from the Latin for sky blue. The next year, in a mineral, they found two deep red lines and named that element rubidium, from the Latin for dark red. Two new elements, found by their colours before anyone had held a pure piece of either.
Step 3: reading the Sun
Kirchhoff went further. Decades earlier, the glass-maker Joseph von Fraunhofer had noticed that sunlight, spread into a rainbow, is crossed by hundreds of thin dark lines. Kirchhoff showed that a cooler gas absorbs exactly the same colours that it gives off when hot. So the dark lines in sunlight are fingerprints of elements in the Sun’s outer layers, absorbing light from the hotter Sun beneath. Sodium’s dark pair sat exactly where sodium’s bright yellow pair would be. For the first time, people could tell what a star is made of, without ever going there.
Guntur, India, 18 August 1868
On that day, a total eclipse of the Sun crossed India. The French astronomer Jules Janssen set up his spectroscope at Guntur, in what is now Andhra Pradesh, and studied the glowing gas leaping off the edge of the darkened Sun. He saw a bright yellow line close to sodium’s, but not quite in the same place. The English astronomer Norman Lockyer saw the same line from England two months later, without needing an eclipse.
No known element on Earth made that line. Lockyer concluded it came from a new element, found so far only in the Sun, and named it after the Greek word for the Sun, helios: helium. Many chemists were doubtful. An element nobody could put in a bottle?
They had to wait twenty-seven years. In 1895 William Ramsay in London dissolved a uranium mineral in acid, collected the gas that came off, and looked at its glow. There was the yellow line. Helium had been found on Earth, after first being discovered 150 million kilometres away.
Step 4: why this matters
Every element gives out and absorbs light of its own particular colours.
So light carries information about the atoms that made it.
That lets us identify elements in tiny amounts, in the lab, in fireworks, in street lamps, and in stars millions of millions of kilometres away.
Spot it in the kitchen
Next time an adult is cooking on a gas stove and a pan of salted water boils over, watch the flame where the water lands: the blue flame flashes bright yellow-orange. That is sodium from the salt, giving off its fingerprint colour. (Just watch: don’t put anything into a flame yourself.) You can also see the same yellow in the old orange street lamps, which are filled with sodium vapour.
The next time you watch fireworks, you are watching a spectroscope experiment in the sky. Every colour is an element announcing itself.
1913 to 1914
Henry Moseley's staircase
Henry Moseley, Antonius van den Broek, Ernest Rutherford
Manchester, 1913
Henry Moseley was 25 when he set up his strangest experiment. He was working in Ernest Rutherford’s laboratory in Manchester, the same place where, a few years earlier, alpha particles had bounced back off gold foil and revealed the nucleus. Rutherford’s team now knew that every atom had a tiny positive centre. But how much positive charge did each nucleus carry, and did it have anything to do with the periodic table?
A Dutch lawyer who did physics as a hobby, Antonius van den Broek, had made a bold guess: perhaps an element’s position in the table, its place number counting from hydrogen, was simply the charge on its nucleus. Hydrogen 1, helium 2, lithium 3. It was a beautiful idea, but nobody had any way to test it. Moseley found one.
A toy railway of elements
Moseley built a long glass tube with the air pumped out. Inside it sat a little trolley that could carry samples of different metals, one after another, into the path of a beam of fast electrons. When electrons slam into a metal, the metal gives off X-rays, invisible light with very short waves. Each metal gives off its own particular X-rays, like a bell ringing its own note.
He measured those notes, one element at a time: calcium, titanium, vanadium, chromium, manganese, iron, cobalt, nickel, copper, zinc, and on through dozens more. And when he plotted them in the right way (taking the square root of each X-ray’s frequency) the points did not scatter. They climbed in a perfectly even staircase: one equal step from each element to the next.
Moseley’s staircase, drawn from the modern values of the strongest X-ray line. Each element’s point is one equal step above the one before. The steps are counting something inside the atom: one extra unit of positive charge in the nucleus each time.
What the steps were counting
Atomic weights do not go up in equal steps; they jump about. But Moseley’s steps were perfectly regular. Something inside every atom increased by exactly one from each element to the next, and the X-rays came from electrons being pulled on by the nucleus. The only sensible conclusion was that the nucleus’s positive charge goes up by one each time. Van den Broek’s guess was right.
That whole number, the charge on the nucleus, is the atomic number. Today we know it is simply the number of protons. It is what makes an element the element it is.
Step by step: why this settled everything
The true order.Mendeleev had arranged elements by weight, but had been forced to put a few elements out of weight order to keep families together, most famously tellurium before iodine. (Argon and potassium, found later, turned out to be the same kind of puzzle.) Moseley’s staircase showed these choices were right. Tellurium is 52 and iodine 53, even though tellurium is slightly heavier (127.6 against 126.9). Order by protons, and the puzzles vanish.
Counting the missing. Because the steps were even, a missing step meant a missing element. Moseley could see exactly where gaps were between aluminium (13) and gold (79): elements 43, 61, 72 and 75 had not been found. All four were found later (hafnium, 72, in 1923; rhenium, 75, in 1925; technetium, 43, and promethium, 61, only after they were made in laboratories).
No room for impostors. Before Moseley, people sometimes announced “new elements” that were really mixtures. After him, any claim could be tested: what is its atomic number? If there is no empty step for it, it is not new.
Careful
“Atomic number and mass number are the same thing.”
They are different counts. The atomic number counts protons only, and it decides the element: every carbon atom has 6. The mass number counts protons and neutrons together, so it can be different for different atoms of the same element: carbon-12 and carbon-14 both have atomic number 6.
The war
In August 1914, the First World War began. Moseley, by then working in Oxford, could have stayed in his laboratory. He chose to join the army, as a signals officer. On 10 August 1915, at Gallipoli in Turkey, he was killed by a sniper’s bullet. He was 27.
Many scientists believed he would soon have won a Nobel Prize. It is often said that the loss of Moseley helped persuade Britain to keep its scientists out of front-line fighting in later wars, though historians debate how much difference it made.
Today
Every periodic table in the world, including the one on the cover of this book, is arranged by Moseley’s numbers. When you read that an element “is” its number of protons, you are reading the conclusion of an experiment done with a toy-sized railway inside a glass tube, by a young man who had only two more years to live.
1902 to 1939
Dots and lines: how atoms hold on to each other
Gilbert Newton Lewis, Irving Langmuir, Linus Pauling
Harvard University, 1902
Chemists in 1900 drew molecules with little lines between the atoms, H–O–H for water, and they were very good at it. They knew which atoms joined to which, and how many lines each kind of atom liked to have: one for hydrogen, two for oxygen, four for carbon. But nobody could say what a line actually was. A bond was a mystery written as a dash.
The electron had been discovered only five years earlier. A young American chemist, Gilbert Newton Lewis, began wondering whether electrons might be the answer. In 1902, while preparing a lecture, he sketched atoms as little cubes, with electrons sitting at the corners. A cube has eight corners. Many atoms seemed to end up, when they combined, with eight outer electrons around them. Could a bond be two atoms sharing corners?
He put the sketches in a drawer, and did not publish them for fourteen years.
The shared pair
Berkeley, California, 1916
By 1916 Lewis was a famous professor at Berkeley, and he finally published his idea, improved. A chemical bond, he proposed, is a pair of electrons shared between two atoms. Each line in H–O–H stands for two electrons that belong to both atoms at once.
He invented a way of drawing it that you will still see in school books today: the elementsymbol, with dots around it for the outer electrons. Hydrogen has one outer electron; oxygen has six. Draw water and you see two shared pairs, one between oxygen and each hydrogen, plus two pairs that belong to oxygen alone.
Lewis’s way of drawing water. Each dot is an outer electron. The pairs between atoms are shared: those are the bonds. Oxygen also keeps two pairs of its own, called lone pairs.
A few years later another American, Irving Langmuir, spread Lewis’s ideas widely and gave a name to sharing bonds: covalent, meaning “sharing strength”. He also popularised the “octet”, the eight outer electrons that Lewis had first drawn on his cubes.
Why does sharing hold atoms together?
Here is the part that matters most, because it is where people start saying atoms “want” to share. They do not want anything. The real reason is electric attraction.
Every nucleus is positive; every electron is negative. Opposite charges pull on each other.
A pair of electrons sitting between two nuclei is pulled by both of them at once, and pulls back on both. It acts like glue between them, held in place by two attractions instead of one.
The nuclei also repel each other, and so do the electrons. If the atoms come too close, the repulsion wins.
The bond length is the balance point, where attraction and repulsion together give the lowest energy. For two hydrogen atoms it is 74 picometres apart.
Pulling the atoms apart takes energy, because you have to work against that attraction. For a mole of hydrogen molecules it takes about 436 kilojoules. That is why breaking bonds always costs energy, an idea that comes back in Chapter 5.
Careful
“Atoms share electrons because they want a full outer shell of eight.”
The “eight” is a useful pattern for many atoms of the lighter elements, and Lewis’s drawings work beautifully for them. But it is a pattern, not a reason. The reason is that shared electrons between two nuclei lower the energy of the whole system, through electric attraction. And plenty of stable molecules break the eight rule.
Pauling makes it scientific
Pasadena, California, 1930s
Lewis’s picture was a sketch. To turn it into science that could calculate, chemists needed the new quantum physics of the 1920s. The person who did more than anyone to bring the two together was Linus Pauling, a young chemist at Caltech who as a boy had collected insects and minerals in Oregon.
Pauling explained why carbon makes four bonds pointing to the corners of a tetrahedron, why some bonds are shared unequally (his scale of electronegativity, in another story), and how to predict bond lengths and energies. In 1939 he collected it all in a book, The Nature of the Chemical Bond, which became one of the most influential science books of the century. He won the Nobel Prize in Chemistry in 1954, and later a second Nobel, for Peace, for his campaign against nuclear weapons testing. He is still the only person to have won two Nobel Prizes on his own, not shared with anyone else.
Lines, dots and real molecules
So when you see a line between two atoms in this book, read it as Lewis taught: two shared electrons, held between two nuclei by electric attraction. A double line is two shared pairs; a triple line, three. More shared pairs pull the atoms closer and hold them tighter: the C=C double bond is shorter and stronger than C–C, and the N≡N triple bond in nitrogen gas is one of the strongest bonds there is, which is why nitrogen in the air is so hard to make react.
Build molecules you can hold
Use soft sweets (jelly sweets or marshmallows) for atoms and toothpicks for bonds. Use one colour for hydrogen and another for oxygen and carbon. Build water: an oxygen with two hydrogens, bent, not straight. Build methane: a carbon with four hydrogens, as far apart from each other as they can go. (Hint: it is not a flat cross; try making the four hydrogens point to the corners of a pyramid with a triangular base.) Each toothpick is one shared pair of electrons. Eat the molecules afterwards.
1827 to 1909
The dance that proved atoms are real
Robert Brown, Albert Einstein, Marian Smoluchowski, Jean Perrin
London, summer 1827
The Scottish botanist Robert Brown was studying how plants make seeds. He put pollen grains from a wildflower into a drop of water and looked at them under his microscope. Inside the pollen were much smaller particles, and when they spilled out into the water, they would not keep still. They jittered and wandered, this way and that, never stopping, never settling.
The obvious explanation was that they were alive: tiny swimming creatures, perhaps, or some “vital force” in the pollen. Brown was a careful scientist, so he tested it. He tried pollen that had been dried for a century in a museum. He tried powdered glass, ground-up rock, and even dust from a fragment of the ancient Egyptian Sphinx. Everything that was small enough jiggled in exactly the same restless way. So it could not be life. But then what was it? Brown had no idea. Nobody did, for almost eighty years. The jiggling was named after him: Brownian motion.
(People sometimes say that the Roman poet Lucretius described the same thing two thousand years ago, in dust dancing in a sunbeam. He did describe the dancing dust, and he guessed it was caused by invisible atoms, but the dust in a sunbeam is mostly tossed about by air currents. It is a lovely passage, but it is not quite the same effect.)
A small grain floating in water, with its wandering path traced out. The grain is pushed about by water molecules far too small to see, a few more on one side than the other at each instant.
Bern, Switzerland, 1905
In 1905 a 26-year-old clerk in the Swiss patent office, Albert Einstein, published several papers that changed physics. One of them was about Brownian motion, although at first he was not even sure that was the right name for what he was describing.
His idea was this. A grain floating in water is being struck by water molecules from every side, all the time. If molecules were infinitely small and infinitely many, the hits from every side would balance perfectly and the grain would sit still. But if water really is made of separate molecules, then at any instant, just by chance, a few more will hit one side than the other. The grain gets a tiny shove. A moment later, a shove in a different direction. Added up, these random shoves make the grain wander, exactly as Brown saw.
Einstein did more than explain it. He worked out how far a grain should wander in a given time, and showed that the answer depends on how big and how numerous the molecules are. In other words: watch the grains carefully enough, and you can count the molecules. A year later the Polish physicist Marian Smoluchowski reached the same conclusion independently.
Step 1: why a big grain is pushed around by tiny molecules
Imagine a huge beach ball being pushed about by a crowd of people who cannot see it. Each person who bumps it gives a tiny nudge. If the crowd is enormous and evenly spread, the nudges cancel and the ball barely moves. If the crowd is made of separate people, there will always be moments when more of them happen to push from the left than from the right, and the ball rolls a little to the right.
A grain of about a thousandth of a millimetre is struck by water molecules more than ten million million million times every second. That number is so big that the pushes almost cancel. Almost. The tiny leftover imbalance, changing every instant, is what makes the grain dance.
Paris, 1908 to 1909
Einstein’s prediction needed testing, and the French physicist Jean Perrin set out to do it. He made thousands of tiny, identical spheres of gamboge, a yellow resin used in paint, which took months of patient work separating them by size in a centrifuge. Then he watched individual grains under his microscope, marking their positions every 30 seconds on squared paper and joining the dots. The pictures he published look like the scribbles of a tired child: zig-zag after zig-zag, never repeating.
Perrin measured how far the grains wandered, used Einstein’s mathematics, and worked out how many molecules there are in a mole. Then he did it again in completely different ways: by how the grains settled into layers in a tall tube, by how they rotated, and more. All the methods gave nearly the same number. It was close to the value we know today, about 6 × 10²³, which Perrin suggested naming after Avogadro.
That agreement settled one of the longest arguments in science. Even the chemist Wilhelm Ostwald, who had spent years insisting atoms were just a convenient idea, admitted around 1909 that the evidence had convinced him. Perrin won the Nobel Prize in Physics in 1926.
Step 2: what this means for you
Every time you see a box of jiggling particles in this book, remember that it is not just a guess. A botanist saw the effect, a patent clerk explained it, and a physicist measured it so carefully that it revealed the number of molecules in a gulp of water.
Careful
“The grains move because they are alive, or because the water is flowing.”
Brown ruled out life by trying dead and non-living specks; the motion was the same. And it is not a current: neighbouring grains move in completely different directions at the same moment, which a flowing current could never do.
Watch the dance yourself
You will need help for this one, and a microscope if your school has one. Add a tiny drop of whole milk to a drop of water on a glass slide and look at it at high magnification. The fat droplets in milk are small enough to show Brownian motion: they shiver and wander without stopping. (Without a microscope, you can see a related effect: shine a torch beam across a dark room and watch the dust. That dancing is mostly air currents, as with Lucretius, but it gives you the feeling.)
So the dance that puzzled Brown for the rest of his life turned out to be the most direct evidence there is that the world is made of molecules. You cannot see them, but you can watch them push.
1772 to 2010
Pencils, diamonds and footballs
Antoine Lavoisier, Smithson Tennant, Harry Kroto, Richard Smalley, Robert Curl, Andre Geim, Konstantin Novoselov
Paris, 1772
On a summer day in 1772, in a garden in Paris, a crowd gathered to watch a diamond disappear. Antoine Lavoisier and his colleagues had set up an enormous magnifying glass, a giant burning lens, to focus sunlight onto a small diamond. As the spot of light grew blinding, the diamond slowly vanished. Many people believed diamonds could not be destroyed by fire. They were wrong.
When the scientists repeated the experiment inside a sealed glass jar, they found that the diamond turned into a gas: the same “fixed air” that charcoal makes when it burns, which we now call carbon dioxide. A precious stone and a lump of charcoal seemed to share something. But what?
Same mass, same gas
London, 1797
Twenty-five years later an English chemist, Smithson Tennant, settled it with a careful measurement. He burned diamond and he burned charcoal, weighed each carefully, and measured the carbon dioxide each one made. Equal masses of diamond and of charcoal produced exactly the same amount of carbon dioxide. There was only one possible conclusion: diamond is pure carbon. So is the graphite in a pencil.
That is one of the most surprising facts in all of chemistry. A diamond is the hardest natural substance known, transparent, sparkling, and it does not conduct electricity. Graphite is so soft it rubs off onto paper, it is grey and shiny, it feels slippery, and it does conduct electricity. Same atoms. Completely different substances.
Same atoms, different arrangement
The difference, as the X-ray crystallographers of the twentieth century confirmed, is entirely in how the carbon atoms are joined.
In diamond, every carbon atom is bonded to four others, pointing to the corners of a tetrahedron. The bonds run in every direction through the whole crystal, so a diamond is one giant molecule with no weak places. To scratch it you would have to break strong carbon–carbon bonds, which is why almost nothing can.
In graphite, every carbon atom is bonded to only three others, in flat sheets of hexagons like chicken wire. Within a sheet the bonds are very strong. But the sheets are held to each other only by weak attractions, 0.335 nanometres apart, so they slide over each other easily. When you draw with a pencil, sheets of graphite slide off and stick to the paper.
Graphite conducts electricity because each carbon uses only three of its four outer electrons for bonds; the fourth is free to wander along the sheet. In diamond all four are locked in bonds.
Different forms of the same element are called allotropes. Oxygen has them too: the O₂ we breathe and ozone, O₃, which protects us from ultraviolet light.
Two ways of joining carbon atoms. In diamond every atom is bonded to four neighbours in a three-dimensional network. In graphite, flat sheets of hexagons slide over each other.
The name graphite comes from the Greek word for “to write”, given in 1789. People had been writing with it for over two hundred years before that, ever since a huge deposit of unusually pure graphite was found in Borrowdale, in the north of England, in the 1500s.
A football made of carbon
Houston, Texas, 1985
For two hundred years chemists believed carbon came in just those two pure forms. Then, in 1985, three scientists, Harry Kroto from England and Richard Smalley and Robert Curl from Texas, were blasting graphite with a laser to study the kinds of carbon molecules that might exist in space. Again and again their instruments showed a very stable molecule with exactly 60 carbon atoms.
What shape could hold 60 carbon atoms with no loose ends? They built paper models, and the answer turned out to be the pattern on a football: 12 pentagons and 20 hexagons, curved into a hollow ball. They named it buckminsterfullerene, after the American architect Richard Buckminster Fuller, whose famous geodesic domes have the same kind of pattern. Most people just call it a buckyball. The three won the Nobel Prize in Chemistry in 1996.
A single sheet
Manchester, 2004
The newest chapter began with a roll of sticky tape. In Manchester, Andre Geim and Konstantin Novoselov liked to spend Friday evenings trying odd experiments. They pressed sticky tape onto graphite, peeled it off, then stuck the tape to itself and peeled again, splitting the flakes thinner and thinner. Eventually they had flakes just one atom thick: a single sheet of graphite, called graphene.
Graphene turned out to be astonishing: about one atom thick, yet much stronger for its weight than steel, and an excellent conductor of electricity. Geim and Novoselov won the Nobel Prize in Physics in 2010. You make a little graphene, tangled up with thicker flakes, every time you draw with a pencil.
Careful
“Diamonds last forever because carbon cannot burn.”
Diamond is carbon, and carbon burns, as Lavoisier showed with his lens. Diamond lasts in everyday life because at room temperature its strong bonds need a great deal of energy to break, so the reaction with oxygen is far too slow to notice. Heated hot enough in air, a diamond burns away to carbon dioxide.
Feel the sheets slide
Scribble hard with a soft pencil (2B or softer) on a scrap of paper until you have a thick, shiny grey patch. Rub it with your fingertip. It feels smooth and slippery: you are feeling sheets of carbon atoms sliding over each other. This is why powdered graphite is used to make stiff locks turn smoothly. Then think of a diamond, made of the very same atoms, which can cut glass.
1912 to 1964
Seeing inside salt: the Braggs and their X-rays
Max von Laue, William Henry Bragg, William Lawrence Bragg, Kathleen Lonsdale, Dorothy Hodgkin, Rosalind Franklin
Munich, 1912
Look at grains of table salt under a magnifying glass and you will see tiny cubes. Sugar grains are little slanted blocks. Snowflakes have six arms. Crystals have flat faces and sharp angles, and for centuries people guessed that this outer shape came from some inner order: atoms stacked in regular rows, like oranges on a market stall. But atoms are far too small to see. How could anyone check?
In 1912 a German physicist, Max von Laue, had an idea. X-rays had been discovered in 1895, and some scientists suspected they were a kind of light with extremely short waves, perhaps about as short as the spacing between atoms. If so, the rows of atoms in a crystal might scatter X-rays the way the fine grooves on a CD split light into rainbow colours. Two of his colleagues shone X-rays through a crystal onto a photographic plate. When they developed it, they found a beautiful pattern of spots. The crystal really was a regular grid of atoms, and X-rays could read it.
A father and son
Leeds and Cambridge, 1913
Laue’s spots were hard to interpret. The puzzle was solved in England by a father and son working together: William Henry Bragg, a professor in Leeds, and his son William Lawrence Bragg, a 22-year-old student at Cambridge.
The son had the key insight while walking along the river in Cambridge. Think of the layers of atoms in a crystal as a stack of very thin mirrors. X-rays bouncing off one layer and off the next layer down travel slightly different distances. At most angles the bounced waves cancel out. But at certain special angles, the extra distance is exactly a whole number of wavelengths, the waves line up, and you get a strong reflection. Measure those angles, and you can calculate how far apart the layers are.
His father built a new instrument, the X-ray spectrometer, to measure the angles precisely. Together they turned it on crystals of ordinary salt, sodium chloride.
Salt has no molecules
What they found surprised many chemists. There were no NaCl molecules in salt at all. Instead, sodium and chlorine took turns, in every direction, in a vast cubic grid: every sodium surrounded by six chlorines, every chlorine surrounded by six sodiums. No sodium belonged to any one chlorine. The formula NaCl did not describe a molecule. It described a ratio: one sodium for every chlorine in the whole crystal.
The sodium chloride lattice the Braggs found: sodium and chloride ions alternating in every direction, each one surrounded by six of the other kind.
Not everyone liked this. Years later, in 1927, a senior English chemist, Henry Armstrong, complained that the idea that salt had no molecules went against common sense. But the X-rays did not care about common sense. They showed the same grid every time.
In 1915 father and son shared the Nobel Prize in Physics. Lawrence Bragg was 25, and he is still the youngest person ever to win a Nobel Prize in Physics. He heard the news while serving as a soldier in France during the First World War.
How X-ray crystallography works, step by step
Grow a crystal: a solid where the atoms or molecules repeat in a regular pattern, over and over, millions of times in every direction.
Shine X-rays at it. Their waves are about the same size as the spacing between atoms, a fraction of a nanometre.
The rows of atoms scatter the X-rays into a pattern of spots. Where the spots fall depends on how the atoms are spaced; how bright they are depends on what kind of atoms they are.
Work backwards from the pattern to the arrangement that must have made it. For salt this was a puzzle of a few hours. For a protein with thousands of atoms it can take years.
Women who read the spots
X-ray crystallography became one of the great tools of the twentieth century, and some of its greatest masters were women at a time when science was hard for women to enter.
Kathleen Lonsdale, who had trained with the elder Bragg in London, showed in 1929 that the ring of six carbon atoms in benzenecompounds is flat, settling an argument that had run for sixty years. Dorothy Hodgkin worked out the structures of penicillin, of vitamin B₁₂, and, after 35 years of effort, of insulin, the hormone that people with diabetes need. She won the Nobel Prize in Chemistry in 1964. And Rosalind Franklin’s X-ray photographs of DNA, taken in London in 1952, were crucial evidence for its famous double-helix shape.
Grow your own salt crystals
Ask an adult for a cup of warm tap water. Stir in salt a teaspoon at a time until no more will dissolve. Pour a little of the clear liquid (not the undissolved salt at the bottom) into a saucer and leave it somewhere still and dry for a few days. As the water evaporates, salt crystals grow. Look at them through a magnifying glass. The cubes you see are the giant, visible version of the Braggs’ grid: their shape comes from the way the ions stack.
Every diagram of a crystal in this book, salt, diamond, graphite, ice, rests on the Braggs’ simple idea: layers of atoms act like mirrors for X-rays, and the angles tell you where the atoms are.
about 450 BCE to 2016
From four elements to 118
Empedocles, Robert Boyle, Antoine Lavoisier, Humphry Davy
Sicily, about 450 BCE
Watch a log burn. Smoke rises into the air, sap hisses out as water, flames dance, and grey ash is left behind on the ground. To the Greek thinker Empedocles, living in Sicily about 2,500 years ago, this looked like a clue to everything. Perhaps the log had been made of four basic ingredients all along, earth, air, fire and water, and burning simply let them go.
That idea was taken up by Aristotle and lasted, in one form or another, for about two thousand years. It was wrong, but it was not stupid. It was an honest attempt to explain the endless variety of the world from a few simple things. That hope, that a few ingredients make everything, turned out to be right. Only the ingredients were wrong.
The alchemists’ long experiment
For centuries, alchemists in the Islamic world, in India, in China and in Europe heated, dissolved, distilled and mixed every substance they could find. Many were hoping to turn lead into gold, which cannot be done by chemistry. But along the way they invented much of the equipment chemists still use, and they discovered new substances: strong acids, alcohol, new salts. They piled up an enormous amount of practical knowledge, without a clear idea of what an element really was.
Boyle asks a better question
Oxford, 1661
In 1661 the Irish-born scientist Robert Boyle published a book with a wonderful title, The Sceptical Chymist. “Sceptical” means doubting, and Boyle doubted the four elements. Show me, he said in effect, that you can actually split gold into earth, air, fire and water. Nobody could.
Boyle suggested that an element should be something real you can find by experiment: a substance that cannot be broken down into anything simpler. It was a new kind of definition, based on what you can do in a laboratory rather than on philosophy.
Lavoisier’s list
Paris, 1789
A little over a century later, Antoine Lavoisier put Boyle’s idea to work. In his great textbook of 1789 he listed 33 “simple substances”, things that no one had managed to break down. Many are on the modern list: oxygen, nitrogen, hydrogen, sulfur, phosphorus, carbon, and metals such as iron, copper, zinc, gold and mercury.
But look closely and you find some surprises. Lavoisier’s list included light and caloric, which he thought was a weightless fluid that carried heat. And it included lime, magnesia and silica, which are not elements at all. Lavoisier had simply not found a way to split them yet. He said so himself: they were simple as far as we know. That honesty is what made the list scientific: it could be corrected.
Davy and the dancing globules
London, October 1807
Correction came with a new tool: electricity. In 1800 Alessandro Volta had invented the battery, and soon chemists were passing electric currents through everything. At the Royal Institution in London, a young chemist named Humphry Davy built one of the most powerful batteries in the world and turned it on potash, a substance people had used for centuries to make soap and glass, and which Lavoisier had suspected might not be simple.
As the current flowed through slightly moist potash, tiny silvery beads appeared, some bursting into flame. Davy had found a new metal, potassium. His cousin Edmund, who was working with him, later told Davy’s brother that Davy bounded about the room in delight. A few days later he did the same with soda and found sodium. In the next year came calcium, magnesium, strontium and barium. Some of the “simple” substances on Lavoisier’s list were metals combined with oxygen, and electricity could pull them apart.
Element, compound or mixture: step by step
By now chemists had three clear words, the same ones you use in Chapter 2.
An element is a substance made of only one kind of atom: all the atoms have the same number of protons. Oxygen gas, gold and diamond are elements.
A compound is a substance made of two or more elements chemically joined in a fixed ratio. Water is always two hydrogens for every oxygen. A compound is a new substance with new properties: sodium is a metal that bursts into flame in water, chlorine is a poisonous green gas, but sodium chloride is the salt on your table.
A mixture is two or more substances simply mingled together, in any proportions, each keeping its own properties. Salt water, air and a fruit salad are mixtures. You can usually separate a mixture by physical means: filtering, evaporating, picking pieces out.
Careful
“Oxygen gas, O₂, is a compound because it is made of molecules.”
Molecules can be elements. O₂ contains only oxygen atoms, so it is an element, even though the atoms come in pairs. A compound needs at least two different elements joined together.
Unmix a mixture
Mix a teaspoon of salt with a teaspoon of ground black pepper on a plate. Now separate them, without picking. Here is one way: rub an inflated balloon on your hair or a wool jumper and hold it a centimetre above the plate. The pepper, which is lighter, jumps up and sticks to the balloon; most of the salt stays behind. (Another way: stir the mixture into water. Salt dissolves, pepper floats. Pour off the water and leave it in a sunny place to dry, and the salt comes back.) You cannot do this with a compound. No balloon will pull the sodium out of salt.
The list today
The number of known elements grew steadily: about 30 by 1800, 63 when Mendeleev made his table in 1869, 92 natural elements up to uranium by the 1940s, and then a new kind of discovery. Scientists began making elements that are not found in nature, by smashing nuclei together. The 118th, oganesson, was named in 2016. Some of the newest elements last less than a thousandth of a second before they fall apart.
Every one of them follows Boyle’s rule. It cannot be broken down by chemistry into anything simpler, and every atom of it has the same number of protons.
1643 to 1804
Air has weight: pumps, tubes and balloons
Evangelista Torricelli, Robert Boyle, Robert Hooke, Jacques Charles, Joseph Gay-Lussac
Florence, 1643
The well-diggers and fountain-builders of Italy had a problem that nobody could explain. A suction pump, the kind you work with a handle, could lift water up a pipe, but only so far. Past about ten metres the water simply stopped rising, however hard the pump worked. The great Galileo had puzzled over it before his death in 1642. His young pupil, Evangelista Torricelli, had an idea that sounded almost silly: perhaps the pump was not pulling the water up at all. Perhaps the air outside, pressing down on the water in the well, was pushing it up, and ten metres of water was simply as much as the weight of the air could hold.
If that was right, a heavier liquid should rise less. Mercury is about 13.6 times as heavy as water. So Torricelli filled a glass tube with mercury, put his thumb over the end, turned it upside down into a dish of mercury and let go. The mercury dropped, and then stopped, leaving a column about 76 centimetres tall and an empty space at the top of the tube. About ten and a third metres divided by 13.6 is about 76 centimetres. The air really did have weight, and it was holding the mercury up.
Torricelli’s tube, the first barometer. The air pressing on the open dish holds up a column of mercury about 76 cm tall. The same push would hold up about 10.3 metres of water, which is why suction pumps could never lift water higher than that.
Torricelli wrote, beautifully, that “we live submerged at the bottom of an ocean of air”. That ocean presses on you all the time. At sea level it pushes on every square centimetre of your skin with the weight of about one kilogram, and on every square metre with the weight of about ten tonnes. You do not feel it because it pushes equally from every side, inside and out. That push is called pressure.
Oxford, 1662
Twenty years later, in England, Robert Boyle and his brilliant assistant Robert Hooke built an air pump that could suck most of the air out of a glass globe. They watched a ringing bell go quiet inside it, and a candle go out. Then Boyle tried something simple and careful. He took a long glass tube bent into a J, sealed at the short end, and poured mercury into the long end. A pocket of air was trapped in the short arm. The more mercury he poured in, the harder it pressed on the trapped air, and the smaller the air pocket became.
When he doubled the pressure, the air squeezed into half the space. When he tripled it, a third. Pressure times volume stayed the same. This is Boyle’s law, and it was one of the first times anyone had found a precise mathematical rule hiding inside the behaviour of an ordinary substance.
Step 1: why squeezing raises the pressure
Today we can explain what Boyle could only measure. A gas is a crowd of tiny particles flying about and bouncing off the walls. Every bounce is a tiny push. Pressure is all those pushes added up.
Squeeze the same particles into half the space and they are packed twice as closely. Each bit of wall gets hit twice as often. Twice the hits means twice the pressure.
Boyle’s rule drawn as a curve. Halve the volume and the pressure doubles; double the volume and it halves.
Paris, 1783
Then came the balloons. In the summer and autumn of 1783 France went balloon-mad. The Montgolfier brothers, paper-makers, discovered that a big bag of hot air would float, and on 21 November 1783 two men rose over Paris under a Montgolfier balloon, the first people ever to fly. Just ten days later the scientist Jacques Charles went up in a different kind of balloon, filled with hydrogen, the lightest gas of all. A huge crowd watched it rise from the Tuileries gardens.
Charles was interested in more than flying. He noticed that gases expand when they are warmed, and by about 1787 he had found that different gases all expand by the same fraction for each degree of warming. He never published it. In 1802 Joseph Gay-Lussac measured it carefully and published it, generously giving Charles the credit. Two years later Gay-Lussac went up in a balloon himself, to a height of about 7,000 metres, higher than anyone had been, to collect samples of thin, freezing air. (They turned out to contain the same mixture of gases as the air at the ground.)
Step 2: why warming raises the pressure
Warm a gas and its particles move faster. Faster particles hit the walls harder and more often. If the gas is in a sealed, rigid box, the pressure goes up. If the gas is in a stretchy balloon, the balloon swells until the pressure inside matches the air outside again.
The same gas warmed from 200 K to 400 K in a sealed box: the particles move faster and the pressure doubles.
The rule only works neatly if you measure temperature from absolute zero, in kelvin, not in degrees Celsius. (The story of how anyone found absolute zero is told in How cold can cold get?)
Step 3: putting it all together
Over the next century these separate rules were joined into one: the ideal gas law. For a fixed amount of gas, pressure goes up when you squeeze it smaller, goes up when you warm it, and goes up when you add more gas. In symbols chemists write it as PV = nRT, but in words it is just those three ideas at once.
A syringe with your thumb over the end.
Pull the plunger out to 20 mL of trapped air, then push it in to 10 mL. Half the space: the pressure inside doubles.
Push it further, to 5 mL: half again, so the pressure is now four times what it was.
That is why it gets harder and harder to push.
It is called “ideal” because it pretends the particles are tiny points that never attract each other. Real gases follow it very closely in everyday conditions, and stop following it when you squeeze them very hard or cool them until they are about to turn into liquid.
Careful
“When you squeeze a gas, the particles get smaller.”
The particles stay exactly the same size. Only the empty space between them shrinks. That is why gases are so easy to squeeze and liquids, whose particles are already touching, are not.
The upside-down glass
Over a sink, fill a glass right to the brim with water. Slide a piece of stiff card over the top so there is no air bubble, hold the card in place, and turn the glass upside down. Take your hand away from the card. The water stays in. The air pushing up on the card is far stronger than the weight of the water pushing down: remember, it could hold up ten metres of water.
A balloon in the freezer
Blow up a balloon, tie it, and measure round its middle with a piece of string. Put it in the freezer for half an hour and measure again. Then let it warm up. The particles inside slow down in the cold and push less hard, so the balloon shrinks; as they warm, it grows back. Nothing got in or out.
Every time this book talks about gases, from boiling water to car tyres to the air in a diver’s tank, it is standing on the shoulders of a pump that would not pump, a tube of mercury, and a sky full of balloons.
1833 to 1903
Charged travellers: Faraday's ions and Arrhenius's risky idea
Michael Faraday, William Whewell, Svante Arrhenius
London, 1833
Michael Faraday left school at 13 to work for a bookbinder. He read the books he was binding, especially the science ones, and taught himself so well that he got a job washing bottles for Humphry Davy at the Royal Institution. Twenty years later he was one of the greatest experimenters in the world.
In the early 1830s Faraday was studying something puzzling. Dry salt does not carry electricity. Pure water hardly carries it. But dissolve salt in water, dip in two metal plates connected to a battery, and a current flows. At the plates, new substances appear: gas bubbles at one, other chemicals at the other. Something in the liquid was carrying electric charge from one plate to the other. What?
Naming the travellers
Faraday did not know what these charge-carriers were, but he needed words to describe his experiments. He wrote to a friend, the scholar William Whewell at Cambridge, who was brilliant at inventing scientific words from Greek. Together they settled on a new vocabulary that every chemist still uses:
ion, from the Greek for “going” or “traveller”, for whatever carries the charge through the liquid;
anode (“the way up”) and cathode (“the way down”) for the two plates;
electrode for any plate, electrolyte for the liquid that carries current, and electrolysis for splitting substances with electricity.
Faraday also found exact rules. The amount of substance produced at a plate was always in proportion to the amount of electricity that passed. Electricity seemed to come in fixed portions, as if it too were made of particles. That hint pointed towards the electron, sixty years before anyone found it.
The student who said the unthinkable
Uppsala, Sweden, 1884
Fifty years later, a young Swede named Svante Arrhenius was measuring how well different salt solutions conduct electricity. His results led him to a startling idea: when salt dissolves in water, it splits up on its own into charged pieces, even when no electric current is flowing at all. Sodium chloride does not wait for a battery to pull it apart. As soon as it dissolves, it is already Na⁺ and Cl⁻, drifting separately through the water.
Most chemists thought this was nonsense. Sodium is a metal that bursts into flame in water, and chlorine is a poisonous gas. How could a glass of salty water be full of free sodium and chlorine? Arrhenius’s thesis was given the lowest passing grade his university could award. He very nearly failed.
The answer to the objection is the key to the whole idea, and you already know it from Chapter 1: an ion is not the same as an atom. Na⁺ has one electron fewer than a sodium atom, and that makes all the difference. It does not react with water the way sodium metal does. Cl⁻ has one electron more than a chlorine atom, and it is not a poisonous gas. They are different particles with different behaviour.
A few scientists, especially Wilhelm Ostwald, then a professor in Riga, took Arrhenius seriously and tested his ideas. The evidence piled up. In 1903, nineteen years after nearly failing, Arrhenius won the Nobel Prize in Chemistry for exactly the idea that had almost sunk him.
Ions, step by step
An ion is an atom (or group of atoms) with a charge, because it has gained or lost electrons. Lose electrons and you are positive; gain electrons and you are negative. The nucleus never changes.
Positive ions are called cations and negative ions anions. (Cations travel towards the cathode, anions towards the anode: Faraday and Whewell’s words again.)
In a solid salt crystal, ions are locked in place, so they cannot carry charge. That is why dry salt does not conduct.
Dissolve the salt (or melt it), and the ions can move. Push them with a battery and positive ions drift one way, negative ions the other: an electric current made of moving atoms.
Some ions are groups of atoms that stay together and carry a charge as a team: sulfate, SO₄²⁻; hydroxide, OH⁻; ammonium, NH₄⁺.
Careful
“Salt water conducts electricity because electrons swim through it.”
In metal wires, current is carried by electrons. In salt water, it is carried by ions, whole charged atoms moving through the liquid. The electrons stay at the plates, where they are handed on to or taken from the ions.
Salt that disappears and comes back
Stir a teaspoon of salt into half a glass of warm tap water until it vanishes. The salt has not gone: the ions have spread out among the water molecules, too small to see. Pour a little onto a dark plate and leave it somewhere warm and dry for a day or two. As the water evaporates, the ions find each other again and lock back together. Look at the white crust with a magnifying glass, or your phone’s camera zoomed in: you should see tiny cubes, the shape of the sodium chloride lattice.
Every time this book writes a charge on a symbol, Na⁺ or O²⁻, it is using Faraday’s word and Arrhenius’s idea: atoms that carry electricity by having one or two electrons too few, or too many.
1738 to 1877
A storm of tiny billiard balls
Daniel Bernoulli, Rudolf Clausius, James Clerk Maxwell, Ludwig Boltzmann
Basel, 1738
Look at the air in your room. It seems perfectly still. Now imagine being told that it is a howling storm: countless tiny particles hurtling about faster than a passenger jet, smashing into each other billions of times every second, and drumming on your skin, the walls and the pages of this book without a moment’s rest. That is what the kinetic theory of gases says. “Kinetic” comes from the Greek word for motion.
The first person to take the idea seriously was the Swiss mathematician Daniel Bernoulli. In a book published in 1738 he imagined a gas as a swarm of tiny particles flying about in a closed cylinder and bouncing off a piston. He showed, with mathematics, that their bombardment would push on the piston, and that squeezing the gas into a smaller space would make the push stronger in exactly the way Boyle had measured. It was a brilliant explanation. Almost nobody paid attention. For another hundred years most scientists thought heat was an invisible fluid called “caloric”, and many doubted that atoms existed at all.
Step 1: pressure is a drumming of particles
Think of hailstones on a tin roof. Each stone makes a tiny bang; thousands of them make a steady roar. A gas does the same to its container. Each particle that hits the wall gives it a tiny push; trillions upon trillions of them make a steady pressure. Bernoulli’s picture explains both of Boyle’s discoveries at once: squeeze the gas and the hits come more often; heat it and they come faster and harder.
Faster particles push harder and more often. Doubling the kelvin temperature doubles the pressure in a sealed box.
Zürich, Aberdeen and Vienna, the 1850s to the 1870s
The idea came back to life in the 1850s, when scientists had finally accepted that heat is a kind of motion. The German physicist Rudolf Clausius worked out how far a particle travels before it bumps into another. In 1859 a young Scottish physicist, James Clerk Maxwell, made the crucial step. He realised that the particles in a gas cannot all be moving at the same speed. They are constantly colliding, swapping speed like players in a giant game of billiards, so at any moment some are slow, most are middling and a few are very fast. Maxwell worked out exactly how the speeds are spread out, using mathematics alone, decades before anyone could measure a single molecule.
In Vienna, Ludwig Boltzmann took Maxwell’s ideas much further. He showed how the everyday laws of heat, which engineers used to design steam engines, could all come from the averaged-out behaviour of enormous numbers of particles. His equations are some of the most beautiful in physics. But many powerful scientists of his day, including the chemist Wilhelm Ostwald, still refused to believe atoms were real, and Boltzmann spent years defending them. He died in 1906, only a few years before the experiments of Jean Perrin convinced the doubters that he had been right all along.
Step 2: how fast is fast?
Using Maxwell’s mathematics we can work out the speed of molecules. In the air of a warm room the nitrogen molecules move, on average, at about 480 metres every second. That is roughly 1,700 kilometres an hour: about twice the cruising speed of a passenger jet. Oxygen molecules are a little heavier and a little slower; water vapour molecules, which are lighter, are faster.
How often does an air molecule bump into another one?
In ordinary air, a nitrogen molecule travels only about 70 nanometres (70 billionths of a metre) between collisions.
At about 480 metres a second, that means about 7 thousand million collisions every second, for every molecule.
Careful
“If air molecules move faster than a jet, a smell should cross a room instantly.”
Each molecule is fast, but it never gets far before crashing into another one and shooting off in a new direction. Its path is a hopeless zig-zag. A perfume molecule released on one side of a still room would take a very long time to wander to the other side on its own; in real rooms, gentle air currents carry smells much faster than the zig-zagging alone could.
Step 3: temperature is average motion
Here is the deepest idea in the story. Temperature is a measure of how much energy of motion the particles have, on average. Hotter means the particles are jiggling and flying faster. Colder means slower. At absolute zero they would have the least motion possible.
Because the energy of motion depends on the square of the speed, doubling the kelvin temperature does not double the speed. It multiplies it by about 1.4 (the square root of 2). And at any temperature there is always a spread: a few fast particles, many middling ones, a few slow ones. That spread matters later in this book: it is why a few particles are always energetic enough to escape from a liquid as vapour, or to get over the energy barrier of a chemical reaction.
Hot water and cold water
Fill one clear glass with cold water from the fridge and another with warm water from the tap. Let them stand for a minute so the water is still. Then, at the same moment, add one drop of food colouring to each, without stirring. Watch for a few minutes. In the warm water the colour spreads much faster, because its molecules are jiggling faster and jostle the colour about more quickly.
None of the scientists in this story could see a single molecule. They imagined one, did the mathematics carefully, and found that it explained pressure, heat and temperature. Then the experiments caught up and proved them right. When this book shows you a box of bouncing particles, you are looking at Bernoulli’s, Maxwell’s and Boltzmann’s storm.
1817 to 2016
The patience game: the story of the periodic table
Johann Döbereiner, John Newlands, Lothar Meyer, Dmitri Mendeleev, William Ramsay, Henry Moseley
St Petersburg, February 1869
Dmitri Mendeleev had a problem, and it was a textbook. He was a chemistry professor in St Petersburg, and he was writing a book for his students called The Principles of Chemistry. He had finished the chapters on a few familiar elements, and now he had to decide what came next. About 63 elements were known, and they looked like a hopeless jumble: gases and metals, soft and hard, some that burst into flame in water and some that sat quietly for centuries. In what order could you possibly teach them?
Mendeleev was not the first person to wonder. The answer he found, and the daring way he used it, became the most famous chart in all of science. But the story starts fifty years earlier.
The first clues: families of three
In 1817, and again in 1829, a German chemist named Johann Döbereiner noticed something odd about certain elements that behave alike. Calcium, strontium and barium are all whitish metals that react with water in similar ways. When Döbereiner looked at their atomic weights, the middle one sat almost exactly halfway between the other two.
Calcium 40.1 and barium 137.3: halfway between is (40.1 + 137.3) ÷ 2 ≈ 88.7. Strontium is 87.6.
Chlorine 35.5 and iodine 126.9: halfway is about 81.2. Bromine is 79.9.
Lithium 6.9 and potassium 39.1: halfway is about 23.0. Sodium is 23.0.
He called these families triads. Was it coincidence? It happened too often for that. Something was ordering the elements, but nobody could see what.
The chemist who was laughed at
In 1865 an English chemist, John Newlands, tried something bolder. He lined up all the known elements in order of atomic weight and noticed that similar elements seemed to turn up every eighth place, like the notes of a musical scale: do, re, mi, fa, so, la, ti, do again. He called it the Law of Octaves.
When he presented it to the Chemical Society in London in 1866, one member asked him, with a straight face, whether he had ever tried arranging the elements in alphabetical order, since that might give patterns too. The Society refused to publish his paper. Newlands was partly right and partly wrong: his pattern worked for the lighter elements and broke down for the heavier ones, and he left no room for elements nobody had found yet. More than twenty years later the Royal Society gave him a medal for it.
The patience game
Now back to Mendeleev. He wrote the name of each element on a card, with its atomic weight and its main properties: what it combined with, and in what proportions. Then, the story goes, he laid the cards out on a table again and again, like the card game called patience (or solitaire), looking for the arrangement where everything fitted.
Careful
“Mendeleev saw the whole periodic table in a dream.”
This story was told by one of his friends years afterwards, and Mendeleev himself never seems to have described it that way. Historians treat it as a legend. What we do know is that he worked on the problem for weeks, with notes and drafts covered in crossings-out that still survive.
On 17 February 1869, by the Russian calendar of the time (1 March by ours), he wrote out his first table. He put elements in order of atomic weight, but in rows and columns so that families lined up: lithium, sodium and potassium together; fluorine, chlorine, bromine and iodine together. And then he did two bold things that nobody before him had dared.
Two bold moves
First, he left gaps. Where the next element by weight did not fit the family pattern, Mendeleev did not force it in. He left a blank and said, in effect: an element belongs here that nobody has found yet. Below aluminium he left a gap and called the missing element eka-aluminium (“one beyond aluminium”). There were other gaps below boron and below silicon.
Second, he predicted. From its neighbours in the table, he forecast what each missing element would be like: its atomic weight, how dense it would be, what it would combine with.
Part of Mendeleev’s idea. Each missing element was surrounded by known neighbours, so he could predict its properties from theirs, the way you might guess a missing puzzle piece from the pieces around it.
Nature answers
In 1875 a French chemist, Paul-Émile Lecoq de Boisbaudran, spotted a new violet line in the light from a zinc ore and tracked down a new metal. He named it gallium, after France (Gallia in Latin). It was Mendeleev’s eka-aluminium. There was one disagreement: Lecoq measured its density as 4.7, and Mendeleev had predicted about 5.9. Mendeleev wrote to him suggesting that his sample was impure. Lecoq purified it, measured again, and got 5.9. A man in St Petersburg had corrected a measurement on a metal he had never seen.
Then came scandium in 1879, matching eka-boron, and germanium in 1886, matching eka-silicon almost perfectly: Mendeleev had predicted an atomic weight of about 72 and a density of about 5.5; germanium turned out to be 72.6 and about 5.3. After that, chemists everywhere took the table seriously.
A whole family nobody expected
Even Mendeleev’s table had a surprise coming. In 1894, Lord Rayleigh and William Ramsay found that nitrogen taken from the air was slightly heavier than nitrogen made by chemical reactions. The difference was tiny, but they did not ignore it. Hidden in the air was a new gas that reacted with nothing at all: argon, from the Greek for “lazy”. Within four years Ramsay had also found helium on Earth, and then, with Morris Travers, neon, krypton and xenon. They formed a completely new column, the noble gases, and slotted neatly onto the end of every row. The table bent to fit them without breaking: the sign of a good model.
The last puzzle: the wrong order
There was one awkward thing. In a few places Mendeleev had to put elements slightly out of order of weight to keep the families together. Tellurium (127.6) is heavier than iodine (126.9), but tellurium clearly belongs with oxygen and sulfur, and iodine with chlorine and bromine. So he swapped them and guessed that tellurium’s weight had been measured wrongly. It hadn’t. The real explanation waited until 1913, when the young physicist Henry Moseley showed that the true order is not by weight at all, but by the number of protons in the nucleus: the atomic number. Tellurium has 52 protons, iodine 53. The swap was right all along.
Reading the table, step by step
Here is how to read the chart that grew out of all this.
Each box is one element, in order of atomic number: hydrogen 1, helium 2, lithium 3, and so on.
A row is a period. Each new row starts when the atoms begin filling a new shell of electrons. So the rows get longer as you go down.
A column is a family, called a group. Atoms in the same column have the same number of outer-shell electrons, so they behave alike: lithium, sodium and potassium in the first column; fluorine, chlorine and bromine in the next-to-last; the noble gases at the far right.
Metals are on the left and in the middle; non-metals on the right. A staircase line separates them.
The table today
The table now holds 118 elements. The last four were named in 2016: nihonium, moscovium, tennessine and oganesson. In 1955, scientists at Berkeley named element 101 mendelevium, in honour of the man who laid out the cards.
A patience game of your own
Take twelve cards or slips of paper. On each write one of these, with its atomic weight: lithium 6.9, sodium 23.0, potassium 39.1 (soft metals that fizz in water); fluorine 19.0, chlorine 35.5, bromine 79.9 (sharp-smelling, poisonous non-metals); beryllium 9.0, magnesium 24.3, calcium 40.1 (harder metals); oxygen 16.0, sulfur 32.1, selenium 79.0. Shuffle them, then lay them out in order of weight in rows so that each family forms a column. You have just rebuilt a corner of Mendeleev’s table.
Every time you look at the periodic table in this book, remember that it began as a set of cards on a professor’s desk, and that its greatest strength was the blank spaces where the professor admitted what he did not know.
1912 to 1932
Who pulls harder? The story of polar molecules
Peter Debye, Linus Pauling
A kitchen, any day
Pour a spoonful of cooking oil into a glass of water and stir as hard as you like. The moment you stop, the oil gathers into drops and floats to the top. Sugar disappears into water without a trace; oil never does. Water and oil are both clear liquids made of small molecules. Why do they refuse to mix?
The answer lies in a tug-of-war that happens inside every bond, and two scientists, a Dutch physicist and an American chemist, learned how to measure it.
An unfair tug-of-war
A bond, as Lewis taught, is a pair of electrons shared between two atoms. But sharing is not always equal. Some atoms pull on shared electrons more strongly than others, because their nucleus has more positive charge acting on the outer electrons, or because those electrons sit closer to it.
When the pull is unequal, the shared electrons spend more of their time near the stronger atom. That end of the bond becomes slightly negative, and the other end slightly positive. Chemists write these “slightly” charges with the Greek letter delta: δ⁻ and δ⁺. A bond like this is called polar, because it has two ends, like the poles of a magnet.
Debye measures the pull
Zürich and Utrecht, 1912
In 1912 the Dutch physicist Peter Debye worked out how molecules with a positive end and a negative end, which he called dipoles (“two poles”), would behave between electrically charged plates. They would tend to turn and line up, and that would change how much electric charge the plates could store. By measuring that change for different gases and liquids, and how it varied with temperature, he could calculate how strongly each molecule was polarised.
His method gave numbers. Water’s dipole is large. Carbon dioxide’s is zero, even though each C=O bond in it is polar: the molecule is straight, so the two pulls point in opposite directions and cancel. Methane’s is zero too, because its four bonds point to the corners of a tetrahedron and cancel perfectly. The unit chemists use for dipoles is named after him: the debye. Water’s is about 1.85 debye. Debye won the Nobel Prize in Chemistry in 1936.
Pauling’s scale
Pasadena, California, 1932
Debye had measured whole molecules. Linus Pauling wanted a number for each atom: how hard does it pull shared electrons? In 1932 he worked one out by comparing bond energies. If a bond between two different atoms is stronger than you would expect from the average of the two similar bonds, the extra strength comes from the unequal sharing. From those differences he built a scale he called electronegativity.
Some values on Pauling’s scale (modern figures):
fluorine 3.98 (the strongest pull of all), oxygen 3.44, nitrogen 3.04, chlorine 3.16,
carbon 2.55, hydrogen 2.20, sodium 0.93.
The bigger the difference between two atoms, the more polar the bond. Oxygen and hydrogen differ by 1.24, so O–H bonds are strongly polar. Carbon and hydrogen differ by only 0.35, so C–H bonds are nearly even. Sodium and chlorine differ by more than 2, so much that sodium’s electron goes over to chlorine almost completely: that is an ionic bond. Polar bonds sit in the middle of a smooth range from perfectly even sharing to complete transfer.
Polar molecules, step by step
Look at each bond. Is one atom much more electronegative than the other? Then the bond is polar, with δ⁻ on the stronger-pulling atom.
Look at the shape. Draw an arrow along each polar bond, pointing to the δ⁻ end.
Add up the arrows. If they cancel (as in straight CO₂ or tetrahedral CH₄), the molecule is non-polar overall. If they do not cancel (as in bent H₂O or pyramid-shaped NH₃), the molecule is polar: it has a positive side and a negative side.
Bond pulls in two molecules. In straight CO₂ they cancel; in bent H₂O they add up, so water has a negative side (the oxygen) and a positive side (the hydrogens).
Back to oil and water
Water molecules are strongly polar. The positive hydrogen side of one molecule is attracted to the negative oxygen side of its neighbours, so water molecules cling tightly to each other. Oil molecules are long chains of carbon and hydrogen, with nearly even C–H bonds: almost non-polar. When you stir oil into water, the water molecules simply hold on to each other and squeeze the oil out. “Like dissolves like”: polar dissolves polar, non-polar dissolves non-polar.
Careful
“You can prove water is polar by holding a charged comb next to a thin stream from the tap: the stream bends.”
The stream does bend, and it is a lovely thing to watch. But careful experiments (published in 2000) showed the bending comes mostly from electric charge that flows onto the stream from the tap, not from the water molecules turning. The real evidence that water is polar comes from measurements like Debye’s.
Oil, water and soap
Half fill a clear jar with water, add a few spoonfuls of cooking oil and a drop of food colouring, put the lid on tightly and shake. Watch the oil separate again. Now add a squirt of washing-up liquid and shake once more. Soap molecules have a polar head, which sits happily in water, and a long non-polar tail, which sits happily in oil. They wrap around tiny oil droplets and let them spread through the water. That is how soap washes grease off your plate.
1593 to 1848
How cold can cold get?
Galileo Galilei, Daniel Fahrenheit, Anders Celsius, Guillaume Amontons, William Thomson (Lord Kelvin)
Padua, around 1593
Hot and cold seem like the simplest things in the world. You can feel them. But try this: put one hand in cold water and the other in hot water for a minute, then put both into the same bowl of lukewarm water. One hand says “warm”, the other says “cold”. Your skin is a terrible thermometer. For most of history nobody could measure how hot something was, only how hot it felt.
Around 1593 Galileo built a gadget called a thermoscope: a glass bulb of air on top of a thin tube dipped in water. When the air in the bulb warmed it expanded and pushed the water down; when it cooled the water rose. It showed changes in hotness, but it had no numbers, and it also wobbled with the weather, because the open water was being pushed by the air outside.
Step 1: putting numbers on hotness
The trick that turned a thermoscope into a thermometer was to choose fixed points: things that always happen at the same hotness, so that everyone’s thermometer could agree. In 1724 the instrument-maker Daniel Fahrenheit, working in Amsterdam, published his scale, using sealed glass tubes of mercury that were far more reliable than anything before. In 1742 the Swedish astronomer Anders Celsius proposed a scale with 100 steps between the freezing and boiling points of water. Oddly, he put the boiling point at 0 and freezing at 100; within a few years others turned it the right way up, and that is the Celsius scale used in India today.
Careful
“40 °C is twice as hot as 20 °C.”
It is not, and the reason is the heart of this story. The zero of the Celsius scale is just where water happens to freeze. It is not “no heat at all”. Doubling a Celsius number does not double anything real, in the same way that doubling the floor number of a building does not double its height above the basement.
Step 2: a gas points to the coldest possible cold
Around 1702 the French scientist Guillaume Amontons noticed something strange about air trapped in a sealed container. As he cooled it, its pressure dropped steadily, by the same amount for every degree. He wondered: if you kept cooling, the pressure would keep falling, and at some temperature it would reach zero. A gas cannot push less than not at all. So that temperature must be the coldest there can possibly be.
Over the next century, more careful measurements by Charles, Gay-Lussac and others showed the same thing for every gas they tried. Draw the straight lines of pressure against temperature, extend them backwards into the cold, and they all meet at zero pressure at the same place: about −273 °C. Today we know the exact value: −273.15 °C. It is called absolute zero.
What happens there? Temperature, it turns out, is a measure of how vigorously particles are moving. At absolute zero they would have the very least motion that the laws of physics allow. You cannot go colder than that, for the same reason you cannot be shorter than zero centimetres.
Glasgow, 1848
In 1848 a 24-year-old professor at Glasgow University, William Thomson, proposed a temperature scale that starts at absolute zero itself. Thomson was a prodigy: he had started at university aged ten. Much later, Queen Victoria made him a lord, and he took his title from the River Kelvin that flows past the university, becoming Lord Kelvin. His scale is now called the kelvin scale, and its unit is the kelvin, written K (with no degree sign).
Step 3: converting between Celsius and kelvin
The steps on the kelvin scale are exactly the same size as Celsius degrees. Only the starting point moves. So converting is just adding:
kelvin = degrees Celsius + 273.15
Water freezes: 0 °C = 273.15 K.
A warm Mumbai afternoon: 30 °C = 303.15 K.
Water boils: 100 °C = 373.15 K.
Absolute zero: −273.15 °C = 0 K.
Now try the “twice as hot” question again, in kelvin. 20 °C is 293 K and 40 °C is 313 K. So 40 °C has only about 7% more of the jiggling we call temperature than 20 °C, not twice as much. To be truly twice as hot as a 20 °C room, in the physicist’s sense, something would have to be at 586 K: about 313 °C, hotter than a kitchen oven.
This is why every gas law in this book uses kelvin. When a gas’s kelvin temperature doubles, its particles have twice as much energy of motion, and if it is sealed in a rigid box, its pressure doubles too. That simple doubling only works if you count from the true zero.
Step 4: the race towards zero
Can anyone actually get to absolute zero? Scientists have been racing towards it for over a century. In 1908 the Dutch physicist Heike Kamerlingh Onnes turned helium into a liquid at about 4 K, and a few years later discovered that some metals lose all electrical resistance when that cold. Today laboratories can cool clouds of atoms to less than a billionth of a kelvin above absolute zero. But the laws of physics say you can never quite reach it: each step closer gets harder than the last. Even deep space is not that cold: the faint glow left over from the Big Bang keeps it at about 2.7 K.
A thermometer’s fixed point
If you have a kitchen thermometer, fill a glass with plenty of crushed ice and a little cold water, stir, and wait a few minutes. It should read very close to 0 °C. Add more ice, wait, and read it again: still 0 °C. While ice and water are both present, the temperature stays put, which is exactly why melting ice was chosen as a fixed point. (If your thermometer reads 1 or 2 degrees off, you have just calibrated it.)
So whenever you see a temperature in kelvin in this book, remember what the number means: how far you are above the stillest possible state of matter, counted in steps the size of a Celsius degree.
1611 to 1920
The strange case of water
Johannes Kepler, Wendell Latimer, Worth Rodebush, Linus Pauling
Prague, winter 1610
On a snowy day in Prague, the astronomer Johannes Kepler was crossing a bridge when a snowflake landed on his coat. He noticed, as people had before him, that it had six points. Every snowflake he looked at had six. Why six, and never five or eight? He wrote a little book about it as a New Year’s present for a friend, published in 1611, and guessed that it had something to do with how tiny particles pack together. He could not go further. Nobody knew what water was made of.
It took three more centuries to understand Kepler’s snowflakes. The answer turned out to explain far more than snow: why ice floats, why lakes freeze from the top down, why water boils at such a high temperature, and why you sweat on a hot Mumbai afternoon.
Step 1: water is an odd liquid
By most of chemistry’s rules, water should be a gas at room temperature. Look at its relatives. Hydrogen sulfide, H₂S, has molecules shaped just like water’s but heavier, and it boils at about −60 °C. Methane, CH₄, with almost the same mass as water, boils at −161 °C. Yet water, with a light little molecule of three atoms, does not boil until 100 °C. Something is holding water molecules to each other unusually tightly.
And then there is ice. Almost every substance shrinks when it freezes: its particles pack more neatly as a solid than as a liquid, so the solid sinks in its own liquid. Water does the opposite. Ice takes up about 9% more space than the water it came from. That is why ice floats, why a full bottle of water in the freezer cracks, and why pipes burst in cold countries.
Berkeley, California, 1920
The explanation came from the laboratory of the great chemist G. N. Lewis, the man who first drew bonds as shared pairs of electrons. In 1920 two young chemists working there, Wendell Latimer and Worth Rodebush, suggested that a hydrogen atom could be held between two oxygen atoms at once: firmly bonded to one, and weakly attracted to the other. This weak link between molecules came to be called the hydrogen bond. In the 1930s Linus Pauling made the idea famous and showed how much of chemistry and biology depends on it.
Step 2: where the hydrogen bond comes from
In a water molecule, the oxygen atom pulls the shared electrons towards itself harder than the hydrogen atoms do. That leaves the oxygen slightly negative and each hydrogen slightly positive. The molecule is also bent, like a boomerang, so the two slightly positive hydrogens are on one side and the slightly negative oxygen on the other.
Now put lots of water molecules together. The slightly positive hydrogen of one molecule is attracted to the slightly negative oxygen of the next. Opposite charges attract: that is all a hydrogen bond is. It is much weaker than the real bonds inside a water molecule, about twenty times weaker, but every water molecule can make several of them, and together they hold the liquid tightly.
Three molecules with ten electrons each and almost the same mass, but very different boiling points. Water’s hydrogen bonds (dotted) hold its molecules together so strongly that it boils at 100 °C.
That is why water boils so late. To turn water into steam you have to pull every molecule away from its neighbours, breaking all those hydrogen bonds. The O–H bonds inside each molecule do not break at all: steam is still H₂O.
Step 3: why ice floats
When water freezes, each molecule settles into a position where it makes four hydrogen bonds with four neighbours, arranged in a very regular, open pattern of six-sided rings. The rings hold the molecules slightly further apart than they are in the jostling liquid. More space between molecules means the same mass fills a bigger volume, so ice is less dense than water, and it floats. Those six-sided rings are also the reason every snowflake has six points: Kepler’s puzzle, solved.
How much of an ice cube is underwater?
Ice has a density of about 0.917 grams per millilitre; liquid water about 1.000.
A floating object sinks until it pushes aside its own weight of water.
So the fraction underwater is 0.917 ÷ 1.000 ≈ 0.92: about nine-tenths of an ice cube, or an iceberg, is below the surface.
This one strange property matters enormously. When a lake freezes in winter, the ice forms on top and floats there, like a lid, keeping the water underneath liquid. Fish and plants survive the winter below. If ice sank, lakes would freeze solid from the bottom up.
Step 4: why sweat cools you
Breaking hydrogen bonds takes energy. When sweat evaporates from your skin, the water molecules that escape carry that energy away with them, taking it from your body, and you cool down. Evaporating about a litre of sweat takes roughly 2.4 million joules: as much energy as it takes to warm 7 litres of water from room temperature to boiling. On a humid monsoon day the air is already so full of water vapour that sweat evaporates slowly, which is why humid heat feels so much stickier and harder to bear than dry heat.
Careful
“Boiling breaks water molecules apart into hydrogen and oxygen.”
Boiling only breaks the weak hydrogen bonds between molecules. The molecules themselves stay whole. Splitting water into hydrogen and oxygen is a completely different, chemical change, which needs electricity or a great deal of heat.
Ice that grows
Fill a small plastic cup (not glass) exactly to a line you draw with a marker, about two-thirds full. Put it in the freezer overnight. In the morning the ice will stand clearly above your line, often with a little bump in the middle. Water expanded as it froze: the hydrogen bonds pushed the molecules into their open six-sided pattern.
A floating paper clip
Fill a bowl with water. Lay a small square of tissue paper flat on the surface and gently place a dry metal paper clip on it. As the tissue soaks and sinks, the paper clip is often left floating, resting on the skin of the water. Hydrogen bonds pulling the surface molecules together make that skin. Add a drop of washing-up liquid at the edge and watch what happens.
So water, the most ordinary substance in your life, is one of the strangest in all of chemistry. Its weak little hydrogen bonds decide whether lakes freeze, whether you can cool down on a hot day, and why every snowflake that ever fell has had six points.
1823 to 1889
Why the match needs striking
Johann Döbereiner, Jöns Jacob Berzelius, Svante Arrhenius
Jena, Germany, 1823
The chemist Johann Döbereiner lets a stream of hydrogen gas flow over a small piece of spongy platinum metal. Nobody has lit a match. Yet within moments the platinum begins to glow red, and the hydrogen bursts into flame. Döbereiner turns the trick into a gadget: a glass jar that makes hydrogen, a nozzle and a pinch of platinum. Press a lever and you have fire. “Döbereiner’s lamp” was sold by the thousands as a lighter for pipes and candles, decades before cheap matches. But nobody understood how it worked. The platinum was not burning, and it was not used up. It just sat there and made the reaction happen.
The puzzle of things that do not happen
Here is a stranger puzzle. Hydrogen and oxygen react violently: Chapter 4 showed that a spark makes them explode. And yet you can mix them in a jar at room temperature and leave them for years, and almost nothing happens. This page is the same. Paper and oxygen react to give carbon dioxide and water and a great deal of heat; that is what burning is. You are surrounded by oxygen. So why doesn’t this book burst into flame?
Berzelius gives it a name
In 1835 Jöns Jacob Berzelius, collecting together several strange cases like Döbereiner’s lamp, gave the effect a name: catalysis, from a Greek word meaning “loosening”. A catalyst is a substance that makes a reaction go faster without being used up itself. Berzelius could name it, but he could not explain it. The explanation needed a new idea about why reactions happen at all.
Arrhenius and the hill
Uppsala and Stockholm, Sweden, 1889
The Swedish chemist Svante Arrhenius (the same man who had explained ions in water a few years earlier) noticed that the speed of many reactions rises steeply with temperature, much more steeply than you would expect if it simply depended on how often particles collide. In 1889 he suggested the reason. For molecules to react, they must hit each other hard enough. Only collisions with more than a certain minimum energy can stretch and break the old bonds so that new ones can form. That minimum is called the activation energy.
Step 1: picture a hill
Think of a ball resting in a valley, with a deeper valley on the other side of a hill. The ball would be lower, and more settled, in the far valley: that is the products, lower in energy than the reactants. But to get there, the ball must first be pushed up the hill. The top of the hill is the barrier. A gentle nudge just rolls the ball back. Only a hard enough push gets it over.
A reaction’s energy hill. The reactants sit in one valley, the products in a lower one, but the path between them climbs over a barrier. A catalyst offers a lower route over the hill (dashed) between the same two valleys.
That is why the book does not burn. Most oxygen molecules hitting the paper are not moving fast enough to get over the barrier. A match is a way of giving a few molecules enough energy to get over; once the burning starts, the heat it releases pushes neighbouring molecules over too, and the fire spreads.
Step 2: why temperature matters so much
In any gas or liquid, molecules have a spread of energies: most are fairly slow, a few are fast. Only the fast few can get over the barrier. Warm things up, and the whole spread shifts: the number of molecules fast enough to get over rises sharply. A useful rule of thumb for many reactions near room temperature is that ten degrees warmer roughly doubles the speed.
Why food lasts longer in the fridge. The chemistry that spoils food runs, as a rough rule, about twice as fast for every 10 °C warmer.
From a 4 °C fridge to a 24 °C kitchen is 20 degrees: two doublings, 2 × 2 = 4 times faster.
To a 44 °C Mumbai rooftop in May: four doublings, 2 × 2 × 2 × 2 = 16 times faster.
(This is only a rule of thumb; real reactions vary.)
Step 3: what a catalyst does
A catalyst does not push the ball harder. It opens a different path, a lower pass through the hills. With a lower barrier, many more molecules have enough energy to get across, so the reaction runs much faster. On Döbereiner’s platinum, hydrogen and oxygen molecules stick to the metal surface, where their bonds are loosened, and they react easily there. The platinum comes out unchanged, ready for the next molecules.
Two things a catalyst does not do. It does not change where the valleys are: the products end up with exactly the same energy, with or without it. And it lowers the hill in both directions, so it speeds up the backward reaction too. Chapter 5 explains why that means a catalyst cannot change how far a reaction goes, only how fast it gets there.
Life’s catalysts
Your body is full of catalysts called enzymes: large protein molecules, each shaped to speed up one particular reaction. An enzyme in your blood called carbonic anhydrase helps carbon dioxide react with water more than a million times faster than it would on its own. Without enzymes, digesting a meal would take years. Cars carry catalysts too: the catalytic converter, coated with tiny amounts of platinum, palladium and rhodium, turns poisonous exhaust gases into less harmful ones.
Careful
“A catalyst gives the reaction extra energy.”
It gives no energy at all. It provides a route that needs less. That is why it is not used up: it is a guide, not a fuel.
Two experiments with heat and enzymes
Glowsticks. Snap two identical glowsticks to start them (do not cut them open). Put one in a glass of warm tap water and one in a glass of ice water. After a minute, compare them in a dark room. The warm one glows brighter, because its light-making reaction runs faster; it will also run out sooner. The cold one glows dimly but for longer.
Pineapple jelly. With an adult, make two small bowls of jelly from gelatin powder. Stir pieces of fresh pineapple into one and pieces of tinned pineapple into the other, and put both in the fridge. The bowl with tinned pineapple sets; the one with fresh pineapple stays runny. Fresh pineapple contains an enzyme that cuts up the gelatin’s protein chains. Tinned pineapple has been heated, which destroys the enzyme’s delicate shape.
So the next time you strike a match, remember the hill: the match is not the energy of the fire, it is the push that gets the first few molecules over the top.
1783 to 1850
Heat is motion
Antoine Lavoisier, Pierre-Simon Laplace, Count Rumford, James Prescott Joule
Paris, winter 1782
A guinea pig sits in a small wire cage. Around the cage is a jacket packed with crushed ice, and around that, another jacket of ice to keep out the warmth of the room. Antoine Lavoisier and the mathematician Pierre-Simon Laplace are waiting to see how much ice the little animal’s body heat will melt. It sounds like a strange way to spend a winter, but they are asking one of the deepest questions in science: what is heat?
Heat as a fluid
In the 1700s most scientists believed that heat was an invisible, weightless fluid called caloric. Hot things were full of it; cold things had less. Caloric flowed from hot to cold the way water flows downhill, which is why your chai cools down and the air around it warms up. Lavoisier even listed caloric among the chemical elements.
The caloric idea explained a lot, and Lavoisier and Laplace’s ice machine, the first calorimeter (heat-measurer), was built to measure it. The melted ice dripped out and was weighed: the more ice melted, the more heat had been given off. They found that the guinea pig, over a few hours, melted about as much ice as burning a small amount of charcoal producing the same amount of carbon dioxide. Their conclusion was beautiful and correct: breathing is a slow, gentle kind of burning. Your body “burns” food with oxygen, and that is where your warmth comes from.
The cannon that never ran out of heat
The army arsenal in Munich, 1798
An American-born soldier and inventor, Benjamin Thompson, who had become Count Rumford in Bavaria, was in charge of making cannons. A cannon barrel was made by spinning a solid metal casting against a sharp drill. Rumford noticed how hot the metal became. So he tried an experiment: he used a deliberately blunt drill, turned by horses, with the cannon sitting in a box of water. After about two and a half hours, the water boiled. The watching crowd was astonished: water boiling without any fire.
What struck Rumford was that the heat never ran out. As long as the horses kept turning, heat kept coming. If heat were a fluid stored inside the metal, surely it would eventually be used up. Instead it seemed to be made by the motion. Rumford suggested that heat is not a substance at all, but a kind of motion.
Joule’s paddle wheel
Salford, near Manchester, 1840s
The person who proved it was James Prescott Joule, the son of a wealthy brewer, who did his experiments at home. His most famous apparatus was a paddle wheel inside a container of water. A weight hanging on a string slowly fell, turning the paddles, which churned the water. Joule measured the temperature of the water with a thermometer so precise it could detect a few hundredths of a degree.
The water warmed up, very slightly. And always by the same amount for the same falling weight. A falling weight is motion; warmer water is heat; and there was a fixed exchange rate between them. In 1850 Joule published his best value: the energy of 772 pounds falling one foot raises one pound of water by one degree Fahrenheit. In today’s units, it takes about 4,200 joules to warm a kilogram of water by one degree Celsius. The unit of energy, the joule, is named after him.
There is a famous story that Joule took a thermometer on his honeymoon in the Alps to test whether the water at the bottom of a waterfall was warmer than at the top. The physicist William Thomson said he met Joule there, thermometer in hand. Whether or not he measured anything, he was right in principle: the water at the bottom of a 100-metre waterfall should be warmer by only about a quarter of a degree, far too little to notice with your fingers.
Step 1: what energy is
Energy is the capacity to make things happen: to move, to warm, to light, to push. It comes in many forms. A falling weight has energy of motion. A stretched spring has stored energy. Chemicals have energy stored in the way their atoms are arranged. Heat is energy too: the energy of particles jiggling.
The great discovery of the 1840s, made by Joule and several others at about the same time, is called the conservation of energy: energy is never created or destroyed. It only changes from one form to another. The horses’ muscles became the drill’s motion became jiggling metal atoms became boiling water.
Step 2: what heat really is
Now we can say what caloric really was. When something is hot, its particles are jiggling fast. When you put a hot cup in cold air, the fast-jiggling particles of the cup bump into slower air molecules and speed them up, and slow down themselves. That flow of jiggling from hot to cold is heat. There is no fluid. There is only motion, passed on by collisions.
How much energy to make a cup of chai? Warming 250 g of water from 25 °C to 100 °C:
Each gram needs about 4.18 joules for each degree. The water warms by 75 degrees.
Energy = 250 × 4.18 × 75 ≈ 78,000 joules, or 78 kilojoules.
Compare Joule’s falling weight: to warm a kilogram of water by just one degree, a kilogram weight would have to fall about 427 metres, higher than most skyscrapers.
Step 3: chemical reactions and heat
When a reaction gives energy out to its surroundings, they warm up: the reaction is exothermic (“heat out”). Burning gas, a hand-warmer and your own breathing are exothermic. When a reaction takes energy in from its surroundings, they cool down: it is endothermic (“heat in”). An instant cold pack is endothermic. In both cases, Joule’s rule holds: whatever energy the chemicals lose, the surroundings gain, and the other way round. Chapter 5 shows where that energy comes from: the breaking and making of bonds.
Exothermic and endothermic changes as energy diagrams. Whatever energy the chemicals lose, the surroundings gain, and the other way round: energy is never lost.
Careful
“Cold is a thing that flows into your hand when you touch ice.”
There is no such thing as “cold” flowing. Energy flows out of your warm hand into the ice. Your hand loses jiggling, so it feels cold. Heat always flows from hotter to colder, never the other way by itself.
A rubber band thermometer and a cooling fizz
Take a thick rubber band, hold it against your top lip (which is very sensitive to temperature), and stretch it quickly: it feels warm. Hold it stretched for a few seconds, then let it go back quickly while touching your lip: it feels cool. Stretching does work on the rubber, and some of that work becomes heat. Then, with a kitchen thermometer, measure the temperature of a few tablespoons of vinegar in a cup, stir in a teaspoon of baking soda, and measure again as it fizzes: the temperature drops by a few degrees. That reaction is endothermic: it takes energy from the liquid around it.
From a guinea pig in ice to a paddle wheel in a brewery, the answer was the same: heat is motion, and energy is never lost. Every energy diagram in this book is an account book that Joule would have recognised.
1799 to 1884
The lakes of Egypt and the balance that never stops
Claude-Louis Berthollet, Cato Guldberg, Peter Waage, Henry Le Châtelier
The Natron Lakes, west of the Nile, 1799
In 1798 Napoleon Bonaparte invaded Egypt, and he brought along not only soldiers but more than a hundred scientists, engineers and artists. One of them was Claude-Louis Berthollet, one of the best chemists in France. In the desert west of the Nile he visited a string of salty lakes, still called the Natron Lakes today, and saw something that puzzled him: a white crust of soda (sodium carbonate, used for centuries to make glass and soap, and by the ancient Egyptians to preserve mummies) forming around their shores.
What puzzled him was this. In the laboratory, everyone knew a reliable reaction: mix soda with calcium chloride and you get chalky calcium carbonate and common salt. It went one way, and only one way, or so chemists thought. But around these lakes there was plenty of common salt and plenty of limestone (calcium carbonate) in the rock. And there, in the desert, soda was being made from them. The laboratory reaction seemed to be running backwards.
Berthollet’s big idea
Berthollet’s explanation was bold. Chemists of his time believed each substance had a fixed “preference” for others, so a reaction always went the same way. Berthollet argued instead that reactions can go both ways, and that which way they actually go depends on the conditions, especially how much of each substance is around. In the lakes there was a huge amount of salt, enough to push the reaction backwards. He published his ideas in 1803. Geologists today think the full story of how those lakes make soda is more complicated, but Berthollet’s central insight, that chemical reactions are reversible, was right, and it changed chemistry.
The Norwegians who did the sums
Christiania (now Oslo), 1864
Sixty years later, two Norwegian chemists who were also brothers-in-law, Cato Guldberg and Peter Waage, turned Berthollet’s idea into mathematics. They measured how far reactions went with different amounts of chemicals, and reasoned about how fast they must run forwards and backwards, and found a simple rule: the more crowded a substance is, the faster it reacts, because its particles meet their partners more often. Put a forward reaction and a backward reaction in the same container, each speeding up or slowing down with how much of its starting material is present, and something remarkable happens.
Step 1: the escalator picture
Imagine two escalators between the ground floor and the first floor of a shopping mall, one going up and one going down. Lots of people start on the ground floor, and nobody upstairs. At first, crowds ride up and hardly anyone rides down. But as people collect upstairs, more of them wander onto the down escalator. Eventually the number riding up each minute equals the number riding down. From then on, the number of people on each floor stays the same, even though people never stop moving.
That is a dynamic equilibrium: two opposite changes happening at the same rate, so the totals stop changing while the particles keep on changing. The word “equilibrium” means balance; “dynamic” means it is a moving balance, not a stopped one.
A reversible reaction A ⇌ B settling down. At first A turns into B quickly; as B builds up, more turns back. The amounts level off, but the reactions never stop.
Step 2: unequal amounts, equal rates
Here is the part people often get wrong. At equilibrium, the rates are equal, but the amounts usually are not.
In Chapter 5’s made-up reaction, each A turns into B at a rate set by 2 (per second), and each B turns back at a rate set by 1.
For the two rates to match, there must be twice as much B as A: 2 × (amount of A) = 1 × (amount of B).
Starting with 10 units of A, it settles at about 3.33 units of A and 6.67 units of B.
Check the rates: 2 × 3.33 = 6.67 and 1 × 6.67 = 6.67. Equal. The amounts are not.
Step 3: push it, and it pushes back
Paris, 1884
The French chemist Henry Le Châtelier noticed a pattern in how equilibrium mixtures respond when you disturb them. Add more of one ingredient, and the mixture shifts to use some of it up. Take a product away, and the mixture shifts to make more. Squeeze a mixture of gases, and it shifts towards the side with fewer gas molecules. Warm it, and it shifts in the direction that absorbs heat.
This pattern, Le Châtelier’s principle, is not because the mixture “wants” to resist you. It follows from the rates. Add more A, and the forward reaction speeds up (more A particles bumping into each other), while the backward one has not changed yet. So more A turns into B than the other way, until the two rates match again. Chapter 5’s live figure lets you watch it happen.
Careful
“At equilibrium, the reaction has stopped.”
It looks stopped, because the amounts stay the same. But both reactions are still going, at equal speeds. Chemists proved it in the twentieth century by adding a few atoms of a slightly heavier isotope to a mixture already at equilibrium: soon the heavy atoms turned up in both the reactants and the products, which could only happen if the reactions were still running both ways.
A fizzy-drink equilibrium
In a sealed bottle of soda water, carbon dioxide gas above the liquid and carbon dioxide dissolved in it are in equilibrium: molecules leave the water and dissolve back at equal rates. Open the bottle and you remove the gas above, so the balance shifts: dissolved gas comes out as bubbles. Try it with two unopened bottles, one from the fridge and one that has sat in a warm room for a few hours. Open them slowly over a sink, with an adult. The warm one fizzes much more, because less gas can stay dissolved in warm water: warming shifts the balance towards the gas.
Berthollet’s lakes, Guldberg and Waage’s sums and Le Châtelier’s rule all say the same thing: most chemical change is a two-way street, and the traffic never stops. In the story of Fritz Haber, a chemist uses exactly these ideas to feed half the world.
1898 to 1913
Bread from air
William Crookes, Fritz Haber, Robert Le Rossignol, Carl Bosch, Alwin Mittasch, Clara Immerwahr
Bristol, England, 1898
A famous scientist, Sir William Crookes, stands up to give the most important speech of the year to Britain’s scientists, and he gives them a fright. The world’s population is growing fast, he says, and so is its hunger for wheat. Wheat needs nitrogen, and the soil runs out of it. The farms of Europe and America are being kept going with nitrogen dug out of the ground on the other side of the world: piles of seabird droppings, called guano, from islands off Peru, and a salty mineral, Chile saltpetre, from the Atacama desert. Those supplies, Crookes warns, will run out within a few decades. Unless chemists find another source, the world faces hunger.
Then he points out something maddening. Every breath you take is about four-fifths nitrogen. There is unimaginably more of it in the air than any farm could ever need. The problem is that plants cannot use it.
Why air nitrogen is so hard to use
Nitrogen in the air is made of N₂ molecules: two nitrogen atoms joined by a triple bond, one of the strongest bonds in chemistry. Plants (and you) need nitrogen to build proteins and DNA, but only in forms where that triple bond has already been broken, such as ammonia, NH₃, or the nitrates made from it. A few bacteria, and lightning, can break the bond. Humans could not, at least not cheaply.
The table-top in Karlsruhe
Karlsruhe, Germany, 1909
The German chemist Fritz Haber decided to try the most direct route of all: join nitrogen straight onto hydrogen.
N₂ + 3 H₂ ⇌ 2 NH₃
That double arrow is the whole difficulty. The reaction is reversible: ammonia breaks back down into nitrogen and hydrogen as well as forming. Haber used everything the equilibrium story teaches. The forward reaction turns four gas molecules into two, so squeezing the gases hard pushes the balance towards ammonia: Haber worked at about 200 times normal air pressure. The forward reaction also gives out heat, so a cooler mixture gives more ammonia at equilibrium; but a cooler mixture reacts too slowly to be useful. So he compromised on a few hundred degrees, and added a catalyst (the rare metal osmium) to make the reaction fast enough. He also kept removing the ammonia as it formed, so the mixture kept making more.
With his assistant Robert Le Rossignol, a young Englishman who was brilliant at building high-pressure equipment, Haber built a machine about the size of a kitchen table. In July 1909 it produced a slow, steady trickle of liquid ammonia from air and hydrogen, and it kept on running.
From table-top to factory
A table-top machine is not a factory. The chemical company BASF gave the job to an engineer, Carl Bosch, who had to solve problems nobody had faced before. Hot hydrogen at enormous pressure soaked into steel and made it brittle, so the first reactors cracked; Bosch designed a steel tube with a soft-iron lining to protect it. Osmium was far too rare, so his colleague Alwin Mittasch tested thousands of possible catalysts, in many thousands of experiments, and settled on a cheap one based on iron. In 1913 the first factory opened at Oppau. The Haber–Bosch process, as it is called, had begun.
Step 1: why it matters so much
Today the world makes well over a hundred million tonnes of ammonia every year, most of it turned into fertiliser. In India, much of it becomes urea, the white granules scattered on fields of rice and wheat. Researchers estimate that about half the people alive today are fed by crops grown with fertiliser from this one reaction, and that roughly half the nitrogen atoms in your own body first passed through a Haber–Bosch factory. Chemistry, quite literally, made bread from air.
Step 2: the chemistry, step by step
Nitrogen comes from the air; hydrogen today comes mostly from natural gas.
The gases are squeezed to a couple of hundred times atmospheric pressure, because four molecules (N₂ + 3 H₂) become two (2 NH₃): squeezing favours fewer molecules.
They are heated to about 400 to 450 °C: hot enough to be fast, not so hot that the balance swings back to nitrogen and hydrogen.
An iron catalyst lowers the energy hill so the reaction is quick.
The ammonia is cooled until it turns liquid and is taken away; the leftover gases go round again.
The other side of the story
Fritz Haber’s story does not end happily, and it would not be honest to pretend it does. When the First World War began in 1914, Haber put his skills to work for Germany’s army. He led the development of poison gas, and on 22 April 1915, near the town of Ypres in Belgium, chlorine gas was released against enemy soldiers for the first time. Thousands were killed or injured. Haber’s wife, Clara Immerwahr, was herself a talented chemist, the first woman to earn a doctorate at the University of Breslau, and she is said to have opposed his work on gas. She died just days after that first attack, a tragedy historians still write about.
Haber received the Nobel Prize in Chemistry for making ammonia, and many scientists protested. In 1933, after the Nazis came to power and ordered him to dismiss his Jewish staff, he resigned from his own institute; he had been born Jewish himself. He left Germany and died the following year in Switzerland.
Haber’s life shows something worth remembering. Chemistry is knowledge, and knowledge can be used to feed people or to hurt them. The same man did both. What science is used for is always a choice made by people, and that is why scientists, and everyone else, have to care about how it is used.
Careful
“The Haber process turns all the nitrogen and hydrogen into ammonia.”
It cannot: the reaction is an equilibrium, so at any moment some ammonia is breaking down again. In one pass through the reactor only a modest fraction becomes ammonia. That is why the factory takes the ammonia out and sends the unreacted gases round again and again.
Nitrogen you can see
Plants show you when they are short of nitrogen: their older leaves turn pale yellow. If you have two pots of the same small plant (or can sprout two pots of mung beans), water one with plain water and the other with water containing a tiny pinch of houseplant fertiliser (follow the packet, ask an adult, and wash your hands afterwards). Over two or three weeks, compare the colour and growth. The nitrogen in that fertiliser was almost certainly pulled out of the air by the reaction in this story.
The next time you eat a chapati, think of the triple bond in N₂, Haber’s table-top, and Bosch’s giant reactors: some of the nitrogen in that wheat was air not so long ago.
AL
Antoine and Marie-Anne Lavoisier
The man who weighed everything
1743 to 1794The tax collector who weighed everything, and the artist who recorded it
Paris, 1774
In his laboratory in Paris, a tax official spends his early mornings and his evenings doing something odd for a rich man: weighing things. Antoine Lavoisier owns the finest balances in Europe, accurate enough to notice a few hundredths of a gram, and he uses them on everything. Beside him works his wife, Marie-Anne Paulze Lavoisier. She keeps the laboratory notebooks, draws the apparatus so well that her pictures are still printed in history books, and learns English so she can read what chemists in Britain are writing. Together they are about to overturn the most popular idea in chemistry.
The puzzle of burning
When wood burns, most of it seems to disappear: a heavy log becomes a little grey ash. So the chemists of the 1700s had a sensible-sounding explanation. Anything that can burn, they said, contains a fiery substance called phlogiston (from the Greek for “burned”). Burning is phlogiston escaping into the air. Wood is full of it, so wood burns well and leaves a light ash behind. Air can only soak up so much phlogiston, which is why a candle in a closed jar goes out.
It was a clever theory, and it explained a lot. But there was an awkward fact. When metals are heated in air, they slowly turn into a powdery crust that chemists called a calx (we would say an oxide). And the calx weighs more than the metal did. If phlogiston was leaving, why did the metal get heavier? Some chemists suggested phlogiston must have negative weight. Lavoisier thought that was nonsense. He suspected something was not leaving at all, but arriving, from the air.
Two discoveries of the same gas
The answer was found by two other men, at almost the same time, without knowing about each other. In Sweden, the pharmacist Carl Wilhelm Scheele heated several substances and collected a gas in which a candle burned brilliantly. He called it “fire air”. He found it first, around 1771 or 1772, but his book about it was delayed at the printer and only came out in 1777.
In England, the minister and chemist Joseph Priestley used a large magnifying lens to focus sunlight onto the red calx of mercury, on 1 August 1774. A gas came off. A candle in it burned with a dazzling flame, and a mouse sealed in a jar of it stayed lively far longer than in ordinary air. Priestley, a firm believer in phlogiston, called it “dephlogisticated air”: air with no phlogiston in it, so hungry for more that things burned fiercely.
That autumn Priestley visited Paris and told Lavoisier about his experiment over dinner. Lavoisier understood at once what Priestley had missed.
The sealed-vessel experiments
Lavoisier repeated the work with his balances, and he did one thing that made all the difference: he kept everything sealed. In one famous experiment he heated mercury in a closed flask connected to a measured volume of air, for twelve days. A red crust slowly grew on the mercury, and the air shrank by about a sixth. The air that was left would not let a candle burn or a mouse breathe. Then he heated the red crust strongly on its own, and out came almost exactly the amount of gas the air had lost: Priestley’s gas.
So burning and rusting are not something leaving. They are something joining: a part of the air combining with the metal. Lavoisier named that part oxygen in 1777. (He chose a Greek name meaning “acid-maker”, because he thought every acid contained it. That part turned out to be wrong, as you will find in Chapter 7, but the name stuck.) Combustion, burning, is a substance combining rapidly with oxygen.
Step 1: why weighing settles the argument
Here is the reasoning, slowly. Suppose you burn 2.4 grams of magnesium ribbon in air. It flares white and leaves a white powder.
Phlogiston says: the magnesium loses its phlogiston, so the powder should weigh less than 2.4 g.
The balance says: the white powder weighs about 4.0 g. It got heavier, by about 1.6 g.
Where did 1.6 g come from? From the air: 1.6 g of oxygen joined the magnesium to make magnesium oxide.
Check with atoms: 2.4 g of magnesium is 0.1 mol; it joins 0.1 mol of oxygen atoms, 1.6 g; together 4.0 g.
And the burning log? It gets lighter only because most of what it turns into, carbon dioxide and water vapour, are gases that float away. Burn it in a sealed container and weigh the whole thing, and the total does not change.
Step 2: the law
In 1789 Lavoisier published his great book, the Elementary Treatise of Chemistry. In it he set out the idea that runs through every chapter of this one: in a chemical change, matter is neither created nor destroyed. The total mass after a reaction is the same as the total mass before. We call this the conservation of mass. Today we can say why it is true: chemical reactions only rearrange atoms, and every atom that goes in comes out.
Careful
“Burning destroys things, so burning must lose mass.”
Burning changes things into new substances, often gases you cannot see. If you catch everything, gases included, the total mass stays the same. A candle seems to vanish only because its wax becomes carbon dioxide and water vapour that drift away.
The bag that does not get lighter
You need a zip-lock sandwich bag, a teaspoon of baking soda, a few tablespoons of vinegar and a kitchen scale. Wrap the baking soda in a small piece of tissue and put it in one corner of the bag. Pour the vinegar into the other corner, keeping them apart, squeeze out most of the air and seal the bag firmly. Weigh the bag. Now tip it so the vinegar soaks the tissue: the mixture fizzes and the bag puffs up with carbon dioxide. Weigh it again: the same. Finally open the bag, let the gas escape and weigh once more: now it is lighter, because the gas has left. Lavoisier’s whole argument, on your kitchen table. (Use small amounts so the bag does not burst.)
A sad ending
Lavoisier’s day job was collecting taxes for the king, as a member of a private company called the General Farm, which was hated by ordinary people. During the French Revolution the tax collectors were arrested, and on 8 May 1794 Lavoisier was executed by guillotine, aged 50. The mathematician Joseph-Louis Lagrange is said to have remarked that it took only a moment to cut off that head, and a hundred years might not produce another like it. Marie-Anne survived, lost almost everything, and spent years afterwards making sure her husband’s work was published and remembered.
Every time this book asks you to count the atoms on both sides of an equation, you are using the idea the Lavoisiers proved with their balance: nothing is lost, it only changes partners.
1808 to 1813
Letters for atoms: the language of chemistry
John Dalton, Jöns Jacob Berzelius
Stockholm, 1813
Imagine trying to write down a recipe in which every ingredient has a different secret picture, and every cook uses different pictures. That was chemistry for most of its history. Then, in 1813, a Swedish chemist named Jöns Jacob Berzelius suggested something so simple that it seems obvious now: use letters. This is the story of how chemistry got its alphabet.
Secret signs
The alchemists of the Middle Ages, who hoped to turn ordinary metals into gold, wrote with symbols borrowed from astronomy. Gold was a circle with a dot in the middle, the sign of the Sun. Silver was a crescent Moon. Mercury, the liquid metal, shared its sign with the planet Mercury. Many of these signs were meant to be mysterious. Alchemists often wanted to keep their methods secret, and a recipe nobody else can read is a recipe nobody else can steal.
That was fine for secrets, and hopeless for science. Science only works when other people can read exactly what you did and repeat it.
Dalton’s circles
In 1808 John Dalton, the Manchester schoolteacher who brought back the idea of atoms, drew each element as a little circle with its own marking. Hydrogen was a circle with a dot in the centre. Oxygen was a plain empty circle. Carbon was a circle filled in black. Nitrogen had a line down the middle. To show a compound, he put circles side by side, so water was a dotted circle next to an empty one.
It was a big step: for the first time, a symbol meant one atom. But Dalton’s circles were hard to print, easy to confuse, and impossible to type. Imagine writing out sugar, which has 45 atoms, as 45 little circles.
Berzelius’s letters
Berzelius was one of the most careful chemists who ever lived. Over about ten years he analysed some two thousand compounds and worked out the relative weights of the elements far more accurately than anyone before. He needed a quick way to write what he found, and in 1813 he proposed one: use the first letter of each element’s name, in capitals, adding a second small letter when two elements start with the same letter.
He used the elements’ Latin names, which every educated European could read. That is why some symbols puzzle English speakers today:
Symbol
Element
Latin name
Na
sodium
natrium
K
potassium
kalium
Fe
iron
ferrum
Cu
copper
cuprum
Ag
silver
argentum
Au
gold
aurum
Pb
lead
plumbum (which also gives us the word “plumber”, because pipes were once made of lead)
Hg
mercury
hydrargyrum, “liquid silver”
To show how many atoms of each kind a compound contained, Berzelius wrote a small number after the symbol. He wrote it raised up, like H²O; later the custom changed to writing it low, H₂O, which is how the whole world writes it today. Dalton never liked the letters, and kept drawing his circles. But the letters won, because anyone can write them with a pen, print them in a book or type them on a keyboard.
Step 1: reading a chemical formula
A chemical formula is a list of the atoms in one molecule (or, for a crystal like salt, the ratio of atoms). Read it like this:
H₂O: two hydrogen atoms (the small 2 belongs to the H just before it) and one oxygen atom (no number means 1).
CO₂: one carbon, two oxygens.
C₁₂H₂₂O₁₁ (table sugar): 12 carbons, 22 hydrogens, 11 oxygens: 45 atoms in every molecule.
Mg(OH)₂: brackets group atoms together, and the 2 after the bracket doubles everything inside. So: 1 magnesium, 2 oxygens, 2 hydrogens.
Step 2: the big number in front
A number written full-size in front of a formula counts whole molecules. 3 CO₂ means three separate carbon dioxide molecules: 3 carbons and 6 oxygens in all. That is completely different from changing the small number inside: CO₂ is carbon dioxide, which you breathe out; CO is carbon monoxide, a poison. The small numbers say what the substance is. The big number says how many of it you have.
Step 3: sentences made of formulas
Put formulas together with a plus sign and an arrow and you have a chemical equation, a sentence describing a reaction:
2 H₂ + O₂ → 2 H₂O
Read it aloud: “two hydrogen molecules and one oxygen molecule react to make two water molecules.” Count the atoms on each side: 4 hydrogens and 2 oxygens on the left, 4 hydrogens and 2 oxygens on the right. Lavoisier’s law, that nothing is lost, becomes a rule you can check with your finger: every kind of atom must balance.
Careful
“To balance an equation, I can change H₂O into H₂O₂.”
Never change the small numbers. H₂O₂ is hydrogen peroxide, a completely different substance. You may only change the big numbers in front, which decide how many molecules take part.
Spell with the elements
Find a periodic table (there is one on the cover of this book) and try to spell words using only element symbols. “Bacon” works: Ba, C, O, N. So does “Amar”: Am (americium) and Ar (argon). Which names in your family can you spell? Which letters of the alphabet never appear in any symbol? (There are two: J and Q. Try spelling “jam” or “queen”.)
Every formula and equation in this book is written in Berzelius’s alphabet: a language shared by every chemist on Earth, in every country, which a twelve-year-old in Mumbai and a professor in Stockholm can read in exactly the same way.
1773 to 2019
How big is Avogadro's number?
Benjamin Franklin, Josef Loschmidt, Jean Perrin, Robert Millikan
Clapham Common, London, 1773
On a windy day the American inventor Benjamin Franklin, who was living in London, carried a little cruet of oil down to a pond on Clapham Common. The wind was whipping up small waves. He poured out no more than a teaspoon of oil onto the water, and watched something remarkable happen. The oil spread, and spread, and kept spreading, until it covered about half an acre of the pond: roughly the area of eight tennis courts. Where it had spread, the waves went flat, “as smooth as a looking glass”, he wrote.
Franklin did not do the sum that was hiding in his experiment. More than a hundred years later, the English physicist Lord Rayleigh did it, with his own careful measurements of oil on water. It is the first clue in our story.
Step 1: how thin can oil get?
If a teaspoon of oil spreads into a film, the film’s thickness is just its volume divided by its area. Let us do it with Franklin’s numbers.
A teaspoon holds about 5 millilitres = 0.000 005 cubic metres (5 × 10⁻⁶ m³).
Half an acre is about 2,000 square metres.
Thickness = volume ÷ area = 5 × 10⁻⁶ ÷ 2,000 ≈ 2.5 × 10⁻⁹ m, about 2.5 nanometres.
The oil cannot spread any thinner than a single layer of its molecules. So an oil molecule can be no more than about 2.5 nanometres long: two and a half millionths of a millimetre. For the first time, a kitchen-sized experiment had put a ceiling on the size of a molecule.
Step 2: from size to number
If you know roughly how big a molecule is, you can estimate how many there are in a given amount. In 1865 the Austrian scientist Josef Loschmidt did exactly that for the molecules in air, using measurements of how fast gases spread and how much they shrink when turned into liquid. His answer for the number in a mole was rough, but it was in the right neighbourhood. For the first time, somebody had put an actual number on the invisible.
Step 3: many roads, one answer
The real proof came early in the twentieth century, when scientists found completely different ways of measuring the same number, and they all agreed.
Jiggling grains (around 1908).Jean Perrin in Paris watched tiny grains of resin bobbing about in water, shoved this way and that by invisible water molecules. From how far they wandered, using a formula that Albert Einstein had worked out in 1905, he could work out how many molecules there must be in a mole. He got roughly 6 to 7 × 10²³.
Charge (1909 onwards). The American physicist Robert Millikan measured the electric charge on a single electron by watching tiny oil droplets float between charged metal plates. Chemists already knew how much charge it takes to deposit one mole of silver in electrolysis: about 96,485 units, called coulombs. Divide the charge for a mole by the charge for one electron, and you get the number of electrons in a mole:
Crystals (from the 1910s). X-rays could measure the exact spacing between atoms in a crystal. Knowing the spacing, you can count how many atoms fit in a given lump.
Perrin listed more than a dozen independent methods, and they all landed near the same value. That, more than anything, convinced the last doubters that atoms were real. Perrin proposed calling the number after Amedeo Avogadro, and in 1926 he won the Nobel Prize for this work.
Step 4: the most perfect sphere in the world
In the 2000s, scientists from many countries joined a project to measure the number better than ever before. They made spheres of almost pure silicon-28, each with a mass of about 1 kilogram and a diameter of about 9.4 centimetres, polished so perfectly that if one were the size of the Earth, its highest mountain would be only a few metres tall. They measured each sphere’s size with lasers and the spacing of its atoms with X-rays, then simply counted: about 2 × 10²⁵ atoms in each sphere.
Their measurements were so good that in 2019 the world agreed to stop measuring and fix the number exactly:
Here is the honest truth: nobody can picture 6 × 10²³. But you can compare it with other huge things, and feel your way.
A glass of water and the oceans. A 250 mL glass of water holds about 8 × 10²⁴ water molecules. All the oceans on Earth together hold about 5 × 10²¹ glassfuls of water.
So one glass of water contains more than 1,500 times as many molecules as there are glasses of water in all the oceans.
Marbles. If you had a mole of marbles, each 1 centimetre across, and spread them evenly over the whole surface of the Earth, land and sea, they would make a layer nearly a kilometre deep.
Sand. One careful estimate puts the number of grains of sand on all of Earth’s beaches at around 7 or 8 × 10¹⁸. A mole is about 80,000 times more than that.
And yet a mole of water is about 18 grams: one gulp. Your gulp holds more molecules than there are sand grains on all the world’s beaches, many thousands of times over. That tells you, more vividly than any number, how tiny a molecule is.
Careful
“Avogadro’s number is just a very big number that someone chose.”
It is two things at once. Since 2019 its exact value is fixed by agreement, like the number of centimetres in a metre. But that value was not picked out of the air: it was chosen to match more than a century of measurements, so that a mole of carbon-12 atoms still has a mass of 12 grams (to within a tiny fraction of a millionth). The mole story shows why that matching matters.
Measure a molecule-thin layer, almost
Ask an adult to help. Fill a large, clean baking tray with water and sprinkle a very light dusting of ground black pepper over the surface. Dip the tip of a toothpick in a drop of washing-up liquid or cooking oil and touch it to the centre. Watch how far the pepper races away from such a tiny amount. Thin films spread enormously, which is exactly what let Franklin, and later Rayleigh, use them to measure molecules.
So when this book writes 6.022 × 10²³, remember a teaspoon of oil on a windy pond, a dozen different experiments all agreeing, and a silicon sphere polished almost perfectly round. That is how we know.
1811 to 1860
The forgotten idea: Avogadro, and the congress that found him again
Joseph Louis Gay-Lussac, John Dalton, Amedeo Avogadro, Stanislao Cannizzaro, Lothar Meyer
Paris, 1808
Joseph Louis Gay-Lussac liked gases, and he liked measuring them. (He also liked danger: a few years earlier he had gone up alone in a hydrogen balloon to about 7,000 metres, higher than anyone had flown, to collect air samples.) Back on the ground, he noticed something strange about how gases react.
Mix hydrogen and oxygen and spark them, and they always combine in a neat ratio by volume: 2 litres of hydrogen to 1 litre of oxygen. Nitrogen and hydrogen make ammonia in the ratio 1 litre to 3. And the steam that comes out also has a simple volume: 2 litres of hydrogen plus 1 litre of oxygen give 2 litres of steam (measured hot, at the same pressure). Whole numbers, every time. Why should gases care about whole numbers?
Step 1: the puzzle with the volumes
John Dalton, in England, had just argued that elements are made of atoms. You might think he would be delighted by Gay-Lussac’s whole numbers. He was not. He thought the result was impossible, and here is why.
If a litre of hydrogen contains some number of hydrogen atoms, and a litre of oxygen contains the same number of oxygen atoms, then 2 litres of hydrogen and 1 litre of oxygen should make 1 litre of water particles (each made from two hydrogen atoms and one oxygen atom). But the experiment gave 2 litres of steam. To get twice as many water particles as there were oxygen atoms, every oxygen atom would have to split in half. And atoms, by definition, cannot be split. Dalton decided Gay-Lussac’s measurements must be wrong. They were not.
Vercelli, near Turin, 1811
Amedeo Avogadro had trained as a lawyer, like his father, before falling in love with physics. In 1811 he was teaching natural philosophy at a college in the small town of Vercelli (he later became a professor in Turin). He read both men’s work and saw a way out that neither had seen. He made two bold guesses.
Guess one: equal volumes of any gases, at the same temperature and pressure, contain the same number of particles. (This is Avogadro’s hypothesis.)
Guess two: the particles of hydrogen gas and oxygen gas are not single atoms. Each is a pair of atoms stuck together: what we now write as H₂ and O₂.
Step 2: why the guesses solve the puzzle
Let us walk through it with small numbers, pretending each litre holds just 10 particles.
2 litres of hydrogen = 20 particles of H₂ = 40 hydrogen atoms
1 litre of oxygen = 10 particles of O₂ = 20 oxygen atoms
Each water molecule, H₂O, needs 2 hydrogen atoms and 1 oxygen atom.
40 hydrogen atoms and 20 oxygen atoms make exactly 20 water molecules.
20 particles of steam take up 2 litres. That is exactly what Gay-Lussac measured.
No atom splits. What splits is the pair: each O₂ molecule breaks into two O atoms, and each goes into a different water molecule. Avogadro had invented the word for the pairs too, more or less: he called them “constituent molecules”. Today we write the reaction as 2 H₂ + O₂ → 2 H₂O, and its numbers, 2 : 1 : 2, are exactly the volumes Gay-Lussac saw.
Step 3: fifty years of silence
Avogadro published his idea in 1811. It was correct, and it explained the measurements perfectly. And for half a century, almost everyone ignored it.
Why? Partly because it sounded wrong to the chemists of the day. Many of them believed that atoms of the same element repel each other, so two hydrogen atoms could never stick together into H₂. Partly because Avogadro wrote in a cautious, mathematical way, far from the big laboratories of Paris and London. And partly because without his idea, chemists could not agree on the formula of anything. Was water HO or H₂O? Different books gave different answers, and the same formula could mean different substances in different countries. In 1861 the chemist August Kekulé printed a list of nineteen different formulas that people had proposed for acetic acid, the acid in vinegar.
Avogadro died in 1856. He never knew that he had been right.
Karlsruhe, Germany, September 1860
The confusion became so bad that about 140 chemists from all over Europe met in the town of Karlsruhe for the first international chemistry conference, to try to agree on what atoms and molecules even were. For three days they argued, and they did not agree.
But one of them, the Italian chemist Stanislao Cannizzaro, had written a short pamphlet two years earlier. It showed, clearly and simply, how Avogadro’s forgotten hypothesis sorted out everything: how to work out the true formulas of gases, and from them the true relative masses of atoms. As the meeting broke up, a friend of Cannizzaro’s handed out copies.
A young German chemist named Lothar Meyer put one in his pocket and read it on the journey home. He later wrote that it was as if the scales fell from his eyes: suddenly everything was clear. Within a few years, with Cannizzaro’s corrected atomic masses, Meyer and the Russian chemist Dmitri Mendeleev were each building tables of the elements that would become the periodic table.
Step 4: what the idea gives us today
Avogadro’s hypothesis is why we know H₂ and O₂ are pairs. It is why chemists could finally agree on formulas like H₂O and CO₂, and so on atomic masses. And because equal volumes of gases hold equal numbers of particles, it led straight to the idea of a fixed number of particles for counting: the mole. The enormous number in a mole is named in his honour, though Avogadro himself never knew how big it was. That number has a story of its own.
Careful
“Avogadro worked out Avogadro’s number.”
He did not. Avogadro only said that the number of particles in a given volume of gas is the same for every gas. How many particles that actually is was first estimated by Josef Loschmidt in 1865, nine years after Avogadro died, and the name “Avogadro’s number” was suggested by Jean Perrin around 1909.
A volume puzzle with balloons
Ask an adult to help. Put two level teaspoons of baking soda into a balloon using a funnel. Pour some vinegar into an empty plastic bottle, stretch the balloon over its neck, then lift the balloon so the powder falls in. The fizzing makes a gas, carbon dioxide, which fills the balloon. Try again with twice the vinegar and twice the soda: does the balloon get about twice as big? Gases from reactions come in amounts you can measure by volume, just as Gay-Lussac found.
So the next time you see Avogadro’s name in this book, remember a patient Italian professor who solved a puzzle in 1811, and a pamphlet read on a train in 1860 that finally made the world listen.
1971
How strong is your sharbat? Concentration, step by step
Dilip Mahalanabis
A refugee camp at Bangaon, West Bengal, 1971
In 1971, during the war that created Bangladesh, millions of people fled across the border into India. In the crowded camps near the border, cholera broke out. Cholera kills by draining water and salt out of the body through terrible diarrhoea. The usual treatment was a drip of salt solution straight into a vein, but there were far too few drips, needles and nurses for so many sick people.
A young Indian doctor, Dilip Mahalanabis, decided to try something that had only just been tested in hospitals: a drink. Not any drink, but water with salt and sugar dissolved in it in exactly the right amounts, so that the gut could soak up the water. Families could give it to their own children with a cup. In his camp, the share of cholera patients who died is reported to have fallen from around 30 in every 100, as in camps without enough treatment, to fewer than 4 in every 100. That drink, oral rehydration solution or ORS, has since saved tens of millions of lives around the world. And the secret of it is one word: concentration.
Step 1: strong and weak
You already know what concentration means; you just may not have the word yet. A glass of sharbat made with lots of syrup is “strong”. With a splash of syrup and a lot of water, it is “weak”. The syrup is the solute (the thing dissolved) and the water is the solvent (the thing it dissolves in).
But “strong” and “weak” are not good enough for a doctor. Too little salt in ORS and it does not work; too much, and it can pull water the wrong way and make things worse. You need a number.
Step 2: how much in each litre
The trick is to ask how much solute there is in each litre of the finished drink. That number does not depend on how big the jug is.
2 spoons of syrup in 1 litre: 2 spoons per litre.
4 spoons of syrup in 2 litres: still 2 spoons per litre. Same strength, more drink.
2 spoons of syrup in 2 litres: 1 spoon per litre. Half the strength.
Chemists do exactly the same, but instead of spoons they count moles of particles. Concentration is written in moles per litre, mol/L:
concentration = amount of solute (in moles) ÷ volume of solution (in litres)
Step 3: a real recipe
The World Health Organization’s ORS recipe for one litre of water includes 2.6 grams of table salt (sodium chloride) and 13.5 grams of glucose. Let us turn those into concentrations.
Salt, NaCl, has a molar mass of about 58.4 g per mole.
2.6 g ÷ 58.4 g/mol ≈ 0.045 mol in 1 litre, so 0.045 mol/L of salt.
Glucose, C₆H₁₂O₆, has a molar mass of about 180 g per mole.
13.5 g ÷ 180 g/mol ≈ 0.075 mol in 1 litre, so 0.075 mol/L of glucose.
(The full recipe also contains a little potassium chloride and sodium citrate, which bring the total sodium up to about 0.075 mol/L, matched to the glucose. The match is the clever part: the gut takes up sodium and glucose together, and water follows them in.)
Please do not mix medicines at home: ORS comes in ready-made packets for a reason. But now you can read the packet like a chemist.
Step 4: watering down, without losing anything
What happens when you add more water? The number of solute particles does not change. They just spread through more liquid. This is dilution.
Start: 0.5 mol of salt in 1 litre: 0.5 mol/L.
Add water until the total is 2 litres. Still 0.5 mol of salt.
New concentration = 0.5 ÷ 2 = 0.25 mol/L. Double the volume, half the concentration.
Notice the word “total”. The volume in the rule is the volume of the finished solution, not the volume of water you poured in. If you dissolve a lot of sugar, the solution takes up more room than the water did.
Careful
“If I pour half the sharbat into another glass, each glass is half as strong.”
No: each glass is exactly as strong as the jug. Pouring some away removes solute and solvent in the same proportion, so the amount per litre stays the same. What changes is the total amount of syrup in each glass. Concentration is about “how crowded”, not “how much altogether”.
Step 5: some concentrations from real life
Seawater: about 0.46 mol of salt per litre (around 27 grams of sodium chloride in each litre).
Your blood: about 0.14 mol of sodium ions per litre.
Two teaspoons of sugar (about 8 g) in a 250 mL cup of chai: about 0.09 mol/L of sugar.
That last one explains why seawater is no use for quenching thirst: it is more than three times as salty as your blood, so drinking it makes your body lose water to get rid of the extra salt.
A dilution staircase
You need five clear glasses, water and food colouring (or strong tea). Put a few drops of colouring in the first glass with 100 mL of water. Pour half of it (50 mL) into the second glass and add 50 mL of water. Pour half of that into the third glass and add 50 mL of water, and so on. Each glass is half as concentrated as the one before. Line them up against a white sheet of paper. Can you still see colour in the fifth glass? It is 16 times more dilute than the first.
So when this book talks about 0.10 mol/L of an acid, picture a jug with a recipe on it: so many moles of particles, crowded into each litre. That one number told a doctor in 1971 exactly how much salt and sugar a drink needed to save a life.
1808 to 2019
The mole, step by step
John Dalton, Wilhelm Ostwald, Jean Perrin
A market street in Mumbai, any morning
Walk through any market and you will see three different ways of counting. The egg seller counts eggs, but in dozens: nobody asks for “fourteen eggs and a bit”. The stationery shop sells paper by the ream, 500 sheets at a time, and nobody counts the sheets. And the rice seller does not count at all. You ask for a kilo, the grains go on the scale, and in a few seconds you have about fifty thousand grains of rice without anyone counting a single one.
That last trick, counting by weighing, is the whole secret of the mole. Chemists had to learn it, because the things they needed to count were far smaller than rice and far, far more numerous. This is the story of how they did it, one step at a time.
Step 1: the problem
By the early 1800s chemists had discovered something wonderful: substances combine in fixed proportions, because atoms combine in small whole numbers. Two hydrogen atoms join one oxygen atom to make water. One carbon atom joins two oxygen atoms to make carbon dioxide. Chemistry happens atom by atom.
But nobody could pick up an atom. In the laboratory you can only weigh things. So the question became: if a recipe says “two hydrogens for every oxygen”, how many grams of hydrogen and how many grams of oxygen do you need? To answer that, you have to know how heavy each kind of atom is, at least compared with the others.
Step 2: weighing atoms against each other
In 1808 an English schoolteacher, John Dalton, published one of the first tables of relative atomic weights. He could not weigh a single atom, but he could compare. If 1 gram of hydrogen combines with 8 grams of oxygen to make water, and each water molecule has two hydrogens for every oxygen, then one oxygen atom must weigh about 16 times as much as one hydrogen atom. (Dalton himself got water’s formula wrong and put oxygen at 7, but his method was right, and later chemists fixed the numbers.)
Repeat that kind of reasoning for every element and you get a list of relative atomic masses: how heavy each atom is compared with the others. Roughly: hydrogen 1, carbon 12, oxygen 16, sodium 23, chlorine 35.5. These numbers have no units. They are comparisons, like saying an elephant is about 70 times as heavy as a person.
Step 3: the trick that makes counting possible
Here is the clever part. Imagine a jar of big glass marbles, each weighing 16 grams, and a jar of small beads, each weighing 1 gram. You want the same number of marbles as beads, but you only have a kitchen scale.
Weigh out 16 g of marbles: that is 1 marble. Weigh out 1 g of beads: that is 1 bead.
Weigh out 1,600 g of marbles: 100 marbles. Weigh out 100 g of beads: 100 beads.
Whatever you choose, if the masses are in the ratio 16 : 1, the numbers are equal.
Atoms work exactly the same way. An oxygen atom is 16 times heavier than a hydrogen atom. So 16 grams of oxygen and 1 gram of hydrogen contain the same number of atoms. So do 12 grams of carbon, 23 grams of sodium and 35.5 grams of chlorine. Take any element, weigh out its relative atomic mass in grams, and you always get the same number of atoms. You do not even need to know what that number is.
That fixed number of atoms is so useful that it needed a name. In the 1890s the German chemist Wilhelm Ostwald gave it one: the Mol, from Molekül, molecule. In English it became the mole. A mole is simply that number of things, just as a dozen is twelve things.
One mole each of three substances: the same number of particles in every pile, but different masses, because the particles themselves have different masses.
Step 4: but how many is it?
For a long time, nobody knew. Chemists used moles happily for decades while having only a rough idea of how many atoms were in one. Think about how odd that is: it is like buying eggs by the dozen without knowing that a dozen is twelve. It worked because, for chemistry, what matters is that the number is the same for every substance.
The first estimate came in 1865 from an Austrian schoolteacher-turned-physicist, Josef Loschmidt, who worked out roughly how big air molecules must be from how gases behave. His answer was in the right range, astonishingly, but rough. Then, around 1909, Jean Perrin in Paris measured the number several independent ways, including by watching tiny grains jiggle in water, and every method gave nearly the same answer. Perrin proposed naming it after Amedeo Avogadro, whose ideas about gases had made all of this possible. Today it is called Avogadro’s constant, and since 2019 it is not measured at all but fixed by definition:
1 mole = 6.022 140 76 × 10²³ things
Step 5: feeling how big that is
Written out in full, that is 602,214,076,000,000,000,000,000. Numbers this big slide straight past the imagination, so here are two ways to get a grip on it.
If you counted one thing every second, day and night, without stopping, counting to one mole would take about 19 thousand million million years: more than a million times the age of the universe.
A grain of rice has a mass of about 0.02 grams. A mole of rice grains would weigh about 12 thousand million million tonnes (1.2 × 10¹⁶ tonnes). The whole world grows roughly 500 million tonnes of rice a year, so growing one mole of rice would take every rice farmer on Earth tens of millions of years.
And yet a mole of water molecules is only 18 grams: a single gulp. That is how small molecules are.
Step 6: using moles, with your hand held
The mass of one mole of a substance is its molar mass, in grams per mole. For an element it is the relative atomic mass in grams; for a molecule you add up its atoms. Water, H₂O, is 1 + 1 + 16 = 18 grams per mole.
How many moles in 9 grams of water?
Each mole is 18 g. 9 g is half of 18 g. So 9 g is 0.5 moles.
As a rule: moles = grams ÷ molar mass = 9 ÷ 18 = 0.5 mol.
How many sugar molecules in a 4-gram teaspoon of sugar?
Sugar (sucrose, C₁₂H₂₂O₁₁) has a molar mass of about 342 g per mole.
Moles = 4 ÷ 342 ≈ 0.0117 mol.
Molecules = 0.0117 × 6.022 × 10²³ ≈ 7 × 10²¹: about seven thousand million million million molecules in one teaspoon.
Understand itMole
What is it?
A counting unit, like a dozen, but holding 6.022 140 76 × 10²³ things. One mole of any substance weighs its formula’s mass in grams.
Why is it called this?
From the German Mol, coined by Wilhelm Ostwald in the 1890s as a short form of Molekül, molecule. Nothing to do with the animal.
What problem did it solve?
Chemists needed to count atoms to follow a recipe, but they could only weigh things. The mole turns weighing into counting.
Why does it work?
Because atoms of different elements have masses in fixed ratios, equal numbers of atoms always have masses in those same ratios. So weighing out each element’s relative mass in grams always gives the same number of atoms.
How does it help?
It lets you go from a recipe in particles (2 H₂ + O₂) to a recipe in grams that you can weigh out on a scale.
Go deeper how do we know, what it isn’t, where does it stop working
How do we know?
Perrin and others measured the number in completely different ways, and all the answers agreed. Since 2019 the number is fixed by definition.
What it isn’t
It is not a mass, like a kilogram. It is a number, like a dozen.
Where does it stop working?
It is a tool for enormous numbers of tiny things. For anything you can count by eye, just count.
Your turn
Explain Mole to a friend in one sentence, in your own words. Then compare it with the book’s.
A counting unit, like a dozen, but holding 6.022 140 76 × 10²³ things. One mole of any substance weighs its formula’s mass in grams.
Careful
“A mole is an amount of mass, like a kilogram.”
It is not. A mole is a number of things, like a dozen. A dozen eggs and a dozen elephants are both twelve, but they do not weigh the same. A mole of hydrogen atoms has a mass of 1 gram; a mole of gold atoms has a mass of 197 grams. Same number, very different weights.
Careful
“A mole of oxygen is 16 grams.”
It depends what you are counting. A mole of oxygen atoms is 16 g. But oxygen gas is made of O₂ molecules, and a mole of O₂molecules is 32 g, because each molecule contains two atoms. Chemists always say what they are counting, and so should you.
Count rice by weighing it
You need a kitchen scale and some uncooked rice. Count out exactly 100 grains and weigh them (a sensitive scale helps; if yours only reads to the nearest gram, weigh 200 or 500 grains). Now weigh a cupful of rice. Divide the cup’s mass by the mass of one grain to find how many grains are in the cup, without counting them. Then count a small part of the cup to check. You have just done what chemists do with moles.
So the next time you see “1 mole” in this book, translate it in your head: six hundred thousand million million million of something, which conveniently weighs its formula’s mass in grams. It is the chemist’s dozen, and it is the bridge between the invisible world of atoms and the kitchen scale on the bench.
1808 to 1961
How do you weigh an atom?
John Dalton, Jöns Jacob Berzelius, Jean Servais Stas
Manchester, 1803
John Dalton was a quiet Quaker schoolteacher who kept a weather diary every single day for over fifty years. He was also colour-blind (the condition was called “Daltonism” after him, because he was the first to describe it scientifically). And in his notebooks in Manchester, around 1803, he did something nobody had dared try. He started to make a list of how heavy atoms are.
He could not weigh one. Nobody could, and nobody would be able to for a long time. So Dalton asked a cleverer question: not “how heavy is an atom?” but “how heavy is one kind of atom compared with another?”
Step 1: comparing, not weighing
Think of a see-saw. You do not need to know anyone’s weight in kilograms to discover that your father is about twice as heavy as you: if he sits half as far from the middle as you do, the see-saw balances. Comparing is often easier than measuring.
Dalton chose the lightest thing he knew, the hydrogen atom, and called its weight 1. Then he looked at compounds. If 1 gram of hydrogen combines with 8 grams of oxygen to make water, and water has one oxygen atom for every two hydrogen atoms, then:
Pretend the sample holds just 10 oxygen atoms. Then it holds 20 hydrogen atoms (two for every oxygen).
20 hydrogen atoms weigh 1 gram, so each hydrogen atom weighs 1 ÷ 20 = 0.05 g (pretend grams).
10 oxygen atoms weigh 8 grams, so each oxygen atom weighs 8 ÷ 10 = 0.8 g.
0.8 ÷ 0.05 = 16. One oxygen atom is 16 times as heavy as one hydrogen atom, whatever the real number of atoms is.
Dalton himself thought water was HO, one of each, so he wrote oxygen as 7 (his measurements were also a little off). The method was brilliant; the formulas were the problem. It took Avogadro’s idea, and the congress at Karlsruhe in 1860, before chemists agreed on formulas and so on the right numbers.
Step 2: arguing about the starting point
If everything is a comparison, you have to choose something to compare with, and chemists argued about this for 150 years.
Dalton said hydrogen = 1.
Berzelius, the great Swedish chemist who measured more atomic weights more carefully than anyone of his time, said oxygen = 100, because oxygen combines with almost everything, which made the measurements easier.
Later chemists, led by the Belgian Jean Servais Stas, whose measurements were famously precise, settled on oxygen = 16, which kept hydrogen close to 1.
Then a new problem appeared. In the 1920s and 1930s physicists discovered that natural oxygen is a mixture of isotopes. Physicists began using one isotope, oxygen-16, as exactly 16; chemists kept using natural oxygen as 16. The two scales differed by about 3 parts in 10,000: tiny, but enough to cause confusion.
In 1961 both sides agreed on a new standard that everybody could use: one atom of carbon-12 counts as exactly 12. The unit this defines is called the unified atomic mass unit, written u, because it unified the two scales. One u is one-twelfth of the mass of a carbon-12 atom.
Step 3: so what does an atom actually weigh?
Once Avogadro’s constant was known, chemists could finally turn comparisons into real masses.
One mole of hydrogen atoms has a mass of about 1.008 g, and contains 6.022 × 10²³ atoms.
Mass of one hydrogen atom = 1.008 ÷ (6.022 × 10²³) ≈ 1.67 × 10⁻²⁴ g.
That is 0.000 000 000 000 000 000 000 001 67 grams. A grain of sugar has more than a hundred million million million times that mass.
Step 4: why the numbers are not whole
Look at a periodic table and you see numbers like chlorine 35.45 and copper 63.55. If atoms are built from protons and neutrons, each with a mass close to 1 u, why are these not whole numbers? There are two reasons, one big and one small.
The big reason: mixtures. Natural chlorine is about three-quarters chlorine-35 and one-quarter chlorine-37. The periodic table gives the average for the natural mixture, which is 35.45, even though no single chlorine atom has that mass. (See the weighted averages tool for how the average is worked out.)
The small reason: binding. Even a single isotope is not exactly a whole number, except carbon-12, which is 12 by definition. When protons and neutrons pull together into a nucleus, a little mass is turned into energy and given off, following Einstein’s famous E = mc². So a nucleus weighs slightly less than the particles it is made from. For carbon-12, the difference is a little under 1%.
Careful
“The relative atomic mass of oxygen is 16 grams.”
Relative atomic mass has no units: it is a comparison, like “16 times as heavy as a hydrogen atom” (more precisely, 16 twelfths of a carbon-12 atom). The grams come in when you take a mole of atoms: a mole of oxygen atoms has a mass of 16 grams.
A see-saw for comparing masses
Make a balance from a ruler resting on a pencil. Put a coin at one end and see how many paper clips (or dried beans) you need at the same distance on the other end to balance it. You have just found the coin’s mass relative to a paper clip, without knowing either mass in grams. Choose a different “standard” object and every number changes, but the comparisons stay true. That is exactly the argument chemists had for 150 years.
Every relative atomic mass in this book, every molar mass, every “18 grams of water”, rests on Dalton’s simple idea: if you cannot weigh one, compare.
1664 to 1923
Sour and slippery: what is an acid?
Robert Boyle, Antoine Lavoisier, Humphry Davy, Svante Arrhenius, Johannes Brønsted, Thomas Lowry
London, the 1660s
Robert Boyle had a favourite trick, and it involved flowers. He would crush violets, soak them, and make a deep purple syrup. Then he added a few drops of different liquids. Vinegar, lemon juice and “spirit of salt” turned the purple syrup red. Other liquids, made from wood ash or lime, turned it green. In 1664 he wrote about it in a book on colours, and he noticed something important: the colour change sorted liquids into two families, no matter where they came from.
People had known the first family for thousands of years. They tasted sour (the Latin word acidus means sour), they fizzed when poured on chalk, and they could eat away metals. The second family felt slippery, like soap, and could cancel out the first. We now call them acids and bases. Boyle had found a way to tell them apart without tasting them: an indicator, a dye that changes colour.
This is the story of how it took two and a half centuries to work out what an acid actually is.
The colour detectives
Boyle was not the first to use plant colours. A purple dye called litmus, made from lichens (crusty growths that cover rocks and tree bark), had been used by dyers for centuries. Litmus turns red in acids and blue in bases, and litmus paper is still in school labs today. Red cabbage, hibiscus flowers, beetroot and even turmeric all contain natural indicators. They work because their colour molecules change shape slightly when an acid or a base gives or takes a tiny particle, which you will meet at the end of this story.
But knowing how to spot an acid is not the same as knowing what one is. That puzzle had several wrong answers first.
Wrong answer 1: oxygen makes acids
In the 1770s Antoine Lavoisier, the great French chemist, burned sulfur, phosphorus and carbon in air and dissolved the products in water. Every time, he got an acid. He concluded that the element he had been studying must be the secret ingredient of all acids, so he named it oxygène, from Greek words meaning “acid-maker”. It was a brilliant guess. It was also wrong, and the name stuck anyway: every time you say “oxygen”, you are repeating Lavoisier’s mistake.
Wrong answer, corrected
In 1810 the young English chemist Humphry Davy took one of the strongest acids known, muriatic acid (we call it hydrochloric acid, HCl), and tried as hard as he could to find oxygen in it. There was none. The greenish gas everyone thought was an oxygen compound turned out to be a new element, which Davy named chlorine. So acids did not need oxygen. But they all contained something else: hydrogen. A few decades later, the German chemist Justus von Liebig suggested that the key was hydrogen that could be swapped for a metal.
Closer: the Swede with the risky idea
In the 1880s a Swedish student named Svante Arrhenius proposed that when an acid dissolves in water, it breaks up into ions, and that every acid releases the same kind of ion: a hydrogen ion, H⁺. Bases, he said, release hydroxide ions, OH⁻, and when the two meet they make water. His examiners were unimpressed and gave his thesis nearly the lowest pass. Twenty years later, in 1903, the same ideas won him the Nobel Prize.
Arrhenius’s idea explained a lot. But it had a hole in it. Ammonia, NH₃, is clearly a base: it turns litmus blue and cancels acids. Yet it contains no OH at all. How can it release hydroxide?
The answer: passing a proton
In 1923 two chemists working separately, Johannes Brønsted in Copenhagen and Thomas Lowry in Cambridge, published the same idea within months of each other. Forget what the substance contains, they said. Look at what it does.
Let’s go through it step by step.
Step 1: what an H⁺ really is
A hydrogen atom is one proton and one electron. Take the electron away and what is left is a bare proton: the smallest, most concentrated speck of positive charge in chemistry. That is all “H⁺” is.
Step 2: an acid gives away a proton
When hydrogen chloride meets water, the proton leaves the chlorine and jumps onto a water molecule. The electrons it shared with the chlorine stay behind.
The water, now carrying an extra proton, becomes a hydronium ion, H₃O⁺. The chlorine, keeping the electrons, becomes a chloride ion, Cl⁻. Count the charges: zero on the left, (−1) + (+1) = 0 on the right. Nothing was created or lost; one proton simply moved house.
Step 3: a base takes a proton
A base is anything that accepts a proton. Ammonia does it beautifully:
NH₃ + H₂O ⇌ NH₄⁺ + OH⁻
Ammonia takes a proton from water, leaving OH⁻ behind. So ammonia makes hydroxide without containing any. The hole in Arrhenius’s idea is closed.
Step 4: water can play both parts
Look again at the two equations. In the first, water took a proton, so it acted as a base. In the second, water gave a proton, so it acted as an acid. Whether something is an acid or a base depends on its partner. Chemistry is full of relationships like this, the way the same person can be a teacher in one room and a student in another.
Careful
“Acids are dangerous and bases are safe.”
Both families include gentle and fierce members. Lemon juice and vinegar are acids you eat; the acid in a car battery can burn skin. Baking soda is a mild base; oven cleaner and drain cleaner are strong bases that can blind. What matters is how strong and how concentrated a substance is, not which family it belongs to.
Back to the colour detectives
Now you can see what Boyle’s violets were doing. Indicator molecules are themselves weak acids. When there are plenty of spare protons around, they hold onto one and have one colour; when protons are scarce, they lose it and their shape and colour change. The colour is a message from the molecules about how many protons are around.
Make a red cabbage rainbow
Ask an adult to help. Chop a few leaves of red cabbage into small pieces, put them in a jug and cover them with hot water from the tap. Squash them with a spoon, wait ten minutes, then strain off the purple juice. That juice is your indicator. Pour a little into several clear glasses. Add a spoonful of vinegar to one, lemon juice to another, plain water to a third, and a spoonful of baking soda dissolved in water to a fourth. Watch the colours: pink and red for acids, purple for neutral, blue and green for bases. Do not taste any of it, and do not mix in cleaning products.
From Boyle’s violets to Brønsted and Lowry’s proton, the story of acids is the story of a question that kept getting a better answer. In Chapter 7 you will use that answer to understand strong and weak acids, and the pH scale that measures them.
1780s to 1836
Frogs' legs and the first battery
Luigi Galvani, Alessandro Volta, John Frederic Daniell
Bologna, Italy, the 1780s
In his laboratory at the University of Bologna, the doctor and anatomy professor Luigi Galvani was studying how nerves make muscles move, and his favourite subjects were frogs. One day (the details vary in different tellings) he touched the nerve of a dissected frog’s leg with a metal instrument while a machine nearby was making electric sparks, and the dead leg kicked.
Galvani spent years on it. He found that a leg would twitch even with no spark machine at all, if he touched it with two different metals joined together, say a brass hook and an iron railing. In 1791 he published his conclusion: animals make their own electricity, stored in their muscles and nerves. He called it “animal electricity”, and Europe went wild for it.
The professor who disagreed
About two hundred kilometres away in Pavia, the physics professor Alessandro Volta read Galvani’s work, repeated it, and became suspicious. Why did it need two different metals? Perhaps, Volta argued, the electricity was not coming from the frog at all. Perhaps it was coming from the metals, and the frog’s leg was simply a very sensitive detector, twitching whenever a current passed through it.
The two men argued for years, politely but stubbornly. And both were partly right: nerves really do work by electricity, as later scientists showed. But Volta’s hunch about the metals led somewhere much bigger.
The pile
To prove his point, Volta needed to make electricity from metals with no animal involved. He stacked up discs: a disc of zinc, a disc of copper (or silver), a piece of cardboard soaked in salt water, then zinc, copper, wet cardboard again, and so on, dozens of layers high. When he touched the top and bottom of the stack at the same time, he felt a tingle, and it kept coming. This was the voltaic pile, the first battery that could give a steady flow of electricity. He described it in a letter to the Royal Society in London in March 1800.
The news spread astonishingly fast. Within weeks, in London, William Nicholson and Anthony Carlisle built a pile and used it to split water into hydrogen and oxygen. In 1801 Volta demonstrated his pile in Paris to Napoleon Bonaparte, who was so impressed he gave him a medal and later made him a count. And every time you say “volt”, you are saying Volta’s name.
Let’s see what was really going on inside the pile, step by step.
Step 1: two metals, two different grips
Some metals give up their outer electrons more readily than others. Zinc gives them up more readily than copper (Chapter 8 explains how chemists know). So if zinc and copper are connected and both touch a salty liquid, electrons tend to leave the zinc, which dissolves a little as Zn²⁺ions, and arrive at the copper side.
Step 2: the long way round
If the two metals touch directly, the electrons hop straight across and the energy just warms things up a tiny bit. The trick of a battery is to give the electrons only one route: through a wire, outside the cell. On the way, they can light a bulb, buzz a buzzer or twitch a frog’s leg.
Step 3: closing the loop
Electrons cannot pile up on one side forever. As they leave the zinc, the liquid around it gains positive ions; as they arrive at the copper, the liquid there would build up negative charge. Something has to keep both sides balanced, or the flow would stop almost instantly. In Volta’s pile, the salty cardboard did the job: ions moving through the liquid carried charge one way while electrons travelled the other way through the wire. A battery always has two paths: electrons through the wire, ions through the liquid.
Step 4: stacking up
One zinc-copper pair gives a push of about one volt. Stack many pairs on top of each other, so the electrons go through one after another, and the pushes add up. Volta’s tall piles gave dozens of volts. Today’s batteries do the same: a 9-volt battery is six small cells stacked inside one box.
The battery that didn’t fade
Volta’s pile had a frustrating problem: its current faded within an hour or so as bubbles of hydrogen formed on the copper and blocked it. In 1836 the London chemist John Frederic Daniell fixed it. He put the copper in a solution of copper sulfate and the zinc in weak sulfuric acid (later versions used zinc sulfate), and kept the two liquids apart with a barrier that let ions through but stopped the liquids mixing: at first a tube made from an ox’s gullet, and later a pot of unglazed, porous clay. Instead of making hydrogen, the copper side now grew a fresh coat of copper metal as Cu²⁺ ions picked up the arriving electrons. The Daniell cell gave a steady push of about 1.1 volts for hours.
Daniell cells powered the electric telegraphs that, from the 1840s, sent messages along wires across countries and later under oceans. In school labs today the porous pot is often replaced by a strip of paper soaked in salt solution, called a salt bridge. It does the same job: it lets ions flow between the two sides, so the electrons can keep flowing through the wire.
Careful
“A battery stores electricity, the way a bottle stores water.”
A battery stores chemicals that are ready to react. The electricity is made as the reaction happens, which is why a battery goes flat when its chemicals are used up. A flat battery is not empty of electrons: it has the same number as a full one. It has simply run out of the reaction that pushes them round.
Make a lemon battery (with an adult)
You need two or three lemons, the same number of zinc-coated (galvanised) nails or screws, the same number of strips of copper (copper wire, or a copper-coated coin), some wire with crocodile clips, and a small red LED. Push one nail and one piece of copper into each lemon, a few centimetres apart, not touching. Each lemon makes a cell of a little under 1 volt. Join the lemons in a chain: the copper of one to the nail of the next. Connect the free copper and the free nail at the ends to the LED’s two legs (if it does not light, swap the legs round). Turn off the lights: the LED should glow faintly. You have rebuilt Volta’s pile. Afterwards, throw the lemons away; do not eat them.
From a twitching frog to the telegraph in about fifty years: Galvani and Volta’s argument turned out to be one of the most useful arguments in history. Chapter 8 opens Daniell’s cell up and follows every electron through it.
1908 to 1916
How your blood stays at 7.4
Lawrence Henderson, Karl Albert Hasselbalch
A school sports day, the 100-metre race
The starter’s whistle goes and you sprint. For ten seconds your leg muscles burn energy faster than your blood can bring them oxygen, and they switch to a quick, messy back-up: they turn sugar into lactic acid. Acid floods out of the muscles and into your bloodstream. You cross the line, gasping.
And here is the strange thing: the pH of your blood has barely changed. Healthy blood stays between about 7.35 and 7.45, almost always. Below about 7.35 or above about 7.45, doctors start to worry, and much further outside that range your cells cannot work properly. A difference of 0.1 in pH is only a 26% change in hydronium, but your body defends that tiny window fiercely. How?
The doctor who did the arithmetic
At the start of the 1900s, Lawrence Henderson, a young doctor and chemist at Harvard University, was puzzled by exactly this. Blood was clearly being flooded with acids all the time, from muscles, from digestion, from carbon dioxide made in every cell, yet its acidity hardly budged. In 1908 he worked out the chemistry of the main reason, and wrote down an equation for it. In 1916 a Danish doctor, Karl Albert Hasselbalch, rewrote Henderson’s equation in terms of the new pH scale, and it has carried both their names ever since. What they had described is called a buffer.
Step 1: a team of two
A buffer is a solution containing two partners: a weak acid, which can give away a proton, and its matching base, which can take one. In blood the main pair is carbonic acid, H₂CO₃, and the hydrogencarbonate ion, HCO₃⁻ (the same ion that is in baking soda). The two are the same particle with and without one proton.
Step 2: when acid arrives, the base catches it
When lactic acid releases extra protons into your blood, hydrogencarbonate ions grab them:
H⁺ + HCO₃⁻ → H₂CO₃
The protons are not destroyed (nothing in chemistry is), but they are locked up inside weak carbonic acid, which keeps hold of most of them. So the hydronium in the blood rises only a little.
Step 3: when base arrives, the acid steps in
If something removes protons or adds a base, the carbonic acid gives up some of its protons to replace them. Either way, the pair absorbs the change.
Step 4: why the pH barely moves
The pH of a buffer depends mainly on the ratio of the two partners, not on how much of each there is. In blood there is about 20 times as much hydrogencarbonate as carbonic acid, and that ratio is what sets the pH at 7.4. A small splash of acid turns a little hydrogencarbonate into carbonic acid, so the ratio changes a little, and the pH changes only a little.
Here is the difference a buffer makes, using the made-up example from Chapter 7:
Add 1.0 millimole of sodium hydroxide (10 mL of a 0.10 mol/L solution) to 50 mL of pure water: the pH jumps from 7.0 to about 12.2.
Add the same amount to 50 mL of an acetic acid / acetate buffer (2.5 millimoles of each): the pH moves from 4.74 to about 5.11.
Same base, same volume. Without a buffer the pH leaps by five units; with one, it shifts by less than half a unit.
Step 5: your body has helpers
The carbonic acid in blood has a clever escape route. It breaks down into carbon dioxide and water, and your lungs breathe the carbon dioxide out:
H₂CO₃ → H₂O + CO₂
That is one reason you breathe so hard after a sprint: getting rid of carbon dioxide gets rid of acid. Over hours and days, your kidneys help too, removing extra acid in urine and making new hydrogencarbonate. Lungs and kidneys keep refilling the buffer so it never runs out.
Careful
“A buffer stops the pH from changing at all.”
It only slows the change down. Every bit of acid added uses up some of the base partner. Add enough and the base runs out; then the pH falls as fast as in plain water. How much a buffer can take before it gives way is called its capacity.
Buffers everywhere
Once you know to look for them, buffers are everywhere. The oceans are buffered by carbonate and hydrogencarbonate, which is why they are absorbing carbon dioxide without turning sour overnight (Chapter 11 tells that story). Shampoo, eye drops, many medicines and the solutions used in hospitals are buffered so they stay gentle. Even milk has buffers in it.
Watch a buffer hold out
You need red cabbage indicator (see Sour and slippery: what is an acid?), two clear glasses, vinegar, a teaspoon and baking soda. Fill both glasses with the same amount of indicator. Stir half a teaspoon of baking soda into one; it turns blue-green. Now add vinegar to both, a few drops at a time, counting the drops. The plain glass turns pink almost at once. The baking soda glass fizzes and holds out for many more drops before it changes. The hydrogencarbonate in baking soda is catching the acid’s protons, just as it does in your blood.
So when you finish a race, red-faced and out of breath, remember that billions of hydrogencarbonate ions are quietly catching protons in your blood. Chapter 7 shows a buffer at work in a titration curve, as the long, gently sloping stretch in the middle.
1970s to 2019
The battery in your pocket
M. Stanley Whittingham, John B. Goodenough, Koichi Mizushima, Akira Yoshino
Stockholm, 9 October 2019
When the Nobel Prize in Chemistry for 2019 was announced, one of the three winners was 97 years old: John Goodenough, the oldest person ever to receive a Nobel Prize. He shared it with Stanley Whittingham, who was 77, and Akira Yoshino, who was 71. The prize was for something you have almost certainly used today: the lithium-ion battery.
The story behind it took place in an oil company’s laboratory in America, a university in England and a chemical company in Japan, and it begins with a worry about oil.
A battery from an oil company
In the early 1970s, oil prices shot up and people began to worry about what would happen when oil ran short. At the research labs of the oil company Exxon in New Jersey, a young English chemist named Stanley Whittingham was looking for new ways to store energy. He discovered that lithium ions could slip in between the layers of a material called titanium disulfide, like letters sliding into the slots of a letter rack, and slip out again. He used this to build a rechargeable battery with a lithium metal electrode, giving about 2 volts.
It worked, but it had a dangerous habit. Lithium metal reacts fiercely with water and air, and as the battery was charged again and again, thin spikes of lithium could grow inside it and cause short circuits and fires.
More voltage: a discovery in Oxford
At the University of Oxford in 1980, John Goodenough and his team, including the Japanese physicist Koichi Mizushima, reasoned that a metal oxide might hold lithium ions more tightly and give a bigger push. They tried lithium cobalt oxide. It gave about 4 volts, twice as much. Oxford did not see much value in it at the time and did not patent it for itself.
Making it safe: a carbon home for lithium
The last piece came from Japan. In 1985 Akira Yoshino, working for the chemical company Asahi Kasei, replaced the dangerous lithium metal with a special kind of carbon that lithium ions could slip into, between its layers, without ever becoming a lump of reactive metal. With Goodenough’s oxide on one side and Yoshino’s carbon on the other, the battery was light, powerful and much safer. The electronics company Sony started selling lithium-ion batteries in 1991, first in video cameras. Today they are in phones, laptops, electric scooters and cars, and in huge banks that store solar power.
Here is how one works, step by step.
Step 1: why lithium?
Lithium is the lightest metal of all: a mole of lithium atoms has a mass of only 6.94 grams, and each atom can give one electron. Compare lead, used in old car batteries: a mole of lead has a mass of 207 grams and gives two electrons.
Lithium: 1,000 g ÷ 6.94 g per mole ≈ 144 moles of electrons per kilogram.
Lead: (1,000 g ÷ 207.2 g per mole) × 2 ≈ 9.7 moles of electrons per kilogram.
Kilogram for kilogram, lithium can move about 15 times as many electrons.
A whole battery has much more in it than just the metal, so a real lithium-ion battery stores several times as much energy per kilogram as a lead-acid one, not 15 times. But that lightness is why you can carry one in your pocket.
Step 2: two shelves for lithium
A lithium-ion cell has two electrodes, and both are like bookshelves with gaps between the shelves. On one side are layers of carbon, graphite. On the other are layers of a metal oxide, such as cobalt oxide. Lithium ions can slide in between the layers of either one. Between the two electrodes is a liquid called the electrolyte, which lets lithium ions through, and a thin plastic separator that keeps the electrodes from touching.
Step 3: discharging, while you use your phone
When the battery is charged, most of the lithium is tucked between the graphite layers. When you switch your phone on, lithium atoms in the graphite each give up an electron. The lithium ions, Li⁺, travel the short way, through the electrolyte, to the oxide. The electrons cannot go that way. They take the long way round, through the wires and chips of the phone, doing useful work as they go, and meet up with the lithium ions at the oxide.
Step 4: charging, when you plug it in
The charger pushes everything back: it drives electrons back to the graphite through the wire, and lithium ions follow through the electrolyte, sliding back between the carbon layers. The reaction runs uphill, storing energy, ready for next time. Nothing is used up; the same lithium shuttles back and forth, hundreds or thousands of times.
How much lithium moves when you use a full charge?
A phone battery labelled 4,000 mAh can deliver a current of 4 amps for 1 hour.
Charge = 4 A × 3,600 s = 14,400 coulombs.
One mole of electrons carries about 96,485 coulombs, so that is 14,400 ÷ 96,485 ≈ 0.149 moles of electrons.
That means 0.149 moles of lithium ions, about 0.149 × 6.94 ≈ 1.0 gram of lithium, crossing from one side to the other.
About one gram of lithium moving back and forth runs your phone for a day.
Careful
“Charging fills the battery up with electrons from the wall.”
The battery has the same number of electrons when it is full as when it is flat. Charging only moves them, together with the lithium ions, from one electrode to the other, into the arrangement with more stored energy. That is why a charged battery is no heavier than a flat one.
Be a battery detective
Look at the labels on a power bank, a phone box or a laptop charger (do not open or damage any battery). Find the numbers marked mAh or Wh and V. Using the working above, estimate how many grams of lithium shuttle across the power bank when it is used from full to empty. Then remember the safety rule every battery engineer knows: never puncture, crush or heat a lithium-ion battery, and tell an adult if one ever looks swollen.
From an oil crisis in America to an oxide in Oxford to a carbon shelf in Japan: the battery in your pocket was built by people who never worked in the same room. Chapter 11 follows the lithium ions inside a real cell.
1909
Sørensen's brewery and the pH scale
Søren Sørensen, Fritz Haber, Zygmunt Klemensiewicz, Arnold Beckman
The Carlsberg Laboratory, Copenhagen, 1909
The Carlsberg brewery in Copenhagen had something unusual for a beer company: its own science laboratory, set up in 1875 by the brewery’s founder, J. C. Jacobsen, who believed that better science would make better beer. In 1901 a chemist called Søren Peder Lauritz Sørensen became head of its chemistry department.
Sørensen was studying enzymes: the proteins that turn grain into sugar and sugar into alcohol. He kept noticing that his enzymes worked beautifully in some solutions and hardly at all in others, and the difference seemed to depend on how acidic the liquid was. So he needed to measure acidity, and to write it down, again and again, for hundreds of experiments. That is where his problem began.
Step 1: the numbers are horrible
Acidity depends on how many hydrogen ions, really hydronium ions, H₃O⁺, are floating in each litre. Chemists count them in moles per litre. Here are some real values:
Stomach acid: about 0.01 mol/L
Lemon juice: about 0.006 mol/L
Pure water: 0.000 000 1 mol/L
Baking soda solution: about 0.000 000 005 mol/L
Imagine writing numbers like 0.000 000 005 in a lab notebook a hundred times a day, and trying not to lose a zero. The numbers stretch over more than a hundred million million times from the most acidic to the most basic. Sørensen wanted something shorter.
Step 2: just count the zeros
Sørensen’s idea was simple. Write the concentration as a power of ten, and use the number of decimal places, the power, as the measure.
That is the whole pH scale. A pH number tells you “the concentration of hydronium is ten to the minus this many moles per litre”. For numbers in between, like 0.006, the pH comes out in between too (about 2.2). Mathematicians call this kind of counting-the-power a logarithm, but you do not need the word to use it: pH just counts how many places the decimal point has moved.
Nobody is completely sure what the “p” originally stood for. Sørensen wrote it as pH, with a small H, and people have guessed it meant potenz (German for power), puissance (French for power), or simply the letter he used for a quantity in his equations. Whatever its origin, it stuck.
Step 3: the upside-down part
Because pH counts how many places the number has shrunk, a smaller pH means more hydronium. pH 1 is far more acidic than pH 3. This trips almost everyone up the first time.
Step 4: every step is ten times
Each step of 1 on the pH scale is a factor of ten. So:
pH 4 has 10 times as much hydronium as pH 5.
pH 3 has 10 × 10 = 100 times as much as pH 5.
pH 2 has 10 × 10 × 10 = 1,000 times as much as pH 5.
That is why a small-looking change in pH can be a big deal. When the surface of the ocean goes from pH 8.2 to 8.1, the hydronium in it has gone up by about 26%.
Careful
“pH 6 is twice as acidic as pH 3, because 6 is twice 3.”
It is the other way round, and much more than twice. pH 3 has 1,000 times as much hydronium as pH 6. Remember: lower number, more acidic; each step, ten times.
Step 5: neutral is 7, and why
Even perfectly pure water is never quite without ions. Now and then two water molecules pass a proton between them, making one H₃O⁺ and one OH⁻. At 25 °C this happens just enough to leave 10⁻⁷ mol/L of each. Equal amounts of the two means neutral, so neutral water is pH 7. Below 7, there is more H₃O⁺ than OH⁻: acidic. Above 7, there is less: basic.
Measuring it: a glass that feels acid
Sørensen measured acidity with electrical cells and with colour indicators, carefully chosen dyes that change at known pH values. A few years earlier, the German scientist Max Cremer had found that a thin wall of glass develops a tiny voltage that depends on the acidity of the liquid around it. In the same year as Sørensen’s scale, 1909, Fritz Haber and his young Polish colleague Zygmunt Klemensiewicz in Germany turned this into a practical glass electrode, which became the heart of the pH meter.
The pH meter as a handy instrument came from an unexpected place. In the 1930s California’s lemon growers needed to test the acidity of lemon juice quickly, and a young chemist named Arnold Beckman built them a sturdy electronic meter in 1934. It was so useful that it started a whole company of scientific instruments. Today a pH meter sits in almost every lab, hospital and water-treatment plant in the world.
Put your kitchen in order
If you have made red cabbage indicator (see the story Sour and slippery: what is an acid?), use it to line up kitchen liquids from most acidic to most basic: lemon juice, vinegar, a fizzy drink, milk, tap water, and a little baking soda in water. Pinker means more acidic; bluer or greener means more basic. You are building your own pH scale, without any numbers.
So pH is a shortcut invented by a brewer’s chemist to save himself from writing zeros. Every time you see a pH number in Chapter 7, read it as “count the zeros”: pH 2 means 0.01 mol/L of hydronium, and every step is ten times.
1777 to today
Rust, fire and moving electrons
Antoine Lavoisier, Humphry Davy
The Royal Institution, London, October 1807
Humphry Davy had a new toy: one of the most powerful batteries in Britain, hundreds of metal plates stacked in troughs of acid. He was using it to tear substances apart with electricity. On 6 October 1807 he pointed it at a lump of potash, a substance made from wood ash that chemists had long suspected contained an unknown metal but had never managed to split.
He took a small piece of potash, just damp enough from the air to carry a current, and passed the current through it until it began to melt. At one wire, tiny bright globules of metal appeared, “having a high metallic lustre”, as he wrote. Some of them burst into flame at once. Davy’s cousin Edmund, who was assisting him, later remembered that Humphry was so delighted he danced about the room. He had discovered potassium. A few days later he did the same with soda and found sodium.
Why was it so hard to get these metals out, and why did they burst into flame the moment they appeared? The answer is one of the most important ideas in chemistry, and it began with rust.
Step 1: the old meaning, adding oxygen
When Lavoisier showed in the 1770s that burning is a reaction with oxygen, chemists started calling any reaction that adds oxygen to a substance oxidation. Iron slowly combining with oxygen and water to make flaky red rust is oxidation. So is wood burning, and a cut apple turning brown. The reverse, taking oxygen away from a compound to get the metal back, they called reduction, from a Latin word meaning “to lead back”: the metal was led back out of its ore. People had been doing reduction for thousands of years without the word, every time they heated iron ore with charcoal in a furnace to make iron.
Step 2: the new meaning, moving electrons
After the electron was discovered in 1897, chemists looked again at these reactions and saw something deeper. When iron combines with oxygen, the iron atoms lose electrons and the oxygen atoms gain them. And exactly the same kind of electron loss happens in many reactions that involve no oxygen at all, like zinc reacting with copper ions in Chapter 8. So the words were widened:
Oxidation is losing electrons. Reduction is gaining electrons.
A favourite way to remember it is OIL RIG: Oxidation Is Loss, Reduction Is Gain.
Step 3: always together
Electrons do not float around loose in a beaker; if one substance loses them, another must gain them. So oxidation and reduction always happen together, as a pair. Chemists call the pair a redox reaction (from REDuction and OXidation). Here is one you can picture:
Zn + Cu²⁺ → Zn²⁺ + Cu
Each zinc atom loses two electrons (it is oxidised); each copper ion gains them (it is reduced). Count the charge on each side: +2 before, +2 after. Electrons were passed, not created.
Step 4: who gives electrons most easily?
Line up metals by how readily they lose electrons in reactions like this and you get the reactivity series. Near the top are potassium and sodium, which give up electrons so readily that they react with water and air almost instantly; that is why Davy’s globules burst into flame. Lower down come magnesium, zinc and iron; further down, copper, silver and gold, which hardly react at all. That is why gold coins dug up after two thousand years still shine, while an iron nail rusts in a single wet monsoon.
It also explains why Davy needed his giant battery. Metals at the top of the series are the hardest to get back from their compounds, because their atoms have lost electrons so readily. To push the electrons back onto them takes a big electrical shove.
Careful
“Oxidation always involves oxygen.”
It used to mean that, and the name comes from oxygen. But today chemists use it for any loss of electrons. When magnesium burns in chlorine gas, there is no oxygen anywhere, yet the magnesium is oxidised, because it loses electrons to the chlorine.
Redox all around you
A green statue: the Statue of Liberty in New York was a shiny copper colour when it was put up in 1886. Over the next few decades, rain and air slowly oxidised the copper surface into a crust of green copper compounds, and that crust now protects the metal underneath. Indian temple bells and old copper pots go green in the same way.
A tarnished spoon: silver turns black when it meets traces of sulfur compounds in air or food (eggs are famous for it), because the silver is oxidised to black silver sulfide.
Your own breath: inside your cells, the food you eat is slowly oxidised by the oxygen you breathe, passing electrons step by step along a chain of proteins. That controlled redox reaction is where your energy comes from.
And every battery, from Volta’s pile to the one in your pocket, is a redox reaction arranged so that the electrons have to take the long way round through a wire.
The browning apple test
You need an apple, a knife (ask an adult), a lemon and a plate. Cut two slices of apple. Squeeze lemon juice all over one slice and leave the other bare. Put both on the plate and look every 15 minutes for an hour. The bare slice turns brown as natural substances in the apple are oxidised by oxygen from the air, helped along by an enzyme. The lemon slice stays pale for much longer: the acid slows the enzyme down, and the vitamin C in lemon juice is oxidised more easily than the apple’s own substances, so it takes the hit first. You can eat both slices afterwards.
So rust on a gate, a flame in a grate and an apple on a plate are the same story, told with electrons. Chapter 8 follows those electrons one at a time.
1823 to 1830
Two chemists, two silver salts
Justus von Liebig, Friedrich Wöhler, Jöns Jacob Berzelius
Paris and Stockholm, 1823
Imagine two young chemists, both in their early twenties, working in two different cities. In Paris, Justus von Liebig is studying a silver compound called silver fulminate. It is dangerous stuff: a pinch of it explodes with a sharp crack if you tap it or warm it. (Tiny amounts are what make the bang in snap toys and party crackers.) In Stockholm, in the laboratory of the great Berzelius, Friedrich Wöhler is studying a different silver compound, silver cyanate. It is calm and well behaved: it does not explode at all.
Both chemists did what chemists of the time did with a new substance: they broke it down and weighed what came out, to find exactly which elements it contained and in what proportions. And when their results were published, there was a problem. The two answers were the same. Silver, carbon, nitrogen and oxygen, one atom of each, in exactly the same proportions. Yet one substance exploded and the other did not.
Step 1: somebody must be wrong
In the 1820s nearly every chemist believed that a substance’s composition decided what it was. If two samples had the same elements in the same proportions, they had to be the same substance. So when Liebig saw Wöhler’s result, he assumed Wöhler had made a mistake in his analysis, and he said so. He even repeated the cyanate analysis himself, expecting to find the error.
He found that Wöhler was right. Both analyses were correct. Two different substances, with completely different behaviour, really did contain exactly the same atoms in the same numbers.
Step 2: from rivals to friends
The story could have turned into a bitter feud. Instead, when the two young men met a few years later, they discovered they liked each other enormously. They became lifelong friends and worked together for decades, writing hundreds of letters and publishing famous research side by side. It is one of the warmest friendships in the history of science, and it began with each of them thinking the other had got his sums wrong.
There were more puzzles like theirs. Wöhler’s urea, made in 1828 from ammonium cyanate, had the same formula as the ammonium cyanate he started with. Two acids from wine-making, tartaric acid and “racemic acid”, had the same composition but behaved differently. Something new was going on.
Step 3: Berzelius gives it a name
In 1830 Berzelius, who had a gift for naming things, proposed a word for substances with the same composition but different properties: isomers, from the Greek isos, “equal”, and meros, “part”. Equal parts, different substances.
But why could equal parts make different substances? Nobody yet knew how atoms were arranged inside molecules. The full answer had to wait for the 1850s and 1860s, when chemists worked out that atoms are joined by bonds in a definite order, and then for 1874, when van ’t Hoff and Le Bel showed that molecules have shapes in space.
The answer, when it came, was simple: same atoms, joined in a different order. Both contain a little group of three atoms, one carbon, one nitrogen and one oxygen. In cyanate the carbon sits in the middle: O–C–N. In fulminate the nitrogen sits in the middle: C–N–O. That small change in who is holding hands with whom changes everything about how the substance behaves.
Careful
Silver fulminate is a genuinely dangerous explosive. It is part of chemistry’s history, not something to make. Chemists who handle compounds like it work with tiny amounts behind blast shields.
Step 4: isomers you can understand with your own eyes
Here are two isomers you met in Chapter 10. Both have the formula C₂H₆O: two carbons, six hydrogens, one oxygen.
In ethanol, the oxygen sits at the end of the chain with a hydrogen attached to it, an –OH group. Ethanol boils at 78.4 °C and mixes with water.
In dimethyl ether, the oxygen sits in the middle, between the two carbons, and every hydrogen is attached to a carbon. It boils at −24.8 °C: it is a gas on any day in Mumbai.
Same atoms, a difference in boiling point of more than 100 °C, just because of where one oxygen sits.
Two pairs of isomers. Butane and isobutane share the formula C₄H₁₀; ethanol and dimethyl ether share C₂H₆O. Different arrangements, different substances.
Step 5: how many ways can you arrange the atoms?
Small formulas allow only a few arrangements, but the number grows astonishingly fast as molecules get bigger. Here is how many different alkanes (chains and branches of carbon with hydrogens) exist for each number of carbon atoms:
Formula
Different isomers
CH₄, C₂H₆, C₃H₈
1 each
C₄H₁₀
2
C₅H₁₂
3
C₆H₁₄
5
C₁₀H₂₂
75
C₂₀H₄₂
366,319
That explosion of possibilities is one reason there are so many millions of carbon compounds. Carbon atoms can be arranged in more ways than anyone could ever list by hand.
Finding the isomers of C₄H₁₀ step by step
Start with the four carbons in a straight row: C–C–C–C. Fill in hydrogens so every carbon has four bonds: that is butane.
Now try a branch: three carbons in a row, with the fourth attached to the middle one. Fill in hydrogens: that is isobutane (2-methylpropane).
Any other drawing you try, such as bending the straight chain, turns out to be one of these two, just turned round. So C₄H₁₀ has exactly 2 isomers.
Build isomers from peas and toothpicks
Use soaked dried peas (or small balls of play dough) for atoms and toothpicks for bonds; ask an adult, as toothpicks are sharp. Make 4 big “carbon” balls and 10 small “hydrogen” balls. Every carbon must end up with exactly four toothpicks, every hydrogen with exactly one. How many genuinely different molecules can you build? (Turning a model round, or bending it, does not count as different: only changing which atom is joined to which does.) You should find exactly two: butane and isobutane. Then try five carbons and twelve hydrogens and see if you can find all three.
Liebig and Wöhler’s quarrel that never happened taught chemistry a lesson it has never forgotten: a formula tells you which atoms are present, but only the arrangement tells you what the substance really is.
1958
The man who measured the air
Charles David Keeling, Roger Revelle, Ralph Keeling
Big Sur, California, 1955
Charles David Keeling was in his late twenties, and he was camping. Not for a holiday: he was collecting air. Day and night, in the forests and mountains of California, he filled glass flasks with air and carried them back to his laboratory, where he measured, with an instrument he had built himself, how much carbon dioxide each flask contained.
Other people had measured carbon dioxide before, and their numbers were all over the place. Keeling was more careful than anyone. He found that if you measured clean air, away from cities and forests breathing on it, the amount was almost the same everywhere he went: about 310 parts in every million. That steadiness was the first surprise. It meant the whole atmosphere was well mixed, and that a careful person in the right place could measure the whole planet at once.
Step 1: the volcano with the cleanest air
In 1958 Keeling, now working at the Scripps Institution of Oceanography with the ocean scientist Roger Revelle, set up an instrument near the top of Mauna Loa, a huge volcano in Hawaii. At 3,400 metres up, in the middle of the Pacific Ocean, the air has travelled thousands of kilometres from the nearest city. It is about as “average” as air gets.
The first measurements, in March 1958, were about 313 parts per million. Keeling expected the number to stay put. Instead, within a couple of years, he saw two things that nobody had seen before.
Step 2: the Earth breathes
The first discovery was beautiful. Every year, the amount of carbon dioxide fell from late spring to autumn, and rose again through winter, by about 6 parts per million. Why? The northern half of the Earth has far more land, and far more forests and fields, than the southern half. In the northern summer, billions of leaves are growing, and plants take carbon dioxide out of the air to build themselves. In winter, leaves fall and rot, and the carbon dioxide comes back. Keeling was watching the whole planet breathe in and out, once a year.
Step 3: the line keeps rising
The second discovery was more worrying. Underneath the yearly breathing, the line kept climbing, year after year, without ever coming back down. It is now called the Keeling curve, and the measurements have continued without a break ever since. After Charles Keeling died in 2005, his son Ralph carried on the work.
The Keeling curve: yearly average carbon dioxide at Mauna Loa (NOAA measurements), from about 316 parts per million in 1959 to about 421 in 2023. The yearly up-and-down wiggle is drawn smoothly here; in the real record it is about 6 parts per million.
The rise comes from burning coal, oil and gas. Every fuel made of carbon compounds turns its carbon into carbon dioxide when it burns, and humans now burn enormous amounts. Before the industrial age, air bubbles trapped in ancient ice show that the level was about 280 parts per million. It has now passed 420: half as much again.
Step 4: what “parts per million” means, step by step
The number looks small, so let us hold it in our hands.
420 parts per million
Out of every million molecules in the air, about 420 are carbon dioxide.
As a percentage: 420 ÷ 1,000,000 × 100 = 0.042%.
One breath of air (about half a litre) contains roughly 1.2 × 10²² molecules.
The carbon dioxide in it: 1.2 × 10²² × 420 ÷ 1,000,000 ≈ 5 × 10¹⁸ molecules.
So carbon dioxide is a tiny fraction of the air, and yet there are still about five million million million molecules of it in every breath you take. A small fraction of a huge number is still a huge number. And small fractions can matter enormously: carbon dioxide traps heat radiating from the Earth’s surface, so even a small change in how much there is changes the climate.
Step 5: the ocean as a sponge
Not all of the carbon dioxide we release stays in the air. Roughly a quarter to a third of it has dissolved into the oceans. That has slowed the rise in the air, but it has a cost, because carbon dioxide dissolving in water makes a weak acid, carbonic acid.
What happens to carbon dioxide in seawater. Most of the hydrogen ions it releases are mopped up by carbonate ions, so the pH falls only a little, but the carbonate that shell-building animals need gets used up.
This is called ocean acidification. The sea is not acidic: its pH is still above 7, so it is slightly basic. But it is becoming less basic. The average surface pH has fallen from about 8.2 to about 8.1. Because each step on the pH scale is a factor of ten, that small-looking drop means about 26% more hydrogen ions (10 to the power 0.1 is about 1.26). Corals, oysters and tiny sea snails called pteropods build their shells from calcium carbonate, and they need carbonate ions to do it. As carbonate gets scarcer, building shells gets harder. Since 1988 scientists at a station called ALOHA, in the ocean north of Hawaii, have measured the seawater regularly, and they have watched its pH slowly fall, just as Keeling watched the air.
Careful
“If the oceans are absorbing carbon dioxide, that solves the problem.”
It slows the rise in the air, but it moves the problem into the sea rather than removing it, and the ocean cannot keep absorbing at the same rate forever. Chapter 11 follows this chemistry step by step.
Make carbon dioxide change a colour
Ask an adult to help you chop a few leaves of red cabbage and soak them in warm tap water for half an hour, then strain the purple water into a clear glass. This is a natural pH indicator: it turns pinker when something acidic is added and greener or bluer when something basic is added. Put a straw in the glass and blow gently through it (blow out only, never suck, and do not drink it) for a few minutes. The carbon dioxide in your breath dissolves and makes a little carbonic acid, and the colour shifts slightly towards pink. Compare it with a glass of the same juice you did not blow into. That is ocean acidification in a glass, made with your own breath.
Keeling’s lesson for every chemist is about patience and care. He did not discover anything by being clever in a single afternoon. He discovered it by measuring the same thing, very carefully, in the same place, every day for decades, and refusing to let the numbers be sloppy. Some of the most important facts about our planet were found exactly that way.
1828
Life's chemistry is just chemistry
Jöns Jacob Berzelius, Friedrich Wöhler, Hermann Kolbe, Asima Chatterjee
Berlin, February 1828
Friedrich Wöhler was 27 years old, and he had been trying to make something quite ordinary: a salt called ammonium cyanate. He mixed his chemicals, heated the solution, and let it cool. White crystals appeared. But when he tested them, they were not ammonium cyanate at all. They behaved exactly like a substance that, until then, had only ever come from living bodies: urea, the main waste chemical in the urine of mammals, including you.
On 22 February 1828 he wrote excitedly to his old teacher, the great Swedish chemist Jöns Jacob Berzelius: he could make urea “without needing kidneys, or even an animal, whether man or dog.”
Why was that so exciting? To understand, you need to know what most chemists believed at the time.
Step 1: two kinds of chemistry?
Around 1806 Berzelius had started using a name for the chemistry of substances that came from living things: sugar, oils, wax, alcohol, urea. He called it organic chemistry, because these substances came from organisms. Everything else, such as salt, metals, rocks and water, was “inorganic”.
Many people felt there was a deep difference between the two. Rocks and salts could be made and remade in a flask. But the substances of life seemed different: they burned easily, they rotted, and nobody could make them from scratch. Perhaps, people thought, only a living body could make them, using some special “life force” that ordinary chemistry did not have. This belief is called vitalism.
Step 2: Wöhler’s crystals
Wöhler had started with substances that nobody would call “living”. Yet out came urea, a substance of life. A flask had done what was supposed to need a kidney.
It also showed something else that puzzled chemists. Ammonium cyanate and urea contain exactly the same atoms in the same numbers: one carbon, one oxygen, two nitrogens and four hydrogens, CH₄N₂O. Heating had simply rearranged them. Two different substances with the same formula: Wöhler and his friend Justus von Liebig had already stumbled on this kind of puzzle with silver salts, and it led to the idea of isomers.
Careful
“Wöhler’s urea killed vitalism overnight.”
This is how the story is often told, but it is too neat. Wöhler’s starting chemicals had themselves been prepared, a few steps back, from animal materials, so a determined vitalist could still argue that the “life force” had sneaked in. Belief in vitalism faded slowly over the next few decades, as chemists made more and more substances of life from simple starting materials. In 1845 Hermann Kolbe made acetic acid (the acid in vinegar) starting from carbon itself, and in the 1850s Marcellin Berthelot made many more, including fats. Wöhler’s crystals were the first famous crack in the wall, not a single blow that knocked it down.
Step 3: so what does “organic” mean now?
Once chemists saw that the same rules apply everywhere, the old meaning of “organic” stopped making sense. But the name stayed, with a new meaning. Today, organic chemistry is the chemistry of carbon compounds, especially carbon joined to hydrogen, and often to oxygen and nitrogen as well.
Why give carbon a whole branch of chemistry to itself? Because carbon is a champion builder. A carbon atom forms four bonds, and it bonds strongly to other carbon atoms. So carbon atoms can link into chains, branches and rings of almost any size, with other atoms decorating them. The great majority of the many millions of compounds chemists have described contain carbon.
Three ways to arrange carbon atoms: a chain, a branched chain and a ring. Carbon’s four bonds make all of them possible.
So the word “organic” in a chemistry book means “built on carbon”. It does not mean “alive”, and it does not mean “grown without pesticides”, which is the meaning on a vegetable packet in the supermarket. Plastic, petrol and paracetamol are all organic compounds in the chemist’s sense.
Step 4: the same rules all the way through
The big lesson of this story is simple, and it runs through this whole book. The atoms in your body are the same kinds of atom as in a rock, the air or a test tube. They obey the same rules: they are counted the same way, they attract and repel the same way, and they rearrange the same way in reactions. Living things are made of extraordinarily complicated and beautifully organised chemistry, but it is chemistry. There is no separate “life chemistry” with different laws.
That is not a sad thought. It is what allows medicine to work. If the molecules of life follow ordinary rules, then chemists can study them, copy them, and design new molecules that fix things when they go wrong.
Kolkata, 1944
Here is one person who did exactly that. Asima Chatterjee grew up in Kolkata and became fascinated by the medicinal plants of India. In 1944 she became the first woman to be awarded a Doctor of Science degree by an Indian university, the University of Calcutta. She spent her career working out the structures of carbon compounds made by plants, including alkaloids from the Madagascar periwinkle (which led elsewhere to important cancer drugs), and her team developed medicines against epilepsy and malaria from plant compounds. Her work rested on Wöhler’s discovery: a molecule made by a plant is a molecule like any other, and it can be studied, understood and, sometimes, made in a flask.
Step 5: reading an organic molecule
Every organic molecule is built from two parts, and once you can spot them, organic chemistry stops looking like alphabet soup:
A carbon skeleton: the chain, branch or ring of carbon atoms, with hydrogens filling the spare bonds.
Functional groups: small groups of other atoms attached to the skeleton, such as –OH or –COOH. These are the parts that do most of the chemistry.
Ethane, C₂H₆, is a two-carbon skeleton and nothing else: a gas that does not mix with water. Swap one hydrogen for an –OH group and you get ethanol, a liquid that mixes perfectly with water. Same skeleton, new functional group, new behaviour.
Ethane and ethanol: the same two-carbon skeleton, but one –OH group turns a gas into a liquid that mixes with water.
Find the organic chemistry in your kitchen
Go round your kitchen with an adult and sort things into two piles in your head: substances built on carbon, and substances that are not. Sugar (C₁₂H₂₂O₁₁), cooking oil, flour (mostly starch, long chains of sugar units), vinegar (acetic acid, CH₃COOH) and butter are all organic. Salt (NaCl), baking soda (NaHCO₃: it contains one carbon atom, but chemists usually count simple carbonates as inorganic) and water are not. Here is a clue you can see without doing anything risky: look at a piece of toast that has been left in the toaster too long. The black, crumbly part is mostly carbon, left behind when the heat broke apart the carbon compounds in the bread. That is the carbon skeleton of organic molecules, with everything else driven off.
Wöhler went on to a long career, but those white crystals from 1828 were his most famous result. They opened the door to the chemistry of carbon, which is the subject of Chapter 10, and to the medicines, plastics and fabrics that organic chemists have built since.
1874
Molecules in three dimensions
Louis Pasteur, August Kekulé, Jacobus van ’t Hoff, Joseph Achille Le Bel, Hermann Kolbe
Utrecht, 1874
In September 1874 a 22-year-old Dutch chemist called Jacobus van ’t Hoff published a little pamphlet, only a dozen or so pages long, with an idea so simple it seems obvious today and so new that it made some famous chemists furious. The idea was this: molecules are not flat. The four bonds of a carbon atom do not lie on paper like the arms of a plus sign. They point out into space, towards the four corners of a tetrahedron.
A few months later, in Paris, a young French chemist called Joseph Achille Le Bel published the same idea, worked out quite independently. When two people reach the same answer on their own, it is often a sign that the answer is right, and that the puzzles of the time were pointing straight at it.
So what were those puzzles?
Step 1: chemists drew molecules flat
By the late 1850s, August Kekulé in Germany and Archibald Scott Couper in Scotland had worked out that a carbon atom forms four bonds, and that carbon atoms can join to each other in chains. Chemists began to draw molecules as diagrams of atoms joined by lines, called structural formulas. Methane, CH₄, looked like a carbon with four hydrogens arranged like a plus sign.
That was a huge step forward. But flat drawings could not explain some strange observations.
Step 2: the mystery of the mirror-image crystals
Back in 1848 the young Louis Pasteur had been looking at crystals of a salt of “racemic acid”, a form of tartaric acid that turned up in the crust that forms inside wine barrels. Under his magnifying lens he noticed that the crystals came in two shapes, which were mirror images of each other, like a left glove and a right glove. Patiently, with tweezers, he sorted them into two piles. Dissolved in water, the two piles behaved differently with polarised light: one twisted the light to the left, the other twisted it to the right, by exactly the same amount.
Yet the two substances had the same formula, and on paper they looked identical. Something about the molecules themselves had to be “left-handed” or “right-handed”. But a flat molecule cannot be left- or right-handed. Flip a flat drawing over and it matches itself.
Step 3: the answer is a shape in space
Van ‘t Hoff and Le Bel saw how to solve it. If a carbon atom’s four bonds point to the corners of a tetrahedron, then a carbon with four different things attached can be built in two ways, which are mirror images of each other and cannot be turned to match, just like your two hands. Hold your hands palm to palm: they are mirror images. Now try to place your right hand exactly on top of your left, both palms down, thumbs on the same side. You cannot. That “handedness” is the secret of Pasteur’s crystals.
Why a tetrahedron? Because the four bonds are pairs of electrons, and electrons repel each other. Four things pushing each other away around a centre settle as far apart as they can be, and in three dimensions that means the corners of a tetrahedron, with every bond at an angle of about 109.5° to every other. On a flat plus sign they would only be 90° apart: crowded closer than they need to be.
Carbon chains, branches and rings. The zig-zag shape of the chains comes from the tetrahedral angle at every carbon atom.
Careful
“The 109.5° angle is just a number to memorise.”
It is not arbitrary. It is the angle you get when four things around a point get as far from each other as they possibly can. Mathematicians can calculate it exactly: it is the angle whose cosine is −1/3, which works out at 109.47°. Nature found it long before mathematicians did.
Step 4: not everyone was pleased
In 1877 the powerful German professor Hermann Kolbe wrote a famously scornful review of van ’t Hoff’s idea. He sneered that van ’t Hoff, then teaching at the veterinary school in Utrecht, seemed to have mounted Pegasus, the flying horse, borrowed from the veterinary school’s stables, and flown off into fantasy. Kolbe thought that guessing at the arrangement of atoms in space was not science.
Kolbe was a great chemist, but this time he was wrong, and the evidence piled up against him. In 1901, van ’t Hoff became the very first person ever to receive the Nobel Prize in Chemistry. (He was honoured for later work on reaction rates and solutions, not for the tetrahedron, but the tetrahedron is what every chemistry student remembers him for.) About forty years after his pamphlet, X-ray crystallography let scientists measure the positions of atoms directly, and the tetrahedral carbon was there, just as he had said.
Step 5: drawing molecules, step by step
Today chemists use several kinds of drawing, each good for a different job:
The molecular formula, such as C₄H₁₀, only counts the atoms. It tells you nothing about how they are joined.
A structural formula shows every atom and every bond as a line. It tells you exactly which atom is joined to which, but it is drawn flat.
A skeletal formula is a shorthand for big molecules. Each corner or end of a zig-zag line is a carbon atom; hydrogens on carbons are not drawn at all (you work them out, because every carbon has four bonds). Only other atoms, such as O or N, are written as letters.
A 3D model, like the ones you can turn in the live figures of Chapter 10, shows the true shape.
Reading a skeletal formula
A zig-zag line with three segments has 4 corners and ends: that is 4 carbon atoms.
Each end carbon has 1 bond in the drawing, so it needs 3 hydrogens. Each middle carbon has 2 bonds drawn, so it needs 2 hydrogens.
Total hydrogens: 3 + 2 + 2 + 3 = 10. So the zig-zag is C₄H₁₀: butane.
Build a tetrahedron with balloons
Blow up four balloons to about the same size and tie them together at their knots (twist the knots round each other, or tie them with a short piece of string). Let go and watch: the balloons push each other into a tetrahedron, all by themselves. Look at it from different sides; no direction is special. That is what the four bonds around a carbon atom do, and for the same reason: things that push each other away settle as far apart as they can. Now try it with three balloons (they make a flat triangle) and with two (a straight line). Those are the shapes of the carbons in ethene and in carbon dioxide.
So when you see a zig-zag chain in this book, remember the two young chemists who first imagined molecules standing up off the page. Every molecule in your body has a shape in space, and in living things that shape matters enormously: for many medicines, one of the two mirror-image forms works much better than the other.
thinking tool
Weighted averages, step by step
Francis Aston
Cambridge, 1920
For a hundred years, chlorine had been an embarrassment. Almost every other light element had a relative atomic mass close to a whole number: carbon 12, nitrogen 14, oxygen 16. Chlorine stubbornly measured 35.46 (the value used then), no matter how carefully it was purified. Some chemists wondered whether atoms of one element could have different weights. Others thought the idea was absurd.
Francis Aston, working in Cambridge, settled it with his new mass spectrograph, a machine that sorts atoms by mass. Chlorine split into two clean streams: one at 35 and one at 37, and nothing at all at 35.5. Chlorine is a mixture of two kinds of atom, and its famous “35.45” is a weighted average. To understand what that means, start at the market.
Step 1: the plain average
You buy two mangoes: one has a mass of 200 g and one 300 g. Their average mass is (200 + 300) ÷ 2 = 250 g. Neither mango weighs 250 g; the average describes the pair, not either one.
Step 2: when there are more of one kind
Now suppose a crate holds 3 small mangoes of 200 g and 1 big mango of 300 g. The plain average of “200 and 300” would still be 250 g, but that is wrong for this crate, because most of the mangoes are small.
Total mass = 3 × 200 + 1 × 300 = 900 g. Number of mangoes = 4.
Average mass = 900 ÷ 4 = 225 g.
The average is pulled towards 200 because there are more 200 g mangoes. That is a weighted average: each value counts according to how common it is.
Step 3: the shortcut with fractions
You can do the same sum using fractions (or percentages) instead of counts. Three out of four mangoes are small, so the fraction of small mangoes is 0.75; the fraction of big ones is 0.25.
Weighted average = 0.75 × 200 + 0.25 × 300 = 150 + 75 = 225 g.
Same answer. Multiply each value by its fraction, then add up. The fractions must add to 1 (here 0.75 + 0.25 = 1), because together they cover everything in the crate.
Step 4: chlorine
Natural chlorine is about 75.8% chlorine-35 and 24.2% chlorine-37. The precise masses of the two isotopes are 34.969 u and 36.966 u.
Average atomic mass = 0.758 × 34.969 + 0.242 × 36.966
= 26.51 + 8.95
= 35.45 u
Chlorine sorted by mass. Two peaks, one at 35 and one at 37, and the average, 35.45, falls between them where there are no atoms at all.
That 35.45 is what you see printed on a periodic table. It is the right number to use when you weigh out a spoonful of salt, because a spoonful contains countless chlorine atoms in exactly that mixture. But it describes the crowd, not any single atom.
Careful
“The average of 35 and 37 is 36, so chlorine’s atomic mass should be 36.”
That would only be true if there were equal numbers of each. There are about three chlorine-35 atoms for every chlorine-37, so the average is pulled down towards 35. Always weight each value by how common it is.
Average a bag of coins
Take a handful of mixed coins. Weigh each kind separately on a kitchen scale (several at once, then divide to get one coin’s mass) and count how many of each you have. Work out the average mass of a coin in the handful in two ways: total mass divided by number of coins, and the weighted-average shortcut with fractions. Do you get the same answer? Now add ten more of the heaviest coins and see how the average moves.
Weighted averages appear wherever things come in mixtures: the average atomic mass of every element on the periodic table, a class’s average mark, the average speed of the molecules in a gas. In each case, the average describes the whole mixture, and it can be a value that no single member has.
thinking tool
Counting zeros: logarithms without fear
John Napier, Henry Briggs
Merchiston Castle, Edinburgh, 1614
In the early 1600s, astronomers and sailors spent weeks of their lives doing sums. Working out where a planet would be, or where a ship was on the ocean, meant multiplying long numbers like 7,382,915 by 4,106,447, by hand, over and over, and a single slip could wreck everything.
John Napier, the laird of Merchiston Castle near Edinburgh, was a mathematician (and, his neighbours suspected, a bit of a wizard). He spent about twenty years building tables of special numbers that would turn hard multiplications into easy additions. In 1614 he published them and gave them a name he invented: logarithms. An English professor, Henry Briggs, was so excited that he travelled all the way to Edinburgh to meet him, and together they agreed to make a version based on powers of ten, which Briggs published over the following ten years. Astronomers like Johannes Kepler seized on them. It was said that logarithms doubled the working life of an astronomer, by halving the time spent on sums.
Step 1: a logarithm counts tens
You already know powers of ten (if not, read powers of ten first). A logarithm just asks the question backwards.
1,000 = 10³. So the logarithm of 1,000 is 3.
1,000,000 = 10⁶. So the logarithm of a million is 6.
10 = 10¹. The logarithm of 10 is 1.
1 = 10⁰. The logarithm of 1 is 0.
For a number that is a 1 followed by zeros, the logarithm is simply how many zeros. That is all a (base-ten) logarithm is: a way of counting zeros.
Step 2: small numbers have minus logarithms
0.001 = 10⁻³. So the logarithm of 0.001 is −3.
0.000 000 1 = 10⁻⁷. The logarithm is −7.
The smaller the number, the more negative its logarithm. It is still counting the zeros, just on the other side of the decimal point.
Step 3: what about numbers in between?
Numbers that are not neat powers of ten have logarithms in between. Here is one worth remembering:
2 is about 10⁰·³, so the logarithm of 2 is about 0.3.
That means: multiplying by 2 adds 0.3 to the logarithm.
Multiplying by 10 adds exactly 1.
This is Napier’s trick in action: multiplying numbers is the same as adding their logarithms. Before calculators, sailors and engineers looked logarithms up in printed tables, added them, and looked the answer back up. Slide rules, which engineers used to design bridges, aeroplanes and even the rockets that flew to the Moon, are just two logarithm rulers sliding past each other.
Step 4: why chemists love logarithms
The amount of hydroniumions in water can be anything from about 1 mole per litre (in strong acid) to about 0.000 000 000 000 01 moles per litre (in strong alkali). Those numbers are horrible to compare. Their logarithms are 0 and −14: easy.
That is exactly why the pH scale was invented. pH is the logarithm of the hydronium concentration, with the minus sign removed so the numbers come out positive:
Hydronium at 0.001 mol/L = 10⁻³ mol/L, so pH = 3.
Hydronium at 0.000 000 1 mol/L = 10⁻⁷ mol/L, so pH = 7.
Each step of 1 in pH is a factor of 10 in hydronium.
A step of 0.3 in pH is a factor of about 2.
The pH scale is a logarithm ruler. Each step to the left multiplies the hydronium concentration by ten.
Careful
“pH 4 is twice as acidic as pH 2, because 4 is twice 2.”
Logarithm scales do not work like that. pH 2 has 100 times more hydronium than pH 4 (two steps, ten times each), so it is much more acidic, not less. Whenever you see a logarithm scale, translate each step into “times ten”.
Logarithms turn up in more places than chemistry. The loudness of sound in decibels, the strength of earthquakes and the brightness of stars all use logarithm scales, for the same reason: the real numbers stretch across too many powers of ten to handle comfortably.
A logarithm ruler on your wall
Take a long strip of paper and mark 0, 1, 2, 3, 4, 5 at equal steps of 10 cm. Above them write 1, 10, 100, 1,000, 10,000, 100,000. Now find where 2 goes: it is about 0.3 of the way from the 0 mark to the 1 mark, so 3 cm along. Where does 20 go? (Hint: 20 is 10 × 2, so add the steps.) You have just made the scale that a slide rule, a pH meter and an earthquake scale all use.
So when you meet pH in Chapter 7, remember Napier in his castle: a logarithm is simply a way of counting zeros, so that numbers spanning many powers of ten fit on one friendly ruler.
What is a scientific model?
A Mumbai local train, the morning rush
Look at the route map above the doors of a Mumbai local train. The stations are evenly spaced dots on straight coloured lines. The real tracks curve, the real stations are close together in some places and far apart in others, and the real city is full of buildings, roads and the sea, none of which appear on the map at all. The map is “wrong” about almost everything.
And yet it is exactly what you need. It tells you which stations come in which order, where to change trains, and how many stops are left. A map that showed every building and every curve would be much harder to use. The route map works because it leaves things out.
That is what scientists mean by a model. A model is a simplified picture, drawing, set of rules or piece of mathematics that captures the part of the truth you need for a particular job, and leaves out the rest on purpose.
Step 1: every model has a job
A globe is a model of the Earth. It gets the shapes of the continents right, but it is far too smooth: on a globe the size of a football, Mount Everest would be a bump about as high as one or two sheets of paper are thick. A model car shows the shape of a car but not how the engine works. Neither is a failure. Each one is good at its own job.
The pictures of atoms in this book are the same. The counting diagrams in Chapter 1 are good at one job: counting protons, neutrons and electrons. They are useless for size (the real nucleus would be invisibly small on the page) and wrong about where electrons are. That is fine, as long as you know which job a picture is for.
Step 2: models improve when evidence surprises them
The history of the atom is a parade of models, each one replaced when an experiment showed something it could not explain.
Five models of the atom. Each was the best explanation of the evidence at the time, and each was improved when a new experiment surprised it.
John Dalton pictured atoms as solid, uncuttable balls. That explained why chemicals combine in fixed proportions. Then J. J. Thomson found electrons coming out of atoms, so atoms could not be solid and uncuttable: he imagined a positive ball with electrons dotted through it. Then Rutherford’s gold-foil experiment showed a tiny, heavy centre, so the model became a nucleus with electrons around it. Niels Bohr added energy levels to explain the colours of light that atoms give out. Today we describe electrons as clouds of likelihood, worked out with quantum physics.
Notice that the old models were not thrown away in shame. Dalton’s solid balls are still perfectly good for balancing chemical equations. Each model is the right tool for some jobs.
Step 3: how to read any model
Whenever you meet a new diagram or rule in this book, ask three questions:
What job is this model doing? (Counting? Showing shape? Predicting a number?)
What does it get right, and how do we know?
Where does it stop being trustworthy?
Careful
“If scientists keep changing their models, they must not really know anything.”
Changing a model is how science gets more right, not less. Each new model explains everything the old one did, plus something new. A map gets better when someone surveys a road that was missing; that does not make the old roads disappear.
The British statistician George Box summed it up in a famous line: “All models are wrong, but some are useful.” The skill is knowing which ones are useful, for what, and why.
Make a model, then break it
Make a “model” of a water molecule from a large orange and two small grapes held on with toothpicks, bent at an angle. Write down three things your model shows truthfully (for example: one oxygen, two hydrogens, a bent shape) and three things it gets wrong (sizes, colours, the fact that real atoms are not solid fruit). Then eat the model.
Chemistry is built from models like these. The trick, all the way through this book, is to use each one boldly for its own job, and to remember that it is a map, not the city.
thinking tool
Powers of ten, step by step
Archimedes, Brahmagupta
Syracuse, Sicily, about 2,250 years ago
The Greek mathematician Archimedes once set himself a strange challenge: to count how many grains of sand it would take to fill the whole universe. People said the grains of sand were beyond number. Archimedes disagreed. The problem, he saw, was not the sand. It was that the Greek way of writing numbers ran out at a myriad, ten thousand. So in a little book called The Sand Reckoner he invented a way of building bigger and bigger numbers by stacking “myriads of myriads” on top of each other, and came up with an answer, which in our notation is less than 10⁶³ grains.
His answer about the universe was wrong (it is much bigger than he thought), but his idea was right: to handle huge numbers, you need a way of writing how many times you multiply by ten. Some centuries later, mathematicians in India developed the place-value digits we still use, with zero as a digit, and in 628 Brahmagupta wrote down rules for calculating with zero. That made writing big numbers easy. And today we have the neatest shorthand of all: powers of ten.
Step 1: counting the tens
You already know that 100 = 10 × 10 and 1,000 = 10 × 10 × 10. A power of ten just counts how many tens are multiplied:
10¹ = 10
10² = 10 × 10 = 100
10³ = 10 × 10 × 10 = 1,000
10⁶ = a million (six tens multiplied; also six zeros after the 1)
10⁷ = ten million: one crore
The little raised number tells you how many zeros follow the 1. In India you already use a few special names for powers of ten: a lakh is 10⁵ (1,00,000) and a crore is 10⁷ (1,00,00,000). Scientists just use the little number instead of a name, so it works for any size.
Step 2: going smaller
What about very small numbers? Each step down divides by ten, and we write it with a minus sign:
10⁰ = 1 (no tens at all)
10⁻¹ = 1 ÷ 10 = 0.1
10⁻² = 1 ÷ 100 = 0.01
10⁻³ = 1 ÷ 1,000 = 0.001, a thousandth (a millimetre is 10⁻³ metres)
10⁻⁹ = a billionth (a nanometre is 10⁻⁹ metres)
The minus sign does not mean “negative”. It means “divide by ten this many times”.
Each step to the right is ten times smaller. Ten powers of ten take you from your own height to a single water molecule.
Step 3: writing any number this way
Most numbers are not neat powers of ten. So we write them as an ordinary number between 1 and 10, multiplied by a power of ten. This is called scientific notation (or standard form).
602,000,000,000,000,000,000,000 = 6.02 × 10²³ (count the places the decimal point moves: 23)
0.000 000 000 3 metres = 3 × 10⁻¹⁰ m (the point moves 10 places the other way)
A quick check: a big power means a big number; a minus power means a small one.
Step 4: multiplying and dividing the easy way
Here is the real magic. To multiply powers of ten, add the little numbers. To divide, subtract them.
10³ × 10⁴ = 10⁷ (a thousand times ten thousand is ten million)
10²³ ÷ 10²¹ = 10²
(6 × 10²³) × (3 × 10⁻²³) = 18 × 10⁰ = 18
That last line is a real chemistry sum: about 6 × 10²³ water molecules, each with a mass of about 3 × 10⁻²³ grams, make 18 grams of water. The giant number and the tiny number cancel out, and you are left with a gulp of water you can hold.
Careful
“10⁻³ is a negative number.”
It is a small positive number: one thousandth. A powers-of-ten number is never negative or zero, however big the minus sign in the little number. 10⁻¹⁰⁰ is unimaginably small, but it is still more than nothing.
Fold your way to the Moon (on paper)
Take a sheet of paper, about 0.1 mm thick, and fold it in half again and again. Each fold doubles the thickness. You will probably manage six or seven folds before it gets too stiff. Now work it out with a calculator: after 10 folds the stack would be about 10 cm thick; after 20 folds, about 100 metres; after 42 folds, about 440,000 km: more than the distance to the Moon. Doubling grows fast, and powers of ten are how we keep track of numbers that grow like that.
Every big and small number in this book, from 10⁻¹⁰ metres for an atom to 6.022 × 10²³ for a mole, is written in this shorthand. Once you can count the tens, those numbers stop being scary and start being useful.
thinking tool
Doubling and halving: proportion
Robert Boyle, Joseph Louis Gay-Lussac
Your kitchen, making chai
Chai for two people needs, say, 1 cup of water, 1 cup of milk and 2 teaspoons of tea leaves. Now four people want chai. You do not need a scientist to tell you what to do: double everything. Two cups of water, two of milk, four teaspoons of tea. If you only doubled the water, the chai would be weak and watery.
You have just used one of the most powerful ideas in science. When two quantities go up and down together, always by the same factor, they are proportional. And there is a second pattern, its mirror image, that is just as important. Between them, they explain a surprising amount of chemistry.
Step 1: going up together
Two quantities are directly proportional if doubling one doubles the other, tripling one triples the other, and halving one halves the other.
The giveaway is that the ratio stays the same: tea per person, grams per mole. Draw a graph of one against the other and you get a straight line that passes through zero.
Step 2: going opposite ways
Now a different situation. You have a fixed job, say 12 samosas to make, and more friends join in to help. With 1 person it takes 12 minutes; with 2 people, 6 minutes; with 3 people, 4 minutes; with 4 people, 3 minutes. As one number doubles, the other halves. These are inversely proportional.
Here the product stays the same. On a graph it makes a curve that swoops down and flattens out, never quite touching the axes.
Squeezing a gas: pressure and volume are inversely proportional at fixed temperature. Halve the volume and the pressure doubles; pressure × volume stays the same.
Step 3: the two patterns in gases
In 1662, Robert Boyle found that if you squeeze a trapped bubble of air into half the space, its pressure doubles: pressure and volume are inversely proportional (when the temperature stays the same). About 140 years later, Joseph Louis Gay-Lussac and others found that if you heat a trapped gas, its pressure rises steadily with temperature: directly proportional, as long as you measure temperature in the right way.
Step 4: the trap, and why kelvin exists
That “right way” matters. Try doubling the temperature of a gas from 10 °C to 20 °C. Does its pressure double? No: it only rises by about 3.5%. Proportion only works if zero on your scale means none of the thing at all. Zero degrees Celsius is just the freezing point of water, not “no temperature”.
The kelvin scale starts at absolute zero, where the molecules have no more energy to give up. On that scale, 10 °C is 283 K and 20 °C is 293 K, and pressure really is proportional to temperature: double the kelvins, double the pressure.
Is going from 10 °C to 20 °C “doubling”?
In kelvin: 283 K to 293 K. The ratio is 293 ÷ 283 ≈ 1.035, a rise of about 3.5%, not 100%.
To double the pressure you would need 566 K, which is about 293 °C.
Careful
“If two things both increase, they must be proportional.”
Not necessarily. Your height increased as you got older, but you are not twice as tall at 12 as you were at 6. Proportional means increasing by the same factor, with a straight-line graph through zero. Always check the ratio (for direct) or the product (for inverse).
Proportion with a balloon and a fridge
Blow up a balloon, not too tightly, and measure its distance around the middle with a piece of string. Put it in the freezer for half an hour (ask first), then measure again quickly. It has shrunk, because the cold gas inside takes up less space. Now let it warm up in the sun. In kelvin, the freezer is about 255 K and a warm room about 298 K: a change of about 17%, so expect a noticeable, but not enormous, change in size.
Whenever this book says “double this and that doubles” or “halve this and that doubles”, it is using one of these two patterns. Look for what stays the same: the ratio, or the product.
thinking tool
The unit-cancelling trick
Mars, 23 September 1999
After a journey of more than nine months, NASA’s Mars Climate Orbiter fired its engine to slip into orbit around Mars. Then it passed behind the planet, and was never heard from again. It had flown far too low and was almost certainly destroyed in the Martian atmosphere.
The investigation found the cause. One team’s software reported the push from the spacecraft’s small thrusters in American units (pound-force seconds). The navigation team’s software expected metric units (newton seconds). One pound-force is about 4.45 newtons, so every number was off by a factor of more than four, and nobody’s computer noticed. A spacecraft worth around 125 million dollars was lost because a number was written without its unit being checked.
Chemists juggle grams, moles, litres, molecules and kilojoules all day. This tool is the habit that keeps them, and you, from crashing into Mars.
Step 1: a unit is part of the number
“18” means nothing on its own. 18 grams? 18 moles? 18 molecules? These are wildly different amounts. So in science, a number always travels with its unit, and you treat the unit almost like a word that is multiplied by the number: 18 g means “18 × gram”.
Step 2: units cancel like fractions
You know from fractions that 3 × (5 ÷ 3) = 5: the 3s cancel. Units do the same.
2 hours × 60 minutes/hour = 120 minutes
The word “hour” appears on top and on the bottom, so it cancels, leaving minutes.
The “60 minutes per hour” is a conversion factor. It is really just a fancy way of writing 1, because 60 minutes and 1 hour are the same amount of time. Multiplying by 1 never changes an amount; it only changes the units you describe it in.
Step 3: chemistry’s favourite chain
The most useful chain in this book goes from grams to moles to particles. Each link is a conversion factor, and the units tell you whether to multiply or divide.
How many molecules in 36 g of water?
36 g × (1 mol / 18 g) = 2 mol (grams cancel)
2 mol × (6.022 × 10²³ molecules / 1 mol) = 1.2 × 10²⁴ molecules (moles cancel)
The bridge between grams and particles. Each arrow is a conversion factor; the units tell you which way to go.
If you set up a chain and the units do not cancel to what you want (for example you end up with g² per mol), you have flipped a factor upside down. The units have caught your mistake before it caught you.
Careful
“To get from grams to moles I just multiply by the molar mass.”
Check the units: 36 g × 18 g/mol gives 648 g² per mol, which is nonsense. Grams to moles needs the factor written so that grams cancel: 36 g × (1 mol / 18 g) = 2 mol. Whenever you are not sure whether to multiply or divide, write the units in and let them decide.
Step 4: the habit
Write every number with its unit. Write every conversion factor as a fraction. Cross out units that appear on top and bottom. If what is left is the unit you wanted, the method is right, even before you check the arithmetic.
A recipe in two languages
Find a recipe that gives amounts in cups or spoons. Using a kitchen scale, find how many grams of flour (or sugar, or rice) are in one cup. Write it as a conversion factor, like “130 g / 1 cup”. Now convert the whole recipe into grams, writing the units at every step. Then make the recipe (with an adult) using the scale instead of the cups. Do the units cancel properly all the way through?
Every calculation in this book, from moles to concentrations to energies, is a little chain of conversion factors. Write the units, let them cancel, and you will always know where you are.
The adventure in time
The ideas in this book were not found in the order a textbook teaches them. Here they are in the order they actually happened: two and a half thousand years of people asking what everything is made of.
For more than two thousand years people argued about whether matter is made of tiny uncuttable pieces. A Manchester schoolteacher turned the argument into science.
A woodcarver’s son from the edge of England who breathed laughing gas, tore new metals out of rocks with electricity, and made chemistry the most exciting show in London.
A blacksmith’s son who left school early, bound books for a living, and talked his way into a laboratory, where he named the words of electrochemistry and lit up the Christmas Lectures.
A young chemist accidentally makes a substance from a living body in a flask, and the wall between “living” and “non-living” chemistry starts to crack.
The youngest child of a Siberian family, carried across Russia by a mother who would not give up on him, who arranged the elements so well that he could describe ones nobody had yet found.
A Glasgow chemist who chased a tiny mismatch in the weight of nitrogen and found a whole new family of elements, most of them hiding in the air we breathe.
The daring idea that a still, quiet room is full of particles racing faster than a jet plane, and the scientists who proved it with nothing but mathematics.
Two friends in Heidelberg found that every element glows with its own colours. With that trick, people discovered new elements in spring water, and found helium in the Sun before anyone found it on Earth.
A teacher in Calcutta discovered a new compound, wrote the history of chemistry in ancient India, started a company in his own rooms, and trained a generation of Indian scientists.
A photographic plate left in a drawer revealed that some atoms are slowly breaking apart. It overturned the oldest idea in chemistry, and it lets us tell the age of ancient bones.
How chemists learned to pull nitrogen out of the air to make fertiliser, feeding billions of people, and why the same chemist’s story also carries a warning.
A student was asked to look for something nobody expected to see. What he found showed that every atom is almost entirely empty space around a tiny, heavy centre.
A New Zealand farm boy with a booming voice who discovered that atoms have a tiny heart, and became the first person to change one element into another on purpose.
A shy Danish student gave the atom its staircase of energy levels, built an institute where the new physics was born, and kept two Nobel medals hidden in a jar of acid.
In two short years a young Englishman used X-rays to give every element its true place in the periodic table, and showed exactly which ones were still missing.
Chemists found atoms that behaved identically but weighed differently. The explanation was a particle with no charge at all, and it took twenty years to catch.
Rutherford’s atom should have collapsed in a split second. A young Dane rescued it with a daring idea: electrons can only have certain energies, like steps on a staircase.
A young government accountant in Calcutta did experiments every evening, asked why the Mediterranean is blue, and found an effect that won India its first Nobel Prize in science.
Lise Meitner worked in a basement because women were not allowed upstairs, fled her country with almost no money, and on a snowy walk at Christmas worked out what it means for an atom to split.
A pharmacist’s son from Oregon who worked his way through college became the chemist who explained how atoms hold together, won two Nobel Prizes, and got some big things wrong too.
The periodic table lets you describe elements nobody has seen properly, and even some that have never been made. Here is how to play Mendeleev’s game yourself.
A girl who grew crystals at home learned to read X-ray patterns so well that she could see the shapes of the molecules of medicine, and spent thirty-four years on insulin.
Rosalind Franklin took the clearest X-ray picture of DNA ever made; others used it to build the double helix, and for years her part was barely mentioned.
Hydrogen from the Big Bang, carbon and oxygen from stars, gold from colliding dead stars: every atom in you has an address in the history of the universe.
A young scientist builds an instrument fussy enough to measure the air properly, takes it to the top of a volcano, and finds the planet breathing, and changing.
Three scientists on three continents, working over fifteen years, built the light, rechargeable battery that powers phones and electric cars.
Answers to Check yourself
Try each question before you look. If your answer differs, the reasoning matters more than the words: see whether you used the same idea.
Chapter 0. The chemist’s way of seeing
0.1
Which of these is an observation and which is an inference? (a) “This liquid boils at 100 °C.” (b) “This liquid is made of H₂O molecules.”
(a) is an observation: anyone with a thermometer can check it. (b) is an inference: a very well-tested explanation, but one built from evidence rather than seen directly.
One mole of water has a mass of about 18 g and contains 6.022 × 10²³ molecules. Each molecule contains three atoms. How many atoms are in that 18 g of water?
3 × 6.022 × 10²³ ≈ 1.8 × 10²⁴ atoms: two hydrogen atoms and one oxygen atom in each of the 6.022 × 10²³ molecules. Always say what you are counting.
A counting diagram shows 6 red tokens marked + in the centre, 6 brown tokens, and 6 blue tokens marked − around the outside. Name one thing this diagram reliably tells you, and one thing it does not.
It reliably tells you the numbers: 6 protons, 6 neutrons and 6 electrons (so this is a carbon atom, and it is neutral). It does not tell you the real size of the nucleus compared with the atom, where the electrons actually are, or what anything looks like; atoms have no colour.
A particle has 8 protons, 8 neutrons and 10 electrons. Which element is it?
Oxygen, because it has 8 protons. The 10 electrons only tell you about its charge (it is an oxide ion, O²⁻), and the 8 neutrons only tell you which isotope it is.
When a candle burns, its wax (made of carbon and hydrogen) seems to disappear. Do any of its carbon atoms turn into atoms of a different element?
No. Burning is a chemical change, and chemical changes only move electrons and rearrange atoms; they never touch the nucleus. Every carbon atom keeps its 6 protons and ends up, still carbon, in carbon dioxide gas that drifts away into the air.
Neutral fluorine has 9 electrons and neutral chlorine has 17. Work out their shell counts. What do they have in common?
Fluorine is 2, 7 and chlorine is 2, 8, 7. Both have 7 electrons in their outermost shell, and indeed they are members of the same chemical family (the halogens). Notice we can say this without claiming that either one “wants” an extra electron.
Is air an element, a compound or a mixture? Give a reason.
A mixture. Air contains several separate substances, mainly nitrogen (N₂), oxygen (O₂) and argon, not joined to each other. Their proportions can vary (for example, humid air has more water vapour than dry air), which a compound’s proportions never do.
Rewrite this sentence so it is scientifically accurate: “Atoms bond because they want to fill their shells.”
One good version: “Atoms bond when sharing or transferring electrons leads to an arrangement with lower energy, because of the electric attraction between nuclei and electrons.” Any answer that talks about attraction and energy, and not about atoms wanting, is right.
Magnesium chloride is an ionic solid with formula MgCl₂. Magnesium ions have a charge of 2+. What does the 2 in MgCl₂ tell you?
That there are two chloride ions (Cl⁻) for every magnesium ion (Mg²⁺) in the crystal. Two charges of −1 balance one charge of +2, so the crystal is neutral. It does not mean there are MgCl₂ molecules.
Can the formula C tell you whether a sample is graphite or diamond? What extra information do you need?
No. Both are pure carbon, so their formula is the same. You need to know the structure: how each atom is bonded to its neighbours (four neighbours in a 3D network for diamond; three, in flat sheets, for graphite).
Ammonia (NH₃) is a pyramid, with the nitrogen at the top. Boron trifluoride (BF₃) is flat, with its three fluorines spread 120° apart. Both have three polar bonds. Which molecule is polar overall, and why?
Ammonia is polar; boron trifluoride is not. In flat, evenly spread BF₃, the three bond pulls cancel exactly, like three equal ropes pulling a ring from three evenly spaced directions. In pyramid-shaped NH₃, all three N–H pulls point partly the same way, so they add up instead of cancelling.
Why is it easy to squash the air in a bicycle pump, but almost impossible to squash a syringe full of water?
In a gas the particles are far apart, with lots of empty space between them, so pushing them closer is easy. In a liquid they are already touching their neighbours, so there is almost no empty space left to squeeze out.
A sealed, rigid container of gas is warmed from 27 °C to 327 °C. By what factor does its pressure change?
Convert to kelvin first: 27 °C = 300 K and 327 °C = 600 K. The kelvin temperature has doubled, so the pressure doubles. (If you had used Celsius, you would wrongly have said it went up more than twelve times.)
What observation in a kitchen shows that the steam from a kettle is still water?
When steam touches something cold, such as a window or a pan lid, it condenses back into drops of liquid water. Hydrogen and oxygen gas would not do that at kitchen temperatures.
Bottle A holds 1 litre of salt solution at 0.50 mol/L. Bottle B holds 4 litres at 0.25 mol/L. Which tastes saltier? Which holds more salt altogether?
Bottle A tastes saltier, because each litre (and each sip) contains more salt: 0.50 mol/L against 0.25 mol/L. But Bottle B holds more salt altogether: 4 × 0.25 = 1.0 mol, compared with 1 × 0.50 = 0.50 mol in Bottle A.
Carbon dioxide (CO₂, 22 electrons per molecule) and hydrogen (H₂, 2 electrons) are both non-polar gases at room temperature. Solid CO₂ turns to gas at −78.5 °C, but hydrogen boils at −252.9 °C. Why the difference?
Neither has dipole attractions or hydrogen bonds, so only dispersion forces hold their molecules together. Dispersion forces are much stronger for bigger molecules with more electrons. CO₂, with 22 electrons, attracts its neighbours far more strongly than H₂ with 2, so it needs a much higher temperature to break free.
When a fizzy tablet is dropped into water, bubbles appear and the water cools slightly. Is that enough to prove a chemical reaction has happened? What would you need to test?
Not on its own. Bubbles could be air that was trapped in the tablet, and cooling can happen when some things simply dissolve. You would need to show that a new substance was made: for example, collect the gas and test it (carbon dioxide turns limewater milky; air does not), or show that the dissolved substances left behind are different from what was in the tablet.
Nitrogen and hydrogen react to make ammonia. Why is 1 N₂ + 1 H₂ → 1 NH₃ unbalanced, and what coefficients balance it?
Left: 2 N and 2 H. Right: 1 N and 3 H. Neither element matches. Put 2 in front of NH₃ to fix nitrogen (2 N, 6 H on the right), then 3 in front of H₂ to supply 6 H: N₂ + 3 H₂ → 2 NH₃. Check: 2 N and 6 H on each side.
What does the balanced equation N₂ + 3 H₂ → 2 NH₃ tell you, and what does it not tell you?
It tells you that if nitrogen and hydrogen react to make ammonia, they are used up in a 1 : 3 ratio of molecules and make 2 ammonia molecules for every nitrogen molecule, with every atom accounted for. It does not tell you whether the reaction happens at room temperature, how fast it is, whether it needs a catalyst (it does, and high pressure, in industry), or whether it gives out or takes in energy.
When the solid in a cold pack dissolves, the pack gets cold. Is dissolving it exothermic or endothermic? Which is higher in energy, the start or the end?
Endothermic. The surroundings (the water, the pack, your hand) lose energy and get colder, because the system took energy in. So the end (dissolved) is higher in energy than the start.
In a schematic profile, the reactants are at 40 units, the products at 10, and the peak at 100. What are the forward barrier, the reverse barrier and the overall energy change?
Forward barrier = 100 − 40 = 60. Reverse barrier = 100 − 10 = 90. Overall change = 10 − 40 = −30 (30 units released). The reverse barrier is bigger because the products sit lower, so they have further to climb.
In the A ⇌ B model with forward constant 2 and reverse constant 1, what are the forward and reverse rates at the very start, when there are 10 units of A and none of B?
Forward rate = 2 × 10 = 20 units per second. Reverse rate = 1 × 0 = 0, because there is no B yet to turn back. That is why the change is fastest at the start.
At a fixed temperature, could a catalyst lower the forward barrier by 30 units while lowering the reverse barrier by only 10? Why or why not?
No. Both barriers are measured up to the same peak. The reactants and products stay where they were, so if the peak drops by 30, both barriers drop by 30.
Set the forward constant to 1 and the reverse constant to 3, starting with 10 units of A. At equilibrium, A = 7.5 and B = 2.5. Show that the rates are equal, and explain why A ends up three times as plentiful as B.
Forward rate = 1 × 7.5 = 7.5 per second. Reverse rate = 3 × 2.5 = 7.5 per second. Equal. B turns back into A three times as readily as A turns into B, so the rates can only balance when there is three times as much A as B.
Methane burns: CH₄ + 2 O₂ → CO₂ + 2 H₂O. Using average bond enthalpies (C–H 413, O=O 498, C=O in CO₂ 799, O–H 463 kJ per mole), estimate the overall energy change. Is it exothermic or endothermic?
Break 4 C–H and 2 O=O: 4 × 413 + 2 × 498 = 2,648 kJ in. Make 2 C=O and 4 O–H: 2 × 799 + 4 × 463 = 3,450 kJ out. Overall 2,648 − 3,450 = −802 kJ: exothermic, which is why methane makes a good cooking gas. (The measured value, with the water as a gas, is also about −802 kJ.)
The A ⇌ B mixture (forward 2, reverse 1) has settled at 3.33 of A and 6.67 of B. You remove half of B. Which rate is bigger immediately afterwards, and where does the mixture settle?
After removing half the B: A = 3.33, B = 3.33. Forward rate = 2 × 3.33 ≈ 6.7, reverse = 1 × 3.33 ≈ 3.3, so the forward reaction is faster and A turns into B. The total is now 6.67, and it settles when B is twice A: A ≈ 2.22, B ≈ 4.44.
Carbon dioxide is CO₂. A carbon atom has a mass of about 12 units and an oxygen atom about 16. What is the atom ratio of carbon to oxygen, and roughly what is the mass ratio?
The atom ratio is 1 : 2 (one carbon, two oxygens). The mass ratio is 12 : 32, which simplifies to 3 : 8. So although carbon dioxide is “one-third carbon” by atoms, it is only about 27% carbon by mass.
Bottle A holds 1.0 L of salt solution at 0.50 mol/L. Bottle B holds 4.0 L at 0.25 mol/L. Which tastes saltier? Which contains more salt in total?
Bottle A tastes saltier, because its concentration is higher. But bottle B contains more salt in total: 4.0 L × 0.25 mol/L = 1.0 mol, against 1.0 L × 0.50 mol/L = 0.50 mol in A.
When ammonia dissolves in water, NH₃ + H₂O ⇌ NH₄⁺ + OH⁻. Which molecule is the acid (proton donor), and which is the base (proton acceptor)?
Water is the acid: it gives a proton to ammonia, leaving OH⁻. Ammonia is the base: it accepts the proton and becomes NH₄⁺. Water can act as an acid or as a base, depending on its partner.
Sketch or describe two beakers of particles: (A) a concentrated weak acid and (B) a dilute strong acid. How does your drawing show concentration, and how does it show strength?
Concentration is shown by how many acid particles there are in total in each beaker: lots in A, few in B. Strength is shown by what fraction of them have split into H₃O⁺ and the negative ion: almost none in A (mostly whole HA molecules), all of them in B (no whole HCl left).
You have 1.0 L of a strong acid at pH 2. How much water must you add to raise its pH to 4?
Going from pH 2 to pH 4 means a hundred times less hydronium per litre, so the acid must be spread through 100 times the volume: a total of 100 L. You need to add 99 L of water. (This works for a strong acid, where every molecule has already given up its proton.)
Why does a mixture of acetic acid and acetate resist a change in pH when a small amount of sodium hydroxide is added?
The added OH⁻ ions react with intact acetic acid molecules, CH₃COOH + OH⁻ → CH₃COO⁻ + H₂O, instead of staying free in the solution. The amounts of acetic acid and acetate only change a little, so their ratio, and hence the pH, changes only a little. It works until the acetic acid runs out.
In Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s), which particle is oxidised and which is reduced? How many electrons move for every zinc atom that reacts?
Zinc is oxidised (it loses electrons, Zn → Zn²⁺). Copper ions are reduced (they gain electrons, Cu²⁺ → Cu). Two electrons move for every zinc atom, because zinc goes from a charge of 0 to +2.
Aluminium forms Al³⁺ and silver ions are Ag⁺. Write the balanced equation for aluminium metal reacting with silver ions, and check that the charge is the same on both sides.
Al(s) + 3 Ag⁺(aq) → Al³⁺(aq) + 3 Ag(s). One aluminium atom gives three electrons, and each silver ion takes one, so three silver ions are needed. Charge on the left: 0 + 3 × (+1) = +3. On the right: +3 + 0 = +3. Balanced.
Magnesium is above zinc in the reactivity series. What happens if you put magnesium ribbon into zinc sulfate solution? What happens if you put zinc into magnesium sulfate solution?
Magnesium in zinc sulfate: magnesium gives electrons to Zn²⁺ ions, so zinc metal forms on the ribbon and Mg²⁺ goes into solution. Zinc in magnesium sulfate: nothing happens, because zinc is below magnesium and cannot push electrons onto Mg²⁺.
As a Daniell cell runs, which plate gets heavier and which gets lighter? Explain using the half-equations.
The copper plate (cathode) gets heavier, because Cu²⁺ + 2 e⁻ → Cu adds copper atoms to it. The zinc plate (anode) gets lighter, because Zn → Zn²⁺ + 2 e⁻ sends zinc atoms off into the solution as ions.
Sodium (2, 8, 1) is much bigger than lithium (2, 1), even though it has 8 more protons. Why?
Sodium’s outer electron is in a third shell, farther from the nucleus, and it is screened by ten inner electrons instead of two. Being farther away and more screened, it is held more weakly, so the atom is bigger.
Lithium’s first ionisation energy is 520 kJ/mol and its second is 7,298 kJ/mol. Explain why the second is so much larger.
The first electron comes from the outer shell (n = 2), where it is farther from the nucleus and screened by the two inner electrons. The second must come from the inner shell, close to the nucleus with nothing screening it, and from an ion that is already positive. (Not because the pull is now shared among fewer electrons: every proton pulls on every electron regardless.) So it is held far more tightly: about 14 times more energy is needed.
Chapter 10. Carbon chains and the chemistry of life
10.1
A straight-chain alkane has 5 carbon atoms. How many hydrogen atoms does it have? Check by counting the bonds each carbon needs.
The two end carbons each have one carbon neighbour, so each needs 3 hydrogens (6 in total); the three middle carbons each have two carbon neighbours, so each needs 2 hydrogens (6 more). That is pentane, C₅H₁₂, matching 2 × 5 + 2 = 12.
Methane does not dissolve in water. Methanol, CH₃OH, mixes with water completely. Explain the difference in terms of what the molecules attract.
Methane’s electrons are shared almost evenly, so it has no charged ends to attract water molecules; water molecules stay stuck to each other instead. Methanol’s –OH group has a slightly negative oxygen and a slightly positive hydrogen, so it forms hydrogen bonds with water molecules, and the two mix.
Propane boils at −42.1 °C and octane at 125.6 °C. One is sold as a liquid fuel for cars; the other is squeezed into gas cylinders for cooking. Which is which, and why?
Octane, with eight carbons, has much stronger dispersion forces, so it is a liquid at room temperature: that is petrol. Propane, with only three carbons, is a gas at room temperature; it is stored as a liquid only by squeezing it under pressure in a cylinder, and turns back into gas when you open the valve.
Pentane, C₅H₁₂, has three isomers: a straight chain; a chain of four with one branch; and a “cross” shape with four carbons around a central one, almost a ball. Put them in order of boiling point, highest first, and explain.
Straight chain (36.1 °C), then the singly branched one (27.7 °C), then the ball-shaped one (9.5 °C). The more compact the molecule, the less surface touches its neighbours, the weaker the dispersion forces, and the lower the boiling point.
Why is a fat whose chains are all straight and saturated more likely to be solid at room temperature than an oil whose chains each have a kinked double bond?
Straight chains pack closely side by side, so a lot of surface touches and the dispersion forces add up; it takes a higher temperature to separate them, so the fat is solid. Kinked chains can’t pack closely, so they attract each other less and the oil melts at a lower temperature.
Glycine, C₂H₅NO₂, has a mass of 75.07 grams per mole. Two glycine molecules join by a peptide bond. What is the formula of the new molecule, and what is its mass per mole? (Water is 18.02 grams per mole.)
Two glycines contain C₄H₁₀N₂O₄. One water, H₂O, leaves, so the new molecule is C₄H₈N₂O₃. Its mass is 2 × 75.07 − 18.02 = 132.12 grams per mole.
Why must lithium ions move through the electrolyte at the same time as electrons move through the wire? What would happen if they could not?
Each electron that leaves the graphite side through the wire takes away a negative charge; the Li⁺ ion leaving the same side through the electrolyte takes away a matching positive charge. Together they keep both sides neutral. If the ions could not move, negative charge would pile up on one side and positive on the other, the build-up would push back against the electrons, and the current would stop almost at once.
A substance that can pass a proton (a hydrogen nucleus, H⁺) to another particle. Acids taste sour and turn litmus red. (Never taste anything in a laboratory.) 7
Activation energy
The extra energy that colliding particles need to get over the hump between reactants and products. It decides how easily a reaction starts, not how much energy it releases overall. 5.2
Alkane
A chain of carbon atoms joined by single bonds, with hydrogen everywhere else. Formula CₙH₂ₙ₊₂: methane, ethane, propane, butane… 10.1
Allotropes
Different forms of the same element, with their atoms joined in different ways. Diamond and graphite are allotropes of carbon; O₂ and O₃ (ozone) are allotropes of oxygen. 2.6
Amino acid
A molecule with both an amino group and a carboxyl group. Twenty kinds are used to build the proteins in living things. 10.6
Amino group
–NH₂. A nitrogen with two hydrogens. Its spare pair of electrons can pick up H⁺, so it acts as a weak base. 10.6
Anode and cathode
The anode is the electrode where oxidation happens; the cathode is where reduction happens. In a cell that makes electricity, the anode is the negative terminal. 8.4
Atom ratio
The ratio of the numbers of atoms of each element, such as 2 hydrogen : 1 oxygen in water. 6.1
Atomic number (Z)
The number of protons in an atom’s nucleus. It decides which element the atom is: 1 is hydrogen, 6 is carbon, 8 is oxygen, 79 is gold. 1.2
Average atomic mass
The average mass of an element’s atoms in a natural sample, weighted by how common each isotope is. This is the decimal number printed on most periodic tables. 1.3
Avogadro’s constant
The number of things in one mole, 6.022 140 76 × 10²³. Since 2019 this is an exact number, fixed by definition. 0.2
Balanced equation
A chemical equation with the same number of atoms of each element on both sides of the arrow. 4.3
Base
A substance that can accept a proton from an acid. 7
Bond enthalpy
The energy needed to break one mole of a particular bond in gas molecules. Tables give average values, so calculations with them are good estimates, not exact answers. 5.6
Buffer
A mixture of a weak acid and the particle it forms when it gives up a proton (here, acetic acid and acetate). It resists changes in pH when small amounts of acid or base are added. 7.4
Calorimeter
A container that measures the energy a reaction gives out or takes in, by measuring the temperature change of water around it. 5.1
Carbonic acid
H₂CO₃, a weak acid formed when carbon dioxide reacts with water. It gives the slight sharpness to fizzy drinks. 11.1
Carboxyl group
–COOH. The functional group of carboxylic acids such as ethanoic acid. It can give an H⁺ to water. 10.6
Catalyst
A substance that speeds up a reaction by providing a route with a lower activation energy. It is not used up overall. 5.4
Change of state
Melting, freezing, boiling (evaporating) or condensing. The substance stays the same; only the arrangement and motion of its particles change. 3.3
Chemical change (reaction)
A change in which atoms are rearranged into new substances, with new properties. The atoms themselves are kept. 4.1
Coefficient
The big number written in front of a formula. It counts how many whole particles there are. 4.2
Compound
A substance made of two or more elements joined together in a fixed ratio, such as water, H₂O. 2.1
Concentration
How much solute there is in each litre of a solution. Concentration = amount of solute ÷ volume of solution. 3.5
Condensation reaction
A reaction in which two molecules join and a small molecule, usually water, is released. 10.6
Counting model
A diagram that shows how many particles of each kind there are. It is not a picture of where they are or how big they are. 1.1
Covalent bond
A link between two atoms that share electrons. Both nuclei are attracted to the shared electrons between them. 2.3
Covalent network
A giant structure in which covalent bonds link atoms throughout a whole crystal, with no separate molecules. Diamond is one. 2.6
Dipole
A molecule (or bond) with a slightly positive end and a slightly negative end. 2.7
Dispersion forces
Weak attractions between all molecules, caused by electrons briefly bunching up on one side. Stronger for bigger molecules with more electrons. 3.6
Double bond
Two shared pairs of electrons between the same two atoms. A C=C double bond is shorter and stronger than a single bond, and cannot twist. 10.5
Dynamic equilibrium
The state of a reversible reaction when the forward and reverse rates are equal, so the amounts stay constant even though both reactions continue. 5.5
Electrolysis
Using electricity from outside to drive a redox reaction that would not happen by itself. 8.4
Electronegativity
How strongly an atom in a bond pulls shared electrons towards itself. Fluorine, oxygen and nitrogen are among the strongest. 2.7
Element
A substance made of atoms that all have the same number of protons. 1.2
Elementary charge
The size of the charge on one proton (+1) or one electron (−1). It is the smallest amount of charge any free particle has. 1.4
Enzyme
A catalyst made by a living thing, usually a protein. 5.4
Equivalence point
The moment in a titration when just enough base has been added to react with all of the acid. 7.4
Excess reactant
A reactant left over once the limiting reactant has run out. 6.4
Exothermic, endothermic
Exothermic: energy flows out of the system and the surroundings get warmer. Endothermic: energy flows into the system and the surroundings get colder. 5.1
Formula unit
The simplest ratio of ions in an ionic compound. NaCl means 1 Na⁺ for every 1 Cl⁻; MgCl₂ means 1 Mg²⁺ for every 2 Cl⁻. 2.5
Functional group
A small group of atoms on a carbon molecule, such as –OH or –COOH, that gives it its typical behaviour. 10.2
Galvanic cell
Two halves of a redox reaction in separate containers, joined by a wire and a salt bridge, so that the electrons travel through the wire as an electric current. 8.4
Half-equation
One half of a redox reaction written on its own, showing the electrons lost (oxidation) or gained (reduction). 8.2
Hydrogen bond
An attraction between a hydrogen atom attached to N, O or F and a nitrogen, oxygen or fluorine atom on a neighbouring molecule. Still far weaker than a covalent bond. 3.6
Hydronium ion (H₃O⁺)
A water molecule that has accepted an extra proton. More hydronium ions means a more acidic solution. 7.1
Ideal gas law
PV = nRT. It links the pressure, volume, amount and kelvin temperature of a gas. It works well for most gases unless they are very squashed or very cold. 3.4
Inference
A conclusion reached by reasoning from evidence. In chemistry, our ideas about particles we cannot see are inferences, built into models. 0.1
Intermolecular forces
Attractions between separate molecules. They are much weaker than the covalent bonds inside a molecule. 3.3
Inverse-square law
A rule where a force gets weaker with the square of the distance: twice as far, one quarter of the force; three times as far, one ninth. 2.2
Ion
An atom or group of atoms with an overall electric charge, because its numbers of protons and electrons are not equal. 1.4
Ionic lattice
A giant, regular, repeating arrangement of positive and negative ions, held together by their attraction in every direction. 2.5
Ionisation energy
The energy needed to pull one electron completely away from an atom. A high value means the electron is held tightly. 1.6
Isomers
Different compounds with the same molecular formula but atoms joined in a different order. 10.4
Isotopes
Atoms of the same element (same number of protons) with different numbers of neutrons. 1.3
Kelvin (K)
A temperature scale that starts at absolute zero (−273.15 °C). Kelvin = degrees Celsius + 273.15. 3.2
Le Châtelier’s principle
A rule of thumb: when a system at equilibrium is disturbed, it shifts in the direction that partly undoes the change. For changes in amounts, it follows from the rates. 5.7
Limiting reactant
The reactant that gets used up first, which stops the reaction and limits how much product can form. 6.4
Lithium-ion cell
A rechargeable cell in which lithium ions move back and forth between layers of graphite and layers of a metal oxide, while electrons travel through the outside circuit. 11.2
Mass number (A)
The number of protons plus the number of neutrons in one nucleus. It is always a whole number. 1.3
Mixture
Two or more substances mingled together but not chemically joined. Their proportions can vary, and they can usually be separated by physical means such as evaporating or filtering. 2.1
Molar mass
The mass of one mole of a substance, in grams per mole (g/mol). For water it is about 18.0 g/mol. 6.3
Mole
A counting unit, like a dozen, but much bigger: one mole is 6.022 × 10²³ things (atoms, molecules, or whatever you say you are counting). 0.2
Molecule
A group of atoms joined by covalent bonds that acts as a single unit. All the molecules of one substance are identical (apart from tiny differences between isotopes). 2.4
Nucleus
The tiny centre of an atom, holding its protons and neutrons, and almost all of its mass. 1.1
Observation
Something you can see or measure directly, such as a colour, a mass, a temperature, or a change of state. 0.1
Ocean acidification
The slow fall in the pH of seawater as it absorbs carbon dioxide from the air. 11.1
Orbital
A region around a nucleus where an electron is likely to be found, with a definite shape and energy. Shells are made up of orbitals. 9.1
Organic compound
A compound built around carbon atoms, usually bonded to hydrogen. The name is old: people once thought only living things could make them. 10.1
Oxidation
Losing electrons. Zinc is oxidised when Zn becomes Zn²⁺. 8.1
Partial charges (δ⁺, δ⁻)
Small charges on atoms in a molecule, caused by electrons being shared unequally. They are fractions of a full charge. 2.7
pH
A number that says how acidic a solution is, by counting the powers of ten in its hydronium concentration. pH 7 is neutral; lower is more acidic; higher is more basic. 7.3
Physical change
A change of state, shape or mixing in which no new substance is made. The particles keep their identity. 4.1
Powers of ten
A short way of writing big and small numbers. 10⁶ is a million; 10⁻⁶ is a millionth. Each step of 1 in the little number is a factor of ten. 0.2
Pressure
The push of a gas (or liquid) on each square metre of surface. Measured in pascals (Pa); normal air pressure is about 101,000 Pa, or 101 kPa. 3.2
Proton, neutron, electron
The three particles that atoms are built from. Charges: proton +1, neutron 0, electron −1. A proton or neutron has nearly 2,000 times the mass of an electron. 1.1
Rate of reaction
How quickly a reaction goes: the amount of a substance used up or made per unit of time. 5.3
Reactivity series
A list of metals in order of how readily they give away electrons. A metal will push a lower metal’s ions out of solution, but not a higher one’s. 8.3
Redox reaction
A reaction in which electrons pass from one substance to another. Oxidation and reduction always happen together. 8.1
Reduction
Gaining electrons. Copper ions are reduced when Cu²⁺ becomes Cu. 8.1
Salt bridge
A path of salt solution between the two beakers of a cell. Ions move along it to keep each beaker electrically neutral, completing the circuit. 8.4
Shell
A group of electrons with similar energy in an atom. Shells are energy levels, not circular tracks. 1.6
Shielding
The way inner electrons reduce the pull of the nucleus on outer electrons, by repelling them. Electrons in the same shell shield each other only weakly. 9.1
Skeletal formula
A shorthand drawing of a molecule: lines for the carbon skeleton, a carbon at each corner and end, hydrogens on carbon left out. 10.1
Solute, solvent, solution
The solute is the substance that dissolves (salt); the solvent is what it dissolves in (water); the mixture is a solution. 3.5
Spectator ions
Ions that are present in a reacting mixture but come out unchanged, like the sulfate ions in copper sulfate solution. 8.1
States of matter
Solid, liquid and gas. The same substance can be in any of them, depending on its temperature and the pressure around it. 3.1
Strong acid
An acid that gives up its protons to water almost completely, such as hydrochloric acid. 7.2
Subscript
The small lowered number in a formula. It counts atoms of the element just before it, in one molecule or formula unit. 2.4
Sub-shell
A group of electron places within a shell. There are four kinds, called s, p, d and f, holding 2, 6, 10 and 14 electrons. S71
Successive ionisation energies
The energies needed to remove an atom’s electrons one after another. A large jump shows that the next electron is in an inner shell. 9.2
System and surroundings
The system is the substances you are studying. The surroundings are everything else, which can give energy to the system or take it away. 5.1
Temperature
A measure of how hot something is. In a gas it goes up and down with the average energy of the particles’ motion. 3.2
Tetrahedron
A pyramid with four triangular faces. The four bonds of a carbon atom with only single bonds point to its four corners, about 109.5° apart. 10.1
Thermal motion
The constant random movement of particles. The higher the temperature, the more vigorous it is. 3.6
Titration
Adding a solution of known concentration, a little at a time, to measure exactly how much of something is in another solution. 7.4
Weak acid
An acid that gives up its protons to water only partly, so most of its molecules stay whole, such as acetic acid. 7.2
About the models and numbers in this book
Where the numbers come from
Most numbers in this book are real measurements: boiling points, atomic masses, ionisation energies, bond lengths, the sizes of atoms, the voltage of a cell. They come from the standard reference collections that chemists everywhere rely on, such as the values published by IUPAC (the International Union of Pure and Applied Chemistry), NIST (the US National Institute of Standards and Technology) and the CRC Handbook of Chemistry and Physics. They have been rounded to make them easier to read, so you may find slightly different last digits in another book. That is normal: different sources measure in slightly different conditions, and round differently.
A few numbers are made up on purpose, to make a model easy to follow: the “12 u and 13 u” isotope mixture, the energy profiles drawn “in model units”, and the reaction A ⇌ B with its neat rate constants. Whenever a number is invented, the text says so.
The models, and where they break
Counting models of atoms. Drawing protons, neutrons and electrons as little balls is perfect for counting. It is useless for size (the real nucleus is tens of thousands of times narrower than the atom) and wrong about electrons, which are not little balls sitting in particular places.
Shells. Grouping electrons into shells (2, then 8, then 8) explains a great deal, from the families of the periodic table to the cliffs in ionisation energies. It works neatly only for the first 18 elements. Beyond that, and to explain the small dips in Figure 1.7, you need orbitals: the regions where electrons are likely to be found, described by quantum physics.
Ideal gases. The rule linking pressure, volume, temperature and amount treats gas particles as points that never attract each other. Real gases follow it well at everyday conditions, and badly when squeezed hard or cooled until they are close to turning into liquid.
Average bond energies. Adding up the energy to break bonds and the energy given out by making them gives good estimates of the energy of a reaction. But a bond’s strength depends a little on the molecule it is in, so the answers are estimates, usually close but not exact.
The rate picture of equilibrium. Explaining equilibrium as forward and backward reactions running at equal speeds is true and useful. The simple rate rules in Chapter 5 hold for single-step reactions; most real reactions happen in several steps, and their rates are worked out by experiment.
Diagrams in general. Every picture in this book has been chosen to show one thing clearly. Colours, sizes and distances are almost always for clarity rather than accuracy, and atoms themselves have no colour at all. When you meet a new diagram, the best question to ask is the one this whole book is about: what does this show truthfully, and how do we know?
Further adventures
When you have finished this book, the adventure does not stop. Here are some places to go next, all free.
MIT OpenCourseWare. The Massachusetts Institute of Technology puts many of its courses online for anyone. A few of the ideas in this book were borrowed from them.
Chemistry Behind the Magic: short videos of demonstrations that look like magic (glowsticks, colour-changing indicators, elements burning with coloured flames), each followed by the chemistry that explains it. These are for watching, not copying: the real experiments need a lab and a trained chemist.
Kitchen Chemistry: a whole MIT course in which every week’s experiment is something you eat, from bread and meringue to ice cream.
In the lab app. Every numbered section of this book has a matching investigation. Build atoms, squeeze gases and balance reactions yourself.
In the kitchen. Every Try it at home box in this book is a real experiment. Keep a notebook: write what you predicted, what happened, and what surprised you. That notebook is exactly what Lavoisier, Faraday and Marie Curie kept.
Sharing this book
This book is free to read, share and adapt under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 licence: give credit, don’t sell it, and share what you make from it the same way. The typefaces, software and map data inside it keep their own licences.