LearnChem · Part I — What is stuff made of?
Chemistry's first working tool was a balance — and a trick for turning a balance into a counting machine.
“Who decided water is H₂O and not HO₂ — how could anyone know?”
Last time we cut a candle flame open and found a reaction you could watch: wax and air in, carbon dioxide and water out, heat as the difference. The scale under the candle kept falling — not because anything was destroyed, but because the products were leaving as gas. That left a question the flame itself cannot answer: how much air does a flame use? How many of those invisible particles? To say how many, you would first have to count them.
Nobody has ever weighed a single atom on a shop balance. The road to the answer starts somewhere humbler: with fire, and with weighing what fire changes.
A burnt match weighs less than a fresh one. You knew that without a balance: what's left is a curl of black char, and char feels like almost nothing. Fire, apparently, makes things lighter. Wood does it, and so did the candle, for a whole chapter.
So here is a pad of steel wool — fine iron threads, the kind used for scrubbing pans. Iron burns, if the threads are thin enough. In the Royal Society of Chemistry's classroom demonstration — one to watch, not to try; glowing metal forgives nothing — a hot wire touches one edge and orange sparks crawl through the pad from end to end. The whole time, the pad stands on a balance.
The steel wool glows from end to end on the balance. When it stops, the reading will be…
Commit before you look. First answers are counted anonymously, never named.
The reading goes up. In the RSC's version the wool sits on a simple see-saw balance, and the see-saw tips towards the burnt side. The iron has taken oxygen out of the air and bound it into a new solid:
4 Fe (s) + 3 O2 (g) → 2 Fe2O3 (s)Every gram the wool gains is a gram the air loses. And the match? It never lost mass either — its carbon and hydrogen left as carbon dioxide and water vapour, which drifted away without troubling the scale. Chemists have burned a match inside a sealed jar, jar and all on the balance: the reading does not move by a hair.
Keep the image: the kitchen scale that will not lie. Mass never appears and never vanishes. It only moves — between solid, liquid and gas, between the stuff and the air. A falling reading means something left; a rising reading means something joined. The balance is bookkeeping for atoms, kept perfectly, by an instrument that has no idea atoms exist.
Quick check — a candle burns on a scale and the reading slowly falls. Where does the mass go?
A bank does not count a bag of coins. It weighs the bag and divides by the mass of one coin — the scale does the counting. Hardware shops do it with screws; builders do it with cement, sold by the 50 kg bag and laid by the count of bags. Counting by weighing is older than chemistry.
One problem: to get the key number, someone counted a hundred grains by hand. Nobody can hand-count atoms. What the early chemists could get — from weighing reactions, like our steel wool — was combining ratios: water always forms from about 1 g of hydrogen for every 8 g of oxygen. Turning that into the mass of one oxygen atom needs one more thing — how many of each atom sit in a water particle. Hold that thought; it cost chemistry fifty years, and it is the next section.
Meanwhile, the trick does not need the count at all. If one sort of atom is twice as heavy as another, then 2 g of the first and 1 g of the second hold the same number of atoms — whatever that number is. Weigh out each substance's relative mass in grams and you hold matching parcels, guaranteed, without ever knowing how many are inside. Chemists gave the parcel a name. The mole: one fixed, agreed count of particles, sized so that a mole of carbon-12 atoms — the commonest sort of carbon atom — weighs 12 g almost exactly. Since 2019 the count itself is pinned by international agreement:
where NA, the Avogadro constant, is the coins-in-the-bag number for the entire material world. The bookkeeping comes out clean: one mole of hydrogen atoms weighs about 1 g, one mole of ordinary carbon 12.011 g — that odd .011 is the blend's average at work, the rice-grain point again — and one mole of water 18 g, taking water's formula on trust for one more section. The relative masses chemists already had become real masses in grams, per mole.
That is the whole secret of the different weights, so slow down on it. A mole of anything is the same count — so a mole's weight in grams simply reports how heavy that substance's own particle is. Nobody ever weighed out a mole of each substance to find these numbers; nobody could. The relative masses came first, from combining ratios like water's 1 : 8 — §3 settles how — and the grams follow from the matching-parcels rule. Compounds cost no new measurement at all: add up the passengers. A water molecule is two hydrogens and one oxygen, so a mole of water weighs 1 + 1 + 16 = 18 g. Carbon dioxide is 12 + 16 + 16 = 44 g. That 44 will earn its keep in §5.
That gives the whole bridge in one line:
In words: 18 g of water, divided by 18 g per mole, is one mole; one mole, times the Avogadro constant, is the count. Four symbols carry it, and the capitals matter:
| symbol | what it stands for |
|---|---|
| m | the mass on the balance, in grams |
| M | the mass of one mole — the molar mass, in g/mol |
| n | the number of moles in your sample |
| N | the count of actual particles |
Little m is what you weighed; big M is what one mole weighs. Weigh, divide, and you have counted the invisible. Try it on real substances:
Slide the mass to 18 g of water and the count reads 0.999 mol — a full mole of water is 18.015 g, and the bench keeps the honest figure. Either way, that is about 6 × 10²³ molecules — six hundred thousand million million million — in one mouthful. A gold ring of a few grams holds more atoms than there are grains of sand on all Earth's beaches. The numbers stop feeling like numbers at this scale; that is normal, and the bridge works anyway.
Quick check — which holds more atoms: 1 g of carbon or 1 g of gold?
Now the question at the top of the page. Combining masses were measurable — about 1 g of hydrogen to 8 g of oxygen in water. But that ratio alone cannot tell you the formula.
John Dalton, 1808, the man who made atoms respectable, needed a starting assumption. His was the simplest possible: when two elements make only one known compound, assume one atom of each. Water, then, was HO — and if oxygen pairs with hydrogen atom for atom, an oxygen atom weighs whatever the mass ratio says. Dalton's own table put it at 7, from an analysis that ran light; better analyses with the same guess gave 8. Either way, half the truth — and every oxide in his tables leaned on it.
The year after, Gay-Lussac measured something strange about gases: they react in tidy whole-number volumes. Two jugs of hydrogen consume one jug of oxygen and make two jugs of steam. Always the same small whole numbers, to within the errors of the day.
Suppose equal jugs of gas hold equal counts of particles. One jug of oxygen becomes two jugs of steam — and every steam particle contains oxygen. Then one oxygen particle must…
This is the actual argument, and you have everything needed to make it.
So oxygen travels in pairs: O2. Hydrogen gives itself away by the same trick — one jug of hydrogen and one jug of chlorine make two jugs of hydrogen chloride, so hydrogen particles split too: H2. Put both into the steam sum:
2 H2 (g) + O2 (g) → 2 H2O (g)Two jugs of hydrogen, one of oxygen, two of steam — the measured volumes, particle for particle. Each steam particle takes one whole hydrogen pair and half an oxygen pair: two hydrogens per oxygen. Water is H₂O, and oxygen's true relative mass is 16 — double anything the HO guess allowed. Dalton's tables were wrong not because his weighing was bad, but because his starting guess was.
That reading of gases is Amedeo Avogadro's, from 1811: equal volumes of gas, at the same temperature and pressure, hold equal numbers of particles. The constant with his name on it came much later; this one sentence is what he actually contributed.
And almost nobody accepted it. Two identical oxygen atoms riding together as O2 looked arbitrary — why would they pair? (Honest answer: nobody could say, and the real reason has to wait until the bonding chapters.) For fifty years, chemists worked from conflicting tables of atomic masses; some wrote water HO, others H₂O, and the literature was a mess of formulas that disagreed with each other.
It ended in September 1860, at Karlsruhe, at the first international chemistry congress ever held — called precisely because the formula chaos had become unbearable. A Sicilian chemist, Stanislao Cannizzaro, showed that taking Avogadro at his word made every measurement fall into one consistent table. Copies of his pamphlet were handed out as delegates left. The younger chemists read it on the way home and were convinced; the older generation grumbled and, in time, retired. That is who decided water is H₂O: no committee and no authority — one clean argument, applied to careful measurements, that only fit together one way.
Avogadro's argument fixes ratios, not the number in the parcel. The number took another century. Jean Perrin watched grains of plant resin — under a thousandth of a millimetre across — jitter in water under the kicks of unseen molecules, and worked out how many kickers there had to be. Then came X-ray counting: weigh a near-perfect sphere of silicon-28, measure the spacing of its atomic planes with X-rays, and work out how many atoms the sphere holds. By 2019 that count was so sharp that the number was fixed exactly, by definition, and the mole has been a defined count ever since. Atoms counted, without ever seeing one.
Quick check — Dalton's oxygen came out at about half its true mass. What was actually wrong?
Idli batter is four measures of rice to one of urad dal. Run out of dal and you stop making batter — however much rice is left in the tin. The recipe does not care what is plentiful; it cares what runs out first, and it counts in measures, not kilograms.
A chemical equation is a recipe written in counts:
2 H2 + O2 → 2 H2OTwo hydrogen molecules to every one of oxygen, no substitutions. Grams are how the ingredients arrive; moles are how the recipe reads them.
A sealed steel vessel holds 4 g of hydrogen and 32 g of oxygen; a spark sets them off. When the flame dies, what is left over?
Take hydrogen as 1 and oxygen as 16, the way chemists do for quick work.
Cross the bridge before judging. 4 g of hydrogen at 2 g per mole is 2 mol of H2; 32 g of oxygen at 32 g per mole is 1 mol of O2. Two to one — the recipe's exact ratio. The grams looked lopsided; the counts were matched, and 36 g of water forms, holding every atom. (With unrounded molar masses a quarter-gram of oxygen would be spare — that is the rounding, not the chemistry.) Watch what happens when the counts do not match:
Set six H₂ against four O₂: more hydrogen molecules than oxygen, and the hydrogen still runs out first — the recipe takes them two at a time. (An odd hydrogen molecule just sits there; the recipe cannot take half a pair.) The ingredient that runs out first and stops everything is the limiting reagent. Factories use the idea on purpose: they flood the reactor with the cheap ingredient, so that the expensive one is the one that runs out completely.
Now run the whole page backwards. If mass is bookkeeping, the books can be read in reverse: chemists burned an unknown substance, weighed what came off, and worked out what it was made of. That is how substances were identified for most of two centuries — no microscope, just a furnace, two traps and a balance. One trap catches the water, the other the carbon dioxide, and each is weighed before and after.
Methane shows the shape of the trick in the forward direction. Burning 16 g of it, rounding to whole grams:
CH4 (g) + 2 O2 (g) → CO2 (g) + 2 H2O (g)The traps gain 44 g of carbon dioxide and 36 g of water — 80 g collected from 16 g of fuel, because 64 g of oxygen joined from the air, exactly as the steel wool promised. All the carbon is in one trap, all the hydrogen in the other, and each is countable:
One catch to hold on to: the traps see only carbon and hydrogen. Anything else in the fuel — oxygen, say — would show up only as mass gone missing when the carbon and hydrogen are added back up. Run on a true unknown, the same arithmetic spells out a formula nobody knew:
Move the mass slider: the trap readings change, the ratio does not. That steadiness is the fingerprint. A formula built this way is called an empirical formula — the one the evidence forces: atom ratios only, reduced to smallest whole numbers.
Fuel C shows the fine print. Its traps spell CH₃ — and nothing stable has that formula. The real fuel is C₂H₆: same ratio, twice the size. Weighing gives ratios; molecule sizes need another tool, and that tool is several chapters away.
Quick check — a 10 g strip of magnesium is burned and every scrap of the white powder is collected. The powder weighs…
These check themselves, and “New numbers” deals a fresh set — there is nothing to memorise. Within two per cent counts as right; the last one is looser.
1. A bottle holds of water. How many moles of water molecules is that? (Water is 18.015 g/mol.)
2. A slab of dry ice — solid CO₂ — holds . How many molecules is that? Give your answer as a number × 10²³.
3. A sealed vessel holds , which is sparked so the §4 recipe — 2 H2 + O2 → 2 H2O — runs until something runs out. How many moles of water form?
4. A throwback to the course's first page, where chemistry sits: rearranging one bond costs about ; changing one nucleus costs about . The nuclear job is how many million times dearer?
0.44 g of a gaseous fuel burns completely. The carbon-dioxide trap gains 1.32 g; the water trap gains 0.72 g. Work out the empirical formula, then type it plainly, like CH4.
(CO₂ is 44.01 g/mol; water is 18.015 g/mol; each water carries two hydrogens.)
Worked through. The carbon trap: 1.32 g of CO₂ at 44.01 g/mol is 0.030 mol, and each CO₂ carries one carbon — 0.030 mol of C. The water trap: 0.72 g at 18.015 g/mol is 0.040 mol of water, each carrying two hydrogens — 0.080 mol of H. The ratio 0.030 : 0.080 is 3 : 8. Mass check: 0.030 mol of carbon plus 0.080 mol of hydrogen weighs 0.36 + 0.08 ≈ 0.44 g — the whole sample accounted for, so nothing else is hiding in it; this is the check that would expose a stowaway like oxygen. The empirical formula is C₃H₈, and here it is also the whole molecule: doubling it to C₆H₁₆ would need more hydrogens than six carbons can carry, a rule the bonding chapters explain. The fuel is propane, one of the two gases in an LPG cylinder.
A famous estimate, yours to attempt: the breath you just took — does it contain any molecules from Julius Caesar's dying breath, two thousand years ago? Assume his breath has had time to mix evenly through the whole atmosphere. You will need NA, a guess at a breath's size, and a guess at the atmosphere's. One more handle: at room temperature, a mole of any gas fills about 24 litres — Avogadro's equal-volumes idea made numerical. There is no marking here; write your reasoning down before looking.
One way through it. A breath is about half a litre — roughly 0.02 mol of air, and 0.02 × NA is about 10²² molecules. The atmosphere weighs about 5 × 10¹⁸ kg; at about 29 g/mol that is around 1.8 × 10²⁰ mol, or 10⁴⁴ molecules. So one breath is one part in 10²² of the atmosphere — and it contains 10²² molecules. The two absurd numbers cancel: on average, about one molecule of Caesar's last breath rides in every breath of yours. The estimate is crude everywhere and the answer survives anyway; that is what NA-sized numbers do.
You cannot count atoms, so weigh them. Mass is the bridge to number.