LearnChem · Part III — Why do some things react and others just sit there?
Burn one crisp and you could warm a canful of water by some fifty degrees. Eat it instead, and your body runs the same ledger, with no flame anywhere in you. Reactions pay out heat — or swallow it — in exact, unfudgeable amounts, and the accounts can be read before any match is struck.
“Why does food give me energy but a stone doesn't? What does breathing oxygen actually do?”
Last time, the stained-glass window: colour as the slice a part-filled shelf subtracts from white light — and the same shelf hired out as a workbench: iron, unspent after years in the reactor, cheapening ammonia's hardest step while changing no ledger. That sentence was left hanging on purpose. A catalyst changes no ledger — so there is a ledger: every reaction pays out heat, or swallows it, in amounts nothing can fudge. Part III opens that book, starting with the first entry: where a reaction's heat actually comes from.
Start where the hook does: at a crisp packet, which makes a quiet, outrageous claim. It prints an energy — about 530 kcal per 100 g — a price on a snack's heat, checkable by an instrument almost insultingly simple: burn the food under a known mass of water and read how warm the water gets. Chemists call it a calorimeter — heat-measurer. Seal the flame entirely inside the water's reach and nothing escapes uncounted: a flame sealed inside a can of water is this module's anchor picture, and the bench below runs the open, leaky version — which is exactly why chemists bother sealing it. Before it runs, commit to the scale of the thing.
Quick check first — a demonstrator burns a single two-gram crisp under a small can holding 200 ml of water. Commit — roughly how much does the water warm?
The books balance on the bench: what the burn releases either lands in the water or escapes past it — nothing else. And the water's share is readable from two held numbers: each gram of water needs 4.18 joules to climb one degree, so mass, times 4.18, times the rise is the measured heat. A two-gram crisp under 200 ml pushes toward fifty degrees when the lagging is good, and would reach 53 if every joule landed. Food is fuel. The packet's number can be checked by fire — though, as §5 will admit, that is not how it was got.
Notice what the water slider showed. Double the water and the rise roughly halves — but multiply out mass × 4.18 × rise and the joules caught barely move. Temperature is how hard the heat pushes; heat is how much arrived. The bigger can is not catching less; it is spreading the same catch thinner. That distinction — module 01 planted it when one molecule had no temperature at all — is the whole craft of calorimetry, and the lagging slider is why real instruments are built like thermos flasks.
— You measure a reaction's heat by what it does to water: mass, times 4.18, times the rise.
So heat comes out in countable joules. Out of what? The gas ring under the pressure cooker burns methane — CH4 + 2 O2 → CO2 + 2 H2O — and an evening's cooking pours out of that one line. Yet the atoms on the right are exactly the atoms on the left, every one accounted for; module 03's bookkeeping says nothing material was spent. Something else changed. Commit first:
A gas ring burns methane under the pressure cooker and the kitchen fills with heat. Commit — where was that energy a minute before the match?
Commit before you look. First answers are counted anonymously, never named.
Module 06 dug the valley: two atoms bond because together they sit lower in energy than apart, and the valley's depth is the bond's price — pulling a mole of H–H apart swallows 436 kJ; letting it re-form pays the same 436 back. Four C–H grips and two O=O grips are torn open: that costs, every time. The same atoms then fall into new valleys — two C=O, four O–H — deeper, taken together, than the old ones, and the difference cannot vanish: it leaves as fast molecular motion — heat. The energy was never in the fuel like petrol in a tank. It sat in the arrangement, and it belongs to the pair — take the oxygen away and there is no deep valley for anything to fall into. Module 02's flame burned only in its thin outer skin, where fuel vapour met air, and this is why: the joules exist only where the pair meets.
Chemists write the difference as ΔH, the change in enthalpy: the heat a reaction hands out or swallows at steady pressure. Negative ΔH: heat leaves; the new valleys are deeper — exothermic. Positive: heat is taken in — endothermic.
Both signs are on sale. An instant cold pack from the chemist's turns icy because dissolving its ammonium nitrate swallows about 25.7 kJ per mole, taken from whatever the pack touches — your sprained ankle included (a standard solution-enthalpy table's figure). And a lime kiln must force roughly 178 kJ into every mole of limestone — CaCO3(s) → CaO(s) + CO2(g) — which is why a kiln burns fuel all day; the figure follows from the data book's own entries. The hiss of quicklime slaked for whitewash is a different reaction paying out its own, separate drop — not the kiln's heat refunded.
Quick check — run the ledger yourself. Burning two moles of hydrogen breaks two H–H grips (436 kJ each, module 06's price) and one O=O (498), and makes four O–H (464 each, the arm module 08 priced). Which way does the heat flow?
— Breaking bonds always costs; making bonds pays; the heat is the difference.
One habit of this ledger makes it more useful than it has any right to be. Carbon burns straight to carbon dioxide — C(s) + O2(g) → CO2(g) — paying out 393.5 kJ a mole. But there is a scenic road: burn carbon only as far as carbon monoxide, then burn the monoxide on — 2 CO(g) + O2(g) → 2 CO2(g) — paying out 283.0 kJ for every mole of CO it consumes. Same start, same finish, two roads. Commit:
Carbon can burn straight to carbon dioxide in one step — or go by two, first to carbon monoxide, then the monoxide burning on. Commit — how does the two-step road's total heat compare?
Suppose the two-step road paid more. Then run a loop: out by the generous road, back by the stingy one, pocket the difference — again, forever — a heat machine fed on bookkeeping alone. Nature sells no such machine; physics has a whole law saying so. The way out is that the total is fixed by the two ends. Enthalpy is a state function: a mixture holds a definite amount, the way a village holds a definite altitude, and a reaction's heat is the difference between two fixed readings — the route between them never enters the arithmetic. Germain Hess measured exactly this in 1840, diluting acids in one gulp or in stages and finding the same total heat (his Recherches thermochimiques, St Petersburg), before anyone knew what a bond was. Chemists call it Hess's law. It is really the discovery that the ledger keeps states, not stories.
And a rule that says the road does not matter is a licence to invent roads. A reaction you cannot run cleanly — or cannot run at all — can still be priced, by building a paper detour out of reactions you can. The bench builds the two classics:
The first cycle prices a reaction no calorimeter can watch — burn carbon gently and some always overshoots to the dioxide, so the half-burn never happens alone — yet the subtraction pins it: −110.5 kJ/mol, a number now printed in every data book, measured by arithmetic. The second manufactures methane from graphite and hydrogen — a reaction no flask will run cleanly for any calorimeter — out of three fires anyone can run, and lands inside the book value's error bar. Answers for free, provided the ledger really does keep states.
Quick check — the kiln swallows about 178 kJ for every mole of limestone it splits into quicklime and carbon dioxide. What is the heat of the reverse — quicklime taking its carbon dioxide back?
— Start and finish fix a reaction's heat; the route between them cannot touch it.
Everything so far reads history — heats somebody has already measured. Module 06 priced the valley; standard tables now price every kind of grip. If reaction heat is bonds-broken minus bonds-made, then a burn you have never seen can be priced from its formula alone: count the grips torn, count the grips formed, sum, subtract — no match struck. Price four fuels first:
Quick check — Bench 3's estimate for methane lands near −680 kJ/mol; the measured value on the same terms (Bench 4 lays the whole table out below) is −802.7. Commit — where does the difference come from?
Your verdict at the check is a hypothesis, and hypotheses about errors are checkable. If the averaged C=O is the culprit, the miss should grow in step with the carbon dioxide made — and a fuel that makes none should land clean. If the calorimeters leak, the misses should wander with no pattern at all. The data decides:
Hydrogen — the one fuel that makes no carbon dioxide — lands within a couple of kilojoules. No great triumph: for H–H, O=O and water's O–H, the table's entries are close to those molecules' own prices, so where no averaging enters, no error does. The averaging is the method's one soft part, and the hydrocarbons press on exactly that. Their drift has a fingerprint: divide each miss by the C=O bonds made and the quotient sits near 60 kJ every time. One culprit, convicted by arithmetic: carbon dioxide's two bonds are stronger than the table's mean C=O, struck as it was across many molecules of which CO₂ is not a typical one. The table is not wrong; it is average — exact where a molecule is ordinary, adrift where it is not, and the miss tells you which is which.
— A bond table prices a hydrocarbon's fire to within about a fifth, and the misses themselves say why.
Now the hook can be paid in full. Food gives you energy; a stone gives you none — and “gives” is the wrong verb in both halves. Your body is no stove: nothing in you glows, nothing reaches even boiling point. Sugar in a calorimeter goes in one flash: C6H12O6 + 6 O2 → 6 CO2 + 6 H2O. Your cells walk the same molecule through dozens of gentle enzyme steps, never a flame. Commit:
Glucose can be burnt in a calorimeter — one hot flash to carbon dioxide and water. Your cells walk the same molecule to the same carbon dioxide and water through dozens of gentle enzyme steps, never a flame. Commit — how do the totals compare?
Same two ends, same total — the ledger cannot tell a flash from an instalment plan. What you exhale is carbon dioxide and water, a burn's exact products, and that is what breathing oxygen actually does: it supplies the missing half of the pair. Oxygen's own double grip is modest beside the C=O and O–H its atoms end up in — price methane on Bench 3 and most of the payout sits on the oxygen trades. Breakfast's energy is the pair's, §2 again — this time inside you. Your cells' advantage is not the total but the collection: instalments small enough to catch as usable currency rather than one hot puff. And the stone? Granite is silicon and aluminium already gripped by oxygen — chemistry's ash, finished long before you were assembled. Its atoms sit at the bottom of the deepest valleys there are: no fall left, nothing to pay out. You could chew a mountain and starve.
By the oldest experiment in this module. In 1783 — the Mémoire sur la chaleur — Lavoisier and Laplace sat a guinea pig in a chamber jacketed with ice and weighed the meltwater its body heat produced; then they burned charcoal until the same amount of carbon dioxide had been made, and weighed that meltwater. The two matched, near enough, and their verdict — commonly quoted as “respiration is therefore a very slow combustion” — was delivered before anyone knew what oxygen does in a cell. A century on, Wilbur Atwater rebuilt the experiment for humans: a copper room where a subject lived for days while every joule in and out was booked, and the books balanced there too. The guinea pig's chamber is this module's anchor picture built from ice — a slow flame sealed where every joule must show itself — and hospitals still run its logic backwards: measure a patient's oxygen use and carbon dioxide output, and the state-function rule prices their inner fire with no thermometer anywhere near them.
One unit trap and one honest surprise. The label's Calorie is the kilocalorie — 4.184 kJ, exactly, by definition; Indian labels simply print kcal (the labelling rule is FSSAI's; the conversion and the factors below are the FAO's food-energy paper). In the 1890s Wilbur Atwater — building on two decades of European food-burning — burned weighed foods in a sealed steel vessel: a “bomb” calorimeter, Bench 1 built for keeps, of a design usually credited to Berthelot. The surprise: your packet was never burned. Labels are computed — protein 4, carbohydrate 4, fat 9 kcal per gram — and those factors sit deliberately below the bomb's readings, because a body never quite finishes the burn: protein leaves as urea with energy still folded in it, and fibre is only part-used, and that by the gut's own microbes. The printed number is your ledger, not the flame's.
One thing this module's ledger will never tell you. It prices the drop exactly, and says nothing about direction — why the smoke never reassembles into a crisp, or why the cold pack climbed uphill on its own when §2 said falls pay. How much is this module. Which way needs a different kind of counting, and it is next.
— Your cells and a flame run the same ledger; instalments never change the total.
These check themselves, and “New numbers” deals a fresh set — there is nothing to memorise. Each stem says how exact to be.
1. Module 06's price list, revisited: pulling apart a mole of costs how many kJ? (A whole number — it is on module 06's own page.)
2. Bench 1's arithmetic: g of water warms by degrees. How many kilojoules did it catch? q = mass × 4.18 × rise. (To ±0.5.)
3. The carbon triangle: (To ±1.)
4. Module 03's bridge, revisited: burning a mole of methane in a calorimeter pays 890.7 kJ (its water caught as liquid). How much heat for g of methane (M = 16 g/mol)? (To ±10.)
Bench 3 never priced ethane — C₂H₆, natural gas's other main ingredient. Its burn is 2 C2H6 + 7 O2 → 4 CO2 + 6 H2O. For one mole of ethane, count the grips yourself from the formula — every C–C and C–H it holds, the O=O its burn consumes, then the C=O and O–H it makes — price both sides from Bench 3's table, and give the estimate in kJ/mol (a negative number, to ±25). Before you peek at the solution, predict the miss too: about how far from measurement should this estimate land, and which way?
Worked through. One mole of ethane holds 1 C–C and 6 C–H, and its burn consumes 3½ O=O: 345 + 6 × 415 + 3.5 × 498 = 345 + 2,490 + 1,743 = 4,578 kJ in. It makes 2 CO₂ and 3 H₂O: 4 × 741 + 6 × 464 = 2,964 + 2,784 = 5,748 kJ out. Estimate: −1,170 kJ/mol. The measured value — Pittam & Pilcher 1972 again, via the data book — is −1,560.7 to liquid water; on Bench 4's to-steam terms, −1,428.7. The miss: about 259 kJ, and this burn makes four C=O bonds — 259 ÷ 4 ≈ 65, the same ≈60 kJ of underselling per carbon-dioxide bond that Bench 4 convicted. You could have priced the miss before the measurement arrived: that is what a prediction machine with a known bias is worth.
A day's food is about 2,000 kcal. Show that a person, averaged over the day, is roughly a 100-watt machine — state your steps and your one big assumption. Then spend the answer: a shut classroom holds thirty students; what happens to the room, and why does the afternoon feel different from the morning? Write your working before looking.
The discussion. 2,000 kcal × 4,184 J = 8.37 million joules, spread over 86,400 seconds: about 97 watts — an old filament bulb's worth of guinea-pig chemistry, running day and night. The assumption doing the work: at steady state — no growth, no stored fat change, no work leaving the room — all of the food's energy ends as heat; §3's rule is why the instalments must add up to exactly the flame's total, whatever the enzymes do in between. The classroom: thirty students is close to three kilowatts — a room heater's worth of breakfast being paid out, hour after hour, with nowhere to go, which is why the last period feels nothing like the first. Lavoisier's guinea pig, scaled to a school.
Reaction heat is the difference between the bonds broken and the bonds made.