9 · Reactions and counting
A chemical reaction is atoms changing partners. No atom is created, destroyed or turned into another kind. The same atoms end up bonded in a new pattern.
Everything else in this chapter follows from that one fact. Because atoms are conserved, you can count: recipes, leftovers, the mole. Because bonds are energy wells (chapter 1), you can keep books on energy: which reactions get hot, which get cold, and why burning things gives off heat.
Same atoms, new partners
Below is a box of two kinds of molecule, A2 (blue pairs) and B2 (orange pairs). When an A2 and a B2 collide hard enough, they can swap partners and leave as two AB molecules:
Think of H2 + Cl2 → 2 HCl. The AB bonds are deeper wells than the A–A and B–B bonds they replace, by an amount Q.
It goes up. Every time a reaction happens, the new pair of molecules sits deeper in its energy wells than the old pair did. Energy is conserved, so the difference has to go somewhere: it goes into motion. The molecules fly apart faster, and faster jiggling is a higher temperature (chapter 7). Watch the dashed temperature line in the chart. Then try the "takes in energy" version, where the products sit in shallower wells, and the box cools as it reacts.
Each molecule is simulated as a single round particle and only drawn as two atoms. A reaction happens when two molecules collide with enough energy along the line between their centres; then they swap atoms and the energy difference goes into (or comes out of) their motion. Real H2 + Cl2 actually reacts through a chain of single-atom swaps started by light, not through direct collisions like these. The bookkeeping is the same either way.
Look at the readout while it runs. The molecule counts change; the atom counts never do. That's the first law of chemistry, found by Lavoisier in the 1780s by weighing things carefully: mass, and with it every kind of atom, is conserved.
The total energy is conserved too, but it moves between two accounts. Chemical energy is the depth of all the wells the atoms sit in. Kinetic energy is all the jiggling. A reaction that gives out energy moves energy from the chemical account into the kinetic one (it gets hot). A reaction that takes in energy moves it the other way (it gets cold). With surroundings on, the extra jiggling leaks out as heat, and the readout tallies it.
Chemists call these exothermic and endothermic. A hand warmer is exothermic (iron rusting, fast). An instant cold pack is endothermic: a salt dissolving in water. Notice that the "takes in energy" version slows down as it goes: the box cools, so fewer collisions are hard enough to react. One more simplification: in this box the reverse reaction, 2 AB → A2 + B2, is switched off, so everything eventually reacts. In reality reactions run both ways, and an uphill reaction only gets part of the way before the two directions balance. Chapter 11 switches the reverse reaction on.
The energy ledger
You can estimate how much heat a real reaction gives out without a calorimeter, just by keeping books. Imagine the reaction in two steps. First, break every bond in the reactants: this always costs energy. Then form every bond in the products: this always releases energy. The net is the difference.
The same bond, O–H for instance, has a slightly different strength in different molecules, so tables list averages. The ledger usually lands within a few percent, as it does here. For bonds in unusual surroundings it can be off by much more.
Notice the shape. The amounts of energy going in and coming out are huge, and the net is a fairly small difference between two large numbers. Notice also where the energy comes from. Burning methane breaks four C–H bonds and two O=O bonds, and forms two C=O and four O–H bonds. Those new bonds are deeper. The energy was never "stored in" the methane; it's the difference between the starting wells and the ending ones.
"Fuels contain energy, released when their bonds break." Breaking bonds always costs energy (chapter 1). Burning releases heat because the products' bonds are deeper than the reactants' bonds. A large share of the difference is due to oxygen: the O=O double bond is unusually weak for a double bond. Klaus Schmidt-Rohr (2015) pointed out that burning almost any ordinary fuel releases roughly 400–450 kJ per mole of O2 used up. It's as fair to say the energy is "in the oxygen" as "in the fuel", and really it's in neither: it's in the rearrangement.
A molecule is a labelled graph: atoms are nodes labelled by element, bonds are edges labelled by order (single, double…). That's literally how cheminformatics stores them. A SMILES string such as CCO (ethanol) is a serialisation of a depth-first walk over that graph, with ring-closure digits for the edges the walk skips, and graph neural networks for chemistry pass messages along those edges.
A reaction is then a graph rewrite rule: delete some edges, add others, and never touch the multiset of node labels. "Atoms are conserved" is the statement that the rewrite only changes edges. Retrosynthesis software (planning how to make a target molecule) searches backwards through these rewrite rules.
The graph picture leaves out 3-D shape (left- and right-handed molecules have the same graph), electrons spread over several bonds (benzene's bonds aren't really alternating single and double), and everything about conditions: temperature, solvent, catalysts. Also, one molecule has many valid SMILES strings, so ML pipelines first canonicalise them.
Counting: recipes and leftovers
Because atoms are conserved, a reaction is a recipe with fixed proportions. Two hydrogen molecules and one oxygen molecule make two water molecules:
Choose how many of each you start with. Whichever runs out first limits how much water you get; the rest is left over.
The mole: counting by weighing
Real reactions involve around 1023 molecules, so chemists count in batches. One mole is exactly 6.02214076 × 1023 things. That number, Avogadro's number, was fixed exactly by definition in 2019. It's chosen so that a mole of a substance weighs about its molecular mass in grams: a mole of water (H2O, 1 + 1 + 16 = 18 mass units) is 18 g, a little more than a tablespoonful.
So "2 H2 + O2 → 2 H2O" also reads "4 g of hydrogen plus 32 g of oxygen make 36 g of water". Mass in equals mass out. The mole is just a unit conversion between the molecule-sized world and the kitchen-scale world, the same idea as a byte to a gigabyte, only with a stranger factor.
Two conversions worth having:
- kT per molecule at room temperature, 0.026 eV, is RT ≈ 2.5 kJ per mole. The gas constant is just R = NAk.
- 1 eV per molecule ≈ 96.5 kJ/mol. So the H–Cl bond above, 431 kJ/mol, is about 4.5 eV per bond.
For things dissolved in water, chemists count concentration in moles per litre (written M, "molar"). Pure water itself is about 55.5 M: 1000 g per litre divided by 18 g per mole. You'll need this in chapters 11 and 12.
- Look
- A bottle with some vinegar in it, a balloon with two spoonfuls of baking soda inside, and the balloon's neck stretched over the bottle's mouth so the soda stays in the balloon for now.
- Wonder
- "What will happen to the balloon when the baking soda falls into the vinegar?"
- Try
- Lift the balloon so the soda pours in. Watch it fizz and the balloon grow. Then touch the bottle: is it warm, cold, or the same?
- True sentence
- "The tiny pieces of baking soda and vinegar swap partners and make brand-new stuff, and one of the new things is a gas. The gas needs lots of room, so it blows up the balloon. Nothing disappeared: the pieces just joined up differently."
The gas is carbon dioxide, not air: say "a new gas", never "air". The bottle usually feels slightly cooler, because this reaction takes in a little energy, like the "takes in energy" setting above. Vinegar stings eyes, so keep faces back when it fizzes.
Play more
- PhET: Reactants, Products and Leftovers. The recipe game with sandwiches first, then molecules. Good with the 6-year-old too.
- PhET: Balancing Chemical Equations. Atom counting as a puzzle.
- Concord: What is a chemical reaction? Molecules with real bonds breaking and forming.
- Theodore Gray, Reactions, a photo book that works for both readers. NileRed on YouTube for real reactions done carefully.