Stoichiometry

Atoms and molecules are far too small and far too many to count one by one. So chemists do exactly what a shopkeeper does with eggs — they count in bundles. A grocer's bundle is the dozen (12); the chemist's bundle is the mole.

• Mole — the gram-atomic, gram-molecular or gram-formula mass of any substance (atoms, molecules or ions) that contains 6.02 × 10²³ particles.

Just as "one dozen" always means twelve — whether of eggs, doughnuts or pencils — "one mole" always means the same enormous count, no matter the substance.

• Avogadro's number (Nₐ) — the number of particles (atoms, ions or molecules) in one mole of any substance = 6.02 × 10²³, regardless of its chemical nature.

You would never count a sack of rice grain by grain — you weigh it, because you know roughly what one grain weighs. Chemists use the same trick. Because one mole of a substance has a known mass, weighing replaces counting: weigh out the molar mass in grams and you have automatically counted out 6.02 × 10²³ particles.

• Atomic / molecular / formula mass — the mass of an atom, molecule or formula unit in a.m.u. H = 1, O = 16, so H₂O = 18 a.m.u.
• Molar mass — the same number, now read in grams per mole. 1 mole of H₂O weighs 18 g.

Think of a kitchen balance with three matched dials. Put grams on the pan; divide by the molar mass and the second dial reads moles; multiply by Avogadro's number and the third dial reads particles. Every numerical in this chapter is one trip across this scale.

• Molar volume — the volume of 1 mole of a gas at standard temperature (273 K) and pressure (1 atm). For all ideal gases it is 22.4 dm³.

Imagine a standard moving box of fixed size — 22.4 litres. Pour in one mole of hydrogen and it just fills the box. Empty it, pour in one mole of carbon dioxide — heavier, bigger molecules — and it fills exactly the same box. Volume cares about the number of molecules, not their size or mass.

Cut any compound open and ask: what share of its mass does each element own? The answer is a pie chart — the same way you might split a pizza bill by who ate what.

• Empirical formula — the simplest whole-number ratio of atoms. CH₂O.
• Molecular formula — the actual number of atoms in one molecule. Glucose, C₆H₁₂O₆.

Think of a patterned floor. The empirical formula is the single repeating tile — the smallest pattern that captures the ratio. The molecular formula is the whole floor: the tile laid down n times.

• Limiting reactant — the ingredient that runs out first; it decides how much product forms.
• Excess reactant — whatever is left over on the counter.

A burger needs 2 buns + 1 patty. You can have a freezer full of patties, but the moment you run out of buns the line stops — the buns limit the order. In 2H₂ + O₂ → 2H₂O it is exactly the same: the reactant that runs out first caps the water made; the rest is excess.

Find it by amount ÷ coefficient — the smaller value limits. Change the sliders in the live panel and press Build to watch one ingredient run out.

• Theoretical yield — the maximum product the balanced equation predicts.
• Practical (actual) yield — what you really collect after the run.
• Percentage yield — actual as a share of theoretical; the efficiency score.

A factory plans for a full crate of product, but spillage, side-reactions and filtering losses mean it never quite gets there. Percentage yield is its report card — marks scored out of marks possible.