The mole and amount of substance

Chemistry happens between individual atoms and molecules, but nobody can count them out one at a time — a visible speck of anything contains a number of particles with more than twenty digits. The mole bridges that gap. It is a counting unit, like "dozen" but vastly larger: one mole is 6.022 × 10²³ entities, the Avogadro number.

The point of fixing that particular number is what it does to masses. The molar mass of a substance in grams per mole is numerically the same as the mass of one of its particles in atomic mass units. Carbon atoms have mass 12 u, so a mole of carbon weighs 12 g. Water molecules have mass 18 u, so a mole of water weighs 18 g. A balance, which measures grams, therefore becomes an instrument for counting molecules — and that is the whole reason chemists can work quantitatively at all.

Two confusions are worth heading off. A mole is not an amount of mass: a mole of helium weighs 4 g and a mole of iron 56 g, but both contain the same number of atoms, which is the point. And molar mass (grams per mole, a property of a bulk sample) is not the mass of one molecule (atomic mass units, a property of a single particle) — the numbers coincide, deliberately, but the units and the meanings do not. Nor does state of matter change anything: a mole is a mole whether the substance is gas, liquid or solid.