What a mole actually counts

A mole is a count, not a weight. It is 6.02214076 × 10²³ of something — molecules, atoms, ions, electrons — in exactly the way a dozen is twelve of something. Most of the confusion around molar mass, molecular mass and molecular weight disappears once that is fixed in place.

The count

The number was chosen so that the arithmetic of the bench lines up with the arithmetic of the molecule. One carbon-12 atom has a mass of exactly 12 daltons; one mole of carbon-12 atoms has a mass of almost exactly 12 grams. Whatever a single molecule weighs in daltons, a mole of them weighs in grams. The unit was defined to make that true.

Molar mass: the mass of the count

Molar mass is the mass of one mole of a substance, in grams per mole (g/mol). It is the number you use at the bench: it turns a target amount in moles into a mass you can weigh, and a weighed mass back into moles. Water is 18.015 g/mol.

Molecular mass: the mass of one

Molecular mass is the mass of a single molecule, in daltons (Da), also written u. For water that is 18.015 Da. The same digits as the molar mass, by the design above, and a different unit, because it answers a different question: one molecule, not a mole of them.

Molecular weight: the older word

Strictly a relative molecular mass, the ratio of the molecule’s mass to one dalton, and so a bare number with no unit. In everyday use “molecular weight” and “MW” mean molar mass, and a label reading MW 180.16 is read as 180.16 g/mol by everyone, without harm.

Worked example: glucose

Count the atoms in C6H12O6, multiply each count by that element’s standard atomic weight, and add.

C   6 × 12.011  =  72.066
H  12 × 1.008   =  12.096
O   6 × 15.999  =  95.994
                    ───────
                    180.156 g/mol

That is the average molar mass, the one for weighing. A mass spectrometer reports 180.06339 Da instead, because it sees one isotopic species at a time; Two masses, one molecule explains the gap. To turn this number into a mass for a given volume and concentration, see Making a solution to a target concentration.