Chemistry · General chemistry I · Concept

The mole, molar mass and Avogadro’s number

To convert grams to moles, divide by the molar mass, the mass of one mole in g/mol, found by adding the atomic masses in the formula. To convert moles to particles, multiply by Avogadro’s number, 6.022 × 10²³ per mole.

What a mole counts

A mole is a counting unit, like a dozen, for particles far too small to count one by one. One mole is exactly 6.02214076 × 10²³ particles, Avogadro’s number, usually rounded to 6.022 × 10²³. The mole is sized so that one mole of a substance has a mass in grams equal, in number, to its formula mass in atomic mass units.

N_{A} = 6.022 \times 10^{23} {mol}^{- 1}

Molar mass from the formula

Add the atomic masses of every atom in the formula, using each subscript as a multiplier. The result, in g/mol, is the mass of one mole of the substance. Water has two hydrogen atoms and one oxygen atom.

M (H_{2} O) = 2 (1.008) + 16.00 = 18.02 g/mol

\begin{aligned} M (H_{2} O) & = 2 (1.008) + 16.00 \\ = 18.02 g/mol \end{aligned}

Grams to moles and back

Molar mass converts between mass and amount. Divide a mass by the molar mass to get moles, and multiply an amount in moles by the molar mass to get grams. Written as a fraction, the factor goes wherever it makes the unwanted unit cancel.

n = \frac{m}{M}, m = n M

Moles to particles

Multiply moles by Avogadro’s number to count particles, and divide to go back. Say which particle you mean: 1 mol of H₂O is 6.022 × 10²³ molecules but three times as many atoms, because each molecule has three atoms.

N = n N_{A}

A map of the conversions

Every conversion between mass, amount and particles passes through moles. Write each step as a factor whose units cancel, and a problem with several steps becomes one chain.

Converting between mass, amount and particles
From	To	Multiply by
grams	moles	1 mol / M grams
moles	grams	M grams / 1 mol
moles	particles	6.022 × 10²³ / 1 mol
particles	moles	1 mol / 6.022 × 10²³

Common mistakes

Multiplying by the molar mass when converting grams to moles: grams must cancel, so the molar mass goes in the denominator.
Missing a subscript when adding atomic masses: CO₂ has two oxygen atoms, so M = 12.01 + 2(16.00) = 44.01 g/mol.
Counting molecules when atoms were asked for, or the reverse.
Rounding the molar mass or a middle result early, which can shift the last reported digit.

Key terms

Mole: The SI unit of amount of substance: exactly 6.02214076 × 10²³ particles. Always say which particles you mean: atoms, molecules or ions.
Molar mass: The mass of one mole of a substance, in g/mol. It converts between grams and moles: moles = mass ÷ molar mass.
Avogadro constant: The exact constant 6.02214076 × 10²³ per mole, the number of particles in one mole. It converts between moles and numbers of particles.
Formula mass: The sum of the atomic masses of all the atoms in a chemical formula, in atomic mass units (amu). For a molecular substance it is the molecular mass.
Molecule: A discrete, electrically neutral group of two or more atoms held together by covalent bonds in a definite arrangement.
Formula unit: The group of ions given by the formula of an ionic compound, such as one Na⁺ and one Cl⁻ for NaCl. An ionic solid is a continuous network, not separate molecules.

Work through an example

How many moles of water, and how many water molecules, are in 25.0 g of H₂O?

Convert grams to moles and molecules →

Convert a number of atoms to grams →

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