What is a Mole? The chemist’s counting unit

A single drop of water holds about 1.7 × 10²¹ molecules. Nobody counts that high — so chemistry uses a counting unit built for atoms: the mole.

In this article you will see what a mole is, where Avogadro’s number comes from, how molar mass turns grams into moles, and how to solve the conversions that appear in every chemistry exam.

A counting unit, like a dozen

A dozen means 12, whatever you are counting: eggs, pencils or planets. A mole works the same way, only the number is astronomically larger. One mole of carbon atoms, one mole of water molecules and one mole of sodium ions all contain the same number of particles.

The number is huge because atoms are tiny. A mole is the amount that makes atoms add up to something you can hold in your hand and weigh on an ordinary balance.

Avogadro’s number

The number of particles in one mole is called Avogadro’s number (or the Avogadro constant, N_A), named after the Italian scientist Amedeo Avogadro. Since the 2019 revision of the SI it is a fixed, exact value:

To feel the size: 6 × 10²³ grains of sand would cover a whole country several metres deep. Yet the same number of carbon atoms weighs just 12 grams — a small piece of charcoal.

Molar mass: grams per mole

The molar mass (M) is the mass of one mole of a substance, in grams per mole (g/mol). For an element it is numerically equal to the atomic mass on the periodic table: carbon is 12.011 u, so its molar mass is 12.011 g/mol.

For a compound you add up the molar masses of its atoms. Water, H₂O, has two hydrogens and one oxygen:

The molar mass calculator does this sum for any formula, including parentheses and hydrates, and shows each step.

The three conversions

Almost every mole problem is one of three moves. Keep the units in sight and they never go wrong:

• Grams → moles: n = m ÷ M. 36.0 g of water ÷ 18.02 g/mol = 2.00 mol.
• Moles → grams: m = n × M. 0.500 mol of NaCl × 58.44 g/mol = 29.2 g.
• Moles → particles: N = n × N_A. 2.00 mol × 6.022 × 10²³ = 1.20 × 10²⁴ molecules.

Why chemists need the mole

Chemical equations are written in particles: 2 H₂ + O₂ → 2 H₂O means two molecules of hydrogen react with one of oxygen. In the lab you cannot pick up molecules — you weigh grams. The mole is the bridge: the same equation also reads “2 mol of H₂ react with 1 mol of O₂”, and molar masses turn that into 4.03 g and 32.00 g.

This is the heart of stoichiometry: predicting how much product a reaction gives, which reactant runs out first, and how concentrated a solution is (molarity is moles per litre).

A short history

• 1811 — Amedeo Avogadro. Proposes that equal volumes of gases at the same temperature and pressure contain equal numbers of particles.
• 1865 — Josef Loschmidt. Makes the first estimate of how many molecules fit in a volume of gas.
• 1909 — Jean Perrin. Measures the constant from Brownian motion and names it after Avogadro (Nobel Prize 1926).
• 1971 — SI base unit. The mole becomes one of the seven base units, defined through 12 g of carbon-12.
• 2019 — Exact value. The SI redefinition fixes N_A at exactly 6.022 140 76 × 10²³ mol⁻¹.

Common misconceptions

“A mole of every substance has the same mass.”

Same number of particles, different masses. One mole of hydrogen gas is about 2 g; one mole of gold is about 197 g.

“Moles and molecules are the same thing.”

A molecule is one particle; a mole is 6.022 × 10²³ of them. Mixing the two is the most common source of errors by a factor of 10²³.