What is a mole in chemistry?

This page is about the mole in chemistry. The unit's symbol is mol, and it is one of the seven base units of the International System of Units (SI), alongside the metre, the kilogram and the second. Think of it like a dozen: a dozen eggs is 12 eggs, and a mole of atoms is 6.022 × 10²³ atoms. The number is just much, much bigger.

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Moles Calculator

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The mole definition

Since 20 May 2019, the mole has been defined by fixing the Avogadro constant at an exact value. In the words of the SI Brochure, one mole contains exactly 6.022 140 76 × 10²³ elementary entities. An entity is whatever you are counting: atoms, molecules, ions or electrons.

Before 2019, a mole was defined as the number of atoms in exactly 12 grams of carbon-12. The new definition fixes the number instead, so the mole no longer depends on weighing anything. For everyday chemistry nothing changed: 12 grams of carbon-12 is still one mole to better than one part in a billion, according to NIST's value of the molar mass constant.

How big is a mole?

6.022 × 10²³ is 602,214,076,000,000,000,000,000. A mole of seconds would last 1.9 × 10¹⁶ years, about 1.4 million times the age of the universe. Yet a mole of water molecules is only 18 grams, about one tablespoon. That is how small molecules are.

Why chemists use moles

Reactions happen between particles, in fixed ratios. The equation 2H₂ + O₂ → 2H₂O says two hydrogen molecules react with one oxygen molecule. But you can't count molecules on a lab bench. You can weigh things, and the mole is the bridge: it turns a mass you can measure into a number of particles you can't see.

The trick is that the mole was chosen so the numbers line up. One carbon-12 atom has a mass of exactly 12 atomic mass units, and one mole of them has a mass of 12 grams. So the mass of one mole of any substance, in grams, has the same number as its relative mass. One mole of oxygen atoms (relative atomic mass 16) is 16 g, and one mole of water (relative formula mass 18) is 18 g.

Molar mass

The molar mass, M, is the mass of one mole of a substance, in grams per mole (g/mol). To find it, add the relative atomic mass of each element in the formula, counted as many times as that element appears. Our guide to relative formula mass covers this step in detail.

These use relative atomic masses rounded to one decimal place, which is what most school exams give you. Relative atomic masses come from the masses and abundances of each element's isotopes, which is why chlorine's is 35.5 rather than a whole number. Try that calculation here, then press Mark to check it in our Atomic Structure course.

The mole formulas

Three formulas cover almost every mole calculation.

Rearrange the first one as needed: m = n × M for mass, and M = m ÷ n for molar mass. One cubic decimetre (dm³) is one litre, which is 1,000 cm³. For gases there is a fourth shortcut: one mole of any gas takes up about 24 dm³ at room temperature and pressure, and about 22.4 litres at 0 °C and 1 atmosphere.

Grams, moles and particles: the mole map

Every conversion goes through moles. Divide by the molar mass to go from grams to moles, and multiply by the Avogadro constant to go from moles to particles. Going the other way, do the opposite.

grams  --- ÷ M --->  moles  --- × 6.022 × 10²³ --->  particles
grams  <--- × M ---  moles  <--- ÷ 6.022 × 10²³ ---  particles

There is no direct step from grams to particles. Students who try to skip moles usually multiply by the wrong thing, so write the moles down as a separate line every time.

Worked examples

Example 1: grams to moles

How many moles are in 36 g of water? M(H₂O) = 18.0 g/mol, so:

Example 2: moles to grams

What is the mass of 0.25 mol of sodium chloride? M(NaCl) = 58.5 g/mol, so m = n × M = 0.25 × 58.5 = 14.6 g to 3 significant figures.

Example 3: counting molecules and atoms

How many molecules, and how many atoms, are in 9.0 g of water?

1. Moles: n = 9.0 ÷ 18.0 = 0.50 mol.
2. Molecules: N = 0.50 × 6.022 × 10²³ = 3.01 × 10²³ molecules.
3. Atoms: each H₂O molecule has 3 atoms, so 3 × 3.01 × 10²³ = 9.03 × 10²³ atoms.

Read the question carefully: molecules and atoms give different answers whenever a molecule has more than one atom.

Example 4: the mass of one atom

What is the mass of one carbon-12 atom? One mole has a mass of 12 g and contains 6.022 × 10²³ atoms, so one atom has a mass of 12 ÷ 6.022 × 10²³ = 1.99 × 10⁻²³ g.

Example 5: using an equation

What mass of water forms when 4.0 g of hydrogen burns completely in oxygen? The equation is 2H₂ + O₂ → 2H₂O.

1. Moles of hydrogen: M(H₂) = 2.0 g/mol, so n = 4.0 ÷ 2.0 = 2.0 mol.
2. Ratio from the equation: 2 mol of H₂ makes 2 mol of H₂O, so 2.0 mol of H₂ makes 2.0 mol of H₂O.
3. Mass of water: m = 2.0 × 18.0 = 36 g.

Always go through moles. You can't compare grams of one substance with grams of another, but you can compare moles, because the equation's numbers are mole ratios. The Stoichiometry Calculator does this for any balanced equation, including limiting reactants.

Example 6: concentration

0.50 mol of a solute is dissolved to make 250 cm³ of solution. What is its concentration? Convert the volume first: 250 cm³ = 0.250 dm³. Then c = 0.50 ÷ 0.250 = 2.0 mol/dm³. The Molarity Calculator handles the unit conversions for you.

Example 7: moles of gas

At room temperature and pressure, one mole of any gas takes up about 24 dm³, whatever the gas. What volume do 0.5 mol of oxygen take up, and what is the mass of 4.8 dm³ of carbon dioxide?

• Volume of oxygen: 0.5 × 24 = 12 dm³.
• Moles of carbon dioxide: 4.8 ÷ 24 = 0.20 mol.
• Mass of carbon dioxide: 0.20 × 44.0 = 8.8 g.

This works because gas particles are so far apart that their own size hardly matters: equal volumes of gases at the same temperature and pressure hold equal numbers of particles. That idea is Avogadro's, and it is how the constant got his name.

Avogadro's number and Avogadro

The constant is named after Amedeo Avogadro, an Italian scientist who suggested in 1811 that equal volumes of gases at the same temperature and pressure contain equal numbers of particles. He never knew the number itself. Scientists only began estimating it decades later, from the 1860s onwards, and modern measurements, including counting the atoms in an almost perfect sphere of silicon-28, pinned it down well enough to fix its value in 2019.

Avogadro's number is the plain number 6.022 140 76 × 10²³. The Avogadro constant is the same number with the unit mol⁻¹, meaning "per mole". In calculations, use the constant, so the units cancel properly.

Mole Day

Chemistry classes in the US and elsewhere celebrate Mole Day on 23 October, from 6:02 a.m. to 6:02 p.m. In the US date format that is 10/23, matching 6.02 × 10²³.

Common mistakes

• Dividing the wrong way round. n = m ÷ M, not M ÷ m. A check: more grams should mean more moles.
• Using the atomic mass of an element instead of the formula mass. Oxygen gas is O₂, so its molar mass is 32.0 g/mol, not 16.0.
• Forgetting to convert cm³ to dm³. Divide by 1,000 before using c = n ÷ V.
• Comparing grams instead of moles in an equation. 2 g of hydrogen does not react with 1 g of oxygen. The numbers in an equation are moles.
• Mixing up molecules and atoms. A mole of CO₂ molecules contains 3 moles of atoms.

Read next

Chemistry · Moles and quantitiesGrams to moles calculator: n = m ÷ M with stepsConvert grams to moles and back with n = m ÷ M, find molar mass, and turn moles into particles with the Avogadro constant, with examples.