What is a mole in chemistry?
A mole is a counting unit chemists use for atoms and molecules, just as a dozen means 12. One mole contains 6.022 × 10²³ particles, a number called Avogadro’s number. The mass of one mole of a substance in grams, its molar mass, comes straight from the atomic masses on the periodic table, so it lets you convert between grams and numbers of particles.
A counting unit, like a dozen
People use special words for counting things in groups: a pair is 2, a dozen is 12 and a ream of paper is 500 sheets. Chemists need a group word too, because atoms are far too small and too numerous to count one by one. Their unit is the mole, written mol.
One mole of anything contains 6.022 × 10²³ particles, which is 602,200,000,000,000,000,000,000. The particles can be atoms, molecules or ions, so it helps to say which: one mole of water means 6.022 × 10²³ water molecules.
To get a feel for how huge this is, imagine counting one particle every second without ever stopping. Counting to one mole would take about 19 quadrillion years, more than a million times the age of the universe.
Avogadro’s number
The number 6.022 × 10²³ is called Avogadro’s number, or the Avogadro constant, in honor of the Italian scientist Amedeo Avogadro. It was originally chosen so that one mole of carbon-12 atoms has a mass of 12 grams. Since 2019, its value has been fixed at exactly 6.02214076 × 10²³, but 6.022 × 10²³ is accurate enough for almost every problem.
Molar mass: from the periodic table to grams
The molar mass of an element is the mass of one mole of its atoms, measured in grams per mole (g/mol). It has the same number as the atomic mass on the periodic table. Carbon’s atomic mass is 12.011, so one mole of carbon atoms has a mass of 12.011 g. Oxygen’s is 15.999, so one mole of oxygen atoms has a mass of 15.999 g.
For a compound, add up the molar masses of all the atoms in its formula. Water, H₂O, has 2 hydrogen atoms and 1 oxygen atom: 2 × 1.008 + 15.999 = 18.015 g/mol. Carbon dioxide, CO₂: 12.011 + 2 × 15.999 = 44.009 g/mol. Table salt, NaCl: 22.99 + 35.45 = 58.44 g/mol.
Converting grams to moles
To change a mass in grams into moles, divide by the molar mass: moles = mass ÷ molar mass. The grams cancel out and leave moles, which is a good way to check that you divided the right way around.
Worked example: how many moles are in 250 g of water, about one glassful? The molar mass of water is 18.015 g/mol, so 250 ÷ 18.015 = 13.88 mol, rounded to two decimal places.
To find the number of molecules, multiply the moles by Avogadro’s number: 13.88 × 6.022 × 10²³ ≈ 8.36 × 10²⁴ water molecules in one glass.
Converting moles to grams
To go the other way, multiply the number of moles by the molar mass: mass = moles × molar mass.
Worked example: what is the mass of 2.5 mol of table salt? 2.5 mol × 58.44 g/mol = 146.1 g. Another: what is the mass of 0.5 mol of carbon dioxide? 0.5 mol × 44.009 g/mol = 22.00 g, and that amount contains 0.5 × 6.022 × 10²³ = 3.011 × 10²³ molecules.
Think of the mole as a bridge. Divide grams by the molar mass to get moles, then multiply moles by 6.022 × 10²³ to get particles. To travel back from particles to grams, do the opposite steps in reverse order.
Key points
- A mole is a counting unit equal to 6.022 × 10²³ particles, a number called Avogadro’s number.
- An element’s molar mass in g/mol equals its atomic mass on the periodic table, such as 12.011 g/mol for carbon.
- Add up atomic masses to get a compound’s molar mass: H₂O is 18.015 g/mol and CO₂ is 44.009 g/mol.
- Divide grams by molar mass to get moles, and multiply moles by molar mass to get grams.
- Multiply moles by 6.022 × 10²³ to find the number of atoms or molecules.
Check yourself
Three quick questions on this lesson.
1. How many particles are in one mole of a substance?
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6.022 × 10²³ — One mole always contains Avogadro’s number of particles, 6.022 × 10²³.2. What is the molar mass of carbon dioxide, CO₂?
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44.009 g/mol — Add one carbon and two oxygen atoms: 12.011 + 2 × 15.999 = 44.009 g/mol.3. How many moles are in 116.88 g of table salt (NaCl, 58.44 g/mol)?