The mole

Chemists count particles in moles. One mole is 6.02 × 10²³ particles (the Avogadro constant), and one mole of a substance has a mass in grams equal to its relative formula mass, Mᵣ. So moles link the mass you weigh out to the number of particles that react: n = m ÷ M.

Key facts

  • Aᵣ is the relative atomic mass of an element; Mᵣ is the sum of the Aᵣ of all the atoms in a formula.
  • One mole contains 6.02 × 10²³ particles (atoms, molecules or ions): the Avogadro constant.
  • The mass of one mole in grams equals the Mᵣ: one mole of H2O has a mass of 18 g.
  • moles = mass ÷ Mᵣ (n = m ÷ M), so mass = moles × Mᵣ.
  • number of particles = moles × 6.02 × 10²³.
  • A number after a bracket multiplies everything inside it: Ca(OH)2 has 1 Ca, 2 O and 2 H.

Worked examples

Example 1

Find the Mᵣ of calcium hydroxide, Ca(OH)2. (Aᵣ: Ca = 40, O = 16, H = 1)

  1. The 2 after the bracket doubles everything inside it: 1 Ca, 2 O and 2 H.
  2. Add the Aᵣ of every atom. Mᵣ = 40 + 2 × 16 + 2 × 1 = 74

Answer: 74

Example 2

How many moles are in 22 g of carbon dioxide, CO2? (Aᵣ: C = 12, O = 16)

  1. Find the Mᵣ. Mᵣ = 12 + 2 × 16 = 44
  2. Divide the mass by the Mᵣ. n = 22 ÷ 44 = 0.5 mol

Answer: 0.5 mol

Example 3

How many molecules are in 9 g of water, H2O? (Aᵣ: H = 1, O = 16; Avogadro constant 6.02 × 10²³ per mole)

  1. Find the Mᵣ of water. Mᵣ = 2 × 1 + 16 = 18
  2. Find the moles. n = 9 ÷ 18 = 0.5 mol
  3. Multiply by the Avogadro constant. 0.5 × 6.02 × 10²³ = 3.01 × 10²³

Answer: 3.01 × 10²³ molecules