A mole is the amount of a substance that contains 6.022 × 10²³ particles (atoms, molecules, ions or formula units). This number is Avogadro's number, Nₐ. One mole of any substance has a mass equal to its relative atomic, molecular or formula mass in grams, and one mole of any gas occupies 22.414 dm³ at STP.
Think of a kiryana store that sells eggs by the dozen: nobody counts eggs one by one, they count dozens. Chemists do the same with atoms, except their "dozen" is 6.022 × 10²³. That counting unit is the mole.
What is Avogadro's number?
Avogadro's number is Nₐ = 6.022 × 10²³ mol⁻¹. It is the number of particles in one mole:
- 1 mole of carbon atoms = 6.022 × 10²³ atoms
- 1 mole of water molecules = 6.022 × 10²³ molecules
- 1 mole of NaCl = 6.022 × 10²³ formula units
Always name the particle. "One mole of oxygen" is ambiguous: one mole of O atoms weighs 16 g, but one mole of O₂ molecules weighs 32 g.
Molar mass: from grams to moles
The molar mass is the mass of one mole, in g mol⁻¹. It has the same number as the relative mass:
| Substance | Relative mass | Molar mass |
|---|---|---|
| C | 12 | 12 g mol⁻¹ |
| H₂O | 2(1) + 16 = 18 | 18 g mol⁻¹ |
| CO₂ | 12 + 2(16) = 44 | 44 g mol⁻¹ |
| NaCl | 23 + 35.5 = 58.5 | 58.5 g mol⁻¹ |
The three formulas you need:
- moles = mass ÷ molar mass
- particles = moles × 6.022 × 10²³
- volume of a gas at STP = moles × 22.414 dm³
Worked example 1: molecules in 9 g of water
- Molar mass of H₂O = 18 g mol⁻¹.
- Moles = 9 ÷ 18 = 0.5 mol.
- Molecules = 0.5 × 6.022 × 10²³ = 3.011 × 10²³ molecules.
Now a favourite follow-up: how many atoms? Each H₂O molecule has 3 atoms (2 H + 1 O), so atoms = 3 × 3.011 × 10²³ = 9.033 × 10²³ atoms.
Worked example 2: volume of 11 g of CO₂ at STP
- Molar mass of CO₂ = 44 g mol⁻¹.
- Moles = 11 ÷ 44 = 0.25 mol.
- Volume = 0.25 × 22.414 = 5.60 dm³ at STP.
Worked example 3: mass of 3.011 × 10²³ glucose molecules
- Moles = 3.011 × 10²³ ÷ 6.022 × 10²³ = 0.5 mol.
- Molar mass of C₆H₁₂O₆ = 6(12) + 12(1) + 6(16) = 180 g mol⁻¹.
- Mass = 0.5 × 180 = 90 g.
Notice the pattern: every question is "convert to moles first, then convert to what is asked". Moles are the bridge between grams, particles and litres.
Common mistakes in the exam
- Not naming the particle. Write "0.5 mol of H₂O molecules", not just "0.5 mol".
- Using 22.414 dm³ for a solid or liquid. Molar volume works only for gases, and only at STP (0 °C and 1 atm).
- Forgetting atoms per molecule. Molecules and atoms are different counts; multiply by the number of atoms in the formula.
- Mixing up relative mass and molar mass. Relative mass has no unit; molar mass is in g mol⁻¹.
Quick revision
- 1 mole = 6.022 × 10²³ particles.
- moles = mass ÷ molar mass.
- 1 mole of any gas = 22.414 dm³ at STP.
- Always go through moles.
Want to practise with an interactive mole converter, board-style model answers and MCQs? Open the free lesson 1.5 The Mole.