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Chemistry 06203.3

The mole and the Avogadro constant

Moles from mass and from concentration, gas volumes, reacting-mass calculations, empirical formulae and yield.

Review these first

Learning objectives

What you need to be able to do

Teacher-mapped phrasing — check against the official Cambridge syllabus for exact wording.

  • 3.3.1Use the relationship between mass, relative formula mass and number of moles (n = m / Mr).Supplement
  • 3.3.2Use the mole ratio in a balanced equation to calculate reacting masses.Supplement
  • 3.3.3Calculate concentration in mol/dm³ and g/dm³ and use it in titration calculations.Supplement
  • 3.3.4Calculate empirical and molecular formulae from composition data.Supplement
  • 3.3.5Calculate percentage yield and percentage purity.Supplement

9 minute read

Moles and reacting masses

The mole is simply a counting unit for particles, the way "dozen" is a counting unit for eggs. One mole contains 6.02 × 10²³ particles — the Avogadro constant.

The three core relationships

  • moles = mass ÷ Mr
  • moles = concentration (mol/dm³) × volume (dm³)
  • moles of gas = volume (dm³) ÷ 24 at room temperature and pressure

Watch the volume unit: 1 dm³ = 1000 cm³. Almost every lost mark in this topic is a cm³ that should have been divided by 1000.

The universal method

Every reacting-mass question follows the same four steps:

  1. Write the balanced equation.
  2. Convert what you are given into moles.
  3. Use the mole ratio from the equation to find the moles of what you want.
  4. Convert those moles back into mass, volume or concentration.

If you can state those four steps, you can do every stoichiometry question in the paper.

Empirical formula

The empirical formula is the simplest whole-number ratio of atoms.

  1. Write the mass (or percentage) of each element.
  2. Divide each by its relative atomic mass.
  3. Divide all the answers by the smallest one.
  4. Round to whole numbers.

The molecular formula is a whole-number multiple of the empirical formula, found by comparing the empirical mass with the given Mr.

Percentage yield and purity

percentage yield = (actual yield ÷ theoretical yield) × 100

Yield is below 100% because reactions may be reversible or incomplete, some product is lost in transfer or purification, and side reactions occur.

Think of it like this

A balanced equation is a recipe. The mole ratio is "2 eggs per cake" — once you know how many eggs you have, you know how many cakes you can make.

Worked examples

Method, step by step

Calculate the mass of magnesium oxide formed when 4.8 g of magnesium burns completely in oxygen. (Mg = 24, O = 16)

  1. 1Balanced equation: 2Mg + O₂ → 2MgO
  2. 2Moles of Mg = 4.8 / 24 = 0.20 mol
  3. 3Mole ratio Mg : MgO is 2 : 2, i.e. 1 : 1, so moles of MgO = 0.20 mol
  4. 4Mr of MgO = 24 + 16 = 40
  5. 5Mass = moles × Mr = 0.20 × 40

8.0 g of magnesium oxide

25.0 cm³ of sodium hydroxide solution is neutralised by 20.0 cm³ of 0.100 mol/dm³ hydrochloric acid. Calculate the concentration of the sodium hydroxide.

  1. 1Equation: NaOH + HCl → NaCl + H₂O, ratio 1 : 1
  2. 2Moles of HCl = c × V = 0.100 × (20.0 / 1000) = 2.00 × 10⁻³ mol
  3. 3Moles of NaOH = 2.00 × 10⁻³ mol (1 : 1 ratio)
  4. 4c = n / V = 2.00 × 10⁻³ / (25.0 / 1000)

0.0800 mol/dm³

A compound contains 40.0% carbon, 6.7% hydrogen and 53.3% oxygen by mass. Determine its empirical formula. (C = 12, H = 1, O = 16)

  1. 1Divide by Ar: C = 40.0/12 = 3.33, H = 6.7/1 = 6.7, O = 53.3/16 = 3.33
  2. 2Divide by the smallest (3.33): C = 1, H = 2, O = 1

CH₂O

Common misconceptions

  • Using the mass ratio instead of the mole ratio. Equations balance particles, not grams.
  • Forgetting that concentration in mol/dm³ needs volume in dm³, not cm³.
  • Assuming percentage yield can exceed 100%. If it does, the product is wet or impure.

In the exam

  • Always write the balanced equation first, even if the question does not explicitly ask for it — it is often worth a mark.
  • Show the moles line separately. Method marks are awarded for it even when the final answer is wrong.
  • Round only at the very end, and give the answer to a sensible number of significant figures with units.