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A2 · Practice questions · The mole

A mole is a count, not a mass.

Six original Cambridge-style questions on amount of substance, the Avogadro constant, N = nNA, molar mass and the mass of a single molecule.

Original questions All questions on this page are original work, written in the Cambridge AS & A Level style. They are not from past papers. They test the same concepts and skills the syllabus rewards.
Keep these straight

Three quantities, two links.

01
Analysis
[2 marks]

State what is meant by the Avogadro constant, and explain why amount of substance is treated as a quantity distinct from mass.

  • The Avogadro constant NA is the number of particles (atoms, molecules or ions) in one mole of a substance, 6.02 × 10²³ mol⁻¹. ✓
  • Amount of substance counts particles, whereas mass depends also on the mass of each particle; one mole of any substance has the same number of particles but a mass that depends on the substance, so the two quantities carry different information and amount of substance is an SI base quantity in its own right. ✓
02
Calculation
[3 marks]

Carbon dioxide has a molar mass of 44 g mol⁻¹. Calculate the mass of one molecule of carbon dioxide, and the number of molecules in 2.2 g of the gas.

  • Mass of one molecule = M / NA = 0.044 / 6.02 × 10²³ = 7.3 × 10⁻²⁶ kg. ✓
  • n = m / M = 2.2 / 44 = 0.050 mol. ✓
  • N = nNA = 0.050 × 6.02 × 10²³ = 3.0 × 10²² molecules. ✓
03
Calculation
[3 marks]

A copper cube has sides of length 2.0 cm. Copper has density 8960 kg m⁻³ and molar mass 63.5 g mol⁻¹. Calculate the mass of the cube, the amount of copper it contains, and the number of copper atoms in it.

  • m = ρV = 8960 × (0.020)³ = 8960 × 8.0 × 10⁻⁶ = 0.0717 kg = 71.7 g. ✓
  • n = m / M = 71.7 / 63.5 = 1.13 mol. ✓
  • N = nNA = 1.13 × 6.02 × 10²³ = 6.8 × 10²³ atoms. ✓
04
Analysis
[3 marks]

One cylinder contains 1.0 mol of hydrogen (molar mass 2.0 g mol⁻¹) and an identical cylinder contains 1.0 mol of argon (molar mass 40 g mol⁻¹). Compare the two samples in terms of the number of particles, the total mass, and the mass of a single particle.

  • Both contain the same number of particles, N = nNA = 6.02 × 10²³, because the amount of substance is the same. ✓
  • The masses differ: m = nM gives 2.0 g of hydrogen and 40 g of argon, twenty times as much. ✓
  • The mass of one particle is M / NA, so an argon atom (6.6 × 10⁻²⁶ kg) is twenty times as massive as a hydrogen molecule (3.3 × 10⁻²⁷ kg); the mass ratio of the samples comes entirely from the particle masses. ✓
05
Calculation
[2 marks]

Water has a molar mass of 18 g mol⁻¹. Calculate the number of water molecules in a glass holding 250 g of water.

  • n = m / M = 250 / 18 = 13.9 mol. ✓
  • N = nNA = 13.9 × 6.02 × 10²³ = 8.4 × 10²⁴ molecules. ✓
06
Calculation
[4 marks]

A gas cylinder contains 2.4 kg of methane, CH₄, which has a molar mass of 16 g mol⁻¹.

(a) Calculate the amount of methane in the cylinder. (b) Calculate the number of methane molecules. (c) Calculate the number of hydrogen atoms in the cylinder. (d) Calculate the mass of one methane molecule.

  • (a) n = m / M = 2400 / 16 = 150 mol. ✓
  • (b) N = nNA = 150 × 6.02 × 10²³ = 9.0 × 10²⁵ molecules. ✓
  • (c) Each molecule has four hydrogen atoms, so 4 × 9.03 × 10²⁵ = 3.6 × 10²⁶ hydrogen atoms. ✓
  • (d) Mass of one molecule = M / NA = 0.016 / 6.02 × 10²³ = 2.7 × 10⁻²⁶ kg (check: 9.03 × 10²⁵ × 2.66 × 10⁻²⁶ = 2.4 kg). ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.