AQA A-Level Chemistry: Relative Mass, the Mole and the Avogadro Constant — Revision Notes

Condensed for the final weeks. For the full explanation, use the Relative Mass, the Mole and the Avogadro Constant study guide.

Relative atomic and molecular mass (3.1.2.1)

Both defined relative to carbon-12 — this is why Ar and Mr have no units, they are ratios, not raw masses.

Term	Applies to
Relative atomic mass (Ar)	A single element
Relative molecular mass (Mr)	Covalently bonded molecules
Relative formula mass	Ionic compounds (e.g. NaCl) — use this term, not Mr

Using “relative molecular mass” for an ionic compound instead of the specification’s preferred relative formula mass is a small but real accuracy issue examiners look for.

The mole and the Avogadro constant (3.1.2.2)

moles = mass / Mr
moles = concentration x volume (in dm^3)
number of particles = moles x Avogadro constant

Practise each as its own rearrangeable formula — exam questions typically give two quantities and ask for the third. The Avogadro constant applies to electrons, atoms, molecules, ions, formulas and equations.

You are NOT expected to memorise the Avogadro constant’s value — questions needing it will provide it. The skill tested is applying it correctly, not recalling it.

Significant figures: report results only to the limits of the least accurate measurement used in the question.

Worked example: concentration to number of particles

250 cm³ of a 0.20 mol dm⁻³ solution of sodium chloride. How many ions, given Avogadro constant = 6.02 × 10²³ mol⁻¹?

Step 1: convert volume to dm3
        250 cm3 = 0.250 dm3

Step 2: moles of NaCl = concentration x volume = 0.20 x 0.250 = 0.050 mol

Step 3: number of formula units = moles x Avogadro constant
                             = 0.050 x 6.02x10^23 = 3.0x10^22 (2 s.f.)

Step 4: NaCl gives 2 ions per formula unit (Na+ and Cl-):
        number of ions = 2 x 3.0x10^22 = 6.0x10^22

Show every step explicitly — AQA mark schemes award method marks for correct intermediate steps even if the final answer has a small arithmetic slip. Always name (or check) the solute — the ionic multiplier depends on how many ions each formula unit releases.

Worked example: mass to moles to particles

Find the number of molecules in 8.8 g of CO₂ (Mr = 44).

moles = mass / Mr = 8.8 / 44 = 0.20 mol
number of molecules = moles x Avogadro constant
                     = 0.20 x 6.02x10^23 = 1.2x10^23 (2 s.f., matching the 8.8 g data)

Worked example: combining two calculation steps

A student reacts magnesium with excess hydrochloric acid and collects 120 cm3 of hydrogen gas. At A-level, gas volumes are found from the ideal gas equation, pV = nRT; the GCSE shortcut that 1 mole of any gas occupies 24,000 cm3 at room temperature and pressure is used here only to keep the arithmetic simple. Given that figure, and the equation Mg + 2HCl -> MgCl2 + H2, find the mass of magnesium reacted (Ar of Mg = 24).

Step 1: moles of hydrogen gas produced
        moles = volume / molar volume = 120 / 24,000 = 0.005 mol

Step 2: use the equation's mole ratio (1 : 1 for Mg : H2)
        moles of Mg reacted = 0.005 mol

Step 3: convert moles of Mg to mass
        mass = moles x Ar = 0.005 x 24 = 0.12 g

This combines a gas-volume calculation with the mass/Mr/moles triangle from 3.1.2.2 across a balanced equation – exactly the kind of multi-step question that links this sub-topic to the ideal gas equation (3.1.2.3) and to stoichiometry more broadly, rather than testing the mole concept in isolation.

Why this sub-topic is foundational

Nearly every quantitative question in A-level chemistry, from titration calculations to organic synthesis yields, ultimately depends on being able to move fluently between mass, moles and number of particles. Treat 3.1.2.1-3.1.2.2 as a toolkit to over-learn early, in the same way Ar/Mr definitions and the three calculation triangles here will reappear silently, without being re-taught, throughout the rest of the course – including the ideal gas equation (3.1.2.3) and empirical/molecular formula (3.1.2.4) that build directly on it.

Key terms

Relative atomic mass (Ar) — weighted mean mass of an atom on the carbon-12 scale, accounting for isotopic abundance. Relative molecular mass (Mr) — weighted mean mass of a molecule, same scale, summed from constituent atoms’ Ar. Relative formula mass — the ionic-compound equivalent of Mr, using the empirical formula unit. Mole — SI unit of amount of substance; one mole contains the Avogadro constant’s worth of specified particles. Avogadro constant — number of particles in one mole, ≈6.02×10²³ mol⁻¹.

A note on significant figures in practice

If a question gives one measurement to 2 significant figures and another to 4 significant figures, the final answer should be rounded to 2 significant figures – matching the LEAST precise input, not an average of the two, and not simply copying the calculator’s full display. This rule applies across every calculation in this sub-topic and is checked by AQA examiners as its own mark, separate from whether the calculation method itself was correct – a numerically correct answer given to the wrong number of significant figures can still lose a mark.

Common mistakes

• Forgetting to convert cm³ to dm³ before using a mol dm⁻³ concentration.
• Using “relative molecular mass” for an ionic compound instead of relative formula mass.
• Reporting an answer to more significant figures than the least accurate given data allows.
• Confusing the number of moles with the number of particles when the Avogadro-constant step is skipped.
• Treating “amount in moles” and “number of particles” as interchangeable.

Quick self-test

• Explain why Ar and Mr have no units.
• Calculate the number of moles in 22 g of CO₂ (Mr = 44).
• Calculate the number of ions in 500 cm³ of a 0.1 mol dm⁻³ solution of NaCl.
• Explain when “relative formula mass” should be used instead of “relative molecular mass.”
• State why the Avogadro constant’s value doesn’t need to be memorised.

Related resources

Relative Mass, the Mole and the Avogadro Constant study guide | Relative Mass, the Mole and the Avogadro Constant practice questions

Official syllabus

AQA A-level Chemistry (7405) specification, for teaching from September 2015 — aqa.org.uk/7405.