Relative masses of atoms and molecules
Relative atomic mass and relative formula mass, and percentage composition.
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.
- 3.2.1Define relative atomic mass and relative formula mass and calculate Mr from a formula.
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Relative atomic mass and relative formula mass
Relative atomic mass
Relative atomic mass (Ar) is the average mass of the isotopes of an element, compared with 1/12 of the mass of an atom of carbon-12. It has no unit, because it is a ratio. You find it on the Periodic Table for every element.
Relative formula mass
Relative formula mass (Mr) is the sum of the relative atomic masses of every atom shown in a formula. Work through a formula systematically:
- List every element in the formula, along with how many atoms of it are present.
- Look up (or recall) the Ar of each element.
- Multiply each Ar by the number of atoms of that element, and add all the results together.
A number in a bracket applies to everything inside the bracket, so Mg(OH)₂ contains 1 Mg, 2 O and 2 H — the bracket subscript of 2 multiplies both O and H inside it.
Percentage composition
Once you know Mr, you can find what percentage of the total mass comes from one element:
% of element = (Ar of element × number of atoms of it) / Mr of compound × 100
Think of it like this
Relative formula mass is like adding up a shopping receipt: you list every item (element), its unit price (relative atomic mass) and quantity (number of atoms), multiply each line, and sum the total.
Worked examples
Method, step by step
Calculate the relative formula mass of ammonium sulfate, (NH₄)₂SO₄. (N = 14, H = 1, S = 32, O = 16)
- 1Atoms: 2 N, 8 H, 1 S, 4 O (the bracket ×2 applies to both N and the 4 H inside it)
- 2Mr = (2 × 14) + (8 × 1) + 32 + (4 × 16)
- 3Mr = 28 + 8 + 32 + 64
Mr = 132
Common misconceptions
- Forgetting that a bracket subscript multiplies everything inside it, not just the atom written immediately before the closing bracket.
- Adding relative atomic masses without multiplying by how many atoms of that element are present — for CO₂, oxygen appears twice, not once.
- Thinking relative atomic mass has a unit like grams. It is a ratio compared with carbon-12, so it has no unit.
In the exam
- Write out the atom count for every element in the formula before doing any arithmetic — this avoids missing an atom hidden inside a bracket.
- Show each step of the sum separately (element by element) rather than jumping to a final total, since method marks are awarded even if the final number is wrong.