3.2 Relative formula mass and percentage by mass

How to calculate the relative formula mass of a substance from relative atomic masses, including formulae with brackets, and how to calculate the percentage by mass of an element in a compound.

AQA Edexcel OCR 1 min read

Relative formula mass

Key terms

Relative atomic mass (A_\mathrm{r}): the average mass of an atom of an element compared with carbon-12. It is the larger number in each box of the periodic table.
Relative formula mass (M_\mathrm{r}): the sum of the relative atomic masses of all the atoms in a formula.

To find M_\mathrm{r}, add up the A_\mathrm{r} of every atom in the formula. M_\mathrm{r} has no units.

Periodic table squares for calcium (40), carbon (12) and oxygen (16) used to work out the Mr of calcium carbonate as 100, and a pie chart of its percentage by mass: Ca 40%, C 12%, O 48%

Examples (A_\mathrm{r}: H = 1, C = 12, N = 14, O = 16, Mg = 24, S = 32, Ca = 40):

H₂O = (2 × 1) + 16 = 18
CO₂ = 12 + (2 × 16) = 44
CaCO₃ = 40 + 12 + (3 × 16) = 100

Brackets: multiply everything inside the bracket by the number outside.

Mg(OH)₂ = 24 + 2 × (16 + 1) = 24 + 34 = 58
(NH₄)₂SO₄ = 2 × (14 + 4) + 32 + (4 × 16) = 36 + 32 + 64 = 132

In a balanced equation, the total M_\mathrm{r} of the reactants equals the total M_\mathrm{r} of the products, because mass is conserved:

2Mg + O₂ → 2MgO: (2 × 24) + 32 = 80 and 2 × 40 = 80

Percentage by mass of an element

percentage by mass = (A_r × number of atoms of the element) ÷ M_r × 100

Example 1: percentage of calcium in CaCO₃ = (40 × 1) ÷ 100 × 100 = 40%

Example 2: percentage of nitrogen in ammonium nitrate, NH₄NO₃ (M_\mathrm{r} = 80):

(14 × 2) ÷ 80 × 100 = 28 ÷ 80 × 100 = 35%

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