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Conservation of Mass and Formula Mass » Relative Formula Mass

What you'll learn this session

Study time: 30 minutes

AQA spec: 4.3.1.2

What relative formula mass (M_r) means
How to work out M_r from a formula, including formulae with brackets
How to check that the masses on both sides of a balanced equation add up to the same total
How to calculate the percentage by mass of an element in a compound

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What is relative formula mass?

Each white grain here is sodium chloride, and its Mr is just its atoms added up: 23 + 35.5 = 58.5

Remember, the relative atomic mass (A_r) of an element is the number you read from the periodic table. It tells you how heavy an atom of that element is compared with other atoms.

Most substances are not single atoms. They are made of atoms joined together, as shown by their formula. To find how heavy one unit of the substance is, you simply add up the A_r values of all the atoms in the formula. This total is called the relative formula mass, written M_r.

Like A_r, M_r is a relative value, so it has no units. You do not write "g" after it.

Key terms:

Relative formula mass (M_r): the sum of the relative atomic masses of the atoms in the numbers shown in the formula.
Percentage by mass: the fraction of a compound's M_r that comes from one element, written as a percentage.

How to calculate M_r

Use the same three steps every time:

Count how many atoms of each element are in the formula.
Multiply each count by that element's A_r.
Add the answers together.

In this lesson we use these A_r values, which match the periodic table you get in the exam: H = 1, C = 12, N = 14, O = 16, Na = 23, Mg = 24, Al = 27, S = 32, Ca = 40.

Worked example 1: water, H₂O

2 hydrogen atoms: 2 × 1 = 2
1 oxygen atom: 1 × 16 = 16
M_r = 2 + 16 = 18

Worked example 2: sulfuric acid, H₂SO₄

2 hydrogen: 2 × 1 = 2
1 sulfur: 1 × 32 = 32
4 oxygen: 4 × 16 = 64
M_r = 2 + 32 + 64 = 98

Formulae with brackets

That milky medicine contains magnesium hydroxide, Mg(OH)2, and the bracket doubles the OH: Mr = 24 + 2 × 17 = 58

A small number after a bracket multiplies everything inside the bracket. The easiest way is to work out the mass of the bracket group first, then multiply it.

⚗ Magnesium hydroxide, Mg(OH)₂

One OH group = 16 + 1 = 17
Two OH groups = 2 × 17 = 34
Magnesium = 24
M_r = 24 + 34 = 58

🌱 Ammonium sulfate, (NH₄)₂SO₄

One NH₄ group = 14 + (4 × 1) = 18
Two NH₄ groups = 2 × 18 = 36
SO₄ = 32 + (4 × 16) = 96
M_r = 36 + 96 = 132

Here is a harder one. Aluminium sulfate is Al₂(SO₄)₃. Two aluminium atoms give 2 × 27 = 54. One SO₄ group is 96, so three of them give 3 × 96 = 288. M_r = 54 + 288 = 342.

Relative formula mass in balanced equations

You already know that atoms are not made or lost in a reaction. This means that in a balanced equation, the total M_r of the reactants, in the quantities shown, equals the total M_r of the products, in the quantities shown.

"In the quantities shown" is the important part. If there is a big number in front of a formula, you multiply that formula's M_r by it.

Worked example 3: making ammonia

N₂ + 3H₂ → 2NH₃

Reactants:
N₂: 2 × 14 = 28
3H₂: each H₂ is 2, so 3 × 2 = 6
Total = 28 + 6 = 34

Products:
NH₃: 14 + 3 = 17
2NH₃: 2 × 17 = 34

Both sides add up to 34, so the equation checks out.

Worked example 4: neutralising sulfuric acid

2NaOH + H₂SO₄ → Na₂SO₄ + 2H₂O

Reactants:
NaOH = 23 + 16 + 1 = 40, so 2NaOH = 80
H₂SO₄ = 98 (from worked example 2)
Total = 80 + 98 = 178

Products:
Na₂SO₄ = (2 × 23) + 32 + (4 × 16) = 46 + 32 + 64 = 142
2H₂O = 2 × 18 = 36
Total = 142 + 36 = 178

Both sides are 178. If your two totals do not match, check your arithmetic and that you used the big numbers.

This is a handy way to check your work. If an exam question asks you to show that mass is conserved in an equation, this is exactly what you do.

Percentage by mass of an element

Once you know the M_r, you can work out how much of a compound's mass comes from one element. Use this formula:

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

Worked example 5: magnesium in magnesium oxide, MgO

M_r of MgO = 24 + 16 = 40
Mass from magnesium = 24
Percentage = 24 ÷ 40 × 100 = 60%

Worked example 6: nitrogen in ammonium nitrate, NH₄NO₃

There are two nitrogen atoms: one in NH₄ and one in NO₃.
M_r = 14 + (4 × 1) + 14 + (3 × 16) = 14 + 4 + 14 + 48 = 80
Mass from nitrogen = 2 × 14 = 28
Percentage = 28 ÷ 80 × 100 = 35%

Compare this with ammonium sulfate. Its M_r is 132 and it also has two nitrogen atoms, so the percentage of nitrogen is 28 ÷ 132 × 100 = 21.2% (to 3 significant figures). Both compounds are used as fertilisers, and this sort of calculation lets you compare how much nitrogen each one contains per gram.

A quick check: the percentages of all the elements in a compound must add up to 100%. In MgO, magnesium is 60%, so oxygen must be 40%.

Common mistakes

Ignoring the bracket. In Mg(OH)₂ the 2 applies to both O and H. Writing 24 + 16 + 2 = 42 is wrong. The answer is 58.

Forgetting the big numbers in an equation. In 2NH₃ you must double 17 to get 34.

Using the atomic number. Oxygen's atomic number is 8, but its A_r is 16. Always use the larger number, the relative atomic mass.

Counting an element only once. In NH₄NO₃ nitrogen appears in two places. Count every atom.

Adding units. M_r has no units. "M_r = 18 g" is wrong.

Exam-style question

Magnesium carbonate breaks down when heated:

MgCO₃ → MgO + CO₂

Relative atomic masses (A_r): C = 12, O = 16, Mg = 24

(a) Calculate the relative formula mass (M_r) of magnesium carbonate. [1 mark]

(b) Show that the total M_r of the reactants equals the total M_r of the products. [2 marks]

(c) Calculate the percentage by mass of magnesium in magnesium carbonate. Give your answer to 3 significant figures. [2 marks]

Model answer

(a) 24 + 12 + (3 × 16) = 24 + 12 + 48 = 84

(b) MgO = 24 + 16 = 40 and CO₂ = 12 + (2 × 16) = 44 (1 mark). Products total 40 + 44 = 84, which equals the M_r of the reactant, 84 (1 mark).

Exam tip

Always show your working line by line, one element or group at a time. If you make a slip with the final sum, you can still pick up a method mark for correct working.

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