Relative Formula Mass

This lesson covers relative atomic mass (Ar) and relative formula mass (Mr) as required by the Edexcel GCSE Chemistry specification (1CH0), Topic 1: Key Concepts in Chemistry and Topic 9: Separate Chemistry 2. Understanding how to calculate Mr is essential because it underpins almost every quantitative calculation in chemistry.

Relative Atomic Mass (Ar)

Every element on the periodic table has a relative atomic mass (Ar). This is the number shown at the top of each element's box on the periodic table (sometimes the bottom, depending on the version).

Relative atomic mass is defined as the average mass of the atoms of an element compared to 1/12 of the mass of a carbon-12 atom.

In practice, for GCSE, you simply read the Ar value from the periodic table:

Element	Symbol	Ar
Hydrogen	H	1
Carbon	C	12
Nitrogen	N	14
Oxygen	O	16
Sodium	Na	23
Magnesium	Mg	24
Chlorine	Cl	35.5
Calcium	Ca	40
Iron	Fe	56

Exam Tip: You will always be given a periodic table in the exam. You do not need to memorise Ar values. However, being familiar with common ones saves time.

What Is Relative Formula Mass (Mr)?

The relative formula mass (Mr) of a compound is the sum of the relative atomic masses of all the atoms shown in its formula.

For example, water has the formula H₂O. This means it contains 2 hydrogen atoms and 1 oxygen atom.

Mr of H₂O = (2 × Ar of H) + (1 × Ar of O) = (2 × 1) + (1 × 16) = 18

The unit of Mr is no unit — it is a relative quantity (a ratio).

Exam Tip: Always show your working clearly when calculating Mr in exam questions. Write out which atoms you are adding and how many of each. This earns method marks even if you make an arithmetic slip.

Worked Examples

Example 1: Sodium Chloride (NaCl)

Formula: NaCl

1 × Na = 1 × 23 = 23
1 × Cl = 1 × 35.5 = 35.5

Mr = 23 + 35.5 = 58.5

Example 2: Carbon Dioxide (CO₂)

Formula: CO₂

1 × C = 1 × 12 = 12
2 × O = 2 × 16 = 32

Mr = 12 + 32 = 44

Example 3: Calcium Carbonate (CaCO₃)

Formula: CaCO₃

1 × Ca = 1 × 40 = 40
1 × C = 1 × 12 = 12
3 × O = 3 × 16 = 48

Mr = 40 + 12 + 48 = 100

Example 4: Sulfuric Acid (H₂SO₄)

Formula: H₂SO₄ (Ar values: H = 1, S = 32, O = 16)

2 × H = 2 × 1 = 2
1 × S = 1 × 32 = 32
4 × O = 4 × 16 = 64

Mr = 2 + 32 + 64 = 98

Dealing with Brackets in Formulae

Brackets in a chemical formula mean that everything inside the brackets is multiplied by the subscript number outside.

Example 5: Magnesium Hydroxide — Mg(OH)₂

The formula Mg(OH)₂ means:

1 × Mg
The (OH) group appears twice, so there are 2 × O and 2 × H

Calculation:

1 × Mg = 1 × 24 = 24
2 × O = 2 × 16 = 32
2 × H = 2 × 1 = 2

Mr = 24 + 32 + 2 = 58

Example 6: Calcium Nitrate — Ca(NO₃)₂

The formula Ca(NO₃)₂ means:

1 × Ca
The (NO₃) group appears twice, so there are 2 × N and 6 × O (2 × 3 = 6)

Calculation:

1 × Ca = 1 × 40 = 40
2 × N = 2 × 14 = 28
6 × O = 6 × 16 = 96

Mr = 40 + 28 + 96 = 164

Exam Tip: A very common mistake is forgetting to multiply all atoms inside the brackets. For Ca(NO₃)₂, there are 2 nitrogen atoms and 6 oxygen atoms, not just 2 oxygens.

Example 7: Aluminium Sulfate — Al₂(SO₄)₃

The formula Al₂(SO₄)₃ means:

2 × Al
The (SO₄) group appears three times, so there are 3 × S and 12 × O (3 × 4 = 12)

Calculation (Ar values: Al = 27, S = 32, O = 16):

2 × Al = 2 × 27 = 54
3 × S = 3 × 32 = 96
12 × O = 12 × 16 = 192

Mr = 54 + 96 + 192 = 342

Using Mr in Further Calculations

Once you can calculate Mr, you can use it in many other calculations throughout the course:

Calculation	Formula
Number of moles	moles = mass ÷ Mr
Mass of a substance	mass = moles × Mr
Percentage composition	% = (Ar × number of atoms ÷ Mr) × 100
Concentration in mol/dm³	mol/dm³ = (g/dm³) ÷ Mr

These will all be covered in detail in later lessons.

Common Mistakes

Forgetting the subscript — In H₂O, there are 2 hydrogens, not 1.
Ignoring brackets — In Mg(OH)₂, multiply both O and H by 2.
Using the wrong Ar — Always double-check the periodic table.
Rounding Ar values — Use the values given in the exam. Chlorine is 35.5, not 35 or 36.

Summary

Relative atomic mass (Ar) is the average mass of an atom of an element relative to carbon-12. Read it from the periodic table.
Relative formula mass (Mr) is the sum of all Ar values in a formula.
To handle brackets, multiply every atom inside the bracket by the subscript outside.
Mr has no unit — it is a dimensionless ratio.
Always show your working clearly in calculations.
Mr is the foundation for moles, reacting masses, concentration and many other calculations in chemistry.