Calculating Relative Formula Mass (Mr)

Relative formula mass (Mr) is the starting point for almost every calculation in IGCSE Chemistry. If you get Mr wrong, every number that follows will be wrong too. The good news is that the method is entirely mechanical: count atoms, multiply by Ar, add up.

The method

1. Write out the chemical formula clearly.
2. Identify every element present and how many atoms of each appear in one formula unit.
3. Look up the Ar (relative atomic mass) of each element from the periodic table.
4. Multiply each Ar by the number of atoms of that element.
5. Add all the results together to get Mr.

The formula

Mr = sum of (Ar of each element x number of atoms of that element)

Where:

• Mr is the relative formula mass of the compound (no units)
• Ar is the relative atomic mass of each element (from the periodic table)

Worked examples

Example 1: Water (H2O)

Question: Calculate the relative formula mass of water, H2O. (Ar: H = 1, O = 16)

Working:

• Hydrogen: 2 atoms x 1 = 2
• Oxygen: 1 atom x 16 = 16
• Mr = 2 + 16 = 18

Answer: Mr of H2O = 18

Examiner note: Even on a 1-mark question, write the addition. If you write just “18” and it is wrong, there is no working to award.

Example 2: Carbon dioxide (CO2)

Question: Calculate the relative formula mass of carbon dioxide, CO2. (Ar: C = 12, O = 16)

Working:

• Carbon: 1 atom x 12 = 12
• Oxygen: 2 atoms x 16 = 32
• Mr = 12 + 32 = 44

Answer: Mr of CO2 = 44

Examiner note: A common error is to write 28 by adding 12 + 16 and forgetting the subscript 2 on oxygen.

Example 3: Sodium hydroxide (NaOH)

Question: Calculate the relative formula mass of sodium hydroxide, NaOH. (Ar: Na = 23, O = 16, H = 1)

Working:

• Sodium: 1 atom x 23 = 23
• Oxygen: 1 atom x 16 = 16
• Hydrogen: 1 atom x 1 = 1
• Mr = 23 + 16 + 1 = 40

Answer: Mr of NaOH = 40

Examiner note: NaOH contains three different elements. List each one separately in your working to avoid missing any.

Example 4: Calcium hydroxide (Ca(OH)2)

Question: Calculate the relative formula mass of calcium hydroxide, Ca(OH)2. (Ar: Ca = 40, O = 16, H = 1)

Working:

• Calcium: 1 atom x 40 = 40
• The bracket (OH) is multiplied by 2:
  • Oxygen: 2 atoms x 16 = 32
  • Hydrogen: 2 atoms x 1 = 2
• Mr = 40 + 32 + 2 = 74

Answer: Mr of Ca(OH)2 = 74

Examiner note: The bracket is the key test here. Students who ignore it get Mr = 57 (counting only one O and one H). Always expand brackets before calculating.

Example 5: Magnesium nitrate (Mg(NO3)2)

Question: Calculate the relative formula mass of magnesium nitrate, Mg(NO3)2. (Ar: Mg = 24, N = 14, O = 16)

Working:

• Magnesium: 1 atom x 24 = 24
• The bracket (NO3) is multiplied by 2:
  • Nitrogen: 2 atoms x 14 = 28
  • Oxygen: 6 atoms x 16 = 96
• Mr = 24 + 28 + 96 = 148

Answer: Mr of Mg(NO3)2 = 148

Examiner note: Inside the bracket there is 1 nitrogen and 3 oxygens. The subscript 2 outside doubles both, giving 2 nitrogen and 6 oxygen atoms total. Writing out the atom count explicitly is the safest approach.

Example 6: Hydrated copper sulfate (CuSO4.5H2O)

Question: Calculate the relative formula mass of hydrated copper sulfate, CuSO4.5H2O. (Ar: Cu = 64, S = 32, O = 16, H = 1)

Working:

• Copper: 1 atom x 64 = 64
• Sulfur: 1 atom x 32 = 32
• Oxygen in sulfate: 4 atoms x 16 = 64
• Water of crystallisation (5H2O):
  • Hydrogen: 10 atoms x 1 = 10
  • Oxygen: 5 atoms x 16 = 80
• Mr = 64 + 32 + 64 + 10 + 80 = 250

Answer: Mr of CuSO4.5H2O = 250

Examiner note: The dot in the formula means “with” not “times.” The 5H2O adds 5 water molecules to the formula. Count the oxygen in the sulfate and the oxygen in the water separately to avoid confusion. This formula has 4 + 5 = 9 oxygen atoms total.

Common mistakes

1. Ignoring brackets. Ca(OH)2 has 2 oxygen atoms and 2 hydrogen atoms, not 1 of each.
2. Miscounting oxygen in hydrates. CuSO4.5H2O has 9 oxygen atoms total (4 from sulfate + 5 from water).
3. Using the wrong Ar. Always check the periodic table on the exam paper rather than relying on memory. Chlorine is 35.5, not 35.
4. Forgetting subscripts. In CO2, there are 2 oxygen atoms. Read every subscript in the formula.
5. Adding units. Mr is a ratio and has no units. Writing “g” or “g/mol” after Mr loses marks in some schemes.

When this appears

Calculating Mr is rarely a standalone exam question beyond Paper 2 multiple choice. Instead, it is the essential first step in almost every stoichiometry calculation. You will need Mr to find moles from mass, percentage composition, empirical formulae, and reacting masses. The stoichiometry topic covers the underlying theory of relative masses and the mole concept.