How to calculate relative molecular mass

Relative molecular mass, Mr, is one of the first calculations in the mole concept chapter, and almost every later calculation, moles, reacting masses, concentration, depends on getting it right. The good news is that it is pure addition. The marks that slip away are almost always from miscounting atoms inside brackets or forgetting the water in a hydrated salt, not from any hard chemistry. This guide gives you a tidy method and the trickier cases worked out in full.

What relative molecular mass actually means

Start with relative atomic mass, Ar: the average mass of one atom of an element compared with one-twelfth the mass of a carbon-12 atom. Because it is a comparison, Ar has no units. Carbon is 12, hydrogen is 1, oxygen is 16, and so on, you read these off the Periodic Table provided in the exam.

Relative molecular mass, Mr, is simply the sum of the relative atomic masses of all the atoms shown in the molecular formula. Since it, too, is a ratio, Mr has no units. A useful bridge to remember: the Mr of a substance is numerically equal to its molar mass in grams per mole, so once you can find Mr you are one short step from molar mass, practise that link at relative atomic mass and molar mass.

A note on the word “molecular”

Strictly, “relative molecular mass” describes substances made of molecules, such as water or carbon dioxide. For an ionic compound like sodium chloride or copper(II) sulfate, which is made of ions, not molecules, the correct term is relative formula mass. The arithmetic is identical: you still add the relative atomic masses in the formula unit. In SPM you may meet either phrase, so calculate the same way and just use the right name.

The three-step method

For any formula, do this:

1. List each element and count its atoms. Read subscripts carefully, and multiply everything inside a bracket by the number outside it.
2. Multiply each atom count by that element’s Ar.
3. Add the results. That total is the Mr (or relative formula mass).

Worked example one: a simple molecule

Find the Mr of carbon dioxide, CO₂. (Ar: C = 12, O = 16)

• Carbon: 1 × 12 = 12
• Oxygen: 2 × 16 = 32
• Mr = 12 + 32 = 44

And water, H₂O: (2 × 1) + 16 = 18. Keep these small ones at your fingertips, they come up constantly.

Worked example two: a formula with brackets

Brackets are where careless marks vanish. Everything inside the bracket is multiplied by the number outside.

Find the Mr of calcium hydroxide, Ca(OH)₂. (Ar: Ca = 40, O = 16, H = 1)

• Calcium: 1 × 40 = 40
• Oxygen: 2 × 16 = 32 (there are two OH groups, so two oxygens)
• Hydrogen: 2 × 1 = 2
• Mr = 40 + 32 + 2 = 74

Try ammonium sulfate, (NH₄)₂SO₄. The “2” outside the first bracket doubles both the nitrogen and the hydrogen inside it: N is 2 × 14 = 28, H is 8 × 1 = 8, S is 32, O is 4 × 16 = 64. Mr = 28 + 8 + 32 + 64 = 132.

Worked example three: a hydrated salt

The dot in a formula like CuSO₄·5H₂O means five water molecules are attached to each formula unit, the “water of crystallisation”, and they must be included.

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

• The CuSO₄ part: 64 + 32 + (4 × 16) = 64 + 32 + 64 = 160
• The 5H₂O part: 5 × 18 = 90
• Total = 160 + 90 = 250

Forgetting the water gives 160 and loses the mark, so always check for that dot.

Guard your marks

Three habits keep Mr calculations clean. First, open out every bracket before you multiply, write the atom count for each element on its own line so nothing is missed. Second, use the exam’s Periodic Table for Ar values rather than half-remembered numbers; chlorine is 35.5, not 35, and copper is 64. Third, never write a unit on an Mr answer, it is a pure ratio, and adding “g” quietly signals a misunderstanding. Then lay out your working element by element so a marker can follow it and award method marks even if one multiplication slips.

Once finding Mr is automatic, the whole mole topic opens up, because molar mass, percentage composition and reacting masses all start here. Drill a mixed set, a molecule, a bracketed formula, a hydrated salt, at relative molecular mass until you never miscount a bracket again. If you would like a teacher to check your formulae and Ar values live and fix the exact step you slip on, our online one-to-one lessons with our experienced SPM Chemistry teachers are built for that, from RM50 an hour with a paid one-hour trial lesson.