Relative masses of atoms and molecules

O Level / IGCSE Chemistry · Stoichiometry. A short explanation of the idea, the rules to remember, the mistake to avoid, a worked example and practice questions with answers.

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The idea

Atoms are far too light to weigh one at a time, so their masses are compared with a standard: one twelfth of the mass of an atom of carbon-12. The relative atomic mass, Ar, of an element is the average mass of its isotopes on this scale. It is an average, which is why chlorine has the value 35.5.

The relative molecular mass, Mr, of a substance is found by adding up the relative atomic masses of all the atoms in its formula. For ionic compounds the same sum is called the relative formula mass.

These values are ratios, so they have no units. The Ar values you need are given in the question or the Periodic Table.

Rules to remember

Common mistake

The usual slip is with brackets: in Ca(OH)2 the 2 applies to both O and H. Count the atoms of each element first, then multiply by the Ar values.

Worked example

What is the relative formula mass of magnesium nitrate, Mg(NO3)2? (N 14, O 16, Mg 24)

  1. Count the atoms: 1 Mg, 2 × 1 = 2 N, and 2 × 3 = 6 O.
  2. Multiply by the Ar values: Mg 1 × 24 = 24; N 2 × 14 = 28; O 6 × 16 = 96.
  3. Add them: 24 + 28 + 96 = 148.

Answer: Mr of Mg(NO3)2 = 148 (no unit).

Practice questions

Try each one, then open the answer.

1. What is the relative formula mass of hydrated copper(II) sulfate, CuSO4·5H2O? (H 1, O 16, S 32, Cu 64)

  1. A
    160
  2. B
    178
  3. C
    250
  4. D
    330
Show answer

Answer: C. CuSO4 = 64 + 32 + 64 = 160; 5H2O = 5 × 18 = 90. Total = 250.

2. The relative atomic mass of an element is the average mass of its atoms compared with

  1. A
    one twelfth of the mass of an atom of carbon-12
  2. B
    the mass of an atom of oxygen-16, the most common oxygen isotope
  3. C
    the mass of an atom of hydrogen, the lightest element
  4. D
    the mass of a single proton in the nucleus
Show answer

Answer: A. The carbon-12 scale defines Ar relative to one twelfth of the mass of a 12C atom.

3. Magnesium consists of three isotopes: magnesium-24 (79%), magnesium-25 (10%) and magnesium-26 (11%). What is the relative atomic mass of magnesium, to one decimal place?

  1. A
    24.0
  2. B
    25.0
  3. C
    24.3
  4. D
    24.7
Show answer

Answer: C. Relative atomic mass is the average mass of the isotopes, taking account of their abundances: (79 × 24 + 10 × 25 + 11 × 26) ÷ 100 = (1896 + 250 + 286) ÷ 100 = 24.32, which is 24.3. It is not a whole number because the isotopes occur in different amounts.

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