Sometimes tested C4.1

Calculating Relative Formula Mass

This topic covers the fundamental skill of calculating the relative molar mass (Mr) of a compound. It involves summing the relative atomic masses (Ar) of all the atoms present in a chemical formula, a crucial first step for most quantitative chemistry problems.

Part of the ESAT Chemistry syllabus — revision for the Engineering and Science Admissions Test (ESAT), the UAT-UK admissions test for Cambridge, Imperial, Oxford and UCL.

Key points

  • The relative molar mass (Mr) is the sum of the relative atomic masses (Ar) of all atoms shown in a substance's chemical formula.
  • Relative atomic masses (Ar) for elements will be provided in the question or in a periodic table.
  • Pay extremely close attention to the small numbers (subscripts) in a formula, especially those outside brackets which multiply every atom inside the bracket.
  • Mr, like Ar, is a ratio of masses and therefore has no units.

Formulae

Mr = sum of (Ar of element × number of atoms of element)

To find the total relative mass of a compound when you know its chemical formula and the Ar values of its elements.

Definitions

Relative Atomic Mass (Ar)
The weighted average mass of an atom of an element relative to 1/12th the mass of a carbon-12 atom. For exam purposes, you can treat this as the mass number (protons + neutrons).
Relative Molar Mass (Mr)
The total mass of a molecule or formula unit, found by adding together the relative atomic masses of all its constituent atoms. It is also known as relative formula mass.

Worked example

Calculate the relative molar mass (Mr) of hydrated magnesium nitrate, Mg(NO₃)₂·6H₂O. [Relative atomic masses: Ar(H)=1, Ar(N)=14, Ar(O)=16, Ar(Mg)=24]

  1. 1

    First, identify and count all the atoms in the formula, paying attention to brackets and the water of crystallisation.

  2. 2

    Mg:

    1 atom

  3. 3

    N:

    1 inside the bracket × 2 outside = 2 atoms

  4. 4

    O (in nitrate):

    3 inside the bracket × 2 outside = 6 atoms

  5. 5

    H (in water):

    2 inside the formula × 6 outside = 12 atoms

  6. 6

    O (in water):

    1 inside the formula × 6 outside = 6 atoms

  7. 7

    Total O atoms = 6 (from nitrate) + 6 (from water) = 12 atoms.

  8. 8

    Now sum the masses:

    Mr = (1 × Ar(Mg)) + (2 × Ar(N)) + (12 × Ar(O)) + (12 × Ar(H))
  9. 9

    Substitute the Ar values:

    Mr = (1 × 24) + (2 × 14) + (12 × 16) + (12 × 1)
  10. 10

    Calculate each part:

    Mr = 24 + 28 + 192 + 12
  11. 11

    Sum the totals:

    Mr = 256

Answer: 256

Common mistakes

  • ×Forgetting to multiply the number of atoms inside a bracket by the subscript on the outside. In Mg(NO₃)₂, this would mean incorrectly counting only 1 nitrogen and 3 oxygens from the nitrate group.
  • ×Mishandling water of crystallisation, for example by adding 6 to the total instead of adding the mass of 6 entire H₂O molecules.

No-calculator tips

  • ✓When calculating, group numbers to make addition easier. For the example (24 + 28 + 192 + 12), you could do (24 + 28 = 52) and (192 + 12 = 204), then 52 + 204 = 256.
  • ✓For tricky multiplications like 12 × 16, use the distributive property: (12 × 10) + (12 × 6) = 120 + 72 = 192.
  • ✓Always write down the count for each atom before you start summing the masses. This simple check can prevent careless counting errors.

Read this topic in the official UAT-UK ESAT guide →

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