Relative formula mass (M_r) and percentage by mass
Atoms are tiny; chemists work with relative masses rather than actual masses in grams. M_r is one of the most-used calculations in GCSE chemistry.
Relative atomic mass (A_r)
The relative atomic mass of an element is the average mass of its atoms compared to ¹⁄₁₂ the mass of a carbon-12 atom. Found on the periodic table — usually the larger number above the symbol (e.g. carbon 12, oxygen 16).
Why it isn't always a whole number: it's a weighted average of the masses of the isotopes, accounting for their abundance.
Relative formula mass (M_r)
For a compound, add up the A_r of every atom in the formula.
Worked examples:
- H₂O: 2(1) + 16 = 18
- CO₂: 12 + 2(16) = 44
- NaCl: 23 + 35.5 = 58.5
- Ca(OH)₂: 40 + 2(16 + 1) = 40 + 34 = 74 (don't forget brackets multiply both atoms inside)
- MgSO₄·7H₂O (epsom salt with water of crystallisation): 24 + 32 + 4(16) + 7(2 + 16) = 24 + 32 + 64 + 126 = 246
Conservation of mass and M_r
In a balanced equation, the sum of M_r of reactants (multiplied by their coefficients) equals the sum of M_r of products.
For 2H₂ + O₂ → 2H₂O:
- Reactant total: 2(2) + 32 = 36
- Product total: 2(18) = 36 ✓
Percentage by mass of an element in a compound
The standard formula:
% mass = (n × A_r of element) ÷ M_r of compound × 100
where n is the number of atoms of that element in the formula.
Worked example 1: % nitrogen in NH₄NO₃ (ammonium nitrate).
- N atoms: 2 (one in NH₄, one in NO₃)
- M_r: 2(14) + 4(1) + 3(16) = 28 + 4 + 48 = 80
- % N = (2 × 14)/80 × 100 = 28/80 × 100 = 35%
Worked example 2: % oxygen in CaCO₃ (chalk).
- M_r: 40 + 12 + 3(16) = 40 + 12 + 48 = 100
- % O = (3 × 16)/100 × 100 = 48/100 × 100 = 48%
Empirical vs molecular formula
- Empirical formula — the simplest whole-number ratio of atoms (e.g. CH₂O for glucose).
- Molecular formula — the actual number of atoms in a molecule (e.g. C₆H₁₂O₆ for glucose).
To find an empirical formula from masses or %:
- Mass (or %) of each element ÷ A_r → moles.
- Divide all moles by the smallest.
- Round to the nearest whole-number ratio (multiply if necessary, e.g. 1, 1.5, 2 → 2, 3, 4).
Worked example: a compound contains 40% C, 6.7% H, 53.3% O.
- C: 40/12 = 3.33; H: 6.7/1 = 6.7; O: 53.3/16 = 3.33
- Divide by 3.33: C = 1, H = 2, O = 1
- Empirical formula: CH₂O
⚠Common mistakes
- Forgetting brackets multiply. Ca(OH)₂ has 2 O and 2 H from the (OH) bracket.
- Confusing A_r and M_r. A_r is per atom; M_r is per formula.
- Wrong number for water of crystallisation. ·5H₂O means 5 water molecules joined to each formula unit — multiply through.
- Empirical formula simplifying error. Always divide by the smallest mole value.
Links
Required for C3.4 onwards (moles use M_r). Percentage composition is standard in C3.7 (concentration), C3.8 (atom economy) and C8.1 (purity).
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