Chemical Measurements and Conservation of Mass (C3.1)

Relative atomic mass (Aᵣ)

The relative atomic mass of an element is the average mass of its atoms compared to 1/12 of the mass of a carbon-12 atom. Values are given in the periodic table (the larger number).

For isotopes, Aᵣ is the weighted average based on abundance.
Example: Chlorine (75% ³⁵Cl, 25% ³⁷Cl): Aᵣ = (75×35 + 25×37) ÷ 100 = 35.5

Relative formula mass (Mᵣ)

The relative formula mass is the sum of all relative atomic masses in a formula.

Example: H₂SO₄ → (2×1) + (1×32) + (4×16) = 2 + 32 + 64 = 98

Example: Ca(OH)₂ → 40 + 2×(16+1) = 40 + 34 = 74

Conservation of mass

In a chemical reaction, no atoms are created or destroyed — they are rearranged. Therefore the total mass of reactants equals the total mass of products.

Balanced equations represent this: same number of each type of atom on both sides.

Example: 2H₂ + O₂ → 2H₂O
Left: 4H, 2O. Right: 4H, 2O ✓

Apparent mass changes

Sometimes the mass appears to change:

• Mass appears to decrease: if a gas is produced and escapes (e.g. CO₂ from calcium carbonate decomposition). Mass is conserved — gas leaves the container.
• Mass appears to increase: if oxygen from the air reacts (e.g. magnesium burning in air). Mass is conserved — oxygen gained from surroundings.

Balancing equations

Method: adjust coefficients (never change formulas) until atoms balance on both sides.

Example: Fe + Cl₂ → FeCl₃
Unbalanced. Right: 1 Fe, 3 Cl. Adjust: 2FeCl₃ needs 2 Fe and 3 Cl₂.
2Fe + 3Cl₂ → 2FeCl₃ ✓

Percentage composition by mass

% by mass of element = (Aᵣ × number of atoms of element / Mᵣ of compound) × 100

Example: % O in H₂O → (16/18) × 100 = 88.9%

Experimental uncertainty

Resolution of an instrument = smallest division it can measure. Error bars and range of repeats indicate uncertainty. For a measurement: uncertainty = ½ × range of repeats (or ½ × resolution for a single reading).

Common exam errors

1. Changing the subscripts in a formula when balancing (e.g. writing H₃ instead of 3H) — never change subscripts; only add coefficients.
2. Forgetting brackets when calculating Mᵣ: Ca(OH)₂ — the 2 multiplies everything inside the bracket.
3. Saying mass is "lost" when a gas escapes — mass is conserved; only the system's mass changes.