Quantitative chemistry

Relative formula mass (Mr)

The relative formula mass (Mr) is the sum of relative atomic masses (Ar) of all atoms in the formula. Use the periodic table for Ar values.

Examples:

• Water H₂O: (2 × 1) + 16 = 18
• Carbon dioxide CO₂: 12 + (2 × 16) = 44
• Sodium hydroxide NaOH: 23 + 16 + 1 = 40
• Calcium carbonate CaCO₃: 40 + 12 + (3 × 16) = 100
• Sulfuric acid H₂SO₄: (2 × 1) + 32 + (4 × 16) = 98

For formulae with brackets like Ca(OH)₂: the subscript multiplies EVERYTHING inside the bracket. Ca(OH)₂ = 40 + 2×(16+1) = 40 + 34 = 74.

Percentage by mass of an element

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

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

Example: % iron in iron(III) oxide (Fe₂O₃), Ar(Fe)=56, Ar(O)=16: Mr = (2×56) + (3×16) = 160 % Fe = (112/160) × 100 = 70%

Conservation of mass

Law of conservation of mass: total mass of products = total mass of reactants. Atoms are rearranged, not created or destroyed.

Why might measured mass appear to change?

• Gas produced and escapes from an open container → measured mass decreases (e.g. CaCO₃ + HCl → CO₂ escapes).
• Gas from the air reacts → measured mass increases (e.g. Mg + O₂ from air).

If all reactants and products including gases are accounted for, total mass is always conserved.

Balancing equations

A balanced equation has equal numbers of each atom on both sides.

Example — balancing propane combustion (C₃H₈ + O₂ → CO₂ + H₂O):

1. C: 3 on left → 3CO₂: C₃H₈ + O₂ → 3CO₂ + H₂O
2. H: 8 on left → 4H₂O: C₃H₈ + O₂ → 3CO₂ + 4H₂O
3. O: 10 on right → 5O₂: C₃H₈ + 5O₂ → 3CO₂ + 4H₂O

Rule: never change formulae — only add coefficients.

Calculating mass of product

Use Mr ratios from the balanced equation. Example: 50 g CaCO₃ decomposes → CaCO₃ → CaO + CO₂ (Mr: 100 → 56 + 44) CO₂ produced = (50/100) × 44 = 22 g