Chemists can't count atoms one by one — they are far too small and far too many. Instead they count by weighing. The clever trick is the mole: a fixed, enormous number of particles (6.02 × 1023, the Avogadro constant) chosen so that the mass of one mole of a substance in grams equals its relative formula mass. Master the mole and almost every calculation in chemistry becomes the same three-step routine.
Relative masses: Ar and Mr
The relative atomic mass (Ar) compares the average mass of an atom to 1⁄12 of a carbon-12 atom; it has no units. The relative molecular / formula mass (Mr) is just the Ar values added up for the formula.
| Formula | Working | Mr |
|---|---|---|
| H₂O | (2×1) + 16 | 18 |
| CO₂ | 12 + (2×16) | 44 |
| CaCO₃ | 40 + 12 + (3×16) | 100 |
| Ca(OH)₂ | 40 + 2×(16+1) | 74 |
The mole triangle
The single most useful relationship is moles = mass ÷ Mr. Rearranged: mass = moles × Mr, and Mr = mass ÷ moles. Cover the quantity you want in the triangle to read off the formula.
moles = mass ÷ Mr = 25 ÷ 100 = 0.25 mol.
Reacting masses from balanced equations
A balanced equation gives the mole ratio of reactants to products. The routine: (1) write the balanced equation, (2) turn the known mass into moles, (3) use the ratio, (4) turn moles back into a mass.
moles Mg = 12 ÷ 24 = 0.5 mol. Ratio Mg : MgO = 1 : 1, so moles MgO = 0.5 mol. mass MgO = 0.5 × 40 = 20 g.
Concentration, gas volume, yield and formulae
- Concentration = moles ÷ volume, in mol/dm³ (remember 1 dm³ = 1000 cm³).
- Molar gas volume: at r.t.p. one mole of any gas occupies 24 dm³ (24 000 cm³). So volume = moles × 24.
- Percentage yield = (actual yield ÷ theoretical yield) × 100.
- Percentage purity = (mass of pure substance ÷ total mass) × 100.
- Empirical formula: divide each element's mass (or %) by its Ar, then find the simplest whole-number ratio. The molecular formula is a whole-number multiple of it.
Mg: 4.8 ÷ 24 = 0.2 mol. O: 3.2 ÷ 16 = 0.2 mol. Ratio 0.2 : 0.2 = 1 : 1, so the empirical formula is MgO.
Exam technique — for “Calculate” command words, always show working: write the equation, then mass → moles → ratio → moles → answer. Method marks are awarded even if the final number slips. Memory hook: “Mr divides, Mr multiplies” — divide by Mr to get moles, multiply by Mr to get mass.