Formulae of elements & compounds

A chemical formula shows the type and number of atoms in a substance. The little subscript number multiplies only the symbol it follows:

• H₂O — 2 hydrogen atoms + 1 oxygen atom.
• CaCO₃ — 1 Ca, 1 C, 3 O.
• Ca(OH)₂ — the bracket means 2 of everything inside: 1 Ca, 2 O, 2 H.

The molecular formula is the number and type of different atoms in one molecule. You can deduce a simple compound's formula from a diagram of its atoms.

Watch out: a big number in front (a coefficient) multiplies the whole formula. 2 H₂O = 4 H + 2 O, but it does not change what one water molecule is.

Counting atoms

Writing & balancing equations

In a reaction, atoms are only rearranged — none are made or lost. So a balanced equation must have the same number of each type of atom on both sides. You balance by changing the big numbers in front (coefficients), never the subscripts.

State symbols show the physical state: (s) solid, (l) liquid, (g) gas, (aq) aqueous (dissolved in water).

Your turn — balance it

Ionic equations

Extended only. An ionic equation shows only the ions and species that actually take part — the spectator ions (those unchanged on both sides) are cancelled out.

Full equation for a neutralisation:

Na⁺ and Cl⁻ are spectators, so the ionic equation is simply:

Tip: for a precipitation such as silver chloride forming, the ionic equation is Ag⁺(aq) + Cl⁻(aq) → AgCl(s). Charges must balance too, not just atoms.

Spot the spectators

Relative atomic & molecular mass

Relative atomic mass, A_r, is the average mass of an element's isotopes compared to 1⁄12 of the mass of a carbon-12 atom.

Relative molecular mass (or relative formula mass), M_r, is just the sum of all the A_r values in the formula. For ionic compounds we say relative formula mass.

Common error: A_r and M_r are ratios, so they have no units. Don't write "98 g" for an M_r — it is just 98.

Your turn — relative formula mass

Why can't you change water's formula?

How do you count atoms by weighing?

The mole & the Avogadro constant

Extended only. The mole (mol) is the unit of amount of substance. One mole always contains the same number of particles — the Avogadro constant:

The link between mass and moles uses the mole triangle. The molar mass (in g/mol) is numerically the same as the M_r:

Your turn — moles from mass

How do you count atoms by weighing?

Reacting masses & the mole ratio

Extended only. The big numbers in a balanced equation give the mole ratio in which substances react. To find a reacting mass:

• 1. Write the balanced equation.
• 2. Convert the known mass to moles.
• 3. Use the mole ratio to get moles of the unknown.
• 4. Convert back to mass (mass = mol × M_r).

Limiting reactant: if one reactant is used up first, it is the limiting reactant (the other is in excess). Compare the moles of each with the mole ratio, then use the moles of the limiting reactant to work out the product.

Your turn — reacting masses

Concentration of solutions

Concentration measures how much solute is dissolved in a given volume. It can be measured in g/dm³ or mol/dm³ (Core: know both units); calculating a concentration in either unit is Supplement. Volumes are in dm³, so remember 1 dm³ = 1000 cm³.

Don't mix them up: g/dm³ uses mass; mol/dm³ uses moles. Convert between them with g/dm³ = mol/dm³ × M_r.

Your turn — concentration in g/dm³

Your turn — concentration in mol/dm³

Why does a mole of any gas fill the same space?

Molar gas volume

Extended only. At room temperature and pressure (r.t.p.), one mole of any gas occupies the same volume:

Key idea: it does not matter which gas — 24 dm³ per mole works for H₂, CO₂, NH₃ alike, because equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.

Your turn — gas volume

Why does a mole of any gas fill the same space?

Percentage yield & purity

Extended only. Reactions rarely give 100% of the expected product. Two different ideas:

% composition by mass of an element = (A_r × number of its atoms ÷ M_r) × 100 — e.g. carbon in CO₂ = (12 ÷ 44) × 100 = 27.3%.

Don't confuse them: % yield compares product made to the theoretical maximum; % purity compares the pure part of a sample to the whole sample. Different questions, different formulae.

Your turn — percentage yield

Empirical & molecular formulae

Extended only. The empirical formula is the simplest whole-number ratio of atoms in a compound. The molecular formula is the real number in one molecule (a whole-number multiple of the empirical one).

• 1. Divide each element's mass (or %) by its A_r → gives moles.
• 2. Divide all by the smallest result → gives the ratio.
• 3. Round to whole numbers.

Remember: the empirical formula is the simplest ratio, so H₂O₂'s empirical formula is HO and C₆H₁₂O₆'s is CH₂O — they are not the same as the molecular formula.

Your turn — empirical formula

Titration calculations

Extended only. A titration finds an unknown concentration by reacting it with a solution of known concentration. The route:

• 1. moles of known = conc × volume (in dm³).
• 2. Use the mole ratio from the equation → moles of unknown.
• 3. conc of unknown = moles ÷ its volume (in dm³).

Watch the units: always convert cm³ to dm³ (÷ 1000) before dividing, or your concentration will be 1000× wrong.

Your turn — titration

Match the skill to its idea

Tap the correct ending for each stoichiometry skill.

The formulae to know

You've covered the key ideas in Cambridge IGCSE Topic 3 — formulae & equations, relative masses, the mole, and every calculation. [S] marks Supplement (Extended-only) content. Press Finish to see your score.