How to do titration calculations for SPM

Titration calculations appear in both the theory and practical sides of acids, bases and salts, and they are among the most reliable marks in SPM Chemistry, because the method is fixed. If you can find an average titre, convert volumes to moles, apply the mole ratio and finish with a concentration, you can do almost any titration question. This guide walks through that method with worked numbers.

What a titration measures

In an acid–base titration you add one solution of known concentration (the standard solution) from a burette to a fixed volume of the other solution, measured with a pipette, until the reaction is exactly complete, the end point, shown by an indicator changing colour. From the volumes and the known concentration, you calculate the unknown concentration. The practical steps are covered in the acid-base titration experiment; here we focus on the arithmetic.

The two formulae you need

Everything rests on two relationships.

• Moles from a solution: moles = M × V ÷ 1000, where M is concentration in mol dm⁻³ and V is volume in cm³. Dividing by 1000 converts cm³ to dm³.
• The mole ratio from the balanced equation tells you how the moles of acid and base relate.

Get these two right and the rest is careful substitution.

The step-by-step method

1. Find the average titre. Use only the concordant readings, titres within about 0.10 cm³ of each other, and average them. Ignore the rough (trial) titration.
2. Write the balanced equation so you know the mole ratio between acid and base.
3. Calculate the moles of the solution whose concentration you know, using M × V ÷ 1000.
4. Apply the mole ratio to find the moles of the unknown solution.
5. Calculate the unknown concentration by rearranging M = moles × 1000 ÷ V.
6. Convert units if asked, for example from mol dm⁻³ to g dm⁻³ by multiplying by the molar mass.

Worked example 1: a 1:1 reaction

25.0 cm³ of sodium hydroxide of unknown concentration is titrated against 0.10 mol dm⁻³ hydrochloric acid. The average titre is 20.0 cm³. Find the concentration of the sodium hydroxide.

• Balanced equation: HCl + NaOH → NaCl + H₂O. The mole ratio is 1:1.
• Moles of HCl = 0.10 × 20.0 ÷ 1000 = 0.0020 mol.
• Mole ratio 1:1, so moles of NaOH = 0.0020 mol.
• Concentration of NaOH = 0.0020 × 1000 ÷ 25.0 = 0.08 mol dm⁻³.

That is the whole method in four lines. Notice how the mole ratio simply carried the moles straight across because it was 1:1.

Worked example 2: a 1:2 reaction

This is where careless students slip. 25.0 cm³ of 0.10 mol dm⁻³ sodium hydroxide is neutralised by sulfuric acid. If the average titre of the acid is required, and the acid is 0.10 mol dm⁻³, find that volume.

• Balanced equation: H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O. The mole ratio of acid to base is 1:2.
• Moles of NaOH = 0.10 × 25.0 ÷ 1000 = 0.0025 mol.
• From the ratio, moles of H₂SO₄ = 0.0025 ÷ 2 = 0.00125 mol.
• Volume of H₂SO₄ = 0.00125 × 1000 ÷ 0.10 = 12.5 cm³.

The single most important step here is dividing by 2 for the mole ratio. If you forget it, you double the acid and the answer is wrong. Always write the balanced equation first so the ratio is in front of you.

Converting to grams per cubic decimetre

Exams often ask for the concentration in g dm⁻³. Just multiply the concentration in mol dm⁻³ by the molar mass. For the sodium hydroxide in example 1, the molar mass of NaOH is 23 + 16 + 1 = 40 g mol⁻¹, so:

• Concentration = 0.08 × 40 = 3.2 g dm⁻³.

You can check any of these conversions against the titration calculation method, and the molarity and dilution calculator is useful while you build confidence.

Common mistakes to avoid

• Averaging the rough titration in with the accurate ones, use only concordant readings.
• Forgetting the mole ratio, especially for diprotic acids like H₂SO₄ (1:2 with NaOH).
• Mixing up which volume goes with which concentration when you rearrange.
• Forgetting to divide by 1000, which throws the answer out by a factor of a thousand.
• Rounding too early; keep extra figures until the final line.

Practise until it is automatic

Titration is a routine, so drill the same five moves on question after question: average titre, balanced equation, moles, mole ratio, concentration. Once the pattern is automatic, these become some of the safest marks in the paper. If the mole ratio or unit conversions keep tripping you up, that is a quick fix with a teacher, our online one-to-one lessons run in English from RM50 an hour, with a paid one-hour trial; see how it works if you would like titration drilled against real Paper 2 questions.