How to calculate the concentration of an acid by titration

A very common SPM question gives you an acid of unknown concentration and a standard alkali, then asks you to work out how concentrated the acid is. This is not a memory question, it is a fixed procedure. Once you can titrate the acid against a base of known concentration, count moles and apply the mole ratio, the concentration falls out every time. This guide from acids, bases and salts shows you exactly how, with two worked examples.

Why a standard alkali is the key

You cannot find the concentration of the acid on its own, you need a reference. That reference is a standard solution: a solution whose concentration you already know accurately, usually a strong alkali such as sodium hydroxide made up carefully in a volumetric flask. If you have not met it yet, the preparing a standard solution experiment shows how one is made. Because you know the standard’s concentration and can measure both volumes, you can back-calculate the acid.

The two relationships you rely on

• Number of moles in a solution: moles = MV ÷ 1000, where M is the concentration in mol dm⁻³ and V is the volume in cm³. The 1000 converts cm³ into dm³.
• The mole ratio from the balanced equation tells you how many moles of acid react with each mole of alkali. For a monoprotic acid it is 1:1; for a diprotic acid like sulfuric acid it is 1:2.

Everything below is just these two ideas used carefully.

The step-by-step method

1. Pipette a fixed volume of the acid (usually 25.0 cm³) into a conical flask and add a suitable indicator.
2. Titrate against the standard alkali in the burette until the indicator just changes colour, the end point.
3. Find the average titre using only the concordant readings (within about 0.10 cm³ of each other); ignore the rough titration.
4. Write the balanced equation to fix the mole ratio.
5. Calculate the moles of alkali used, with moles = MV ÷ 1000.
6. Apply the mole ratio to get the moles of acid.
7. Divide by the acid volume to get the acid concentration: M = moles × 1000 ÷ V.

Worked example 1: a monoprotic acid

25.0 cm³ of dilute nitric acid of unknown concentration is neutralised by 22.5 cm³ of 0.200 mol dm⁻³ sodium hydroxide. Find the concentration of the acid.

• Balanced equation: HNO₃ + NaOH → NaNO₃ + H₂O. The mole ratio of acid to alkali is 1:1.
• Moles of NaOH = 0.200 × 22.5 ÷ 1000 = 0.00450 mol.
• Mole ratio 1:1, so moles of HNO₃ = 0.00450 mol.
• Concentration of HNO₃ = 0.00450 × 1000 ÷ 25.0 = 0.180 mol dm⁻³.

If the question wants grams per cubic decimetre, multiply by the molar mass. For HNO₃ that is 1 + 14 + (16 × 3) = 63 g mol⁻¹, so 0.180 × 63 = 11.34 g dm⁻³.

Worked example 2: a diprotic acid

This is where marks are lost. 25.0 cm³ of sulfuric acid of unknown concentration is neutralised by 30.0 cm³ of 0.100 mol dm⁻³ sodium hydroxide. Find the concentration of the acid.

• Balanced equation: H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O. The mole ratio of acid to alkali is 1:2.
• Moles of NaOH = 0.100 × 30.0 ÷ 1000 = 0.00300 mol.
• From the ratio, moles of H₂SO₄ = 0.00300 ÷ 2 = 0.00150 mol.
• Concentration of H₂SO₄ = 0.00150 × 1000 ÷ 25.0 = 0.0600 mol dm⁻³.

The one step that catches students is dividing by 2. Sulfuric acid gives two moles of hydrogen ions per mole of acid, so it needs twice as much alkali. Forget the ratio and you double the answer. Writing the balanced equation first keeps that ratio in front of you.

Choosing the indicator

For a strong acid neutralised by a strong alkali, the two examples above, either methyl orange or phenolphthalein works, because the pH changes sharply through both their ranges at the end point. If a weak acid such as ethanoic acid is involved, phenolphthalein is the safer choice. The indicator does not change the calculation; it only tells you when to stop.

Common mistakes to avoid

• Averaging the rough titration in with the accurate ones, use only concordant readings.
• Forgetting the mole ratio for diprotic acids like H₂SO₄ (1:2 against NaOH).
• Swapping the volumes when you rearrange, so the acid volume ends up with the alkali concentration.
• Forgetting to divide by 1000 and throwing the answer out by a factor of a thousand.
• Rounding part-way through instead of keeping extra figures until the final line.

Practise the pattern until it is automatic

Finding an acid’s concentration is one routine repeated: average titre, balanced equation, moles of alkali, mole ratio, acid concentration. You can check your arithmetic against the titration calculation method whenever you are unsure. Drill it on real Paper 2 questions until you no longer have to think about the order. If the mole ratio or unit conversions keep tripping you, that is a fast thing to fix with a teacher, our online one-to-one lessons run in English from RM50 an hour, with a paid one-hour trial, and we drill titration against past-paper questions until these become some of your safest marks.