Titration calculations: how to find an unknown concentration

Titration calculations use the volume of one solution of known concentration to find the concentration of another. Work out the moles of the known solution with moles = concentration × volume (in dm³), use the balanced equation to find the moles of the other substance, then divide by its volume to get its concentration in mol/dm³. Multiply by Mr to convert to g/dm³.

The titration formula

• n is the amount in moles.
• c is the concentration in mol/dm³.
• V is the volume in dm³. Divide cm³ by 1000 to get dm³.

AQA's GCSE Chemistry specification (4.3.4, chemistry only, higher tier) asks you to calculate the concentration of one solution from the reacting volumes when you know the concentration of the other, and 4.4.2.5 covers calculating chemical quantities in titrations in mol/dm³ and g/dm³. At A-level (3.1.2.5) you use balanced equations to calculate concentrations and volumes for reactions in solution.

How to do a titration calculation

1. Write the balanced equation and note the mole ratio.
2. Find the mean titre from your concordant results (the titres that agree closely, leaving out the rough run).
3. Convert volumes from cm³ to dm³ by dividing by 1000.
4. Calculate the moles of the solution whose concentration you know: n = c × V.
5. Use the mole ratio to find the moles of the other substance.
6. Divide by its volume in dm³ to find its concentration: c = n ÷ V.
7. If asked, convert to g/dm³ by multiplying by Mr.

Working out the mean titre

The rough titre is a first quick run, so leave it out. The other three agree closely, so the mean titre is (21.95 + 22.05 + 22.00) ÷ 3 = 22.00 cm³.

Worked examples

Example 1: a 1 : 1 reaction (GCSE)

25.0 cm³ of sodium hydroxide solution is neutralised by 21.60 cm³ of 0.100 mol/dm³ hydrochloric acid. NaOH + HCl → NaCl + H₂O, a 1 : 1 ratio.

• Moles of HCl = 0.100 × (21.60 ÷ 1000) = 0.00216 mol
• Moles of NaOH = 0.00216 mol (1 : 1)
• Concentration of NaOH = 0.00216 ÷ (25.0 ÷ 1000) = 0.0864 mol/dm³
• In g/dm³: 0.0864 × 40 = 3.46 g/dm³ (Mr of NaOH = 40)

Example 2: a 1 : 2 reaction

25.0 cm³ of 0.200 mol/dm³ sodium hydroxide reacts with 18.75 cm³ of sulfuric acid. H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O.

• Moles of NaOH = 0.200 × 0.0250 = 0.00500 mol
• Moles of H₂SO₄ = 0.00500 ÷ 2 = 0.00250 mol (one acid for every two alkali)
• Concentration of H₂SO₄ = 0.00250 ÷ 0.01875 = 0.133 mol/dm³

Example 3: ethanoic acid in vinegar (A-level)

Vinegar is diluted by a factor of 10. A 25.0 cm³ sample of the diluted vinegar needs 20.50 cm³ of 0.100 mol/dm³ NaOH. CH₃COOH + NaOH → CH₃COONa + H₂O.

• Moles of NaOH = 0.100 × 0.02050 = 0.00205 mol, so moles of acid = 0.00205 mol
• Concentration in the diluted vinegar = 0.00205 ÷ 0.0250 = 0.0820 mol/dm³
• The original vinegar is 10 times stronger: 0.820 mol/dm³, or 0.820 × 60.0 ≈ 49.2 g/dm³

Doing the titration

AQA's required practicals are GCSE Required practical 2 (chemistry only), finding the reacting volumes of a strong acid and a strong alkali, with the concentration calculation at higher tier, and A-level Required practical 1, making up a volumetric solution and carrying out an acid-base titration. In outline:

• Use a pipette to put a known volume of one solution in a conical flask with a few drops of indicator.
• Fill a burette with the other solution and note the starting reading, with your eye level with the meniscus and reading its lowest point.
• Add the solution from the burette, swirling, until the indicator just changes colour. Go drop by drop near the end point.
• Record the final reading, repeat until you have concordant titres, and use their mean.

You can try this in our virtual titration lab, which also draws the pH curve. Our guide to the titration practical gives AQA's full method, a results table and the sources of error.

Common mistakes

• Forgetting to convert cm³ to dm³. Divide by 1000 before using n = c × V.
• Ignoring the mole ratio. Check the balanced equation; not every reaction is 1 : 1.
• Including the rough titre in the mean. Use only the concordant results.
• Rounding too early. Keep full values until the end, then give 3 significant figures.
• Forgetting a dilution factor. If the sample was diluted, scale the answer back up.

Practise with a short timed paper

Titrations are in GCSE Chemistry and the first year of A-level Chemistry. The daily GCSE Chemistry Higher paper, and the The daily A-level Chemistry: Year 1 paper are short timed papers of 8 questions, with a new one every day.

Read next

Chemistry · Acids and basesTitration practical: method, results and calculationsThe titration required practical: equipment, method, results table, concordant titres, working out the acid's concentration, errors and exam tips.