How to Do A-Level Chemistry Titration Calculations (Step by Step)

1. The three-step method

Nearly every acid-base titration calculation is the same three moves. You know everything about one solution (its concentration and the volume used), and you want the concentration of the other. Learn this pattern once and it works for every question.

1. 1Find moles of the solution you know: Use moles = concentration × volume, with the volume in dm³ (divide cm³ by 1000).
2. 2Use the mole ratio: Read the ratio straight off the balanced equation to convert to moles of the unknown substance.
3. 3Find the unknown concentration: Rearrange to concentration = moles ÷ volume, again with the volume in dm³.

The rest of this guide walks through the one formula you need, a fully worked example, what to do when the ratio is not 1:1, and the marks students lose most often.

2. The one formula you must know

Everything hangs off a single equation:

moles = concentration × volume

Concentration is measured in mol/dm³ and volume in dm³, so the dm³ cancels and the answer comes out in mol. The catch is that burette and pipette readings are in cm³, and you must convert them first:

• volume in dm³ = volume in cm³ ÷ 1000
• 25.0 cm³ = 0.0250 dm³
• 23.50 cm³ = 0.02350 dm³

You will rearrange the same formula three ways, so it helps to think of a triangle with moles on top and concentration × volume underneath: moles = concentration × volume, concentration = moles ÷ volume, volume = moles ÷ concentration.

3. Worked example: finding the concentration of NaOH

25.0 cm³ of sodium hydroxide solution is exactly neutralised by 23.50 cm³ of 0.100 mol/dm³ hydrochloric acid. Find the concentration of the sodium hydroxide.

1. 1Write the balanced equation and read off the ratio: NaOH + HCl → NaCl + H2O. The ratio of NaOH to HCl is 1 : 1.
2. 2Find moles of the substance you know fully (HCl): You know its concentration (0.100 mol/dm³) and its volume (23.50 cm³ = 0.02350 dm³). moles HCl = 0.100 × 0.02350 = 0.00235 mol (2.35 × 10⁻³ mol).
3. 3Apply the mole ratio: The ratio is 1 : 1, so moles of NaOH = moles of HCl = 0.00235 mol.
4. 4Find the unknown concentration: Rearrange to concentration = moles ÷ volume. Volume of NaOH = 25.0 cm³ = 0.0250 dm³. concentration NaOH = 0.00235 ÷ 0.0250 = 0.094 mol/dm³.
5. 5Round to the right significant figures and sanity-check: The data is given to 3 significant figures, so the answer is 0.0940 mol/dm³. Check it makes sense: the NaOH is slightly less concentrated than the acid (0.0940 vs 0.100), which fits because the same number of moles is spread over a slightly larger volume (25.0 vs 23.50 cm³).

That final value, 0.0940 mol/dm³, is your answer. Notice the whole calculation stayed in the calculator until the last line, so nothing was rounded early.

4. When the ratio is not 1:1

The 1:1 ratio in the last example is the easy case. Plenty of titrations are not 1:1, and the mole ratio is the single most common thing students forget. Sulfuric acid is diprotic (it releases two H⁺), so it reacts with twice as much alkali:

2NaOH + H2SO4 → Na2SO4 + 2H2O. The ratio of NaOH to H2SO4 is 2 : 1.

Example: 25.0 cm³ of 0.100 mol/dm³ NaOH is neutralised by 20.00 cm³ of sulfuric acid. Find the concentration of the acid.

• moles NaOH = 0.100 × (25.0 ÷ 1000) = 0.100 × 0.0250 = 0.00250 mol
• ratio NaOH : H2SO4 = 2 : 1, so moles H2SO4 = 0.00250 ÷ 2 = 0.00125 mol
• volume of acid = 20.00 cm³ = 0.02000 dm³
• concentration H2SO4 = 0.00125 ÷ 0.02000 = 0.0625 mol/dm³

If you had assumed a 1:1 ratio you would get 0.125 mol/dm³, exactly double the correct value. Always balance the equation before you touch the ratio.

5. Concordant titres and why you average

In the lab you do not use a single titre. Your first run is a rough (trial) titration, done quickly to find roughly where the endpoint is. You then repeat carefully until your results agree.

• Concordant titres are results that agree within 0.10 cm³ of each other.
• Discard the rough titre and any obvious outliers.
• Take the mean of the concordant titres only (usually two or three of them).
• Use that mean titre in your calculation, never the rough value.

6. Common mistakes to avoid

If a titration answer looks wildly off (like a concentration of 94 mol/dm³ or 0.0000094 mol/dm³), the cause is almost always a cm³/dm³ slip somewhere. Check your unit conversions before anything else.

7. How to get faster and more accurate

Titration questions are worth easy marks once the method is automatic, because every question follows the same three steps. The way to lock it in is to work through past-paper questions and check each one against the mark scheme, paying attention to where your method actually breaks: usually the conversion, the ratio, or the rounding.

If you keep dropping the same marks, a bit of one-to-one help is often faster than grinding alone, because a tutor can watch you work a full calculation and catch the cm³/dm³ and mole-ratio slips the moment they happen. StudyGuru's £15 Starter Pack is four sessions with a DBS-checked tutor, and the first lesson is refundable within 24 hours if it is not the right fit, so it is a low-risk way to try it.

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