What you'll learn
Once you have carried out a titration and found the mean titre, the real power of the technique is using that result to calculate an unknown concentration. For AQA GCSE Chemistry (higher tier) you need to be able to work with moles, use titration results to find concentration in mol/dm³ and g/dm³, and use balanced equations to relate the amounts of acid and alkali. This guide covers the key equations, how to convert between volume, concentration and moles, and how to work through a titration calculation step by step. By the end you should be able to calculate an unknown concentration confidently from titration data. (The practical method itself is covered in a separate guide.)
Key terms and definitions
Mole (mol) — The unit for amount of substance; equal to a fixed number of particles.
Concentration — The amount of solute dissolved in a given volume of solution, in mol/dm³ or g/dm³.
Titre — The volume of solution added from the burette to reach the end point.
mol/dm³ — Concentration in moles per cubic decimetre (moles per litre).
g/dm³ — Concentration in grams per cubic decimetre.
Molar ratio — The ratio of moles of reactants shown in the balanced equation.
Relative formula mass (Mr) — The sum of the relative atomic masses in a formula.
Cubic decimetre (dm³) — A unit of volume equal to 1000 cm³ (one litre).
Core concepts
The key relationship
Titration calculations are built on the relationship between moles, concentration and volume:
moles = concentration (mol/dm³) × volume (dm³)
This can be rearranged to find any of the three. The most common trap is the volume: burette and pipette volumes are measured in cm³, but concentration is in mol/dm³, so you must convert cm³ to dm³ by dividing by 1000.
The steps of a titration calculation
Almost every titration calculation follows the same four steps:
- Calculate the moles of the substance you know the concentration and volume of (usually the one measured by pipette). Use moles = concentration × volume (in dm³).
- Use the balanced equation to find the moles of the other substance, using the molar ratio.
- Calculate the concentration of the unknown substance using concentration = moles ÷ volume (in dm³).
- If required, convert to g/dm³ by multiplying the concentration in mol/dm³ by the relative formula mass (Mr).
Setting the work out in these steps keeps it clear and earns method marks even if you slip on the arithmetic.
Using the balanced equation
The balanced equation tells you the ratio in which the substances react. For example, in:
HCl + NaOH → NaCl + H₂O
the ratio of acid to alkali is 1:1, so the moles of HCl equal the moles of NaOH. But in:
H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O
the ratio is 1:2, so you need twice as many moles of NaOH as of H₂SO₄. Always check the ratio — using the wrong ratio is a common mistake.
Converting between mol/dm³ and g/dm³
Concentration can be given in two ways:
- mol/dm³ — moles of solute per cubic decimetre.
- g/dm³ — grams of solute per cubic decimetre.
To convert from mol/dm³ to g/dm³, multiply by the relative formula mass (Mr):
concentration (g/dm³) = concentration (mol/dm³) × Mr
To convert the other way, divide by the Mr.
Why unit conversion matters
The single most important thing in titration calculations is keeping the volumes in dm³. A titre of 25.0 cm³ is 0.025 dm³. Forgetting to divide by 1000 makes every answer wrong by a factor of a thousand. Always convert volumes before using the moles equation.
Understanding the mole in titrations
The mole is the key idea that makes titration calculations work. A mole is simply a fixed, very large number of particles, used so that chemists can count atoms and molecules by weighing or measuring. In a titration, the balanced equation tells you the ratio of moles in which the substances react, not the ratio of volumes or masses. That is why every calculation converts volumes and concentrations into moles first: only in moles can you use the ratio from the equation. Once you have the moles of the unknown, you convert back to concentration. Keeping the idea of "work in moles" at the centre stops most mistakes.
Choosing sensible values and checking your answer
A good habit is to check whether your final answer is sensible. Concentrations in these problems are usually small numbers (often between about 0.05 and 1 mol/dm³), so an answer of, say, 80 mol/dm³ is a sign that a volume was not converted from cm³ to dm³. Similarly, if two solutions react in a 1:1 ratio and use similar volumes, their concentrations should be similar; a wildly different answer suggests an error. Estimating the rough size of the answer before doing the full calculation, and checking it afterwards, helps you catch the common factor-of-1000 slip and other mistakes before you write down a final value.
Why concordant titres are used in calculations
The volume you use in a titration calculation should be the mean of the concordant titres from the practical, not a single reading. Concordant results are those within 0.10 cm³ of each other, and averaging them reduces the effect of small random errors, giving a more reliable volume. A rough first titration and any anomalous results are left out of the mean. Using an accurate mean titre matters because the whole calculation depends on it: an error in the volume feeds straight through into the final concentration. This is where the practical technique and the calculation meet — careful measurement gives the accurate number that the calculation then turns into a concentration.
Worked examples
Example 1: A 1:1 titration
25.0 cm³ of sodium hydroxide is neutralised by 20.0 cm³ of hydrochloric acid of concentration 0.100 mol/dm³. The equation is HCl + NaOH → NaCl + H₂O. Find the concentration of the sodium hydroxide.
Step 1 — moles of HCl = concentration × volume = 0.100 × (20.0 ÷ 1000) = 0.00200 mol. Step 2 — the ratio is 1:1, so moles of NaOH = 0.00200 mol. Step 3 — concentration of NaOH = moles ÷ volume = 0.00200 ÷ (25.0 ÷ 1000) = 0.0800 mol/dm³.
Example 2: Converting to g/dm³
Convert the sodium hydroxide concentration of 0.0800 mol/dm³ to g/dm³. The Mr of NaOH is 23 + 16 + 1 = 40. Concentration (g/dm³) = 0.0800 × 40 = 3.2 g/dm³.
Example 3: A 1:2 ratio
20.0 cm³ of sulfuric acid is neutralised by 25.0 cm³ of 0.200 mol/dm³ sodium hydroxide. The equation is H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O. Find the concentration of the acid.
Step 1 — moles of NaOH = 0.200 × (25.0 ÷ 1000) = 0.00500 mol. Step 2 — the ratio of H₂SO₄ to NaOH is 1:2, so moles of H₂SO₄ = 0.00500 ÷ 2 = 0.00250 mol. Step 3 — concentration of H₂SO₄ = 0.00250 ÷ (20.0 ÷ 1000) = 0.125 mol/dm³.
Example 4: Finding a volume
What volume of 0.100 mol/dm³ HCl is needed to neutralise 0.00300 mol of NaOH (ratio 1:1)? Moles of HCl needed = 0.00300 mol. Volume = moles ÷ concentration = 0.00300 ÷ 0.100 = 0.0300 dm³ = 30.0 cm³.
Common mistakes and how to avoid them
The most common error by far is not converting the volume from cm³ to dm³. Divide the titre by 1000 before using moles = concentration × volume. Forgetting this makes the answer wrong by a factor of a thousand.
Students often use the wrong molar ratio. Always look at the balanced equation: a 1:2 ratio means the two amounts of moles are different. Do not assume everything is 1:1.
Another mistake is confusing mol/dm³ and g/dm³. To convert mol/dm³ to g/dm³, multiply by the Mr; to go the other way, divide. Check which unit the question asks for.
When calculating Mr for the conversion, take care to add up every atom in the formula correctly, including any in brackets.
Finally, keep enough significant figures during the calculation and only round at the end, giving your final answer to a sensible number of significant figures (usually 3).
Exam technique for "Titrations and calculations from titration data"
Always set out the calculation in clear steps: moles of the known substance, then the molar ratio, then the concentration of the unknown, then any unit conversion. Showing each step earns method marks even if the final figure is slightly off.
Convert volumes to dm³ at the start (divide cm³ by 1000), and write the balanced equation so you can read off the correct ratio. Double-check whether the question wants mol/dm³ or g/dm³.
Practise rearranging moles = concentration × volume to find any of the three quantities, and be ready to convert to g/dm³ using the Mr. Quote your answer to about 3 significant figures with the correct unit.
Quick revision summary
- moles = concentration (mol/dm³) × volume (dm³) — always convert cm³ to dm³ by dividing by 1000.
- Titration calculation steps: moles of the known substance → use the molar ratio from the balanced equation → concentration of the unknown → convert units if needed.
- Check the balanced equation for the ratio (e.g. 1:1 for HCl + NaOH, 1:2 for H₂SO₄ + 2NaOH).
- Convert mol/dm³ to g/dm³ by multiplying by the Mr; divide to go the other way.
- Keep volumes in dm³ throughout, and round only at the end to about 3 significant figures.