How to do titration calculations
The route from titre to concentration, a worked acid-base example, and why concordant results matter before you calculate anything.
What the examiner is testing
Two separate things: whether you select the right titres, and whether you can carry a mole ratio through a calculation with the units intact. Both are marked.
The formula:
$$ n = c \times \frac{V}{1000} $$
with \( n \) in moles, \( c \) in mol/dm³ and \( V \) in cm³.
Before any calculation: concordant results
Use only titres within 0.10 cm³ of one another, and never the rough titre. Averaging in a rough run is one of the most common mark losses on the whole topic.
| Run | Titre (cm³) | Use it? |
|---|---|---|
| Rough | 25.40 | No — always discarded |
| 1 | 24.75 | Yes |
| 2 | 24.80 | Yes |
| 3 | 25.15 | No — outside 0.10 of the others |
Mean titre: \( (24.75 + 24.80)/2 = 24.78 \text{ cm}^3 \).
The method
- Average the concordant titres only.
- Write and balance the equation.
- Moles of the substance you know everything about.
- Cross to the other substance using the balancing numbers.
- Divide by its volume in dm³ to get concentration.
Worked example
25.0 cm³ of sodium hydroxide is titrated against 0.100 mol/dm³ hydrochloric acid. The mean concordant titre is 24.78 cm³. Find the concentration of the sodium hydroxide.
Step 2 — equation.
$$ \text{HCl} + \text{NaOH} \rightarrow \text{NaCl} + \text{H}_2\text{O} $$
The ratio is \( 1 : 1 \).
Step 3 — moles of acid (the substance with both values known):
$$ n(\text{HCl}) = 0.100 \times \frac{24.78}{1000} = 2.478 \times 10^{-3} \text{ mol} $$
Step 4 — cross the equation. With a 1:1 ratio:
$$ n(\text{NaOH}) = 2.478 \times 10^{-3} \text{ mol} $$
Step 5 — concentration of the alkali.
$$ c = \frac{n}{V/1000} = \frac{2.478 \times 10^{-3}}{0.0250} = 0.0991 \text{ mol/dm}^3 $$
Answer: 0.0991 mol/dm³ (3 s.f.).
Sanity check: the titre was slightly less than the 25.0 cm³ pipetted, so the alkali must be slightly less concentrated than the acid. 0.0991 against 0.100 fits.
If the acid were sulfuric
$$ \text{H}_2\text{SO}_4 + 2\text{NaOH} \rightarrow \text{Na}_2\text{SO}_4 + 2\text{H}_2\text{O} $$
Only step 4 changes: \( n(\text{NaOH}) = 2 \times n(\text{H}_2\text{SO}_4) \). Everything else is identical.
The three mistakes that lose marks
1. Including the rough titre in the mean. Discard it, always.
2. Forgetting the 1000. Working in cm³ throughout gives an answer a thousand times out. Write the units beside every number.
3. Assuming a 1:1 ratio. Check the balanced equation. Diprotic acids and Group 2 hydroxides are where this is deliberately tested.
30-second recap
Concordant titres only. Balance the equation. Moles of the fully-known substance, cross using the balancing numbers, divide by the other volume in dm³. Then ask whether the size of your answer makes sense against the titre.