In a titration, one solution is added to another until an indicator changes colour, and the volume added lets you calculate an amount. To explain an endpoint, name what the colour change shows, choose the valid results, and then use the equation ratio. Questions usually give you the observations and ask you to interpret them. The practical procedure itself belongs to your school laboratory and your teacher.
This lesson follows choosing a salt-preparation principle and closes the set of lessons in acids, bases and salts.
What does the endpoint mean?
The indicator changes colour when the solution passes from one side of neutral to the other, so the colour change shows that one reactant has just run out. The volume added to reach that point is the titre.
For hydrochloric acid added from a burette to sodium hydroxide in a flask with methyl orange, the colour moves from yellow (alkaline) to orange. Orange is the endpoint colour, because it lies between the acid colour (red) and the alkali colour (yellow). Phenolphthalein would go from pink to colourless in the same titration.
How to work from a results table
- Ignore the rough titre if the question labels one.
- Choose concordant titres, meaning results that agree within the stated limit (usually 0.10 cm³).
- Calculate the mean of those values only.
- Find the amount of the known solution using amount = concentration × volume (dm³).
- Use the equation ratio to find the amount of the unknown.
- Divide by the volume of the unknown to find its concentration.
Worked example
The data are invented for teaching. A flask contains 25.0 cm³ of sodium hydroxide of unknown concentration with a few drops of methyl orange. The burette contains 0.100 mol/dm³ hydrochloric acid.
| Titration | Rough | 1 | 2 | 3 |
|---|---|---|---|---|
| Titre / cm³ | 21.20 | 20.10 | 20.05 | 20.15 |
Step 1, valid results: drop the rough titre. Titres 1, 2 and 3 lie between 20.05 and 20.15, a spread of 0.10 cm³, so they are concordant.
Step 2, mean: (20.10 + 20.05 + 20.15) ÷ 3 = 60.30 ÷ 3 = 20.10 cm³.
Step 3, amount of HCl: 0.02010 dm³ × 0.100 mol/dm³ = 0.002010 mol.
Step 4, ratio: HCl + NaOH → NaCl + H₂O, which is 1:1, so NaOH = 0.002010 mol.
Step 5, concentration of NaOH: 0.002010 mol ÷ 0.0250 dm³ = 0.0804 mol/dm³.
Explanation of the endpoint: the methyl orange turned from yellow to orange when the last of the sodium hydroxide had been neutralised, and the first excess of acid changed the indicator.
Check: 0.0804 × 0.0250 = 0.00201 mol, which matches the HCl.
The mistake to watch for
Mistaken answer: mean titre = (21.20 + 20.10 + 20.05 + 20.15) ÷ 4 = 20.375 cm³
The student averaged every value, including the rough titre.
The rough titre is not accurate because the endpoint was overshot, and including it pulls the mean away from the true value. The correction is to choose the concordant results first and then calculate the mean. Another common slip is to divide by the titre instead of the 25.0 cm³ in the flask at the last step.
Check yourself
1. Titres are 18.80 (rough), 18.30, 18.40 and 18.35 cm³. Find the mean titre.
Show answer
Ignore the rough value. The other three lie between 18.30 and 18.40, so they are concordant. Mean = (18.30 + 18.40 + 18.35) ÷ 3 = 55.05 ÷ 3 = 18.35 cm³.
2. 25.0 cm³ of 0.0500 mol/dm³ H₂SO₄ needs a mean titre of 20.00 cm³ of NaOH. Equation: H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O. Find the concentration of the NaOH.
Show answer
H₂SO₄ amount = 0.0250 × 0.0500 = 0.00125 mol. The ratio is 1:2, so NaOH = 0.00250 mol. Concentration = 0.00250 ÷ 0.0200 = 0.125 mol/dm³.
3. In the worked example, a student adds acid past the endpoint in a final titration. Does the calculated NaOH concentration become too high or too low?
Show answer
The titre is too large, so the calculated amount of HCl is too large. Dividing by the same 25.0 cm³ gives a NaOH concentration that is too high.
Where this leads next
You have now covered the whole module. Work through the acids, bases and salts practice set and record repeated errors with the mistake log and retest queue. The mole and equation-ratio tutor helps you check each ratio step.
If result tables keep tripping you up even when the chemistry is clear, our teachers can rehearse them with you in online one-to-one Chemistry tuition.