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If you record the pH after every addition during a titration and plot it against the volume added, you get a titration curve. It’s one of the most information-rich graphs in chemistry. From its shape you can tell whether the acid and base are strong or weak, find the equivalence point precisely, read off the pKa of a weak acid, and decide which indicator will work.
This guide walks through the four standard combinations, using calculated values so you can see exactly where each feature of the curve comes from.
All examples use 25.0 cm³ of a 0.100 mol/dm³ solution in the flask, titrated with a 0.100 mol/dm³ solution from the burette, at 25 °C. The equivalence point is therefore always at 25.0 cm³.
Anatomy of a titration curve
Every curve has the same four regions:
- Starting pH: the pH of the solution in the flask before anything is added.
- Gradual region: the pH changes slowly as titrant is added.
- Vertical section: near the equivalence point, a tiny volume causes a big jump in pH.
- Final region: excess titrant; the pH levels off towards the pH of the titrant itself.
The equivalence point is the middle of the vertical section, where moles of acid equal moles of base (adjusted for the reaction ratio).
1. Strong acid titrated with strong base
25.0 cm³ of 0.100 mol/dm³ HCl in the flask; 0.100 mol/dm³ NaOH added.
| NaOH added (cm³) | What’s in the flask | pH |
|---|---|---|
| 0.0 | 0.100 mol/dm³ HCl | 1.00 |
| 12.5 | Half the acid neutralised | 1.48 |
| 24.0 | Slight excess of acid | 2.69 |
| 24.9 | Very slight excess of acid | 3.70 |
| 25.0 | Neutral NaCl solution | 7.00 |
| 25.1 | Very slight excess of alkali | 10.30 |
| 26.0 | Slight excess of alkali | 11.29 |
| 35.0 | Excess alkali | 12.22 |
Shape: starts low (pH 1), rises slowly, then a huge vertical jump from about pH 3.7 to 10.3 in just 0.2 cm³, centred on pH 7. That’s one or two drops from a burette.
Why: before equivalence, the pH is set by the leftover strong acid. Because pH is logarithmic, you have to neutralise 90% of the acid just to raise the pH by one unit. Near equivalence, the last tiny amount of acid disappears and the pH shoots up.
Indicators: almost any indicator that changes between pH 4 and 10 works, including both methyl orange and phenolphthalein.
2. Weak acid titrated with strong base
25.0 cm³ of 0.100 mol/dm³ ethanoic acid (pKa 4.76); 0.100 mol/dm³ NaOH added.
| NaOH added (cm³) | What’s in the flask | pH |
|---|---|---|
| 0.0 | Weak acid only | 2.87 |
| 5.0 | Buffer: more acid than salt | 4.16 |
| 12.5 | Half-equivalence: [HA] = [A⁻] | 4.76 |
| 20.0 | Buffer: more salt than acid | 5.36 |
| 25.0 | Sodium ethanoate solution (0.050 mol/dm³) | 8.72 |
| 26.0 | Slight excess of alkali | 11.29 |
| 30.0 | Excess alkali | 11.96 |
Shape: starts higher (pH 2.87, because the acid is weak), rises quickly at first, then flattens into a buffer region, then jumps more briefly, centred above pH 7.
Key features:
- The buffer region. Between about 10% and 90% of the way to equivalence, the flask contains both ethanoic acid and ethanoate ions. That’s a buffer, so the pH changes slowly. The pH here follows the Henderson–Hasselbalch equation, pH = pKa + log([A⁻] ÷ [HA]).
- Half-equivalence point. At 12.5 cm³, exactly half the acid has been converted to ethanoate, so [HA] = [A⁻] and pH = pKa. This is how pKa values are measured in practice. (See Ka and pKa.)
- Equivalence above 7. At 25.0 cm³, the flask contains only sodium ethanoate. Ethanoate is a weak base, so the solution is alkaline: pH 8.72. The calculation is shown in pH of weak bases.
- A shorter vertical section, roughly from pH 7 to 11.
Indicator: phenolphthalein (changes around pH 8.2–10). Methyl orange would change far too early, during the buffer region.
3. Weak base titrated with strong acid
25.0 cm³ of 0.100 mol/dm³ ammonia (pKb 4.75; pKa of NH₄⁺ = 9.25); 0.100 mol/dm³ HCl added.
| HCl added (cm³) | What’s in the flask | pH |
|---|---|---|
| 0.0 | Weak base only | 11.13 |
| 12.5 | Half-equivalence: [NH₃] = [NH₄⁺] | 9.25 |
| 25.0 | Ammonium chloride solution (0.050 mol/dm³) | 5.28 |
| 26.0 | Slight excess of acid | 2.71 |
| 35.0 | Excess acid | 1.78 |
Shape: this is the mirror image of the weak acid curve. It starts high, falls through a buffer region, passes through pH = pKa of the conjugate acid (9.25) at half-equivalence, and has its equivalence point below 7 because ammonium ions are weakly acidic.
Indicator: methyl orange (changes around pH 3.1–4.4). Phenolphthalein would change during the buffer region, far too early.
4. Weak acid titrated with weak base
Ethanoic acid titrated with ammonia.
There’s no sharp vertical section. The pH rises steadily and only bends gently around the equivalence point (which happens to be close to pH 7 for this pair, because Ka of ethanoic acid and Kb of ammonia are almost equal).
Indicator: no ordinary indicator gives a sharp, reliable end point. Chemists use a pH meter and find the point of steepest slope, or they measure electrical conductivity instead. In practice, weak–weak titrations are avoided.
Comparing all four
| Titration | Starting pH | pH at equivalence | Vertical section | Suitable indicator |
|---|---|---|---|---|
| Strong acid + strong base | 1.0 | 7.0 | about 3.7 → 10.3 | methyl orange or phenolphthalein |
| Weak acid + strong base | 2.9 | 8.7 | about 7 → 11 | phenolphthalein |
| Strong acid + weak base | 11.1 (starts with base) | 5.3 | about 3 → 7 | methyl orange |
| Weak acid + weak base | — | near 7 | none | pH meter |
Reading a titration curve in an exam
If you’re given an unknown curve, work through these questions:
- Starting pH: around 1 means a strong acid at about 0.1 mol/dm³; around 3 suggests a weak acid.
- Is there a flat buffer region? If yes, the substance in the flask is weak.
- Equivalence pH: above 7 means weak acid + strong base; below 7 means strong acid + weak base.
- Half-equivalence: read the pH at half the equivalence volume to get pKa.
- Final pH: tells you roughly the strength and concentration of the titrant.
Diprotic acids
A diprotic acid with well-separated pKa values, such as the first two protons of phosphoric acid, gives a curve with two vertical sections and two equivalence points, the second at twice the volume of the first. See polyprotic acids.
Common mistakes
- Assuming every equivalence point is at pH 7. Only for strong + strong.
- Confusing equivalence point with end point. The end point is where the indicator changes; a good indicator makes it coincide with the equivalence point. See equivalence point vs end point.
- Reading pKa at the equivalence point. pH = pKa at half-equivalence.
- Plotting volume on the y-axis. Titrant volume goes on the x-axis; pH on the y-axis.
Key takeaways
- Titration curves show pH against volume of titrant; the steep section marks the equivalence point.
- Strong/strong: equivalence at pH 7 with a very large jump.
- Weak acid/strong base: buffer region, pH = pKa at half-equivalence, equivalence above 7.
- Strong acid/weak base: mirror image, equivalence below 7.
- Weak/weak: no sharp jump, so indicators don’t work well.
- For the practical method, see acid–base titration.
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