pH Titration Curves

Learning Objectives (OCR Spec 5.1.3)

By the end of this lesson you should be able to:

• Sketch pH titration curves for all four combinations of strong/weak acid and strong/weak base
• Identify the equivalence point and the half-equivalence point
• Recognise the buffer region in a weak acid / strong base titration
• Explain the shape of each curve using Ka, Kw and buffer behaviour
• Use titration curves to obtain pKa values experimentally

What Is a pH Titration Curve?

A pH titration curve is a graph of pH (y-axis) against volume of titrant added (x-axis) during an acid-base titration. The shape of the curve depends on whether the acid and the base are strong or weak.

There are four combinations to know:

1. Strong acid + strong base (e.g. HCl titrated with NaOH)
2. Weak acid + strong base (e.g. CH3COOH titrated with NaOH)
3. Strong acid + weak base (e.g. HCl titrated with NH3)
4. Weak acid + weak base (e.g. CH3COOH titrated with NH3)

OCR requires you to sketch and interpret all four.

Decision Tree: Which Curve to Expect

graph TD
  A[Titration] --> B{Is the acid strong?}
  B -->|Yes| C{Is the base strong?}
  B -->|No| D{Is the base strong?}
  C -->|Yes| E[Strong-Strong: vertical jump from ~1 to ~13, equivalence at pH 7]
  C -->|No| F[Strong acid - weak base: jump to equivalence below pH 7]
  D -->|Yes| G[Weak acid - strong base: gradual rise, buffer region, equivalence above pH 7]
  D -->|No| H[Weak-weak: no sharp jump, gradual S-curve through pH 7]

The Equivalence Point

The equivalence point (or stoichiometric point) is where the moles of acid and base added are equal, according to the balanced equation. It is not always at pH 7 - the pH at equivalence depends on which species is in the flask at that moment.

• Strong acid + strong base: equivalence at pH = 7 (the salt formed is neutral).
• Strong acid + weak base: equivalence at pH < 7 (the salt is acidic, e.g. NH4Cl).
• Weak acid + strong base: equivalence at pH > 7 (the salt is basic, e.g. CH3COONa).
• Weak acid + weak base: equivalence around pH 7 but no sharp jump.

The equivalence point is identified on the graph as the steepest part (or centre of the near-vertical section) of the curve.

Curve 1: Strong Acid + Strong Base (HCl + NaOH)

Titrating 25.0 cm3 of 0.100 mol dm-3 HCl in the flask with 0.100 mol dm-3 NaOH from the burette.

Volume NaOH / cm3	pH (approx)
0	1.00
10	1.37
20	1.95
24	2.69
24.9	3.70
25.0 (equivalence)	7.00
25.1	10.30
26	11.29
30	12.05
50	12.52

Shape: starts at low pH (strong acid), stays almost flat through the early additions (small changes as acid is consumed), then has a very sharp vertical jump (about 6 units, from pH ~3.7 to ~10.3) around the equivalence point at 25 cm3. After the equivalence point, the pH rises slowly as excess NaOH is diluted.

Equivalence point: pH = 7.0. The salt NaCl is neutral.

Indicator choice: any indicator that changes colour within the vertical section. Methyl orange (red->yellow, 3.1-4.4) and phenolphthalein (colourless->pink, 8.3-10.0) both work.

Curve 2: Weak Acid + Strong Base (CH3COOH + NaOH)

Titrating 25.0 cm3 of 0.100 mol dm-3 ethanoic acid with 0.100 mol dm-3 NaOH. pKa = 4.76.

Volume NaOH / cm3	pH (approx)
0	2.88 (weak acid)
5	4.14
12.5 (half-equivalence)	4.76 = pKa
20	5.38
24	6.14
24.9	7.14
25.0 (equivalence)	8.72
25.1	10.30
30	11.96
50	12.52

Shape: starts at pH ~2.88 (higher than for strong acid because only weak acid). Rises steeply initially (as A- forms), then levels off into a gradual, nearly flat region from about 5 cm3 to 20 cm3 - this is the buffer region, where CH3COOH and CH3COO- coexist. At 12.5 cm3 (half-equivalence) [HA] = [A-] and pH = pKa. From about 22 cm3 onwards the curve steepens into a vertical jump centred on the equivalence point, which is above pH 7 because CH3COO- (formed at equivalence) is a weak base.

Equivalence point: pH ~ 8.72, not 7. The salt CH3COONa is basic.

Half-equivalence point: at half the equivalence volume, exactly half the HA has been converted to A-, so [HA] = [A-] and pH = pKa. This is how pKa is measured experimentally - read off the pH at 12.5 cm3 in this example.

Indicator choice: must change within the vertical region (roughly pH 7 to 10). Phenolphthalein (8.3-10) works; methyl orange (3.1-4.4) does not - it would change too early, in the buffer region.

Buffer region explanation: during the titration, NaOH is converting HA to A-, but both are always present, so the solution is a buffer. The pH only changes by about 2 units across the whole buffer region, illustrating buffer action directly.

Curve 3: Strong Acid + Weak Base (HCl + NH3)