Interpreting Acid-Base Titration Curves

A titration curve plots the pH of the solution against the volume of titrant added, and its shape shows the strength of the acid and base, the position of the equivalence point and, for weak acids, the pK_a at the half-equivalence point. In brief: for 25.00 mL of 0.1000 mol/L HCl titrated with 0.1000 mol/L NaOH, the pH rises slowly from 1.00 to 3.70 at 24.90 mL, jumps to 7.00 at 25.00 mL and to 10.30 at 25.10 mL; for acetic acid, the equivalence point is at pH 8.72 and the pH at half-equivalence (12.50 mL) equals pK_a = 4.76.

Titration curves are the picture of everything learned about pH, buffers and hydrolysis. This article explains how to read each region of a curve, gives calculated data for strong acid–strong base and weak acid–strong base titrations, compares curve features, covers weak bases and polyprotic acids, shows how to find the equivalence point and pK_a, works through examples and gives some history.

What does a strong acid–strong base curve look like?

The data are for 25.00 mL of 0.1000 mol/L HCl (2.500 mmol) titrated with 0.1000 mol/L NaOH.

What does a weak acid–strong base curve look like?

The data are for 25.00 mL of 0.1000 mol/L acetic acid (pK_a 4.76) with 0.1000 mol/L NaOH.

How do the curves compare?

How do you calculate the pH in each region?

1. Start: pH of the acid alone (strong: −log c; weak: from K_a).
2. Before equivalence, strong acid: excess H⁺ moles ÷ total volume.
3. Before equivalence, weak acid: buffer, pH = pK_a + log(n(base added) ÷ n(acid remaining)).
4. At equivalence, strong–strong: pH 7. For a weak acid: hydrolysis of A⁻, [OH⁻] = √(K_bc).
5. After equivalence: excess OH⁻ moles ÷ total volume.

What about weak bases and polyprotic acids?

A weak base titrated with a strong acid gives a mirror image: a curve that starts at a high pH, has a buffer region around pK_a of the conjugate acid, and an equivalence point below 7 (ammonia with HCl: pH about 5.3 for 0.05 mol/L NH₄⁺). A polyprotic acid shows several steps. Sodium carbonate titrated with HCl shows equivalence points near pH 8.3 (HCO₃⁻ formed) and near pH 3.9 (H₂CO₃). Phosphoric acid shows two clear steps near pH 4.7 and 9.8; the third (pK_a 12.35) is too weak to show clearly.

Worked examples

1. Equivalence volume. 20.00 mL of 0.150 mol/L acid with 0.100 mol/L NaOH (1 : 1): V = 0.150 × 20.00 ÷ 0.100 = 30.0 mL.
2. pK_a from the curve. A weak acid has its equivalence point at 40.0 mL. The pH at 20.0 mL (half-equivalence) is 3.85, so pK_a = 3.85 and K_a = 1.4 × 10⁻⁴.
3. pH at 10.00 mL, strong acid. Excess H⁺ = 2.500 − 1.000 = 1.500 mmol in 35.00 mL: 0.04286 mol/L; pH 1.37.

4. pH at equivalence for acetic acid. Acetate = 2.500 mmol in 50.00 mL = 0.0500 mol/L. K_b = 5.6 × 10⁻¹⁰: [OH⁻] = 5.3 × 10⁻⁶; pOH 5.28; pH 8.72.
5. Choose an indicator. For acetic acid, a color change between pH 7.2 and 10.3 is needed: phenolphthalein (8.2 to 10.0) works, methyl orange (3.1 to 4.4) would change far too early (at about 5 mL).
6. pH after equivalence. At 26.00 mL: excess OH⁻ = 0.100 mmol in 51.00 mL = 1.96 × 10⁻³ mol/L; pOH 2.71; pH 11.29.

How are curves used?

Curves allow chemists to find unknown concentrations, to determine pK_a values of new compounds and to design buffers. Potentiometric titration with a glass electrode was developed in the early 20th century, and the derivative of the curve (the steepest point) is used to locate equivalence points automatically. Hydrogen ion titration curves of proteins reveal their ionizable groups.

Which mistakes are common?

Mistake 1: Expecting pH 7 at every equivalence point

Only for strong acid with strong base.

Mistake 2: Using the half-equivalence rule for a strong acid

It applies to weak acids, where a buffer forms.

Mistake 3: Calculating the pH after equivalence from the acid

After equivalence, the pH comes from the excess titrant.

Mistake 4: Forgetting the total volume

Concentrations must be divided by the sum of the volumes of acid and titrant.