Titration Curves

You’ll be able to

Read the key features of strong–strong and weak–strong titration curves
Locate the equivalence and half-equivalence points and interpret each
Use the half-equivalence point to read pKa directly from a curve

What a titration curve shows

A titration adds a base of known concentration to an acid (or vice versa) while tracking pH. Plotting pH against volume of titrant gives an S-shaped titration curve. The steep, near-vertical jump marks the equivalence point — the moment moles of added base equal the original moles of acid. Everything the acid needed to be neutralized has been supplied.

Strong–strong vs. weak–strong

For a strong acid + strong base, the equivalence point sits at pH = 7 because the product salt is neutral. For a weak acid + strong base, the equivalence point is above 7: all the acid has become its conjugate base A⁻, which is itself a weak base and raises the pH. A weak-acid curve also starts higher and rises more gently at first, and it features a flat buffer region the strong-acid curve lacks.

The half-equivalence point reveals pKa

The half-equivalence point is where exactly half the weak acid has been neutralized, so [HA] = [A⁻]. Plugging that equal ratio into Henderson–Hasselbalch makes the log term zero, giving pH = pKa. On the curve it is the midpoint of the buffer region — the flattest, best-buffered spot. Reading its pH off the graph hands you the acid’s pKa directly.

Half-equivalence point

at half-equivalence: [HA] = [A⁻] ⇒ pH = pKa

This is Henderson–Hasselbalch with log([A⁻]/[HA]) = log(1) = 0. It is the single most useful point for extracting pKa from a curve.

Worked example

A weak acid with Ka = 1.8 × 10⁻⁵ is titrated with NaOH. What is the pH at the half-equivalence point?

1.At the half-equivalence point, half the HA has been converted to A⁻, so [HA] = [A⁻].
2.Henderson–Hasselbalch: pH = pKa + log([A⁻]/[HA]) = pKa + log(1) = pKa.
3.pKa = −log(Ka) = −log(1.8 × 10⁻⁵) = 4.74.
4.Therefore pH = 4.74.

Answer: pH = 4.74 (equal to the pKa)

Watch out

Do not confuse the equivalence point with the half-equivalence point. Equivalence is where neutralization is complete (and for a weak acid, pH > 7); half-equivalence is halfway there, where pH = pKa. They are different points on the curve.

Checkpoint

A weak acid is titrated with a strong base. What is true of the pH at the equivalence point?

Checkpoint

A weak acid with Ka = 1.0 × 10⁻⁵ is titrated with NaOH. What is the pH at the half-equivalence point?

On the exam

Polyprotic acids (H₂CO₃, H₃PO₄) donate protons one at a time, each with its own Ka, so their curves show multiple equivalence points — one steep jump per ionizable proton, with Ka1 > Ka2 > Ka3 since each successive H⁺ is harder to pull off a more negative ion.

Answer the 2 checkpoints as you read.