half-equivalence point

Meaning: The half-equivalence point is where exactly half of the weak acid (or weak base) being titrated has been neutralized, at half the titrant volume needed to reach the equivalence point. For HA titrated with strong base, half the HA has become A⁻, so [HA] = [A⁻]. This is the midpoint of the buffer region, where pH changes least per addition of titrant. For a weak base B titrated with strong acid, [B] = [BH⁺] and pOH = pKb.

Equation: pH = pKa + log([A⁻]/[HA]) = pKa + log 1 = pKa. pH and pKa are dimensionless; [A⁻] and [HA] are in mol/L.

On the MCAT: Given a titration curve, halve the equivalence-point volume and read the pH there to get pKa. Then Ka is 10 raised to the power −pKa. A lower pH at the half-equivalence point means a stronger acid. A polyprotic acid has one half-equivalence point per proton, each giving its own pKa.

Common confusion: Students mix it up with the equivalence point or assume the pH is 7. For a weak acid titrated with strong base, the equivalence point has a pH above 7 because the conjugate base hydrolyzes water. At half that volume, the pH equals pKa, which is usually not 7.