Question

The half-equivalence point of a titration occurs half way to the end point, where half of the analyte has reacted to form its conjugate, and the other half still remains unreacted. If 0.240 moles of a monoprotic weak acid (Ka = 4.5 × 10-5) is titrated with NaOH, what is the pH of the solution at the half-equivalence point?

Answer 1

use:

Ka =[H3O+][A-]/[HA]

or the Henderson Hasselbach equation:

pH = pKa + log([A-]/[HA])

Answer 2

there's also a special relationship that the pH has at the half-equivalence point. at the half-equivalence point, since exactly half of the acid is neutralized, your [HA] and [A-] concentrations are equal. If you use the H-H equation, as @aaronq correctly points out, the log function cancels, because the log(1) = 0

That means your Ka = [H+] at the half-equivalence point.

This further means that the pH = pKa, but only at the half-equivalence point.