Question

A diprotic acid is titrated with a strong base. The first midpoint (half equivalence point) is at pH = 3.27. The second midpoint (half equivalence point) is at pH = 8.53. What is the value of k_a2?

Answer 1

Half-equivalence point is the point at which the added base is exactly half the original concentration of the acid. The added base forms the acid's salt, whose concentration at the half-equivalence point is equal to that of the acid left in the medium. This leaves a buffer in the medium whose pH is given by Henderson-Hasselbach equation as pH = pK_a + log([salt]/[acid]). At half-equivalence, the equation given reduces as pH = pKa. Therefore, pK_a2 is equal to 8.53 and pKa = -logKa giving Ka = 10^-pKa. Thus, the K_a2 of the diprotic acid is 2.9512x10^-9.