A diprotic acid H₂A has K_a1 = 1 × 10⁻⁴ and K_a2 = 1 × 10⁻⁸. The corresponding base A²⁻ is titrated with aqueous HCl, both solutions being 0.1 mol L⁻¹. Which one of the following diagrams best represents the titration curve which will be seen?

Question

Quizplus · Accepted Answer

Since the acid in question is diprotic, it will have two equivalence points. The first equivalence point will correspond to the reaction of the first H+ ion with the base, and the second equivalence point will correspond to the reaction of the second H+ ion with the base. The pH at the first equivalence point will be determined by the first dissociation constant (K1) of the acid, and the pH at the second equivalence point will be determined by the second dissociation constant (K2) of the acid.

At the beginning of the titration, the pH of the solution will be determined by the presence of the weak base. As H+ ions are added from the HCl, the pH will decrease slightly, as the weak base reacts with the added acid.

When the added H+ ions are equal in equivalent amount to the amount of base that was originally present in the solution, the first equivalence point will be reached. At this point, all of the weak base will have reacted with the added acid, and the pH will be determined by the first dissociation constant of the acid. The pH will be less than 7, because the acid is more acidic than water.

As more H+ ions are added beyond the first equivalence point, the pH will continue to decrease, until it reaches a minimum at some point between the two equivalence points. This minimum corresponds to the point where the concentrations of the weak base and weak acid are equal. At this point, the pH is equal to the pKa of the acid, which is the average of the two dissociation constants.

When the added H+ ions are equal in equivalent amount to twice the amount of base that was originally present in the solution, the second equivalence point will be reached. At this point, all of the weak acid will have been neutralized by the added acid, and the pH will be determined by the second dissociation constant of the acid. The pH will be less than the pH at the first equivalence point, because the second dissociation constant is smaller than the first.

Based on this analysis, the best choice is B, as it shows two equivalence points and a minimum at the average of the two pKa values. The other choices do not show all of these features.

A Diprotic Acid H2A Has Ka1 = 1 × 10−4

A Diprotic Acid H₂A Has K_a1 = 1 × 10⁻⁴