Geometric-algebraic approach to aqueous solutions of diprotic acids and its buffer mixtures

A closed-form analytical expression for [H3O+] has been obtained for aqueous solutions of diprotic acids and its soluble salts. This formula allows to calculate the pH of aqueous solutions of diprotic acids, their buffer solutions, and the titrations of these two by a strong base, from the values of pK(1), pK(2), and the effective concentrations of the acid and the base, (C) over bar (a) and (C) over bar (b) respectively. It is shown that a strong base titration of an acid, or its buffer solutions, is always a linear path in the (C) over bar (a)- (C) over bar (b) plane, which allows a simple analysis of the pH stability of buffer solutions. The mathematical analysis of the equilibrium equations of the dissolution of a diprotic acid in water and the physical constraints allowed to obtain two approximate equations for the diprotic acids. One of the approximations is useful for acids with pK(2) - pK(1) <= log(10)4, the other for acids with pK(2) - pK(1) <= - log(10)4.

Automated summary

This study presents a formula to calculate the pH value of aqueous solutions and buffer solutions of diprotic acids based on their pK(1) and pK(2) values, as well as their concentrations. It is also discovered that the titration of an acid or its buffer solution by a strong base always follows a linear path in the (C) over bar (a)- (C) over bar (b) plane, which simplifies the analysis of pH stability in buffer solutions.