Question

Find the pH of 25mM phosphoric acid at each point of acid-base equilibria

Answer 1

If we take the -log₁₀, or "p", of this equation

Since [H₃PO₄]=[H₂PO₄^-], and log₁₀(1) = 0, pH=pK_a1.

Second, you might notice that the concentrations of the conjugate bases are maximum half-way between the pK_a points. For example, the point where [H₂PO₄^-] is a maximum lies half-way between between pK_a1 and pK_a2. Since H₂PO₄^- is the major species present in solution, the major equilibrium is the disproportionation reaction

This equilibrium cannot be used to solve for pH because [H₃O⁺] doesn't occur in the equilibrium equation. We solve the pH problem adding the first two equilibria equations

Note that when we add chemical equilibria, we take the product of the equilibrium equations. Taking the -log₁₀ of the last equation

Since the disproportionation reaction predicts [H₃PO₄]=[HPO₄^2-]