Which relationship holds for the ionization constants of water?

Which relationship holds for the ionization constants of water?

• A. Ka x Kb = Kw
• B. Ka = Kb
• C. Ka + Kb = Kw
• D. Kw = Ka - Kb

Answer: (A)

Understanding how water behaves as both an acid and a base in water helps here. The ion-product of water, Kw, is [H+][OH−] at a given temperature. For water acting as an acid, the dissociation constant Ka describes the reaction H2O ⇌ H+ + OH−. For water acting as a base, the base dissociation constant Kb describes the reaction H2O + H+ ⇌ H3O+. When these two equilibria are considered together in aqueous solution, and you account for the fact that [H3O+] ≈ [H+] in dilute solutions and [H2O] is effectively constant, their constants multiply to give Kw. In other words, Ka × Kb equals Kw at that temperature. At 25°C, Kw is 1.0 × 10^−14, so Ka × Kb = 1.0 × 10^−14. This is why the correct relationship is Ka × Kb = Kw.

Understanding how water behaves as both an acid and a base in water helps here. The ion-product of water, Kw, is [H+][OH−] at a given temperature. For water acting as an acid, the dissociation constant Ka describes the reaction H2O ⇌ H+ + OH−. For water acting as a base, the base dissociation constant Kb describes the reaction H2O + H+ ⇌ H3O+. When these two equilibria are considered together in aqueous solution, and you account for the fact that [H3O+] ≈ [H+] in dilute solutions and [H2O] is effectively constant, their constants multiply to give Kw. In other words, Ka × Kb equals Kw at that temperature. At 25°C, Kw is 1.0 × 10^−14, so Ka × Kb = 1.0 × 10^−14. This is why the correct relationship is Ka × Kb = Kw.