Ionization of Water and the pH Scale

Every aqueous solution contains hydronium (H₃O⁺) and hydroxide (OH^-) ions as a result of the water autoionization process,

          (1.1)

[H₂O] does not appear in the equilibrium constant expression since, in dilute solutions, H₂O is very close to the standard state condition of pure liquid. In pure water at 25°C, [H₃O⁺] = [OH^-] = Kw_1/2 = 1.00 × 10-7 M.

Because the water ionization is endothermic, Kw increases with increasing T. In 0.10 M HCl solution, HCl is completely ionized,

and [H₃O⁺] = 0.10 M, [OH-] = 1.0 × 10^-13 M. Similarly 0.10 M NaOH is completely ionized,

and [OH^-] = 0.10 M, [H₃O⁺] = 1.0 × 10^-13 M. Because of the enormous range in the concentrations of H₃O⁺ and OH- ions, we usually use a logarithmic scale to express these concentrations:

         (1. 2)

                (1. 3)

Since the H₃O⁺ and OH^- concentrations are related by Eq. (1.1),

                                 (1.4)

(In general, pX = -log₁₀[X].) Thus, for 0.10 M HCl, pH = 1.00, pOH = 13.00, and for 0.10 M NaOH, pH = 13.00, pOH = 1.00.

Water is not unique in undergoing auto-ionization. Several other solvents are capable of acting both as acids and bases, e.g., the following equilibrium occurs in liquid ammonia (bp -33°C):