1. K_w is closely realated to the equilibrium constant for the dissociation of water. It differs from K_eq by (reasonably) assuming the concentration of water to be a constant at 55 M. Because the ion product is an equilibrium constant, at a given temperature, its value (10⁻¹⁴ M) will be fixed, and may be used to calculate [H⁺] from [OH⁻], or vice versa.
2. pH = 14 − pOH. This is a consequency of the constancy of K_w.
3. Nitric acid is strong, and completely ionised in dilute solution. Consequently, a 10 mM solution (0.01 M), will contain very nearly 0.01 M protons. pH is the negative log to the base ten of the molar proton concentration, so the pH = − log₁₀( 0.01 ) = 2.
4. CH₃COOH (acid I) + OH⁻ (base II) → CH₃COO⁻ (base I) + H₂O (acid II).
5. pH = pK_a + log₁₀ [base] ⁄ [acid] = 9.2 + log₁₀( 15 ⁄ 20 ) = 9.07.