Kw

Meaning: Kw is the equilibrium constant for the autoionization of water, 2 H₂O ⇌ H₃O⁺ + OH⁻. Liquid water is left out of the expression. In any dilute aqueous solution at a given temperature, [H₃O⁺] times [OH⁻] equals Kw, so raising one concentration lowers the other. Autoionization is endothermic, so heating water increases Kw.

Equation: Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 °C, where concentrations are in mol/L (the constant is treated as unitless). Taking the negative log gives pKw = pH + pOH = 14 at 25 °C. For a conjugate acid-base pair, Kw = Ka × Kb.

On the MCAT: Expect to convert between [OH⁻] and [H₃O⁺] for a strong acid or base, then find pH. A common setup gives Kb of a weak base and asks for Ka of its conjugate acid using Kw = Ka × Kb. Another passage lists Kw at a higher temperature and asks for the pH of pure water, or whether pH + pOH still equals 14.

Common confusion: Students equate neutral with pH 7. Neutral means [H₃O⁺] = [OH⁻]. Because Kw increases with temperature, hot pure water has pH below 7 and is still neutral. Adding acid or base shifts the individual concentrations, but their product stays equal to Kw as long as the temperature is unchanged.