The ion-product constant for water, Kw, is defined by which expression?

• A. Kw = [H+][OH-]
• B. Kw = [H3O+][OH-]
• C. Kw = [H3O+]+[OH-]
• D. Kw = [H3O+][H2O]

Answer: (B)

The key idea is the autoprotolysis (autoionization) of water and how its equilibrium is described. Water can self-ionize to produce hydronium and hydroxide ions, and in aqueous solutions the proton exists as a hydrated species, hydronium (H3O+). The ion-product constant of water is the product of the activities of these two ions: a(H3O+) × a(OH−). When we’re dealing with dilute solutions, activities are well approximated by concentrations, so Kw ≈ [H3O+] [OH−]. At standard room temperature this value is about 1.0 × 10^−14, reflecting that equal amounts of hydronium and hydroxide are present in pure water.

Using H+ instead of H3O+ is a common shorthand, but the more accurate representation in water is H3O+ because the proton is promptly hydrated. The expression that multiplies by water is not used because water’s activity is essentially constant (about 1) in dilute solutions, so it doesn’t appear in Kw. And adding the two concentrations would not reflect an equilibrium constant, which is formed from the product of the activities, not their sum.

So the correct form captures the actual species in solution and the multiplicative relationship that defines the equilibrium for water’s autoionization.