Kw equals Ka × Kb. Which of the following expresses this relation correctly?

Kw equals Ka × Kb. Which of the following expresses this relation correctly?

• A. Ka × Kb
• B. Ka + Kb
• C. Ka / Kb
• D. Kw × Ka

Answer: (A)

In acid-base equilibria, the strengths of a weak acid and its conjugate base are linked to water's autoionization constant. For a weak acid HA, Ka = [H3O+][A−]/[HA], and for its conjugate base A− acting with water, Kb = [OH−][HA]/[A−]. Multiplying these two expressions gives Ka × Kb = [H3O+][OH−] = Kw. This shows that the product of Ka and Kb equals the ionic product of water. Therefore, the expression that correctly expresses the relation is Ka × Kb, since it directly yields Kw. At room temperature, Kw is about 1.0 × 10^−14, so Ka × Kb for a conjugate pair matches that value.

In acid-base equilibria, the strengths of a weak acid and its conjugate base are linked to water's autoionization constant. For a weak acid HA, Ka = [H3O+][A−]/[HA], and for its conjugate base A− acting with water, Kb = [OH−][HA]/[A−]. Multiplying these two expressions gives Ka × Kb = [H3O+][OH−] = Kw. This shows that the product of Ka and Kb equals the ionic product of water. Therefore, the expression that correctly expresses the relation is Ka × Kb, since it directly yields Kw. At room temperature, Kw is about 1.0 × 10^−14, so Ka × Kb for a conjugate pair matches that value.