For a conjugate acid-base pair, which relation is correct at a given temperature?

For a conjugate acid-base pair, which relation is correct at a given temperature?

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

Answer: (A)

Relates to how acid and base constants for conjugate pairs multiply to the autoionization constant of water. For an acid HA, Ka = [H+][A-]/[HA]. For its conjugate base A-, Kb = [HA][OH-]/[A-]. Multiplying these two expressions gives Ka × Kb = ([H+][A-]/[HA]) × ([HA][OH-]/[A-]) = [H+][OH-] = Kw, the water ion-product at that temperature. So the correct relation is that the product of Ka and Kb equals Kw. This is temperature-dependent (Kw changes with temperature), and it also underpins the familiar pKa + pKb = pKw relationship. The other proposed relations don’t follow from the definitions of Ka and Kb.

Relates to how acid and base constants for conjugate pairs multiply to the autoionization constant of water. For an acid HA, Ka = [H+][A-]/[HA]. For its conjugate base A-, Kb = [HA][OH-]/[A-]. Multiplying these two expressions gives Ka × Kb = ([H+][A-]/[HA]) × ([HA][OH-]/[A-]) = [H+][OH-] = Kw, the water ion-product at that temperature. So the correct relation is that the product of Ka and Kb equals Kw. This is temperature-dependent (Kw changes with temperature), and it also underpins the familiar pKa + pKb = pKw relationship. The other proposed relations don’t follow from the definitions of Ka and Kb.