ACS Organic Chemistry Practice Test

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

Ka × Kb = Kw Ka × Kw = Kb Ka / Kb = Kw Ka + Kb = Kw

Correct Answer:

Ka × Kb = Kw

Explanation:

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.

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