The product of Ka and Kb for the reversible reaction

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Multiple Choice

The product of Ka and Kb for the reversible reaction

The main idea is that for a conjugate acid–base pair in water, the acid dissociation constant and the base hydrolysis constant multiply to give the ion-product constant of water. For the weak acid HA with conjugate base A−, Ka = [H+][A−]/[HA] and Kb for A− is [HA][OH−]/[A−]. Multiplying these two expressions cancels the concentrations of HA and A−, leaving Ka × Kb = [H+][OH−] = Kw. That’s why the product of Ka and Kb is the ion-product constant of water at that temperature. So the best description is that their product equals Kw, the ion-product constant. This value is temperature-dependent, so the numeric value changes with temperature, but the relation Ka × Kb = Kw holds at any given temperature. The other options aren’t correct because the product is not a fixed 1, nor is it Ka/Kb.

The main idea is that for a conjugate acid–base pair in water, the acid dissociation constant and the base hydrolysis constant multiply to give the ion-product constant of water. For the weak acid HA with conjugate base A−, Ka = [H+][A−]/[HA] and Kb for A− is [HA][OH−]/[A−]. Multiplying these two expressions cancels the concentrations of HA and A−, leaving Ka × Kb = [H+][OH−] = Kw. That’s why the product of Ka and Kb is the ion-product constant of water at that temperature. So the best description is that their product equals Kw, the ion-product constant. This value is temperature-dependent, so the numeric value changes with temperature, but the relation Ka × Kb = Kw holds at any given temperature. The other options aren’t correct because the product is not a fixed 1, nor is it Ka/Kb.

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