The product Ka multiplied by Kb for a reversible acid-base reaction is always equal to the ion-product constant.

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The product Ka multiplied by Kb for a reversible acid-base reaction is always equal to the ion-product constant.

When an acid HA donates a proton in water, its dissociation constant is Ka = [H+][A-]/[HA]. For the conjugate base A-, the base dissociation constant is Kb = [OH-][HA]/[A-]. Multiplying these two expressions gives Ka × Kb = [H+][OH-], because [A-] and [HA] cancel. That product is exactly Kw, the ion-product constant of water, which is defined as [H+][OH-] at a given temperature. Therefore, Ka × Kb equals Kw for that temperature. Kw is about 1.0×10^-14 at 25°C, but it varies with temperature, so the numerical value changes with temperature while the relationship Ka × Kb = Kw remains. Hence the statement is true.

When an acid HA donates a proton in water, its dissociation constant is Ka = [H+][A-]/[HA]. For the conjugate base A-, the base dissociation constant is Kb = [OH-][HA]/[A-]. Multiplying these two expressions gives Ka × Kb = [H+][OH-], because [A-] and [HA] cancel. That product is exactly Kw, the ion-product constant of water, which is defined as [H+][OH-] at a given temperature. Therefore, Ka × Kb equals Kw for that temperature. Kw is about 1.0×10^-14 at 25°C, but it varies with temperature, so the numerical value changes with temperature while the relationship Ka × Kb = Kw remains. Hence the statement is true.

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