Which relation correctly expresses the base hydrolysis constant for carbonate ion, given Kw and Ka2?

Which relation correctly expresses the base hydrolysis constant for carbonate ion, given Kw and Ka2?

• A. Kb = Ka2/Kw
• B. Ka2 = Kw/Kb
• C. Ka = Kw/Kb
• D. Kb = Kw/Ka2

Answer: (D)

The base hydrolysis constant for carbonate is tied to how bicarbonate can donate a proton and how carbonate can accept a proton in water. In water, Kw = [H+][OH-]. For the two related equilibria, you have the acid dissociation of bicarbonate: HCO3- ⇌ H+ + CO3^2- with Ka2, and the base hydrolysis of carbonate: CO3^2- + H2O ⇌ HCO3- + OH- with Kb. If you multiply these two equilibrium expressions, the [H+] and [CO3^2-] terms cancel appropriately and you’re left with Ka2 × Kb = [H+][OH-] = Kw. Rearranging gives Kb = Kw / Ka2. This is the correct relationship, reflecting how the strength of the bicarbonate acid governs the basicity of carbonate in water. At 25 °C, Kw has a standard value, and Ka2 is the appropriate dissociation constant for bicarbonate in the same conditions.

The base hydrolysis constant for carbonate is tied to how bicarbonate can donate a proton and how carbonate can accept a proton in water. In water, Kw = [H+][OH-]. For the two related equilibria, you have the acid dissociation of bicarbonate: HCO3- ⇌ H+ + CO3^2- with Ka2, and the base hydrolysis of carbonate: CO3^2- + H2O ⇌ HCO3- + OH- with Kb.

If you multiply these two equilibrium expressions, the [H+] and [CO3^2-] terms cancel appropriately and you’re left with Ka2 × Kb = [H+][OH-] = Kw. Rearranging gives Kb = Kw / Ka2. This is the correct relationship, reflecting how the strength of the bicarbonate acid governs the basicity of carbonate in water. At 25 °C, Kw has a standard value, and Ka2 is the appropriate dissociation constant for bicarbonate in the same conditions.