Chapter 12.2, Problem 12.2PSP

When carbon dioxide dissolves in water it reacts to produce carbonic acid, H₂CO₃(aq), which can ionize in two steps.

$\begin{array}{c}{H}_{2}C{O}_3(aq)\rightleftharpoons HC{O}_3^{-}(aq)+H^{+}(aq){\text{ K}}_{c_1}=4.2\times {10}^{-7}\\ HC{O}_3^{-}(aq)\rightleftharpoons C{O}_3^{2-}(aq)+H^{+}(aq){\text{ K}}_{c_2}=4.8\times {10}^{-11}\end{array}$

Calculate the equilibrium constant for the reaction

$H_{2}C{O}_3(aq)\rightleftharpoons C{O}_3^{2-}(aq)+2H^{+}(aq)$