Solution :
[tex]H_2CO_3[/tex] is considered a diprotic acid.
Sp it can dissociate in solution by giving two protons.
Chemical equations for the first step of carbonic acid is :
First ionization
[tex]$H_2CO_3(aq) + H_0(1) \rightleftharpoons H_.O^+(aq) + HCO_3^-(aq)$[/tex]
Equilibrium constant expression is
[tex]$K_{a}_{1}=\frac{[H_3O^+][HCO_3^-]}{[H_2CO_3]}$[/tex]
Second ionization -
[tex]$HCO_3^-(aq) + H_2O(l) \rightleftharpoons H_3O^+(aq) + CO_3^{2-}(aq)$[/tex]
Equilibrium constant expression is
[tex]$K_{a2}=\frac{[H_3O^+][CO_3^{2-}]}{[HCO_3^-]}$[/tex]