Answer
$$K_{c} = 2.0 \times 10^{-17}$$
Work Step by Step
Adding reactions (1) and (2) we get:
$$H_2CO_3(aq) + HC{O_3}^-(aq) \leftrightharpoons HC{O_3}^-(aq) + C{O_3}^{2-}(aq) + 2H^+(aq)$$
* Removing the repeated compounds:
$$H_2CO_3(aq) \leftrightharpoons C{O_3}^{2-}(aq) + 2H^+(aq)$$
Therefore:
$$K_{c3} = K_{c1} \times K_{c2} = (4.2 \times 10^{-7}) \times (4.8 \times 10^{-11})$$
$$K_{c3} = 2.0 \times 10^{-17}$$
