Write equilibrium constant expressions for \(K_{\mathrm{c}}\) and for \(K_{P}\), if applicable, for these processes: (a) \(2 \mathrm{CO}_{2}(g) \rightleftharpoons 2 \mathrm{CO}(g)+\mathrm{O}_{2}(g)\) (b) \(3 \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{O}_{3}(g)\) (c) \(\mathrm{CO}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{COCl}_{2}(g)\) (d) \(\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{C}(s) \rightleftharpoons \mathrm{CO}(g)+\mathrm{H}_{2}(g)\) (e) \(\mathrm{HCOOH}(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{HCOO}^{-}(a q)\) (f) \(2 \mathrm{HgO}(s) \rightleftharpoons 2 \mathrm{Hg}(l)+\mathrm{O}_{2}(g)\)

The equilibrium constant expressions for each set can be summarized as follows: (a) \(K_{\mathrm{c}} = \frac{[\mathrm{CO}]^2\times [\mathrm{O}_{2}]}{[\mathrm{CO}_{2}]^2}\) and \(K_{P} = \frac{(P_{\mathrm{CO}})^{2}\times P_{\mathrm{O}_{2}}}{(P_{\mathrm{CO}_{2}})^{2}}\), (b) \(K_{\mathrm{c}} = \frac{[\mathrm{O}_{3}]^2}{[\mathrm{O}_{2}]^3}\) and \(K_{P} = \frac{(P_{\mathrm{O}_{3}})^{2}}{(P_{\mathrm{O}_{2}})^{3}}\), (c) \(K_{\mathrm{c}} = \frac{[\mathrm{COCl}_{2}]}{\mathrm{[CO]}\times\mathrm{[Cl}_{2}]}\) and \(K_{P} = \frac{P_{\mathrm{COCl}_{2}}}{P_{\mathrm{CO}}\times P_{\mathrm{Cl}_{2}}}\), (d) \(K_{\mathrm{c}} = \frac{\mathrm{[CO]}\times \mathrm{[H}_{2}]}{\mathrm{[H}_{2}\mathrm{O}}\) and \(K_{P} = \frac{P_{\mathrm{CO}}\times P_{\mathrm{H}_{2}}}{P_{\mathrm{H}_{2}\mathrm{O}}}\), (e) \(K_{\mathrm{c}} = \frac{\mathrm{[H}^{+}\mathrm{]}\times \mathrm{[HCOO}^{-}]}{\mathrm{[HCOOH]}}\), and (f) \(K_{\mathrm{c}} = [\mathrm{O}_{2}]\) and \(K_{P} = P_{\mathrm{O}_{2}}\).