Write a chemical equation for an equilibrium system that would lead to the following expressions (a-d) for \(K\). (a) \(K=\frac{\left(P_{\mathrm{CO}_{2}}\right)^{3}\left(P_{\mathrm{H}_{2} \mathrm{O}}\right)^{4}}{\left(P_{\mathrm{C}, \mathrm{H}_{4}}\right)\left(P_{\mathrm{O}_{2}}\right)^{5}}\) (b) \(K=\frac{P_{\mathrm{C}_{0} \mathrm{H}_{12}}}{\left(P_{\mathrm{C}, \mathrm{H}_{6}}\right)^{2}}\) (c) \(K=\frac{\left[\mathrm{PO}_{4}^{3-}\right]\left[\mathrm{H}^{+}\right]^{3}}{\left[\mathrm{H}_{3} \mathrm{PO}_{4}\right]}\) (d) \(K=\frac{\left(P_{\mathrm{CO}_{2}}\right)\left(P_{\mathrm{H}_{2} \mathrm{O}}\right)}{\left[\mathrm{CO}_{3}^{2-}\right]\left[\mathrm{H}^{+}\right]^{2}}\)

Question: Based on the given equilibrium expressions, provide the balanced chemical equations for each. a) \(K = \frac{(P_{\mathrm{CO}_{2}})^{3}(P_{\mathrm{H}_{2}\mathrm{O})^{4}}{(P_{\mathrm{C},\mathrm{H}_{4}})(P_{\mathrm{O}_{2}})^{5}}\) b) \(K = \frac{P_{\mathrm{C}_{0}\mathrm{H}_{12}}}{(P_{\mathrm{C},\mathrm{H}_{6}})^2}\) c) \(K = \frac{[\mathrm{PO}_{4}^{3-}][\mathrm{H}^{+}]^3}{[\mathrm{H}_{3}\mathrm{PO}_{4}]}\) d) \(K = \frac{(P_{\mathrm{CO}_{2}})(P_{\mathrm{H}_{2}\mathrm{O})}{[\mathrm{CO}_{3}^{2-}][\mathrm{H}^{+}]^2}\) Answer: a) \(\mathrm{CH_{4}}(g) + 5\,\mathrm{O}_{2}(g) \longleftrightarrow 3\,\mathrm{CO}_{2}(g) + 4\,\mathrm{H}_{2}\mathrm{O}(g)\) b) \(2\,\mathrm{CH}_{6}(g) \longleftrightarrow \mathrm{C}_{2}\mathrm{H}_{12}(g)\) c) \(\mathrm{H}_{3}\mathrm{PO}_{4}(aq) \longleftrightarrow \mathrm{PO}_{4}^{3-}(aq) + 3\,\mathrm{H}^{+}(aq)\) d) \(\mathrm{CO}_{3}^{2-}(aq) + 2\,\mathrm{H}^{+}(aq) \longleftrightarrow \mathrm{CO}_{2}(g) + \mathrm{H}_{2}\mathrm{O}(g)\)