Write the expression for \(K_{c}\) for the following reactions. In each case indicate whether the reaction is homogeneous or heterogeneous. (a) \(3 \mathrm{NO}(g) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}(g)+\mathrm{NO}_{2}(g)\) (b) \(\mathrm{CH}_{4}(g)+2 \mathrm{H}_{2} \mathrm{~S}(g) \rightleftharpoons \mathrm{CS}_{2}(g)+4 \mathrm{H}_{2}(g)\) (c) \(\mathrm{Ni}(\mathrm{CO})_{4}(g) \rightleftharpoons \mathrm{Ni}(s)+4 \mathrm{CO}(g)\) (d) \(\mathrm{HF}(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{F}^{-}(a q)\) (e) \(2 \mathrm{Ag}(s)+\mathrm{Zn}^{2+}(a q) \rightleftharpoons 2 \mathrm{Ag}^{+}(a q)+\mathrm{Zn}(s)\) (f) \(\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{OH}^{-}(a q)\) (g) \(2 \mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons 2 \mathrm{H}^{+}(a q)+2 \mathrm{OH}^{-}(a q)\)

(a) For the reaction \(3 \mathrm{NO}(g) \rightleftharpoons \mathrm{N}_{2}\mathrm{O}(g)+\mathrm{NO}_{2}(g)\), the equilibrium expression is: \[K_c = \frac{[\mathrm{N}_2\mathrm{O}][\mathrm{NO}_2]}{[\mathrm{NO}]^3}\] and it is homogeneous. (b) For the reaction \(\mathrm{CH}_{4}(g)+2 \mathrm{H}_{2} \mathrm{~S}(g) \rightleftharpoons \mathrm{CS}_{2}(g)+4 \mathrm{H}_{2}(g)\), the equilibrium expression is: \[K_c = \frac{[\mathrm{CS}_2][\mathrm{H}_2]^4}{[\mathrm{CH}_4][\mathrm{H}_2\mathrm{~S}]^2}\] and it is homogeneous. (c) For the reaction \(\mathrm{Ni}(\mathrm{CO})_{4}(g) \rightleftharpoons \mathrm{Ni}(s)+4\mathrm{CO}(g)\), the equilibrium expression is: \[K_c = \frac{[\mathrm{CO}]^4}{[\mathrm{Ni(CO)_4}]}\] and it is heterogeneous. (d) For the reaction \(\mathrm{HF}(aq) \rightleftharpoons \mathrm{H}^{+}(aq)+\mathrm{F}^{-}(aq)\), the equilibrium expression is: \[K_c = \frac{[\mathrm{H}^+][\mathrm{F}^-]}{[\mathrm{HF}]}\] and it is homogeneous. (e) For the reaction \(2 \mathrm{Ag}(s)+\mathrm{Zn}^{2+}(aq) \rightleftharpoons 2 \mathrm{Ag}^{+}(aq)+\mathrm{Zn}(s)\), the equilibrium expression is: \[K_c = \frac{[\mathrm{Ag}^+]^2}{[\mathrm{Zn}^{2+}]}\] and it is heterogeneous. (f) For the reaction \(\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}^{+}(aq)+\mathrm{OH}^{-}(aq)\), the equilibrium expression is: \[K_c = \frac{[\mathrm{H}^+][\mathrm{OH}^-]}{[\mathrm{H}_2\mathrm{O}]}\] and it is heterogeneous. (g) For the reaction \(2 \mathrm{H}_{2}\mathrm{O}(l) \rightleftharpoons 2 \mathrm{H}^{+}(aq)+2\mathrm{OH}^{-}(aq)\), the equilibrium expression is: \[K_c = \frac{[\mathrm{H}^+]^2[\mathrm{OH}^-]^2}{[\mathrm{H}_2\mathrm{O}]^2}\] and it is heterogeneous.