Question

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) \(2 \mathrm{Ag}(s)+\mathrm{Zn}^{2+}(a q) \rightleftharpoons 2 \mathrm{Ag}^{+}(a q)+\mathrm{Zn}(s)\)

Short answer

(a) Homogeneous. \(K_c = \frac{[\mathrm{N}_{2}\mathrm{O}][\mathrm{NO}_{2}]}{[\mathrm{NO}]^3}\) (b) Homogeneous. \(K_c = \frac{[\mathrm{CS}_{2}][\mathrm{H}_{2}]^4}{[\mathrm{CH}_{4}][\mathrm{H}_{2}\mathrm{S}]^2}\) (c) Heterogeneous. \(K_c = [\mathrm{CO}]^4\) (d) Homogeneous. \(K_c = \frac{[\mathrm{H}^+][\mathrm{F}^-]}{[\mathrm{HF}]}\) (e) Heterogeneous. \(K_c = \frac{[\mathrm{Ag}^+]^2}{[\mathrm{Zn}^{2+}]}\)

Step-by-step solution

(a) Identify reaction type and write Kc expression

The reaction is given as: \(3 \mathrm{NO}(g) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}(g)+\mathrm{NO}_{2}(g)\) All species are in the gas phase, so the reaction is homogeneous. The expression for Kc is: \[K_c = \frac{[\mathrm{N}_{2}\mathrm{O}][\mathrm{NO}_{2}]}{[\mathrm{NO}]^3}\]

(b) Identify reaction type and write Kc expression

The reaction is given as: \(\mathrm{CH}_{4}(g)+2 \mathrm{H}_{2} \mathrm{S}(g) \rightleftharpoons \mathrm{CS}_{2}(g)+4 \mathrm{H}_{2}(g)\) All species are in the gas phase, so the reaction is homogeneous. The expression for Kc is: \[K_c = \frac{[\mathrm{CS}_{2}][\mathrm{H}_{2}]^4}{[\mathrm{CH}_{4}][\mathrm{H}_{2}\mathrm{S}]^2}\]

(c) Identify reaction type and write Kc expression

The reaction is given as: \(\mathrm{Ni}(\mathrm{CO})_{4}(g) \rightleftharpoons \mathrm{Ni}(s)+4 \mathrm{CO}(g)\) We have one species in the gas phase and one in the solid phase, so the reaction is heterogeneous. The expression for Kc is: \[K_c = [\mathrm{CO}]^4\] (Since the concentration of solid Ni is constant, it is not included in the Kc expression)

(d) Identify reaction type and write Kc expression

The reaction is given as: \(\mathrm{HF}(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{F}^{-}(a q)\) All species are in the aqueous phase, so the reaction is homogeneous. The expression for Kc is: \[K_c = \frac{[\mathrm{H}^+][\mathrm{F}^-]}{[\mathrm{HF}]}\]

(e) Identify reaction type and write Kc expression

The reaction is given as: \(2 \mathrm{Ag}(s)+\mathrm{Zn}^{2+}(a q) \rightleftharpoons 2 \mathrm{Ag}^{+}(a q)+\mathrm{Zn}(s)\) We have species in the aqueous and solid phases, so the reaction is heterogeneous. The expression for Kc is: \[K_c = \frac{[\mathrm{Ag}^+]^2}{[\mathrm{Zn}^{2+}]}\] (The concentrations of solid Ag and Zn are constant and not included in the Kc expression)