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) \(2 \mathrm{Ag}(s)+\mathrm{Zn}^{2+}(a q) \rightleftharpoons 2 \mathrm{Ag}^{+}(a q)+\mathrm{Zn}(s)\) (f) \(\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{OH}^{-}(a q)\) (g) \(2 \mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons 2 \mathrm{H}^{+}(a q)+2 \mathrm{OH}(a q)\)

Short answer

The expressions for the equilibrium constants Kc for the given reactions are: (a) Homogeneous reaction: \[ K_c = \frac{[N_{2}O][NO_{2}]}{[NO]^3} \] (b) Homogeneous reaction: \[ K_c = \frac{[CS_{2}][H_{2}]^4}{[CH_{4}][H_{2}S]^2} \] (c) Heterogeneous reaction: \[ K_c = [CO]^4 \] (d) Homogeneous reaction: \[ K_c = \frac{[H^{+}][F^{-}]}{[HF]} \] (e) Heterogeneous reaction: \[ K_c = \frac{[Ag^{+}]^2}{[Zn^{2+}]} \] (f) Heterogeneous reaction: \[ K_c = [H^{+}][OH^{-}] \] (g) Heterogeneous reaction: \[ K_c = [H^{+}]^2[OH^{-}]^2 \]

Step-by-step solution

Reaction (a)

\(3 NO (g) \rightleftharpoons N_{2}O (g) + NO_{2} (g)\) All species are in the gas phase, so this is a homogeneous reaction. To write the Kc expression, we have: \[ K_c = \frac{[N_{2}O][NO_{2}]}{[NO]^3} \] #b)# Write Kc expression for reaction (b) and determine if it is homogeneous or heterogeneous.

Reaction (b)

\(CH_{4}(g) + 2 H_{2}S (g) \rightleftharpoons CS_{2}(g) + 4 H_{2}(g)\) All species are in the gas phase, so this is a homogeneous reaction. To write the Kc expression, we have: \[ K_c = \frac{[CS_{2}][H_{2}]^4}{[CH_{4}][H_{2}S]^2} \] #c)# Write Kc expression for reaction (c) and determine if it is homogeneous or heterogeneous.

Reaction (c)

\(Ni(CO)_{4}(g) \rightleftharpoons Ni(s) + 4 CO(g)\) There are species in the gas phase and solid phase, so this is a heterogeneous reaction. To write the Kc expression, we have: \[ K_c = [CO]^4 \] #d)# Write Kc expression for reaction (d) and determine if it is homogeneous or heterogeneous.

Reaction (d)

\(HF(aq) \rightleftharpoons H^{+}(aq) + F^{-}(aq)\) All species are in the aqueous phase, so this is a homogeneous reaction. To write the Kc expression, we have: \[ K_c = \frac{[H^{+}][F^{-}]}{[HF]} \] #e)# Write Kc expression for reaction (e) and determine if it is homogeneous or heterogeneous.

Reaction (e)

\(2 Ag(s) + Zn^{2+}(aq) \rightleftharpoons 2 Ag^{+}(aq) + Zn(s)\) There are species in the aqueous phase and solid phase, so this is a heterogeneous reaction. To write the Kc expression, we have: \[ K_c = \frac{[Ag^{+}]^2}{[Zn^{2+}]} \] #f)# Write Kc expression for reaction (f) and determine if it is homogeneous or heterogeneous.

Reaction (f)

\(H_{2}O(l) \rightleftharpoons H^{+}(aq) + OH^{-}(a q)\) The species are in liquid and aqueous phases, so this is a heterogeneous reaction. To write the Kc expression, we have: \[ K_c = [H^{+}][OH^{-}] \] #g)# Write Kc expression for reaction (g) and determine if it is homogeneous or heterogeneous.

Reaction (g)

\(2 H_{2}O(l) \rightleftharpoons 2 H^{+}(aq) + 2 OH^{-}(a q)\) The species are in liquid and aqueous phases, so this is a heterogeneous reaction. To write the Kc expression, we have: \[ K_c = [H^{+}]^2[OH^{-}]^2 \]

Key concepts

Homogeneous Reactions

Homogeneous reactions involve reactants and products that are in the same phase, such as all gases or all aqueous solutions. These reactions are uniform throughout because the substances involved are uniformly distributed. An example from the textbook solution is reaction (a), where all reactants and products are gases: \( 3 NO (g) \rightleftharpoons N_{2}O (g) + NO_{2} (g) \). The equilibrium constant expression for a homogeneous reaction, like the one mentioned, takes the form of \( K_c = \frac{[N_{2}O][NO_{2}]}{[NO]^3} \), where the concentration of each gas is used.

Understanding the nature of homogeneous reactions aids in predicting behavior such as mixing rates and reaction speeds. It's crucial to remember that in writing the equilibrium constant expression for homogeneous reactions, we use concentrations of reactants and products that are in the same state of matter.

Heterogeneous Reactions

In contrast, heterogeneous reactions involve substances in different phases, like solids reacting with gases or liquids. An instance from the exercise solutions is reaction (c): \( Ni(CO)_{4}(g) \rightleftharpoons Ni(s) + 4 CO(g) \), where nickel carbonyl gas decomposes into solid nickel and carbon monoxide gas. It's critical to note that solids and pure liquids are not included in the equilibrium constant expression because their concentration doesn't change during the reaction. Therefore, the \( K_c \) expression for the aforementioned reaction would simply be \( K_c = [CO]^4 \), omitting the solid nickel as it's in a different phase.

Heterogeneous reactions have different rates of reaction and mixing compared to homogeneous ones due to the nature of the contact between different phases. This concept is fundamental in fields like catalysis and materials science.

Kc Expression

The \( K_c \) expression, or the equilibrium constant expression, quantifies the balance between the products and reactants at a chemical equilibrium for a particular reaction at a constant temperature. For example, in reaction (d) having all species in aqueous solution: \( HF(aq) \rightleftharpoons H^{+}(aq) + F^{-}(aq) \), the equilibrium constant expression is written as \( K_c = \frac{[H^{+}][F^{-}]}{[HF]} \).The square brackets signify concentration in moles per liter. Each concentration is raised to the power of its coefficient in the balanced chemical equation.

The magnitude of the equilibrium constant gives insight into the position of the equilibrium. A larger \( K_c \) means a greater concentration of products at equilibrium, indicating the reaction favors the product side, while a smaller \( K_c \) favors reactants.

Chemical Equilibrium

Chemical equilibrium occurs when the rates of the forward and reverse reactions in a system become equal, leading to no net change in the concentrations of reactants and products. This is a dynamic equilibrium as the reactions continue to occur but do so in a way that maintains a constant state. The state of chemical equilibrium is described by the equilibrium constant \( K_c \), derived from the law of mass action. In this state, the ratio of the product of the concentrations of products to that of the reactants, each raised to the power of their respective coefficients in the balanced equation, remains constant. For example, reaction (b) from the solutions provided: \( CH_{4}(g) + 2 H_{2}S (g) \rightleftharpoons CS_{2}(g) + 4 H_{2}(g) \), is at equilibrium with a constant ratio specified by \( K_c = \frac{[CS_{2}][H_{2}]^4}{[CH_{4}][H_{2}S]^2} \).

Equilibrium can be shifted by changes in concentration, pressure, and temperature. This is explained by Le Chatelier's principle, which predicts how a system at equilibrium will respond to disturbances, a concept essential for optimizing industrial chemical processes.