Question

Write the expressions for \(K_{c}\) for the following reactions. In each case indicate whether the reaction is homogeneous or heterogeneous. (a) \(\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{O}(g)\) (b) \(\mathrm{Si}(s)+2 \mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{SiCl}_{4}(g)\) (c) \(\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{HCl}(g)\) (d) \(\mathrm{O}_{2}(g)+2 \mathrm{CO}(g) \rightleftharpoons 2 \mathrm{CO}_{2}(g)\) (e) \(\mathrm{HCO}_{3}^{-}(a q) \rightleftharpoons \mathrm{CO}_{3}^{2-}(a q)+\mathrm{H}^{+}(a q)\) (f) \(\mathrm{Fe}^{2+}(a q)+\mathrm{Ce}^{4+}(a q) \rightleftharpoons \mathrm{Fe}^{3+}(a q)+\mathrm{Ce}^{3+}(a q)\) (g) \(\mathrm{CaCO}_{3}(s) \rightleftharpoons \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)\)

Short answer

(a) Homogeneous reaction, Kc = \(\frac{[\mathrm{O}]^2}{[\mathrm{O}_{2}]}\) (b) Heterogeneous reaction, Kc = \(\frac{[\mathrm{SiCl}_{4}]}{[\mathrm{Cl}_{2}]^2}\) (c) Homogeneous reaction, Kc = \(\frac{[\mathrm{HCl}]^2}{[\mathrm{H}_{2}][\mathrm{Cl}_{2}]}\) (d) Homogeneous reaction, Kc = \(\frac{[\mathrm{CO}_{2}]^2}{[\mathrm{O}_{2}][\mathrm{CO}]^2}\) (e) Homogeneous reaction, Kc = \(\frac{[\mathrm{CO}_{3}^{2-}][\mathrm{H}^{+}]}{[\mathrm{HCO}_{3}^{-}]}\) (f) Homogeneous reaction, Kc = \(\frac{[\mathrm{Fe}^{3+}][\mathrm{Ce}^{3+}]}{[\mathrm{Fe}^{2+}][\mathrm{Ce}^{4+}]}\) (g) Heterogeneous reaction, Kc = \([CO_2]\)

Step-by-step solution

(a) Reaction and Kc expression for O2(g) ⇌ 2 O(g) equilibrium

This is a homogeneous reaction since both species are in the gas phase. The equilibrium constant, Kc, can be expressed as follows: Kc = \(\frac{[\mathrm{O}]^2}{[\mathrm{O}_{2}]}\)

(b) Reaction and Kc expression for Si(s) + 2 Cl2(g) ⇌ SiCl4(g) equilibrium

This is a heterogeneous reaction, as there are solid and gas species involved. The equilibrium constant, Kc, can be expressed as follows: Kc = \(\frac{[\mathrm{SiCl}_{4}]}{[\mathrm{Cl}_{2}]^2}\) (Note: we don't include the solid Si in the expression)

(c) Reaction and Kc expression for H2(g) + Cl2(g) ⇌ 2 HCl(g) equilibrium

This is a homogeneous reaction since all species are in the gas phase. The equilibrium constant, Kc, can be expressed as follows: Kc = \(\frac{[\mathrm{HCl}]^2}{[\mathrm{H}_{2}][\mathrm{Cl}_{2}]}\)

(d) Reaction and Kc expression for O2(g) + 2 CO(g) ⇌ 2 CO2(g) equilibrium

This is a homogeneous reaction since all species are in the gas phase. The equilibrium constant, Kc, can be expressed as follows: Kc = \(\frac{[\mathrm{CO}_{2}]^2}{[\mathrm{O}_{2}][\mathrm{CO}]^2}\)

(e) Reaction and Kc expression for HCO3-(aq) ⇌ CO32-(aq) + H+(aq) equilibrium

This is a homogeneous reaction since all species are in the aqueous phase. The equilibrium constant, Kc, can be expressed as follows: Kc = \(\frac{[\mathrm{CO}_{3}^{2-}][\mathrm{H}^{+}]}{[\mathrm{HCO}_{3}^{-}]}\)

(f) Reaction and Kc expression for Fe2+(aq) + Ce4+(aq) ⇌ Fe3+(aq) + Ce3+(aq) equilibrium

This is a homogeneous reaction since all species are in the aqueous phase. The equilibrium constant, Kc, can be expressed as follows: Kc = \(\frac{[\mathrm{Fe}^{3+}][\mathrm{Ce}^{3+}]}{[\mathrm{Fe}^{2+}][\mathrm{Ce}^{4+}]}\)

(g) Reaction and Kc expression for CaCO3(s) ⇌ CaO(s) + CO2(g) equilibrium

This is a heterogeneous reaction, as there are solid and gas species involved. The equilibrium constant, Kc, can be expressed as follows: Kc = \([CO_2]\) (Note: we don't include the solid CaCO3 and CaO in the expression)

Key concepts

Equilibrium Constant

The equilibrium constant, denoted as \( K_c \) or \( K_p \), is a crucial concept in chemical equilibrium. It gives the ratio of the concentrations of products to reactants at equilibrium, each raised to the power of their respective coefficients in the balanced chemical equation. The equilibrium constant allows us to predict the direction of the reaction and the extent to which a reaction proceeds.

For a general reaction: \[ aA + bB \rightleftharpoons cC + dD \]The expression for the equilibrium constant \( K_c \) is: \[ K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b} \]

It's important to understand that while calculating \( K_c \), only species in the gas or aqueous phase are included. Solids and pure liquids do not appear in the equilibrium expression.

Homogeneous Reaction

A homogeneous reaction is one where all reactants and products are in the same phase. This means they are either all gases or all in a solution (aqueous phase). These reactions often have a straightforward equilibrium constant expression since every species is included.

Some characteristics of homogeneous reactions include:

• Uniform composition throughout the mixture.
• Easy calculation of equilibrium expressions because no components are omitted.
• Tend to have faster reaction rates due to the uniform nature of the phase allowing better molecular interaction.

Examples from the exercise include reactions such as \( \mathrm{H}_2(g) + \mathrm{Cl}_2(g) \rightleftharpoons 2\mathrm{HCl}(g) \), where every species is in the gas phase, making the expression uniform and simple.

Heterogeneous Reaction

Heterogeneous reactions occur when the reactants and products are in different phases, such as a reaction involving solids, liquids, and gases. One of the unique aspects of these reactions is that the equilibrium constant expression only includes species that are in the gas or aqueous phase.

Key points about heterogeneous reactions include:

• Presence of multiple phases like solid-gas or liquid-solid.
• The equilibrium expression excludes solids and pure liquids; only gases and aqueous solutions are considered.
• These reactions can have complex dynamics due to phase interactions.

For example, the reaction \( \mathrm{CaCO}_3(s) \rightleftharpoons \mathrm{CaO}(s) + \mathrm{CO}_2(g) \) involves a solid reactant and products and thus is a heterogeneous reaction. Here, the equilibrium constant expression is simplified to \( K_c = [\mathrm{CO}_2] \).

Gas Phase Reactions

Gas phase reactions involve only gaseous reactants and products. The behavior of these reactions can be described using the ideal gas law, which can link concentration and pressure; hence, \( K_p \) is sometimes used as the equilibrium constant based on partial pressures.

Advantages of gas phase reactions include:

• Ability to relate pressure changes directly to concentration changes.
• Well-suited to the use of Le Chatelier's principle to predict shifts in equilibrium with pressure changes.

Common examples are reactions like \( \mathrm{O}_2(g) + 2\mathrm{CO}(g) \rightleftharpoons 2\mathrm{CO}_2(g) \), which makes laboratory and industrial manipulations easier due to the gas state of all components.

Aqueous Phase Reactions

Aqueous phase reactions involve substances dissolved in water. These reactions are important as they relate to a vast number of biological and chemical processes in nature and industrial applications.

Characteristics of aqueous phase reactions include:

• Involvement of ions and molecules dissolved in water, often leading to intricate ionic equations.
• The equilibrium constant expressions involve only the concentrations of those ions and molecules in the solution.

For instance, the reaction \( \mathrm{HCO}_3^{-}(aq) \rightleftharpoons \mathrm{CO}_3^{2-}(aq) + \mathrm{H}^+(aq) \) shows how equilibrium is established in a solution phase and affects processes like buffer systems in biological organisms.