Problem 16 - Chemistry The Central Science In Si Units

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) \(\mathrm{CaCO}_{3}(s) \rightleftharpoons \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)\)

Step-by-Step Solution

Answer

(a) Homogeneous: \\[K_{c} = \frac{[O]^2}{[O_2]}\\] (b) Heterogeneous: \\[K_{c} = \frac{[SiCl_4]}{[Cl_2]^2}\\] (c) Homogeneous: \\[K_{c} = \frac{[HCl]^2}{[H_2][Cl_2]}\\] (d) Homogeneous: \\[K_{c} = \frac{[CO_2]^2}{[O_2][CO]^2}\\] (e) Homogeneous: \\[K_{c} = \frac{[CO_3^{2-} ] [H^+ ] }{[HCO_3^- ]}\\] (f) Homogeneous: \\[K_{c} = \frac{[Fe^{3+}][Ce^{3+}]}{[Fe^{2+}][Ce^{4+}]}\\] (g) Heterogeneous: \\[K_{c} = [CO_2]\\]

Step 1: Understanding Homogeneous and Heterogeneous Reactions

A homogeneous reaction is one in which all the reactants and products are in the same phase. A heterogeneous reaction involves reactants and products in different phases.

Step 2: Write Expression for Reaction (a)

The reaction is \(\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{O}(g)\). All reactants and products are in the gas phase, so this is a homogeneous reaction. The equilibrium constant is given by \[K_{c} = \frac{[O]^2}{[O_2]}\]

Step 3: Write Expression for Reaction (b)

The reaction is \(\mathrm{Si}(s)+2 \mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{SiCl}_{4}(g)\). This is a heterogeneous reaction because Si is a solid and the others are gases. Solids do not appear in the expression for \(K_c\), so \[K_{c} = \frac{[SiCl_4]}{[Cl_2]^2}\]

Step 4: Write Expression for Reaction (c)

The reaction is \(\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{HCl}(g)\). This is a homogeneous reaction as all components are gases. The equilibrium expression is \[K_{c} = \frac{[HCl]^2}{[H_2][Cl_2]}\]

Step 5: Write Expression for Reaction (d)

The reaction is \(\mathrm{O}_{2}(g)+2 \mathrm{CO}(g) \rightleftharpoons 2 \mathrm{CO}_{2}(g)\). This is a homogeneous gas-phase reaction. The equilibrium constant is \[K_{c} = \frac{[CO_2]^2}{[O_2][CO]^2}\]

Step 6: Write Expression for Reaction (e)

The reaction is \(\mathrm{HCO}_{3}^{-}(a q) \rightleftharpoons \mathrm{CO}_{3}^{2-}(a q)+\mathrm{H}^{+}(a q)\). This is a homogeneous reaction as all components are in aqueous phase. The equilibrium expression is \[K_{c} = \frac{[CO_3^{2-}][H^+]}{[HCO_3^-]}\]

Step 7: Write Expression for Reaction (f)

The reaction is \(\mathrm{Fe}^{2+}(a q)+\mathrm{Ce}^{4+}(a q) \rightleftharpoons \mathrm{Fe}^{3+}(a q)+\mathrm{Ce}^{3+}(a q)\). This is a homogeneous aqueous reaction. The equilibrium constant expression is \[K_{c} = \frac{[Fe^{3+}][Ce^{3+}]}{[Fe^{2+}][Ce^{4+}]}\]

Step 8: Write Expression for Reaction (g)

The reaction is \(\mathrm{CaCO}_{3}(s) \rightleftharpoons \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)\). This is a heterogeneous reaction involving solids and a gas. The equilibrium expression only includes the gas phase, therefore \[K_{c} = [CO_2]\]

Key Concepts

Homogeneous Reactions

In homogeneous reactions, all reactants and products are in the same phase, usually gas or liquid. This means that every substance involved is either entirely in the gaseous state or completely dissolved in a solution. Homogeneous reactions are straightforward when it comes to writing chemical equilibrium expressions because you consider all reactants and products directly.
For example, in the reaction \( \mathrm{H}_{2}(g)+ \mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{HCl}(g) \), all reactants and products are gases. The equilibrium expression for this is:

• \( K_{c} = \frac{[HCl]^2}{[H_2][Cl_2]} \)

This expression illustrates that homogeneous reactions are efficiently handled by including the concentrations of all gaseous species involved. It highlights how concentration changes might influence the direction of the equilibrium.

Heterogeneous Reactions

Heterogeneous reactions involve reactants and products that are in different phases, such as solids, liquids, and gases. In these reactions, while solids and pure liquids participate in the reaction, they do not appear in the equilibrium constant expression. This is because their activity is considered constant.
For instance, consider \( \mathrm{Si}(s)+2 \mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{SiCl}_{4}(g) \). Si is a solid whereas others are gases. Here, the equilibrium constant expression is:

• \( K_{c} = \frac{[SiCl_4]}{[Cl_2]^2} \)

Notice that only the gas-phase species' concentrations are included in the equilibrium expression. This simplification helps when calculating the reactions involving substances of different phases.

Chemical Equilibrium Expressions

At equilibrium, the rate of the forward reaction equals the rate of the reverse reaction. The expression for the equilibrium constant, \( K_c \), provides a ratio of the concentrations of products to reactants at equilibrium. When writing these expressions, it's essential to remember:

• The concentrations of gases and aqueous solutions only should be considered.
• Solids and liquids are omitted from the \( K_c \) expression.
• Exponents in the expression correspond to the coefficients of substances in the balanced equation.

For example, in the reaction \( \mathrm{O}_{2}(g)+2 \mathrm{CO}(g) \rightleftharpoons 2 \mathrm{CO}_{2}(g) \), the equilibrium expression is:

• \( K_{c} = \frac{[CO_2]^2}{[O_2][CO]^2} \)

This highlights the balanced nature of reactions at equilibrium, as well as the importance of considering only reactive phases when constructing equilibrium expressions.