Question

Write the equilibrium expression for each of the following heterogeneous equilibria. a. \(\mathrm{P}_{4}(s)+5 \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{P}_{4} \mathrm{O}_{10}(s)\) b. \(\mathrm{CO}_{2}(g)+2 \mathrm{NaOH}(s) \rightleftharpoons \mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(g)\) c. \(\mathrm{NH}_{4} \mathrm{NO}_{3}(s) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)\)

Short answer

a. \[K_{eq} = [\mathrm{O}_{2}]^{5}\] b. \[K_{eq} = \frac{[\mathrm{H}_{2}\mathrm{O}]}{[\mathrm{CO}_{2}]}\] c. \[K_{eq} = [\mathrm{N}_{2}\mathrm{O}] \cdot [\mathrm{H}_{2}\mathrm{O}]^{2}\]

Step-by-step solution

Identify the gaseous species in the reaction

Identify the gaseous species in the reaction, in this case, O2(g).

Write the equilibrium expression

Write the equilibrium expression considering only the concentrations of the gaseous species: \[K_{eq} = [\mathrm{O}_{2}]^{5}\] b. CO2(g) + 2 NaOH(s) ⇌ Na2CO3(s) + H2O(g)

Identify the gaseous species in the reaction

Identify the gaseous species in the reaction, in this case, CO2(g) and H2O(g).

Write the equilibrium expression

Write the equilibrium expression considering only the concentrations of the gaseous species: \[K_{eq} = \frac{[\mathrm{H}_{2}\mathrm{O}]}{[\mathrm{CO}_{2}]}\] c. NH4NO3(s) ⇌ N2O(g) + 2 H2O(g)

Identify the gaseous species in the reaction

Identify the gaseous species in the reaction, in this case, N2O(g) and H2O(g).

Write the equilibrium expression

Write the equilibrium expression considering only the concentrations of the gaseous species: \[K_{eq} = [\mathrm{N}_{2}\mathrm{O}] \cdot [\mathrm{H}_{2}\mathrm{O}]^{2}\]

Key concepts

Heterogeneous Equilibria

Understanding heterogeneous equilibria is key to solving problems involving chemical reactions that have reactants and products in different phases. A typical heterogeneous equilibrium involves solids, liquids, and gases. In such systems, the concentrations of solid and liquid reactants and products remain essentially constant. Therefore, they are not included in the equilibrium expression.

For example, in the reaction \(\mathrm{P}_{4}(s)+5 \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{P}_{4} \mathrm{O}_{10}(s)\), only the gaseous oxygen is included in the equilibrium expression. This is because the solid substances, \(\mathrm{P}_{4}\) and \(\mathrm{P}_{4} \mathrm{O}_{10}\), have constant concentrations due to their condensed states. In practice, only gas and aqueous solution concentrations are typically included in the equilibrium constant expression for heterogeneous equilibria.

Equilibrium Constant (Keq)

The equilibrium constant (Keq) quantitatively expresses the ratio of products to reactants at equilibrium for a reversible chemical reaction. This value is a constant at a given temperature and is crucial for predicting the direction of the reaction and understanding system kinetics.

To write the correct Keq expression, it is essential to follow the convention of excluding solids and liquids, as seen in the step-by-step solutions of the exercise. For instance, in the reaction \(\mathrm{CO}_{2}(g)+2 \mathrm{NaOH}(s) \rightleftharpoons \mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(g)\), the equilibrium expression is \[K_{eq} = \frac{[\mathrm{H}_{2}\mathrm{O}]}{[\mathrm{CO}_{2}]}\], indicating the ratio of the concentration of gaseous water to that of carbon dioxide gas. The equilibrium constant helps us to determine how far the reaction has proceeded and in which direction it would shift if any changes occur in the system.

Gas-phase Reactions

Importance of Gas Concentration in Equilibrium

In gas-phase reactions, the state of equilibrium considers the partial pressures or concentrations of the gaseous reactants and products. The gas phase is especially important because gases are highly compressible and their concentrations can change with pressure. As seen in the equation \(\mathrm{NH}_{4} \mathrm{NO}_{3}(s) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)\), the equilibrium expression involves only the gas-phase species, \[K_{eq} = [\mathrm{N}_{2}\mathrm{O}] \cdot [\mathrm{H}_{2}\mathrm{O}]^{2}\].

Dynamic Nature of Equilibrium

Equilibrium in a gas-phase reaction is dynamic, meaning that the forward and reverse reactions continue to occur, but at the same rate, thus maintaining constant concentrations of reactants and products. Understanding this dynamic nature helps explain why changes in conditions (like pressure or temperature) can shift the position of the equilibrium, in accordance with Le Chatelier's principle, affecting the Keq and ultimately the reaction yield.