Question

Write the equilibrium expression for each of the following heterogeneous equilibria. a. \(2 \mathrm{NBr}_{3}(s) \rightleftharpoons \mathrm{N}_{2}(g)+3 \mathrm{Br}_{2}(g)\) b. \(\operatorname{CuO}(s)+\mathrm{H}_{2}(g) \rightleftharpoons \mathrm{Cu}(l)+\mathrm{H}_{2} \mathrm{O}(g)\) c. \(\operatorname{PbCO}_{3}(s) \rightleftharpoons \operatorname{PbO}(s)+\operatorname{CO}_{2}(g)\)

Short answer

a. \(K = [\mathrm{N}_{2}][\mathrm{Br}_{2}]^3\) b. \(K = \frac{[\mathrm{H}_{2}\mathrm{O}]}{[\mathrm{H}_{2}]}\) c. \(K = [\operatorname{CO}_{2}]\)

Step-by-step solution

Identify gaseous species

For each reaction, identify the gaseous reactants and products. The equilibrium expression will only involve these species and will exclude solid and liquid reactants and products. a. In the first reaction, N₂ and Br₂ are both in the gas phase. b. In the second reaction, H₂ and H₂O are both in the gas phase. c. In the third reaction, CO₂ is the only species in the gas phase.

Write the equilibrium expression

Based on the stoichiometry of the reaction, write the equilibrium expression, called the equilibrium constant (K), which is the ratio of the concentrations of the products raised to their stoichiometric coefficients divided by the concentrations of the reactants raised to their stoichiometric coefficients. Remember to only include the gaseous species in the expression. a. The equilibrium expression for the first reaction is: \(K = \frac{[\mathrm{N}_{2}]^1[\mathrm{Br}_{2}]^3}{[\mathrm{NBr}_{3}]^2}\) However, since NBr₃ is a solid, its concentration remains constant and is not included in the equilibrium expression. So, the revised expression is: \(K = [\mathrm{N}_{2}][\mathrm{Br}_{2}]^3\) b. For the second reaction, the equilibrium expression is: \(K = \frac{[\mathrm{Cu}]^1[\mathrm{H}_{2}\mathrm{O}]^1}{[\mathrm{CuO}]^1[\mathrm{H}_{2}]^1}\) Since CuO is a solid and Cu is a liquid, we exclude their concentrations from the equilibrium expression. The revised equilibrium expression for the second reaction is: \(K = \frac{[\mathrm{H}_{2}\mathrm{O}]}{[\mathrm{H}_{2}]}\) c. The equilibrium expression for the third reaction is: \(K = \frac{[\operatorname{PbO}]^1[\operatorname{CO}_{2}]^1}{[\operatorname{PbCO}_{3}]^1}\) In this case, PbCO₃ and PbO are both solids, so we exclude their concentrations from the equilibrium expression. The revised equilibrium expression for the third reaction is: \(K = [\operatorname{CO}_{2}]\)

Key concepts

Heterogeneous Equilibria

Heterogeneous equilibria involve reactants and products in different phases, such as solids, liquids, and gases. Unlike homogenous equilibria where all participants are in the same phase, solid and liquid reactants and products do not have concentrations that change with the progress of the reaction. Therefore, they are not included in the equilibrium expression.
In a heterogeneous equilibrium, the position of equilibrium depends only on the concentration of gaseous and aqueous species. This is because the amounts of solids and liquids are effectively constant during the reaction and do not affect the equilibrium condition. A classic example can be seen in the decomposition of calcium carbonate, where only the carbon dioxide gas is considered in the equilibrium expression, while the solid calcium carbonate and solid calcium oxide are excluded.
It's critical for students understanding such equilibria to remember that when writing the equilibrium expression, the concentrations of pure solids and pure liquids are omitted as they are deemed to have an activity of one. This simplifies the expression and reflects the actual behavior of the system as it moves towards equilibrium.

Equilibrium Constant (K)

The equilibrium constant, denoted as K, is a crucial concept in chemical equilibrium that quantifies the ratio of the concentrations of products to reactants, each raised to the power of their stoichiometric coefficients from the balanced equation. For gaseous reactions, concentrations are often expressed in terms of partial pressures.
It is important to note that K is constant at a given temperature and provides insight into the extent of a reaction. A large value of K indicates that the products are favored at equilibrium, while a small K suggests that the reactants are prevalent. As shown in the exercise's sample reactions, equilibrium constants for heterogeneous equilibria only include the gaseous and aqueous species involved in the reaction. By convention, the equilibrium constant for reactions involving pure solids or liquids do not include these phases as their concentrations do not change during the reaction.
Understanding the correct formulation of the equilibrium expression, including which species to include and exclude, is essential for precisely determining the equilibrium constant and consequently predicting the reaction's behavior at equilibrium.

Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. In the context of equilibrium, stoichiometry is used to determine the coefficients needed in the equilibrium expression.
When writing an equilibrium expression, the stoichiometric coefficients from the balanced chemical equation become the exponents for the respective concentrations of reactants and products. It is important to balance the chemical equation accurately before attempting to write the equilibrium expression as any mistake in stoichiometry will lead to an incorrect expression and an erroneous value for the equilibrium constant, K.
The stoichiometric coefficients act as a bridge between the microscopic (molecules, atoms) and the macroscopic (grams, liters) worlds, making sure that the atoms are conserved and the reaction obeys the law of mass action. Students need to practice balancing chemical equations and applying these balances to determine the correct form of the equilibrium expression for both homogeneous and heterogeneous reactions.