Question

Write the equilibrium expression for each of the following heterogeneous equilibria. a. \(4 \mathrm{Al}(s)+3 \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{Al}_{2} \mathrm{O}_{3}(s)\) b. \(\mathrm{NH}_{3}(g)+\mathrm{HCl}(g) \rightleftharpoons \mathrm{NH}_{4} \mathrm{Cl}(s)\) c. \(2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{MgO}(s)\)

Short answer

a. \[K_{eq} = \frac{1}{[\mathrm{O}_{2}]^3}\] b. \[K_{eq} = \frac{1}{[\mathrm{NH}_{3}][\mathrm{HCl}]}\] c. \[K_{eq} = \frac{1}{[\mathrm{O}_{2}]}\]

Step-by-step solution

a. Equilibrium Expression for 4 Al(s) + 3 O₂(g) ⇌ 2 Al₂O₃(s)

1. Identify the reactants and products: In this reaction, the reactants are Al(s) and O₂(g) while the products are Al₂O₃(s). 2. Write the equilibrium expression: Since the equilibrium expression involves only the concentrations of gases and aqueous species, we'll consider only the O₂(g) as a term in the expression. \[K_{eq} = \frac{1}{[\mathrm{O}_{2}]^3}\]

b. Equilibrium Expression for NH₃(g) + HCl(g) ⇌ NH₄Cl(s)

1. Identify the reactants and products: In this reaction, the reactants are NH₃(g) and HCl(g), while the product is NH₄Cl(s). 2. Write the equilibrium expression: Since the equilibrium expression involves only the concentrations of gases and aqueous species, we'll consider NH₃(g) and HCl(g) as terms in the expression. \[K_{eq} = \frac{1}{[\mathrm{NH}_{3}][\mathrm{HCl}]}\]

c. Equilibrium Expression for 2 Mg(s) + O₂(g) ⇌ 2 MgO(s)

1. Identify the reactants and products: In this reaction, the reactants are Mg(s) and O₂(g), while the products are MgO(s). 2. Write the equilibrium expression: Since the equilibrium expression involves only the concentrations of gases and aqueous species, we'll consider only the O₂(g) as a term in the expression. \[K_{eq} = \frac{1}{[\mathrm{O}_{2}]}\]

Key concepts

Heterogeneous Equilibria

In chemistry, equilibrium can form in systems where reactants and products exist in different phases. This type of equilibrium is known as heterogeneous equilibrium. In the reactions given in the exercise, we see mixtures of solids (s) and gases (g). For example:

• Aluminum (solid) reacting with oxygen (gas) to form aluminum oxide (solid).
• Ammonia (gas) reacting with hydrogen chloride (gas) to form ammonium chloride (solid).

The key idea is that solids and liquids don't generally change concentration. Thus, they are not part of the equilibrium expression. Only gases and aqueous phases contribute to the equilibrium constant, since their concentrations do change during reactions.

Equilibrium Expressions

Equilibrium expressions are mathematical representations of a chemical reaction at equilibrium. They relate the concentrations of reactants and products. However, in heterogeneous equilibria, only gases and aqueous species are included. This is because their concentrations can change, unlike solids whose concentrations are constant. For example, in the reaction with aluminum and oxygen - \[4\, \text{Al(s)} + 3\, \text{O}_2(\text{g}) \rightleftharpoons 2\, \text{Al}_2\text{O}_3(\text{s})\] The equilibrium expression only includes oxygen as:\[ K_{eq} = \frac{1}{[\text{O}_{2}]^3} \] Here are some tips to remember:

• Include only gases and aqueous species. Solids and pure liquids are left out.
• The coefficients in the balanced equation become the exponents in the expression.

Le Chatelier's Principle

Le Chatelier's Principle provides insight into how equilibrium systems respond to changes. When a dynamic equilibrium is disturbed, it will adjust to counteract the disturbance and restore balance. This principle allows us to predict the effect of changes in concentration, pressure, temperature, or even the addition of catalysts. For example, if you increase the concentration of a reactant, the equilibrium shifts towards producing more products to regain balance. Consider the reaction: \[ \text{NH}_3(\text{g}) + \text{HCl}(\text{g}) \rightleftharpoons \text{NH}_4\text{Cl}(\text{s}) \]

• If you add more NH₃, the system will balance by forming more NH₄Cl.
• If you remove some HCl, the system will try to produce more HCl from NH₄Cl.

By understanding Le Chatelier’s principle, one can control the conditions of a reaction to favor the formation of desired products.