Question

Write the equilibrium expression for each of the following heterogeneous equilibria. a. \(2 \mathrm{LiHCO}_{3}(s) \rightleftharpoons \mathrm{Li}_{2} \mathrm{CO}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}_{2}(g)\) b. \(\mathrm{PbCO}_{3}(s) \rightleftharpoons \mathrm{PbO}(s)+\mathrm{CO}_{2}(g)\) c. \(4 \mathrm{Al}(s)+3 \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{Al}_{2} \mathrm{O}_{3}(s)\)

Short answer

a. Equilibrium expression: \(K = \frac{[H_2O][CO_2]}{1}\) b. Equilibrium expression: \(K = \frac{[CO_2]}{1}\) c. Equilibrium expression: \(K = \frac{1}{[O_2]^3}\)

Step-by-step solution

a. 2LiHCO3(s) ⇌ Li2CO3(s) + H2O(g) + CO2(g)

First, identify the reactants and products in the balanced chemical equation. Reactants: 2LiHCO3(s) Products: Li2CO3(s), H2O(g), CO2(g) Now, write the equilibrium expression using the equilibrium constant (K). Remember to only include gas and aqueous species. In this case, we have H2O(g) and CO2(g). Equilibrium expression: \(K = \frac{[H_2O][CO_2]}{1}\). The presence of "1" in the denominator indicates no effect from solid components in the equilibrium.

b. PbCO3(s) ⇌ PbO(s) + CO2(g)

First, identify the reactants and products in the balanced chemical equation. Reactants: PbCO3(s) Products: PbO(s), CO2(g) Now, write the equilibrium expression using the equilibrium constant (K). Remember to only include gas and aqueous species. In this case, we only have CO2(g). Equilibrium expression: \(K = \frac{[CO_2]}{1}\). The presence of "1" in the denominator indicates no effect from solid components in the equilibrium.

c. 4Al(s) + 3O2(g) ⇌ 2Al2O3(s)

First, identify the reactants and products in the balanced chemical equation. Reactants: 4Al(s), 3O2(g) Products: 2Al2O3(s) Now, write the equilibrium expression using the equilibrium constant (K). Remember to only include gas and aqueous species. In this case, we only have O2(g) as a reactant. Equilibrium expression: \(K = \frac{1}{[O_2]^3}\). The presence of "1" in the numerator indicates no effect from solid components in the equilibrium.

Key concepts

Heterogeneous Equilibrium

Heterogeneous equilibrium involves chemical reactions where different phases (solid, liquid, gas) are present among the reactants and products. In such equilibria, the concentration of solids and pure liquids are considered constant and don't appear in the equilibrium constant expression. This is because their concentrations do not change during the reaction. These reactions often involve solids and gases.

For example, in the reaction \(\mathrm{PbCO}_{3}(s) \rightleftharpoons \mathrm{PbO}(s) + \mathrm{CO}_{2}(g)\), we only consider the gaseous component, \(\mathrm{CO}_{2}(g)\), in writing the equilibrium expression. Solids \(\mathrm{PbCO}_3(s)\) and \(\mathrm{PbO}(s)\) do not affect the quotient as they remain unchanged. This distinct feature simplifies the construction of equilibrium expressions for reactions involving multiple phases.

Chemical Equation Balancing

Balancing chemical equations is a fundamental skill in chemistry necessary for writing accurate equilibrium expressions. A balanced equation ensures that the same number of each type of atom is present in both reactants and products, adhering to the law of conservation of mass.

To balance a chemical equation, follow these steps:

• List all reactants and products with their respective chemical formulas.
• Adjust the coefficients before each formula to balance atoms of each element on both sides.
• Recheck the entire equation to confirm all elements are balanced.

Once balanced, these coefficients assist in determining which components will appear in the equilibrium expression. For instance, in \(4 \mathrm{Al}(s) + 3 \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{Al}_{2} \mathrm{O}_{3}(s)\), the coefficients help in deriving the equilibrium constant expression and in understanding the ratio of consumed and produced substances.

Equilibrium Constant (K)

The equilibrium constant \(K\) is a numerical value that indicates the ratio of product concentrations to reactant concentrations at equilibrium. For heterogeneous reactions, \(K\) only includes species in the gas or aqueous phases. Solid and pure liquid reactants/products don't figure in the calculation as they maintain constant concentration.

For the reaction \(2 \mathrm{LiHCO}_{3}(s) \rightleftharpoons \mathrm{Li}_{2} \mathrm{CO}_{3}(s) + \mathrm{H}_{2} \mathrm{O}(g) + \mathrm{CO}_{2}(g)\), the equilibrium expression based on gaseous products is \(K = \frac{[H_2O][CO_2]}{1}\). Such expressions determine how different conditions may impact the system and provide insight into the reaction's dynamic state at equilibrium.

Knowing the value of \(K\) helps in predicting the direction of the reaction. A large \(K\) implies more products than reactants at equilibrium, while a small \(K\) suggests the opposite.

Solid and Gas Species in Equilibria

In equilibrium studies, the treatment of solid and gas species varies due to their phase differences. Solids, because their concentration is constant over the course of the reaction, do not contribute to the expression of the equilibrium constant. Gases, meanwhile, do contribute because their concentrations can change.

In an equilibrium system like \(\mathrm{PbCO}_{3}(s) \rightleftharpoons \mathrm{PbO}(s) + \mathrm{CO}_{2}(g)\), the equilibrium expression \(K = \frac{[CO_2]}{1}\) only includes \(\mathrm{CO}_{2}(g)\) as it is a gas. Such a separation simplifies calculations.

Understanding which species to include in \(K\) is vital for analyzing how a system responds to changes such as pressure, temperature, or concentration variations. Knowing that solids are excluded from \(K\) reinforces focus on the reactive participants (gases) whose concentrations directly affect how equilibria adapt or resist changes.