Question

Mercury(I) oxide decomposes into elemental mercury and elemental oxygen: \(2 \mathrm{Hg}_{2} \mathrm{O}(s) \rightleftharpoons 4 \mathrm{Hg}(l)+\mathrm{O}_{2}(g)\) (a) Write the equilibrium-constant expression for this reaction in terms of partial pressures. (b) Explain why we normally exclude pure solids and liquids from equilibrium-constant expressions.

Short answer

Part (a): The equilibrium constant expression for the given reaction in terms of partial pressures is: \[K_p = P_{O_2}\] Part (b): Pure solids and liquids are excluded from equilibrium-constant expressions because their concentrations do not change significantly during a reaction, and thus do not influence the position of the equilibrium. Including them would only result in a constant factor, which would not provide useful information about the reaction.

Step-by-step solution

Part (a): Writing the Equilibrium Constant Expression

The equilibrium-constant expression for a reaction is a way to quantitatively describe the relationship between the concentrations or pressures of reactants and products at a given temperature. Using partial pressure instead of concentration, the expression can be written using the given reaction: \[2 \mathrm{Hg}_2 \mathrm{O}(s) \rightleftharpoons 4 \mathrm{Hg}(l) + \mathrm{O}_2(g)\] The equilibrium constant (K_p) is defined as the product of the partial pressures of the products raised to their stoichiometric coefficients, divided by the product of the partial pressures of reactants raised to their stoichiometric coefficients. Since there are no gaseous reactants in the given reaction, we only need to consider the product, which is O_2(g). The equilibrium constant expression is then written as: \[K_p = \frac{P_{O_2}^{n_{O_2}}}{1}\] Where \(P_{O_2}\) is the partial pressure of oxygen gas produced, and \(n_{O_2}\) is the stoichiometric coefficient of oxygen gas in the balanced reaction (in this case, 1).

Part (b): Reason for Excluding Pure Solids and Liquids from Equilibrium-Constant Expressions

Pure solids and liquids are excluded from equilibrium-constant expressions because their concentrations do not change significantly during a reaction. Equilibrium constants are intended to capture the relationship between reactant and product concentrations or pressures as a reaction proceeds, and for pure solids and liquids, this relationship does not change. In other words, they do not influence the position of the equilibrium. Since the concentration of a pure solid or liquid remains constant throughout the reaction, it can be considered included in the equilibrium constant itself. If we were to include pure solids and liquids into the expression, the concentration term would be constant, and we would essentially be multiplying the actual constant by a constant factor, which would not provide any useful information about the reaction. By excluding pure solids and liquids, we can focus on the concentrations or pressures of the substances that actually change during a reaction and obtain a more informative equilibrium constant expression.

Key concepts

Chemical Equilibrium

Chemical equilibrium is a state in a reversible reaction where the rates of the forward and reverse reactions are equal, resulting in no net change in the concentration of reactants and products over time. This balance is dynamic, meaning that the reactions continue to occur, but because they proceed at equal rates, the concentrations remain constant.

In chemical equilibrium, the equilibrium-constant expression is vital as it quantifies the ratio of product concentrations to reactant concentrations, each raised to the power of their stoichiometric coefficient. The value of the equilibrium constant (K) is specific for a particular reaction at a given temperature. For the decomposition of mercury(I) oxide, the equilibrium can be disturbed by changes in pressure, temperature, or the presence of a catalyst, but the value of K will remain the same unless the temperature changes.

Partial Pressures

What Are Partial Pressures?

Partial pressures refer to the pressure exerted by a particular gas in a mixture of gases. Each gas in a mixture contributes to the total pressure of the system in proportion to its mole fraction. Dalton's Law of Partial Pressures states that the total pressure of a gas mixture is the sum of the partial pressures of each individual gas.

When dealing with gaseous reactions at equilibrium, the equilibrium-constant expression can be written in terms of partial pressures, denoted as K_p. This is particularly useful in reactions involving gases, as the concentrations of gases are often more conveniently expressed as pressures. In the given reaction, the equilibrium-constant expression, K_p, involves only the partial pressure of oxygen gas since mercury is in liquid form and mercury(I) oxide is a solid.

Stoichiometry

Understanding Stoichiometry in Equilibrium

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction based on the balanced chemical equation. When writing equilibrium-constant expressions, stoichiometry plays a crucial role. The coefficients from the balanced equation tell us how each reactant and product is involved in the reaction.

In our example of mercury(I) oxide decomposition, stoichiometry dictates that 2 moles of mercury(I) oxide produce 4 moles of elemental mercury and 1 mole of molecular oxygen. This ratio is reflected in the equilibrium-constant expression being written based on the stoichiometric coefficients. Hence, the power to which the partial pressure of oxygen is raised corresponds to its stoichiometric coefficient in the balanced equation, which is 1.

Exclusion of Pure Solids and Liquids in Equilibrium

Addressing why pure solids and liquids are excluded from equilibrium-constant expressions, it's due to their constant concentration during a reaction. Their physical states do not allow for an appreciable change in concentration under typical reaction conditions. As the concentration of these phases remains constant, they do not affect the equilibrium in the way that gases or solutes in solution do.

Therefore, including them in equilibrium-constant expressions would only multiply the value of K by a constant factor, which would not change over the course of the reaction. This is why K is typically used without these constant concentration terms, focusing only on reactant and product species whose concentrations do change appreciably and thereby influence the position of equilibrium.