Question

Which of the following statements is true regarding the general equilibrium expression? (a) \(K_{\text {eq }}\) for gaseous equilibria does not depend on temperature. (b) \(K_{\text {eq }}\) for gaseous equilibria does not include solid substances.

Short answer

Statement (b) is true.

Step-by-step solution

Understanding Equilibrium Constants

The equilibrium constant, represented by \( K_{eq} \), is a ratio of the concentrations of products to reactants at equilibrium, each raised to the power of their coefficients in the balanced equation.

Assessing Statement (a)

Statement (a) suggests that \( K_{eq} \) for gaseous equilibria is independent of temperature. This is incorrect because \( K_{eq} \) is temperature-dependent; changing the temperature will change the equilibrium constant.

Evaluating Statement (b)

Statement (b) indicates that \( K_{eq} \) for gaseous equilibria does not include solid substances. This is true, as equilibrium expressions do not include solids or pure liquids; they only include gaseous and aqueous species.

Conclusion

With statement (a) being false and statement (b) being true, we can conclude that statement (b) correctly describes a characteristic of the equilibrium expression \( K_{eq} \).

Key concepts

Equilibrium Constant

The equilibrium constant, denoted as \( K_{eq} \), is a crucial concept in chemical equilibrium. It helps us understand the ratio of the concentration of products to reactants when a reaction reaches equilibrium. When we express the equilibrium constant, each concentration is raised to the power of its coefficient from the balanced chemical equation. For example, in the reaction \( \text{aA} + \text{bB} \leftrightarrow \text{cC} + \text{dD} \), the equilibrium constant \( K_{eq} \) is defined as: \[ K_{eq} = \frac{[C]^c [D]^d}{[A]^a [B]^b} \] This formula tells us how far the reaction has proceeded at equilibrium. A high \( K_{eq} \) value indicates that the products are favored, while a low \( K_{eq} \) suggests that the reactants are predominant. Understanding \( K_{eq} \) is essential for predicting the direction of the reaction and gauging the extent of reaction at equilibrium.

Temperature Dependence

The equilibrium constant \( K_{eq} \) is sensitive to temperature changes. This means that if the temperature of a reaction mixture is altered, the value of \( K_{eq} \) can change as well. This dependence arises because temperature affects the kinetics of the chemical reaction by either absorbing (endothermic) or releasing (exothermic) heat. According to Le Chatelier’s principle:

• For an endothermic reaction (absorbing heat), an increase in temperature causes \( K_{eq} \) to rise.
• For an exothermic reaction (releasing heat), an increase in temperature leads to a decrease in \( K_{eq} \).

Thus, knowing the temperature dependence is crucial in industrial processes and laboratory experiments for fine-tuning reactions to get desired products.

Gaseous Equilibria

Gaseous equilibria describe reactions where all reactants and products are gases. These equilibria play a significant role in understanding how reactions behave in the gaseous state. In the context of equilibrium expressions, it is important to note that solids and pure liquids are not included in the calculation of the equilibrium constant \( K_{eq} \) for gaseous reactions. Only gaseous reactants and products are considered. This is because concentrations of solids and pure liquids do not change during the reaction. Thus, if a reaction involves a solid or pure liquid in equilibrium with gases, the solid or liquid is ignored in the fractionation of \( K_{eq} \). For instance, in the reaction \( \text{CaCO}_3(s) \leftrightarrow \text{CaO}(s) + \text{CO}_2(g) \), the equilibrium expression is: \[ K_{eq} = [CO_2] \] This approach highlights the dynamic nature of gaseous equilibria and ensures accurate representation of the system at equilibrium.