Question

At 500 K, for a reversible reaction \(A_{2_{(g)}}+B_{2_{(g)}}⇌2AB_{(g)}\) in a closed container, K_C = 2 × 10^-5. In the presence of catalyst, the equilibrium is attaining 10 times faster. The equilibrium constant K_C in the presence of catalyst at the same temperature is

• A. 2 × 10^-4
• B. 2 × 10^-6
• C. 2 × 10^-10
• D. 2 × 10^-5

Answer 1

The Correct Option is D

Equilibrium Constant with Catalyst 

Given:

• At 500 K, \( K_c = 2 \times 10^{-5} \)
• Equilibrium is attained 10 times faster in the presence of a catalyst

 

Objective: Determine the equilibrium constant \( K_c \) in the presence of a catalyst at the same temperature.

The equilibrium constant \( K_c \) for the reaction: \[ A_2(g) + B_2(g) \rightleftharpoons 2AB(g) \] is given by: \[ K_c = \frac{[AB]^2}{[A_2][B_2]} \]

The presence of a catalyst affects the rate of reaction but does not change the equilibrium constant. Therefore, the equilibrium constant \( K_c \) remains: \[ \boxed{2 \times 10^{-5}} \]

Answer 2

The equilibrium constant, \( K_C \), for a reversible reaction is a thermodynamic quantity. It depends only on the temperature of the system and the nature of the reaction, and it is independent of the concentration of reactants and products at equilibrium or the presence of a catalyst. 

In the given reaction, A₂ + B₂ ⇌ 2AB, the equilibrium constant \( K_C \) is given as 2 × 10^-5 at 500 K. The presence of a catalyst in the reaction speeds up the attainment of equilibrium but does not affect the value of the equilibrium constant. 

A catalyst lowers the activation energy of both the forward and reverse reactions, thus increasing the rate at which equilibrium is reached. However, it does not change the position of the equilibrium or the equilibrium constant. 

Since the equilibrium constant \( K_C \) depends only on the temperature and the chemical reaction, and not on the presence of the catalyst, the value of \( K_C \) remains unchanged. Therefore, the equilibrium constant in the presence of the catalyst at the same temperature will still be 2 × 10^-5. 

Hence, the correct answer is (D): 2 × 10^-5.