The equilibrium constant for the reaction `N_2(g) +O_2(g) hArr 2NO(g) "is" 4 xx 10^(-4)` at 200 k . In the presence of a catalyst the equilibrium is attained 10 times faster therefore, the equillbrium constant in presence of the catalyst at 200 k is

Options

A. `4 xx 10^(-3)`
B. `4xx 10^(-4)`
C. `4xx 10^(-5)`
D. none

Answer

To solve the problem regarding the equilibrium constant for the reaction \( N_2(g) + O_2(g) \rightleftharpoons 2NO(g) \) at 200 K, we need to understand the effect of a catalyst on the equilibrium constant.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- The equilibrium constant \( K \) for the reaction at 200 K is given as \( 4 \times 10^{-4} \).
- A catalyst is introduced, which speeds up the attainment of equilibrium by a factor of 10.

2. **Understand the Role of a Catalyst:**
- A catalyst increases the rate of both the forward and reverse reactions equally. This means that while the time taken to reach equilibrium is reduced, the position of equilibrium (and thus the equilibrium constant) does not change.
- The equilibrium constant \( K \) is defined as the ratio of the concentration of products to the concentration of reactants at equilibrium, and it is only affected by changes in temperature, not by the presence of a catalyst.

3. **Conclusion About the Equilibrium Constant:**
- Since the catalyst does not affect the equilibrium constant, the equilibrium constant remains the same even in its presence.
- Therefore, the equilibrium constant \( K \) at 200 K in the presence of a catalyst is still \( 4 \times 10^{-4} \).

4. **Final Answer:**
- The equilibrium constant in the presence of the catalyst at 200 K is \( 4 \times 10^{-4} \).