The equilibrium constant for the reaction `N_(2)(g)+O_(2)(g) hArr 2NO(g)` is `4.0xx10^(-4)` at `2000 K`. In the presence of a catalyst, the equilibrium is attained `10` times faster. Therefore, the equilibrium constant in presence of the catalyst at `2000 K` is

Options

A. `4xx10^(-4)`
B. `40xx10^(-4)`
C. `4xx10^(-2)`
D. Difficult to compute without more data

Explanation

To solve the problem, we need to understand the effect of a catalyst on the equilibrium constant of a reaction.

### Step-by-Step Solution:

1. **Identify the Reaction and Given Data**:
The reaction is:
\[ N_2(g) + O_2(g) \rightleftharpoons 2NO(g) \]
The equilibrium constant \( K \) at \( 2000 \, K \) is given as:
\[ K = 4.0 \times 10^{-4} \]

2. **Understand the Role of a Catalyst**:
A catalyst is a substance that increases the rate of a reaction without being consumed in the process. It helps the system reach equilibrium faster but does not affect the position of the equilibrium or the value of the equilibrium constant.

3. **Effect of Catalyst on Equilibrium Constant**:
Since the catalyst does not change the equilibrium constant, the value of \( K \) remains the same regardless of whether a catalyst is present or not.

4. **Conclusion**:
Therefore, even in the presence of a catalyst, the equilibrium constant at \( 2000 \, K \) remains:
\[ K = 4.0 \times 10^{-4} \]

### Final Answer:
The equilibrium constant in the presence of the catalyst at \( 2000 \, K \) is:
\[ 4.0 \times 10^{-4} \]

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