The equilibrium constant for the reaction `N_(2(g))+O_(2(g)) Leftrightarrow 2NO_((g))` at 2000K is 4 * 10^-4 In presence of a catalyst the equilibrium is attained three times faster. The equilibrium constant in presence of the catalyst at 2000 K

Options

A. `40 * 10^(-4)`
B. `4 * 10^(-4)`
C. `4 * 10^(-3)`
D. `4 * 10^(-8)`

Answer

To solve the question regarding the equilibrium constant for the reaction \( N_2(g) + O_2(g) \leftrightarrow 2NO(g) \) at 2000 K, we need to understand the role of a catalyst in a chemical reaction.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- The equilibrium constant \( K \) for the reaction at 2000 K is given as \( 4 \times 10^{-4} \).
- The presence of a catalyst speeds up the attainment of equilibrium but does not change the value of the equilibrium constant.

2. **Understand the Role of a Catalyst:**
- A catalyst increases the rate of both the forward and reverse reactions equally, allowing the system to reach equilibrium faster.
- Importantly, a catalyst does not change the position of equilibrium or the equilibrium constant.

3. **Conclusion:**
- Since the equilibrium constant is a function of temperature and does not depend on the presence of a catalyst, the equilibrium constant remains the same in the presence of a catalyst.
- Therefore, the equilibrium constant in the presence of the catalyst at 2000 K is still \( 4 \times 10^{-4} \).

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

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