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, we need to understand the concept of the equilibrium constant and how it is affected by various factors.

### Step-by-Step Solution:

1. **Identify the given information:**
- The equilibrium constant \( K \) for the reaction \( N_2(g) + O_2(g) \rightleftharpoons 2NO(g) \) is given as \( 4 \times 10^{-4} \) at a temperature of 200 K.
- A catalyst is used which speeds up the attainment of equilibrium by 10 times.

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.
- However, it does not change the position of equilibrium or the value of the equilibrium constant.

3. **Determine the effect of the catalyst on the equilibrium constant:**
- The equilibrium constant \( K \) is a function of temperature only. It does not depend on the presence of a catalyst or the speed at which equilibrium is reached.
- Therefore, the equilibrium constant remains the same regardless of whether a catalyst is present or not.

4. **Conclude the value of the equilibrium constant in the presence of the catalyst:**
- Since the catalyst does not affect the equilibrium constant, the equilibrium constant in the presence of the catalyst at 200 K is still \( 4 \times 10^{-4} \).

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

---