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 of the above

Answer

To solve the question regarding the equilibrium constant for the reaction \( N_2(g) + O_2(g) \rightleftharpoons 2NO(g) \) at 200 K, we will follow these steps:

### Step 1: Understand the given information
The equilibrium constant \( K_c \) for the reaction at 200 K is given as \( 4 \times 10^{-4} \). We need to determine the effect of a catalyst on this equilibrium constant.

### Step 2: Recall the role of a catalyst
A catalyst is a substance that increases the rate of a reaction without being consumed in the process. It does this by lowering the activation energy for both the forward and reverse reactions equally. Importantly, a catalyst does not change the equilibrium constant of a reaction.

### Step 3: Analyze the effect of the catalyst on the equilibrium constant
Since the catalyst does not affect the equilibrium constant, the value of \( K_c \) remains unchanged regardless of the presence of the catalyst. Therefore, the equilibrium constant in the presence of the catalyst at 200 K will still be \( 4 \times 10^{-4} \).

### Step 4: Conclusion
Thus, the equilibrium constant in the presence of the catalyst at 200 K is:

\[ K_c = 4 \times 10^{-4} \]

### Final Answer
The correct answer is \( 4 \times 10^{-4} \).

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