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. `40xx10^(-4)`
B. `4xx10^(-4)`
C. `4xx10^(-2)`
D. The data is insufficient

Answer

To solve the problem, we need to understand the relationship between equilibrium constants and catalysts. Here’s a step-by-step breakdown of the solution:

### Step 1: Identify the given information
We are given the equilibrium constant (K) for the reaction:
\[ N_2(g) + O_2(g) \rightleftharpoons 2NO(g) \]
The equilibrium constant at 2000 K is:
\[ K = 4.0 \times 10^{-4} \]

### Step 2: Understand the effect of a catalyst
A catalyst speeds up the rate at which equilibrium is reached but does not change the position of the equilibrium or the value of the equilibrium constant. The equilibrium constant is only affected by changes in temperature.

### Step 3: Analyze the situation
In this case, the problem states that the presence of a catalyst allows the equilibrium to be attained 10 times faster. However, since the temperature remains constant at 2000 K, the equilibrium constant will not change.

### Step 4: Conclusion
Thus, the equilibrium constant in the presence of the catalyst at 2000 K remains the same:
\[ K = 4.0 \times 10^{-4} \]

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

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