The equilibrium constant for the reaction
`N_2+3H_2 hArr 2NH_3` is K , then the equilibrium constant for the equilibrium `2NH_3hArr N_2+3H_2` is

Options

A. `sqrtk`
B. `sqrt(1/k)`
C. `1/k`
D. `1/(K^2)`

Answer

To find the equilibrium constant for the reaction \( 2NH_3 \rightleftharpoons N_2 + 3H_2 \) given that the equilibrium constant for the reaction \( N_2 + 3H_2 \rightleftharpoons 2NH_3 \) is \( K \), we can follow these steps:

### Step 1: Identify the original reaction and its equilibrium constant
The original reaction is:
\[ N_2 + 3H_2 \rightleftharpoons 2NH_3 \]
The equilibrium constant for this reaction is given as \( K \).

### Step 2: Understand the relationship of equilibrium constants for reverse reactions
When a reaction is reversed, the equilibrium constant for the reverse reaction is the inverse of the equilibrium constant for the forward reaction. Therefore, if the forward reaction has an equilibrium constant \( K \), the reverse reaction will have an equilibrium constant of:
\[ K' = \frac{1}{K} \]

### Step 3: Write the reverse reaction
The reverse reaction of the original reaction is:
\[ 2NH_3 \rightleftharpoons N_2 + 3H_2 \]

### Step 4: Apply the relationship of equilibrium constants
Since we have identified that the equilibrium constant for the reverse reaction is the inverse of the original reaction's equilibrium constant, we can write:
\[ K' = \frac{1}{K} \]

### Conclusion
Thus, the equilibrium constant for the reaction \( 2NH_3 \rightleftharpoons N_2 + 3H_2 \) is:
\[ \frac{1}{K} \]