The equilibrium constant for the reactions
`A+B hArr AB` is `0.5` at `200K`. The equilibrium constant for the reaction `AB hArr A+B` would be

Options

A. `1`
B. `2`
C. `3`
D. `4`

Explanation

To find the equilibrium constant for the reaction \( AB \rightleftharpoons A + B \), we can use the relationship between the equilibrium constants of forward and reverse reactions.

### Step-by-Step Solution:

1. **Identify the Given Information**:
- The equilibrium constant \( K_c \) for the reaction \( A + B \rightleftharpoons AB \) is given as \( 0.5 \) at \( 200 \, K \).

2. **Understand the Relationship**:
- The reaction \( AB \rightleftharpoons A + B \) is the reverse of the reaction \( A + B \rightleftharpoons AB \).

3. **Use the Reciprocal Relationship**:
- The equilibrium constant for the reverse reaction is the reciprocal of the equilibrium constant for the forward reaction. This can be expressed mathematically as:
\[ K_c' = \frac{1}{K_c} \]
where \( K_c' \) is the equilibrium constant for the reverse reaction.

4. **Calculate the Equilibrium Constant for the Reverse Reaction**:
- Substitute the known value of \( K_c \):
\[ K_c' = \frac{1}{0.5} = 2 \]

5. **Conclusion**:
- Therefore, the equilibrium constant for the reaction \( AB \rightleftharpoons A + B \) is \( 2 \).

### Final Answer:
The equilibrium constant for the reaction \( AB \rightleftharpoons A + B \) is \( 2 \).

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