The equilibrium constants for `A_2 (g) hArr 2A(g)` at 400 k and 600 k are `1xx 10^(-8) and 1 xx 10^(-2)` respectively . The reaction is

Options

A. Exothermic
B. Endothermic
C. May be exodhermic or endothermic
D. No heat is evolved or abosorbed

Answer

To solve the problem, we need to analyze the given equilibrium constants for the reaction \( A_2 (g) \rightleftharpoons 2A(g) \) at two different temperatures, 400 K and 600 K. The equilibrium constants are given as:

- \( K_1 = 1 \times 10^{-8} \) at 400 K
- \( K_2 = 1 \times 10^{-2} \) at 600 K

### Step-by-Step Solution:

1. **Understanding the Reaction**:
The reaction is \( A_2 (g) \rightleftharpoons 2A(g) \). This indicates that one mole of \( A_2 \) dissociates into two moles of \( A \).

2. **Analyzing the Equilibrium Constants**:
The equilibrium constant \( K \) for the reaction can be expressed as:
\[ K = \frac{[A]^2}{[A_2]} \]
A higher value of \( K \) indicates that the products are favored at equilibrium.

3. **Comparing \( K_1 \) and \( K_2 \)**:
- At 400 K, \( K_1 = 1 \times 10^{-8} \) (very small, indicating that the reaction favors the reactants).
- At 600 K, \( K_2 = 1 \times 10^{-2} \) (much larger, indicating that the reaction favors the products).

4. **Determining the Nature of the Reaction**:
The increase in the equilibrium constant from \( K_1 \) to \( K_2 \) as the temperature increases suggests that the reaction shifts towards the products with an increase in temperature.

5. **Applying the Van 't Hoff Equation**:
The Van 't Hoff equation relates the change in the equilibrium constant with temperature to the enthalpy change of the reaction:
\[ \ln \left( \frac{K_2}{K_1} \right) = -\frac{\Delta H}{R} \left( \frac{1}{T_2} - \frac{1}{T_1} \right) \]
Since \( K_2 > K_1 \), this indicates that \( \Delta H \) must be positive, which is characteristic of an endothermic reaction.

6. **Conclusion**:
Since the equilibrium constant increases with temperature, the reaction is endothermic. Therefore, the correct answer to the question is that the reaction is **endothermic**.