Which are correct statement for the reaction: `A_(2) hArr `2C+ D

Options

A. If `Delta H= 0 :K_(p)` and dissociation of `A_(2)` are independent of temperature
B. If `Delta H = + ve : K_(p)` increases with temperature and dissociation of `A_(2)` increases
C. If `Delta H = +ve : K_(p)` idecreases with temperature and dissociation of `A(2)` increases
D. `K_(p) = 4 alpha^(3) [ (p)/(1 + 2 alpha ) ]^(2)`

Answer

To analyze the reaction \( A_2 \rightleftharpoons 2C + D \) and determine which statements are correct, we can follow these steps:

### Step 1: Understand the Reaction
The reaction involves the dissociation of \( A_2 \) into products \( 2C \) and \( D \). We need to consider how changes in temperature affect the equilibrium constant \( K_p \) and the degree of dissociation.

### Step 2: Consider the Enthalpy Change (\( \Delta H \))
1. **If \( \Delta H = 0 \)**: The equilibrium constant \( K_p \) and the degree of dissociation of \( A_2 \) are independent of temperature.
2. **If \( \Delta H > 0 \)**: The reaction is endothermic. According to Le Chatelier's principle, increasing the temperature will shift the equilibrium to the right, increasing \( K_p \) and the degree of dissociation of \( A_2 \).
3. **If \( \Delta H < 0 \)**: The reaction is exothermic. Increasing the temperature will shift the equilibrium to the left, decreasing \( K_p \) and the degree of dissociation of \( A_2 \).

### Step 3: Derive the Expression for \( K_p \)
For the reaction \( A_2 \rightleftharpoons 2C + D \):
- Let \( \alpha \) be the degree of dissociation of \( A_2 \).
- Initial moles: \( A_2 = 1, C = 0, D = 0 \).
- At equilibrium: \( A_2 = 1 - \alpha, C = 2\alpha, D = \alpha \).

The change in moles gives:
\[ K_p = \frac{(P_C)^{2} \cdot (P_D)}{(P_{A_2})} \]
Substituting the values:
\[ K_p = \frac{(2\alpha)^2 \cdot \alpha}{(1 - \alpha)} = \frac{4\alpha^3}{(1 - \alpha)} \]

### Step 4: Analyze the Statements
1. **Statement A**: If \( \Delta H = 0 \), \( K_p \) and dissociation of \( A_2 \) are independent of temperature. **(Correct)**
2. **Statement B**: If \( \Delta H > 0 \), \( K_p \) increases with temperature and dissociation of \( A_2 \) increases. **(Correct)**
3. **Statement C**: If \( \Delta H < 0 \), \( K_p \) decreases with temperature and dissociation of \( A_2 \) increases. **(Incorrect)**
4. **Statement D**: The derived expression for \( K_p \) is correct. **(Correct)**

### Conclusion
The correct statements are A, B, and D.

---