STATEMENT-1: For a hypotherical equlibrium, `AB_(2)(g)hArr2AB(g), K_(rho)` is always greater than `K_(c).`
STATEMENT-2: Relation of `K_(rho)and K_(c)` will be `K_(rho)=K_(c)(RT)Delta_(ng).`

Options

A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-10
B. Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-10
C. Statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True

Answer

To solve the given problem, we need to analyze both statements and the relationship between \( K_p \) and \( K_c \).

### Step-by-Step Solution:

**Step 1: Understand the Equilibrium Reaction**
The equilibrium reaction given is:
\[ AB_2(g) \rightleftharpoons 2AB(g) \]
This indicates that one mole of \( AB_2 \) dissociates into two moles of \( AB \).

**Step 2: Define \( K_p \) and \( K_c \)**
- \( K_p \) is the equilibrium constant expressed in terms of partial pressures.
- \( K_c \) is the equilibrium constant expressed in terms of molar concentrations.

**Step 3: Determine \( \Delta n \)**
Calculate the change in the number of moles of gas (\( \Delta n \)):
- Moles of products = 2 (from \( 2AB \))
- Moles of reactants = 1 (from \( AB_2 \))
\[ \Delta n = \text{Moles of products} - \text{Moles of reactants} = 2 - 1 = 1 \]

**Step 4: Relate \( K_p \) and \( K_c \)**
The relationship between \( K_p \) and \( K_c \) is given by the formula:
\[ K_p = K_c (RT)^{\Delta n} \]
Substituting \( \Delta n = 1 \):
\[ K_p = K_c (RT)^{1} = K_c (RT) \]

**Step 5: Analyze the Relationship**
Since \( R \) (the gas constant) and \( T \) (temperature) are both positive values, it follows that:
\[ K_p > K_c \]
This confirms that for the given equilibrium, \( K_p \) is always greater than \( K_c \).

**Step 6: Evaluate the Statements**
- **Statement 1**: \( K_p \) is always greater than \( K_c \) → This is **True**.
- **Statement 2**: The relation \( K_p = K_c (RT)^{\Delta n} \) is correct → This is **True**.

### Conclusion
Both statements are correct, and Statement 2 correctly explains Statement 1.

### Final Answer
Both Statement 1 and Statement 2 are correct, and Statement 2 is the correct explanation for Statement 1.

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