Each question contains STATEMENT-1 (Assertion) and STATEMENT-2( Reason).
Examine the statements carefully and mark the correct answer according to the instruction given below:
STATEMENT-1: The equilibrium of `A(g) iffB(g)+c(g)` is not affected by changing the volume.
STATEMENT-2: `K_(c)` for the reaction does not depend on volume of the container.

Options

A. If both the statements are TRUE and STATEMENT-2 is the correct explanation of STATEMENT-1
B. If both the statement are TRUE but STATEMENT-2 is NOT the correct explanation of STATEMENT-1
C. If STATEMENT-1 is TRUE and STATEMENT-2 is FALSE
D. If STATEMENT-1 is FALSE and STATEMENT-2 is TRUE

Answer

To solve the question, we need to evaluate both statements provided:

**STATEMENT-1:** The equilibrium of \( A(g) \rightleftharpoons B(g) + C(g) \) is not affected by changing the volume.

**STATEMENT-2:** \( K_c \) for the reaction does not depend on the volume of the container.

### Step-by-Step Solution:

1. **Understanding the Reaction:**
The reaction given is \( A(g) \rightleftharpoons B(g) + C(g) \). Here, we have 1 mole of gas \( A \) on the reactant side and 2 moles of gases \( B \) and \( C \) on the product side.

2. **Effect of Volume Change on Equilibrium:**
According to Le Chatelier's principle, if the volume of the container is changed, the equilibrium will shift to counteract that change.
- If the volume is decreased (which increases pressure), the equilibrium will shift towards the side with fewer moles of gas. In this case, that would be the reactant side (1 mole of \( A \)).
- Conversely, if the volume is increased (which decreases pressure), the equilibrium will shift towards the side with more moles of gas, which is the product side (2 moles of \( B \) and \( C \)).

Therefore, the equilibrium is indeed affected by changing the volume.

3. **Evaluating STATEMENT-1:**
Since the equilibrium does shift based on volume changes, STATEMENT-1 is **false**.

4. **Understanding \( K_c \):**
The equilibrium constant \( K_c \) is defined in terms of the concentrations of the reactants and products at equilibrium. It is given by:
\[ K_c = \frac{[B][C]}{[A]} \]
The value of \( K_c \) depends only on the temperature of the system and not on the volume of the container or the concentrations of the reactants/products.

5. **Evaluating STATEMENT-2:**
Since \( K_c \) does not depend on the volume of the container, STATEMENT-2 is **true**.

### Conclusion:
- **STATEMENT-1:** False
- **STATEMENT-2:** True

Thus, the correct answer is that STATEMENT-1 is false and STATEMENT-2 is true.

### Final Answer:
**Option D:** STATEMENT-1 is false and STATEMENT-2 is true.

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