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: For the reaction `A(g)iff B(g)+C(g)`, `K_(p)`=1atm. If we start with equal moles of all gases at 9 tm of initial pressure, then at equilibrium partial pressure of A increases.
STATEMENT-2: Reaction quotient `Q_(p)gtK_(p)` hence equilibrium shifts in backward direction.

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 problem, we need to analyze both statements carefully:

### Step 1: Understand the Reaction and Given Data
The reaction is given as:
\[ A(g) \rightleftharpoons B(g) + C(g) \]
We are provided with the equilibrium constant \( K_p = 1 \, \text{atm} \) and the initial pressure of all gases is \( 9 \, \text{atm} \) with equal moles of each gas.

### Step 2: Calculate Initial Partial Pressures
Since we start with equal moles of A, B, and C, we can calculate the initial partial pressures:
- Total moles = 1 (A) + 1 (B) + 1 (C) = 3 moles
- Mole fraction of each gas = \( \frac{1}{3} \)
- Initial partial pressure of each gas = \( \text{Mole fraction} \times \text{Total pressure} = \frac{1}{3} \times 9 \, \text{atm} = 3 \, \text{atm} \)

Thus, the initial partial pressures are:
- \( P_A = 3 \, \text{atm} \)
- \( P_B = 3 \, \text{atm} \)
- \( P_C = 3 \, \text{atm} \)

### Step 3: Calculate the Reaction Quotient \( Q_p \)
The reaction quotient \( Q_p \) is calculated as:
\[ Q_p = \frac{P_B \cdot P_C}{P_A} = \frac{3 \, \text{atm} \cdot 3 \, \text{atm}}{3 \, \text{atm}} = 3 \, \text{atm} \]

### Step 4: Compare \( Q_p \) and \( K_p \)
We have:
- \( Q_p = 3 \, \text{atm} \)
- \( K_p = 1 \, \text{atm} \)

Since \( Q_p > K_p \), the equilibrium will shift to the left (backward direction).

### Step 5: Analyze the Effect on Partial Pressures
When the equilibrium shifts to the left, it means that more A will be produced from B and C. Therefore, the partial pressure of A will increase.

### Conclusion
- **Statement 1 (Assertion)**: "At equilibrium, the partial pressure of A increases." - This is **true**.
- **Statement 2 (Reason)**: "Reaction quotient \( Q_p > K_p \) hence equilibrium shifts in backward direction." - This is also **true**.

Since both statements are true and the reason correctly explains the assertion, the correct answer is:
**A: Both statements are true and statement 2 is the correct explanation for statement 1.**