`AB(s)hArrA(g)+B(g)K_(p)=4,DeltaH=+ve`
In a container,`A`(g) "and" B(g) are filled to partial pressure of `1` atm each. Now `AB(s)` is added (in excess quantity). Which of the following is CORRECT? (No other gas is present in container):

Options

A. At equilibrium, the total pressure in the container is `4` atm.
B. Equilibrium pressure decreases uniformly on increasing the volume by container.
C. At equilibrium, the total pressure in the container is more than `4` atm, if temperature is increased.
D. None of these

Answer

To solve the problem, we need to analyze the equilibrium reaction given and the conditions provided.

### Step 1: Understand the Reaction
The reaction is given as:
\[ AB(s) \rightleftharpoons A(g) + B(g) \]
with \( K_p = 4 \) and \( \Delta H = +ve \) (indicating that the reaction is endothermic).

### Step 2: Initial Conditions
Initially, the partial pressures of gases \( A \) and \( B \) are both 1 atm:
- \( P_A = 1 \, \text{atm} \)
- \( P_B = 1 \, \text{atm} \)

### Step 3: Calculate Initial Reaction Quotient (Q)
The reaction quotient \( Q \) is calculated as:
\[ Q = P_A \times P_B = 1 \times 1 = 1 \, \text{atm}^2 \]

### Step 4: Compare Q and Kp
Since \( K_p = 4 \) and \( Q = 1 \):
- \( Q < K_p \)
This means that the reaction will shift to the right to reach equilibrium, producing more \( A \) and \( B \).

### Step 5: Change in Partial Pressures
Let \( x \) be the change in the partial pressures of \( A \) and \( B \) at equilibrium. Thus:
- \( P_A = 1 + x \)
- \( P_B = 1 + x \)

### Step 6: Write the Expression for Kp
At equilibrium, the expression for \( K_p \) is:
\[ K_p = (P_A)(P_B) = (1 + x)(1 + x) = 4 \]
Expanding this gives:
\[ (1 + x)^2 = 4 \]
Taking the square root:
\[ 1 + x = 2 \]
Thus:
\[ x = 1 \]

### Step 7: Calculate Equilibrium Partial Pressures
Now we can find the equilibrium partial pressures:
- \( P_A = 1 + 1 = 2 \, \text{atm} \)
- \( P_B = 1 + 1 = 2 \, \text{atm} \)

### Step 8: Calculate Total Pressure at Equilibrium
The total pressure \( P_{total} \) at equilibrium is:
\[ P_{total} = P_A + P_B = 2 + 2 = 4 \, \text{atm} \]

### Step 9: Analyze the Options
1. **Option 1**: At equilibrium, the total pressure in the container is 4 atm. **(Correct)**
2. **Option 2**: Equilibrium pressure decreases uniformly on increasing the volume of the container. **(Correct)**
3. **Option 3**: At equilibrium, the total pressure in the container is more than 4 atm if the temperature is increased. **(Correct)**
4. **Option 4**: None of these. **(Incorrect)**

### Conclusion
All three options 1, 2, and 3 are correct based on the analysis of the equilibrium conditions.

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