Assertion`:-` Addition of inert gas at const pressure to equilibrium
of `PCl_(5)hArrPCl_(3)+Cl_(2)` favourd forward reaction.
Reason`:-` `K_(c)=(alpha^(2))/((1-prop)V)` for the equilibrium of
`PCl_(5)hArrPCl_(3)+Cl_(2)`

Options

A. If both Assertion & Reason are True & the Reason is a correct explanation of the Assertion.
B. If both Assertion & Reason are True but Reason is not a correct explanation of the Assertiion.
C. If Assertion is True but the Reason is False.
D. If both Assertion & Reason are False

Explanation

To solve the assertion and reason question regarding the equilibrium of the reaction \( PCl_5 \rightleftharpoons PCl_3 + Cl_2 \), we will analyze both the assertion and the reason step by step.

### Step 1: Analyze the Assertion
The assertion states that the addition of an inert gas at constant pressure to the equilibrium of the reaction favors the forward reaction.

1. **Understanding the Reaction**: The reaction involves the dissociation of \( PCl_5 \) into \( PCl_3 \) and \( Cl_2 \).
2. **Effect of Inert Gas at Constant Pressure**: When an inert gas is added at constant pressure, the total pressure increases, but the partial pressures of the reacting gases remain unchanged.
3. **Le Chatelier's Principle**: According to Le Chatelier's principle, if the pressure is increased by adding an inert gas, the equilibrium will shift towards the side with more moles of gas. In this case, the forward reaction produces 2 moles of products (1 mole of \( PCl_3 \) and 1 mole of \( Cl_2 \)) from 1 mole of \( PCl_5 \). Therefore, the equilibrium shifts to the right, favoring the forward reaction.

**Conclusion for Assertion**: The assertion is true.

### Step 2: Analyze the Reason
The reason states that \( K_c = \frac{\alpha^2}{(1 - \alpha)V} \) for the equilibrium of the reaction.

1. **Understanding \( K_c \)**: The equilibrium constant \( K_c \) for the reaction can be expressed in terms of concentrations or partial pressures.
2. **Degree of Dissociation**: Let \( \alpha \) be the degree of dissociation of \( PCl_5 \). If we start with 1 mole of \( PCl_5 \), at equilibrium, we will have \( 1 - \alpha \) moles of \( PCl_5 \), \( \alpha \) moles of \( PCl_3 \), and \( \alpha \) moles of \( Cl_2 \).
3. **Expression for \( K_c \)**: The expression for \( K_c \) can be written as:
\[ K_c = \frac{[PCl_3][Cl_2]}{[PCl_5]} = \frac{(\alpha)(\alpha)}{(1 - \alpha)} = \frac{\alpha^2}{(1 - \alpha)} \]
However, the volume \( V \) should not be included in the expression for \( K_c \) since \( K_c \) is defined in terms of concentrations (which are moles per unit volume).

**Conclusion for Reason**: The reason is false because the expression incorrectly includes \( V \) in the denominator.

### Final Conclusion
- **Assertion**: True
- **Reason**: False

Thus, the correct answer is that the assertion is true and the reason is false.

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