For the equilibrium, `PCl_(5) Leftrightarrow PCl_(3)+Cl_(2), K_(c)=alpha^(2)//(1-alpha)V`, temperature remaining constant

Options

A. `K_c` will increase with increase in volume
B. `K_c` will increase with decrease in volume
C. `K_c` will not change with the change in volume
D. `K_c` may increase or decrease with the change in volume depending upon its numerical value

Answer

To solve the problem regarding the equilibrium of the reaction \( PCl_5 \leftrightarrow PCl_3 + Cl_2 \) and the behavior of the equilibrium constant \( K_c \) with changes in volume, we can follow these steps:

### Step 1: Understand the equilibrium expression
The equilibrium constant \( K_c \) for the reaction is given as:
\[ K_c = \frac{\alpha^2}{(1 - \alpha)V} \]
where \( \alpha \) represents the degree of dissociation of \( PCl_5 \) and \( V \) is the volume of the system.

### Step 2: Analyze the effect of volume on \( K_c \)
According to Le Chatelier's Principle, the equilibrium constant \( K_c \) is dependent on temperature. It does not change with changes in volume or pressure as long as the temperature remains constant.

### Step 3: Conclusion on the effect of volume
Since the problem states that the temperature is constant, we can conclude that changes in volume will not affect the equilibrium constant \( K_c \). Therefore, regardless of whether the volume increases or decreases, \( K_c \) remains unchanged.

### Final Answer
The correct option is:
- **Kc will not change with change in volume.**

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