On addition of inert gas at constant volume into container in which following equilibrium is established `:`
`PCl_(5(g))hArrPCl_(3(g))+Cl_(2(g))`. Which is incorrect `:-`

Options

A. No effect on equilibrium
B. Partial pressure of each gas remain unchanged
C. Total pressure & total moles increases.
D. None of the above

Explanation

To solve the problem regarding the effect of adding an inert gas at constant volume to the equilibrium established by the reaction:

\[ \text{PCl}_5(g) \rightleftharpoons \text{PCl}_3(g) + \text{Cl}_2(g) \]

we need to analyze the effects of the addition of an inert gas on the equilibrium conditions.

### Step-by-Step Solution:

1. **Understanding the Equilibrium**:
The equilibrium established involves the decomposition of phosphorus pentachloride (PCl5) into phosphorus trichloride (PCl3) and chlorine gas (Cl2).

2. **Effect of Inert Gas at Constant Volume**:
When an inert gas (like helium or argon) is added to the system at constant volume, it does not react with the components of the equilibrium.

3. **Equilibrium Constant (Kc)**:
The equilibrium constant \( K_c \) for the reaction is defined as:
\[ K_c = \frac{[\text{PCl}_3][\text{Cl}_2]}{[\text{PCl}_5]} \]
Since the addition of an inert gas does not change the concentrations of the reactants and products, \( K_c \) remains unchanged.

4. **Partial Pressures**:
The partial pressure of each gas is given by the formula:
\[ P_i = \frac{n_iRT}{V} \]
where \( n_i \) is the number of moles of gas \( i \), \( R \) is the gas constant, \( T \) is the temperature, and \( V \) is the volume. Since the volume is constant and the number of moles of the reacting gases does not change, the partial pressures of PCl5, PCl3, and Cl2 remain unchanged.

5. **Total Pressure**:
Although the partial pressures of the individual gases remain unchanged, the total pressure of the system increases due to the presence of the added inert gas. This is because the inert gas contributes to the total pressure without affecting the equilibrium concentrations.

6. **Conclusion**:
- The equilibrium remains unaffected.
- The partial pressures of each gas remain unchanged.
- The total pressure increases due to the addition of the inert gas.
- The number of moles in the system increases due to the addition of the inert gas.

### Incorrect Statement:
The incorrect statement among the options provided would be related to a misunderstanding of how the addition of the inert gas affects the equilibrium or the pressures.