Addition of I mole of `N_(2)` is made to an equilibrium mixture of `PCl_(5)` in a piston fittcd cylinder. Which of the following is correct.

Options

A. No effect on equilibrium constant `K_(c) or K_(p)`
B. The degree of dissociation of `PCl_(5)` decreases
C. The volume of container does not change
D. No effect on equilibrium concentration

Answer

To solve the problem regarding the addition of 1 mole of nitrogen to an equilibrium mixture of \( PCl_5 \), we can follow these steps:

### Step 1: Understand the Equilibrium Reaction
The equilibrium reaction for the dissociation of \( PCl_5 \) can be represented as:
\[ PCl_5 \rightleftharpoons PCl_3 + Cl_2 \]
In this reaction, \( PCl_5 \) dissociates into \( PCl_3 \) and \( Cl_2 \).

**Hint:** Identify the equilibrium reaction and the species involved.

### Step 2: Analyze the Effect of Adding Nitrogen
When 1 mole of nitrogen (\( N_2 \)) is added to the system, it is important to note that nitrogen is an inert gas in this context. This means it does not react with any of the components of the equilibrium mixture.

**Hint:** Consider whether the added substance participates in the reaction.

### Step 3: Assess the Volume of the Container
Since the problem states that the addition occurs in a piston-fitted cylinder, the volume of the container can adjust to maintain constant pressure. However, since nitrogen is inert and does not react, the effective volume of the gaseous reactants and products remains unchanged.

**Hint:** Think about how the addition of an inert gas affects the volume and pressure of the system.

### Step 4: Evaluate the Changes in Concentration and Partial Pressure
The addition of nitrogen does not change the number of moles of the reactants or products in the equilibrium mixture. Therefore, the concentrations of \( PCl_5 \), \( PCl_3 \), and \( Cl_2 \) remain the same. Consequently, the partial pressures of each gas also remain unchanged.

**Hint:** Remember that the concentrations and partial pressures are crucial for determining the position of equilibrium.

### Step 5: Determine the Effect on the Equilibrium Constant
Since the concentrations and partial pressures of the reactants and products do not change, the equilibrium constant (\( K_c \)) for the reaction remains unaffected. The equilibrium constant is dependent only on the temperature and the nature of the reaction, not on the presence of inert gases.

**Hint:** Recall that the equilibrium constant is only influenced by changes in concentration or temperature of the reactants and products.

### Conclusion
Based on the analysis:
1. The addition of nitrogen has **no effect on the equilibrium constant** (\( K_c \)).
2. The **degree of dissociation of \( PCl_5 \) does not decrease** because the equilibrium concentrations remain unchanged.
3. The **volume of the container does not change** effectively in terms of the reacting gases.
4. There is **no effect on the equilibrium concentrations** of the reactants and products.

Thus, the correct statements are:
- No effect on equilibrium constant \( K_c \)
- Volume of container does not change
- No effect on equilibrium concentration

**Final Answer:** 1, 3, and 4 are correct.