`N_(2)` gas id added to the reaction equilibrium `PCl_(5) (g) hArr PCl_(3) (g) + Cl_(2) (g)` at constant temperature . If pressure is kept constant, equilibrium constant will `……` and equilibrium will shift in the `……….` direction.

Answer

To solve the question regarding the equilibrium of the reaction \( PCl_5 (g) \rightleftharpoons PCl_3 (g) + Cl_2 (g) \) when \( N_2 \) gas is added at constant temperature and pressure, we can follow these steps:

### Step-by-Step Solution

1. **Understanding the Reaction**:
The reaction involves the dissociation of \( PCl_5 \) into \( PCl_3 \) and \( Cl_2 \). It is important to note that all species are in the gaseous state.

2. **Effect of Adding Inert Gas**:
When \( N_2 \) (an inert gas) is added to the reaction mixture at constant temperature, it does not react with any of the species involved in the equilibrium.

3. **Constant Temperature and Pressure**:
The equilibrium constant \( K \) for a reaction is only dependent on temperature. Since the temperature is constant, the equilibrium constant will remain unchanged regardless of the addition of \( N_2 \).

4. **Volume and Concentration Changes**:
Adding \( N_2 \) increases the total pressure of the system. However, since the pressure is kept constant, the volume of the system must adjust. The addition of an inert gas at constant pressure effectively increases the volume of the system, which leads to a decrease in the concentration of the gaseous reactants and products.

5. **Le Chatelier's Principle**:
According to Le Chatelier's Principle, if a system at equilibrium experiences a change in concentration, pressure, or temperature, the system will adjust to counteract that change. In this case, since the concentration of the products \( (PCl_3 + Cl_2) \) decreases due to the increase in volume, the equilibrium will shift towards the side with more moles of gas to increase the concentration back.

6. **Conclusion**:
In this reaction, there are 1 mole of \( PCl_5 \) on the reactant side and 2 moles of products \( (PCl_3 + Cl_2) \) on the product side. Therefore, the equilibrium will shift to the right (forward direction) to produce more products.

### Final Answers:
- The equilibrium constant will **remain unchanged**.
- The equilibrium will shift in the **forward direction**.