Introduction of inert gas (at the same temperature) will affect the equilibrium if :

Options

A. volume is constant and `Deltan_(g)cancel=0`
B. pressure is constant and `Deltan_(g)cancel=0`
C. volume is constant and `Deltan_(g)=0`
D. pressure is constant and `Deltan_(g)=0

Explanation

To determine how the introduction of an inert gas at the same temperature affects the equilibrium, we need to analyze the conditions under which this addition occurs. Let's break down the steps:

### Step-by-Step Solution:

1. **Understanding the Role of Inert Gas**:
- An inert gas does not react with the reactants or products in the equilibrium system. Its primary effect is to change the total pressure of the system without altering the concentrations of the reacting species.

2. **Equilibrium Constant (K)**:
- The equilibrium constant (K) is dependent on the concentrations of the reactants and products at a given temperature. It is expressed as:
\[ K = \frac{[Products]}{[Reactants]} \]
- The addition of an inert gas does not change the concentrations of the reactants and products directly, as it does not participate in the reaction.

3. **Effect of Volume and Pressure**:
- If the volume of the container is kept constant while adding an inert gas, the pressure of the system increases, but the concentrations of the reactants and products remain unchanged. Therefore, the equilibrium position is unaffected, and K remains constant.
- If the volume is allowed to change (for example, if the inert gas is added and the system expands), the concentrations of the reactants and products will change, potentially shifting the equilibrium position.

4. **Analyzing the Options**:
- **Option A**: Volume constant and ΔNG = 0 → No effect on equilibrium.
- **Option B**: Pressure constant and ΔNG ≠ 0 → This will affect the equilibrium as the volume will change, leading to a shift in equilibrium.
- **Option C**: Volume constant and ΔNG = 0 → No effect on equilibrium.
- **Option D**: Pressure constant and ΔNG = 0 → No effect on equilibrium.

5. **Conclusion**:
- The introduction of an inert gas at constant volume does not affect the equilibrium. However, at constant pressure with ΔNG not equal to zero, the equilibrium will shift. Therefore, the correct option is **Option B**.