Which one of the following changes would result in a darkening of the colour
`N_(2)O_(4) hArr 2NO_(2)(g) DeltaH=+ve`

Options

A. Increasing pressure
B. Increase temperature
C. Adding inert gas at constant pressure
D. addition of charcol

Answer

To determine which change would result in a darkening of the color in the equilibrium reaction \( N_2O_4 \rightleftharpoons 2NO_2 \) with \( \Delta H = +ve \), we need to analyze the effects of different changes on the equilibrium position.

### Step-by-Step Solution:

1. **Identify the Reaction Components**:
- The reaction involves \( N_2O_4 \) (colorless) and \( NO_2 \) (dark brown).
- The equilibrium shifts towards the product side (right) will lead to a darker color due to the formation of \( NO_2 \).

2. **Understand the Nature of the Reaction**:
- The reaction is endothermic (\( \Delta H = +ve \)), meaning it absorbs heat when moving from reactants to products.

3. **Evaluate the Options**:
- **Option A: Increasing Pressure**:
- Increasing pressure shifts the equilibrium towards the side with fewer moles of gas. In this case, \( N_2O_4 \) has 1 mole and \( 2NO_2 \) has 2 moles. Thus, increasing pressure will shift the equilibrium to the left (towards \( N_2O_4 \)), which is not desired for darkening the color.

- **Option B: Increasing Temperature**:
- For an endothermic reaction, increasing the temperature shifts the equilibrium towards the right (towards products). This will increase the concentration of \( NO_2 \), leading to a darker color. This is the correct option.

- **Option C: Adding an Inert Gas at Constant Pressure**:
- Adding an inert gas at constant pressure increases the volume of the system. This would shift the equilibrium towards the side with more moles, which is the left side (towards \( N_2O_4 \)). This would not darken the color.

- **Option D: Adding a Catalyst**:
- Adding a catalyst does not affect the position of equilibrium; it only speeds up the rate at which equilibrium is reached. Therefore, it will not lead to a change in color.

4. **Conclusion**:
- The only change that results in a darkening of the color is **Option B: Increasing Temperature**.

### Final Answer:
**Increasing Temperature** (Option B) will result in a darkening of the color.