When a sample of `NO_(2)` is placed in a container, this equilibrium is rapidly estabilished.
`2NO_(2)(g) hArr N_(2)O_(4)(g)`
Iff this equilibrium mixture is a darker colour at high temperatures annd at low pressure, which of these statements about the reaction is true?

Options

A. The reaction is exothermic and `NO_(2)` is darker in colour than `N_(2)O_(4)`
B. The reaction is exothermic and `N_(2)O_(4)` is darker in colour than `NO_(2)`
C. The reaction is endothermic and `NO_(2)` is darker in colour than `N_(2)O_(4)`
D. The reaction is endothermic and `N_(2)O_(4)` is darker in colour than `NO_(2)`

Answer

To solve the problem, we need to analyze the equilibrium reaction given:

\[ 2NO_2(g) \rightleftharpoons N_2O_4(g) \]

1. **Identify the colors of the gases involved**:
- \( NO_2 \) is a dark brown gas.
- \( N_2O_4 \) is colorless.

2. **Understand the effect of temperature on the equilibrium**:
- The equilibrium shifts according to Le Chatelier's principle.
- If the equilibrium mixture is darker at high temperatures, it suggests that the reaction favors the formation of \( NO_2 \) (the darker species) at high temperatures.

3. **Analyze the effect of pressure on the equilibrium**:
- The reaction has 2 moles of \( NO_2 \) on the left and 1 mole of \( N_2O_4 \) on the right.
- According to Le Chatelier's principle, decreasing the pressure will favor the side with more moles of gas, which is the reactant side (2 moles of \( NO_2 \)).
- Therefore, at low pressure, the equilibrium will shift to the left, producing more \( NO_2 \), which is darker.

4. **Determine the nature of the reaction**:
- Since increasing temperature favors the formation of \( NO_2 \) and decreasing pressure also favors the formation of \( NO_2 \), we can conclude that the forward reaction (formation of \( N_2O_4 \)) is exothermic.
- This means that increasing temperature shifts the equilibrium to the left, favoring the formation of \( NO_2 \).

5. **Conclusion**:
- Since the equilibrium mixture is darker at high temperatures and low pressures, it indicates that the reaction is exothermic and that \( NO_2 \) is darker than \( N_2O_4 \).

**Final Answer**: The correct statement is that the reaction is exothermic and \( NO_2 \) is darker in color than \( N_2O_4 \).