Question

The size of a flask containing colorless \(\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g})\) and brown \(\mathrm{NO}_{2}(\mathrm{g})\) at equilibrium is rapidly reduced to half the original volume. $$\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g}) \approx 2 \mathrm{NO}_{2}(\mathrm{g})$$ (a) What color change (if any) is observed immediately upon halving the flask size? (b) What color change (if any) is observed during the process in which equilibrium is reestablished in the flask?

Short answer

(a) The flask becomes less brown immediately. (b) Little to no further color change as equilibrium is reestablished.

Step-by-step solution

Understanding the Reaction

The chemical equilibrium given is \(\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g}) \rightleftarrows 2 \mathrm{NO}_{2}(\mathrm{g})\). Here, \(\mathrm{N}_{2} \mathrm{O}_{4}\) is colorless and \(\mathrm{NO}_{2}\) is brown. Reducing the volume of the flask increases the pressure and shifts the equilibrium towards the side with fewer moles of gas according to Le Chatelier's principle.

Identifying the Immediate Effect

Immediately upon reducing the flask size to half, the pressure increases, which causes the equilibrium to shift towards the formation of \(\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g})\) because it reduces the number of gas moles. Since \(\mathrm{N}_{2} \mathrm{O}_{4}\) is colorless, the immediate observable effect is that the brown color becomes less intense.

Evaluating the Equilibrium Re-establishment

Over time, as the system re-establishes equilibrium, there may be a slight re-adjustment, but the visible change will not be significant because the shift favors the new higher-pressure state which contains more \(\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g})\). Therefore, the brown color remains less intense compared to the original state.

Key concepts

Le Chatelier's Principle

Le Chatelier's Principle is a fundamental concept in the study of chemical equilibria. It states that if a dynamic equilibrium is disturbed by changing the conditions, such as concentration, temperature, or pressure, the system will adjust itself to minimize the effect of the disturbance and reach a new equilibrium.
In the context of the given reaction, \(\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}_{2}(\mathrm{g})\), we focus on pressure changes. When the volume of the container is reduced, the pressure increases.
According to Le Chatelier's Principle, the system will shift the equilibrium to decrease the pressure. This behavior is achieved by favoring the side of the reaction with fewer gas molecules.

• In our reaction, \(\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g})\) has 1 mole of gas, while \(2\ \mathrm{NO}_{2}(\mathrm{g})\) has 2 moles of gas.
• The system shifts toward \(\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g})\) to reduce the number of gas moles and thus the pressure.

Reaction Dynamics

Reaction dynamics involves understanding how chemical reactions progress and how they are influenced by changes in conditions. In this equilibrium scenario, the quick reduction in flask size results in immediate changes due to pressure alterations.
The reaction \(\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}_{2}(\mathrm{g})\) is reversible, and internal adjustments happen rapidly to accommodate the change in external conditions.
Upon halving the volume:

• The pressure surge causes an immediate shift towards forming more \(\mathrm{N}_{2} \mathrm{O}_{4}\), which is colorless.
• This shift reduces the amount of brown \(\mathrm{NO}_{2}\) present.

Initially, you may observe a quick decrease in brown color intensity as the reaction shifts, showcasing dynamic reactivity.

Gas Equilibria

Gas equilibria pertain to conditions under which gaseous reactions achieve a balance between reactants and products. These equilibria are sensitive to changes in pressure and volume, unlike those involving only solids or liquids.
With the mixture of \(\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g})\) and \(\mathrm{NO}_{2}(\mathrm{g})\) at equilibrium, the amount of space decreases by halving the flask's size.
The increase in pressure leads to minimizing the total gas molecules to regain equilibrium.

• During re-establishment, the system balances pressures by favoring fewer moles of gas—shifting towards \(\mathrm{N}_{2} \mathrm{O}_{4}\).
• Even though the color change is initially noticeable, it lessens over time since the equilibrium still will mostly favor the side with fewer moles of gas under sustained high pressure.

Thus, understanding gas equilibria helps predict and explain how observable properties, like color in this case, change with system adjustments.