Problem 70 - Chemistry and Chemical Reactivity

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. $$ \mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}_{2}(\mathrm{g}) $$ (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?

Step-by-Step Solution

Answer

(a) Immediately, the brown color becomes more intense. (b) During reequilibration, the color fades as \( \mathrm{N_2O_4} \) forms.

Step 1: Determine Initial Reaction Direction

The equilibrium reaction is \( \mathrm{N_2O_4(g)} \rightleftharpoons 2 \mathrm{NO_2(g)} \). When the volume of the flask is halved, the pressure of the gases is increased, shifting the equilibrium to the side with fewer gas molecules to counteract the change in pressure. \( \mathrm{N_2O_4} \) has fewer moles than \( \mathrm{2NO_2} \), so the equilibrium will shift towards \( \mathrm{N_2O_4} \), which is colorless.

Step 2: Observe Immediate Color Change

Immediately after the flask size is reduced, the concentration of all gases increases due to decreased volume. Initially, there is no time for the equilibrium to shift, and because \( \mathrm{NO_2(g)} \) is brown, the color should become darker as its concentration is increased.

Step 3: Assess Equilibrium Adjustment

Over time, as the system reaches a new equilibrium, the reaction shifts towards the formation of \( \mathrm{N_2O_4} \) to reduce pressure. Hence, the brown color of \( \mathrm{NO_2(g)} \) will lighten as \( \mathrm{N_2O_4} \) is produced, replacing some of the \( \mathrm{NO_2} \).

Step 4: Predict Final Color Change

During reestablishment of equilibrium, the production of more \( \mathrm{N_2O_4} \) will cause the brown color to gradually fade, resulting in a less intense color compared to immediately after the volume was halved.

Key Concepts

Le Chatelier's principle

Le Chatelier's principle helps us understand how a chemical system at equilibrium responds to external changes. When a system at equilibrium is disturbed, it will shift to counteract that disturbance and reestablish equilibrium. In the context of the given exercise, when the volume of the flask is reduced, the pressure of the gases inside increases. This increase in pressure acts as a disturbance.

• If pressure is increased, the equilibrium shifts toward the side with fewer gas molecules. This shift relieves some of the increased pressure.
• Conversely, if the pressure decreases, the system shifts toward the side with more gas molecules to raise the pressure back up.

In the reaction \( \mathrm{N_2O_4(g)} \rightleftharpoons 2 \mathrm{NO_2(g)} \), the side with \( \mathrm{N_2O_4} \) is favored when pressure rises, as there are fewer moles compared to \( \mathrm{NO_2} \). Hence, Le Chatelier's principle predicts that the reaction will shift towards \( \mathrm{N_2O_4} \), countering the increase in pressure.

Gas pressure

Gas pressure plays a critical role in how a gaseous equilibrium responds to volume changes. Let's consider what pressure really is: it's the force that gas particles exert against the walls of their container. Naturally, any change in the container's size directly impacts this pressure.When the flask's volume is halved, the same number of gas particles now occupies a smaller space. This results in a higher pressure because particles are more congested and collide more frequently with the container walls.

• Increasing gas pressure tends to favor the direction with fewer gas particles, as fewer collisions will help to relieve the pressure.
• This is why the equilibrium shifts towards \( \mathrm{N_2O_4} \), a molecule with fewer gas moles than \( \mathrm{2NO_2} \).

Understanding gas pressure helps explain why the color changes observed in the reaction occur as they do. Initially, the pressure doesn't immediately cause the equilibrium to shift, so the color initially darkens because \( \mathrm{NO_2} \)'s concentration is higher.

Equilibrium shift

An equilibrium shift represents the adjustment a reaction undergoes in response to changes in pressure, temperature, or concentration. In this scenario, once the equilibrium is disturbed by a rapid change in volume—and therefore pressure—the equilibrium shifts to oppose the change.For this specific reaction:

• The system initially becomes darker as the concentration of the brown \( \mathrm{NO_2} \) increases due to the decreased volume.
• Gradually, the equilibrium processes the pressure change, which prompts more \( \mathrm{N_2O_4} \) to form.

As \( \mathrm{N_2O_4} \) molecules increase, the brown color associated with \( \mathrm{NO_2} \) fades. Thus, a lighter color indicates that the system is adjusting and shifting toward equilibrium with fewer gas particles, aligning with Le Chatelier's principle. Ultimately, observing these shifts helps us verify that the reaction is heading back towards equilibrium, even if the visible color takes some time to lighten.