Question

When a gas was heated under atmospheric conditions, its color deepened. Heating above \(150^{\circ} \mathrm{C}\) caused the color to fade, and at \(550^{\circ} \mathrm{C}\) the color was barely detectable. However, at \(550^{\circ} \mathrm{C},\) the color was partially restored by increasing the pressure of the system. Which of the following best fits the preceding description: (a) a mixture of hydrogen and bromine, (b) pure bromine, (c) a mixture of nitrogen dioxide and dinitrogen tetroxide. (Hint: Bromine has a reddish color, and nitrogen dioxide is a brown gas. The other gases are colorless.) Justify your choice.

Short answer

(c) A mixture of nitrogen dioxide and dinitrogen tetroxide fits the description.

Step-by-step solution

Analyze Temperature and Color Changes

Given that heating above 150°C causes the color to fade, and at 550°C the color is barely detectable, consider which gas or mixture behaves in this manner. Nitrogen dioxide (NO₂) is a brown gas that behaves according to its equilibrium with dinitrogen tetroxide (N₂O₄), where high temperatures favor the lighter color N₂O₄.

Consider Pressure Effects

The problem states that increasing pressure at 550°C partially restores the color. Consider how pressure affects gas equilibria. For NO₂ and N₂O₄, higher pressure favors the formation of N₂O₄ from NO₂, according to Le Chatelier's principle, partially restoring the color as N₂O₄ is less colored.

Eliminate Non-fitting Options

Bromine is reddish but does not have a pressure or temperature dependent color equilibrium like NO₂ and N₂O₄. Hydrogen and dinitrogen gases are colorless and do not exhibit color changes with temperature or pressure as described. Therefore, pure bromine and a hydrogen-bromine mixture do not fit the description.

Conclusion

Based on the analysis, the behavior of the gas changing color with temperature and pressure aligns with the equilibrium between nitrogen dioxide (brown) and dinitrogen tetroxide (colorless). The restored color under pressure further supports this as higher pressure shifts the equilibrium toward N₂O₄, which has less color.

Key concepts

Le Chatelier's Principle

Le Chatelier's principle is a fundamental concept used to predict how a system at equilibrium responds to external changes, such as temperature or pressure. When a change is applied to a system at equilibrium, the system will adjust to counteract the effect of the change and restore equilibrium. For instance, if a reaction at equilibrium is disturbed by increasing temperature, the system will favor the reaction direction that absorbs heat, opposing the temperature increase.
This principle plays a key role in understanding how nitrogen dioxide ( ext{NO}_2) and dinitrogen tetroxide ( ext{N}_2 ext{O}_4) interact, especially when conditions change.

• When temperature increases, the equilibrium between ext{NO}_2 and ext{N}_2 ext{O}_4 shifts to favor the endothermic reaction, which produces ext{NO}_2. This is why color changes occur.
• Increasing pressure will shift the equilibrium towards fewer moles of gas, thus favoring the formation of ext{N}_2 ext{O}_4 from ext{NO}_2.

This approach helps to predict and explain changes in the observed properties of chemical systems, such as color change in this exercise.

Nitrogen Dioxide

Nitrogen dioxide ( ext{NO}_2) is a toxic, reddish-brown gas with a sharp, pungent odor. It is an important atmospheric component, contributing to air pollution and has notable effects on human health.
In chemistry, ext{NO}_2 demonstrates interesting behaviors due to its equilibrium with dinitrogen tetroxide ( ext{N}_2 ext{O}_4). This equilibrium is temperature sensitive:

• At lower temperatures, more ext{N}_2 ext{O}_4 is present, and the gas appears lighter because ext{N}_2 ext{O}_4 is colorless.
• As temperatures rise, more ext{NO}_2 is formed, making the gas appear browner.

Given the context of the exercise, understanding this reaction aids in identifying gas behavior when exposed to varying temperatures.

Dinitrogen Tetroxide

Dinitrogen tetroxide ( ext{N}_2 ext{O}_4) is a colorless gas in equilibrium with nitrogen dioxide. The equilibrium nature of these gases is often expressed as:
\[ \text{N}_2\text{O}_4(g) \rightleftharpoons 2\text{NO}_2(g) \]
In this reaction, ext{N}_2 ext{O}_4 can dissociate to form two molecules of ext{NO}_2, and vice versa. This equilibrium is strongly temperature and pressure-dependent. At lower temperatures, the equilibrium shifts towards the formation of ext{N}_2 ext{O}_4, which explains the fading color at higher temperatures noticed in the exercise.
Additionally, the behavior of ext{N}_2 ext{O}_4 solves the exercise by exploring the impact of pressure changes in a chemical system, thus confirming the observations made about gas color changes.

Temperature Effects

Temperature effects are crucial in determining the state of equilibrium in chemical reactions, especially for the ext{NO}_2 and ext{N}_2 ext{O}_4 system. In this case:

• An increase in temperature will generally shift the equilibrium towards the endothermic process. Here, it favors the breakdown of ext{N}_2 ext{O}_4 into ext{NO}_2, increasing the concentration of the brownish ext{NO}_2 gas.
• On cooling, the reverse happens, as more ext{N}_2 ext{O}_4 is favored, leading to a lighter coloration.

Thus, when the observed color faded at higher temperatures and reappeared partially by changing pressure, it confirmed the dependence on temperature, supporting the existence of a dynamic equilibrium according to Le Chatelier's principle.

Pressure Effects

Pressure effects can significantly influence gas-phase equilibria. According to Le Chatelier's principle, increasing pressure on an equilibrium system will shift the reaction towards the side with fewer gas molecules. For nitrogen dioxide and dinitrogen tetroxide:

• When pressure increases, the equilibrium shifts from ext{2NO}_2 to ext{N}_2 ext{O}_4 because it involves fewer gas molecules (from 2 moles of ext{NO}_2 to 1 mole of ext{N}_2 ext{O}_4).
• This shift towards ext{N}_2 ext{O}_4 is why the color is restored when pressure is increased at high temperatures.

This ability to visually observe changes highlights how pressure variations can affect chemical equilibria, supporting the details described in the exercise with the system of ext{NO}_2 and ext{N}_2 ext{O}_4.