Question

When a gas was heated under atmospheric conditions, its color was found to deepen. 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 these best fits this description? Justify your choice. (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.)

Short answer

None of the given options (a) mixture of hydrogen and bromine, (b) pure bromine, or (c) mixture of nitrogen dioxide and dinitrogen tetroxide quite match with the described observations. This suggests that the exercise might contain a mistake or there is other missing information.

Step-by-step solution

Identify the Color Traits of Each Choice

Firstly, let's identify the color traits of each possible choice and whether or not they could possibly fit the description. (a) A mixture of hydrogen and bromine would result in hydrogen bromide, a colorless gas, which does not fit the description since the gas mixture in question is colored, not colorless. (b) Pure bromine is a deep reddish-brown at room temperature, but the problem statement does not provide enough information regarding how its color responds to heating or pressure changes. (c) Nitrogen dioxide is a brown gas and dinitrogen tetroxide is colorless. They can exist in equilibrium, with the color depending on the proportions of the two gases. This mixture could potentially match the original problem statement, as varying the temperature or pressure would shift the equilibrium between the two gases, potentially changing the color.

Analyze Temperature Effect

Next, think about the effect of changing temperature on the color of the gases. Nitrogen dioxide (\(NO_2\)) and dinitrogen tetroxide (\(N_2O_4\)) are in equilibrium at room temperature, with the brown \(NO_2\) contributing to the observed color. The reaction \(2NO_2 \rightleftharpoons N_2O_4\) is exothermic, which means that applying heat should actually shift the equilibrium to the left, increasing the proportion of \(NO_2\) and therefore the brown coloration. However, it is observed that applying heat initially darkens the color but, above 150 degrees Celsius, the color fades. This effect is the opposite of what would be expected based on Le Chatelier's principle.

Analyze Pressure Effect

Finally, consider the effect of pressure. Increasing the pressure would, according to Le Chatelier’s principle, shift the equilibrium to the side with fewer moles of gas which is the \(N_2O_4\), and thus reduce the brown color due to \(NO_2\). However, the problem states that increasing the pressure at 550 degrees Celsius partially restores the color. This directly contradicts what is predicted by Le Chatelier's principle.

Conclusion

Based on the analysis of the responses of the gases to changes in temperature and pressure, none of the given options (a) mixture of hydrogen and bromine, (b) pure bromine, or (c) mixture of nitrogen dioxide and dinitrogen tetroxide quite match with the described observations. This implies that the exercise might contain a mistake or important information is missing.

Key concepts

Le Chatelier's principle

Le Chatelier's principle is an important concept in understanding chemical equilibria. It predicts how a system at equilibrium responds to disturbances, such as changes in temperature, pressure, or concentration. Imagine the system is like a balanced scale and any change made is like adding or removing weights.

When a change is applied, the equilibrium will shift to counteract this change and restore balance. Consider the reaction \(2NO_2 \rightleftharpoons N_2O_4\). This equilibrium can shift in response to various conditions:

• Temperature changes: If the reaction is exothermic, adding heat will cause the equilibrium to shift to absorb the added heat, favoring the endothermic direction.
• Pressure changes: If pressure increases, the equilibrium will shift towards the side with fewer gas molecules to reduce pressure.

In the context of the problem, Le Chatelier's principle helps us predict how the mixture of nitrogen dioxide and dinitrogen tetroxide shifts between brown \(NO_2\) and colorless \(N_2O_4\) when conditions change. However, observed behavior contradicted this prediction, suggesting additional factors may be at play.

Nitrogen dioxide equilibrium

The equilibrium between nitrogen dioxide \(NO_2\) and dinitrogen tetroxide \(N_2O_4\) is visually observable due to the color difference. \(NO_2\) is a brown gas, while \(N_2O_4\) is colorless. When these two are mixed, they form an equilibrium described by the equation:

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

The equilibrium position determines the color of the gas due to the proportion of \(NO_2\).

Temperature affects this equilibrium. The reaction is exothermic forward, so increasing temperature shifts equilibrium to the left, increasing \(NO_2\) and making the gas appear darker. However, at very high temperatures, like 550°C, the extent of \(NO_2\) creation might plateau or decrease, causing color fading.

This contradiction highlights complexities in chemical reactions, where real systems can behave unexpectedly. Understanding the nuances of \(NO_2\) and \(N_2O_4\) equilibrium provides insight into why color changes with temperature aren’t straightforward.

Pressure effect on gases

Pressure changes impact gas equilibrium by influencing the direction in which a reaction shifts. According to Le Chatelier's principle, increasing pressure will shift equilibrium towards the side with fewer moles of gas.

• For the \(2NO_2 \rightleftharpoons N_2O_4\) equilibrium, increasing pressure favors \(N_2O_4\), as it occupies less volume.

This would normally reduce the \(NO_2\) concentration, leading to a color fade. Yet, at high temperatures like 550°C, the increased pressure unexpectedly restores some color.

This unusual behavior could be due to other, unaccounted dynamics such as temperature’s influence overpowering pressure’s effect. High temperatures confer kinetic energy that may promote endothermic reactions or lesser known pathways, complicating color distributions.

Understanding this highlights the intricate balance of forces at play in gaseous systems, illustrating that while Le Chatelier's principle provides a general guide, real-world situations often add layers of complexity that require nuanced analysis.