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.)

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.

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.

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.

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.