A certain gaseous solute dissolves in water, evolving \(12.0 \mathrm{~kJ}\) of heat. Its solubility at \(25^{\circ} \mathrm{C}\) and \(4.00\) atm is \(0.0200 M .\) Would you expect the solubility to be greater or less than \(0.0200 M\) at (a) \(5^{\circ} \mathrm{C}\) and 6 atm? (b) \(50^{\circ} \mathrm{C}\) and 2 atm? (c) \(20^{\circ} \mathrm{C}\) and 4 atm? (d) \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm} ?\)

In an exothermic reaction, as the temperature increases, the equilibrium will shift towards the side that absorbs heat, which in this case is the side with less dissolution of the gaseous solute. Therefore, the solubility of the gas will be lower at higher temperatures.

According to Henry's law, the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid. Therefore, when the pressure increases, the solubility of the gas will also increase.

(a) At \(5^{\circ} \mathrm{C}\) and 6 atm, the temperature is lower and the pressure is higher compared to the given conditions. The lower temperature will cause an increase in solubility due to the exothermic nature of the reaction, and the higher pressure will also cause an increase in solubility according to Henry's law. Therefore, the solubility will be greater than \(0.0200 M\). (b) At \(50^{\circ} \mathrm{C}\) and 2 atm, the temperature is higher and the pressure is lower compared to the given conditions. The higher temperature will lead to a decrease in solubility due to the exothermic nature of the reaction, and the lower pressure will lead to a decrease in solubility according to Henry's law. Therefore, the solubility will be less than \(0.0200 M\). (c) At \(20^{\circ} \mathrm{C}\) and 4 atm, the temperature is lower compared to the given conditions, while the pressure remains the same. The lower temperature will lead to an increase in solubility due to the exothermic nature of the reaction. Since pressure is the same, it won't affect the solubility. Therefore, the solubility will be greater than \(0.0200 M\). (d) At \(25^{\circ} \mathrm{C}\) and 1 atm, the temperature is the same as the initial conditions, while the pressure is lower. Since the temperature remains the same, it won't affect the solubility. However, the lower pressure will lead to a decrease in solubility according to Henry's law. Therefore, the solubility will be less than \(0.0200 M\).