Final answer:
When the temperature of a sample of Xe gas is increased from 37.2 °C to 59.6 °C at constant volume, the average kinetic energy of the gas molecules will increase, as kinetic energy is directly proportional to temperature in Kelvin.
Step-by-step explanation:
The question pertains to the average kinetic energy of xenon gas particles as the temperature is raised while keeping the volume constant. In this scenario, the average kinetic energy of the gas molecules is directly proportional to the temperature of the gas in Kelvin. Therefore, when the temperature of the 1.24 mol sample of Xe gas in a 31.6-liter container is increased from 37.2 °C to 59.6 °C, the average kinetic energy of the gas molecules will increase, because the temperature increase means more energy is being added to the system.
This concept is in accordance with the kinetic molecular theory, which states that the average kinetic energy of gas molecules is proportional to the absolute temperature (measured in Kelvin). We can apply Charles's law to explain that the increase in temperature at constant volume must lead to an increase in pressure because the gas molecules move faster and have more frequent and forceful collisions with the walls of the container. However, as the question only asks about kinetic energy, we can conclude that only the kinetic energy increases.