Final answer:
The molecules of a gas have energy stored in the form of kinetic energy, primarily recognized as thermal energy, which is proportional to the gas's temperature as described by the kinetic theory of gases.
Step-by-step explanation:
The molecules of a gas in constant random motion contain energy in the form of kinetic energy, which is the energy of motion. Since these molecules move freely and collide elastically with each other and the container walls, they possess thermal energy. This thermal energy is directly related to the temperature of the gas—the higher the temperature, the greater the kinetic energy of the gas molecules. In a gas, particles can also have rotational and vibrational energies, but in the context of ideal gas behavior, we often focus on the translational kinetic energy as being representative of the gas' thermal energy.
The behavior of gas molecules is well described by the kinetic theory of gases, which models properties such as pressure and volume in terms of the continuous random motion of atoms and molecules. The average translational kinetic energy of a gas molecule is proportional to the gas's kelvin temperature, demonstrating a direct link between molecular motion and thermal energy.