The average kinetic energy of a molecule of the gas is

According to the kinetic theory of gases, the average kinetic energy of a molecule is given by

$$\langle KE \rangle = \frac{3}{2} k_B T$$

where $$k_B$$ is the Boltzmann constant and $$T$$ is the absolute temperature.

From this expression, the average kinetic energy is directly proportional to the absolute temperature $$T$$ and does not depend on the volume, pressure, or the nature of the gas. This means that at the same temperature, molecules of all gases (regardless of their molecular mass) have the same average kinetic energy.

Hence, the correct answer is that the average kinetic energy of a molecule is proportional to absolute temperature.