Figure 2.14b. The Maxwell-Boltzmann Distribution of the kinetic energies of ideal gas molecules at equilibrium. This figure shows statistical probabilities that gas molecules will have particular kinetic energies (KE) based on the kinetic theory of gases. The most probable kinetic energy for a gas molecule (red line) and the average kinetic energy of all molecules (blue line) are indicated on the diagram. Move the temperature slider to see how the probability distribution changes with temperature. As the temperature rises, more more of the molecules will have higher energies. Press the "Show %" button to see what fraction of molecule are likely to have kinetic energies between the KE bounds, which you can change with sliders. Press the "Show Velocities" button to see a probability graph of the velocities of molecules based on the same Maxwell-Boltzmann model. Notice that the molar mass of the gas molecules has no effect on the kinetic energy distribution. You can read more about the kinetic energy distribution here.
If T is the temperature (K) and R is the gas constant (8.31 J M-1K-1), the Maxwell-Boltzmann Distribution gives the most probable kinetic energy as (1/2)*R*T and the average kinetic energy as (3/2)*R*T for a gas, regardless of molar mass.
