**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^{-1}K^{-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.