**Figure 2.14a. The Maxwell-Boltzmann Distribution of the velocities of ideal gas molecules at equilibrium.** This figure shows statistical probabilities that gas molecules will have particular velocities based on the kinetic theory of gases. The most probable velocity for a gas molecule (red line) and the average velocity of all molecules (blue line) at the seleted temperature are indicated on the diagram, as is the root mean squared velocity (**black line**). **Move the temperature slider** to see how the probability distribution changes with temperature. As the temperature rises, more of the molecules will have higher velocities. **Press the "Show %" button** to see what fraction of gas molecules are likely to have velocities between the velocity bounds, which you can change with sliders. **Move the molar mass slider** to see how the mass of the molecules affects the velocity distributon. **Press the "Show KE" button** to see a probability graph of the kinetic energies of gas molecules based on the same Maxwell-Boltzmann model.

If T is the temperature (K), M is the molar mass (kg), and R is the gas constant (8.31 J M^{-1}K^{-1}), the Maxwell-Boltzmann Distribution gives the most probable velocity as √(2*R*T/M), the average velocity as √(8*R*T/[πM]), and the root mean square velocity as √(3*R*T/M).