Velocity (m/s) Fraction of molecules 0 800 1600 2400 3200 4000 0.0030 0.0024 0.0006 0.0000
773  K
500 °C



Most probable velocity = 678 (m/s)
Average velocity = 765 (m/s)
Root mean square velocity = 830 (m/s)
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within velocity bounds
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distribtion of kinetic energy

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-1K-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).