Maxwell–Boltzmann Speeds

In a classical ideal gas, the speeds of molecules are distributed according to the Maxwell–Boltzmann distribution. This statistical distribution depends on both the macroscopic absolute temperature of the gas and the microscopic molar mass of the particles. Instead of all particles having a single average speed, there is a continuous range of speeds defined by a probability density function.

Interactive Experiment

Open Maxwell–Boltzmann Speeds to visualize the distribution. The module allows you to change the temperature and molar mass to see how the speed distribution curve and the characteristic speeds change.

1. Set the temperature to 300 K and molar mass to 0.028 kg/mol (Nitrogen). Verify that the characteristic speeds match our worked example. The most probable speed is at the peak of the density curve, with the mean and RMS speeds at progressively higher values.
2. Increase the temperature to 600 K. The entire distribution broadens and shifts to higher speeds, reflecting the increased kinetic energy, while the peak density decreases because the total area must remain 1.
3. Change the molar mass to 0.002 kg/mol (Hydrogen) at 300 K. The lighter molecules move significantly faster on average. The distribution is much wider and the speeds are higher than those of nitrogen at the same temperature.
4. Use the speed probe to find the probability density at different speeds. Notice how the density drops significantly at extremely high speeds or approaches zero at 0 m/s.