Gases represent enormous numbers of atoms and molecules, not just one or two. The behavior of the collection of atoms or molecules of a gas can be described using statistics. Ludwig Boltzmann and James Clerk Maxwell contributed to the science of statistical thermodynamics. Predicting the behavior of any one molecule with any precision is nearly impossible. Predicting the averages of some behaviors for large collections of molecules is fairly straight forward, however.

Absolute temperature is a direct measure of average kinetic energy and average molecular speed. Since the motion of molecules will determine whether they interact and react, chemists are interested in the velocities of molecules.

Statistical thermodynamics assumes that speeds of a collection of gas particles are distributed. As the result of collisions, the speed of any one particle changes often. The distribution of particle speeds is called the Maxwell-Boltzmann distribution [local; Burton site no longer available].

From the Maxwell-Boltzmann distribution, the following speed calculations [local; Plambeck site no longer available] are most often discussed:

Most Probable Speed		Average (Mean) Speed		Root Mean Square (RMS) Speed
Example Problem		Example Problem		Example Problem

Notice that each speed depends directly on the square root of temperature and inversely on the square root of the molar mass. In other words, the higher the temperature, the faster the molecules; the less massive the molecules, the faster the molecules.

The most probable speed is the speed that a randomly-selected molecule is most likely to have. It is the speed of the molecules represented at the top of the Maxwell-Boltzmann distribution curve. Half of the particles move with a speed faster than the average speed, while the other half are slower. Of all of the kinetic energy available, half of it is possessed by molecules moving faster than the RMS speed, while the other half is possessed by those moving slower than the RMS speed.

The following quantities also are often computed:

Mean Free Path		Collision Frequency
Example Problem		Example Problem

Mean free path is the average distance traveled between collisions of gas particles. This depends upon the size of the particle, represented in the formula by the parameter σ.

Changing the temperature has predictable effects on the Maxwell-Boltzmann Distribution.