The kinetic theory predicts that gas molecules will move in all directions at a range of speeds. The average kinetic energy of the molecules is 3/2*RT* per mole, where *R* (the gas constant) = 8.31 J/mol K. Since the kinetic energy is related to speed, we can show that for an ideal gas, the root-mean-square speed (a quantity that is usually very close to the average speed) is given by

(3*RT/M*)^{1/2}

where *M* is the molar mass in g/mol.

In the following graph, the curves show the fraction of molecules having a given speed, for the temperatures of 300K and 600K.