Mean free path of the molecules λ (cm)
The concept that a gas comprises a large number of distinct particles between which – aside from the collisions – there are no effective forces, has led to a number of theoretical considerations which we summarize today under the designation “kinetic theory of gases”. One of the first and at the same time most beneficial results of this theory was the calculation of gas pressure p as a function of gas density and the mean square of velocity c² for the individual gas molecules in the mass of molecules m_T:
The gas molecules fly about and among each other, at every possible velocity, and bombard both the vessel walls and collide (elastically) with each other. This motion of the gas molecules is described numerically with the assistance of the kinetic theory of gases. A molecule’s average number of collisions over a given period of time, the so-called collision index z, and the mean path distance which each gas molecule covers between two collisions with other molecules, the so-called mean free path length λ, are described as shown below as a function of the mean molecule velocity c - the molecule diameter 2r and the particle number density molecules n – as
a very good approximation:
Thus the mean free path length λ for the particle number density n is, in accordance with equation p = n·k·T, inversely proportional to pressure p. Thus the following relationship holds, at constant temperature T, for every gas λ ⋅ p = const.