Kinetic theory of gases

It is defined as the distance that a molecule advances between two successive collisions. Let $\bar{v}_1$ be the average speed of type 1 molecules. In a time t it travels a distance $\bar{v}_1t$ where the number of collisions is $[z_{11}+z_{12}] t$. Therefore, the average distance traveled by a molecule 1 between two collisions is: \begin{equation} \lambda=\frac{\bar{v}_1}{z_{11}+z_{12}} \end{equation} If the gas is pure: \begin{equation} \lambda=\frac{\bar{v}_1}{z_{11}}=\frac{1}{\sqrt{2}\pi d_1^2}\frac {V}{N_1} \end{equation} Using the equation PV=NkT, V/N=kT/P. \begin{equation} \lambda=\frac{1}{\sqrt{2}\pi d_1^2}\frac{kT}{P} \end{equation}