We define the collision frequencycollision frequency, $${\widetilde{\nu }}_{12}$$, as the number of collision per unit time between a single molecule of type 1 and any of the molecules of type 2 present in the same container. We find $${\widetilde{\nu }}_{12}=N_2\pi {\sigma }^2_{12}\left\langle v_{12}\right\rangle$$. If there are $$N_1$$ molecules of type 1 present in a unit volume of the gas, the total number of collisions between type 1 molecules and type 2 molecules is $$N_1$$ times greater. For clarity, let us refer to the total number of such collisions, per unit volume and per unit time, as the collision rate, $${\rho }_{12}$$. We have
${\rho }_{12}=N_1{\widetilde{\nu }}_{12}=N_1N_2\pi {\sigma }^2_{12}\left\langle v_{12}\right\rangle =N_1N_2{\sigma }^2_{12}{\left(\frac{8\pi kT}{\mu }\right)}^{1/2}$