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4.13: The Rate of Collisions between Unlike Gas Molecules

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  • 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

    \[{\rho }_{12}=N_1{\widetilde{\nu }}_{12}=N_1N_2\pi {\sigma }^2_{12}\left\langle v_{12}\right\rangle =N_1N_2{\sigma }^2_{12}{\left(\frac{8\pi kT}{\mu }\right)}^{1/2}\]

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