Effective cross section for collision

For a spherical particle, the effective cross section for collision, a, is... 

The rate constant is given by the number of collisions between the molecules multiplied by the probability of reaction. The number of collisions follows from the average velocity of the molecules and their effective cross section for collision. The energy distribution over the different degrees of freedom of the molecules is equal to the Boltzmann distribution as long as the number of collisions between the molecules is large compared to their probability of reaction. 

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