Relationship between the rate of reaction and collision frequency:
If Z is the collision frequency and f is the fraction of molecules whose collisions are effective, then evidently:
Rate of reaction = – dx / dt = Z x f …………………………….. (1)
Further according to kinetic theory of gases, the fraction of molecules having energy more than a particular value, E at temperature T is given by:
F = e-E / RT …………………………………………… (2)
Substituting this value in equation (2), we will get:
Rate = Z e-E / RT
As rate of reaction is directly related to rate constant, k, we can also be written as:
k = Z e-E / RT
Hence
The relationship between the rate of reaction k and collision frequency Z is k = Z e-E / RT
