What is the relationship between the rate of reaction and collision frequency?

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}