This threshold energy, E_a is called the energy of activation. It can be thought of as a barrier that the reaction must surmount before it can go to completion (see fig 10 opposite).

From the usual random distribution of energy among molecules, the fraction of molecules that have enough kinetic energy to collide with energy E_a or greater is
f= e^-Ea/RT

This fraction increases with temperature. At absolute zero, it has the value:
f = e^-Ea/0 = e^-=0
This is reasonable, since if the molecules are motionless at absolute zero, none of them have enough energy to react.

As the temperature approaches infinity, the fraction of molecules capable of reacting approaches unity, no matter how large the activation energy, E_a, might be:
f=e^-Ea/ =e^-0= 1

At any finite temperature, the larger the activation energy, the smaller the fraction of molecules that have enough energy to surmount this barrier and react. The simple collision theory of chemical reaction states that the rate constant can be represented by
k= Ae^-Ea/RT
in which A is a constant derived from the Collision frequency. It depends on the molecular weight, the molecular diameter, and the square root of the temperature.