Temperature Dependence of Reaction Rate and Arrhenius Equation

We know that the kinetic energy of a gas is directly proportional to its temperature. Thus as the temperature of a system is increased, more and more molecules will acquire necessary energy greater that E_a to cause productive collisions.

This increases the rate of the reaction. In 1889, Arrhenius suggested as simple relationship between the rate constant, k, for a reaction and the temperature of the system

This is called the Arrhenius equation in which Ais an experimentally determined quantity, E_a is the activation energy, Ris the gas constant, and Tis Kelvin temperature.

Taking natural logs of each side of the Arrhenius equation, it can be put in a more useful form :

Arrhenius equation is valuable because it can be used to calculate the activation energy, E_a if the experimental value of the rate constant, k, is known.