# Activation Energy Formula

Activation energy is the least possible energy required to start a  chemical reaction. The molecules need some kinetic energy or velocity to collide with other molecules to start a reaction. No reaction will take place if the collision doesn’t happen, or molecules don’t have enough kinetic energy. The energy needs to initiate the reaction is known as Activation energy.

The activation energy (Ea) of a reaction is measured in joules(J),  kilojoules per mole(kJ/mol) or kilocalories per mole (kcal/mol)

## Activation Energy Formula

If we know the rate constant k1 and k2 at T1 and T2 the activation energy formula is

Where

$log\frac{k_{2}}{k_{1}}=\frac{E_{a}}{2.303R}\left [ \frac{T_{2}-T_{1}}{T_{1}T_{2}} \right ]$

k1,k2 = the reaction rate constant at T1 and T2

Ea = activation energy of the reaction

R = ideal gas constant=8.3145 J/K·mol

T1,T2 = Absolute Temperature in Kelvin

## Solved Examples

Question 1: The rate of a reaction quadruples when the temperature changes from 290 to 330K. Find the energy of activation of the reaction assuming that it does not change with temperature.

Solution:

Given:

T1 = 290K

T2 = 330K

K2 =4K1

From the Arrhenius equation, we obtain

$log\frac{k_{2}}{k_{1}}=\frac{E_{a}}{2.303R}\left [ \frac{T_{2}-T_{1}}{T_{1}T_{2}} \right ]$

by substituting all the values we get,

$0.6021=\frac{E_{a}}{2.303R}\left [ \frac{40}{(290)(330)} \right ]$

Ea = 1,103276.8/40

=27,581.9 J/mol

Ea = 27.5819 kJ/mol