How can I calculate the activation energy of a reaction?

You can calculate the activation energy of a reaction by measuring the rate constant k over a range of temperatures and then use the Arrhenius Equation to find #E_a#.

According to his theory molecules must acquire a certain critical energy #E_a# before they can react. The Boltzmann factor #e^(-E_a/(RT)# is the fraction of molecules that managed to obtain the necessary energy. The rate constant of a reaction is related to temperature by the Arrhenius Equation:

From BBC GCSE:

#k=Ae^((-E_(a))/(RT)#

A is a constant termed the frequency factor

e is the base of natural logs

R is the gas constant = 8.31J/K/mol

T is the absolute temperature in degrees Kelvin.

If you take natural logs of both sides of the equation you get:

#lnk=lnA -(E_a)/(RT)#

You then measure k over a range of temperatures, the method you use depends very much on the type of reaction you are studying.

You can then plot #lnk# against #(1/T)#. You should get a straight line graph. This is an equation of the form #y=mx+c#.

So the gradient of the line is equal to #-(E_a)/R# so you can get #E_a#.

This is an example taken from Wikipedia relating to the decomposition of nitrogen (IV) oxide.