Question

How can I calculate the activation energy of a reaction?

Answer 1

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.