# How can I calculate the activation energy of a reaction?

Oct 2, 2014

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:

$\ln k = \ln A - \frac{{E}_{a}}{R T}$

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 $\ln k$ against $\left(\frac{1}{T}\right)$. You should get a straight line graph. This is an equation of the form $y = m x + c$.

So the gradient of the line is equal to $- \frac{{E}_{a}}{R}$ so you can get ${E}_{a}$.

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