How can I calculate the activation energy of a reaction?

1 Answer
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:

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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.

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