Determination of Activation Energy
Once the order of the reaction is determined, if data is given for more than two
temperatures an Arrheneus plot can be made to determine the activation
energy. The following equations apply:
In an Arrhenius plot the lnk is plotted against 1/T and a graph is obtained
with a linear slope that is equal to –Ea/R. Since the gas constant (R) is known to
be 8.314 J/mol*K and the slope is now know the activation energy can be easily
calculated.
Here is an example of an Arrhenius plot:
For our particular example and for problems with data from only two
temperatures a more mathematical approach can be used to determine the
activation energy.
The second equation can be subtracted from the first to yield:
This equation can be rearranged to achieve an equation for the calculation for
the activation energy.
For our example the activation energy was calculated to be:
Below is a view of the excel sheet for our particular example. The data in
purple and the time and change in pressure was given. Using that information PA
was calculated followed by a calculation of the natural log of PA and the inverse
of PA. The boxes in green are a linest function in excel in which the y values are
the natural log of PA and the x values are the corresponding time. The box in blue
is a calculation done to obtain the activation energy for this particular reaction.