How to experimentally determine the value of Ea for a chemical reaction
The Arrhenius equation was discussed today in class, but I did not get to one topic that would
help prepare you for this Friday’s experiment: how to experimentally determine the value of Ea
(activation energy). I will address that here.
Basically, the answer to this question (how to get Ea) comes from taking the natural log of both
sides of the Arrhenius equation. Note: This derivation may look “bad” or long, but really, it is
not as long as it looks since I am showing every little step to make sure you see how I get to the
final relationship:
k  Ae


Ea
RT

ln k  ln  Ae

Start with the Arrhenius Equation
E
 a
RT



  Ea 
 lnA + ln  e RT 


E
 lnA +  a

RT
E
  a  ln A
RT
E 1
  a
 ln A
R T
Take the natural log of both sides
Use “product rule” of logs: ln(AB) = lnA + lnB
Simplify using ln(ex) = x
Rewrite using x + y = y + x (swap the terms)
Rewrite using
x
x 1
 
yz y z
Note: The only variables in this equation are k and T. Ea is
Ea 1
a constant for a given reaction, A is a constant
 ln A
(effectively) for a given reaction, and R is the gas
R T
constant (a fundamental constant in nature).

y =
m x + b

The boxed equation above shows that a plot of lnk vs. 1/T for a particular chemical reaction should be linear, and the
activation energy, Ea, is related to the slope of this line. Specifically, the slope equals the opposite of Ea divided by R:
E
m   a As such, one can solve for Ea if one knows m (since R is a constant, having a value of 8.314 J/mol∙K)
R

ln k
 
Thus, to determine Ea experimentally:
1) Determine values of k as a function of T experimentally (i.e., change T and determine k at each T)
2) Create a table of k values and T values. Make sure to convert T values into absolute (i.e. Kelvin) temperatures.
3) Calculate lnk from the k values, and 1/T values from the T values.
4) Make a plot using 1/T values as the x values and lnk values as the y values. (i.e., Plot lnk vs 1/T)
5) Draw a “best-fit” line to the data (or better yet, have a software program calculate the best fit line [or
“Trendline” in Excel] to the data).
6) Find slope of the best-fit line (or better yet, have a software program determine it for you)
7) Set up the equation, m = -Ea/R (using R = 8.314 J/mol∙K)
8) Solve for Ea algebraically (Note: Ea has units! Look closely at the units on your x-axis; the y-axis variable has
no units)