Kinetics Of A Reaction - Calculating Activation Energy

The rate constant of a reaction can be expressed as

k = Ae-Ea/RT

which is called the Arrhenius equation. Taking the natural log of both sides of the Arrhenius equation gives

ln k = -Ea/R(1/T) + ln A

The equation above is of the form y = mx + b, where y = ln k, m = -Ea/RT, x = 1/T, and b = ln A. For a reaction whose rate constant obeys the Arrhenius equation, a plot of ln k vs 1/T gives a straight line and it's slope can be used to determine Ea.

Sample data shown in the following table was used to produce the two graphs.


Average Time
Rate Of Reaction
Rate Constant (k)
ln k
3.61 x 10-3
4.8 x 10-8
3.39 x 10-3
8.1 x 10-8
3.22 x 10-3
1.9 x 10-7




Using the slope from the graph displaying the trendline:

Slope = -3.2549 K x 1000 = -3300 K

Slope = -Ea/R

Ea = -Slope x R = -(-3300 K x 8.314 J mol-1 K-1)

Ea = 27000 J mol-1 = 27 kJ mol-1

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