Table of Contents
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.
|
Temp
|
Temp-1
|
Average Time
|
Rate Of Reaction
|
Rate Constant (k)
|
ln k
|
|---|---|---|---|---|---|
|
(K)
|
(K-1)
|
(s)
|
(M/s)
|
(M-3s-1)
|
()
|
|
277
|
3.61 x 10-3
|
289
|
4.8 x 10-8
|
15
|
2.7
|
|
295
|
3.39 x 10-3
|
173
|
8.1 x 10-8
|
25
|
3.2
|
|
311
|
3.22 x 10-3
|
74
|
1.9 x 10-7
|
58
|
4.1
|
 |
 |
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
Kx 8.314 J mol-1K-1)Ea = 27000 J mol-1 = 27 kJ mol-1
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