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 K x 8.314 J mol-1 K-1)

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

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