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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