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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