REACTIONS: THERMODYNAMIC ASPECTS, KINETICS, AND CATALYSIS - Biomass as a Sustainable Energy Source for the Future - page 135

In the Arrhenius equation, the activation energy (E a ) is used to describe the energy
required to reach the transition state:

k=k 0 e −E a = R u T ð Eq : 5 : 4 Þ

where k = reaction rate coefficient in the rate law

k 0 = pre-exponential factor (unit is reaction rate expression dependent)
E a = activation energy [J mol −1 ]

R u = universal gas constant [=8.314 J

mol −1 K −1 ]

T = reaction temperature [K]

Example 5.1 Find (a) the order of reaction and (b) the reaction rate
coefficient for the reaction

CH 3 CHO g ðÞ! CH 4 g ðÞ +CO g ðÞ

at 518 C (thus 791.15 K) using the following experimental data:

Initial concentration
[molL −1 ]
of acetaldehyde

Formation rate
of acetaldehyde
[molL −1 s −1 ]

1.5 × 10 − 7 0.150

6.0 × 10 − 7

0.300

24.0 × 10 − 7 0.600

Solution
As the decomposition rate of the acetaldehyde quadruples when the initial concen-
tration doubles, we can deduce that the reaction is a second-order reaction.
From the reaction rate law and using the experimental data, we can write

5×10 −7 mol L −1 s −1 0×10 −7

0

= 24 × 10 −7
0

r
CH 3 CHO

2 = 1

:

= 6

:

k=

150 2 mol 2 L −2 300 2 600 2 0 : : :

½

7×10 −6 L mol −1 s −1 =6 :

Example 5.2 Calculation of the activation energy of a higher-order
reaction

A second-order reaction was observed. The reaction rate coefficient was found to
be 8.9 × 10 −3 L

mol −1 s −1 at 3 C and 7.1 × 10 −2 L mol −1 s −1 at 35 C. What is the

activation energy of this reaction?