REACTIONS: THERMODYNAMIC ASPECTS, KINETICS, AND CATALYSIS - Biomass as a Sustainable Energy Source for the Future - page 136

Solution
The activation energy is the amount of energy required to initiate a chemical reac-
tion. The activation energy can be determined from the reaction rate coefficients at
different temperatures from the equation

= E a

k 2
k 1

1
T 1 −

1
T 2

ln

R u

where

T 1 and T 2 are absolute temperatures
k 1 and k 2 are the reaction rate coefficients at T 1 and T 2
Step 1: Convert the temperatures from CtoK
T= C + 273.15

T 1 = 3 + 273.15 = 276.15 K
T 2 = 35 + 273.15 = 308.15 K
Step 2: Find E a using the equation given previously E

0
@

1
A =

0
@

1
A

10 −2

7 : 1 E a 1

276

1
308

ln

3145 15 −

10 −3

: : :

8 : 9 8 15

E a

76 × 10 −4 ln 7 ð Þ : 98 =

3145

3 :

8 :

52 × 10 −5

2 : 077 = E a 4 :

59 × 10 4 J mol −1 =45 mol −1

E a =4 : : 9kJ

5.1.2 Unimolecular First-Order Reactions

A reaction involving one molecular entity is called unimolecular and is given by

M ! products ð RX : 5 : 17 Þ

If this reaction is a first-order reaction, the reaction rate is proportional to the concen-
tration of the reactant:

dM ½

dt

dc
dt =k f c

r f = − = − ð Eq : 5 : 5 Þ

With n i the number of moles of species i at t = 0, n i the number of moles of species i at
time t, and x i the number of reacted moles at time t, we can write
n i =n i −

x i ð Eq : 5 : 6 Þ