Some Basics En Route to Isoconversional Methodology - Isoconversional Kinetics of Thermally Stimulated Processes - page 17

cess gives rise to the effective activation energy, whose value is a temperature- and/
or conversion-dependent function of the activation energies of the individual steps.
This holds true for any multistep process regardless of whether it involves diffusion
or not. For example, if a reaction involves two competing steps, its rate is described
by the following equation

d
d

α
t

= kTfT kTfT ()() () (). + (1.22)

1 1 2 2

The effective activation energy of such reaction can be determined by taking the
logarithmic derivative of the reaction rate at a constant extent of conversion (cf.,
Eq. 1.13):

ER t
T

∂ ln( dd

1

α / ) Ek Tf ()() α + Ek Tf () () α

11 1 2 2 2

=− =

() () () .

(1.23)

α

−

kTf () α + kTf α

∂

α 1 1 2 2

This equation clearly suggests that the effective activation energy depends on both
temperature and extent of conversion. An example of the dependence is displayed in
Fig. 1.12 . The dependence has been simulated [ 39 ] by using the activation energies
and reaction models experimentally established for the two competing steps in the
thermal decomposition of nickel formate. It should also be noted that the occurrence
of multiple steps is the most common reason why the activation energy experimen-
tally determined for a condensed-phase reaction happens to be variable.
Although examples of variable activation energy are plentiful, we finish by men-
tioning the one that has a special significance. It is the inversion of sucrose. As
widely accepted [ 40 ], the birth of chemical kinetics is marked by the work of Wil-
helmy, who in 1850 measured the rate of this reaction. It seems symptomatic that
this initial reaction later became known [ 41 ] as having variable activation energy.

Fig. 1.12 Process that
involves two paral-
lel reactions having the
following kinetic trip-
lets: f 1 ( ʱ ) = ( 1 − ʱ ) 2/3 ,
E 1 = 200 kJ mol − 1 ,
A 1 = 10 16 min − 1 and
f 2 ( ʱ ) = ʱ ( 1 − ʱ ) and
E 2 = 100 kJ mol − 1 ,
A 2 = 10 7 min − 1 . (Reproduced
from Vyazovkin [ 39 ] with
permission of Taylor &
Francis)