Some Basics En Route to Isoconversional Methodology - Isoconversional Kinetics of Thermally Stimulated Processes - page 14

of the energy barrier as well as of the activation energy representing this barrier
does not raise much of a doubt. Nonetheless, the situation presented in this graph
is grossly oversimplified. It represents a reaction between two reactant molecules
that get converted to two product molecules. That is, there is no reaction medium,
in which the energies of the molecules, engaged in the reaction act, would be af-
fected by intermolecular interactions with surrounding inactive molecules. Such
simplification may be appropriate only for gas-phase reactions and thus is of little
relevance to condensed-phase and heterogeneous kinetics. Nevertheless, it is wor-
thy a note that even in the gas-phase reactions the energy barrier height is known
[ 27 ] to demonstrate a variation with temperature due to temperature dependence of
the heat capacity of activation and tunneling effects.
When it comes to condensed-phase kinetics, the processes take place in the liq-
uid or solid medium. In this situation, the energy barrier becomes dependent on
the properties of the medium. The size of the barrier may thus change as the prop-
erties of the medium change with either temperature or reaction progress. Let us
first illustrate [ 28 ] a variation with conversion by considering a single-step reaction
A → B such as isomerization. In general, the energetic state of the reactant A is af-
fected by the molecules that surround it. At the early stage of the reaction, when
ʱ is close to 0, the reactant is surrounded by other molecules of A . As the reaction
nears completion (i.e., ʱ is close to 1) the reactant will be predominantly surrounded
by the product molecules B . If intermolecular forces between A and A are stronger
than the forces between A and B, the molar enthalpy of A will be lower in initial
( ʱ = 0) than in final ( ʱ = 1) stages of the reaction (Fig. 1.10 ). By similar argument,
in the final stages ( ʱ = 1) when the product B is surrounded by the molecules B, its
molar enthalpy is lower than in the initial stages of reaction ( ʱ = 0). Obviously, as
this reaction progresses from ʱ = 0 to ʱ = 1, its exothermicity should increase and
its energy barrier should decrease. In other words, the observed activation energy
should progressively decrease as a function of conversion, ʱ .
A variation of the energy barrier with temperature follows directly from the
activated-complex theory developed for reactions of ions or polar molecules in so-
lutions [ 29 ]. In accord with this theory, the rate constant of reaction between two
ions is given as

2

zze

(1.17)

ln k = ln k −

AB

,

0

ε d kT

AB B

Fig. 1.10 Illustration of how
intermolecular interactions
may affect the height of the
energy barrier throughout the
reaction progress