Chemistry Reference
In-Depth Information
of collisions between the reactants. The collision theory assumes that all the
reactants are hard spheres, and that any collision that has sufficient energy to
reach the activated state will proceed to complete the reaction.
13
Another candidate was the
thermodynamic
formulation, in which the reaction
rate constant is expressed in thermodynamic quantities as
kT
h
K
{
k
¼
ð
2
:
4
Þ
Since the equilibrium between the activated state and the reactants is a normal
chemical equilibrium it can be related to the thermodynamic theory of chemical
reactions, and hence, it can be related to the normal thermodynamic entities free
energy, enthalpy (
), entropy and so forth. This yields a measure of the
entropy changes associated with the reaction.
Absolute reaction rate theory is a theory that aims to provide explanations for
both the
heat content
'
'
activation energy
and the pre-exponential factor
A
(the
frequency
'
'
'
factor
) in the rate equation from first principles. The underlying theories that it
uses are quantum mechanics and statistical mechanics. The rate formula of the
absolute theory of reaction rates is given in terms of the partition functions
Z
of the
reactants and the transition state by
'
Z
00
{
Z
A
Z
B
Z
kT
h
E
0
¼
{
=
RT
ð
:
Þ
k
exp
2
5
...
The advantage of this formulation is that the partition functions for all compounds
featuring in the reaction can be calculated using statistical mechanics for vibra-
tional and rotational motion of mechanical systems. While this is still a difficult
problem, a detailed consideration of different reacting systems yields a mechanistic
insight in how the reaction occurs on a molecular level.
A detailed summary of absolute reaction rate theory was given in Wigner
s
(
1938
) presentation at the 1937 Faraday conference, where he summarised the
'
13
A modified collision theory often introduces a
P
which measures the
probability that a collision will lead to a completed chemical reaction. Hence, in the modified
collision theory
probability factor
'
'
PZ
exp
E
RT
k
¼
ð
2
:
3
Þ
P
is introduced since the collision cross section of a molecule bears no clear
relationship to the probability for a chemical reaction. While the collision theory works well for
reactions between mono-atomic gases, it breaks down for reactions between more complex
molecules. In this respect, the collision theory is not capable of clarifying the internal mechanisms
of chemical reactions in the necessary detail.
The
fudge factor
'
'
