Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...

7.2 Applications of transition state theory 154
7.2 Applications of transition state theory
( )=
‡ µ
exp − ∆
0
(7.38)
TST has gained enormous importance in all areas of physical chemistry because it
provides the basis for understanding – and/or calculating –
• quantitative values of preexponential factors,
• ∆ 0 from measured values,
• -dependence of and deviations from Arrhenius behavior,
• gas phase and liquid phase reactions (proton transfer, electron transfer, organic
reactions, reactions of ions in solutions),
• pressure dependence of reaction rate constants (activation volumes),
• kinetic isotope effects,
• structure-reactivity relations (e.g., Hammett relations in organic chemistry),
• features of biological reactions (enzyme reactions),
• heterogeneous reactions (heterogeneous catalysis, electrode kinetics), . . .
7.2.1 The molecular partition functions
In order to evaluate Eq. 7.29 for a given reaction, we need, besides ∆ 0 , the molecular
partition functions for the reactants and the TS. We summarize only the main points
here; further information is given in Appendix G.
I
Definition:
= P −
(7.39)
I
Physical interpretation:
• The molecular partition function is a number which describes how many states
are available to the molecule at a given temperature .
• The ratio
‡
(7.40)
in Eq. 7.29 is thus the ratio of the number of states available to the TS and
‡
the reactant molecules. Since each state is equally likely, is the relative
probability of the TS vs. the probability of the reactants.
Note again that ‡
motion along the RC.
is the partition function of the TS excluding the translational