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

7.3 Thermodynamic interpretation of transition state theory 160
7.3 Thermodynamic interpretation of transition state theory
7.3.1 Fundamental equation of thermodynamic transition state theory
As shown above,
( )=
‡ (7.59)
‡ can often be interpreted using thermodynamic arguments, i.e., ∆ ‡ , ∆ ‡ ,and
∆ ‡ . For liquid phase reactions, this is straightforward. For gas phase reactions, we
have to take into account the difference between ‡ and .
‡
a) Thermodynamic transition state theory for unimolecular gas phase reactions
For unimolecular isomerization and dissociation reactions of the type
or
we have
ABC → ABC ‡ → ACB ‡ (7.60)
ABC → ABC ‡ → A+BC ‡ , (7.61)
£ ¤
ABC
‡
‡ ( )=
[ABC]
= ABC ‡
ABC
= ‡ ( ) (7.62)
‡ ( )= ‡ ( )= ‡ ( ) is dimensionless (∆ ‡ =0) and we do not have to worry
about a difference between ‡ ( )= ‡ ( ) and about units or different standard
states.
I Results: Eq. 7.59 thus gives the following results:
• Rate constant:
y
( )=
‡ ( )= µ
exp − ∆‡
( )= µ
∆
‡
exp exp
µ− ∆‡
(7.63)
(7.64)
• Arrhenius activation energy:
y
= 2 ln
= 2 ∙ µ
ln ∆
‡
exp
exp
¸
µ− ∆‡
(7.65)
= ∆ ‡ + + 2 ∆‡
= ∆ ‡ + + ∆‡
(7.66)
(7.67)
If ∆ ‡ 6= ( ) in the temperature range of interest, we obtain
= ∆ ‡ + (7.68)