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

7.3 Thermodynamic interpretation of transition state theory 163
• Note: and are given above in units of lmol −1 s −1 (we may denote this by
writing them as and ), while ∆ ª‡ and ∆ ª‡ used above are referred to
the standard state for gases of ª =1bar.
— For ideal gases, ∆ ‡ and ∆ ‡ are related via
∆ ª‡ = ∆ ª‡ + ∆ ‡ ( )=∆ ª‡ − = ∆ +‡ − (7.87)
— Likewise, ∆ ª‡ and ∆ +‡ for are related via
∆ +‡ − ∆ ª‡ =
y
Z
+
ª
Z
+
=
ª
= Z
+
ª
= Z
+
ª
∆ ‡
(7.88)
= ∆ ‡ +
ln
+ 0 = +
ª ∆‡ ln
+ 0 = ª
ª ∆‡ ln (7.89)
+ 0
= ∆ ‡ ln + 0
(7.90)
ª
with ª =1barand + = +
+ =1moll−1 .
∆ ª‡ = ∆ +‡ − ln + 0
ª (7.91)
c) Thermodynamic transition state theory for reactions in the liquid phase
For reactions in condensed phases,
∆ ≈ ∆ (7.92)
and
y
£
ABC
‡ ¤
‡ ( ) =
[A] [BC] = ¡ +¢ ∆ ‡ exp
≈ ¡ +¢
∆ ‡ exp
µ− ∆+‡
exp
• for unimolecular reactions:
( )= µ
exp
• for bimolecular reactions:
( )= µ
+ exp
− ∆+‡
µ− ∆+‡
− ∆+‡
µ− ∆+‡
exp
exp
+‡
∆
exp
µ−
µ− ∆+‡
µ− ∆+‡
(7.93)
(7.94)
(7.95)
(7.96)
Note: The conversion between values for ∆ +‡ and ∆ ª‡ and, likewise, between
values for ∆ +‡ and ∆ ª‡ for a given reaction in the liquid and gas phase requires
some caution. 46
46 See,e.g.,D.M.Golden,J.Chem.Ed.48, 235 (1971).