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

7.3 Thermodynamic interpretation of transition state theory 161
• Arrhenius preexponential factor:
∆ ‡ = − (7.69)
y
y
( )= µ µ
∆
‡
exp exp −
= µ
∆
‡
exp
(7.70)
(7.71)
b) Thermodynamic transition state theory for bimolecular gas phase reactions
I Conversion from K
‡ (T ) to K‡
(T ): For bimolecular reactions
A+BC→ ABC ‡ , (7.72)
we have to account for the different numbers of species ∆ ‡ = ‡ − reactants :
We therefore have to convert from ‡ ( ) to ‡ ( ) via
∆ ‡ = −1 . (7.73)
£ ¤
ABC
‡ ABC
‡ ABC ‡ ª
‡ ( )=
[A] [BC] =
A BC
=
A ª BC ª × 1
µ −∆
‡
= ª ‡ ( ) ×
.
ª
(7.74)
Here, ‡ ( ) is conveniently given in units of lmol −1 . 44 However, , ‡ ∆ ‡ , ∆ ‡ and
∆ ‡ arerelatedtothestandardstateat ª =1bar. 45 To keep track of units in the
conversion , it is useful to apply in
lbar by writing
mol K
=83145
J
mol K =83145 m3 Pa
lbar
=0083145
mol K mol K = 0 (7.76)
44 With ‡ ( ) in units of ¡ mol l −1¢ ∆
, we get as close as possible to the standard state ∗ =
1molkg −1 for reactions in aqueous solution.
45 We recall that the thermodynamic equilibrium constant ( )=exp(−∆ ª ) referred to
the standarrd state at ª =1baris dimensionless. Instead of the dimensionless ‡ ( ), onemay
also decide to use the equilibrium constant in pressure units ‡ 0 :
hABC ‡i ABC ‡
‡ ( )=
[A] [BC] =
A BC
= ‡ 0 ( ) × 0 (7.75)