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

7.3 Thermodynamic interpretation of transition state theory 165
b) Thermochemical estimation of A-factors*
Equations 7.71 and 7.86 allow us to estimate the -factors of chemical reaction rate
constants by the following procedure (Benson1976):
(1) We setup a model for the TS, with a certain structure and vibrational freuqencies.
(2) We take a reference molecule that is similar to the TS and use the ref of the
reference molecule for a zero-order estimation of ∆ ‡ according to
∆ ‡ = ref −
X
( reactants ) (7.108)
reactants
(3) We apply corrections for the differences between ref and ‡ basedonthestatistical
thermodynamics result of
= ln + ln
(7.109)
y
µ
∆ cor = ‡ − ref = ln ‡
‡
+
ref ln (7.110)
ref
Usually, the correction term accounts for differences of the entropies for translation,
rotation, internal rotations, vibrations, symmetry, electron spin, plus sometimes
other terms (e.g., optical isomers).
I Example 7.1: Estimation of the -factor for the reaction O+CH 4 →
(O ···H ···CH 3 ) ‡ → OH + CH 3 .
∆ ‡ = (O ···H ···CH 3 ) ‡ − (O) − (CH 4 ) (7.111)
ref = (CH 3 F) (7.112)
∆ cor thus depends on a comparison of CH 3 F and OHCH ‡ 3 (see Table ). ¤
I Table 7.4: Estimation of the -factor for the reaction O+CH 4 →
(O ···H ···CH 3 ) ‡ → OH + CH 3 .
Contribution ∆ ‡ (Jmol −1 K −1 )
ª (CH 3F) − ª (O) − ª (CH 4)
−1243
Spin: + ln 3 + 91
external rotation: 1 3 ln ( 1 2 3 ) ‡
( 1 2 3 ) ref + 79
translation − 04
CF =1000cm −1 → − 04
OH =2000cm −1 + 00
2 OHC ()
³
=600cm −1 ´
+ 42
∆ ‡ = ª
O ···H ···CH ‡ 3 − ª (O) − ª (CH 4) −1039
Correction ∆ ‡ → ∆ ‡ : + ln ( 0 ) y ∆ ‡ = −198 Jmol −1 K −1 .