Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...
Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ... 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 .
7.3 Thermodynamic interpretation of transition state theory 166 Estimated -value: = 2 µ ∆ ‡ exp (7.113) µ −197Jmol −1 =739 × 625 × 10 12 K −1 × exp 831 J mol −1 K −1 cm 3 mol −1 s −1 (7.114) =43 × 10 12 cm 3 mol −1 s −1 (7.115) Experimental -value: expt =19 × 10 12 cm 3 mol −1 s −1 (7.116) The difference is probably due to a poor estimate of the TS structure — one can do much better, I just didn’t try hard enough here. 47 7.3.3 Kinetic isotope effects I Figure 7.5: The kinetic isotope effect due to the difference in the zero-point energies of the reactants and the respective TS structures. 47 For H abstraction reactions from a series of hydrocarbons by 3 CH 2 , the agreement that was achieved was better than ±30 %.
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7.3 Thermodynamic interpretation of transition state theory 166<br />
Estimated -value:<br />
= 2 µ <br />
∆<br />
‡<br />
exp (7.113)<br />
<br />
µ −197Jmol −1<br />
=739 × 625 × 10 12 K −1 <br />
× exp<br />
831 J mol −1 K −1 cm 3 mol −1 s −1 (7.114)<br />
=43 × 10 12 cm 3 mol −1 s −1 (7.115)<br />
Experimental -value:<br />
expt =19 × 10 12 cm 3 mol −1 s −1 (7.116)<br />
The difference is probably due to a poor estimate of the TS structure <strong>—</strong> one can do<br />
much better, I just didn’t try hard enough here. 47<br />
7.3.3 Kinetic isotope effects<br />
I<br />
Figure 7.5: The kinetic isotope effect due to the difference in the zero-point energies<br />
of the reactants and the respective TS structures.<br />
47 For H abstraction reactions from a series of hydrocarbons by 3 CH 2 , the agreement that was achieved<br />
was better than ±30 %.
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