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

7.2 Applications of transition state theory 157
7.2.3 Example 2: The reaction F + H 2 → F···H···H ‡ → FH + H
I
Exercise 7.1: Evaluatetherateconstantforthereaction
F+H 2 → F ···H ···H ‡ → FH + H (7.47)
using the data in Table 7.2 at =200, 300, 500, 1000 and 2000 K, determinethe
Arrhenius parameters, and compare the results with the experimental value of
=2× 10 14 exp (−800 )cm 3 mol s (7.48)
¤
I Table 7.2: Properties of the reactants and transition state of the reaction F + H 2 .
parameter F ···H ···H ‡ a F H 2
2 (F ···H) ( Å) 1602
1 (H ···H) ( Å) 0756
07417 b
1 (cm −1 ) 40076 43952
2 (cm −1 ) 3979
3 (cm −1 ) 3979
4 (cm −1 ) 3108 c
³ (u) 21014 189984 2016
u Å 7433
0277
1 2
d
4 4 1
0 ¡ kJ mol −1¢ 657 000
a The transition state FHH ‡ is assumed to be linear.
b = (H-H).
c One imaginary frequency describes the TS along the RC.
d The electronic ground state of F is 2 32 . We neglect the 2 12 spin-orbit component at ( 2 12 )=
404 cm −1 because it does not correlate with the products H + HF. The electronic state of linear
FHH ‡ is 2 Π. The ground state of H 2 is 2 Σ + .
I Solution 7.1:
( )= ‡ µ
exp − ∆
0
2
Ã
!
= ‡
( )( 2 )
µ
× exp − ∆
0
à !
‡
2
à !
‡
2
(7.49)
à !
‡
2
(7.50)