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

5.4 Advanced collision theory 137
• Withalong-rangeattractivetermoftheform− ¡
¢
, the intermolecular potential
thus has the form
µ 2
() =− + (5.213)
µ 2
= − + ~2 ( +1)
(5.214)
2 2
i.e.,
() ∝− − + −2 (5.215)
— The −2 term is important in practice if 3. In effect, it leads to an
effective energy barrier (“centrifigual” barrier).
— The larger for a given , the larger the orbital angular momentum .
I
Figure 5.28: Potential energy curves with centrifugal barriers for a diatomic system.
d) Langevin “capture” rate constant for ion-molecule reactions*
An nice illustration of the above results is the rate constant for ion-molecule reactions.
The intermolecular interaction is governed by the point charge-induced dipole interaction.
40 In addition, the centrifugal barrier has to be taken into account, so that
() =−
µ 2 ()2
(4 0 ) 2 2 + 4 (5.216)
The resulting expression for the rate constant is
à !
4 () 2 12 µ 1
( )=
(4 0 ) 2 × Γ
(5.217)
2
Typical values of are 100 ×
40 () needs to be checked again!!