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

5.4 Advanced collision theory 116
We shall now derive the fundamental equation of collision theory that allows us to
account for those effects.
5.4.1 Fundamental equation for reactive scatteringincrossedmolecularbeams
• Consider the following reactive scattering process (Fig. 5.13):
A+B→ C (5.133)
• IntensityofbeamofA:
= × (5.134)
Is this reasonable? ⇒ Look at the physical dimensions of × :
[cm s] × £ molecules/ cm 3¤ = £ molecules cm 2 s ¤ =[intensity] (5.135)
• Depletion of intensity of A due to scattering by B:
= − () × × ×
↑
↑
↑
(5.136)
y rate equation:
= −() (5.137)
• Rate coefficient for a given value of :
() =() (5.138)
• Averaging over the speed distribution () leads to the fundamental equation
of all improved collision theories:
( )=h()i (5.139)
i.e.,
( )= ∞ R
0
() ( ) (5.140)
• Frequently used approximation: Since the explicit form of () is usually not
known, we write
( )=hi h()i (5.141)
with
and
hi =
µ 8
12
(5.142)
h()i = -averaged (reactive) cross section (5.143)