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

5.1 Hardspherecollisiontheory 95
5.1 Hard sphere collision theory
5.1.1 The gas kinetic collision frequency
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The gas kinetic collision frequency as upper limit for rate constants of bimolecular
reactions: The gas kinetic collision frequency constitues an upper limit for the
rate constant of bimolecular gas phase reactions. We assume that the molecules A and
B are structureless hard spheres (radii , ) moving around with fixedmeanspeeds
and and look at the number of collisions between A and B per unit time.
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Figure 5.1: Derivation of the hard sphere gas kinetic collision frequency.
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Discussion of the molecular quantities affecting the rate constant:
• collision parameter (= projected distance between centers of gravity):
(5.1)
• maximal collision parameter = max value leading to a collision max :
≤ max = + = (5.2)
• collision cross section = 2 (= reactive cross section) 34 :
= 2 = ( + ) 2 (5.3)
34 Deutsch: reaktiver Wirkungsquerschnitt.