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

5.4 Advanced collision theory 125
I Non-equilibrium energy distribution:* The above expression for ( ) is valid if
the reacting molecules are in internal equilibrium, i.e., the energy states are populated
according to the Boltzmann distribution.
Deviations from the Boltzmann distributions will occur in the case of very fast reactions,
if the reaction is faster than the relaxation between the energy states. In this case, ( )
decreases because the mean energy of the reacting molecule decreases.
Mean energy of the reacting molecules (see Fig. 5.19):
= X
=
Z ∞
0
() (5.163)
(1) For thermal equilibrium:
() =() (5.164)
with () being the Boltzmann distribution.
y
(2) Non-equilibrium:
() () (5.165)
non-eq. eq. (5.166)
I
Figure 5.19: Mean energy of the reacting molecules in thermal equilibrium and for a
non-eqilibrium situation.
I Conclusion: The non-equilibrium distribution leads to a reduced rate coefficient.