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

2.7 Temperature dependence of rate coefficients 37
I
I
It is important to realize, however, that the value of E is not equal to the
true height of the potential energy barrier for the reaction!
As said above, is an empirical quantity! Its relation to the true threshold energy 0 ,
which is the minimum energy above which reaction may occur, will be a main subject
in the theory of bimolecular and unimolecular reactions (Sections 5 — 8). There is also
a statistical interpretation of (see Section 8).
Figure 2.15: The reaction HCO → H + CO (G. Friedrichs).
2.7.2 Deviations from Arrhenius behavior
In general, is dependent on temperature, i.e., = ( ). For gas phase reactions,
for example, there is at least the √ dependence of the hard sphere collision frequency.
The -dependence of is often small compared to so that within experimental
error the dependence of ( ) is determined by .
If the -dependence of is not small compared to ,wewillhavetouseamore
general expression for ( ), as explained in the following.
I Generalized three-parameter expression for k (T ): To account for deviations
from Arrhenius because of ( ), one conveniently employs the three parameter expression
( )= − 0
(2.168)
with and 0 now being -independent quantities.
Range of values for specific bimolecular reactions (justified by theory; see later):
− 15 ≤ ≤ +3 (2.169)