rate constants of the order of n Á 10
À9 cm
3
=s (n < 10). Even more often, constants
are many orders of magnitude less than a gas-kinetic one, and not always the
activation energy of the process is to blame; the matter is in the steric factor, i.e., as
a rule, in the symmetry forbiddance for this process.
As to termolecular processes, sometimes the recombination rate constant can be on
the order of 10
–28 cm
6 /s, i.e., the value is 4 orders of magnitude higher than mentioned
above. But in this case, the main ‘fault’ does not fall on large gas-kinetic diameters.
The reason is that the reaction mechanism cannot be described in any way within the
framework of a simultaneous collision of three species (see [9] and references).
Very often, when the activation energy is large, the term (T
1/2 ) is neglected,
since the dependence of the k value on T is determined mainly by the exponent. In
these cases, the Arrhenius equation takes the simple form
k ¼ A exp ÀE a =RT
ð
Þ ;
ð2:3:9Þ
where A Pk gk is the so-called pre-exponential factor, independent of temperature.
As mentioned above, activation energy can be both positive and negative. It is
clear that for endothermic reactions, i.e., reactions in which the internal energy of
the products is greater than those of the initial species, the activation energy simply
has to be positive. However, it is often positive for exothermic processes, and the
matter is that there are potential barriers at the process coordinate, which we will
also discuss in Sect. 3.5. Very often (but not always) for the recombination processes, the activation energy is negative, and a decrease of reaction rate with
temperature occurs (see below).
To measure the activation energy and the pre-exponential factor A, in those cases
when one represents k in the form of (2.3.9), it is necessary to use the dependence ln
k = f(1/T). It is clear from (2.3.9) that this dependence ‘should’ be direct, and
(Fig. 2.3)
dlnk
d
1
T
¼ À
E a
R
ð2:3:10Þ
lnk
1/T
Fig. 2.3 To the activation
energy calculation
2.3 Arrhenius Equation
27
À9 cm
3
=s (n < 10). Even more often, constants
are many orders of magnitude less than a gas-kinetic one, and not always the
activation energy of the process is to blame; the matter is in the steric factor, i.e., as
a rule, in the symmetry forbiddance for this process.
As to termolecular processes, sometimes the recombination rate constant can be on
the order of 10
–28 cm
6 /s, i.e., the value is 4 orders of magnitude higher than mentioned
above. But in this case, the main ‘fault’ does not fall on large gas-kinetic diameters.
The reason is that the reaction mechanism cannot be described in any way within the
framework of a simultaneous collision of three species (see [9] and references).
Very often, when the activation energy is large, the term (T
1/2 ) is neglected,
since the dependence of the k value on T is determined mainly by the exponent. In
these cases, the Arrhenius equation takes the simple form
k ¼ A exp ÀE a =RT
ð
Þ ;
ð2:3:9Þ
where A Pk gk is the so-called pre-exponential factor, independent of temperature.
As mentioned above, activation energy can be both positive and negative. It is
clear that for endothermic reactions, i.e., reactions in which the internal energy of
the products is greater than those of the initial species, the activation energy simply
has to be positive. However, it is often positive for exothermic processes, and the
matter is that there are potential barriers at the process coordinate, which we will
also discuss in Sect. 3.5. Very often (but not always) for the recombination processes, the activation energy is negative, and a decrease of reaction rate with
temperature occurs (see below).
To measure the activation energy and the pre-exponential factor A, in those cases
when one represents k in the form of (2.3.9), it is necessary to use the dependence ln
k = f(1/T). It is clear from (2.3.9) that this dependence ‘should’ be direct, and
(Fig. 2.3)
dlnk
d
1
T
¼ À
E a
R
ð2:3:10Þ
lnk
1/T
Fig. 2.3 To the activation
energy calculation
2.3 Arrhenius Equation
27