Untitled - Aerobib - Universidad Politécnica de Madrid

1.8. CHEMICAL KINETICS 33
This structure can be obtained from Quantum Mechanics or be postulated from the
structure of the molecules. The Absolute Reaction Rate Theory has been successfully
applied to the study of a great number of reactions well as to many other physical
and physicochemical phenomena. A full development of the theory can be found, for
instance, in the works mentioned in Refs. [24] and [25].
In the previous study it has been assumed that a single one directional reaction
takes place within the mixture. Generally, all reactions proceed simultaneously in both
senses at different rates. Thus, reaction (1.112) must be substituted by the following
∑
ν iA ′ i ⇄ ∑
i
i
ν ′′
i A i , (1.134)
and the rate w i of production of species A i is given by the expressions
(
)
∏ ∏
w i = M i (ν i ′′ − ν i)
′ k f c ν′ i
− k b c ν′′ i
. (1.135)
Here k f and k b are the specific rates corresponding to the forward and backward reactions
respectively.
i
On the other hand to be able to form the products, the reacting molecules must
contact one another. This reduces the molecularity of a single elementary reaction to
1, 2 or 3, since the probability of a collision of more than three molecules is practically
nil. Consequently, when the reaction rate depends in a complicated way on the
concentrations, it can be assured that it proceeds from the combination of several elementary
reactions. The basic problem of Chemical Kinetics is then the establishment
of the set of elementary reactions that produce within the mixture. For example, the
stoichiometric equation for the decomposition of ozone is
While the following is the actual system of reactions [28]:
i
i
i
2O 3 ⇄ 3O 2 . (1.136)
O 3 +G k fi
⇄
k b1
O+O 2 +G, (1.137)
O+O 3
k f2
⇄
k b2
2O 2 , (1.138)
O 2 +G k f3
⇄
k b3
2O+G. (1.139)
Here G is one of the atoms or molecules of the mixture. Each one of these reactants
acts at its own reaction rate and the rate of consumption of the ozone results from