Untitled - Aerobib - Universidad Politécnica de Madrid

32 CHAPTER 1. THERMOCHEMISTRY
which can be identified with Eq. (1.122) by making
√ ( )
k = Nσ12
2 M1 + M 2
8πRT
e −E/RT , (1.130)
M 1 M 2
that is, from Eq. (1.124),
α = 1 2
(1.131)
and
B = Nσ 2 12
√
8πR
( )
M1 + M 2
. (1.132)
M 1 M 2
When comparing Collisions Theory with experimental results, an exact numerical
agreement between the reaction rates predicted and observed is not to be expected,
but an agreement of the orders of magnitude. In fact, Collisions Theory does not include,
among others, the influence of the relative orientation of the molecules as they
collide which can decide the success of the collision. Such an effect can be of importance
specially in molecules of complicated structure. It is taken into consideration
by including in Eq. (1.129) a numerical factor P of orientation equal or smaller than
unity
dc 1
dt = dc 2
dt = − dc 3
dt =
− P
√
ρ2
Nσ 2
M 1 M
12Y 1 Y 2 8πRT
2
( )
M1 + M 2
e −E/RT .
M 1 M 2
(1.133)
Experimental reaction rates agree, fairly, with those predicted by Collision Theory
only for a short number of reactions, yet in other cases experimental rates are as much
as 10 8 times larger or smaller than those predicted by theory. Such a discrepancy can
not be justified within the theory. These results that in the best cases Collision Theory
represents approximately the actual facts only for a short number of reactions. A more
correct formulation is provided by the so-called Theory of Absolute Reaction Rates.
In this theory it is assumed that the passing of the reacting species to the products
takes place through the formation of an activated complex resulting from the
assembly of the reacting species. This complex is considered as located at the top of
an energy barrier which separates the species from the products. The reaction rate
is determined by the velocity at which the activated complex crosses the barrier. It
is, furthermore, assumed that such complex stands in equilibrium with the reacting
species and that its dissociation in products is due to the action of one of the vibrational
degree of freedom. Then, by applying the laws of Statistical Mechanics the
reaction rate can be computed when the structure of the activated complex is known.