Page 152 - Introduction to chemical reaction engineering and kinetics

134 Chapter 6: Fundamentals of Reaction Rates

SOLUTION

From equation 6.4-15, with E* given by equation 6.4-17, and MA = (12WlOOO) kg mol-‘,

ksCTIp = 2.42 X 10P3L mol- 1 -1
s
This is remarkably coincident with the value of kobs, with the result that p = 1. Such
closeness of agreement is rarely the case, and depends on, among other things, the cor-
rectness and interpretation of the values given above for the various parameters.
For the bimolecular reaction A + B + products, as in the reverse of the reaction in
Example 6-2, equation 6.4-15 is replaced by

k S C T = 1000pNA,,d~,[8~R(MA + M,)IM,M,]‘“T’i2e-E”RT (6.4-17)

The proof of this is left to problem 6-3.

6.4.1.6 Energy Transfer in Bimolecular Collisions
Collisions which place energy into, or remove energy from, internal modes in one
molecule without producing any chemical change are very important in some pro-
cesses. The transfer of this energy into reactant A is represented by the bimolecular
process

M+A-+M+A*

where A* is a molecule with a critical amount of internal energy necessary for a sub-
sequent process, and M is any collision partner. For example, the dissociation of I, dis-
cussed in Section 6.3 requires 149 kJ mol-l to be deposited into the interatomic bond.
The SCT rate of such a process can be expressed as the rate of collisions which meet the
energy requirements to deposit the critical amount of energy in the reactant molecule:

r = Z,, exp( -E*IRT) = kETcAcM

where E* is approximately equal to the critical energy required. However, this simple
theory underestimates the rate constant, because it ignores the contribution of internal
energy distributed in the A molecules. Various theories which take this into account
provide more satisfactory agreement with experiment (Steinfeld et al., 1989, pp. 352-
357). The deactivation step

A*+M-+A+M

is assumed to happen on every collision, if the critical energy is much greater than k,T.

6.4.2 Collision Theory of Unimolecular Reactions
For a unimolecular reaction, such as I, -+ 21’, there are apparently no collisions nec-
essary, but the overwhelming majority of molecules do not have the energy required
for this dissociation. For those that have enough energy (> 149 kJ mol-l), the reaction
occurs in the time for energy to become concentrated into motion along the reaction
coordinate, and for the rearrangement to occur (about the time of a molecular vibra-
tion, lOPi3 s). The internal energy can be distributed among all the internal modes, and
so the time required for the energy to become concentrated in the critical reaction co-
ordinate is greater for complex molecules than for smaller ones. Those that do not have