Page 45 - Modeling of Chemical Kinetics and Reactor Design

Reaction Mechanisms and Rate Expressions 15
 σ +σ B  2  M + M  05 .
A
B
Z AB =  A 2  n • n B   8 π kT• M • M  
A
A
B
 σ +σ B  2 N  M + M  05 . (1-61)
2
= A  8 π kT• A B  CC
 2  10 6  MM  A B
.
B
A
where σ = diameter of a molecule, cm
M = (molecular weight)/N, mass of a molecule, gm
23
N = 6.023 × 10 molecules/mol, Avogadro’s number
C = concentration of A, mol/l
A
C = concentration of B, mol/l
B
3
n = NC /10 , number of molecules of A/cm 3
A
A
3
n = NC /10 , number of molecules of B/cm 3
B
B
k = R/N = 1.30 × 10 –16 erg/K, Boltzmann constant
The rate equation is given by
− ( r A ) =− 1 dN A = kC C B
A
V dt
fraction of collision 
 collision rate  (1-62)

=   involving energies 
mol / l sec•  
in excess of E 
where E is the minimum energy.
10 3 −ERT
= Z • e
AB
N
 σ +σ  2 N  M + M  . 05 (1-63)
= A B  8π kT• A B  CC e −ERT
 2  10 3  MM B  A B
A

where e –E/RT represents the fraction of collisions involving molecules
with the necessary activation energy E.

TRANSITION STATE THEORY

The transition state theory describes reactants combining to form
unstable intermediates called activated complexes, which rapidly