Page 184 - Modeling of Chemical Kinetics and Reactor Design

154 Modeling of Chemical Kinetics and Reactor Design

C = C AO k 1 { 1 − e −( 1 k ) t } (3-189)
k + 2
k + )
B
( 1 k 2
Correspondingly, the solution for the concentration of C is

k
C = C AO 2 { 1 − e −( 1 k ) t } (3-190)
k + 2
k + )
C
( 1 k 2
Concentration profiles can be developed with time using the differential
Equations 3-180, 3-181, and 3-182, respectively, with the Runge-Kutta
fourth order method at known values of k and k for a batch system.
1
2
PSEUDO-ORDER REACTION

The results of the types of reaction being considered show that the
treatment of kinetic data becomes rapidly more complex as the reaction
order increases. In cases where the reaction conditions are such that
the concentrations of one or more of the species occurring in the rate
equation remain constant, these terms may be included in the rate
constant k. The reactions can be attributed to lower order reactions.
These types of reactions can be defined as pseudo-nth order, where n
is the sum of the exponents of those concentrations that change during
the reaction. An example of this type of reaction is in catalytic
reaction, where the catalyst concentration remains constant during
the reactions.
A kinetic study of a reaction can be simplified by running the
reaction with one or more of the components in large excess, so that
the concentration remains effectively constant. Mc Tigue and Sime [2]
consider the oxidation of aliphatic aldehydes such that ethanal with
bromine in aqueous solution follows second-order kinetics:

+
Br + CH CHO + H O → CH COOH + 2H + 2Br – (3-191)
3
2
2
3
The rate equation of the reaction for a constant volume batch system is
dC
− Br 2 = kC CH CHO C (3-192)
2
dt 3 Br 2