Page 180 - Modeling of Chemical Kinetics and Reactor Design

150 Modeling of Chemical Kinetics and Reactor Design

Examples of first-order reversible reactions are gas phase cis-trans
isomerization, isomerizations in various types of hydrocarbon systems,
and the racemization of α and β glucoses. An example of a catalytic
reaction is the ortho-para hydrogen conversion on a nickel catalyst.

SECOND ORDER REVERSIBLE REACTIONS

Bimolecular-type second order reactions are:

A + [ C + D (3-170)
k 1
B
k 2
1 k
2A[ C + D (3-171)
k 2

1 k
2A [ 2C (3-172)
k 2

k 1
B
A + [ 2 C (3-173)
k 2
With the restrictions that C AO = C and C = C DO = 0 in Equation
CO
BO
3-170, the rate equation for a constant volume batch system becomes

− ( r A ) =− dC A =C AO dX A = kC 2 A − k C 2 C (3-174)
1
2
dt dt
2
= kC 2 (1 − X ) − k 2 X 2
1 AO A A (3-175)
k 1
where the fractional conversion X = 0 at t = 0. At equilibrium,
A
dX /dt = 0 and the final solution is:
A
 X −(2 X − X ) 1   1 
ln  Ae Ae A  =2 kC AO  −1  t (3-176)
1
 X Ae − X A   X Ae 