Page 118 - Introduction to chemical reaction engineering and kinetics

100 Chapter 5: Complex Systems

That is,

gf = CA = cAo c1 - fA>

and

gr = cD = CAofA
Hence, from equation 5.3-26,

Topt = Ml 1qfyl (5.3-27)

where fA = fA(%,max 7 ) and on solving equation (5.3-27) for fA, we have

fA(at rD,man) = [l + M2 exp(-MIW1-’ (5.3-28)

where

(5.3-29)

and

(5.3-30)
M2 = ArEArIAfEAf
(b) Whether the reaction is exothermic or endothermic, equation 5.3-15a can be written

rD = CA@f - (kf + kr)fAl (5.3-31)
from which

(d@fA)T = -c&f + k,) < o (5.3-32)

That is, ro decreases as fA increases at constant T.

The optimal rate behavior with respect to T has important consequences for the
design and operation of reactors for carrying out reversible, exothermic reactions. Ex-
amples are the oxidation of SO, to SO, and the synthesis of NH,.
This behavior can be shown graphically by constructing the rD-T-fA relation from
equation 5.3-16, in which kf, k,, and Ke4 depend on T. This is a surface in three-
dimensional space, but Figure 5.2 shows the relation in two-dimensional contour form,
both for an exothermic reaction and an endothermic reaction, with fA as a function of
T and (-rA) (as a parameter). The full line in each case represents equilibrium con-
version. Two constant-rate ( -I~) contours are shown in each case (note the direction
of increase in (- rA) in each case). As expected, each rate contour exhibits a maximum
for the exothermic case, but not for the endothermic case.

r
5 . 4 PARALhLkEACTIONS

A reaction network for a set of reactions occurring in parallel with respect to species A
may be represented by