Page 133 - Elements of Chemical Reaction Engineering 3rd Edition

Sec. 3.4 Expressing Concentrations in Terms Other Than Conversion 105

As expected, the dependence of reaction rate on conversion for a con-
stant-volume batch s,ystem [Le., Equation (E3-8.1 I)] is different than that for
a flow system [Equation (E3-8. lo)] for gas-phase reactions.

3.4 Expressing Concentrations in Terms
Other Tlhan Conversion
As we shall see later in the book, there are some instances in which it is much
more convenieint to work in terms of the number of moles (N,,N,) or imolar
flow rates (FA, F, , etc.) rather than conversion. Membrane reactors and
gas-phase multiple reactions are two such cases where molar flow rates rather
than conversion are preferred. Consequently, the concentrations in the rate
laws need to be expressed in terns of the molar flow rates. We start by recall-
ing and combining Equations (3-40) and (3-41):

Used for:
Multiple rxns
Membranes

to give

(3-47)

For the case of an ideal gas (2 = l), the concentration is

c, = -
FA
u
Substituting foir u gives

(3-48)

In general (j =c A, B, C, D, 1)

(3-45)

1
with the total molar flow rate given as the sum of the flow rates of the individ-
ual species:

F, = FA + F, + F, + FD + F, (3-49)
The molar flow rate of each species 5 is obtained from a mole balance on
each species.