Page 65 - Elements of Chemical Reaction Engineering 3rd Edition

Sec. 2.2 Design Equations 37
2.2.2 Flaw Systems

Normally, conversion increases with the time the reactants spend in the
reactor. For continuous-flow systems, this time usually increases with increas-
ing reactor volume; consequently, the conversion X is a function of reactor vol-
ume ll If FA, is the molar flow rate of species A fed to a system operated at
steady state, the molar rate at which species A is reacting within the entire sys-
tem will be FAcIX.

moles of A fed moles of A reacted
.-
[FA, 1 . XI =
time mole of A fed
moles of A reacted
[FA0 XI = time

The molar feed rate of A to the system minus the rate of reaction of A within
the system equaZs the molar flow rate of A leaving the system FA. The preced-
ing sentence can be written in the form of the following mathematical state-
ment:

molar flow rate 1 [ molar rate at molar flow rate
which A is
[ at which Ais ] - consumed within at which A leaves
fed to the system the system
1 the system
['FAO 1 - [ - [F4 1
-
Rearranging gives

(:!-lo)

The entering molar flow rate, FA, (mol/s), is just the product of the entering
conceintration, CAo (mol/dm3), and the entering volumetric flow rate, u,
(dm3/ s) :

For liquid systems, CAo is commonly given in terms of molarity, for exarnple,
CAo = 2 mol/dm3. For gas systems, CAo can be calculated from the entering
temperature and pressure using the ideal gas law or some other gas law. For an
ideal gas (see Appendix B):