Page 122 - Elements of Chemical Reaction Engineering 3rd Edition

Rate Laws and Stoichiometry Chap. 3

In gas-phase systems that we shall be studying, the temperatures and pressures
are such that the compressibility factor will not change significantly during the
course of the reaction; hence Zo = 2. For a batch system the volume of gas at
any time t is

Volume of gas for
a variable volume
batch reaction

Equation (3-38) applies only to a variable-volume batch reactor. If the reactor
is a rigid steel container of constant volume, then of course V = Vo. For a
constant-volume container, V = V,, and Equation (3-38) can be used to calcu-
late the pressure inside the reactor as a function of temperature and conversion.
An expression similar to Equation (3-38) for a variable-volume batch
reactor exists for a variable-volume flow system. To derive the concentrations
of the species in terms of conversion for a variable-volume flow system, we
shall use the relationships for the total concentration. The total concentration'at
any point in the reactor is

F~
C --=- p
T- u ZRT
At the entrance to the reactor,

Taking the ratio of Equatlon (3-40) to Equation (3-39) and assuming neg-
ligible changes in the compressibility factor, we have upon rearrangement

From Table 3-3, the total molar flow rate is

FT = FTo + FAo 6X
Substituting for FT in Equation (3-41) gives