Page 120 - Elements of Chemical Reaction Engineering 3rd Edition

92 Rate Laws and Stoichiometry Chap. 3

(3-29)
Therefore, for a given
rate law we have
-rA = g (x)

However, for gas-phase reactions the volumetric flow rate most often
changes during the course of the reaction due to a change in the total number
of moles or in temperature or pressure. One cannot always use Equation (3-29)
to express concentration as a function of conversion for gas-phase reactions.

3.3.4 Volume Change with Reaction

In our previous discussions, we considered primarily systems in which
the reaction volume or volumetric flow rate did not vary as the reaction pro-
gressed. Most batch and liquid-phase and some gas-phase systems fall into this
category. There are other systems, though, in which either V or u do vary, and
these will now be considered.
A situation in which a varying flow rate occurs quite frequently is in
gas-phase reactions that do not have an equal number of product and reactant
moles. For example, in the synthesis of ammonia,
N2+3H2 e
2NH3

4 mol of reactants gives 2 mol of product. In flow systems where this type of
reaction occurs, the molar flow rate will be changing as the reaction
progresses. Because only equal numbers of moles occupy equal volumes in the
gas phase at the same temperature and pressure, the volumetric flow rate will
also change.
Another variable-volume situation, which occurs much less frequently, is
in batch reactors where volume changes with time. Examples of this situation
are the combustion chamber of the internal-combustion engine and the expand-
ing gases within the breech and barrel of a firearm as it is fired.
In the stoichiometric tables presented on the preceding pages, it was not
necessary to make assumptions concerning a volume change in the first four
columns of the table (i.e., the species, initial number of moles or molar feed
rate, change within the reactor, and the remaining number of moles or the
molar effluent rate). All of these columns of the stoichiometric table are inde-
pendent of the volume or density and they are identical for constant-volume
(constant-density) and varying-volume (varying-density) situations. Only when
concentration is expressed as a function of conversion does variable density
enter the picture.
Individual concentrations can be determined by expressing the vdume V
for a batch system (or volumetric flow rate u for a flow system) as a function
of conversion using the following equation of state: