Page 148 - Elements of Chemical Reaction Engineering 3rd Edition

120 Rate Laws and Stoichiometry Chap. 3

Then
(1) Express P, and C, for all species as functions of conversion for a
constant-pressure batch reactor operated isothermally. Express vol-
ume as a function of X.
(2) Express P, and C, for all species as functions of conversion for a
constant-volume reactor. Express P, as a function of X.
(3) Express P, and C, for all species as functions of conversion for a
flow reactor.
(d) Referring to Section 3.4, write the combined mole balance and rate law
[cf. Equations (E3-9.8 and E3-9.9)] solely in terms of the molar flow
rates and rate law parameters. Assume elementary reaction.
P3-14B Reconsider the decomposition of nitrogen tetroxide discussed in Example 3-8.
The reaction is to be carried out in PFR and also in a constant-volume batch
reactor at 2 atm and 340 K. Only N204 and an inert I are to be fed to the reac-
tors. Plot the equilibrium conversion as a function of inert mole fraction in the
feed for both a constant-volume batch reactor and a plug flow reactor. Why is
the equilibrium conversion lower for the batch system than the flow system in
Example 3-8? Will this lower equilibrium conversion result always be the
case for batch systems?
P3-15, (a) Express the rate of formation of hydrogen bromide in terms of the con-
stants k, and k, and the conversion of bromine, X. Evaluate numerically
. all other quantities. The feed consists of 25% hydrogen, 25% bromine,
and 50% inerts at a pressure of 10 atm and a temperature of 400°C.
(b) Write the rate of decomposition of cumene, -r&, in terms of conversion,
initial concentration of cumene, and the specific rate and equilibrium
constants. The initial mixture consists of 75% cumene and 25% inerts.
P3-16, The gas-phase reaction
2A+4B --+ 2C

which is first-order in A and first-order in B is to be carried out isothermally
in a plug-flow reactor. The entering volumetric flow rate is 2.5 dm3/min, and
the feed is equimolar in A and B. The entering temperature and pressure are
727°C and 10 atm, respectively. The specific reaction rate at this temperature
is 4 dm3/g molamin and the activation energy is 15,000 cal/g mol.
(a) What is the volumetric flow rate when the conversion of A is 25%?
(Ans.: u = 1.88 dm3/min.)
(b) What is the rate of reaction at the entrance to the reactor
(i.e., X = O)? (Ans.: -rA = 1.49 X loe2 g mol/dm3.min.)
(c) What is the rate of reaction when the conversion of A is 40%?
(Hint: First express -r, as a function of X alone.)
(Ans.: -r, = 4.95 X g mol/dm3-min.)
(a) What is the concentration of A at the entrance to the reactor?
(Am.: CAo = 6.09 X g mol/dm3.)
(e) What is the concentration of A at 40% conversion of A?
(Ans.: C, = 6.09 X g mol/dm3.)
(0 What is the value of the specific reaction rate at 1227"C?
(Ans.: k = 49.6 dm3/g mol a mm.)
P3-17B Calculate the equilibrium conversion and concentrations for each of the fol-
lowing reactions.
(a) The liquid-phase reaction