CHE 304 (Spring 2010)
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LAST NAME, FIRST
Problem set #6
(1)1 Run Tic Tac Toe (http://www.engin.umich.edu/~cre/icm/cre.html)
Click on the CHE 304 distribution folder, then copy the Tictac Race folder to your flash
drive or H:\ drive. Open this folder and click on the appropriate program name (Tic Tac
Toe.exe). Turn in the last page of the program with performance number.
2. (p. 3.562) A fermentation broth consists of an aqueous solution of nutrients and cells. As the
cells grow, they cluster into spherical pellets of radius R(t). On average, the cell density
inside a pellet is 0.02 mg of cell mass per cubic millimeter of pellet volume. The dissolved
oxygen concentration in the broth is 5 g/cm3. The cells utilize oxygen at a rate of 1.2 mmol
of oxygen per hour per gram of cell mass, via a zero-order reaction. Assume that the
diffusion coefficient DAB of oxygen within the pellet is 1.810-5 cm2/s. How large can R(t)
become before the oxygen concentration becomes zero at the center of a pellet? Assume that
the broth external to the pellets is well mixed. The cells and broth have densities close to that
of water.
3. Repeat problem (2), but allow for the presence of a finite convective resistance to mass
transfer to the surface of the pellet, such that the flux to the surface is given by
molar flux = kc(CP  CB)
where CB is the broth oxygen concentration and CP is the (unknown) concentration of oxygen
at the pellet surface. Calculate the critical value of R(t) (at which the oxygen concentration
becomes zero at the center of a pellet) for two cases: 2kcR/DAB = 2, and 2kcR/DAB = 20.
(4)1 The gaseous reaction A  B has a unimolecular reaction rate constant of 0.0015 min-1 at
80oF. This reaction is to be carried out in a parallel tubes 10 ft long and 1 in. inside diameter
under a pressure of 132 psig at 260oF. A production rate of 1000 lb/hr of B is required. Assuming
an activation energy of 25,000 cal/mol, how many tubes are needed if the conversion of A is to
be 90%? Assuming perfect gas laws. A and B each have molecular weights of 58.
(5)1 The irreversible elementary reaction 2A  B takes place in the gas phase in an isothermal
tubular reactor. Reactant A and a diluent C are fed in equimolar ratio, and conversion of A is
80%. If the molar feed rate of A is cut in half, what is the conversion of A assuming that the feed
rate of C is left unchanged? Assume ideal behavior and that the reactor temperature remains
unchanged.
(6)1 Compound A undergoes a reversible isomerization reaction, A  B, over a supported metal
catalyst. Under pertinent conditions, A and B are liquid, miscible, and of nearly identical density;
the equilibrium constant for the reaction (in concentration units) is 5.8. In an isothermal PFR, a
feed of pure A undergoes a net conversion to B of 55%. The reaction is elementary. If a second,
identical flow reactor at the same temperature is placed downstream from the first, what overall
conversion of A would you expect if:
(a) The reactors are directly connected in series?
2
1
Middleman, An Introduction to Mass and Heat Transfer, Wiley, 1998, p.107
Fogler, H. S., Elements of Chemical Reaction Engineering, Prentice Hall
(b) The products from the first reactor are separated by appropriate processing and only the
unconverted A is fed to the second reactor?
(7)1 It is desired to carry out the gaseous reaction A  B in an existing tubular reactor consisting
of 50 parallel tubes 40 ft long with a 0.75-in. inside diameter. Bench-scale experiments have
given the reaction rate constant for this first-order reaction as 0.00152 s-1 at 200oF and 0.0740 s-1
at 300oF. At what temperature should the reactor be operated to give a conversion of A of 80%
with a feed rate of 500 lb/hr of pure A and an operating pressure of 100 psig? A has a molecular
weight of 73. Departures from perfect gas behavior may be neglected, and the reverse reaction is
insignificant at these conditions.
(8) 1Consider the anaerobic fermentation of glucose to ethanol by yeast in a CSTR.
C6H12O6 + 0.0462 NH3  0.2309 CH1.74N0.2O0.45 + 1.6840 C2H5OH
+ 0.2021 C3H8O3 + 1.7948 CO2 + 0.0162 H2O
The growth of yeast cell mass concentration Cc can be described by the Monod relationship
dCc
CC
= Cc =  max s c
dt
K s  Cs
In this equation, Cs is the substrate or glucose concentration and the Monod constants are Ks
= 1.5 g/L and  max = 0.15 hr-1. The feed stream to the fermentor contains no yeast cells,
ethanol, or glycol. The concentration of glucose in the feed stream is 100 g/L. The fermentor
has a volume of 2000 L and the feed flow rate F to the fermentor is 100 L/hr. Calculate the
exiting concentrations of the yeast cells Cc, glucose Cs, ethanol Cet, and glycerol Cgly.