CHE 304 (Spring 2010)
__________________
LAST NAME, FIRST
Problem set #10
(1) Run Heat Effects II (http://www.engin.umich.edu/~cre/icm/cre.html)
Click on the CHE 304 distribution folder, then ICMw, then Menu.exe. Click on the
appropriate program name on the menu. Turn in the last page of the program with
performance number.
(2)1 Run EnzymeMan (http://www.engin.umich.edu/~cre/icm/cre.html)
Click on the CHE 304 distribution folder, then ICMw, then Menu.exe. Click on the
appropriate program name on the menu. Turn in the last page of the program with
performance number.
(3) Consider a spherical organism of radius R within which respiration occurs at a uniform
volumetric rate of rA =  ko. That is, oxygen (species A) consumption is governed by a zeroorder, homogeneous chemical reaction.
(a) If a molar concentration of CA(R) = CA,0 is maintained at the surface of the organism, obtain
an expression for the radial distribution of oxygen, CA(r), within the organism. What is the
minimum value of CA,0 so that the solution will be applicable?
(b) Obtain an expression for the rate of oxygen consumption within the organism.
(c) Consider an organism of radius R = 0.10 mm and a diffusion coefficient for oxygen transfer
of DAB = 10-8 m2/s. If CA,0 = 510-5 kmol/m3 and ko = 1.210-4 kmol/sm3, what is the molar
concentration of O2 at the center of the organism?
Ans:
CA must be  0 at any location within the organism  CA 
ko R 2
6 DA
(b) Obtain an expression for the rate of oxygen consumption within the organism.
Rcons . = 4R3ko/3
(c) Consider an organism of radius R = 0.10 mm and a diffusion coefficient for oxygen transfer
of DAB = 10-8 m2/s. If CA,0 = 510-5 kmol/m3 and ko = 1.210-4 kmol/sm3, what is the molar
concentration of O2 at the center of the organism?
at r = 0, CA = CA,0 
ko R 2
6 DA
CA = 510-5 
(1.2  104 )(0.1  103 )2
= 310-5 kmol/m3
6  108
(4) The following data as obtained in a batch reactor for the yeast Saccharomyces cerevisicae
t(h)
CC(g/L)
CS(g/L)
dCC/dt(g/Lh)
0
1
250
0.30
1
1.39
245
0.45
2
1.93
238
0.63
3
2.66
229
0.87
4
3.7
216
1.21
6
7.12
197
2.32
8
13.7
94.4
4.42
(a) Determine the rate law parameter max and Ks, assuming the data can be described by
Monod Equation
dCC
 CC
= rg = max S C
dt
K S  CS
Use fminsearch with initial guess: max = 0.1 L/gh, Ks = 2 g/L
(b) Determine the rate law parameter max and k, assuming the data can be described by
Tessier Equation
dCC
C

= rg = max 1  exp   S
dt
 k

 C
 C

Use fminsearch with initial guess: max = 0.5 /h, k = 100 g/L
Plot out the experimental and calculated rg for both models on the same graph.
Ans:
Monod Equation
umax = 0.328438, Ks = 1.6943
Tessier Equation
umax = 0.32582, k = 20.4075
(5)1 Normal butane (A), C4H10, is to be isomerized to isobutane (B) in a plug-flow reactor5. The
reaction is to be carried out adiabatically in the liquid phase under high pressure using essentially
trace amount of a liquid catalyst, which gives a specific rate constant of 0.5 h-1 at 300oK.
Calculate the fractional conversion of a PFR with a volume of 2.0 m3 necessary to process 163
kmol/h of a mixture 80 mol % n-butane and 20 mol % i-pentane, which is considered an inert.
The feed enter at 330oK.
k


A k
B
b

Data: HRx =  6,900 J/mol, Cp,n-B = CpA = 141 J/moloK, Cp,i-B = CpB = 141 J/moloK, Cp,i-P =
k
161 J/moloK, activation energy = 65.7 kJ/mol, CA0 = 8.5 kmol/m3, Keq =
= 3.0 at 333oK.
kb
Ans: For V = 2 m3, X = 0.69343
(6) The hydrolysis of esters1, i.e., RCOOR’ + H2O  RCOOH + R’OH frequently is
catalyzed by acids. As the above hydrolysis reaction proceeds, more acid is produced and the
concentration of catalyst increases. This phenomenon, known as “autocatalysis,” is captured
by the rate equation
 rE = (k0 + k1[A])[E][H2O]
Here k0 is the rate constant in the absence of the organic acid that is produced by the
reaction. Given the following values:
E0 (ester concentration in feed) = 1.0 mol/L
W0 (water concentration in feed) = 1.0 mol/L
A0 (acid concentration in feed) = 0
[R’OH] (alcohol concentration in feed) = 0
k0 = 0.01 L/molh, k0 = 0.20 L2/mol2h
Assume that the reaction takes place in the liquid phase:
a)
Using Matlab plot 1/( rE) versus XE for 0  XE  0.7.
b)
What kind of continuous reactor system would you use if a final ester conversion
of 0.60 were desired, and if the reaction were to take place isothermally. Choose the
reactor or combination of reactors that has the smallest volume. Justify your answer.
5
1
Fogler, H. S., Elements of Chemical Reaction Engineering, Prentice Hall, 1999, pg. 454
Roberts, G. W., Chemical Reactions and Chemical Reactors, Wiley, 2006, pg. 59, P. 3-10
The smallest total reactor volume occurs when a CSTR and a PFR are used in series. The CSTR
comes first, and it is designed to operate at the value of XE at which 1/( rE) is a minimum (at XE
= 0.3). The PFR follows the CSTR
(7) Use Comsol Multiphysics to simulate an adiabatic reactor (Example 7.6-2 in the notes). Turn
in Figure 3, 4, 5, and 6 of this example.