CHE 304 (Spring 2010) __________________
LAST NAME, FIRST
Problem set #8
(1) Run Heterogeneous Catalysis ( http://www.engin.umich.edu/~cre/icm/cre.html
)
Click on the CHE 304 distribution folder, then copy the Hetero folder to your flash drive or
H:\ drive. Open this folder and click on the appropriate program name (Heterogeneous
Catalysis.exe) . Turn in the last page of the program with performance number.
(2) (p. 3.28
2 ) An airborne spherical cellular organism, 0.015 cm in diameter ( D ), utilizes 4.5 mol
O
2
per hour, per kilogram of cell mass. Assume Sh = k m
D / D
AB
= 4 (based on D
AB
in the gas phase.) Assume zero-order kinetics for respiration. What is the concentration of O
2
at the center of the cell? The diffusion coefficient for O
2
through the cellular material is 10 and the diffusion coefficient for O
2
in air is 0.18 cm 2 /s at 298 o
-5 cm 2 /s
K. The equilibrium concentration ( C
A
) of O
2
in the cellular materials is related to the partial O
2
pressure ( p
A
) by the relation C
A
(mol/cm 3 ) = 7.0
 10 -6 p
A
(atm). Density of cell is 1 g/cm 3 .
(3) 1 Why do we grow cells in batch, competition between T cells and bacteria?
Typical reaction A B, but there may be contaminants in the feed stream, so you may get a little of C D, or C doesn’t react, but in general, the quantity of C does not grow. With Cells, A 2A, and with our contaminant, C 2C. If, during T cell expansion (10 days in batch culture), you initially started with 10 7 T cells, and only
10 E coli, what would be the ratio of bacteria to T cells at the end of the culture period? The rate constant for first order growth of T cells is 0.030 h -1 . The rate constant for first order bacterial growth is 0.46 h -1 .
(4) 2 The enzymatic hydrolization of fish oil extracted from crude eel oil has been carried out using lipase L. One of the desired products is docosa-hexamic acid, which is used as a medicine in China. For 40 mg of enzyme the Michaelis constant is 6.2
 10 -2 (mL/mL) and V
 mol/mL  min. The balance for fish oil is then given by max
is 5.6 dC s dt
= 
V max
K m

C s
C s
%
% where C s
is fish oil concentration in  mol/mL, and C s%
is fish oil concentration in mL of fish oil/mL of solution (vol %). Calculate the time necessary to reduce the concentration of fish oil from 1.4% to 0.2 vol %. The fish oil density is 0.9 g/cm 3 and its molecular weight is 300.
2 Middleman, An Introduction to Mass and Heat Transfer, Wiley, 1998, p.107
1 Fogler, H. S., Elements of Chemical Reaction Engineering, Prentice Hall, 1999
2 Fogler, H. S., Elements of Chemical Reaction Engineering, Prentice Hall, 1999

(5) 1 Beef catalase has been used to accelerate the decomposition of hydrogen peroxide to yield water and oxygen. The concentration of hydrogen peroxide is given as a function of time for a reaction mixture with a pH of 6.76 maintained at 30 o C. t (min)
C
H2O2
(mol/L)
0
0.02
10
0.01775
20
0.0158
50
0.0106
100
0.005 a) Determine the Michaelis Menten parameters V max
and K m
. b) If the total enzyme concentration is tripled, what will the substrate concentration be after 20 min?
(6) 1 Show that for uncompetitive inhibition r
P
= dC
P dt
= k
2
C
ES
=
K
M k
2
C
E 0
C
S

C
S

 1

C
I


=
K
M
 r max
C
S
C
S

 1

C
K
I
I


K
I
Let r max
= 20 mM/s, K m
= 10 mM, and K i
= 5 mM, using Matlab, plot (a) r
P
vs. C s
for C
I
= 10, 30, and 60 mM; (b) 1/ r
P
vs. 1/ C s
for C
I
= 10, 30, and 60 mM. You need to put your own name on the graph using the Matlab statement “ title ” to receive credit for this problem. ( Note: In the Matlab program given in the notes, change “Kmp” to “Km”, second “rp1” to “rp2”, third “rp1” to “rp3”, …)
(7) Endothelial cells 2 are present on the luminal surfaces of arteries and veins and are constantly exposed to blood flow. Laboratory studies of the response of endothelial cells to laminar flow have shown that the metabolism of ATP (Adenosine triphosphate) increases dramatically after the onset of shear stresses as low as 1 dyne/cm 2 . ATP is metabolized by enzymes that are present on the cell surface. Some have speculated that the rate of ATP metabolism is influenced by mass transfer. To assess whether this hypothesis is correct, a mathematical model has been used to analyze mass transfer and heterogeneous reaction on an endothelial cell layer cultured on the bottom surface of a flow chamber. For the concentration of ATP in blood, the metabolism of
ATP is a first-order surface reaction. Using the following data and Matlab, plot the ratio of reaction rate with mass transfer consideration to the reaction rate without mass consideration for
0.5 cm  L  10 cm. (See Example 5.1-1 p. 5-26). You need to put your own name on the graph using the Matlab statement “ title ” to receive credit for this problem. a
W
0.02 cm
2.5 cm
0.5 cm

L

10 cm
Gap height of the flow chamber
Width of the flow chamber
L k "
<
D v ij
>
0.005 cm/s
5 cm/s
2.6

10
-6
cm
2
/s
Length of surface on which endothelial cells are cultured
First-order heterogeneous rate constant
Average velocity
Diffusion coefficient of ATP in water
The average mass transfer coefficient can be estimated from the following correlation
1 Fogler, H. S., Elements of Chemical Reaction Engineering, Prentice Hall, 1999
2 Truskey G. A., Yuan F., and Katz D. F. Transport Phenomena in Biological Systems, Prentice Hall, 2004, pg. 485.

k f
= 1.4674
D ij


D La ij
 1/ 3

