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 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) (p. 3.28[2]) An airborne spherical cellular organism, 0.015 cm in diameter (D), utilizes 4.5 mol O2 per hour, per kilogram of cell mass. Assume Sh = kmD/DAB = 4 (based on DAB in the gas phase.) Assume zero-order kinetics for respiration. What is the concentration of O2 at the center of the cell? The diffusion coefficient for O2 through the cellular material is 10-5 cm2/s and the diffusion coefficient for O2 in air is 0.18 cm2/s at 298oK. The equilibrium concentration (CA) of O2 in the cellular materials is related to the partial O2 pressure (pA) by the relation CA(mol/cm3) = 7.0´10-6 pA(atm). Density of cell is 1 g/cm3.
Ans: CA(mol/cm3) = 2.98´10-7 at the center of the cell.
(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 107 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.
Ans: 6.6´1038
(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 Vmax is 5.6 mmol/mL×min. The balance for fish oil is then given by
= -
where Cs is fish oil concentration in mmol/mL, and Cs% is fish oil concentration in mL/mL (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/cm3 and its molecular weight is 300.
Ans: 7106 min
(5)[3] 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 30oC.
t (min) / 0 / 10 / 20 / 50 / 100CH2O2 (mol/L) / 0.02 / 0.01775 / 0.0158 / 0.0106 / 0.005
a) Determine the Michaelis Menten parameters Vmax and Km.
b) If the total enzyme concentration is tripled, what will the substrate concentration be after 20 min?
Ans:
a) Vmax = 6.39´10-4 mol/(L×min), Km = 0.0355 mol/L
b) 0.0092 mol/L
(6) Show that for uncompetitive inhibition
rP = = k2CES = =
Let rmax = 20 mM/s, Km = 10 mM, and KI = 5 mM, using Matlab, plot (a) rP vs. Cs for CI = 10, 30, and 60 mM; (b) 1/rP vs. 1/Cs for CI = 10, 30, and 60 mM. (Note: In the Matlab program given in the notes, change “Kmp” to “Km”, second “rp1” to “rp2”, third “rp1” to “rp3”, …)
Ans.
(7) Endothelial cells[4] 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/cm2. 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 asses 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, 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).
W
L
k"
v
Dij / 0.02 cm
2.5 cm
0.5 cm £ L £ 10 cm
0.005 cm/s
5 cm/s
2.6´10-6 cm2/s / Gap height of the flow chamber
Width of the flow chamber
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
kf = 1.4674Dij
Ans.
[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
[3] Fogler, H. S., Elements of Chemical Reaction Engineering, Prentice Hall, 1999
[4] Truskey G. A., Yuan F., and Katz D. F. Transport Phenomena in Biological Systems, Prentice Hall, 2004, pg. 485.