Page 443 - Elements of Chemical Reaction Engineering Ebook

414 Nonelementary Reaction Kinetics Chap. 7

about 1.5%, the bacteria concentration is 10" cells/dm3, and the acid concen-
tration at which all metabolic activity ceases is 1.4% lactic acid.
(a) Determine the activation energy for the reaction.
(b) How long would it take to reach 1.10% acid at 38"F?
(c) If you left yogurt out at room temperature, 77"F, how long would it take
to reach 1.10% lactic acid?
(d) Assuming that the lactic acid is produced in the stationary state, do the
data fit any of the modules developed in this chapter?
[Problem developed by General Mills, Minneapolis, Minnesota]
P7-10, The enzymatic hydrolization of fish oil extracted from crude eel oil has been
carried out using lipase L (Proc. 2nd Joint ChindUSA Chemical Engineering.
Conference, Vol. 111, p. 1082, 1997). One of the desired products is docosa-
hexaenic acid, which is used as a medicine in China. For 40 mg of enzyme the
Michaelis constant is 6.2 X (mLlmL) and V,, is 5.6 pmol/mL. min.
Calculate the time necessary to reduce the concentration of fish oil from 1.4%
to 0.2 vol %. Note: There may be an inconsistency in the article. The half life
for an initial volume of 25% fish oil is stated to be 4.5 days. However, this
yields a different initial fish oil concentration one finds from looking in the lit-
erature. Search the web forjsh oil. Suggest a way to resolve this controversy.
P7-llB Beef catalase has been used to accelerate the decomposition of hydrogen per-
oxide to yield water and oxygen [Chem. Eng. Educ., 5, 141 (1971)l. The con-
centration of hydrogen peroxide is given as a function of time for a reaction
mixture with a pH of 6.76 maintained at 30°C.
t (min) I o 10 20 50 100

CHZo2 (mol/L) I 0.02 0.01775 0.0158 0.0106 0.005
(a) Determine the Michaelis-Menten parameters V,, and K,.
(b) If the total enzyme concentration is tripled, what will the substrate con-
centration be after 20 min?
(c) How could you make this problem more difficult?
P7-12B In this problem three different types of reaction inhibition are explored:
(a) In competitive inhibition, an inhibitor adsorbs on the same type of site as
the substrate. The resulting inhibitor-enzyme complex is inactive. Show
that the rate law for competitive inhibition
E+S <e E*S
E+I <I
E.1
E.S __$ E+P
is

(b) In uncompetitive inhibition the inhibitor attaches itself to enzyme-substrate
complex, rendering it inactive. Show that for uncompetitive inhibition,
E+S e
E*S
I+E-S e
IES
E-S P+E