Page 296 - Introduction to chemical reaction engineering and kinetics

10.5 Problems for Chapter 10 277

(CE~ for each experiment was 0.039 g L-l):

cs,/mmol L-l 0.0097 0.016 0.021 0.034 0.065 0.14 0.32
(- rs,)lpmol L-l s-l 0.067 0.093 0.12 0.15 0.17 0.19 0.20

0 10-4 Calculate the maximum rate parameter, V,,,, and the Michaelis constant, Km, from these
data.
v
Phosphofructokinase is an enzyme that catalyzes one of the steps in the degradation of car-
‘7O.F
bohydrates. Initial rates of the
di- reaction that converts fructose-6-phosphate (S) to fructose-1,6-
phosphate (P) as a function of csO (the initial fructose-6-diphosphate concentration) are
as follows (the concentration of enzyme added, CEO, is the same in each case):

c& pm01 L-l 50 60 80 100 150 200 250 300 400
(-rsO)/ PmolL-’ min -l 61 65 72 77 84 88 90 93 95

Calculate the maximum rate parameter, Vmax, and the Michaelis constant, Km, from these
data (Bromberg, 1984, p. 923).
10-5 Repeat Example IO-1 using a linearized form of equation 10.3-1 that is alternative to the
0 10-6 form over the other. (There is more than one possible alternative form.)
linearized form 10.3-2 (the Lineweaver-Burk form). Comment on any advantage(s) of one
v
Suppose, at a particular temperature, results for the hydrolysis of sucrose, S, catalyzed by
‘7O-v
in a batch reactor are given by:
the enzyme invertase (CE~
= 1 X 10m5
mol L-l)
cs/mmol L-’ 1 0.84 0.68 0.53 0.38 0.27 0.16 0.09 0.04 0.018 0.006 0.0025
t/h 0 1 2 3 4 5 6 7 8 9 10 11
0 10-7 Show that the results conform to the Michaelis-Menten rate law, and determine the values
of the kinetics parameters V,,,, Km, and k,.
v
Benzyl alcohol can be produced from benzaldehyde (S) by a dehydrogenation reaction cat-
7O-v
alyzed by yeast alcohol dehydrogenase (YADH). Nikolova et al. (1995) obtained initial-rate
data for this reaction using immobilized YADH immersed in iso-octane with 1% v/v water.
The following data were obtained:

cs&mol L-l 0.50 1.0 2.0 3.0 5.0 7.5
(-rs,)/pmol mg(YADH)-’ h-l 0.58 1.2 2.7 3.3 4.6 5.2

Determine the kinetics parameters K,,, and V,,,,,, assuming that the standard Michaelis-
Menten model applies to this system, (a) by nonlinear regression, and (b) by linear regression
of the Lineweaver-Burk form.
10-8 Confirm (by derivation) the results given by
(a) equation 10.4-12;
(b) equations 10.4-13, -14;
(c) equations 10.4-15, -16, -17;
(d) equation 10.4-18.
10-9
Compare the Lineweaver-Burk linear forms resulting from the four cases in problem 10-8,
v
together with those given by equations 10.3-2 and 10.4-11. Note which cases have the same
7O-v
0 lo-10 In the production of L-DOPA from L-tyrosine (S) using tyrosinase (E) (Pialis, 1996; Pialis
and different intercepts and slopes. Sketch plots to show the relative magnitudes of both
intercepts and slopes.
and Saville, 1998),
the following data were obtained:
t/II 0 i 2 3 4 5 6 7
cs/mmol L-l 2.50 1.77 1.42 1.14 1.04 0.96 0.81 0.77