The enzyme urease is immobilized in Ca-alginate beads 2 mm in diameter. Find Vma

Question

The enzyme urease is immobilized in Ca-alginate beads 2 mm in diameter. Find Vmax, thielle modulus, and effectiveness factor. I only need part a done, as I can figure out part B on my own if I know how its done. I'm currently stuck because the posted solution by chegg is incorrect, supposedly the answer to a is Vmax = 14.9 mmol/h, phi=3.7, and n=.94

3.15. The enzyme. urease, is immobilized in Ca-alginate beads 2 mm in diameter. When the urea concentration in the bulk liquid is 0.5 mM the rate of urea hydrolysis is v 10 mmoles-l-h. Diffusivity of urea in Ca-alginate beads is D 1.5x10 5 cm2/sec, and the Michaelis constant for the enzyme is K 0.2 mM. By ncglccting thc liquid film resistance on the beads (i.e [Sol z ISJ) determine the following: a. Maximum rate of hydrolysis Vnt, Thiele modulus (D), and effectiveness factor (m). b. What would be the Vm, D, and n values for a particle size of Dp 4 mm? Hint: Assume m 3/ for large values of (O 2).

Explanation / Answer

thieles modules(MT)=L(k'/D)1/2

HERE L=R/3 , R=D/2=2/2=1mm

L=1/3=0.33MM=3.3*10^-4 m, given k'=.2mM,Dffusivity=1.5*10^-5cm2/s=1.5*10^-7 m2/s

MT=3.3*10^-4(0.2/(1.5*10^-7))1/2=0.38105

effectiveness factor=tanhMT/MT

=tanh(0.38105)/0.38105

=0.954255=95%

vmax-=0.5*10+10=15

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