A substrate S will be converted to a product P by an irreversible uni-molecular enzyme reaction with the Michaelis constant Km = 0.010 kmol m^-3 and the maximum rate Vmax = 2.0 x 10^-5 kmol m^-3 s^-1. 1. A substrate solution of 0.1 kmol m^-3 is reacted in a stirred-batch reactor using the free enzyme. Determine the initial reaction rate and the conversion of the substrate after 10 min. 2. Immobilized-enzyme beads with a diameter of 10 mm containing the same amount of the enzyme above are used in the same stirred-batch reactor. Determine the initial reaction rate of the substrate solution of 0.1 kmol m^-3. Assume that the effective diffusion coefficient of the substrate in the catalyst beads is 1.0 x 10^-6 cm^2 s^-1. 3. How small should the diameter of immobilized-enzyme beads be to achieve an effectiveness factor larger than 0.9 under the same reaction conditions, as in case (2)?
A substrate S will be converted to a product P by an irreversible uni-molecular enzyme reaction with the Michaelis constant Km = 0.010 kmol m^-3 and the maximum rate Vmax = 2.0 x 10^-5 kmol m^-3 s^-1.
1. A substrate solution of 0.1 kmol m^-3 is reacted in a stirred-batch reactor using the free enzyme. Determine the initial reaction rate and the conversion of the substrate after 10 min.
2. Immobilized-enzyme beads with a diameter of 10 mm containing the same amount of the enzyme above are used in the same stirred-batch reactor. Determine the initial reaction rate of the substrate solution of 0.1 kmol m^-3. Assume that the effective diffusion coefficient of the substrate in the catalyst beads is 1.0 x 10^-6 cm^2 s^-1.
3. How small should the diameter of immobilized-enzyme beads be to achieve an effectiveness factor larger than 0.9 under the same reaction conditions, as in case (2)?
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