Question

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).

Answer 1

To determine the maximum rate of hydrolysis (Vmax), effectiveness factor (η), and Thiele modulus (Φ) in an enzyme-catalyzed reaction one can use the Michaelis-Menten kinetics and the provided data. changing the particle size from 2 mm to 4 mm would affect these values typically decreasing the effectiveness factor as diffusion becomes more of a limiting factor.

Step-by-step explanation:

The student has asked a question regarding a biochemical engineering problem, specifically the kinetics of enzyme hydrolysis. They have provided data about urease immobilized in Ca-alginate beads and the parameters involved in the urea hydrolysis reaction.To determine the maximum rate of hydrolysis (Vmax), one needs to use the given reaction rate (v) and the Michaelis constant (Km) along with the substrate concentration (S). When [S] >> Km, Vmax can be approximated by the observed rate v as the enzyme will be acting at its maximum capacity.The Thiele modulus (Φ) is a dimensionless number that compares the rate of reaction within a porous catalyst particle to the rate of diffusion into the particle. It is calculated using the formula Φ^2 = (R^2 * Vmax) / (D * Km), where R is the particle radius and D is the diffusivity of the substrate.

The effectiveness factor (η) describes the ratio of the actual reaction rate to the rate if the entire particle were at the bulk concentration. When Thiele modulus is large, η can be estimated using η ≈ 3 / Φ for spherical particles.When the particle size changes, these values will also change. The Thiele modulus is proportional to the radius of the particle, so doubling the diameter to 4 mm will increase Φ. The effectiveness factor will decrease as a result, indicating that not all active sites within larger particles are being used efficiently due to limitations in diffusion.