Urea dissolved in aqueous solution is degraded to ammonia and CO2 by the enzyme urease immobiliz

step 1 So here first under the given condition the surface concentration of urea is 200 mg per liter th

Urea dissolved in aqueous solution is degraded to ammonia...

Urea dissolved in aqueous solution is degraded to ammonia and $\mathrm{CO}_{2}$ by the enzyme urease immobilized on surfaces of nonporous polymeric beads. Conversion rate is controlled by transfer of urea to the surface of the beads through liquid film, and the conversion takes place on the surfaces of the beads. The following parameters are given for the system. $k_{L}=0.2 \mathrm{~cm} / \mathrm{s} ; K_{m}=200 \mathrm{mg} / 1$ $V_{m}^{\prime}=0.1 \mathrm{mg}$ urea/cm $^{2}$ support surface $-\mathrm{s}$. $S_{b}=1000 \mathrm{mg}$ urea/l a. Determine the surface concentration of urea. b. Determine the rate of urea degradation under mass transfer controlled conditions.

Urea dissolved in aqueous solution is degraded to ammonia and $\mathrm{CO}_{2}$ by the enzyme urease immobilized on surfaces of nonporous polymeric beads. Conversion rate is controlled by transfer of urea to the surface of the beads through liquid film, and the conversion takes place on the surfaces of the beads. The following parameters are given for the system.
$k_{L}=0.2 \mathrm{~cm} / \mathrm{s} ; K_{m}=200 \mathrm{mg} / 1$
$V_{m}^{\prime}=0.1 \mathrm{mg}$ urea/cm $^{2}$ support surface $-\mathrm{s}$.
$S_{b}=1000 \mathrm{mg}$ urea/l
a. Determine the surface concentration of urea.
b. Determine the rate of urea degradation under mass transfer controlled conditions.

Key Concepts

Mass Transfer Coefficient

This concept relates to the parameter that quantifies the rate at which a solute is transferred from the bulk fluid to a surface due to molecular diffusion and convection. It is essential in situations where the rate of a reaction is controlled not by the intrinsic kinetics at the catalyst surface but by the ability of the reactant to reach that surface.

Film Diffusion

Film diffusion refers to the transport of chemical species through a thin boundary layer (or film) adjacent to a solid surface. In systems where the reaction occurs at a surface (such as with immobilized enzymes), the thickness and properties of this film can limit how fast reactants are supplied to the active sites, thus controlling the overall reaction rate.

Michaelis?Menten Kinetics

Michaelis–Menten kinetics describe the rate of enzyme?catalyzed reactions as a function of substrate concentration, characterized by parameters such as Km (the substrate concentration at half?maximum velocity) and Vm (the maximum rate). In systems where enzymes are immobilized, these kinetics are integrated with mass transfer phenomena to determine the effective reaction rate.

Immobilized Enzyme Reactors

These reactors utilize enzymes that are fixed on solid supports, allowing for repeated or continuous use. The performance of such systems depends not only on the enzymatic kinetics but also on mass transfer characteristics, such as the rate of substrate diffusion from the bulk solution to the enzyme sites located on the support surfaces.

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