Uric acid is degraded by uricase enzyme immobilized in...

Uric acid is degraded by uricase enzyme immobilized in porous Ca-alginate beads. Experiments conducted with different bead sizes result in the following rate data: $\begin{array}{lllllllll}\text { Bead Diameter, Dp }(\mathrm{cm}) & 0.1 & 0.2 & 0.3 & 0.4 & 0.5 & 0.6 & 0.7 & 0.8 \\ \text { Rate, } v(\mathrm{mg} / \mathrm{l} . \mathrm{h}) & 200 & 198 & 180 & 140 & 100 & 70 & 50 & 30\end{array}$ a. Determine the effectiveness factor for particle sizes $D p=0.5 \mathrm{~cm}$ and $D p=0.7 \mathrm{~cm}$. b. The following data were obtained for $\mathrm{Dp}=0.5 \mathrm{~cm}$ at different bulk uric acid concentrations. Assuming negligible liquid film resistance, calculate $V_{m}$ and $K_{x}$ for the enzyme. Assume no substrate or product inhibition. $\begin{array}{llllrrr}\mathrm{S}_{0}(\mathrm{mg} \text { UA/1) } & 10 & 25 & 50 & 100 & 200 & 250 \\ v(\mathrm{mg} \text { UA } / \mathrm{L} . \mathrm{h}) & 10 & 20 & 30 & 40 & 45 & 46\end{array}$

Uric acid is degraded by uricase enzyme immobilized in porous Ca-alginate beads. Experiments conducted with different bead sizes result in the following rate data:
$\begin{array}{lllllllll}\text { Bead Diameter, Dp }(\mathrm{cm}) & 0.1 & 0.2 & 0.3 & 0.4 & 0.5 & 0.6 & 0.7 & 0.8 \\ \text { Rate, } v(\mathrm{mg} / \mathrm{l} . \mathrm{h}) & 200 & 198 & 180 & 140 & 100 & 70 & 50 & 30\end{array}$
a. Determine the effectiveness factor for particle sizes $D p=0.5 \mathrm{~cm}$ and $D p=0.7 \mathrm{~cm}$.
b. The following data were obtained for $\mathrm{Dp}=0.5 \mathrm{~cm}$ at different bulk uric acid concentrations. Assuming negligible liquid film resistance, calculate $V_{m}$ and $K_{x}$ for the enzyme. Assume no substrate or product inhibition.
$\begin{array}{llllrrr}\mathrm{S}_{0}(\mathrm{mg} \text { UA/1) } & 10 & 25 & 50 & 100 & 200 & 250 \\ v(\mathrm{mg} \text { UA } / \mathrm{L} . \mathrm{h}) & 10 & 20 & 30 & 40 & 45 & 46\end{array}$

Key Concepts

Enzyme Immobilization

Enzyme immobilization involves fixing enzymes to a support or matrix, which allows them to be reused and facilitates separation from the reaction mixture. This technique can impact the enzyme’s microenvironment, leading to potential changes in activity, stability, and mass transfer characteristics that are critical in biochemical reactions and industrial applications.

Effectiveness Factor

The effectiveness factor is a measure of how effectively an immobilized enzyme or catalyst particle is being utilized. It is defined as the ratio between the actual observed reaction rate inside the catalyst particle and the rate that would be achieved if the entire particle were operating at the external bulk concentration. This concept highlights the extent of internal mass transfer limitations within porous structures.

Internal Diffusion Limitations

Internal diffusion limitations refer to the resistance to the transport of substrates and/or products within the pores of a catalyst particle. In immobilized enzyme systems, these limitations can lead to gradients in substrate concentration, causing the reaction rate within the pores to be lower than the rate at the particle’s surface, thereby affecting the overall efficiency of the process.

Thiele Modulus

The Thiele modulus is a dimensionless number that characterizes the balance between the reaction rate and the rate of diffusion within a porous catalyst. It provides insight into whether a reaction is limited by kinetics or by diffusion, and is critical for predicting and optimizing the performance of immobilized enzyme or catalyst systems.

Michaelis-Menten Kinetics

Michaelis-Menten kinetics describe the rate of enzymatic reactions by relating the reaction rate to the concentration of substrate available. The model provides two parameters—Vmax (the maximum reaction rate) and Km (the substrate concentration at which the reaction rate is half of Vmax)—that are essential for understanding the efficiency and behavior of enzyme-catalyzed processes under varying substrate concentrations.

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