## Description

Students will be lead through a classical chemical engineering problem: to calculate the concentration profile of cyclohexane within a catalyst pellet by solving a second order linear differential equation. Then students will analyze the concentration as the radius of the catalyst shrinks to zero. Finally, they will explore a Mathematica Module where they can explore the relationships between the various parameters within the problem. In particular, they will see that decreasing the radius of the catalyst pellet results in a lower chemical concentration at the center of the pellet than at the surface. An optional set of questions related to a hydrogel model for knee joint replacements, using similar mathematics, is also included.

A *catalyst *is a material which is capable of accelerating a chemical reaction without being consumed during the reaction process. Catalysts often consist of a porous material with high surface area, in which particles of a precious metal have been dispersed. Catalytic particles are often referred to as pellets. Surrounding each pellet, there is a thin gas film that contains a mix of reactants and products;

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