Summarize briefly about :
give me answer in humanised only without using bullet pointsThe simultaneous internal diffusion and chemical reaction within a spherical catalyst pellet of
radius Rinvolves

Question

Summarize briefly about :
give me answer in humanised only without using bullet pointsThe simultaneous internal diffusion and chemical reaction within a spherical catalyst pellet of
radius Rinvolves a localized temperature gradient that modifies the effective diffusivity Diy.
The reaction is a non-isothermal, reversible first-order decomposition where the equiibrium
constant JK, is a sensitive function of the local radial temperature T(r).
Establish the effectiveness factor 1 by solving the coupled differential equations for mass and
energy balance: & [12 D, 7; 94] = k(T)C and
2 (120, 4Z] = (— AH)k(T) Ca. The Thiele modulus bis provided in the following
data array, representing the transition from kinetic control to strong pore-cliffusion resistance.
Dimensionless Radius € [ 0.0 [0.2 70.4 [0.6 [ 0.8 [0.0 [1.0 |
Local Thiele ¢(r) | 0.15 | 0.52 | 0.88 | 1.54 2.10 | 2.85 | 3.50
Calculate the global reaction rate if the surface concentration C5, = 2.0mol/m® and the
Prater number 8 = 0.05 at the pellet exterior.

VIPSolutions · Accepted Answer

This problem deals with a spherical pellet where both internal diffusion and chemical reaction occur at the same time, leading to a temperature gradient that affects how easily molecules can move (diffuse) inside the pellet. The reaction is reversible and its speed depends on temperature, which varies within the pellet. You’re asked to find the effectiveness factor by solving coupled equations for both mass and energy, considering how reaction and diffusion compete. The local Thiele modulus, which shows how much diffusion or reaction dominates at different points, is given in a table for different positions inside the pellet. Using the data provided, you're to calculate the overall reaction rate when the concentration at the surface and the Prater number (which reflects heat effects) are specified.

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