Problem #2: In a diffusion-reaction system, reactant 'A' diffuses through a porous catalyst pellet and reacts in a 1st order reaction to produce 'B'. Efficacy of the catalyst in converting 'A' to 'B' is a function of x' such that the mass balance equation describing the system at steady-state is: d?C D dx? - k-C = 0 C is the concentration of 'A' that varies in the x-direction, k is the 1st order reaction rate constant, and D is the diffusion coefficient of 'A'. L is the thickness of the catalyst layer, and can be treated as a constant. First, non-dimensionalize the equation (e.g., assume x = x/L and y = C!Ca0) and then determine the approximate concentration distribution of 'A' in the catalyst layer using regular perturbation assuming that reaction rate is slow compared to diffusion, i.e., kL'ID (=ɛ) is very small. Assume the dimensionless concentration of 'A’ to have the following form: y = yo + ɛyı + s'y2. You will need to use the following boundary conditions: В.С. 1: В.С. 2: at x = 0; C = Cao or y = 1 at x = L; C= 0 or y = 0

Problem #2: In a diffusion-reaction system, reactant 'A' diffuses through a porous catalyst pellet and reacts in a 1st order reaction to produce 'B'. Efficacy of the catalyst in converting 'A' to 'B' is a function of x' such that the mass balance equation describing the system at steady-state is: d?C D dx? - k-C = 0 C is the concentration of 'A' that varies in the x-direction, k is the 1st order reaction rate constant, and D is the diffusion coefficient of 'A'. L is the thickness of the catalyst layer, and can be treated as a constant. First, non-dimensionalize the equation (e.g., assume x = x/L and y = C!Ca0) and then determine the approximate concentration distribution of 'A' in the catalyst layer using regular perturbation assuming that reaction rate is slow compared to diffusion, i.e., kL'ID (=ɛ) is very small. Assume the dimensionless concentration of 'A’ to have the following form: y = yo + ɛyı + s'y2. You will need to use the following boundary conditions: В.С. 1: В.С. 2: at x = 0; C = Cao or y = 1 at x = L; C= 0 or y = 0

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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