Answered: 218 ac D 08 ac dr Solve for the…

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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Transcribed Image Text:ac at Da r² dr ac dr Solve for the concentration profile at steady state assuming a concentration C=0 as r →∞0 and C=C₁ at r = R (the surface of the sphere).

Expert Solution

Step 1

Steady state solutions can be applied when the concentration gradient may vary in space but does not change with time, ∂C/∂t=0. Under those conditions, the diffusion eq. (10.1.4) simplifies to Laplace’s equation

∇²C=0

For certain conditions this can be integrated directly by applying the proper boundary conditions, and then the steady state flux at a target position is obtained from Fick’s first law,

At steady state, we solve eq. by taking the diffusion to depend only on the radial coordinate r and not the angular ones.

We begin by assuming that the quantity in parenthesis is a constant and integrate twice to give:

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