HomeworkSolutions_C13

HomeworkSolutions_C13 - Homework Set # 13: The species...

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Homework Set # 13: The species equation of continuity Problem #1: (a) A solid sphere of substance A is suspended in a liquid B in which it is slightly soluble, and with which it undergoes a first-order chemical reaction with rate constant . At steady state, the diffusion is exactly balanced by the chemical reaction. Show that the concentration profile is 1 k ′′′ / 0 br R A b A C Re Cr e = In which R is the radius of the sphere, C A0 is the molar solubility of A in B (i.e. concentration of A at the sphere surface), and (hint: convert the molar balance of component A into a dimensionless form. Look for a solution of this dimensionless differential equation from the table below) 22 1 / bk R D = (b) Show by quasi-steady state arguments how to calculate the rate of decrease of in diameter of the sphere as A dissolves and reacts. Answer: (a) Because A is slightly soluble in liquid B, we may assume that the amount of reaction product is negligible, and that the total concentration of liquid B is constant. With these assumptions, the liquid mixture can be treated as a binary system. Therefore, the
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This note was uploaded on 09/01/2011 for the course PGE 312 taught by Professor Peters during the Fall '08 term at University of Texas.

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HomeworkSolutions_C13 - Homework Set # 13: The species...

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