spnere hich A undergoes a first-order chemical reaction with rate constant k. At steady state, the diffusio = exactly balanced by the chemical reaction. O Show that the concentration profile is CRe CA In which Ris the radius of the sphere, Co is the molar solubility of A in B, and b' = k,R°/D O Show by quasi-steady-state arguments how to calculate the gradual decrease in diameter of th sphere as A dissolves and reacts. Show that the radius of the sphere is given by 1+ k, /D,R &CMA -(R-R,)-In D
spnere hich A undergoes a first-order chemical reaction with rate constant k. At steady state, the diffusio = exactly balanced by the chemical reaction. O Show that the concentration profile is CRe CA In which Ris the radius of the sphere, Co is the molar solubility of A in B, and b' = k,R°/D O Show by quasi-steady-state arguments how to calculate the gradual decrease in diameter of th sphere as A dissolves and reacts. Show that the radius of the sphere is given by 1+ k, /D,R &CMA -(R-R,)-In D
Chemistry
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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:A solid sphere of substance A is suspended in a liquid B in which it is slightly soluble, and with
which A undergoes a first-order chemical reaction with rate constant kj. At steady state, the diffusion
is exactly balanced by the chemical reaction.
a) Show that the concentration profile is
C RebR
In which R is the radius of the sphere, Co is the molar solubility of A in B, and b = k,R/DAn-
b) Show by quasi-steady-state arguments how to calculate the gradual decrease in diameter of the
sphere as A dissolves and reacts. Show that the radius of the sphere is given by
-(R-R,)-In-
VDA
1+ Jk/DR k,CMA
1+ k/D R
In which Ro is the sphere radius at time ta, and paph is the density of the sphere. What are the units
of k?
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