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Consider the diffusion of Li+ ions through a composite membrane. The membrane consists of three layers characterized by diffusion coefficients D₁ = 2.104 cm²/s, D₂ = 5.10-4 cm²/s, and D3 = 10-4 cm²/s, and thicknesses 8₁ = 0.1 cm, 82 = 0.2 cm, and 83 = 0.15 cm. Furthermore, the solubility of Lit in the central layer (2) is half that of the two other layers (1 and 2). Thus, a concentration of c₁ in layer 1 is in equilibrium with a concentration c₁/2 in layer 2 at the interface between 1 and 2, and similarly, a concentration c₂ in layer 2 is in equilibrium with 2 c2 in layer 3 at the interface between 2 and 3.

Consider the diffusion of Li+ ions through a composite membrane. The membrane consists of three layers characterized by diffusion coefficients D₁ = 2.104 cm²/s, D₂ = 5.10-4 cm²/s, and D3 = 10-4 cm²/s, and thicknesses 8₁ = 0.1 cm, 82 = 0.2 cm, and 83 = 0.15 cm. Furthermore, the solubility of Lit in the central layer (2) is half that of the two other layers (1 and 2). Thus, a concentration of c₁ in layer 1 is in equilibrium with a concentration c₁/2 in layer 2 at the interface between 1 and 2, and similarly, a concentration c₂ in layer 2 is in equilibrium with 2 c2 in layer 3 at the interface between 2 and 3.

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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Consider the diffusion of Li+ ions through a composite membrane. CA The membrane consists of three layers characterized by diffusion coefficients D₁ = 2.104 cm²/s, D₂ = 5.10-4 cm²/s, and D3 = 10-4 cm²/s, and thicknesses d₁ = 0.1 cm, 82 = 0.2 cm, and 83 = 0.15 cm. Furthermore, the solubility of Li+ in the central layer (2) is half that of the two other layers (1 and 2). Thus, a concentration of c₁ in layer 1 is in equilibrium with a concentration c₁/2 in layer 2 at the interface between 1 and 2, and similarly, a concentration c₂ in layer 2 is in equilibrium with 2°C₂ in layer 3 at the interface between 2 and 3. a) Derive the expression that describes the steady-state molar flux L across the composite wall as a function of the concen- tration difference between C3 and Co. b) Assuming that co is 1 mol/cm³ and c3 = 0 mol/cm³, calculate the magnitude of the steady-state Li* flux across this mem- brane. Co C1 202 C₁/2 C2 δι 52 03
Transcribed Image Text:Consider the diffusion of Li+ ions through a composite membrane. CA The membrane consists of three layers characterized by diffusion coefficients D₁ = 2.104 cm²/s, D₂ = 5.10-4 cm²/s, and D3 = 10-4 cm²/s, and thicknesses d₁ = 0.1 cm, 82 = 0.2 cm, and 83 = 0.15 cm. Furthermore, the solubility of Li+ in the central layer (2) is half that of the two other layers (1 and 2). Thus, a concentration of c₁ in layer 1 is in equilibrium with a concentration c₁/2 in layer 2 at the interface between 1 and 2, and similarly, a concentration c₂ in layer 2 is in equilibrium with 2°C₂ in layer 3 at the interface between 2 and 3. a) Derive the expression that describes the steady-state molar flux L across the composite wall as a function of the concen- tration difference between C3 and Co. b) Assuming that co is 1 mol/cm³ and c3 = 0 mol/cm³, calculate the magnitude of the steady-state Li* flux across this mem- brane. Co C1 202 C₁/2 C2 δι 52 03
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