AB y yB A//x xB A(1yyA A )//x1 (A xA)
For a separation process in which α =1, the compositions of component A would be the same in both phases, separation is not possible when this occurs since the driving force for mass transfer is zero. When the value of α is above 1, a separation is possible. The value of α may change as concentration and total pressure change.
Diffusion in gases
• A simple theory for gases shows that D is proportional to the product of the average molecular velocity and the mean free path .
Boiling-Point Diagrams and x-y Plots
• the boiling-point diagram • x-y diagram
• maximum boiling azeotrope • minimum boiling azeotrope
7.2. Equilibrium-Stage Operations
• Raoult’s law applies to each component over entire concentration range, such mixtures are called ideal.
Relative Volatility of Vapor–Liquid Systems
• Definition
• The reciprocal of the overall resistance is an overall coefficient.
Chapter7.
7.1 Equilibrium Relations
Equilibrium data can be shown in tables, equations, or graphs.
7.1.1 gas-liquid equilibrium
• Henry's law
The equilibrium relation between partial pressure in the gas phase and xA The equilibrium relation between mole fraction in the gas phase and mole fraction in the liquid xA
• The Chapman-Enskog equation for binary diffusion
0 .0
D AB
0T 1 3 /2M 8A 5 M B 8/M A M B1 /2 PA 2 B D
Diffusion in liquids
• The diffusivities in liquids are generally 4 to 5 orders of magnitude smaller than in gases, but the fluxes for a given mole fraction gradient in liquid or gas may be nearly the same because of the much greater liquid densities.
D 1 u
3
• The mean free path for ideal gases varies inversely with pressure and increases with T1.0
• The mean molecular velocity depends on T0.5
D for ideal gases varies with T1.5 and varies inversely with pressure
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Equimolal diffusion
• For equimolal diffusion in gases, the net volumetric and molar flows are zero
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The concentration gradient for A is linear in the film, and the gradient for B has the same magnitude but the opposite sign
7.1.2 Vapor-Liquid Equilibrium Relations
• Raoult's Law
Equilibrium relation
• At low pressure the vapor of mixture approaches ideal behavior and fol• rectifying section • Stripping • Reboiler and vapor stream • Reflux • Total condenser and partial condenser • Vapor enriched in boiler • Liquid enriched in heavier boiler
Two-Film Theory
• In the two-film theory, equilibrium is assumed at the interface, and the resistances to mass transfer in the two phases are added to get an overall resistance, just as is done for heat transfer.