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# Vapor-Liquid-Liquid Equilibrium (VLLE)

This Demonstration shows the phase equilibrium for a binary system of two partially miscible liquids, A and B. Because of the partial miscibility, vapor-liquid equilibrium (VLE), liquid-liquid equilibrium (LLE), and vapor-liquid-liquid equilibrium (VLLE) are present on the phase diagram. You can vary the mole fraction of component B and the heat added (location of the black dot). The heat added changes the temperature, except when at 77C, where all three phases are in equilibrium: liquid (), liquid (), and vapor (). At this temperature, one phase must completely evaporate (or condense if removing heat) before the temperature increases (or decreases). The amount of heat added is used to illustrate the system behavior and to show how at 77C all three phases exist. The relative amounts of each phase are determined from the lever rule (mole balance) and shown in the bar graph. The mole fraction(s) of component B in each phase are also displayed on the bar graph, for the phases present. In the multiple phase regions, dashed lines in the diagram show what the mole fraction of B is where the vertical lines cross the x-axis.

### DETAILS

The relative amounts of each phase in the two-phase regions are found using the lever rule. An example of using the lever rule in the liquid plus liquid region is given by the following equations:
relative amount of liquid ,
relative amount of liquid ,
where is the overall mole fraction of the mixture (the mole fraction of the point in the diagram).
When the system is in vapor-liquid-liquid equilibrium, the relative amounts of each phase are found from mass balances. For example, using 10% vaporization and an initial mole fraction of B of 0.7 in the diagram:
• determine the initial mole fraction of B
• determine the mole fraction of component B in each phase
• set a basis for the amount of total moles in the system
total moles = 1
• determine the percentage of vaporization
percent vaporization = 10%
• determine the amount of vapor in the system
= (percent of vaporization) × (total moles) = 0.1 × 1 = 0.1
• perform a mole balance on the whole system
total moles = vapor + liquid + liquid
• perform a mole balance on component B
× total moles = ( × ) + ( x ) + ( x V)
0.7 × 1 = (0.275 × ) + (0.81 × ) + (0.6 × 0.1)
0.7 = (0.275 × ) + (0.81 × ) + 0.06
• simultaneously solve the equations with unknown variables (the number of equations should equal the number of unknown variables)
0.7 = (0.275 × ) + (0.81 × ) + 0.06
• relative amounts of each phase
= 0.166 = relative amount of liquid phase
= 0.734 = relative amount of liquid phase
= 0.1 = relative amount of vapor

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