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

= mole fraction of B in the alpha phase

= mole fraction of B in the beta phase

= mole fraction of B in the vapor 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 = (0.276 × ) + (0.81 × ) + (0.6 × 0.1)

0.7 = (0.276 × ) + (0.81 × ) + 0.06

• simultaneously solve the equations with unknown variables (the number of equations should equal the number of unknown variables)

0.7 = (0.276 × ) + (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