Apply the appropriate material balance equations to verify that the lever rule gives the relative amount of species in each phase along a tie line as depicted in Figure 8.2.

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Pressure Psys Psat Subcooled liquid Line segment v P-Ya Superheated vapor P-Xa Constant T Za yeq Vapor and liquid Line segment I Tie line Mole fraction a (a) Pxy Phase Diagram Lever rule: psat a Temperature Tboll T sys Superheated vapor Vapor and liquid Subcooled liquid eq The proportion of the amount of vapor to the amount liquid is given by the ratio of line segment v to line segment I Tie line V 1 Constant P Zeq yeq Mole fraction a (b) Txy Phase Diagram T-Ya T-Xa Tboil Figure 8.2 Phase diagrams for a binary mixture following Raoult's Law (a) Pxy diagram and (b) Txy diagram.