Physical Chemistry , 1st ed.

at that composition. Only when the vapor pressure reaches the surrounding

pressure will the two-component liquid be at its boiling point. (This detail is

important only for systems that are open and exposed to some external pres-

sure pext.)

Line AB in Figure 7.6 is called a tie line.It connects the liquid-phase com-

position with the resulting vapor-phase composition of the two components

in the system.

Suppose your system is set up in a way that you can condense the vapor

phase in a smaller subsystem. What would the composition of the new liq-

uid phase be? If you’re just condensing the vapors, then the composition of

the new liquid phase would be exactly the same as the original vapor phase.

Figure 7.7 shows that this new liquid phase can be represented on the bub-

ble point line at point C. But now this subsequent liquid phase also has an

equilibrium vapor phase, whose composition is given by the tie line CD in

Figure 7.7. This second vapor phase is even more enriched in one compo-

nent. If your system is set up to allow for multiple evaporations and con-

densations, each step between the bubble point line and the dew point line

generates a vapor and subsequent liquid phase that are progressively richer

and richer in one component. If the system is set up properly, ultimately you

will get liquid and vapor phases that are essentially pure single component.

The steps leading to this pure component are shown in Figure 7.8. What has

happened is that we have started from the two-component mixture and have

separated one component from the other. Such a procedure is called frac-

tional distillation,and it is particularly common in organic chemistry. Each

individual step, represented by a pair of horizontal and vertical lines, is called

a theoretical plate.In practice, systems that are set up to perform fractional

distillations can have as few as three or as many as tens of thousands of theo-

retical plates.

Figure 7.9 shows three setups for performing fractional distillations. The first

two are apparatus that you might see in lab, using either macroscale or microscale

glassware. The last is a fractional distillation apparatus on an industrial scale.

176 CHAPTER 7 Equilibria in Multiple-Component Systems

p* 2

p* 1

Partial pressure

0.5

B

A

C

D

x 1 , y 1

0.0 1.0

Composition

of second

vapor phase

Composition

of first vapor

and subsequent

liquid phase

Composition

of initial

liquid phase

Figure 7.7 A vapor phase will condense into a

liquid having the exact same composition, line

AC. But that new liquid will not vaporize into a

vapor having the same composition; rather, this

new liquid will be in equilibrium with a vapor

having composition D.

p* 2

p* 1

Partial pressure

0.5

x 1 , y 1

0.0 1.0

Figure 7.8 With repeated condensations and

evaporations, eventually a pure liquid can be

separated from the system. This is called frac-

tional distillation.