Physical Chemistry , 1st ed.

(Darren Dugan) #1
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.
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