Physical Chemistry , 1st ed.

example, we can start with two pure components A and B, which have specific

melting points (MPs), as shown in the temperature-composition phase dia-

gram in Figure 7.21a. These mole fractions are represented by xA1 and xA

0, respectively. Starting from each side of the diagram, as each pure com-

ponent gets impure—that is, as we move from each side toward the middle of

the phase diagram—the melting point drops (Figure 7.21b). The phase dia-

gram represents this as a boundary line between a solid phase—either pure B

or pure A—in equilibrium with a liquid phase, as marked. As we get more and

more impure from either side, eventually the two solid-liquid equilibrium lines

will meet, as shown in Figure 7.21c. At this point, both solids A and B will

freeze.

Starting from either side of the phase diagram, the situation is very much

like a liquid-vapor phase change: one component will preferentially change

phase, and the other component will become more and more concentrated

within the remaining liquid. Until, that is, a certain composition labeled xEis

reached: then the two components will freeze simultaneously, and the solid

that forms will have the same composition as the liquid. This composition is

called the eutectic composition.At this composition, this liquid acts as if it were

a pure component, so the solid and liquid phases have the same composition

when in equilibrium at the eutectic temperature TE. This “pure component” is

called the eutectic.The eutectic is similar to the azeotrope in liquid-vapor

phase diagrams. Not all systems will have eutectics, some systems may have

more than one, and the composition of the eutectic(s) of a multicomponent

system is characteristic of the components. That is, you cannot predict a eu-

tectic for any given system.

Figure 7.21c therefore shows the behavior of the solid mixture of A and B

and how the solid and liquid phases behave with change in temperature. Below

the eutectic temperature TE, the system is a solid. Above the eutectic tempera-

ture, it may be either only a liquid phase (if at the eutectic composition), or a

combination of pure solid plus a liquid mixture.

Example 7.13

Figure 7.22a shows a phase diagram of two components, A and B. It also

shows two initial points, the dots M and N.

a.Explain the behavior of the components as the system starts at point M

and cools.

b.Explain the behavior of the components as the system starts at point N and

warms.

Solution

a.Point M represents a liquid having mostly component B, since the mole

fraction of A is approximately 0.1. As you go down the phase diagram verti-

cally, the two-component liquid drops in temperature until it reaches the

solid-liquid equilibrium line. At this point, pure component B solidifies, and

the remaining liquid actually gets more concentrated in component A. When

it reaches 0.2 mole fraction in A, the eutectic composition is reached and the

liquid solidifies as if it were a pure substance, continuing to cool as a eutec-

tic solid of A and B. Figure 7.22b shows a dotted-line path indicating these

changes.

b.Point N represents a solid phase having roughly equal parts of A and B. As

the temperature increases, eventually a point is reached in which component

190 CHAPTER 7 Equilibria in Multiple-Component Systems

MPB

MPA

TE

Temperature

xA

xE

01

(c)

Liquid (A + B)

Solid B +

liquid (A + B)

Solid A +

liquid (A + B)

Solid A and B

MPB

MPA

Temperature

xA

01

(b)

Liquid (A + B)

Solid B +

liquid (A + B) Solid A +

liquid (A + B)

MPB

MPA

Temperature

xA

01

(a)

Figure 7.21 Construction of a simple solid-
liquid phase diagram for a solid solution. (a) The
pure solid components have well-defined melting
points. (b) Moving in from either side, as some of
the other component is introduced, the melting
point drops. Above each line segment, the system
is in the liquid state. Below each line segment,
there is some liquid and some of the majority
component is freezing. (c) At some point, the two
lines will meet. Below this point, the system is
solid. The phase diagram can thus be divided into
areas of all solid, solid liquid, and liquid. The
two “solid liquid” regions have different com-
positions, however.