Physical Chemistry Third Edition

290 6 The Thermodynamics of Solutions

eutectic point, the compositions of the three phases are not variable at constant

pressure.

Exercise 6.30

a.Describe what happens when LaCu 4 melts.

b.For each area in Figure 6.22 and for each tie line connecting three phases, tell what phase or

phases occur and give the number of independent intensive variables.

12

X 2

X 3

X 1

3

Figure 6.23 Mole Fractions of a
Three-Component System Plot-
ted in an Equilateral Triangle.

Three-Component Phase Diagrams

For three components a complete phase diagram would require four dimensions,

representingT,P, and two mole fractions. If the pressure is held fixed, a temperature–

composition phase diagram is obtained that requires three dimensions. If the temper-

ature and the pressure are both held fixed we have a composition–composition phase

diagram with two independent mole fractions and one dependent mole fraction. Instead

of plotting the two independent mole fractions on two perpendicular axes, an equilat-

eral triangle is customarily used to plot the mole fractions, as depicted in Figure 6.23. A

theorem of plane geometry asserts that the sum of the three perpendicular distances to

the sides of an equilateral triangle has the same value for any point inside the triangle. If

the size of the triangle is chosen so that this sum equals unity, these three perpendicular

distances can represent the three mole fractions. Each vertex of the triangle represents

a pure component.

Figure 6.24 shows the composition–composition phase diagram of water, acetone,

and ethyl acetate for a constant temperature of 30◦C and a constant pressure of 1.00 atm.

There is a one-phase region of complete miscibility and a two-phase region containing

tie lines, representing the compositions of two liquid phases that coexist at equilibrium.

Since all points in the diagram correspond to the same temperature and pressure, the

tie lines must remain in the plane of the diagram but are not required to be parallel to

each other. Their directions must be determined experimentally.

One

liquid

Tie

lines

Two liquids

with compositions

at ends of tie lines

Water (1) Ethyl

acetate (2)

Acetone (3)

Figure 6.24 Liquid Composition–Composition Phase Diagram of Water, Acetone,

and Ethyl Acetate at 1 atm and 30◦C.