Physical Chemistry Third Edition

6.6 Phase Diagrams of Nonideal Mixtures 283

Anazeotropic mixtureis sometimes called aconstant-boiling mixture, since it distills

without any change in composition. It is impossible to distill from one side of an

azeotrope to the other. For example, ethanol and water at 1.00 atm have an azeotrope

at an ethanol mole fraction equal to 0.90. Any mixture of ethanol and water can be

distilled to this composition, but no further.

Exercise 6.27

At 1.000 atm the boiling temperature of water is 100◦C and that of ethanol is 78.3◦C. The

azeotrope boils at 78.17◦C at this pressure.

a.Sketch the liquid–vapor temperature–composition phase diagram of ethanol and water.

b.By drawing a “staircase” of line segments representing distillation, as in Figure 6.7, show

that a distillation process beginning with a mole fraction of ethanol less than 0.90 cannot give

a distillate with an ethanol mole fraction greater than 0.90.

300

200

100

P

/torr

0

0

Mole fraction of ethanol

Azeotrope

Tie line

area

Tie line

area

Area of

liquid states

Coexisting

states of

two phases

Area of

vapor states

0.2 0.4 0.6 0.8 1

Figure 6.13 Liquid–Vapor Pressure–

Composition Phase Diagram of

Ethanol and Benzene, Showing an

Azeotrope. Drawn from data in J. Tim-

mermans, Physicochemical Constants

of Binary Systems, Vol. 2, Interscience

Publishers, New York, 1959, p. 61.

Area of liquid states

Tie line

areas

Azeotrope

Area of vapor states

65

t 60

/C

8 C

CHCl 3 mole fraction

55

0 0.2 0.4 0.6 0.8 1

Figure 6.14 Liquid–Vapor Tempera-

ture–Composition Phase Diagram of

Acetone and Chloroform.

If a binary mixture has a sufficiently large positive deviation from ideality, the

system at equilibrium can contain two liquid phases. Figure 6.15 shows schematically

the temperature–composition phase diagram of two hypothetical substances, called A

and B. Below the temperature labeledTcthere is a region of tie lines. A tie line in this

region connects points representing the compositions of the two liquids that can be at

equilibrium with each other. The compositions to the right or to the left of this region

are possible equilibrium compositions of a single liquid phase.

The highest point in the tie-line region at temperatureTcis called anupper critical

solution pointor anupper consolute point. It has a number of properties similar to

those of the gas–liquid critical point in Figure 1.5. If a mixture has the same overall

composition as that of the consolute point, it will be a two-phase system at a temperature

below the consolute temperature. If its temperature is gradually raised, the meniscus

between the phases becomes diffuse and disappears, in the same way that the meniscus

Area of vapor states

Tie line areas

(one vapor phase,

one liquid phase)

Area of states

of one liquid

Azeotrope

Consolute

point

Two coexisting

liquid states

Tie line

region –

two liquids

01

Mole fraction

T

Ta

Tc

Figure 6.15 Temperature–Composition Phase Diagram of a System with Liquid–

Liquid Phase Separation (Schematic).