Thermodynamics and Chemistry

CHAPTER 12 EQUILIBRIUM CONDITIONS IN MULTICOMPONENT SYSTEMS

12.5 SOLID–LIQUIDEQUILIBRIA 384

0 0:2 0:4 0:6 0:8 1:0

240

250

260

270

280

xB

Tf

;A

=K

ut

ut

ut

ut

ut

bc

bc

bc

bc

bc

bc

Figure 12.4 Dependence on composition of the freezing point of binary liquid mix-

tures with benzene as component A.aSolid curve: calculated for an ideal liquid mix-

ture (Eq.12.5.2), taking the temperature variation ofÅsol,AH into account. Open

circles: B = toluene. Open triangles: B = cyclohexane.

aExperimental data from Ref. [ 122 ].

0:5

1

2

5

0

1

(^0) xB 1
Tf
;A
=T
f
Figure 12.5 Freezing-point curves of ideal binary liquid mixtures. The solid is com-
ponent A. Each curve is calculated from Eq.12.5.4and is labeled with the value of
Åfus,AH=RTf;A.
The result, after some rearrangement, is
lnxAD
Åfus,AH
R

1

Tf;A

1

Tf;A

!

(12.5.4)

(ideal liquid mixture,

Åsol,AHDÅfus,AH)

This equation was used to generate the curves shown in Fig.12.5. Although the shape of the
freezing-point curve (Tf;AversusxB) shown in Fig.12.4is concave downward, Fig.12.5
shows this is not always the case. WhenÅfus,AH=RTf;Ais less than 2 , the freezing-point
curve at lowxBis concaveupward.