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T Section 12.7
One phase
220 C Two-Component
Liquid–Liquid Equilibrium
T
80 C
Figure 12.17
140 C Two phases Temperature-versus-composition
50 C Two phases liquid–liquid phase diagrams
for (a) water–triethylamine;
(b) water–nicotine. The horizontal
axis is the weight fraction of the
20 C 60 C organic liquid. In (b), the pressure
One phase One phase
of the system equals the vapor
pressure of the solution(s) and so
0 0.5 1 0 0.5 1
is not fixed.
w(C H N) w(C H N )
6 15
10 14 2
(a) (b)
in Sec. 8.3. In both cases, as the critical point is approached, the properties of two
phases in equilibrium become more and more alike, until at the critical point the two
phases become identical, yielding a one-phase system.
For certain pairs of liquids, decreasing temperature leads to greater miscibility, and
the liquid–liquid diagram resembles Fig. 12.17a. An example is water–triethylamine.
Occasionally, a system shows a combination of the behaviors in Figs. 12.16 and 12.17a,
and the phase diagram resembles Fig. 12.17b. Such systems have lower and upper crit-
ical solution temperatures. Examples are nicotine–water and m-toluidine–glycerol. The
lower critical solution temperatures in Fig. 12.17 are due to an increase in the hydro-
gen bonding between water and the amine as T decreases; see J. S. Walker and C. A.
Vause, Scientific American, May 1987, p. 98.
The two-phase regions in Figs. 12.16 and 12.17 are called miscibility gaps.
Although it is often stated that gases are miscible in all proportions, in fact sev-
eral cases of gas–gas miscibility gaps are known. Examples include CO –H O, NH –
2
2
3
CH , and He–Xe. These gaps occur at temperatures above the critical temperatures of
4
both components and hence by the conventional terminology of Sec. 8.3 involve two
gases. Most such gaps occur at rather high pressures and liquidlike densities; however,
n-butane–helium shows a miscibility gap at pressures as low as 40 atm. See R. P.
Gordon, J. Chem. Educ., 49, 249 (1972).

EXAMPLE 12.5 Phase compositions in a two-phase region
One
phase
Figure 12.18 shows the liquid–liquid phase diagram of water (W) plus 1-butanol
(B) at the vapor pressure of the system. Find the number of moles of each sub- Two
stance in each phase if 4.0 mol of W and 1.0 mol of B are shaken together at phases
30°C.
The overall x is (1.0 mol)/(5.0 mol) 0.20. At 30°C, the point x 0.20
B
B
lies in the two-phase region. Drawing a tie line at 30°C across the width of the
two-phase region, we get line RS. Let a and b denote the phases present. Point
b
a
R lies at x 0.02. Point S lies at x 0.48. We have
B
B
a a
b b
b
a
n n n x n x n
B
B
B
B
B
a
a
1.0 mol 0.02n 0.4815.0 n 2 Figure 12.18
a
b
n 3.04 mol, n 5.00 mol 3.04 mol 1.9 mol Butanol–water liquid–liquid phase
6
diagram at 1 atm.