Chemistry 232
Phase Diagram Questions
G. Marangoni
Date: April 17, 2012.
1.
Figure 1 gives the experimentally determined phase diagrams for the nearly ideal solution
of hexane and heptane.
a)
Label the regions of the phase diagram including the degrees of freedom F’.
b)
For a solution containing 1.0 mol each of hexane and heptane, estimate the vapour
pressure on the pressure-composition diagram when vapourization on reduction of
the pressure just begins.
c)
What is the vapour pressure of the solution on the pressure-composition diagram
when one drop of liquid remains?
d)
Estimate the compositions of the liquid and vapour phases in equilibrium in parts
b and c.
e)
A liquid mixture is composed of 3 moles of hexane and 2 moles of heptane. If the
pressure over the mixture, at what pressure does the first vapor form?
f)
What is the composition of the first trace of vapor formed?
g)
If the pressure is reduced further, at what pressure does the last trace of liquid
disappear and what is the composition of the last trace of liquid?
h)
What will be the pressure, the composition of the liquid, and the composition of
the vapor when 1 mole of the mixture has been vaporized? (Hint: Lever rule)
2.
Construct the solid-liquid phase diagram for the following system of A and B.
a)
The system exhibits one eutectic at xB = 0.37 and 233 K. The melting points of A
and B are 280 K and 260 K respectively.
b)
Describe the phase changes that take place when a liquid mixture of 3.0 mol of A
(melting point 280 K) and 2.0 mol of B (melting point 260 K) is cooled from 270
K to 220 K.
c)
Describe the phase changes that occur when a mixture of 4.0 mol of A and 1.0
mol of B are cooled from 300 K to 200 K.
3.
Draw and label completely the L/V phase diagram of the acetone chloroform system
given the following data.
a)
Only one liquid phase exists; there are no miscibility gaps.
b)
There is an azeotrope at 64.0 mole% chloroform with taze = 64.4 C.
c)
Pure acetone and chloroform boil at 56.1 and 61.2C respectively.
4.
Repeat question 2 above phase diagram using the temperature/composition diagram for
the hexane/heptane system.
2
Figure 1 – Pressure Composition and Temperature Composition Diagrams for n-Hexane/n-Heptane Mixtures
3
Answers
Question 1 and 4
4
Figure 1 gives the experimentally determined phase diagram for the nearly ideal solution of
hexane and heptane. (The answers for the 50:50 mixture are shown on the P-Z diagram; those
for the 40:60 mixture are shown on the T-Z phase diagram)
a) Label the regions of the phase diagram including the degrees of freedom F’
b) For a solution containing 1.0 mol each of hexane and heptane, estimate the vapour
pressure on the pressure-composition diagram when vapourization on reduction of the
pressure just begins. 625 Torr, y(hept) = 0.30
c) What is the vapour pressure of the solution on the pressure-composition diagram when
one drop of liquid remains? 490 Torr,
d) Estimate the compositions of the liquid and vapour phases in equilibrium in parts b and
c. x(hept) = 0.744; y(hept) = 0.30
e) A liquid mixture is composed of 3 moles of hexane and 2 moles of heptane. If the
pressure over the mixture is reduced, at what pressure does the first vapor form? 680
Torr
f) What is the composition of the first trace of vapor formed? y(hept) = 0.20
g) If the pressure is reduced further, at what pressure does the last trace of liquid disappear
and what is the composition of the last trace of liquid? 520 Torr, x(hept) = 0.68
h) What will be the pressure, the composition of the liquid, and the composition of the
vapor when 1 mole of the mixture has been vaporized? (Hint: Lever rule) 630 Torr;
x(hept) = 0.48; y(hept) = 0.27
i) Repeat the above for the temperature/composition diagram. For the 50:50 mixture,
78C, y(hept) = 0.28; 84C, x(hept) = 0.80. For the 40:60 mixture, 75C, y(hept) =
0.20; 82C, x(hept) = 0.60. Lever Rule satisfied at 77C; x(hept) = 0.60; y(hept) =
0.27.
5
Question 2
Solid Liquid Phase diagram for A + B
30
0
29
0
28
0
liquid, F' = 2
Part C
27
0
Part B
26
0
T/K
25
0
Solid A + liquid, F' = 1
Solid B + liquid, F' = 1
24
0
23
0
22
0
Solid A + Solid B, F' = 1
21
0
20
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
XB
In Part B, we begin with a liquid at 270 K; the mixture freezes at  240 K; at 238 K, we
have a solution of solid B in equilibrium with a solution of xB = 0.39; there is only a small
amount of solid precipitating out at that point since the distance ratio from the Lever rule,
l(solid)/l(liq), is very large.
In Part C, we begin with a liquid at 300 K; the mixture freezes at  258 K; at 250 K, we
have a solution of solid A in equilibrium with a solution of xB = 0.26; the ratio of liquid to
solid is about 3:1 from the Lever rule (n(liq) l(liq) = n(solid) l(solid)).
6
Question 3
70
Vapour
65
60
O
t/ C
L+V
L+V
55
Liquid
50
45
40
35
0
0.2
0.4
0.6
XChl
0.8
1