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Binary Phase Diagrams
Chemistry 232
Raoult’s Law
Variation in the total vapour pressure of a two component liquid mixture according to Raoult’s Law
PB*
PA*
vapour
liquid
XA
The Variation in Terms of Gas Phase Mole Fractions
yA the vapour phase mole fraction of A.
PB*
yA
PA*
vapour
liquid
A Liquid-vapour Phase Diagram
composition axis: )vap(n)liq(n
)vap(n)liq(nZ AA
A
PB*
ZA
PA*
vapour
liquid
F c P
2
2 1 2 3 =
F c P
2
2 1 2 3 =
F c P
2
2 2 2 2 =
A Blow-up of the Two-phase Region
the lever rule: nl = l’n’
ZA
l’l
liquid
vapour
n n’
P
PB*
PA*
Moving Down an Isopleth
isopleth - constant total composition.
ZA
b
d
liquid
vapour
nn’
P (torr)
200
250
300
350
450
0.25 1.000.750.500.0
a
c
e
Temperature-composition Phase Diagrams
TA*
250
300
350
400
450
500
0 0.2 0.4 0.6 0.8 1
TB*
ZA
T / K
xAyA
Simple Distillation of Liquid Mixtures
Vapour at composition a’2 is condensed, it becomes richer in the more volatile component.
TA*
250
300
350
400
450
500
0 0.2 0.4 0.6 0.8 1
TB*
ZA
T / K
a1
boil condense
a2a’2
a3
Fractional Distillations
Repeat the evaporation and condensation cycle!
TA*
300
320
340
360
380
400
420
440
460
480
500
0 0.2 0.4 0.6 0.8 1
TB*
ZA
T / Ka1
yA
boilcondense
condensecondense
a2
a’3
a’2
a3
a4
a’4
250
300
350
400
450
500
0 0.2 0.4 0.6 0.8 1
TA*
TB*
ZA
T / K
a1
boil
a2
a4Taze
a3
e’
condensea’5
a6
a’2a5
a’6
Azeotropes
From the Greek - to boil unchanged. A low boiling azeotrope.
Azeotropes
A High Boiling Azeotrope
TA*
250
300
350
400
450
500
0 0.2 0.4 0.6 0.8 1
TB*
ZA
T / K
a1boil
a’2 a’5
Taze
a4
e’
boilcondense
a2
a3
a5
Liquid-Liquid Phase Diagrams
TUC - the upper critical temperature.
260
265
270
275
280
285
290
295
300
0 0.2 0.4 0.6 0.8 1
T / K
XA
Tuc
a’ l ’ a``l ``
tie-line
F`=2
F`=1
Liquid-Liquid Phase Diagrams
TLC - the lower critical temperature.
260
265
270
275
280
285
290
295
300
0 0.2 0.4 0.6 0.8 1
T / K
XA
TLC
a’ l ’ a``l ``
tie-line
F`=2
F`=1
Liquid-Liquid Phase Diagrams
A system exhibiting and upper and a lower critical solution temperature!
260265270275280285290295300305310
0 0.2 0.4 0.6 0.8 1
T / K
XA
TLC
TUC
The distillation of partially miscible liquids
Complete miscibility occurs before boiling commences.
260
280
300
320
340
360
380
400
0 0.2 0.4 0.6 0.8 1
ZA
T / K
vapour
1 phase liquid
2 phase liquid
L + V
L + V
a1
a2
a’2
The distillation of partially miscible liquids
Liquids remain immiscible even up to the boiling temperature.
260
280
300
320
340
360
380
400
0 0.2 0.4 0.6 0.8 1
ZA
T / K
vapour
1 phase liquid2 phase
liquid
L + VL + V
ba c
Liquid-Solid Phase Diagrams
Freezing points of solutions are dependent on the compositions of the solutions!
We have already examined briefly the freezing point depression of dilute solutions.
where fus,AH = enthalpy of fusion of A TA and T*
A are the freezing points of the solution and pure A, respectively.
*AA
A,fusA T
1
T
1
R
Hxln
For a solution of B in liquid A.
260
280
300
320
340
360
380
400
0 0.2 0.4 0.6 0.8 1
T/K
T*B
XA
liquid
solid
liquidus curve
For a solution of A in liquid B.
260
280
300
320
340
360
380
400
0 0.2 0.4 0.6 0.8 1
T/K
T*A
XA
liquid
solid
liquidus curve
Overlapping the curves leads to the liquid-solid phase diagram for A and B.
260
280
300
320
340
360
380
400
0 0.2 0.4 0.6 0.8 1
liquid
solid B + solution
T*A
solid A + solid B solid A + solution
XA
eutecticT*B
A Blow-up of the Two-phase Region
Tie lines connect the liquid phase of specified composition in equilibrium with either solid A or B.
320
330
340
350
360
370
380
0 0.2 0.4 0.6 0.8 1
liquid
solid B + solution
T*B
solid A + solid B solid A + solution
XA
eutectictie line
