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Chemistry 232
Multicomponent Phase Equilibria
Raoult’s Law

Variation in the total vapour pressure of
a two component liquid mixture
according to Raoult’s Law
PA*
liquid
vapour
PB*
XA
The Variation in Terms of Gas Phase
Mole Fractions

yA the vapour phase mole fraction
of A.
PA*
liquid
vapour
PB*
yA
A Liquid-vapour Phase Diagram

composition axis:Z
A

n A (liq )  n A (vap ) 
n (liq )  n (vap ) 
F c P 2
liquid
= 2 1  2  3
PA*
F c P 2
F c P 2
= 2 2 2  2
vapour
PB*
ZA
= 2 1  2  3
A Blow-up of the Two-phase Region
Moving Down an Isopleth

isopleth - constant total composition

lever rule:
nl = l’n’
450
350
P (torr)
liquid
n
300
a
b
c
l
l’
d
250
e
200
0.0
0.25
0.50
ZA
0.75
n’
vapour
1.00
Temperature-composition Phase
Diagrams
500
TB*
T/K
450
400
350
TA*
300
xA
250
0
0.2
yA
0.4
0.6
ZA
0.8
1
Simple Distillation of Liquid Mixtures

TB*
Vapour at composition a’2 is condensed, it
becomes richer in the more volatile
component.
500
450
T/K
400
a’2
a2
350
boil
300
condense
a1
250
0
0.2
0.4
0.6
ZA
0.8
a3
TA*
1
Fractional Distillations

Repeat the evaporation and condensation cycle!
Azeotropes

A low boiling azeotrope.
Azeotropes

A High Boiling Azeotrope
Liquid-Liquid Phase Diagrams

TUC - the upper critical temperature.
Tuc
T/K
F`=2
F`=1
tie-line
a’
l’
XA
l ``
a``
Liquid-Liquid Phase Diagrams

TLC - the lower critical temperature.
300
T/K
295
F`=2
290
a’
l’
l `` a``
F`=1
285
tie-line
280
275
270
TLC
265
260
XA
0
0.2
0.4
0.6
0.8
1
Liquid-Liquid Phase Diagrams

A system exhibiting and upper and a
lower critical solution temperature!
TUC
T/K
TLC
XA
The distillation of partially miscible liquids

Complete miscibility occurs before boiling
commences.
vapour
T/K
L+V
a’2
L+V
a2
1 phase
liquid
a1
2 phase
liquid
ZA
The distillation of partially miscible
liquids

Liquids remain immiscible even up
to the boiling temperature.
400
380
vapour
360
L+V
T/K
340
L+V
a
b
320
c
2 phase
liquid
300
1 phase
liquid
280
260
0
0.2
0.4
ZA
0.6
0.8
1
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 soutions.
fus , A H  1
1 


ln x A  

* 

R
TA 
T A


where fus,AH = enthalpy of fusion of A
TA and T*A are the freezing points of the solution
and pure A, respectively.
The Liquidus Curve for B in A

For a solution of B in liquid A.
Compound A
T*A
370
T/K
360
liquid
350
340
solid
330
liquidus curve
320
310
0
0.1
0.2
0.3
0.4
0.5
XA
0.6
0.7
0.8
0.9
1
The Liquidus Curve for A in B

For a solution of A in liquid B.
370
360
T/K
T*B
350
liquidus curve
340
330
liquid
solid
320
310
0
0.1
0.2
0.3
0.4
0.5
XA
0.6
0.7
0.8
0.9
1
The S-L Phase Diagram
Overlapping the curves leads to the
liquid-solid phase diagram for A and B.
380
liquid
370
T*A
360
eutectic
T*B
350
T (K)

340
solid A + solution
solid B +
solution
330
320
solid A + solid B
310
300
0
0.2
0.4
0.6
XA
0.8
1
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.
T*A
370
liquid
360
T*B
T (K)
350
tie line
eutectic
340
solid A + solution
solid B +
solution
330
320
solid A + solid B
310
0
0.1
0.2
0.3
0.4
0.5
XA
0.6
0.7
0.8
0.9
1
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