chemistry 232 multicomponent phase equilibria. raoult’s law variation in the total vapour...
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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
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
3212=
2PcF
2222=
2PcF
A Liquid-vapour Phase Diagram
composition axis: )()(
)()(vapnliqnvapnliqn
Z AAA
PB*
ZA
PA*
vapour
liquid 3212=
2PcF
A Blow-up of the Two-phase Region
the lever rule: nl = l’n’
ZA
l’l
liquid
vapour
n n’
P
PB*
PA*
lliqlvap
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
xA yA
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
condense
condensea2
a’3
a’2
a3a4
a’4
250
300
350
400
450
500
0 0.2 0.4 0.6 0.8 1
a5
TA*
TB*
ZA
T / K
a1
boil
a2
a4Taze
a3
e’
condensea’5
a6
a’2
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
TUC - the upper critical temperature.
T / K
Tuc
XA
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 / KF`=2
XA
TLC
a’ l ’ a``l ``
tie-line
F`=1
Liquid-Liquid Phase Diagrams
Liquid-Liquid Phase Diagrams
A system exhibiting and upper and a lower critical solution temperature!
T / K
XA
TLC
TUC
The distillation of partially miscible liquids
Complete miscibility occurs before boiling commences.
T / K
ZA
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 1ZA
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 soutions.
where fus,AH = enthalpy of fusion of A TA and T*
A are the freezing points of the solution and pure A, respectively.
*,ln
AA
AfusA T
1T1
R
Hx
Compound A
310
320
330
340
350
360
370
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
The Liquidus Curve for B in A
For a solution of B in liquid A.
T/K
T*A
XA
liquid
solidliquidus curve
310
320
330
340
350
360
370
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
The Liquidus Curve for A in B
For a solution of A in liquid B.
T/KT*B
XA
liquid
solid
liquidus curve
300
310
320
330
340
350
360
370
380
0 0.2 0.4 0.6 0.8 1
XA
T (
K)
The S-L Phase Diagram
Overlapping the curves leads to the liquid-solid phase diagram for A and B.
liquid
solid B + solution
T*A
solid A + solid B
solid A + solution
eutecticT*B
310
320
330
340
350
360
370
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
XA
T (
K)
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.
liquid
solid B + solution
T*B
solid A + solid B
solid A + solution eutectic
tie line
T*A