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Chemistry 232. Multicomponent Phase Equilibria. P A *. liquid. vapour. Raoult’s Law . Variation in the total vapour pressure of a two component liquid mixture according to Raoult’s Law . P B *. X A. The Variation in Terms of Gas Phase Mole Fractions.

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chemistry 232

Chemistry 232

Multicomponent Phase Equilibria

raoult s law

PA*

liquid

vapour

Raoult’s Law
  • Variation in the total vapour pressure of a two component liquid mixture according to Raoult’s Law

PB*

XA

the variation in terms of gas phase mole fractions
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
A Liquid-vapour Phase Diagram
  • composition axis:

liquid

PA*

vapour

PB*

ZA

moving down an isopleth
Moving Down an Isopleth
  • isopleth - constant total composition
    • lever rule: nl = l’n’

450

liquid

a

350

b

P (torr)

c

l’

n

300

n’

l

d

250

vapour

e

200

0.0

0.25

0.75

1.00

0.50

ZA

simple distillation of liquid mixtures
Simple Distillation of Liquid Mixtures
  • Vapour at composition a’2 is condensed, it becomes richer in the more volatile component.

TB*

a’2

T / K

a2

boil

condense

a1

TA*

a3

ZA

fractional distillations
Fractional Distillations
  • Repeat the evaporation and condensation cycle!
azeotropes
Azeotropes
  • A low boiling azeotrope.
azeotropes1
Azeotropes
  • A High Boiling Azeotrope
liquid liquid phase diagrams
Liquid-Liquid Phase Diagrams
  • TUC - the upper critical temperature.

Tuc

T / K

F`=2

F`=1

tie-line

a’

l ’

l ``

a``

XA

liquid liquid phase diagrams1
Liquid-Liquid Phase Diagrams
  • TLC - the lower critical temperature.

T / K

F`=2

a’

l ’

l ``

a``

F`=1

tie-line

TLC

XA

liquid liquid phase diagrams2
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
The distillation of partially miscible liquids
  • Complete miscibility occurs before boiling commences.

vapour

L + V

T / K

a’2

L + V

a2

1 phase

liquid

2 phase

liquid

a1

ZA

the distillation of partially miscible liquids1
The distillation of partially miscible liquids
  • Liquids remain immiscible even up to the boiling temperature.

vapour

L + V

T / K

L + V

a

b

c

1 phase

liquid

2 phase

liquid

ZA

liquid solid phase diagrams
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.
the liquidus curve for b in a
The Liquidus Curve for B in A
  • For a solution of B in liquid A.

T*A

T/K

liquid

solid

liquidus curve

XA

the liquidus curve for a in b
The Liquidus Curve for A in B
  • For a solution of A in liquid B.

T*B

liquidus curve

T/K

liquid

solid

XA

the s l phase diagram
The S-L Phase Diagram
  • Overlapping the curves leads to the liquid-solid phase diagram for A and B.

liquid

T*A

eutectic

T*B

solid A + solution

solid B +

solution

solid A + solid B

a blow up of the two phase region1
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

liquid

T*B

tie line

eutectic

solid A + solution

solid B +

solution

solid A + solid B