1. Liquid – Liquid, Liquid – Solid, Gas – Solid Equilibrium
Chapter 11

2. Applications
Distillation is the major application of vapor – liquid equilibrium
Larger variety of applications for other equilibria
Extraction
Decantation
Vapor Phase Deposition
Metallurgy

3. Liquid–Liquid Equilibrium
The most common combination is water and organic compounds
For a binary combination of liquids
Totally miscible
Partly miscibile
Practically Immiscible
Depends on molecular interactions

4. Solubility Data Temperature 0C Solubility of Benzene in Water
Solubility of Water in Benzene
0.04 mole%
0.133 mole% 20
0.252 mole% 50
mole%
0.664 mole% 70
mole%
1.19 mole%
Solubility usually increases with temperature

5. Practically Insoluble Liquid Pairs
Water is practically insoluble in hydrocarbons that do not contain oxygen or nitrogen
Those hydrocarbons are practically insoluble in water
Adding oxygen increases the solubility
Adding nitrogen further increases the solubility

6. Miscible Pairs
If we lower the number of carbons in an organic compound, we increase the solubility
The low molecular weight alcohols are completely miscible
Glycols are completely miscible

7. Other Miscible pairs Similar chemically
All straight chain liquid hydrocarbons are miscible with each other
Chlorinated hydrocarbons
Most molten metals
Many molten salts
They do not necessarily have an activity coefficient of one
Most form Type II solutions
May have an azeotrope

8. Ternary LLE Mixtures of three liquids Might be completely miscible
Might form three liquid phases, each primarily one of the species with small amounts of the other species dissolved
Might form two liquid phases
Water
Ethanol
Benzene
Completely miscible
Completely miscible
Immiscible pair

9. Three Component Phase Diagrams
So far we have only looked at 2 component phase diagrams (like those in chapter 8)
Three component phase diagrams can be very complicated – they require a three dimensional phase diagram
A 2-D slice can tell us a lot though

10. Z
80 %
60 %
40 %
20 %
Wt% X
80%
60%
40%
20%
20%
40%
60%
80%
Wt % Y
Wt% Z Y X

11. Pure Ethanol
One Phase Region
Two Phase Region
Pure Water
Pure Benzene

12. Tie lines connect equilibrium concentrations from each phase
Pure Ethanol
Not to Scale
The plait point represents the concentration where the compositions of the two phases becomes the same
Tie lines connect equilibrium concentrations from each phase
Plait Point
Tie Lines
Pure Water
Pure Benzene

13. Pure Ethanol
Not to Scale
What is the composition of each of the phases?
If the overall composition is: 40% benzene 40% water 20 % ethanol, How many phases are present?
How much of each phase? Use the lever law
Pure Water
Pure Benzene

14. Remember that solubility is temperature dependent
You need a triangular phase diagram like the one on the previous slide for each temperature (Figure 11.6)
For binary systems, a solubility diagram may be useful

15. Solubility is temperature dependant

16. Solubility temperature diagram
Single phase region
Solubilty diagrams that represent several different behavior patterns are shown in Figures 11.3, 11.4 and 11.5
Temperature
Two phase region
Mole fraction, xa

17. Elementary Theory of LLE
There is a lot of literature describing liquid- liquid equilibria
However, theoretical models give fair to good estimates of liquid-liquid behavior – and it’s a lot easier to calculate than to search through the literature.
Usually implemented on computers
Simplified calculations can be done by hand

18. Back to basics
The pure component vapor pressure is the same in each phase

19. This is true for any number of species and any number of liquid phases

20. Now consider only a binary system in two liquid phases
If the species under consideration are practically insoluble our math gets easier
If phase two is almost pure i, then it’s mole fraction is almost one and it’s activity coefficient is almost one in phase two
Section 8.5

21. This is a great way to find activity coefficients for practically insoluable species – but doesn’t work for species with intermediate solubility – our approach must go back to some sort of an activity coefficient estimating equation– Like the Van Laar equation or any of the equations described in Chapter 9. We’ll also need to return to Gibbs Free Energy calculations, like those in chapter 6.

22. Remember this?
xa=.833 in phase 2
xa=.166 in phase 1

23. Example 11.5 Consider a binary system, with compounds a and b
The pure species Gibbs free energies are:
ga0=2 kJ/mol
gb0=1 kJ/mol
Their liquid phase activity coefficients can be represented by the symmetric or two suffix Margules equation (Chapter 9) – which is simpler than the van Laar equation

24. Example 11.5 cont
Prepare a Gibbs free energy plot for this mixture at 298 K, for values of the constants in the activity coefficient correlation of:
a = 0
a = 1
a = 2
a = 3

25. Equation for Gibbs free Energy
Developed in Chapter 9
from the symmetric equation….
So… if we know a and x, we can find g of the mixture!!

26. The simplest case is for a=0
which means that the activity coefficient is 1 .. and we have an ideal solution!!
Ideal solutions do not separate into two liquid phases

27. a=0

28. What happens when a=1?
when xa is 1, γa is 1
when xa is 0, γa is 2.718

29. a=1

30. What happens when a=2?
when xa is 1, γa is 1
when xa is 0, γa is 7.389

31. a=2

32. What happens when a=3?
when xa is 1, γa is 1
when xa is 0, γa is 20.09

33. a=3

34. Two phase region

35. Remember that equality of the partial molal Gibbs free energy, is what determines the equilbrium
However, the values of pure component Gibbs Free energies does not influence whether or not there are two phases
This is the quantity usually plotted in figures

36. You can use this procedure with whatever activity coefficient equation matches the expermental data best
Example 11.6 asks us to:
Find the equilibrium compositions for the n-butanol water system at 92 C
Use the van Laar equation to find the activity coefficients

37. Two phase region

38. This approach only gives fair results
In the n-butanol - water example we predicted two phases with compositions of
0.47 water and .97 water
Experimental results show
0.67 water and 0.98 water
This is common – computer programs use more complicated activity coefficient correlations

39. Effect of pressure on LLE
Pressure has very little effect on liquid – liquid equilibria

40. Effect of temperature
Temperature has effect on the Gibbs Free energy of the mixture, and so we would expect it to have an effect on the solubility of liquids

41. Solubility is a function of temperature

42. Distribution coefficients
Consider a multi component system, like the benzene – ethanol – water system

43. Recall…

44. Thus…

45. Distribution Coefficients

46. Liquid Solid Equilibria
Solids often dissolve in liquids, but liquids rarely dissolve in solids
For example, consider salt (NaCl) and water
Solid NaCl dissolves in water
Water does not dissolve into the solid salt significantly
Solubility products are usually used to quantify solubilities

47. Effect of temperature
Solids are usually more soluble as the temperature goes up – but not always
Pressure rarely has a significant effect

48. Most solids increase in solubility with temperature
Gypsum becomes less soluble

49. Solid – Liquid Phase Diagrams
The salt – water phase diagram is fairly simple
It contains a eutectic point, and an intermediate compound
NaCl·2H2O

51. Iron-Iron Carbide Phase Diagram 1 atmFe
1% C
2% C
3% C
4% C
5% C
6% C
6.70% C
a, ferrite
g, austenite
d, ferrite
Molten Metal -- Liquid
γ + liquid
Eutectic
cementite + liquid
γ + cementite
γ + ferrite
Eutectoid
Cementite (Fe3C
ferrite + cementite

52. Gas – solid equilibria (GSE)
Pressure does not change the properties of the solid very much, but it does change the properties of the gas
Temperature affects the solid some – but it affects the gas significantly
First let’s look at low pressures

53. Low pressure GSE Very similar to VLE
sublimation instead of vaporization
ends at the triple point
We need tables of data, like the steam tables
The Antoine equation does not apply

54. Examples
If you hang your laundry out to “dry” when it is below freezing outside, eventually the lce sublimes
If you place a glass mug in the freezer it develops a layer of frost – vapor deposition
Vapor deposition is used industrially in the semiconductor business

55. GSE at High Pressures The gas is affected, not the solid
At pressures above the critical pressure, the resulting “dense fluid” or “supercritical fluid” display significantly different properties
They often serve as good solvents for solids
Supercritical fluids are used in the production of coffee to remove impurities that affect taste