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

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

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

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 0.0474 mole% 0.664 mole% 70 0.0615 mole% 1.19 mole% Solubility usually increases with temperature

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

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

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

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

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

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

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

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

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

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

Solubility is temperature dependant

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

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

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

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

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

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.

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

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

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

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!!

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

a=0

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

a=1

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

a=2

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

a=3

Two phase region

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

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

Two phase region

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

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

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

Solubility is a function of temperature

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

Recall…

Thus…

Distribution Coefficients

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

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

Most solids increase in solubility with temperature Gypsum becomes less soluble

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

Iron-Iron Carbide Phase Diagram 1 atm Fe 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

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

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

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

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