1. ERT 108 : PHYSICAL CHEMISTRY Phase Diagrams
By; Mrs Hafiza Binti Shukor
ERT 108/3 PHYSICAL CHEMISTRY
SEM 2 (2010/2011)
By; Mrs Hafiza Binti Shukor

2. Subtopics Definitions The Phase Rule Two-component Systems:
Vapour pressure Diagrams
Temperature-composition Diagrams
Liquid-liquid Phase Diagrams
Liquid-solid Phase Diagrams
ERT 108/3 PHYSICAL CHEMISTRY
SEM 2 (2010/2011)

3. Definitions
A phase of a substance is a form of matter that is uniform throughout in chemical composition & physical state (solid, liquid, gas).
The number of phases in a system is denoted P.
A solution of NaCl in water is a single phase (P=1).
A slurry of ice & water is two-phase system (P=2).
A calcium carbonate system undergoes thermal deposition – two solid phase (CaCO3 & CaO)
one gaseous phase (CO2) so, Total: (P=3)
An alloy of two metals is a two-phase system (P=2) if they are immiscible but a single-phase system (P=1) if they are miscible.
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4. A mixture of ethanol & water – Two constituents.
A phase transition is the spontaneous conversion of one phase into another phase occurs at a characteristics temperature for a given pressure.
Constituent – a chemical species (an ion or a molecule) that is present.
A mixture of ethanol & water – Two constituents.
A solution of sodium chloride – Three constituents
(water, Na+ ions & Cl- ions).
Component – a chemically independent constituent of a system. Each phase in the system may be considered to be composed of one or more components. The number of components in the system must be the minimum required to define all of the phases.
For example, in our system salt and water, we might have the components Na, Cl, H, and O (four components), NaCl, H, and O (three components), NaCl and HO (two components), or NaCl-H2O (one component). However, the possible phases in the system can only consist of crystals of halite (NaCl), H2O either liquid or vapor, and NaCl-H2O solution. Thus only two components (NaCl and H2O) are required to define the system, because the third phase (NaCl - H2O solution) can be obtained by mixing the other two components
Phase Diagram – one of the most ways of presenting the physical changes of state that a substance can undergo.
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5. The Phase Rule
Phase rule – relation between the degree of freedom or variance (F), the number of component (C) & the number of phases at equilibrium (P) for a system of any composition:
In a system of solid sucrose in equilibrium with an aqueous solution of sucrose:
the system has two components (C) – water & sucrose.
the system has two phases (P) – solution & solid sucrose
the degree of freedom (F) = 2 – = 2
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6. Such system is has two degrees of freedom.
Variance (F) – the number of intensive variables (P, T & mole fractions in each of the phases) that can be changed independently without disturbing the number of phases in equilibrium.
In a single-component, single phase system (C=1, P=1), the P & T may be changed independently without the number of phases – F = C-P+2=1-1+2=2.
Such system is has two degrees of freedom.
If two phases are in equilibrium (a liquid & its vapor) in a single component system (C=1, P=2), the change of T & P can demands an accompanying change in P (or T) to preserve the number of phases in equilibrium ,F=C- P+2=1-2+2=1.
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7. Two-component systems
When two components are present in a system:
C = 2, ……….F=C-P+2= 2-P+2=4-P.
If the temperature is constant, F = 3-P (which max value of 2).
One of these two remaining F – P & composition (mole fraction of one component).
One form of the phase diagram is a map of P & compositions at which each phase is stable.
Alternatively, the pressure could be held constant & the phase diagram depicted in terms of T & composition.
ERT 108/3 PHYSICAL CHEMISTRY
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8. Example 1
There are Three phases ( 2solid phase + 1 gaseous phase) & Three constituents.
To specify the composition of Phase 3 – need CO2
To specify the composition of Phase 2 – need CaO
To specify the composition of Phase 1 – do not need an additional species (stoichiometry).
The system has only Two components (C=2).
ERT 108/3 PHYSICAL CHEMISTRY
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9. Example 2
In a system in which ammonium chloride undergoes thermal decompositaion:
How many phases & constituents in the system?
How many components are present in the system?
There are Three constituents & Two phases (one solid & one gas).
NH3 & HCl are formed in fixed stoichiometric proportions by the reaction.
The compositions of both phases can be expressed in terms of the single species NH4Cl.
It follows that there is only one component in the system (C=1).
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10. Vapour Pressure Diagrams
Raoult’s law:
Used to calculate the total vapour pressure of a binary system of 2 volatile liquids.
Dalton’s law:
Used to calculate the composition of the vapour in equilibrium with a binary system
Lever Rule
Used to deduce the relative abundances of each phase in equilibrium
The compositions of the vapour and the liquid phase in equilibrium are located at each end of a tie line
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11. So, total vapour pressure,P of the mixture is:
The partial pressure of the components of an ideal solution of two volatile liquids are related to the composition of the liquid mixture ( by Roult’s Law)
So, total vapour pressure,P of the mixture is:
It shows that the total vapour pressure change linearly with the composition from P*B to P*A as XA change from 0 to 1
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12. The composition of the vapour
The composition of the liquid & vapour that are in mutual equilibrium are not necessarily the same.
The vapour should be richer in the more volatile component.
The mole fraction in the gas:
Provided the mixture is ideal:
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13. The composition of the vapour
In all cases, yA>xA, the vapour is richer than the liquid in the more volatile component.
If B is non-volatile, so that at the temperature of interest, then it makes no contribution to the vapour (yB=0).
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14. The composition of the vapour
The relation of the total vapor pressure to the composition of the vapour:
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15. The interpretation of the diagrams
In distillation, both vapour & the liquid compositions are of equal interest – combine graph of pressure vs mole fraction of A & graph total vapour pressure vs mole fraction of A the graphs into one.
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16. ‘ a’ indicates the vapour pressure of a mixture of composition, xA ‘b’ indicates the composition of the vapour that is in equilibrium with the liquid at that pressure
2 phases present (liq & vapour)
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17. Effect of lowering the pressure on a liquid mixture of overall composition ‘a’
(a) A liquid in a container exist in equilibrium with its vapour.
(b) Drawing out piston – P change. The composition of the phase adjust as shown by the tie line in phase diagram.(> vapour than liq)
(c) Piston is pulled so far out – all liquid has vaporized and only vapour is present. (P falls as the piston is withdrawn and the point on the phase diagram moves into the one-phase region.
Vapour phase
Liq phase
Lowering P –
by drawing out a piston
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18. Effect lowering P- p1 to p2 Composition of such liq is a2.
Changes to the system do not affect the overall composition, so the state of the system moves down the verticle line (isopleth / equal abundance) that pass through ‘a’.
Tie line
Until ‘a1’ is reached (P reduced to P1) –the sample consist of a single liquid phase.
At ‘a1’, the liq can exist in eq with its vapour (composition of the vapour phase is ‘a’1’.
The composition of liq is the same as initially (a1 lies on the isopleth through a) – conclude that at this P, no vapour present , however the tiny amount of vapour that is present has the composition ‘a’1’
Effect lowering P- p1 to p2
Composition of such liq is a2.
Composition of the vapour in eq with that liq is a’2
A further decrease in P- take system to a4 (only vapour is present) where composition of vapour is the same as the initial overall composition of the original liq.
ERT 108/3 PHYSICAL CHEMISTRY
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19. The lever rule
A point in the two-phase region of a phase diagram indicates not only qualitatively that both liquid & vapour are present, but represents quantitatively the relative amount of each.
to find the relative amounts of two phases α & β that are in equilibrium – measure the distances l α & lβ along the horizontal line & then use lever rule.
Lever rule:
Amount of phase α
Amount of phase β
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20. Temperature-Composition Diagrams
Temperature-composition diagram (to discuss distillation) :
a phase diagram – the boundaries show the composition of the phases that are in equilibrium at various temperatures (at a given P [1atm]).
The distillation of mixtures:
When liq composition a1 is heated, its boils when reach T2 (so, Liq has comp a2 same as a1 & vapour has comp a’2) – vapour is reacher at in the > volatile comp A (at lower boiling point)
We can state the vapour comp at the boiling point and from the location of tie line joining a2 to a’2 we can read off the boiling temp, T2 of the original liq mixture.
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21. The Distillation of Mixtures
Simple Distillation:
The vapour is withdrawn and condensed.
it is used to separate a volatile liquid from a non- volatile solute or solid.
Fractional Distillation:
The boiling & condensation cycle is repeated successively.
It is used to separate volatile liquids.
Theoretical plates – expressed the efficiency of a fractionating column.
The number of effective vaporization & condensation steps that are required to achieve a condensate of given composition from a given distillate.
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22. The Distillation of Mixtures
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23. Azeotropes
is a mixture of two or more liquids in such a ratio that its composition cannot be changed by simple distillation.
This occurs because, when an azeotrope is boiled, the resulting vapor has the same ratio of constituents as the original mixture.
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24. Vapour at a’2 at a2 is richer in A.
If that vapour is removed (condensed), remaining liq will move to a composition that is richer in B.
(vapour is eq in a3 at a’3)
As evaporation proceeds- composition of remaining liq shifts towards B as A is drawn off.
Boiling point of liq rises, vapour becomes richer in B.
When so much A has been evaporated, the liq reached comp b(vapour has same comp as liq)
Evaporation occurs without change of composition(azeotrope)
Composition vapour=composition liquid
(azeotrope)
condensed
A high boiling azeotrope. When the liq of composition a is distilled, the composition of the remaining liq changes towards b but not further
Eg; HCl/water: azeotropic at 80% mass of water & boils unchanged at C.
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25. Mixture boils at a2 (give vapour comp of a’2)
Start from mixture of composition a1, and follow the changes in the comp of the vapour rises through a fractionating column.
Mixture boils at a2 (give vapour comp of a’2)
Vapour condensed in the column to a liq of the same comp of a’2 (a3)
Liq reach eq with its vapour at a’3 (same liq comp as a4)
Fractionation shifts the vapour towards the azeotropeic comp at b but not beyond.
Eg;
Ethanol/water: Azeotropic at 4% mass water content & boils unchanged at 780C (below normal boiling point of water n ethanol..
100% ethanol cannot be prepared by distillation at 1atm of a dilute aqueous solution of ethanol
A low boiling azeotrope. When the liq of composition a is fractionally distilled, vapour in eq in the fractioning column moves towards b and then remain unchange
ERT 108/3 PHYSICAL CHEMISTRY
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26. Liquid-liquid phase diagrams
Temperature-composition diagrams
for partially miscible liquids systems (occur when the temp is below the upper critical solution temp or lower critical solution temp).
Liquids that do not mix in all proportions at all temperatures.
E.g. hexane/nitrobenzene
1 phase
2 phases
Upper critical solution temp – highest temp at which phase separation occurs
Lower critical solution temp – temp below which component not mix in all proportions (form 2 phase)
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27. Liquid-liquid phase diagrams: Phase separation
The composition of the former
Small amount of a liq B is added to a sample of another liq A at T’. Liq B dissolved completely & binary system remains a single phase. As > B is added, a stage comes at which no > dissolves. (2 phases in eqm- A saturated with B.
The relative abundances amount of the 2 phases in equilibrium are given by the LEVER RULE.
B added, A dissolves in it slightly.(the compositions of the 2 phases in eq remain a’ and a’’)-B dilutes the solution and from then on a single phase remains.
The composition of the 2 phases at eqm varies with the temp
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28. Example 3
A mixture of 50 g of hexane (0.59 mol C6H14) & 50 g of nitrobenzene (0.41 mol C6H5NO2) was prepared at 290K.
What are the compositions of the phases?
In what proportions /ratio do they occur?
To what temperature must the sample be heated in order to obtain a single phase?
Lets denote hexane by H and nitrobenzene by N
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29. Answer (Example 3)
The composition of phases in eqm is given by the points where the tie line representing intersects the phase boundry.
XN = 0.41, T=290K (occur in 2 phases region)
XN=0.35 & XN=0.83
Those are the composition of the two phases.
(b) The proportion s are given by the Lever rule (ratio amount of each phase=ratio of distance Iα & Iβ:
The temp at which the components are completely miscible is found by following isopleth upwards and noting the temp at which it enters the 1 phase region of the phase diagram
There is about 7 times more hexane rich phase than nitrobenzene rich phase.
(c) Heating the sample to 292K takes it into the single- phase region.
0.83
0.35
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30. Liquid-liquid phase diagrams: upper critical solution temperature
The upper critical solution temperature (TUC):
the highest temperature at which phase separation occurs.
Above the upper critical temperature the two components are fully miscible.
E.g. palladium/hydrogen system.
2 phases:
Solid solution of H2 in palladium
Palladium hydride
(up to 300oC, but form a single phase at highest temp)
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31. Liquid-liquid phase diagrams: lower Critical solution temperature
The lower critical solution temperature (TLC):
the lowest temperature at which phase separation occurs.
Below TLC, they mix in all proportions.
Above TLC, they form two phases.
E.g. Water/triethylamine
At low temp, the 2 components are > miscible bcz they form a weak complex
At higher temp, the complexes break up and the 2 components are < miscible.
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32. Liquid-liquid phase diagrams: upper & lower Critical solution temperature
By combining figure 6,21 & 6.24.
Some systems have both upper & lower critical solution temperatures.
Occur because after the week complexes have been disrupted, leading to partial miscibility, the normal motion at higher temp homogenizes the mixture again, just as in the case of ordinary partially miscible liquids
E.g. nicotine/water
Partially miscible between 61oC and 210oC
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33. Liquid-solid phase diagrams
Summarizes the temp- composition properties of a binary system with solid n liquid phases
Immiscible solid in phase + miscible in liq phase
Temperature-composition diagrams for solid mixtures guides the design of important industrial processes: liquid crystal displays (LCD) & semiconductors.
Figure: The temperature-composition phase diagram for two almost immiscible solids & their completely miscible liquids.
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34. Liquid-solid phase diagrams
Eutectic composition:
Consider the 2 component liq (liq solution of A & B)of composition a1. (the changes that occur as the system is cooled)
a1 to a2: system enters 2-phase region (Liq +solid B). Pure solid B begins to come out of solution and the remaining liq becomes richer in A)
a2 to a3 : > of solid B forms and the relative amounts of the solid & liq (in eqm) are given by lever rule (equal amount of each).the liq phase is richer in A than before (b3) because some B has been deposited.
a3 to a4 : less liq than at a3 (composition e). This liq now freezes to give a 2-phase system of pure solid B and pure solid A.
Eutetic composition – the mixture with the lowest melting point.
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35. Liquid-solid phase diagrams
Eutectic composition:
the mixture with the lowest melting point (point e).
A liquid with the eutectic composition freezes at a single temperature, without previously depositing solid A or B.
A solid with the eutectic composition melts, without change of composition, at the lowest temperature of any mixture.
E.g. Plumbum/ antimony, tin/plumbum, Silicon/ aluminium, benzene/napthalene, chloroform/aniline
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36. The end……..
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