Phase DiagramsMrs Khadijah Hanim Abdul Rahman

Week 14- 21&24 May 2012

Ability to evaluate problems concerning chemical kinetics, phase diagrams and electrochemistry

Course Outcome

DefinitionsThe Phase RuleTwo-component Systems:

a) Vapour pressure Diagrams

b) Temperature-composition Diagrams

c) Liquid-liquid Phase Diagrams

d) Liquid-solid Phase Diagrams

Subtopics

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.

Definitions

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.

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 + 2 = 2

The Phase Rule

2 PCF

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.

Phase rule is a general relation between the variance, F, the no of components, C and no of phases at equilibrium, P for a system of any composition:

F = C – P + 2 In a single component, single-phase system (C=1, P=1),

the pressure and temperature may be changed independently without changing the no of phases, so F=2.

If 2 phases are in equilibrium, (a liquid and its vapour for eg) in a single component system (C=1, P=2), the temp (or pressure) can be changed at will, but the change in temp (or pressure) demands an accompanying change in pressure (or temp) to preserve the no of phases in equilib. The variance of the system has fallen to 1.

Example 1

)()()(3

22

1

3 gCOsCaOsCaCOPhasePhase

Phase

A phase is a homogenous portion of a system: There are Three phases ( 2solid phase + 1 gaseous phase)The system has 3 chemical species CaCO3, CaO and CO2

The system has Three components (C=3).

Vapour-pressure diagrams The partial vapour pressures of the

components of an ideal solution of two volatile liquids are related to the composition of the liquid mixture by Roult’s law:

Where is the vapour pressure of pure A and

that of pure B. The total vapour pressure P of the mixture is therefore

Two-components system

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.

Dalton’s law: The mole fraction in the gas:

Provided the mixture is ideal:

a) The composition of the vapour

P

py AA

P

py BB

ABAB

AAA xppp

pxy

***

*

AB yy 1

*

*

BBB

AAA

pxP

pxP

ABAB XPPPP )( ***

The composition of the vapour

Figure shows the composition of the vapour plotted against the composition of liquid.

In all cases, yA>xA, that is 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).

1*

*

B

A

p

p

ABAB

AAA xppp

pxy

***

*

The composition of the vapour Since we can relate

the composition of the liquid to the composition of vapour, we can also relate the total vapor pressure to the composition of the vapour using this equation:

AABA

BA

yppp

ppp

***

**

1*

*

B

A

p

p

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.

b) The interpretation of the diagrams

‘ 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

Points that lie between the two lines correspond to a system in which there are two phases present, one a liquid and other a vapour.

AA xz

AA yz

The changes to the system do not affect the overall composition, so the state of the system moves down the vertical line (isopleth) that passes thru a.

Until a1 is reached (when pressure has been reduced to p1), the sample consist of single liquid phase.

At a1, the liquid can exist in equilibrium with its vapour. The composition of the vapoour is given by point a1

’.

Line joining 2 points representing phases in equilibrium, ‘tie-line’.

The composition of the liquid is the same as initially (a1 lies on the isopleth thru a), we can conclude that at this P there is virtually no vapour present, however the tiny amount of vapour that is present has the composition a1

’.

Now consider the effect of lowering the pressure to P2: taking the system to a pressure and overall composition represented by point a2

”.

This new P is below the vapour pressure of original liquid, so it vapourizes until the vapour pressure of the remaining liquid falls to P2.

The composition of such a liquid must be a2.

The composition of the vapour in equilibrium is given by the point a2’ at the other end of tie-line.

Pressure is further reduced to P3,

The compositions of liquid and vapour are represented by the points a3 and a3’.

a3‘ corresponds to a system in which the composition of the vapour is the same as the overall composition, we can conclude that the amount of liquid present is virtually 0, but the tiny amount of liquid present has composition a3.

A further decrease in P, take the system to point a4.

a4: only vapour present and its composition is the same as the initial overall composition of the system.

Effect of lowering the pressure on a liquid mixture of overall composition ‘a’

Lowering P – by drawing out a

piston

(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 p

hase

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:

lnln Amount of phase α

Amount of phase β

Temperature-Composition Diagrams Temperature-composition diagram (to

discuss fractional distillation) : a phase diagram in which the

boundaries show the composition of the phases that are in equilibrium at various temperatures (at a given P [1atm]).

a) 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 component A (the component with lower boiling point)

From the location of a2, 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.

In simple distillation, the vapour is withdrawn and condensed.

Technique used to separate a volatile liquid from a non-volatile solute/solid,

In fractional ditillation, the boiling and condensation cycle is repeated successively. Used to separate volatile liquids.

We can follow the changes: by seeing what happen when the 1st condensate of composition a3 is reheated.

The mixture boils at T3 and yield vapour composition a3’ which is even richer in the more volatile component.

The vapour is withdrawn and the 1st drop condenses to a liquid of composition a4.

The cycle is repeated until almost pure A is obtained in the vapour and pure B remains in the liquid.

a) The ditillation of mixtures

The efficiency of a fractionating column is expressed in terms of the no. of theoretical plates: the no of effective vaporization and condensation steps that are required to achieve a condensate of given composition from a given distillate.

To achieve the degree of separation shown in (a) the fractionating column must correspond to 3 theoretical plates.

To achieve the same separation for the system shown in (b), in which the components have more similar partial pressures, the fractionating column must be designed to have 5 theoretical plates.

Although many liquids have temp-composition phase diagrams resembling the ideal version, there are deviations.

Deviations from ideality are not always so strong as to lead to a max or min in the phase diagram, but when they do there are important consequences to ditillation.

Consider a liquid of composition a on the right of the max in the figure.

The vapour (at a2’) of the boiling mixture (at a2) is richer in A.

If that vapour is removed and the remaining liquid will move to a composition that is richer in B, such as represented by a3, and the vapour that is in equilibrium is a3’.

As that vapour is removed, the composition of the boiling liquid shifts to a4 and a4’.

b) Azeotropes

As evaporation proceeds, the composition of remaining liquid shifts towards B as A is drawn off.

The boiling point of the liquid rises, and the vapour becomes richer in B.

When so much of A has been evaporated that the liquid has reached composition b, the vapour has the same composition as the liquid.

Evaporation then occurs without change of composition

The mixture is said to form azeotrope.

When azeotrophic composition is reached, distillation cannot separate the 2 liquids because the condensate has the same composition

Example: HCl/water, which is azeotrophic at 80% by mass of water and boils unchanged at 108.6oC.

A high boiling azeotrope (Maximum azeotrope) When the liq of composition a is distilled, the composition of the remaining liq changes towards b but not further

Start with a mixture of composition a1, and follow the changes in the composition of the vapour that rises through fractionating column.

The mixture boils at a2 to give vapour composition of a2’.

This vapour condenses in the column to a liquid of the same composition, a3. liquid at equilibrium with its vapour at a3’.

a3’ condenses higher up the tube to give a liquid of the same composition, a4.

The fractionation therefore shifts the vapour towards the azeotrophic composition at b.

Eg: ethanol/water which boils unchanged when the water content is 4% by mass and the temp is 78oC.

Minimum azeotrope

A low boiling azeotrope (Minimum azeotrope). When the liq of composition a is fractionally distilled, vapour in eq in the fractioning column moves towards b and then remain unchange

Phase separation of partially miscible liquids may occur when temp is below the upper critical solution temp OR above the lower critical solution temp.

Partially miscible=liquids that do not mix in all proportions at all temp.

Example: hexane and nitrobenzene. The upper critical solution temp: is the highest

temp at which phase separation occurs. The lower critical solution temp: temp below

which components not mix in all proportions- which they form 2 phases.

Liquid-liquid phase diagrams

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 )-

The most abundant- consisting of A saturated with B

The minor- trace of B saturated with A. In the temp-composition diagram, the most

abundant is represented by the point a’ and the minor is represented by point a”.

The relative abundances of the 2 phases are given by Lever rule.

When more B is added, A dissolves in it slightly. The compositions of the 2 phases in eqm

remain a’ and a”. A stage is reached when so much of B is

present that it can dissolve all A and the system reverts to a single phase.

The composition of the 2 phases at eqm varies with temp. For hexane/nitrobenzene, raising the temp increases their miscibility.

a) Phase separation

1 phase

2 phases

A mixture of 50 g of hexane (0.59 mol C6H14) & 50 g of nitrobenzene (0.41 mol C6H5NO2) was prepared at 290K.

a) What are the compositions of the phases?

b) In what proportions /ratio do they occur?

c) To what temperature must the sample be heated in order to obtain a single phase?

Lets denote hexane by H and nitrobenzene by N

Example 2

a) Composition of the phases The compositions of phases in eqm are

given by the points where the tie line representing the tem intersects the phase boundary.

The point xN=0.41, T=290 K occurs in 2 phase region of the phase diagram

The horizontal line cuts the phase boundary at xN=0.35 and xN=0.83 composition of the 2 phases.

b) Proportions Given by lever rule, the ratio of amounts of

each phase = ratio of distances lα and lβ:

That is, there are about 7 times more hexane-rich phase than nitrobenzene-rich phase.

c) Temp needed to obtain single phase

- 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 = 292K

Answer (example 2)

Upper critical solution temp, Tuc: the higest temp at which phase seperation occurs.

Above the upper critical temp the 2 components are fully miscible.

Example of solid solution is the palladium/hydrogen system:

-1 phase: a solid solution of hydrogen in palladium

-1 phase: palladium hydrideUp to 300oC but forms a single

phase at higher temp.

b) Critical solution temperatures

Tlc: below which they mix in all proportions and above which they form 2 phases.

The lowest temp at which phase separation occurs.

Example: water/triethylamine At low temp the two

components are more miscible because they form a weak complex,

at higher temp the complexes break up and the two components are less miscible.

Lower critical solution temperature

They occur because, after the weak complexes have been disrupted, leading to partial miscibility

The thermal motion at higher temp homogenizes the mixture again, just in the case of ordinary partially miscible liquid.

Example: nicotine and

water, which are partially miscible between 61oC and 210oC.

Upper and lower critical solution temperatures.

Knowledge of the temp-composition diagrams for solid mixtures guides the design of important industrial processes such:

Manufacturing of liquid crystal display (LCD) Semiconductors

Liquid-solid phase diagrams

a) Eutectics 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 + 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.

The isopleth at e corresponds to the eutectic composition, the mixture with the lowest melting point

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

Eutetic composition – the mixture with the lowest melting point.

At 90oC, the vapour pressure of methylbenzene is 53.3 kPa and that of 1,2-dimethylbenzene is 20.0 kPa. What is the composition of a liquid mixture that boils at 90oC when the pressure is 0.50 atm? What is the composition of the vapor produced?

Exercises 1

The vapour pressure of pure liquid A at 300 K is 76.7 kPa and that of pure liquid B is 52.0 kPa. These two compounds form ideal liquid and gaseous mixtures. Consider the equilibrium composition of a mixture in which the mole fraction of A in the vapour is 0.350. Calculate the total pressure of the vapour and the composition of the liquid mixture.

Exercise 2

Benzene and toluene form nearly ideal solutions. Consider an equimolar solution of benzene and toluene are 9.9 kPa and 2.9 kPa, respectively. The solution is boiled by reducing the external pressure below the vapour pressure. Calculate

a) The pressure when boiling beginsb) The composition of each component in the

vapourc) The vapour pressure when only a few drops of

liquid remains.Assume that the rate of vaporization is low enough

for the temp to remain constant at 20oC.

Exercise 3

The following temperature/composition data were obtained for a mixture of two liquids A and B at 1.00 atm, where x is the mole fraction in the liquid and y is the mole fraction in the vapour at equilibrium.

The boiling points are 124oC for A and 155oC for B. Plot the temperature/composition diagram for the mixture.

what is the composition of the vapour in equilibrium with the liquid composition (a) xA=0.50 and (b) xB=0.33?

Exercise 4

θ/oC 125 130 135 140 145 150

xA 0.91 0.65 0.45 0.30 0.18 0.098

yA 0.99 0.91 0.77 0.61 0.45 0.25

1-Butanol and chlorobenzene form a minimum-boiling azeotropic system. The mole fraction of 1-butanol in the liquid (x) and vapour (y) phases at 1.00 atm is given below for a variety of boiling temperatures.

Pure chlorobenzene boils at 404.86 K(a) Construct the chlorobenzene-rich portion of the phase

diagram from these data(b) Estimate the temp at which a solution whose mole

fraction of 1-butanol is 0.3 begins to boil(c) State the compositions and relative proportions of the 2

phases present after a solution initially 0.300 1-butanol is heated to 393.94 K.

Exercise 5

T/K 396.57

393.94

391.6 390.15

389.03

388.66

388.57

X 0.1065 0.1700 0.2646 0.3687 0.5017 0.6091 0.7171

y 0.2859 0.3691 0.4505 0.5138 0.5840 0.6409 0.7070