applied physical chemistry

8/3/2019 Applied Physical Chemistry

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PHASE DIAGRAMSPHASE DIAGRAMS

Chapter 6Chapter 6


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Phase DiagramsPhase Diagrams

Lets apply our knowledge of theLets apply our knowledge of the

thermodynamics of simple mixtures to discussthermodynamics of simple mixtures to discuss

the physical changes of mixtures when they arethe physical changes of mixtures when they are

heated or cooled and when their compositionsheated or cooled and when their compositions

are changed.are changed.

We will see how phase diagrams can be used toWe will see how phase diagrams can be used to

judge whether two substances are mutuallyjudge whether two substances are mutuallymiscible.miscible.


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We will see whether equilibrium can exist over aWe will see whether equilibrium can exist over a

range of conditions or whether a system must berange of conditions or whether a system must be

bought to a definite pressure, temperature andbought to a definite pressure, temperature and

composition before equilibrium is established.composition before equilibrium is established.

Phase diagrams are industrially and commerciallyPhase diagrams are industrially and commercially

important.important.


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Semiconductor, ceramics, steel and alloySemiconductor, ceramics, steel and alloy

industries rely heavily on phase diagrams toindustries rely heavily on phase diagrams to

ensure uniformity of a product.ensure uniformity of a product.

Phase diagrams are also the basis for separationPhase diagrams are also the basis for separation

procedures in the petroleum industry and theprocedures in the petroleum industry and the

formulation of foods and cosmetic preparations.formulation of foods and cosmetic preparations.


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DefinitionsDefinitions

A phase is a state of matter that is uniformA phase is a state of matter that is uniform

throughout, not only in composition but also inthroughout, not only in composition but also in

physical state.physical state.

A pure gasA pure gas

A gaseous mixtureA gaseous mixture

Two totally miscible liquidsTwo totally miscible liquids A crystalA crystal


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A solution of sodium chlorideA solution of sodium chloride

IceIce

A slurry of ice and waterA slurry of ice and water


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An alloy of two metals?An alloy of two metals?


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An alloy of two metals is a two phase system ifAn alloy of two metals is a two phase system if

the metals are immiscible, but a single phasethe metals are immiscible, but a single phase

system if they are miscible.system if they are miscible.

Dispersion can be uniform on a macroscopicDispersion can be uniform on a macroscopic

level, but not on a microscopic scale.level, but not on a microscopic scale.

Dispersions are important in many advancedDispersions are important in many advanced

materials.materials.


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Heat treatment cycles are used to achieve theHeat treatment cycles are used to achieve the

precipitation of a fine dispersion of particles ofprecipitation of a fine dispersion of particles of

one phase within a matrix formed by a saturatedone phase within a matrix formed by a saturated

solid solution phase.solid solution phase.

The ability to control this microstructureThe ability to control this microstructure

resulting from phase equilibria makes it possibleresulting from phase equilibria makes it possible

to tailor the mechanical properties of theto tailor the mechanical properties of thematerials.materials.


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A constituent of a system is a chemical speciesA constituent of a system is a chemical species

(an ion or a molecule) that is present.(an ion or a molecule) that is present.

A

mixture of water and ethanol has twoA

mixture of water and ethanol has twoconstituents.constituents.

A solution of sodium chloride has threeA solution of sodium chloride has three

constituents: Naconstituents: Na++, Cl, Cl--, H, H22O.O.


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A component is a chemically independentA component is a chemically independent

constituent of a system.constituent of a system.

The number of components in a system is theThe number of components in a system is theminimum number of independent speciesminimum number of independent species

necessary to define the composition of all thenecessary to define the composition of all the

phases present in the system.phases present in the system.


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When no reaction takes place and there are noWhen no reaction takes place and there are no

other constraints, the number of components isother constraints, the number of components is

the equal to the number of constituents.the equal to the number of constituents.

Pure water is a one component systemPure water is a one component system

A mixture of ethanol and water is twoA mixture of ethanol and water is two

component system.component system.


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An aqueous solution of sodium chloride is a twoAn aqueous solution of sodium chloride is a two

component system, because by charge balance,component system, because by charge balance,

the number of Nathe number of Na++ ions must be the same as theions must be the same as the

number of Clnumber of Cl-- ions.ions.

A system that consists of hydrogen, oxygen andA system that consists of hydrogen, oxygen and

water at room temperature has threewater at room temperature has three

components.components.


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When a reaction can occur under the conditionsWhen a reaction can occur under the conditions

prevailing in the system, we need to decide theprevailing in the system, we need to decide the

minimum number of species that, after allowingminimum number of species that, after allowing

for reactions in which one species is synthesizedfor reactions in which one species is synthesized

from others, can be used to specify thefrom others, can be used to specify the

composition of all the phases.composition of all the phases.


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CaCOCaCO3(s)3(s) CaOCaO(s)(s) + CO+ CO2(g)2(g)

3 phases3 phases

3 constituents3 constituentsTo specify the composition of the gas phase, weTo specify the composition of the gas phase, we

need the species COneed the species CO22, and to specify the, and to specify the

composition of the solid phase on the right, wecomposition of the solid phase on the right, we

need the species CaO.need the species CaO.


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CaCOCaCO3(s)3(s) CaOCaO(s)(s) + CO+ CO2(g)2(g)

We do not need an additional species to specifyWe do not need an additional species to specify

the composition of the phase on the right,the composition of the phase on the right,because its identity (CaCObecause its identity (CaCO33) can be expressed in) can be expressed in

terms of the other two constituents by makingterms of the other two constituents by making

use of the stoichiometry of the reaction.use of the stoichiometry of the reaction.

2 component system.2 component system.


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NHNH44ClCl(s)(s) NHNH3(g)3(g) + HCl+ HCl(g)(g)

2 phases2 phases

3constituents

3constituents

1 component1 component


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The number of phases, P.The number of phases, P.

The number of components, C.The number of components, C.

The variance of the system, F is the number ofThe variance of the system, F is the number ofintensive variables (e.g. p and T) that can beintensive variables (e.g. p and T) that can be

changed independently without disturbing thechanged independently without disturbing the

number of phases in equilibrium.number of phases in equilibrium.


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Phase RulePhase Rule

F = CF = C P + 2P + 2

This is not an empirical rule based uponThis is not an empirical rule based upon

observations, it can be derived from chemicalobservations, it can be derived from chemical

thermodynamics (Justification 6.1).thermodynamics (Justification 6.1).

For a one component system F = 3For a one component system F = 3 PP

When only one phase is present, F = 2 and bothWhen only one phase is present, F = 2 and both

p and T can be varied without changing thep and T can be varied without changing the

number of phases.number of phases.


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Phase RulePhase Rule

When two phases are present, F = 1 whichWhen two phases are present, F = 1 which

implies that pressure is not freely variable if theimplies that pressure is not freely variable if the

pressure is set. This is why at a givenpressure is set. This is why at a given

temperature a liquid has a characteristic vaportemperature a liquid has a characteristic vapor

pressure.pressure.

When three phases are present, F = 0. ThisWhen three phases are present, F = 0. This

special case occurs only at a definite temperaturespecial case occurs only at a definite temperatureand pressure that is characteristic of theand pressure that is characteristic of the

substance.substance.


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Experimental ProceduresExperimental Procedures

Thermal analysisThermal analysis a sample is allowed to coola sample is allowed to cool

and it temperature is monitored. When a phaseand it temperature is monitored. When a phase

transition occurs, cooling may stop until thetransition occurs, cooling may stop until the

phase transition is complete and is easilyphase transition is complete and is easily

observed on a thermogram.observed on a thermogram.


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Modern work on phase transitions often dealModern work on phase transitions often deal

with systems at very high pressures and morewith systems at very high pressures and more

sophisticated detection properties must besophisticated detection properties must be

adopted.adopted.

A diamond anvil cell is capable of producingA diamond anvil cell is capable of producing

extremely high pressures.extremely high pressures.


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A sample is placed in a cavity between to gemA sample is placed in a cavity between to gem--

quality diamonds and then pressure is exerted byquality diamonds and then pressure is exerted by

turning a screw. Pressures up to ~2Mbar can beturning a screw. Pressures up to ~2Mbar can be

achieved.achieved.

One application is the study the transition ofOne application is the study the transition of

covalent solids to metallic solids.covalent solids to metallic solids.


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Iodine, IIodine, I22, becomes metallic at ~ 200 kbar and, becomes metallic at ~ 200 kbar and

makes a transition to a monatomic metallic solidmakes a transition to a monatomic metallic solid

at around 210 kbar.at around 210 kbar.

Relevant to the structure of material deep insideRelevant to the structure of material deep inside

the Earth and in the interiors of giant planets,the Earth and in the interiors of giant planets,

where even hydrogen may be metallic.where even hydrogen may be metallic.


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Two Component SystemsTwo Component Systems

When two components are present in a system,When two components are present in a system,

C = 2, so F = 4C = 2, so F = 4 P.P.

If the temperature is constant, the remainingIf the temperature is constant, the remaining

variance is F = 3variance is F = 3 P.P.

F indicates that one of the degrees of freedom hasF indicates that one of the degrees of freedom has

been discardedbeen discarded in this case the temperature.in this case the temperature.

The two remaining degrees of freedom are theThe two remaining degrees of freedom are thepressure and the compositionpressure and the composition


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The partial vapor pressure of the components of anThe partial vapor pressure of the components of an

ideal solution of two volatile liquids are related toideal solution of two volatile liquids are related to

the composition of the liquid mixture by Raoultsthe composition of the liquid mixture by Raoults

Law:Law:pA ! xApA

*pB ! xBpB

*

p ! pA p

B! x

Ap

A

* x

Bp

B

*! x

Ap

A

* (1 x

A)p

B

*

p ! xApA* pB

* xApB

*

p ! pB* (pA

* pB

* )xA


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This expression shows that the total vapor pressureThis expression shows that the total vapor pressure

(at a fixed temperature) changes linearly with the(at a fixed temperature) changes linearly with thecomposition from pcomposition from pBB

** to pto pAA

** as xas xAA

changes from 0changes from 0

to 1.to 1.

p ! pB* (pA

* pB

* )xA


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p ! pB* (pA

* pB

*)xA


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The compositions of the liquid vapor that are inThe compositions of the liquid vapor that are in

mutual equilibrium are not necessarily the same.mutual equilibrium are not necessarily the same.

The more volatile the component, the higherThe more volatile the component, the higher

amount of that substance should be in the vapor.amount of that substance should be in the vapor. yy

AAand yand yBB are the mole fractions ofA and B in theare the mole fractions ofA and B in the

gas.gas.

yA ! pAp

yB ! pBp


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yA!p

A

p!

xAp

A

*

pB (pA* pB

*

)xA

yB!1 y

A

pA

*

pB

*


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p !pA

* pB*

pA* (pB

* pA

*)yA

pA*

pB*


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p !pA

* pB*

pA* (pB

* pA

*)yA

ppA

*! pB

*

pA*

when yA is zero


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If we are interested in distillation, both vaporIf we are interested in distillation, both vapor

and liquid compositions are of equal interest.and liquid compositions are of equal interest.

So it makes sense to present data showing bothSo it makes sense to present data showing both

the dependence of vapor and liquid compositionthe dependence of vapor and liquid composition

upon mole fraction.upon mole fraction.


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The lever ruleThe lever rule

A point in the twoA point in the two--phase of a phase diagramphase of a phase diagram

indicates not only qualitatively that both liquidindicates not only qualitatively that both liquid

and vapor present, but represents quantitativelyand vapor present, but represents quantitatively

the relative amounts of each.the relative amounts of each.

To find the relative amounts of two phasesTo find the relative amounts of two phases EE

andand FF that are in equilibrium, we measure thethat are in equilibrium, we measure the

distances ldistances lEE and land lFF along the horizontal tie line,along the horizontal tie line,and then use the lever rule.and then use the lever rule.


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The lever ruleThe lever rule

Where nWhere nEE is the amount of phaseis the amount of phase EE and nand nFF is theis the

amount of phaseamount of phase FF..

nE lE ! nF lF

nE

nF!

lF

lE


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TemperatureTemperature--compositioncomposition

diagramsdiagramsTo discuss distillation we need a temperatureTo discuss distillation we need a temperature--

composition diagram instead of a pressurecomposition diagram instead of a pressure--

composition diagram.composition diagram. Such a diagram shows composition at differentSuch a diagram shows composition at different

temperatures at a constant pressure (typically 1temperatures at a constant pressure (typically 1

atm).atm).


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diagramsdiagrams In a simple distillation the vapor is withdrawnIn a simple distillation the vapor is withdrawn

and condensed. This technique is used toand condensed. This technique is used to

separate a volatile liquid from a nonseparate a volatile liquid from a non--volatilevolatile

solute or solid.solute or solid.

In a fractional distillation, the boiling andIn a fractional distillation, the boiling and

condensation cycle is repeated successively. Thiscondensation cycle is repeated successively. This

technique is used to separate volatile liquids.technique is used to separate volatile liquids.


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diagramsdiagramsThe efficiency of a fractionating column isThe efficiency of a fractionating column is

expressed in terms of the number of theoreticalexpressed in terms of the number of theoretical

plates, the number of effective vaporization andplates, the number of effective vaporization and

condensation steps that are required to achieve acondensation steps that are required to achieve a

condensate of given composition from a givencondensate of given composition from a given

distillate.distillate.


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AzeotropesAzeotropes

Although many liquids have temperatureAlthough many liquids have temperature--

composition phase diagrams resembling the idealcomposition phase diagrams resembling the ideal

version, a number of important liquids deviate fromversion, a number of important liquids deviate from

ideality.ideality. If a maximum occurs in the phase diagram,If a maximum occurs in the phase diagram,

favorable interactions between A and B moleculesfavorable interactions between A and B molecules

stabilize the liquid.stabilize the liquid.

If a maximum occurs in the phase diagram,If a maximum occurs in the phase diagram,

unfavorable interactions between A and Bunfavorable interactions between A and B

molecules demolecules de--stabilize the liquid.stabilize the liquid.


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AzeotropesAzeotropes

An azeotrope is a mixture of two (or more) miscibleAn azeotrope is a mixture of two (or more) miscible

liquids that when boiled produce the sameliquids that when boiled produce the same

composition in the vapor phase as that is present incomposition in the vapor phase as that is present in

the original mixture.the original mixture.


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Immiscible liquidsImmiscible liquids

Lets consider the distillation of two immiscibleLets consider the distillation of two immiscible

liquids, such as octane and water.liquids, such as octane and water.

The system can be considered as the jointThe system can be considered as the joint

distillation of the separated components.distillation of the separated components.

Total vapor pressure p = pTotal vapor pressure p = pAA

** + p+ pBB**

Mixture boils when p = 1 atm, and so the mixtureMixture boils when p = 1 atm, and so the mixture

boils at a lower temperature than either componentboils at a lower temperature than either componentwould alone.would alone.


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LiquidLiquid--liquid phaseliquid phase

diagramsdiagrams Lets consider temperatureLets consider temperature--composition diagramscomposition diagramsfor systems that consist of pairs of partially misciblefor systems that consist of pairs of partially miscible

liquids.liquids.

Partially miscible liquids are liquids that do not mixPartially miscible liquids are liquids that do not mix

at all proportions at all temperatures.at all proportions at all temperatures.


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Phase separationPhase separation

Suppose a small amount of liquids B is added toSuppose a small amount of liquids B is added to

another liquid A at a temperature T.another liquid A at a temperature T.

If it dissolves completely the binary mixture is aIf it dissolves completely the binary mixture is a

single phase.single phase.

As more B is added, A becomes saturated in B andAs more B is added, A becomes saturated in B and

no more B dissolvesno more B dissolves 2 phases.2 phases.

Most abundant phase is A saturated with B.Most abundant phase is A saturated with B. Minor phase is B saturated with A.Minor phase is B saturated with A.


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Phase separationPhase separation

The relative abundance of each phase is given byThe relative abundance of each phase is given by

the lever rule.the lever rule.

As the amount of B increases the composition ofAs the amount of B increases the composition of

each phase stays the same, but the amount of eacheach phase stays the same, but the amount of each

changes with the lever rule.changes with the lever rule.

Eventually a point is reached when so much B isEventually a point is reached when so much B is

present that it can dissolve all the A, and systempresent that it can dissolve all the A, and systemreverts to a single phase.reverts to a single phase.


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Critical solutionCritical solution

temperaturestemperatures The upper critical solution temperature, TThe upper critical solution temperature, Tucuc is theis thehighest temperature at which phase separationhighest temperature at which phase separation

occurs.occurs.

Above the critical temperature the two componentsAbove the critical temperature the two components

are fully miscible.are fully miscible.

On the molecular level, this can be interpreted asOn the molecular level, this can be interpreted as

the kinetic energy of each molecule over comingthe kinetic energy of each molecule over comingmolecular interactions that want molecules of onemolecular interactions that want molecules of one

type to come close together.type to come close together.


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temperaturestemperatures Some systems show a lower critical solutionSome systems show a lower critical solutiontemperature, Ttemperature, Tlclc..

Below this temperature the two components mix inBelow this temperature the two components mix in

all proportions and above which they form twoall proportions and above which they form two

phases.phases.

An example is water and triethylamine.An example is water and triethylamine.


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temperaturestemperatures The molecular reason for this is that water andThe molecular reason for this is that water andtriethylamine form a weak molecular complex. Attriethylamine form a weak molecular complex. At

higher temperatures the complexes break up andhigher temperatures the complexes break up and

the two components are less miscible.the two components are less miscible.

Some systems have upper and lower criticalSome systems have upper and lower critical

solution temperatures.solution temperatures.


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Distillation of partiallyDistillation of partially

miscible liquidsmiscible liquids What happens when you distill partially miscibleWhat happens when you distill partially miscibleliquids?liquids?

A pair of liquids that are partially miscible oftenA pair of liquids that are partially miscible often

form a lowform a low--boiling azeotrope.boiling azeotrope.

Two possibilities can exist: one in which the liquidTwo possibilities can exist: one in which the liquid

become fully miscible before they boil; the other inbecome fully miscible before they boil; the other in

which boiling occurs before mixing is complete.which boiling occurs before mixing is complete.


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LiquidLiquid--solid phase diagramssolid phase diagrams

The knowledge of temperatureThe knowledge of temperature--compositioncomposition

diagrams for solid mixtures guides the design ofdiagrams for solid mixtures guides the design of

important industrial processes, such as theimportant industrial processes, such as the

manufacture of liquid crystal displays andmanufacture of liquid crystal displays andsemiconductors.semiconductors.


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EutecticsEutectics

The isopleth at e corresponds to the eutecticThe isopleth at e corresponds to the eutectic

composition, the mixture with the lowest meltingcomposition, the mixture with the lowest melting

point.point.

A liquid with a eutectic composition freezes at aA liquid with a eutectic composition freezes at asingle temperature without depositing solid A or B.single temperature without depositing solid A or B.

A solid with the eutectic composition melts withoutA solid with the eutectic composition melts without

any change of composition at the lowestany change of composition at the lowesttemperature of any mixture.temperature of any mixture.


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EutecticsEutectics

SolderSolder 67% tin and 33% lead by mass melts at67% tin and 33% lead by mass melts at

183183rrC.C.

23% NaCl and 77% H23% NaCl and 77% H22O by mass forms a eutecticO by mass forms a eutectic

mixture which melts atmixture which melts at --21.121.1 rrC. Above thisC. Above thistemperature the mixture melts.temperature the mixture melts.


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Reacting SystemsReacting Systems

Many binary mixtures react produce compounds.Many binary mixtures react produce compounds.

Gallium arsenide is a technologically importantGallium arsenide is a technologically important

exampleexample semiconductor.semiconductor.

Ga + AsGa + As GaAsGaAs


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applied physical chemistry

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