Phase Rule

PHASE PHASE DIAGRAMSDIAGRAMS

Phase DiagramsPhase Diagrams Phase diagrams are industrially and Phase diagrams are industrially and

commercially important.commercially important.

Phase DiagramsPhase Diagrams Semiconductor, ceramics, steel and alloy Semiconductor, ceramics, steel and alloy

industries rely heavily on phase diagrams industries rely heavily on phase diagrams to ensure uniformity of a product.to ensure uniformity of a product.

Phase diagrams are also the basis for Phase diagrams are also the basis for separation procedures in the petroleum separation procedures in the petroleum industry and the formulation of foods and industry and the formulation of foods and cosmetic preparations.cosmetic preparations.

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

throughout, not only in composition but also in throughout, 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

Definitions: Phase an homogeneous physically distinct and

mechanically separable portion of system. which is separated from other such parts of the system by definite boundary surfaces.

i) at freezing point , water consists of three phases

ii) a gaseous mixture, being thoroughly misible in all portions, will constitute one phase only. Thus, a mixture of N2 and H2 forms one phase only.

iii) if two liquids are immiscible, they will form two separate phases.

If 2 solutions are miscible they will form one liquid phase only.

A solution of a substance in a solvent consists of one phase only.

eg: glucose solution Each solid makes up a separate phase. eg: S can exist together, but these are all separate phases. A heterogeneous mixture like CaCO3(s) ↔ CaO(s) + CO2

consists three phases Fe(s) + H2O(g) ↔ FeO + H2

Consists three phases. A homogenous solid solution of a salt constitutes a single

phase. eg:FeSO4.(NH4)2SO4.6H2O solution constitutes a

single phase although it consists of FeSO4.(NH4)2SO4 &H2O

COMPONENT: The smallest number of independent variable

constitutes, taking part in the state of equilibrium , by means of which the composition of each phase can be expressed in the form of chemical equation.

i) in water system the chemical composition of all the three phases in H2O.

Hence it is one component system ii) the sulphur system consists of four phases,

rhombic, monoclinic, liquid and vapour. the chemical composition of all phases is S.

hence, it is one component system. iii) a system of saturated solution of NaCl consists

of solid salt, salt solution and water vapour. the chemical composition of all the three phases

can be expressed in terms of NaCl & H2O. Hence it is a 2 component system.

Degree of freedom: The minimum number of

independently variable factors, such as T,P & composition of the phases, which must be arbitrarily specified in order to represent prefectly the condition of a system.

In case of water system. if all the 3 phases are present in

equilibrium, then no condition need to be specified, as the 3 phases can be equilibrium only at particular T and P.

the system is, therefore zero variant or non-variant or invariant or has no degree of freedom. if the condition is altered, three phases will not remain in equilibrium and one of the phase disappears.

water(l) , vapour(g) we must state either the T or P to define it

completely, hence degree of freedom is one or system is univariant.

For a system consisting water vapour phase only. We must state the values of both T & P in order to describe the system completely. Hence, the system is bivariant.

NaCl(s) ↔ NaCl-water(aq) ↔ water vapour(g)

we must state either the T or P. because the saturation solubility is fixed at a particular T or P.

DefinitionsDefinitions 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 The variance of the system, F is the

number of intensive variables (e.g. p number of intensive variables (e.g. p and T) that can be changed and T) that can be changed independently without disturbing independently without disturbing the number of phases in equilibrium.the number of phases in equilibrium.

Phase RulePhase Rule F = C – P + 2F = C – P + 2 This is not an empirical rule based This is not an empirical rule based

upon observations, it can be derived upon observations, it can be derived from chemical thermodynamics .from chemical thermodynamics .

For a one component system F = 3 – P For a one component system F = 3 – P When only one phase is present, F = 2 When only one phase is present, F = 2

and both p and T can be varied without and both p and T can be varied without changing the number of phases.changing the number of phases.

Phase RulePhase Rule When two phases are present, F = 1 When two phases are present, F = 1

which implies that pressure is not freely which implies that pressure is not freely variable if the pressure is set. This is why variable if the pressure is set. This is why at a given temperature a liquid has a at a given temperature a liquid has a characteristic vapor pressure.characteristic vapor pressure.

When three phases are present, F = 0. When three phases are present, F = 0. This special case occurs only at a definite This special case occurs only at a definite temperature and pressure that is temperature and pressure that is characteristic of the substance.characteristic of the substance.

Phase DiagramPhase Diagram Liquid Liquid Vapor eqlbm is represented Vapor eqlbm is represented

by its vapor pressure curve.by its vapor pressure curve. solid solid vapor eqlbm is represented by vapor eqlbm is represented by

sublimation curve.sublimation curve.The representation of the effects of The representation of the effects of

temp & pressure on the liq-solid,solid-temp & pressure on the liq-solid,solid-gas,gas-liquid like equilibria in a gas,gas-liquid like equilibria in a graph is called phase diagram.graph is called phase diagram.

Description :Description :PointsPoints in phase diagram represent non- in phase diagram represent non-

variant system.variant system.CurvesCurves represent univariant system.represent univariant system.AreaArea between any two curves represent between any two curves represent

bivariant system.bivariant system.If more than one point is present in phase If more than one point is present in phase

diagram, there will be more number of diagram, there will be more number of non-variant conditions for that system.non-variant conditions for that system.

Dotted curves represent meta stable Dotted curves represent meta stable equilibria(i,e they are obtained only equilibria(i,e they are obtained only under special conditions)under special conditions)

THE PHASE RULE-WATER THE PHASE RULE-WATER SYSTEM-ONE COMPONENT SYSTEM-ONE COMPONENT

SYSTEMSYSTEM Water exists in three phases i,e Water exists in three phases i,e ice, water and vapor.ice, water and vapor. The chemical composition of each The chemical composition of each

phase is written as Hphase is written as H22O.O. So, the no. of components of this So, the no. of components of this

system is one.system is one.

When phase rule is applied to water When phase rule is applied to water system the results are as follows.system the results are as follows.

a.a. If all three phases are to co exist If all three phases are to co exist P=3.P=3.

F= C+2-PF= C+2-P =1+2-3=0=1+2-3=0They exist at a particular temp & They exist at a particular temp &

prssure,if slight variation in temp or prssure,if slight variation in temp or pressure will make one of the phases pressure will make one of the phases dissappear.dissappear.

This point is called This point is called Triple Point.Triple Point.

It is defined as the It is defined as the one at which all the one at which all the three phases coexist. It is represented by three phases coexist. It is represented by point “O” in the fig. point “O” in the fig.

The effect of heat on it causes more & The effect of heat on it causes more & more of the solid to melt with out more of the solid to melt with out bringing any rise in temp & pressure.This bringing any rise in temp & pressure.This continues till the whole solid gets continues till the whole solid gets completely changed in to the liquid state.completely changed in to the liquid state.

b.b. If any two phases are to co-exist in If any two phases are to co-exist in eqlbm,P=2eqlbm,P=2F=C+2-PF=C+2-P =1+2-2=1=1+2-2=1

Even if either temp or pressure are varied Even if either temp or pressure are varied simultaneously, one phase in eqlbm simultaneously, one phase in eqlbm disappears. The system is univariant.disappears. The system is univariant.

This is represented by curve in phase This is represented by curve in phase doagram.doagram.

c.c. If only one phase exists,P=1If only one phase exists,P=1F=1+2-1=1F=1+2-1=1

Even if P & T are simultaneously Even if P & T are simultaneously changed,the phase still exists.changed,the phase still exists.

The system is represented by area in phase The system is represented by area in phase diagm.diagm.

These can be verified experimentally.These can be verified experimentally.

Vapor pressure curves of water or Vapor pressure curves of water or sublimation curves of ice under sublimation curves of ice under different temp. are studied.different temp. are studied.

The results are plotted in graph The results are plotted in graph known as the known as the

Phase Diagram Of WaterPhase Diagram Of WaterFusion curve

Vapourpressure curve

O

A

B

C

A’

The vapor of water at different temp. The vapor of water at different temp. is measured & similarly m.pts of ice is measured & similarly m.pts of ice at different pressures are measured at different pressures are measured & drawn in the graph.& drawn in the graph.

1.1. OA is the vapor pressure curve of OA is the vapor pressure curve of water. It represents the equilibrium water. It represents the equilibrium between water & its vapor.The two between water & its vapor.The two phases water & vapor are in phases water & vapor are in equilibrium on curve OA. equilibrium on curve OA. water water vapor vapor

2.2. OC is the effect of pressure on the m.pt of OC is the effect of pressure on the m.pt of ice.This curve represents the eqlbm betn ice.This curve represents the eqlbm betn solid(ice) & water.solid(ice) & water. water water ice ice

3.3. The above two curves meet in a point ‘O’ The above two curves meet in a point ‘O’ is showing only one set of pressure & is showing only one set of pressure & temp. & slight variation in temp or temp. & slight variation in temp or pressure will make the point move on to pressure will make the point move on to the curve OA or OB. So, degrees of the curve OA or OB. So, degrees of freedom is “Zero” & the system is non-freedom is “Zero” & the system is non-variant at the point ‘O’. The values are variant at the point ‘O’. The values are 4mm & temp. is 0.00754mm & temp. is 0.0075ooC.C.F=C+2-P=1+2-3=0F=C+2-P=1+2-3=0

4.4. OB is the sublimation curve of ice.The OB is the sublimation curve of ice.The eqlbm betwn ice & vapor is represented eqlbm betwn ice & vapor is represented by this curve. by this curve. ice ice vapor vapor

It is to be noted that this curve passes It is to be noted that this curve passes that through the triple point ‘O’ b’coz that through the triple point ‘O’ b’coz ice ice Vap eqlbm is part of triple point. Vap eqlbm is part of triple point.

The curve OB ends at absolute zero.The curve OB ends at absolute zero.5.5. The curve OA ends abruptly at 374 k The curve OA ends abruptly at 374 k

temp & a pressure of 218.5 atm. This temp & a pressure of 218.5 atm. This corresponds to critical pressure of corresponds to critical pressure of water & beyond this pointwater & beyond this point

gaseous & liq phases cannot be distinguished.gaseous & liq phases cannot be distinguished. when water vapor is cooled slowly, it becomes when water vapor is cooled slowly, it becomes

solid at 0solid at 0ooC, but on rapid cooling (super C, but on rapid cooling (super cooledwater) the vapor cooledwater) the vapor liq eqlbm liq eqlbm continues to exist & this meta stable state is continues to exist & this meta stable state is represented by curve OA’ on which liq & vap represented by curve OA’ on which liq & vap are in eqlbm.are in eqlbm.

6.6. The lines OA(OA’), OB & OC in diagram The lines OA(OA’), OB & OC in diagram represent the eqlbm betwn any two phases.represent the eqlbm betwn any two phases.By changing the temp, the pressure will be By changing the temp, the pressure will be adjusting in such a way that two phases adjusting in such a way that two phases continue to exist & vice versa.continue to exist & vice versa.

F=C+2-P=1+2-2=1F=C+2-P=1+2-2=1Thus on any curve, the system has one Thus on any curve, the system has one

degree of freedom.degree of freedom.7.7.From diagm it is clear that the solid From diagm it is clear that the solid

phase can be changed to vap. Phase only phase can be changed to vap. Phase only below the triple point ‘O’. This below the triple point ‘O’. This sublimation of any substance(solid to sublimation of any substance(solid to vapor) possible only below the condn of vapor) possible only below the condn of triple point.triple point.

8.8.The curve OC is having a slope towards The curve OC is having a slope towards the pressure axis indicating that the the pressure axis indicating that the m.pt of ice decreases with increase of m.pt of ice decreases with increase of pressure.pressure.

9.9. The area AOB represents water The area AOB represents water vapor only i,e one phase only. vapor only i,e one phase only.

10.10. The area AOC represents liquid The area AOC represents liquid water only i,e one phase only.water only i,e one phase only.

11.11. The area BOC represents ice phase The area BOC represents ice phase only i,e one phase only.only i,e one phase only.

F=C+2-P=1+2-1=2F=C+2-P=1+2-1=2Thus the system is bivariant if only Thus the system is bivariant if only

one phase has to exist.one phase has to exist.

Metastable or super cooled Metastable or super cooled water/vapor:-water/vapor:-

Water can be super cooled by Water can be super cooled by carefully eliminating the solid carefully eliminating the solid particles. The super cooled particles. The super cooled water/vapor system OA is water/vapor system OA is metastable(unstable).metastable(unstable).

If a slight disturbance is caused or if If a slight disturbance is caused or if crystal of ice is introduced then it crystal of ice is introduced then it reverse to a stable system ice/vapor.reverse to a stable system ice/vapor.

Two Component Two Component Systems-Silver Lead Systems-Silver Lead

systemsystemIt is a two component system, the two It is a two component system, the two components being silver & lead.components being silver & lead.

These two metals are completely These two metals are completely miscible in liq state and donot react to miscible in liq state and donot react to form any compd but on solidification, form any compd but on solidification, the form of a eutectic(an easy melting the form of a eutectic(an easy melting mixture).Thus it is also example for mixture).Thus it is also example for eutectic system.eutectic system.

The four phases take part in eqlbm The four phases take part in eqlbm areare

i.i. Solid leadSolid leadii.ii. Solid silverSolid silveriii.iii.Solution of lead & silverSolution of lead & silveriv.iv.VaporVaporBut since the b.pts of Ag & Pb are But since the b.pts of Ag & Pb are

high, the gaseous phase is absent, high, the gaseous phase is absent, therefore the pressure has negligible therefore the pressure has negligible effect.effect.

So, solid-liquid system with gas phase So, solid-liquid system with gas phase absent is called condensed system.absent is called condensed system.

So, according to phase ruleSo, according to phase rule

Therefore the system is nonvariant, Therefore the system is nonvariant, when phases are three.when phases are three.

The eqlbm phase diagm taking temp. The eqlbm phase diagm taking temp. & composition along the axis can be & composition along the axis can be shown asshown as

F = C + 1 - P

Reduced phase rule eqn

F.Pt curve

of AgF.Pt curve of Pb

FE

the phase diagram of system consists of the phase diagram of system consists of two curves AC & BC intersecting at the two curves AC & BC intersecting at the point C.point C.

CURVESCURVESCurve AC :Curve AC :The m.pt of Ag is 961°C.The The m.pt of Ag is 961°C.The

continous addn of Pb in it lowers the m.pt continous addn of Pb in it lowers the m.pt along AC.The point A is the M.pt of silver along AC.The point A is the M.pt of silver falls gradually at the point C.If more lead is falls gradually at the point C.If more lead is added, it separates out as a solid. AC is added, it separates out as a solid. AC is called as F.pt curve of silver.Two phases called as F.pt curve of silver.Two phases exist in eqlbm along AC i,e solid Ag & exist in eqlbm along AC i,e solid Ag & solution of pb & Ag. Thus the system is solution of pb & Ag. Thus the system is monovariant at constant pressure. monovariant at constant pressure. F=C-P+1=2-2+1=1F=C-P+1=2-2+1=1

Curve BC :Curve BC :The m.pt of pure Pb is The m.pt of pure Pb is 327°C.The continous addn of Ag in it 327°C.The continous addn of Ag in it lowers the m.pt along BC.The point B lowers the m.pt along BC.The point B is the M.pt of lead falls gradually at is the M.pt of lead falls gradually at the point C. If more silver is added, it the point C. If more silver is added, it separates out as a solid. BC is called separates out as a solid. BC is called as F.pt curve of lead.Two phases exist as F.pt curve of lead.Two phases exist in eqlbm along BC i,e solid Pb & in eqlbm along BC i,e solid Pb & solution of pb & Ag. Thus the system solution of pb & Ag. Thus the system is monovariant at constant pressure. is monovariant at constant pressure. F=C-P+1=2-2+1=1F=C-P+1=2-2+1=1

EUTECTIC POINT(C) :EUTECTIC POINT(C) : Eutectic point is defined as the lowest Eutectic point is defined as the lowest

temp at which the liq mixture of two temp at which the liq mixture of two components separate simultaneously in components separate simultaneously in solid form having same composition in solid form having same composition in solution.solution.

It is the point (c) at which AC & BC It is the point (c) at which AC & BC meet.The pt. C being common to both meet.The pt. C being common to both curves, the three phases solid Pb, solid curves, the three phases solid Pb, solid Ag and their liq soln co-exist. The Ag and their liq soln co-exist. The degree of freedom is zero I,e it is non-degree of freedom is zero I,e it is non-variant. variant.

The point C has lowest temp. of 303°C The point C has lowest temp. of 303°C at which the liq can exist and if liq is at which the liq can exist and if liq is cooled below this temp, both cooled below this temp, both components separate in solid form components separate in solid form having composition 2.6% of Ag and having composition 2.6% of Ag and 97.6% of Pb. An alloy of Ag & Pb with 97.6% of Pb. An alloy of Ag & Pb with this composition,Ag melts at 303°C this composition,Ag melts at 303°C lower than M.pt of Ag & Pb.lower than M.pt of Ag & Pb.

A liq mixture of two components such A liq mixture of two components such as Ag & pb which as lowest freezing as Ag & pb which as lowest freezing pt compared to all other liq mixtures pt compared to all other liq mixtures is called Eutectic mixture. is called Eutectic mixture.

Below the line EF, the diagram is Below the line EF, the diagram is divided into two regions on left of divided into two regions on left of line CD, crystalline Pb & eutectic line CD, crystalline Pb & eutectic mixture are stable. On the right line mixture are stable. On the right line CD, crystalline Ag & eutectic CD, crystalline Ag & eutectic mixture are stable.mixture are stable.

If a fused mixture rich in Ag is If a fused mixture rich in Ag is cooled, Ag begins to crystallise out. cooled, Ag begins to crystallise out. Similarly rich in Pb is cooled, Pb Similarly rich in Pb is cooled, Pb begins to crystallise out.begins to crystallise out.

AREAS:AREAS:The region above the curve ACB The region above the curve ACB

represents the molten mix of Ag & Pb. represents the molten mix of Ag & Pb. The region enclosed by the curve BCE The region enclosed by the curve BCE

represents the molten mix of Ag & Pb & represents the molten mix of Ag & Pb & solid lead.solid lead.

The region enclosed by the curve ACF The region enclosed by the curve ACF represents the molten mix of Ag & Pb & represents the molten mix of Ag & Pb & solid Ag.solid Ag.

Therefore change of both composition & Therefore change of both composition & temp will not change the of phases & the temp will not change the of phases & the system in any region is bivariant.system in any region is bivariant.

Application of silver lead system in Application of silver lead system in desilverisation of lead:desilverisation of lead:

The behaviour of Pb-Ag system on cooling The behaviour of Pb-Ag system on cooling is used to enrich the content of Ag in a is used to enrich the content of Ag in a mixture containing less than 2.4% Ag in mixture containing less than 2.4% Ag in Pattisons Process. Pattisons Process.

Pattisons Process:Pattisons Process:It is used for the desilverisation of lead is It is used for the desilverisation of lead is

based on phase diagram of Pb-Ag system.based on phase diagram of Pb-Ag system.Galena, an ore associated with small Galena, an ore associated with small

amount i,e traces of Ag. When lead is amount i,e traces of Ag. When lead is extracted, some traces extracted, some traces

of Ag pass in to lead, bcos silver is of Ag pass in to lead, bcos silver is soluble in lead to some extent. The Pb soluble in lead to some extent. The Pb obtained is called as Argentiferrous obtained is called as Argentiferrous Lead.Lead.

The argentiferrous Lead is heated above The argentiferrous Lead is heated above its m.pt.So,the system attains liq state.its m.pt.So,the system attains liq state.

The pt. x in the phase diagm represents The pt. x in the phase diagm represents the molten state which is allowed to the molten state which is allowed to cool. The temp will fall along the line cool. The temp will fall along the line xy with out any change in concn till the xy with out any change in concn till the point y is reached.point y is reached.

And then the lead begins to crysatallise And then the lead begins to crysatallise out and there is increase in the amount out and there is increase in the amount of Ag.of Ag.

The separated lead is removed by means The separated lead is removed by means of ladels.of ladels.

The amount of Ag rises to 2.4.The amount of Ag rises to 2.4. The original Argentiferrous lead The original Argentiferrous lead

contains 0.1% of Ag, but now contains contains 0.1% of Ag, but now contains 2.4% of Ag metal.2.4% of Ag metal.

The process of increasing the proportion The process of increasing the proportion of Ag in alloy is known as Pattisons of Ag in alloy is known as Pattisons process.process.

Pattisons Process