Phase Rule1

8/3/2019 Phase Rule1

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PHASE DIAGRAM OF CO2

Resembles with the phase diagram

of H2O because CO2 can also exist inthree different phases under

different conditions


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PHASE DIAGRAM OF CO2


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PHASE DIAGRAM OF CO2 Salient features

CO2(liq.) CO2(g)

On CURVE OA

Number of phases, P = 2

Number of components, C = 1

Applying Phase RuleDegrees of freedom, F = C P + 2 = 1 2 + 2 = 1

Hence the curve OA is univariant.

(i) Curve -OA Representsvaporizationcurve of CO2

Along this curve liquid & gas phase of CO2are in equilibrium


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CO2(solid) CO2(gas)

On CURVE OB



Applying Phase RuleDegrees of freedom, F = C P + 2 = 1 2 + 2 = 1

Hence the curve OB is univariant.

ii. Curve -OB

Representssublimation curve of CO2 Along this curve solid & gas phase of CO2are in equilibrium


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CO2(solid) CO2(liq.)

On CURVE OC



Applying Phase Rule

Degrees of freedom, F = C P + 2

= 1 2 + 2 = 1

Hence the curve OC is univariant

Noteworthy- The curve OC is inclined away from the P axis

indicating that M.P. of solid CO2 increases with the increase in P

iii. Curve -OC

RepresentsFusioncurve of CO2 Along this curve solid & liquid phase of CO2are in equilibrium


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CO2(solid) CO2(liq.) CO2(gas)

Hence, at point O

Number of phases, P = 3Number of components, C = 1

Applying Phase Rule


= 1 3 + 2 = 0

Hence the curve OC is univariant

Thus point O represents an invariant point as both T & P are fixed

at this point. It is obtained at -57C & 5.2 atm pressure

iv. Triple point -O

At this point O, 3 phases of CO2exist in equilibrium


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SoIn AREA BOC

Number of phases, P = 1Number of components, C = 1

Applying Phase Rule


= 1 1 + 2 = 2

Hence the curve OC is Bivariant

In all the 3 areas, F = 2; So, in all these areas system is bivariant

v. Areas between Curves BOC, AOC, AOB

In each area 1 particular phase is present, e.g. area BOC consistsof solid CO2only.


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TWO COMPONENT SYSTEMS (C=2)

System containing two different chemicalconstituents is called a 2 C system

For the analysis of2 C systems following termsneed to be understood

(i) Reduced phase rule

(ii) Eutectic Mixture

(iii) Cooling Curve

Applications of Phase Rule to two component system


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Reduced Phase Rule

The degrees of freedom of any 2 C system can beascertained by the application of phase rule

F = C - P + 2 or = 2 P + 2 or = 4 P

Since the minimum no of phase is 1 in any 2C

system, the maximum no of degrees of freedom

in a 2C system can be 3.

It means 3 variables are required to describe the systemcompletely


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To analyze these variable a 3 D graph is needed to be

drawn.

Since it is difficult to draw a 3D graph, so for the sake of

convenience, P is taken as constant

(because in 2C systems consisting only solid and liquid phase,

vapor phase is not +nt, effect of v.p. is negligible)

So the value ofF is reduced by 1.

In such a case, phase rule reduces to

F = C - P + 1

So the phase diagram is drawn in between T & Composition

Reduced Phase Rule


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Eutectic Mixture

System with a mixture of two substances which are miscible in allproportions in liquid phases but do not react chemically is called aEutectic System

(Eutectic = easy to melt)

The components of eutectic system has the property to lowering the

freezing point of each other

A eutectic mixture is defined as the mixture of 2 substances in solidphase which has the lowest freezing point.

e.g. when Pb (m.p.=327C) and Ag (m.p.=961C) are mixed in ratio,

97.4% Pb and 2.6% Ag, the resulting mixture is called eutecticmixture with a freezing point at 303C (lower than Pb & Ag)


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Eutectic temperature OR Eutectic point

The lowest freezing Temp. obtained in a eutectic system

Applications of Eutectic Mixtures

1. As safety devices in fire extinguishers, automobiles and boilers

2. In preparing solders for joining 2 metal pieces together

Very low melting alloys can be made by suitable choice of metals

e.g. An alloy containing 50 % Bi, 25 % Pb, 12.5 % Cd & 12.5 % Sn has a

m.p. of 65 C.

This alloy is called woods metal.


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Some representative eutectic systems


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COOLING CURVE OF A 1 COMPONENT SYSTEM

A cooling curve represents the decrease in temp.

of a system when it is continuously cooled Consider a 1 C system consisting of a

chemical X

At point A system is in liquid phase.

On cooling, T of system decreases

along line AB.

Suppose the T corresponding to point

B is the freezing point of chemical X

Then, at point B, freezing of chemical

X will start.

At point c, only solid phase is +nt and further cooling will decrease

the T of X so CD is obtained

Further cooling will result in complete freezing of X (line BC)(conversion of liq. phase into solid)


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COOLING CURVE OF A 2-COMPONENT SYSTEM

Consider a 2 C system consisting a mixture of 2 chemicals X & Y

On cooling the system, T decreases alongline AB

Suppose point B corresponds to thefreezing of X, then freezing of X will start

at point B but Y will remain in liq phase.Hence line BC is obtained

At point C, chemical Y will also start

freezing and line CD is obtained

At point D only solid phase is +nt

Hence curve DE represents the cooling ofsolid

T corresponding to CD is

called eutectic T, as it is the

lowest freezing point.


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PHASE DIGRAM OF 2C SYSTEM

In this phase diagram- 3 phases are present

(i) Solid Lead

(ii) Solid Silver

(iii) Homogeneous solution of Pb & Ag

(completely miscible-constitute 1 phase)

Lead Silver System


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Lead-Silver System Salient featuresPhase Diagram


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Lead-Silver System Salient features

The co-existence of different phasesin Pb-Ag System is shown in fig.

(a) Area -ACB

Within ACB a homogeneous singlephase of molten liquid of twocomponents (Pb and Ag) existsi.e. P=1, C=2

Applying the reduced phase rule-

F= C P + 1 = 2 1 +1 = 2 (T & C)

Hence system in area ACB is bivariant(to describe any point in area ACB,both T and C have to bespecified)


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(b) Melting Point curves

-AC & BC

Points A & B represents M.P.of pure Pb (327C) & pure Ag

(961C) respectively

The curve AC represents thevariation of meltingTemp. of Pb, while curve

BC indicates the decreaseof melting point of Agwith the addition of Pb


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The states of equilibrium curvesAC & BC represent a 2 phaseequilibrium

1. Pb (s) Molten liquid (Melt)

P = 2, C = 22. Ag (s) Molten liquid (Melt)

P = 2, C = 2

Applying reduced phase rule

F = C P + 1 = 2 2 + 1 = 1 (T or C)

Hence system is univariant i.e. Cchanges with T, withoutdisturbing 2 P equilibrium


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(c) Eutectic of Pb & Ag

Point C denotes a Eutectic

point, all the 3 phases,

Pb(s), Ag(s) and molten

liquid exists at a definitecomposition & Temp.

P = 3, C = 2

Applying reduced phase rule

F = C P + 1 = 2 3 + 1 = 0

(invariant)


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Eutectic point C is a state of 2 C (Pb & Ag)- Ahomogeneous solid of definite composition (97.4% Pb

and 2.6% Ag) which melts at the lowest Temp. (303C)



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It can be seen from the graph that below the tie line DD,

corresponding to the eutectic temp. (303C), only solidphases co-exist

For compositionbelow the tie lineDCD,

The area below DC, contains Pb (s) & solid Eutecticmixture of Pb & Ag

The area below CD, contains Ag (s) & solid Eutecticmixture of Pb & Ag

For composition exactly at point C, a homogeneous solidof eutectic (97.4% Pb and 2.6% Ag) crystallizes out.

This eutectic melts exactly at 303C



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Understanding of Pb-Ag system is useful to understand the concept of

Pattinsons process and the enrichment of Ag in argentiferrous Pb

Application of Lead-Silver SystemDesilverizationof Lead

PATTINSONS PROCESS

Galena- ore of Pb


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Desilverizatio of LeaPATTINSONS PROCESS

If a molten liq. ofargentiferrous lead of

composition X (0.1% Ag) is allowed tocool gradually solid Pb crystallizes outat the point Y (at T) on the AC curveand the composition of theargentiferrous lead changes along YCwith the enrichment of Ag.

The crystallized Pb is constantlyremoved.

The melt becomes continuously richerand richer in the Ag content until theeutectic point C is reached where thecontent of Ag is 2.6%.

This process of increasing the relativeproportion of Ag in argentiferrous Pb isknown as Pattinsons process.


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Phase Rule1

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