What is the phase rule? Explain in the brief two-component system with a diagram. (CO4)

Two-component system

System in which the composition of all the phases can be expressed in terms of two substances

For two component system the phase rule becomes

F = C - P+ 2

= 2 - P + 2 = 4 - P

Minimum P = 1

∴ $ F_(Max)$ = 2-1 + 2 = 3

Thus three variable would be necessary to describe the system

Besides Temperature and Pressure another variable will be Concentration

A. 3-D model is required : Difficult to Plot

3 options:

P-T Diagram (at constant concentration) - Isoplethal

C-P Diagram (at constant temperature) - Isothermal

T-C (Temperature – Composition) Diagram (at constant pressure) - Isobaric

Easy to keep Pressure constant at atmospheric value and take T-C (Temperature - composition) diagram

This reduces the Degree of Freedom of system by one and

Phase rule equation is written as

F' = C-P+1 (Reduced Phase Rule)

= 2 - P+1 = 3 –P.

Eutectic system

• Eutectic – Easy to melt

• Binary system in which

• two components are miscible in all proportions in the liquid (molten) state and

  • these components do not react chemically

  • each component has the property of lowering each other's freezing point

Freezing point Temp. at which Liquid ⇔ Solid at $P_(atomospheric) $

• Eutectic mixture:

• a solid solution of two component system which has the lowest freezing point of all the possible mixtures of the components

Type A: Simple Eutectic Systems

Eutectic system

A single chemical composition of a mixture (of chemical compounds or elements) that solidifies at a lower temperature than any other composition

Composition: Eutectic composition and

Temperature: Eutectic temperature

At Constant Pressure

• Point A and B (m.pt.)

• Adding increasing quantities of B to

• Curve AC and BC called

• No. of phases along AC (or BC) = 2

• F' = C-P+1 = 2 - 2 + 1 = 1 (at constant pressure Composition varies with Temp. along AC (or BC) Two curves intersect at point C (lowe m.pt.)

At point C;

F' = C-P + 1

F' = 2 – 3+ 1 = 0

Point C: lowest temperature at which liquid (solution) can exist in equilibrium with A(solid) and B(solid)

• Consider temperature t, and tz

Composition varies with temperature along AC (or BC)

• Curve AC, Asolid) is in equilibrium with solutions of varying composition depending upon T Liquid mixture of composition a (cooled at constant P)

• At b; A(solid) separate out; temp. can change only when system moves along path bc At point C, second B(solid) also begins to crystallize out

• 3 Phases (at constant Pressure), it becomes invariant • F' = C-P+1 - = 2 - 3 + 1 = 0

• On cooling further, A(solid) and B(solid) continue to separate in the same ratio as that of solution composition (i.e., fixed ratio) and T remains constant (till 3 phases coexist)

• Composition of solution also remains constant (Point C)

•When solution phase solidifies completely, only then Temp. can fall below line DD'

• Now, mixture of Assolid) and B(solid) present; F' = C-P+1 F'= 2 - 2 + 1 = 1; monovariant

•Further cooling result in fall of Temp. below DD' line

•At a' and

• At z

Eutectic Point

• Minimum freezing point attainable corresponding to the eutectic mixture is called eutectic point (i.e., lowest melting point)

• The eutectic mixture has a definite composition and a sharp melting point. In this respect it resembles a compound

• However, it is not a compound as the components are not present in stoichiometric proportions

• When such a solid is examined under a powerful microscope, both the constituents are seen to lie as separate crystals

• Moreover, physical properties such as density and heat of solution of eutectic solid are almost equal to the mean values of the constituents

Phase Diagram of Lead-Silver System

Metals completely miscible in liquid state and do not form any compound

• M.pt. of Pb and Ag

•Freezing point curves of Pb and Ag

• Along curve AC: Pb(solid) and sol. coexist

• Curve AC and BC, P=2, F'=1 (Pressure = 1 atm.), Monovariant

• Ponit C (Eutectic: 303°C, 2.6% Ag): P = 3 [Pb(solid), Ag(solid) and solution coexist], F' = 0

• Area above AC and BC

Desilverization of Lead

•Argentiferous lead consisting of very small (about 0.1 %) of Ag is heated to temperature above its melting point (above 327°C) – liquid phase (point a)

Allowed to cool

• At b, Lead will begin to crystalize out and solution will become richer in Ag

Further cooling: along bc

• Pure Pb(solid) separated out (i.e.,Desilverization of lead) and constantly removed with ladle

At Eutectic point (C) argentiferous lead contains 2.6% Ag

• Process of raising relative proportion of Ag is called Pattinson's Process

Alloys

• Few useful properties possessed by metals are

• High malleability

• ductility

• luster and

• good electrical conductivity

These properties of metals are not sufficient for most of the applications that also requires

• tensile strength

• corrosion resistance and

• hardness

• Properties of metal can be improved by mixing (alloying) it with some other metal / non-metall

Applications

• Use of alloys as

• 'fail – safe' device in boilers

• as plugs in automobiles

• fire – splinklers and

• other such safety devices

• Eutectic systems, because of their low melting points are also used for

• joining two metal pieces together (e.g., Pb – Sn solders)