Alloys & Phase Rule Notes FE Sem 1 Applied Chemistry | MU

Pure metals rarely have the right combination of strength, hardness, melting point and corrosion resistance, so engineers use alloys. This module explains why alloys are made and introduces the Gibbs phase rule, a thermodynamic tool that predicts how many variables can be changed without disturbing an equilibrium. The reduced phase rule is then applied to the lead-silver system, a simple eutectic that explains the desilverisation of lead. Questions on phase rule terms, degree-of-freedom calculations and the Pb-Ag diagram are regular in MU papers.

Summary

An alloy is a metallic material made by mixing two or more elements, usually in the molten state, at least one of which is a metal; it may be a single-phase solid solution or a mixture of phases (like the Pb-Ag eutectic). Alloys are made to increase hardness and tensile strength (steel, duralumin), to lower the melting point (solder, a Pb-Sn alloy, melts below either metal), to improve corrosion resistance (stainless steel with Cr and Ni), to improve castability and machinability (bronze, brass), to modify colour (brass, gold alloys), to change electrical and magnetic properties (nichrome for heating elements, alnico magnets), and to reduce cost while retaining useful properties.

The Gibbs phase rule states that for a heterogeneous system in equilibrium, influenced only by temperature, pressure and concentration, the number of degrees of freedom F is related to the number of components C and the number of phases P by F = C - P + 2. It is derived from thermodynamics and applies to both physical and chemical equilibria.

A phase is any homogeneous, physically distinct and mechanically separable part of a system, separated from other parts by a definite boundary. All gases mix completely and form one phase; miscible liquids form one phase while immiscible liquids form separate phases; every solid forms a separate phase. Examples: water system ice-water-vapour has 3 phases; CaCO3(s) = CaO(s) + CO2(g) has 3 phases (two solids and one gas); a sugar solution is one phase.

The number of components is the smallest number of independently variable chemical constituents needed to express the composition of every phase. Water system has C = 1; sulphur system C = 1; CaCO3 decomposition C = 2 (any two of CaCO3, CaO, CO2); NH4Cl(s) = NH3(g) + HCl(g) heated in a closed vessel C = 1 because NH3 and HCl are in fixed 1:1 ratio; NaCl-water C = 2. Degree of freedom is the minimum number of independent variables (T, P, concentration) that must be specified to define the system completely. Water at its triple point is invariant (F = 0), ice-water equilibrium is univariant (F = 1), and pure liquid water is bivariant (F = 2).

In solid-liquid (condensed) systems such as alloys, the gas phase is practically absent and pressure has little effect, so experiments are done at constant atmospheric pressure. One degree of freedom is thus already fixed, giving the reduced or condensed phase rule F' = C - P + 1. A two-component system is then described by a temperature-composition diagram.

The Pb-Ag system is a simple eutectic system with two components. Point A (961 C) is the melting point of pure Ag and point B (327 C) that of pure Pb. Curve AO is the freezing point curve of Ag, along which solid Ag is in equilibrium with the melt; curve BO is the freezing point curve of Pb, along which solid Pb is in equilibrium with the melt; on both curves P = 2 and F' = 1. The curves meet at the eutectic point O (303 C, 2.6% Ag and 97.4% Pb), where solid Ag, solid Pb and melt coexist, so P = 3 and F' = 0 (invariant). The area above AOB is a single liquid phase with F' = 2; the area below AO has solid Ag + melt and below BO solid Pb + melt (F' = 1); below the eutectic line the system is fully solid (Ag + eutectic or Pb + eutectic).

The Pb-Ag diagram explains Pattinson's process for desilverisation of argentiferous lead, which contains only a small percentage of silver. When such molten lead is cooled, pure lead crystallises along curve BO and is removed with ladles, so the melt becomes richer in silver until it reaches the eutectic composition of 2.6% Ag at 303 C. The silver is then recovered from this enriched alloy by cupellation (oxidising the lead).

Merits of the phase rule: it applies to physical and chemical equilibria alike; it uses macroscopic variables only, without needing the molecular structure; it classifies systems as invariant, univariant or bivariant and predicts their behaviour; it shows that different systems with the same F behave alike; and it is useful for studying alloys, metallurgy and phase diagrams. Limitations: it applies only to systems in true equilibrium, so slow-equilibrating systems are difficult; it considers only temperature, pressure and concentration and ignores electric, magnetic and gravitational effects; all phases must be at the same temperature and pressure; solids and liquids must not be so finely divided that surface effects matter; and it gives only qualitative information, not the amount of each phase or the rate of change.

Mind map

Cooling of argentiferous lead in Pattinson's process (Pb-Ag diagram)

Important definitions

Formulas

Key points to remember

• Gases always form a single phase; each solid is a separate phase.
• For CaCO3 = CaO + CO2: C = 2, P = 3, F = 1.
• For NH4Cl = NH3 + HCl from pure NH4Cl: C = 1; if extra NH3 or HCl is added, C = 2.
• Water triple point: C = 1, P = 3, F = 0.
• Pb mp 327 C, Ag mp 961 C, eutectic 303 C at 2.6% Ag, 97.4% Pb.
• At the eutectic point F' = 2 - 3 + 1 = 0.
• On curves AO and BO, F' = 1; in the liquid area F' = 2.
• A eutectic is not a compound; it has a fixed composition only at the given pressure and shows a mixture of crystals under a microscope.
• Pattinson's process is a practical application of the Pb-Ag diagram.
• The phase rule tells how many variables can be changed, not how much of each phase is present.

Solved examples

Example 1. Find the number of phases, components and degrees of freedom for water at its triple point.

Phases: ice, liquid water and water vapour, P = 3. Component: all phases are H2O, C = 1. F = C - P + 2 = 1 - 3 + 2 = 0. The system is invariant: the triple point occurs at a fixed temperature (0.0098 C) and pressure (4.58 mm Hg).

Example 2. Calculate P, C and F for the thermal decomposition CaCO3(s) = CaO(s) + CO2(g) in a closed vessel.

Phases: solid CaCO3, solid CaO and gaseous CO2, P = 3. Species N = 3, independent reactions R = 1, so C = 3 - 1 = 2. F = C - P + 2 = 2 - 3 + 2 = 1. The system is univariant: at a given temperature the CO2 pressure is fixed.

Example 3. Calculate the degrees of freedom for NH4Cl(s) = NH3(g) + HCl(g) when pure NH4Cl is heated in a closed vessel. What happens if extra NH3 is added?

Phases: solid NH4Cl and one gas phase, P = 2. Species N = 3, one reaction, and the gases are formed in 1:1 ratio (a concentration restriction), so C = 3 - 1 - 1 = 1. F = 1 - 2 + 2 = 1 (univariant). If extra NH3 is added, the 1:1 restriction is lost, C = 2, and F = 2 - 2 + 2 = 2 (bivariant).

Example 4. Find F for a saturated solution of NaCl in water in contact with excess solid NaCl and water vapour.

Phases: solid NaCl, solution, vapour; P = 3. Components: NaCl and H2O; C = 2. F = 2 - 3 + 2 = 1. Fixing temperature fixes both vapour pressure and solubility.

Example 5. Find P, C and F for Fe(s) + H2O(g) = FeO(s) + H2(g).

Phases: solid Fe, solid FeO and one gas phase (H2O + H2), P = 3. Species N = 4, one reaction R = 1, so C = 3. F = 3 - 3 + 2 = 2.

Example 6. Apply the reduced phase rule to the Pb-Ag system at (a) the liquid area, (b) a point on curve BO and (c) the eutectic point.

C = 2 throughout and F' = C - P + 1. (a) Liquid melt only, P = 1: F' = 2 - 1 + 1 = 2; both temperature and composition must be stated. (b) Curve BO: solid Pb + melt, P = 2: F' = 2 - 2 + 1 = 1; fixing temperature fixes melt composition. (c) Eutectic point O: solid Pb + solid Ag + melt, P = 3: F' = 2 - 3 + 1 = 0; temperature (303 C) and composition (2.6% Ag) are both fixed.

Example 7. How many phases and degrees of freedom are there in a mixture of N2 and O2 gases?

Gases mix completely, so P = 1. Two independent species, C = 2. F = 2 - 1 + 2 = 3: temperature, pressure and one composition variable must be specified.

Important questions and answers

Q1. What is the purpose of making alloys? Give examples. (4 marks)

(1) To increase hardness and strength: steel (Fe + C), duralumin (Al with Cu, Mg, Mn). (2) To lower the melting point: solder (Pb + Sn) and Wood's metal. (3) To resist corrosion: stainless steel (Fe with Cr and Ni). (4) To improve casting: bronze (Cu + Sn) gives sharp castings. (5) To modify colour: brass (Cu + Zn) has a gold-like colour. (6) To modify electrical and magnetic properties: nichrome (Ni + Cr) for heating coils, alnico for magnets.

Q2. State Gibbs phase rule and explain the terms involved with examples. (6 marks)

Statement: if the equilibrium between any number of phases is influenced only by temperature, pressure and concentration, then F = C - P + 2. Phase: homogeneous, physically distinct, mechanically separable part; e.g. ice, water and vapour (P = 3); gas mixture (P = 1); CaCO3 decomposition (P = 3). Component: smallest number of independently variable constituents to express the composition of each phase; e.g. water system C = 1, CaCO3 = CaO + CO2 C = 2, NH4Cl from pure salt C = 1. Degree of freedom: minimum number of independent variables needed to define the system; e.g. triple point F = 0, water-vapour equilibrium F = 1, water alone F = 2.

Q3. What is the reduced phase rule? Why is it used for alloy systems? (3 marks)

For solid-liquid equilibria the vapour phase is negligible and pressure has very little effect, so such systems are studied at constant atmospheric pressure. Since pressure is fixed, one degree of freedom is lost and the rule becomes F' = C - P + 1. Alloy systems such as Pb-Ag are condensed systems, hence the reduced phase rule is used.

Q4. Draw and explain the phase diagram of the Pb-Ag system. (6 marks)

Axes: temperature (y) vs composition from 100% Ag to 100% Pb (x). A = mp of Ag (961 C); B = mp of Pb (327 C). Curve AO: freezing point curve of Ag; adding Pb lowers the freezing point of Ag; solid Ag + melt, F' = 1. Curve BO: freezing point curve of Pb; adding Ag lowers it; solid Pb + melt, F' = 1. Eutectic point O: 303 C, 2.6% Ag, 97.4% Pb; solid Ag + solid Pb + melt, P = 3, F' = 0. Area above AOB: liquid melt, F' = 2. Area below AO: solid Ag + melt; below BO: solid Pb + melt. Below the eutectic temperature line: solid Ag + eutectic (left) and solid Pb + eutectic (right). Application: Pattinson's process.

Q5. Explain Pattinson's process for desilverisation of lead. (4 marks)

Argentiferous lead containing a small amount of silver is melted and allowed to cool slowly. Its composition lies to the Pb side of the eutectic, so when the temperature reaches curve BO pure lead crystallises out. The lead crystals are removed with ladles; the melt becomes richer in Ag and moves along BO. The process is repeated until the melt reaches the eutectic composition of 2.6% Ag at 303 C. Silver is then recovered from this enriched alloy by cupellation.

Q6. Give the merits and limitations of the phase rule. (4 marks)

Merits: applies to physical and chemical equilibria; uses only macroscopic variables; independent of molecular structure; classifies systems as invariant, univariant, bivariant; similar F gives similar behaviour; useful for alloys and metallurgy. Limitations: only for systems in equilibrium; considers only T, P and concentration, not electric, magnetic or gravitational forces; all phases must be at the same T and P; solids and liquids must not be finely divided; gives no information on amounts of phases or rates.

Q7. Calculate the number of components in (i) CaCO3 = CaO + CO2 and (ii) NH4Cl = NH3 + HCl. (3 marks)

(i) Three species, one reaction: C = 3 - 1 = 2. (ii) Three species, one reaction, and NH3 and HCl in fixed 1:1 ratio when formed from pure NH4Cl: C = 3 - 2 = 1.

Q8. Define eutectic mixture and eutectic point. Why is the eutectic point invariant? (3 marks)

A eutectic mixture is the mixture of two components with the lowest melting point possible in that system; it melts at constant temperature like a pure substance. The eutectic point is where the two freezing point curves meet. At this point three phases coexist (two solids and melt) in a two-component system at constant pressure, so F' = 2 - 3 + 1 = 0; temperature and composition are fixed.

Q9. Calculate F for water at the triple point and for the ice-water equilibrium. (3 marks)

Triple point: C = 1, P = 3, F = 1 - 3 + 2 = 0. Ice-water: C = 1, P = 2, F = 1 - 2 + 2 = 1; if pressure is fixed, the melting temperature is fixed.

Exam tips

• Draw the Pb-Ag diagram with all labels: A (961 C), B (327 C), O (303 C, 2.6% Ag), curves, areas and F' values.
• Always state which rule you use: full phase rule for systems with a gas phase, reduced rule for condensed alloy systems.
• For component counting, write C = N - R and list the reactions and restrictions.
• Give an example for each term (phase, component, degree of freedom) in the 6-mark definition question.
• Learn three merits and three limitations; they are asked as 4-mark short notes.

FAQs

Why does the eutectic point have zero degrees of freedom?

Because three phases (solid Pb, solid Ag and melt) coexist in a two-component system at constant pressure: F' = 2 - 3 + 1 = 0.

Is a eutectic mixture a compound?

No. It is a mixture of fine crystals of both components; its composition changes with pressure and it shows separate crystals under a microscope.

Why is the gas phase ignored in the Pb-Ag system?

The vapour pressures of Pb and Ag are negligible at the temperatures studied, and pressure hardly affects solid-liquid equilibria, so the system is treated as condensed at constant pressure.

Is the phase rule useful for alloys?

Yes, it predicts the number of phases and variables at each temperature and composition, which helps in choosing alloy compositions and in processes such as desilverisation of lead.

These notes follow the University of Mumbai first-year engineering syllabus (NEP 2020, Applied Chemistry) and were prepared with AI help and checked.