Unit 5 Phase Rule

UNIT 5 PHASE RULE PART – A 1. State Phase Rule. (Jan 14) If the equilibrium between any number of phases is not affected by external factors such as gravity, or electrical, or magnetic forces, or by surface action, and affected only by temperature, pressure and concentration, then number of degrees of freedom (F) of the system is related to number of components (C) and number of phases (P) by phase rule equation, F=C–P+2 (for any system in equilibrium at a definite temperature and pressure). 2. Define Phase with examples. (May 16, Nov 16) Phase is defined as a homogeneous, physically distinct and mechanically separable portion of a system which is separated from other such parts of the system by definite boundary surfaces. Examples (i) A gaseous mixture of nitrogen and hydrogen forms one phase only. (ii) Immiscible liquids (water and benzene) form two phases. Miscible liquids (alcohol and water) forms a single phase. (iii) Sulphur exists in monoclinic and rhombic forms. 3. Define Component with examples. (Jan 14) It is the smallest number of independent variable constituents taking part in the state of equilibrium, by means of which the composition of each phase in the system can be expressed in the form of chemical equation. While expressing the composition of a phase in terms of components, zero and negative quantities of components are permissible. Examples (i) Water exists in three phases in equilibrium. But chemical composition of each phase can be expressed in terms of H2O. Hence water is one component system. (ii) Similarly Sulphur exists in four phases namely Monoclinic, Rhombic, liquid and vapour. As chemical composition of all phases is S, it is also one component system. 4. Define Degree of Freedom with examples. (Jan 13, May 13, May 15, May 16, May 18) It is the minimum number of independent variable factors such as temperature, pressure and composition, which must be specified in order to define condition of system completely. A system having 1, 2, 3 and 0 degree of freedom are called univariant, bivariant, trivariant and non-variant respectively. Examples (i) In water system, Ice (s) Water (l) Vapour (g) all three phases may be in equilibrium only at a definite temperature and definite pressure. If T or P is altered, then three phases will not be in equilibrium and one of the phases will 1 disappear. Thus the system has no degrees of freedom. Such a system is said to be nonvariant or invariant. (ii) For a gaseous mixture of nitrogen and hydrogen, pressure and temperature are needed to define the system completely. Hence it has two degrees of freedom. 5. Explain phase diagram with it’s significance. Phase diagram is a graphical representation by plotting one variable against another. In case of one component system, temperature is plotted in X–coordinate and pressure in Y–coordinate and diagram is called as P - T phase diagram. In two component system, a plot of temperature against composition is called T – C diagram. Significance Phase diagram is used to study the relative stability and equilibrium between phases and compositions. They help in studying and controlling various processes such as phase separation, solidification of metals and change of structure during heat treatment, etc. 6. What is condensed phase rule or reduced phase rule? (May 13, Jan 14, May 14, Jan 15, Jan 16, Nov 16, May 18) In a solid-liquid equilibrium of an alloy which has practically no gas phase and the effect of pressure is small on this type of equilibrium. Therefore, experiments are usually conducted under atmospheric pressure. Thus, keeping the pressure constant of a system, in which vapour phase is not considered, is known as condensed system. Since degree of freedom of the system is reduced by one, the phase rule becomes, F=C–P+1 This is known as reduced or condensed phase rule, having two variables, temperature and concentration (or composition) of constituents. 7. Explain melting point, triple point & eutectic point. (May13, May15, Nov 17) (a) At melting point, solid and liquid having same composition are in equilibrium. At triple point, three phases are in equilibrium. At eutectic point, two solids and liquid are in equilibrium. (b) All eutectic points are melting points, but all melting points need not be eutectic points. All eutectic points are triple points, but all triple points need not be eutectics. (c) Melting involves only solid and liquid; vapour may or may not be present. If vapour is present, then melting point becomes a triple point. At eutectic point, instead of liquid if there is third solid, it is called a eutectoid. 8. What are the significance of triple point? (Jan 13) (i) Triple point is temperature at which three phases are in equilibrium. Solid Liquid Vapour (ii) At triple point, all three phases are coexisting and P=3 and phase rule becomes, F = 3 – P = 3 – 3 = 0. Since three phases co-exists, the system is invariant or non-variant. 2 (iii) As degree of freedom at triple point is zero, it is not possible to alter temperature or pressure without disturbing the equilibrium. 9. Differentiate Triple point, Melting point & Eutectic point. (May 13, May 15, May 17) Melting point Temperature at which solid and liquid having same composition are in equilibrium. Eutectic point Temperature at which two solids and one liquid phase are in equilibrium. Triple point Temperature at which three phases are in equilibrium Solid A Solid A + Solid B Solid Liquid A Liquid Liquid Vapour By definition, all eutectic points are melting points, but all the melting points need not be eutectic points. Similarly, all the eutectic points are triple points, but all triple points need not be eutectic points. 10. Write short note on eutectic system with its application. A binary system consisting of two substances, which are miscible in all proportions in liquid phase, which do not react chemically, is known as Eutectic system (easy to melt). E.g. Mixture of lead and silver. Applications Low-melting alloys can be obtained by suitable choice of metals. Low- melting alloys are used in safety devices as plugs in automobiles, fire-sprinklers and fail safe in boilers. 11. Explain Eutectic mixture & Eutectic point. (Jan 13, May 13, Jan 14, Jan 15, Nov 17) Eutectic mixture Eutectic mixture is a solid solution of two or more substances having lowest freezing point of all possible mixture of the components. In Lead–Silver alloy system, at 303 ºC, a fixed composition of Ag = 2.6% and Pb = 97.4% is called as eutectic mixture. Eutectic point Two or more solid substances capable of forming solid solutions with each other have the property of lowering each others freezing point. The minimum freezing point attainable corresponding to eutectic mixture is termed as Eutectic point. The composition corresponding to this eutectic mixture is known as eutectic composition. The temperature corresponding to this eutectic mixture is known as eutectic temperature. 12. Explain solidus and liquidus solution. (May 13) When two substances, particularly metals, are completely miscible in both solid and liquid states, they form solid solutions. Cu - Ni and Ag - Pt are systems in which two metals are mutually soluble in all proportions. Two smooth curves forming a loop characterize the solid solution type. The upper curve is liquidus or freezing curve, above which only liquid is present and lower curve is solidus or melting curve below which only solid phase is present. 3 13. What is meant by Congruent melting point? A compound, which melts sharply at a constant temperature into a liquid of same composition as the solid, is said to possess a congruent melting point. Zn – Mg system is an example of binary alloy with congruent melting point. The components form one or more compounds in some stoichiometric proportions. These compounds are such that they melt into liquid state, having same composition as the solid. 14. Calculate number of phases present in the following systems: (i) MgCO3 (s) MgO (s) + CO2 (g) (ii) Rhombic (s) Monoclinic sulphur (s) (iii) NH4Cl (s) NH3 (g) + HCl (g) (iv) I2 (s) I2 (g) (v) Ice (s) Water (l) Water vapour (g) (vi) an emulsion of oil in water (vii) when CaCO3 (s) is heated (May 16) (viii) system consists of benzene and water (ix) a gaseous mixture of N2, H2 and NH3 in equilibrium (x) saturated solution of NaCl (xi) mixture of hydrogen and oxygen Answer (i) 3 (ii) 2 (iii) 2 (iv) 2 (v) 3 (vi) 2 (vii) 3 (viii) 2 (ix) 1 (May 14) (Jan 15) (Jan 15) (Jan 15) (x) 2 (xi) 1 15. Calculate number of components present in the following systems: (i) CaCO3 (s) CaO (s) + CO2 (g) (ii) Ag (s) + Pb (s) Ag - Pb (l) + Pb + Ag (g) (iii) H2O (l) ½ H2 (g) + O2 (g) (iv) H2O (s) H2 (g) + H2O (g) (v) NH4Cl (s) NH3 (g) + HCl (g) (Jan 14, May 14) (vi) NH4Cl (s) x NH3 (g) + y HCl (g) (May 15) (vii) NaCl (s) NaCl (aq) (viii) Fe (s) + H2O (g) FeO (s) + H2 (g) (ix) water water vaour (Nov 17) (x) KCl + water KCl hydrate (Nov 17) Answer (i) 2 (ii) 2 (iii) 1 (iv) 2 (v) 1 (vi) 2 (vii) 2 (viii) 3 (ix) 1 (x) 2 16. How many degrees of freedom are present in the following systems? (i) A gas in equilibrium with its solution (ii) Solution of a solid in liquid in equilibrium with solvent vapour (iii) Two partially miscible liquids in the absence of vapour (iv) I2 (s) I2 (g) 4 (v) NH3 (g) (vi) NaCl (s) NaCl - water (aq) water-vapour (g) (May 16, May 18) (vii) Rhombic (s) Monoclinic sulphur (s) (May 14) (viii) CaCO3 (s) CaO (s) + CO2 (g) (May 14, May 17) (ix) NH4Cl (s) NH3 (g) + HCl (g) (May 14) (x) ice water (xi) silver and lead at eutectic oint Answer (i) F = C – P + 2 = 2 – 2 + 2 = 2 (ii) F = C – P + 2 = 2 – 2 + 2 = 2 (iii) F = C – P + 2 = 2 – 2 + 2 = 2 (iv) F = C – P + 2 = 1 – 2 + 2 = 1 (v) F = C – P + 2 = 1 – 1 + 2 = 2 (vi) F = C – P + 2 = 2 – 3 + 2 = 1 (vii) F = C – P + 2 = 1 – 2 + 2 = 1 (viii) F = C – P + 2 = 2 – 3 + 2= 1 (ix) F = C – P + 2 = 1 – 2 + 2 = 1 (x) F = C – P + 2 = 1 – 2 + 2= 1 (xi) F = C – P + 1 = 2 – 2 + 1 = 1 17. Give the classifications of two-component system. (i) Simple eutectic formation (ii) Formation of solid solution (iii) Formation of compounds with congruent melting point (iv) Formation of compound with incongruent melting point 18. Give the merits and limitations of Phase rule. Merits (i) It provides simplest method of classifying equilibrium states of various systems. It is applicable to both physical and chemical equilibria. (ii) It indicates that different systems with same degree of freedom behave similarly. Limitations (i) It can be applied only for heterogeneous equilibrium systems and not applicable to systems which are slow in reaching equilibrium state. (ii) It considers only three variables temperature, pressure and composition. The other variables such as electric and magnetic influence have not been considered. (iii) It applies only to a single equilibrium system and provides no information regarding any other possible equilibrium in the system. 5 UNIT 5 PHASE RULE PART – B 1. State Phase rule and explain the terms involved in phase rule. (May 10, Nov 10, May 11, Nov 11, May 12, Jan 13, May 13, Jan 14, May 14, Jan 15, May 15, Jan 16, Nov 16, May 17) Phase rule If the equilibrium between any number of phases is not affected by external factors such as gravity, or electrical, or magnetic forces, or by surface action, and affected only by temperature, pressure and concentration, then the number of degrees of freedom (F) of the system is related to number of components (C) and number of phases (P) by the phase rule equation, F=C–P+2 existing at equilibrium with one another at definite T and P. Terms involved in phase rule PHASE Phase is a homogeneous, physically distinct and mechanically separable part of a system which is separated from other parts of the system by definite boundary surfaces. Examples (i) Gaseous mixture thoroughly miscible in all proportions, contribute one phase. Thus, a mixture of N2 and H2 forms one phase only. (ii) Immiscible liquids (water and benzene) forms two phases. Miscible liquids (alcohol and water) forms a single phase. (iii) Each solid makes separate phase, except in solid solutions. For example, Sulphur exists in monoclinic and rhombic forms. COMPONENT It is the minimum number of independent species necessary to state composition of all phases present in the system in the form of chemical equation. Examples (i) Water exists in three phases, Ice (s) Water (l) Vapour (g) but chemical composition of each phase can be expressed in terms of H 2O. Hence water system is one component system. Similarly, Sulphur exists in four phases namely, Monoclinic, Rhombic, liquid and vapour. As the chemical composition of all phases is S, it is also one component system. (ii) When reactions involving various species, situation is slightly different. In the thermal decomposition of CaCO3, composition of each phase can be expressed in terms of any two independently variable constituent. CaCO3 (s) CaO (s) + CO2 (g) If CaCO3 and CaO are chosen, then composition of solid CaCO3 can be expressed by CaCO3 + 0 CaO. 6 DEGREE OF FREEDOM It is the minimum number of independent variable factors such as temperature, pressure and composition, which must be specified in order to represent the condition of the system completely. Examples (i) In water system, when all three phases present in equilibrium, Ice (s) Water (l) Vapour (g) then no conditions need to be specified, because three phases can exist in equilibrium only at a particular temperature and pressure. Thus this system is invariant or it has no degree of freedom. (ii) In gaseous mixture of N2 and H2, both pressure and temperature are needed to define the system and hence it has two degrees of freedom. 2. Give the merits and limitations of Phase rule. (Jan 11, Jan 13) Merits (i) It provides simplest method of classifying equilibrium states of various systems. (ii) It is applicable to both physical and chemical equilibria and it requires no information regarding molecular structure. (iii) Helps to predict behavior of system under different sets of variables. (iv) It indicates that different systems with same degree of freedom behave similarly. (v) It takes no account of the nature of either reactant or product in phase reaction. (vi) It predicts that number of substances would remain in equilibrium or not, if some substances have been transformed into new substances. (vii) It accounts for the behavior of system when they are subjected to changes in state variables, such as temperature, pressure & volume. Limitations (i) It can be applied only for heterogeneous equilibrium systems and not applicable to systems which are slow in reaching equilibrium state. (ii) It considers only three variables temperature, pressure and composition. Other variables such as electric and magnetic influence have not been considered. (iii) It applies only to a single equilibrium system and provides no information regarding any other possible equilibria in the system. (iv) It requires utmost care in deciding the number of phases existing in equilibrium state, since it considers only the number of phases, rather than their amounts. Thus, even if a trace of the phase is present, it accounts towards the total number of phases. (v) It conditions that all phases of system must be present simultaneously under identical conditions of temperature and pressure. (vi) It conditions that solid and liquid phases must not be in finely divided state, otherwise deviations occurs. 7 3. Derive the Phase rule equation. (Jan 15) Consider a system in equilibrium containing C components (C1, C2, C3, …… Cc) distributed between P phases (, , , , ….. P). Assume that passage of a component from one phase to another does not constitute a chemical reaction. The state of each phase of system is completely specified by two variables, temperature and pressure and also by composition of each phase. The composition of each phase can be specified if the amount of each component is known. The need here is to describe the mole fraction of each component. If C is the number of components required to describe the composition of a phase, then the total number of composition variables for P phases are PC. Thus, the total number of independent variables is PC + 2. Here, 2 stand for the two variables Pressure and Temperature. In each phase there is a relationship between the mole fractions. X1 + X2 + X3 + ----- + Xc = 1 Or  Xi = 1 where Xi = x1,  + x2,  + x3,  + ---The mole fraction of any component in a phase can be calculated if the mole fractions of all other components are known. When a heterogeneous system is in equilibrium at a constant temperature and pressure, the chemical potential of a particular component must be the same in all the phases in which it appears. For a one component system having phases ,  and , the equality of chemical potential implies, () = () = () Thus, two additional equilibrium relations between the variables exist. In general, for each component in P phases, (P–1) relations are possible. Since there are C components, total numbers of these equations are C (P–1). Thus the total number of restricting conditions is given as P + C (P–1). Degrees of freedom or number of independent variables F is given by, F = (Total no. of variables required to specify the state of system) – (Total no. of restricting conditions) F = (PC + 2) – {P + C (P–1)} = (PC + 2) – (P + CP – C) = PC + 2 – P – CP + C F = C – P + 2 Phase rule equation 8 From phase rule equation, it is clear that for a system having a given number of components, greater the number of phases, smaller will be the number of degrees of freedom. On the other hand, for a system with given number of phases, larger the number of components, greater will be the number of degrees of freedom. Phase rule does not depend upon nature or amount of substances present in the system at equilibrium. It does not give anything regarding the composition of matter. It merely states that systems having same number of degrees of freedom behave alike thermodynamically. The phase rule is an important generalization and enables to classify equilibria and study more complex heterogeneous systems. 4. Explain Water system. (May 10, Nov 10, Jan 11, Nov 11, May 14, Jan 15, May 15, Jan 16, May 16, Nov 16, May 17) Water system consists of three phases namely Ice, Water and Water Vapour. As all three phases can be represented by one chemical species H2O, water system is one component system. These phases form: (i) 3 single phases exist separately: solid Ice, liquid water & water vapour (ii) 3 two phase equilibrium Ice (s) Water (l) Water (l) Vapour (g) Ice (s) Vapour (g) (iii) 1 three phase equilibrium: Ice (s) Water (l) Vapour (g) From the phase rule, when C = 1, the phase rule equation becomes, F=C–P+2 =1–P+2 F=3–P Phase diagram of Water system Thus, degree of freedom depends on number of phases present in equilibrium. Three possible cases are, (i) P = 1; F = 2 (bivariant system) 9 (ii) (iii) P = 2 ; F = 1 (univariant system) P = 3 ; F = 0 (invariant system) Thus for one component system, maximum number of degrees of freedom is two. Therefore, such a system can be explained completely by a two-dimensional phase diagram considering the convenient variables pressure and temperature. Phase diagram for water system consists of, (a) Areas – AOB, AOC and BOC (b) Boundary lines or Curves – OA, OB and OC (c) Triple Point – O (d) Metastable Curve – OA’ (a) Areas Areas BOC, AOC and AOB are the fields of existence of solid ice, liquid water and water vapour phase, respectively. Each area represents a single phase. Within these areas, water system is bivariant, because to describe any point in an area, both temperature and pressure co-ordinates need to be known. This is predicted from phase rule: F = 3 – P = 3 – 1 = 2 Thus, in any area, both temperature and pressure can be varied without affecting stability of the system. (b) Boundary lines or Curves Different areas are separated by boundary lines or curves at which, two phases co-exist in equilibrium. Thus, P = 2 and phase rule becomes, F = 3 – P = 3 – 2 = 1 and the system is univariant. In order to define any point on a particular line either temperature or pressure should be known because when one co-ordinate is fixed, the second one is automatically fixed. In other words, any point on curves has one degree of freedom or the system is univariant. There are three curves which separates three areas. Curve OC: It represents the equilibrium between ice and water and is called as fusion curve or melting curve. This curve shows the effect of pressure on melting point of ice. From phase diagram, line OC is inclined towards the pressure co-ordinate which indicates melting point of ice is lowered by increasing pressure. Curve OA: This curve separates water from water vapour and is called as vapour pressure curve of water or simply vapourization curve. At any given temperature, there exists one and only vapour pressure at which water vapour is in equilibrium with liquid water. This curve has a natural upper limit at + 374C and 218 atm. pressure, which are called as critical temperature and critical pressure, respectively. Beyond this limit the liquid phase merges with vapour phase and they are no longer distinguishable from each other. Curve OB: It represents the equilibrium between ice and water vapour and is called as vapour pressure curve of ice or sublimation curve. It gives the conditions under which ice is in equilibrium with vapour. The point B has a natural limit at – 273C, beyond which solid and vapour phase merges into each other. 10 (c) Triple Point The three curves OA, OB and OC meet at point O. This point, at which all three phases solid ice, liquid water and water vapour exists in equilibrium is called Triple Point. Thus at triple point all three phases are coexisting and P = 3 and phase rule equation becomes F = 3 – P = 3 – 3 = 0. Since three phases co-exists, the system is invariant or non-variant and there is no degree of freedom or three phases can coexist in equilibrium only at a definite temperature and pressure. The fixed value of temperature and pressure at triple point is 0.0098C and 4.58 mm respectively. As degree of freedom at triple point is zero, it is not possible to alter temperature or pressure without disturbing the equilibrium. If pressure or temperature altered even slightly, one of the three phases disappear and system changes from non-variant and system are no longer in triple point. (d) Metastable curve When water is cooled gradually in a vessel which is perfectly clean and free from dust, freezing may not occur at 0C and continue to remain as a liquid below its freezing point without the formation of ice. It is called super-cooled water and the curve is called as Metastable curve. The dotted curve OA’ is unstable and said to be in metastable equilibrium, because as soon as a small particle of ice is brought in contact with super cooled water, the entire liquid will become solid. It is observed from the phase diagram that the vapour pressure of super cooled water is higher than the vapour pressure of ice. Effect of change of Temperature and Pressure The changes that occur on altering T or P of water system, may be made clear from the following consideration. Suppose if it is required to know effect of heating ice when it is under a pressure of 1 atmosphere and at certain temperature represented by the point X in phase diagram of water. The system is bivariant at X, the temperature can have any value at same pressure. When heating the ice slowly at constant pressure, it will shift the system along the line XY. At Y, ice begins to melt and the temperature remains constant until fusion is complete. As liquid phase appears, the system has now two phases and therefore it has one degree of freedom. Now the temperature cannot alter without alteration of pressure. The effect of continued heating will be simply to cause fusion of ice at constant temperature. After complete fusion, the system again becomes bivariant and has only one phase, i.e., ice has changed completely into water. The temperature now rises along the line YZ. At Z vaporization begins. The number of phases rises to two, liquid and vapour and system becomes univariant. The continued heating will not alter the temperature as pressure has been kept constant. The only effect will be to convert more of liquid into vapour. When the liquid phase disappears completely, the system will have only one phase, vapour and will become again bivariant. The temperature of vapour will rise along the line ZZ’. 11 5. Discuss Sulphur system. (May 11, May 12, Jan 13, Jan 14, May 16) Sulphur exists in two enentiotropic forms, rhombic form and monoclinic form (crystalline forms that undergo reversible change at a transition temperature are enentiotropic). Stable form at room temperature is Rhombic (S R) form and on heating it is transformed to Monoclinic (SM) sulphur. Apart from these allotropic forms, there are liquid sulphur (Sl) and vapour sulphur (Sv) contributes totally four possible phases. As all the four phases are chemically Sulphur denoted by a chemical formula S, it is a one component system. From phase rule, when C = 1, P = 4, then F = C – P + 2 = 1 – 4 + 2 = – 1 As degree of freedom cannot be negative, out of four possible phases only three can coexist at a time. As sulphur is one component system, convenient variables are pressure and temperature. The possible equilibriums are, (i) P = 3, F = 0 (invariant) (ii) P = 2, F = 1 (univariant) (iii) P= 1, F = 2 (bivariant) The phase diagram for sulphur system consists of (a) Areas, (b) Curves, (c) Triple Points and (d) Metastable curves Phase diagram of Sulphur system (a) Areas Phase diagram is divided into four areas ABEF, DCEF, ABCD and BCE. These are the fields of existence of only one phase, sulphur Rhombic (SR), sulphur liquid (SL), sulphur vapur (Sv) and sulphur Monoclinic (SM) respectively. Within these single-phase areas, the system is bivariant, because to locate any point in any of the area, both variables, temperature and pressure need to be specified. This is followed from the phase rule equation, F = 3 – P = 3 – 1 = 2 (bivariant). In triangular area bounded by lines represents monoclinic, existence of this form is limited on all sides. 12 (b) Curves There are six stable curves AB, BC, CD, BE, EF and CE representing stable equilibria of two phases side-by-side. Any point on these lines is univariant because for a given value of pressure, the temperature is fixed on the curve. This result is from the phase rule equation, F = 3 – P = 3 – 2 = 1. (i) Curve AB is sublimation curve of Rhombic sulphur (SR Sv). Rhombic sulphur is stable upto point B (95.6C, 0.006 mm), above which monoclinic sulphur is stable. The curve BA ends at A (50C), below which the vapour pressure of SR is not measurable. (ii) Curve BC is sublimation curve of monoclinic sulphur (SM Sv). Monoclinic sulphur is stable upto C (120C, 0.04 mm). (iii) Curve CD is vapour pressure curve for liquid sulphur (Sl Sv). The variation of vapour pressure of liquid sulphur with temperature can be studied by this curve. (iv) Curve BE is transition curve for rhombic to monoclinic sulphur (S R SM). Since density of monoclinic sulphur (1.95) is less than rhombic sulphur (2.05), increase of pressure raises the transition temperature. Therefore curve BE slopes away from the pressure axis. (v) Curve CE is melting curve for monoclinic sulphur (SM Sl). The density of liquid sulphur is less than that of the monoclinic solid sulphur and hence, this curve slopes to right side. (vi) Curve EF is melting curve for rhombic sulphur (SR Sl ). (c) Triple points There are three stable triple points (Triple Point is a point at which all the three phases are in equilibrium). All these triple points are invariant because changes in anyone of the variable, temperature or pressure, causes disappearance of one of the three phases. This is also from phase rule equation, F = 3 – P = 3 – 3 = 0 (invariant). The three Triple points and the equilibriums are, (i) Triple point B (95.6C, 0.006 mm) (SR SM Sv ). Point B is transition temperature at which S R changes into SM. (ii) Triple point C (120C, 0.04 mm) (SM Point C is the melting point of monoclinic sulphur. SL SV ). (iii) Triple point E (151C, 1290 mm) (SR SM Sl ). Point E is the melting point of rhombic sulphur. (d) Metastable Equilibriums (i) Metastable curves There are four curves BG, CG, EG and BB’ which are continuations of stable curves, indicating metastable equilibria between two phases. Unless heating is done extremely slowly, there is a probability that the first solid may not change into second solid at normal transition point. The first solid therefore will exist in metastable equilibrium with its vapour, represented by the dotted line BG. 13 If liquid sulphur is allowed to cool along the curve CD, monoclinic sulphur may not separate out at C unless cooling is extremely slow. The curve EG is fusion curve of metastable rhombic sulphur. (ii) Metastable Triple point There is a metastable triple point G (114C, 0.03 mm), which represents equilibrium of SR, Sl and SV. Slight variation in condition causes all these three phases to disappear and monoclinic sulphur is obtained. Point G, therefore represents melting point of metastable rhombic sulphur. 6. Explain Thermal Analysis. (Jan11, May 11, Jan 13, May 13, Jan 14, May 14, Jan 15, May 15, Jan 16, Nov 16) Cooling Curve When a pure substance in fused or liquid state is allowed to cool slowly and temperature is noted at definite times, a graphic representation of rate of cooling will be continuous curve. The graph represented by plotting fall of temperature with time is called as cooling curve. Thermal Analysis Construction of phase diagram from cooling curves is called Thermal Analysis. It involves the study of cooling curves for pure metals and for various compositions of two components of a system during solidification. The form of cooling curve indicates the composition of solid. One component (i) When a pure substance in liquid state is allowed to cool slowly and the temperature is noted at definite times, a continuous curve is obtained. When freezing point is reached and the solid makes its appearance, it is indicated by a break in continuity of cooling curve. At this point the temperature will remain constant, until the liquid is completely solidified. Thereafter, the fall in temperature will again become continuous due to heat dissipation. Two components (ii) When a mixture of two solids in fused state is allowed to cool slowly and the cooling curve is obtained in a similar manner as above. 14 A continuous line is obtained as long as the mixture is in liquid state. When a solid phase begins to form, the rate of cooling suddenly alters and the cooling curve exhibits a break. But the temperature does not remain constant as in previous case. It decreases continuously, but at a different rate. When the mixture forms an eutectic, the fall of temperature continues till eutectic point is reached. The temperature remains constant, until solidification is complete. Thereafter, fall of temperature becomes uniform, but is different from previous one. (iii) In actual practice, pure metals A and B and a number of mixture of metals A and B of various compositions between 100% of A and 100% of B are prepared. These are heated above their respective melting point to give homogeneous liquid. Each liquid is then allowed to cool slowly and the temperature is recorded after small interval of time. In this way several cooling curves are obtained. A break in the curve indicates the appearance of new phase. The first break in each curve occurs at freezing point. The pure metal will freeze at one constant temperature and the cooling curve will show a horizontal line. For any mixture, it is possible to obtain its freezing point and eutectic point. As the mixtures differ in their compositions, their freezing will commence at different temperatures. The second break occurs at which the temperature remains constant. This gives eutectic temperature, which will be same in all mixtures irrespective of their initial composition. The freezing point of pure A and B (100%) are also determined in a similar manner. Now the cooling curve of an alloy system of same metals, but of unknown composition is 15 determined and its freezing point located in the T–C diagram. The composition corresponding to this freezing point yields the composition of that alloy. Thus, the thermal analysis procedure can be used to determine the phase diagram of any two component system. 7. Give the classifications of two-component system. Possible cases of two-component solid-liquid equilibria are, (i) Simple eutectic formation Binary system consisting of two substances which are completely miscible in liquid state but completely immiscible in solid state. (ii) Formation of solid solution Two substances especially metals are completely miscible in both solid and liquid state and they form solid solutions. (iii) Formation of compounds with congruent melting point In binary alloy system, two substances form one or more compound with definite proportions. A compound is said to possess a congruent melting point if it melts exactly at a constant temperature into liquid having the same composition as that of solid. (iv) Formation of compound with incongruent melting point A compound is said to possess an incongruent melting point if it decomposes completely at a temperature below its melting point yielding a new solid phase with a composition different from that of the original. 8. Explain Lead – Silver system forming eutectic alloy. (Nov 10, Jan 11, May 11, Nov 11, May 13, Jan 14, May 14, Jan 15, Jan 16, May 16, Nov 16, May 17) Lead and Silver metals are completely miscible in liquid state and do not give rise to any compound formation. Such systems are known as simple eutectic system. This is a two–component system with four possible phases – solid Ag, solid Pb, solution of Ag and Pb and vapour. As pressure has no effect on these equilibriums, the system can be conveniently represented by a temperature – composition diagram at constant atmospheric pressure, as the gaseous phase is practically absent. As the variable pressure is neglected, the condensed phase rule becomes, F = C – P + 1 = 2 – P + 1 = 3 – P will be applicable. Phase diagram for Pb – Ag system consists of (a) areas, (b) curves and (c) eutectic point. (a) Areas Pb – Ag system mainly consists of three areas. Area AOB represents solution of Pb and Ag. Area AOA’ represents mixture of liquid with solid lead. Area BOB’ represents mixture of liquid with solid silver. 16 Phase diagram of Lead – Silver alloy system (b) Curves (i) Curve AO: Pure lead melts at 327C and addition of silver lower its melting point along AO. The curve AO is the freezing point curve of Pb. It represents the effect on freezing point of Pb, on gradual addition of small amounts of Ag to it. Along AO, solid lead and solution co-exit. The system, at constant pressure, is monovariant along AO. Along AO, the melting point gradually falls on addition of Ag, till lowest point O is reached, where the solution gets saturated with respect to Ag and the melting point of lead does not fall any more. On cooling, the whole mass crystallizes out. (ii) Curve BO: Pure silver melts at 961C and the addition of lead lowers its melting point along BO. Thus, BO is the freezing point curve of silver. Along BO, solid silver and solution co-exist. The system, at constant pressure is mono variant along BO. This curve indicates that the melting point of Ag falls gradually on adding Pb along BO, till lowest point O is reached where the solution gets saturated with respect to lead. At O, no more lead can go in solution and consequently, melting point of Ag does not fall further and if any lead is added, it separates as solid phase. Along this curve, solid Ag and solution co-exist and hence, according to reduced phase rule equation, F = 3 – P = 3 – 2 = 1, system is univariant. On cooling beyond O, whole mass crystallizes out completely. (c) Point O (Eutectic Point) Point O is the eutectic point where three phases, solid Pb, solid Ag and their liquid solution coexist. According to condensed phase rule the system is invariant. F = 3 – P = 3 – 3 = 0 (invariant) Point O (303C) where two lines meets represents a fixed composition of Ag = 2.6% and Pb = 97.4% and is called as eutectic composition. No mixture of lead and silver has a melting point lower than the eutectic temperature. At this point, the temperature remains constant, until whole of the melt solidified. 17 However, further cooling results in simultaneous crystallization of a mixture of Ag and Pb in relative amounts corresponding to eutectic point O. Below temperature line of eutectic temperature, two regions in the phase diagram are, (i) region, eutectic + solid Ag, in which crystalline silver and solid eutectic are stable. (ii) region, eutectic + solid Pb, in which crystalline lead and solid eutectic are stable. Application Phase diagram of lead-silver system has special significance in connection with desilverization of lead. The argentiferous lead consisting of a very small percentage of silver is first heated to a temperature well above its melting point so that the system consists only of liquid phase represented by the point a. It is then allowed to cool when temperature of melt will fall along the line ab. As soon as the point b is reached, lead will begin to separate out and the solution will contain relatively increasing amounts of silver. Further cooling will shift the system along the line bO. Lead continues to separate out and is constantly removed by means of ladels. The melt continues to be richer and richer in silver until the point O is reached when the percentage of silver rises to 2.6%. Thus, original argentiferous lead which might have contained 0.1% (or less) of silver, can now contain upto 2.6% of silver. This process of raising relative proportion of silver in alloy is known as Pattinson’s process. 9. Explain the Zn-Mg alloy system. (May 12, Jan 13, May 15, May 17) A compound, which melts sharply at constant temperature into a liquid of same composition as solid, is said to possess congruent melting point. Zn – Mg system is an example of binary alloy with congruent melting point. The components form one or more compounds in some stoichiometric proportions. These compounds are such that they melt into liquid state, having the same composition as solid. Zinc and Magnesium melts at 419.5C and 650C respectively and they form a compound MgZn2, i.e., in which the ratio of Mg and Zn in molecular proportions is 1:2. This compound melts at B (590C). This phase diagram may be considered as equivalent to two-phase diagrams of Pb–Ag system type placed side-by-side. The one on left consists of Zn and MgZn2 system; while the other on right is formed by two components MgZn2 and Mg. The curve AE1 and CE2 represent composition of liquids in equilibrium with solid Zn and solid Mg respectively. The central portion of curve E1BE2 has maxima at B (590C). This gives the conditions of equilibrium of liquid with solid compound, MgZn2. At maxima B, liquid has same composition as solid in equilibrium. Thus, temperature at B (590C) represents melting point of compound MgZn2. As MgZn2 can co-exist as solid and liquid of same composition, MgZn2 is said to possess congruent melting point. 18 Phase diagram of Zing – Magnesium alloy system The composition corresponding to maxima is 33.3% Mg and 66.7% Zn. i.e., in the ratio of 1:2. The sharpness of maxima gives information about the stability of compound formed. The sharp maxima indicate that the compound does not dissociate appreciably; whereas a flat maxima indicates as appreciable dissociation, as in the present case. There are two eutectic points, E1 and E2. At E1, the solid Zn and MgZn2 deposits; while at E2, Mg and MgZn2 are the two phases. Molar composition at E1 is 79% Zn and 21% MgZn2 and at E2 is 61% MgZn2 and 39% Mg. In some cases, the compound may be so unstable that it decomposes at a temperature below its melting point. The solid in this case cannot be in equilibrium with a liquid of same composition as solid. The compound is then said to have an in-congruent melting point or peritectic point. 10. Discuss the effect of temperature on composition in Copper - Nickel system and mention its application. (Nov 11, May 13, Jan 14, May 16) A homogeneous solid solution constitutes a single phase and there is only one liquid phase. Maximum number of phases can be 2, and according to phase rule, F = C – P + 1 = 2 – 2 + 1= 1, minimum number of degrees of freedom is one. Thus, the system can never be invariant. These types of phase diagram similar to those of miscible liquid systems are known as continuous series of solid solutions. The phase diagram is constructed from a series of cooling curves obtained for different alloy compositions. First break in the curve occurs when solid begins to separate from the melt. The second discontinuity occurs when solidification is complete. It shows complete miscibility of materials in the solid phase. There are two one-phase areas and one two-phase 19 area. This type results from the ability of one substance to substitute freely for others in crystal lattice because of similarity in size of molecules. Phase diagram of Cu – Ni system Copper and Nickel are soluble in each other in all proportions in solid state. The freezing points of Cu and Ni are 1083C and 1452C respectively. The addition of Ni to Cu raises freezing point, whereas addition of copper to nickel depresses the freezing point. Consequently, freezing point of mixture of Cu and Ni or any composition lies between individual freezing points of copper and nickel. The upper curve represents Liquidus or freezing curve, since above this, the system is completely liquid only. On the other hand, lower curve represents Solidus or melting curve, since below it, only solid phase exists. In between solidus and liquidus, both solid and liquid phases co-exist. The two components form continuous series of solutions, without any minimum or maximum convergence point of the two curves. Composition of a liquid solution in equilibrium with solid solution is given by a tie line. Thus, a liquid solution of composition a is in equilibrium with solid solution of composition b. This state of affair happens all along curve between melting points of Cu and Ni, between 1083C and 1452C. Effect of cooling Any mixture of Cu and Ni in molten state represented by point x has two degrees of freedom, since it is a two component system in one phase. F = C – P + 1 = 2 – 1 + 1 = 2. Consequently, such a liquid can be cooled directly, till the temperature characterised by a is reached, when the solid phase appears. This system now has two phases (one solid and the other liquid) and hence, its degree of freedom, F = C – P + 1 = 2 – 2 + 1 = 1. i.e., univariant or the system now cannot be cooled without affecting its composition. With cooling, the composition is automatically changed. In fact, the solid that appears is neither pure Cu nor pure Ni, but a solid solution of Ni in Cu (because in the present case under consideration, Cu is in excess and is, therefore, looked upon as solvent). The 20 corresponding composition of solid phase separated would be given by b. The ratio of Ni to Cu in solid state is higher than in original liquid x and hence, the liquid becomes richer in Cu. As presence of Cu tends to diminish freezing point, the liquid if cooled, will now freeze at a still lower temperature. For a particular composition of liquid, there is a corresponding composition of solid obtained. Due to exothermic nature of change from liquid to solid, the rate of cooling is slowed down. The system at c consists of liquid with composition d in equilibrium with solid solution of composition e. Hence line dce is the tie line. Thus, it is clear that the residual liquid (left after separation of solid phase) becomes richer in Cu and poorer in Ni. The composition of liquid solution moves along aA: while that of solid along Bf. At f (a point vertically below a) the system solidifies completely. Application - Fractional crystallization (May 10) Theory of separation of components, by fractional crystallization, becomes clear in the light of phase diagram at once. Suppose a mixture of Cu and Ni is taken at the composition and temperature represented by the point x. The system has two degrees of freedom and can therefore, be cooled without change of composition, till at the temperature of a, the solid appears and the system becomes univariant. Any change of temperature will be attended with a change in composition, because solid phase will have the composition characterised by b. If system is allowed to cool for some time, the composition of liquid during cooling will tend to move along aA; while that of solid along bB. If it is stopped at c, the solid separated out will have composition richer in Ni. So the mean composition of solid separated out will be at e. If this solid is separated out and heated, a molten mass of the same composition e will be obtained, which on cooling will deposit solid at g and the corresponding composition of solid will be h, in which Ni percentage is more than at e. If this solid at g is again heated to melt and then cooled, another solid of composition richer in Ni will be obtained. Thus it may be noticed that each time the solid which is obtained is richer in Ni than that obtained by previous separation operation. By repeating the processes of heating, cooling and separating the solid, pure component Ni can be obtained. Instead of taking solid, if it is started with liquid phase and allows it to cool, the liquid will get richer in Cu and thus, it is possible to separate out Cu in this way. In other words, both components can be separated by this so-called fractional crystallization process. Thus, in the process of fractional crystallization, the component which tends to depress the freezing point of mixture occurs in greater amounts in the liquid state. 21