Phase Rule PDF

Phase Rule Phase: A chemically homogeneous, physically distinct and mechanically separable part of a system is called a phase. Three phases of matter: Solid, Liquid, and Gas.  Phase (P) A phase is defined as “any homogenous, physically distinct and mechanic...

Phase Rule Phase: A chemically homogeneous, physically distinct and mechanically separable part of a system is called a phase. Three phases of matter: Solid, Liquid, and Gas.  Phase (P) A phase is defined as “any homogenous, physically distinct and mechanically separable portion of system having all the physical and chemical properties the same throughout the system. A system may consist of one phase or more than one phase. For example: (1) At freezing point, water consists of three phases: Ice (s) Water (l) Water vapour (g) (2) A gaseous mixture, being thoroughly miscible in all proportions, will constitute one phase only. Thus, a mixture of N2 and H2 forms one phase only. (3) If two liquids are miscible (e.g. ethanol and water), they will form one liquid phase only. (4) A solution of a substance in a solvent consists of one phase only, e.g. glucose solution in water. (5) If two liquids are immiscible (e.g. benzene and water), they will form two separate phases. (6) Each solid makes up a separate phase, except in the case of solid solutions, e.g. many forms of sulphur can exist together, but these are all separate phases. (7) A heterogeneous mixture like CaCO3(s) CaO (s) + CO2 (g) Consists of three phases (i.e., two solids and one gaseous) Similarly, in the equilibrium reaction, Fe (s) + H2O (g) FeO (s) + H2(g) There are two sold phases, Fe and FeO and one gaseous phase consisting H2O (g) and H2 (g). Thus, three phases exist in equilibrium. (8) A homogenous solid solution of a salt constitutes a single phase. Mohr’s salt [FeSO4.(NH4)2SO4.6H2O] solution constitutes a single phase. A part of a system is homogeneous if it has identical physical properties and chemical composition throughout the part. ❑ A phase may be gas, liquid or solid. ❑ A gas or a gaseous mixture is a single phase. ❑ Totally miscible liquids constitute a single phase. ❑ In an immiscible liquid system, each layer is counted as a separate phase. ❑ Every solid constitutes a single phase except when a solid solution is formed. ❑ A solid solution is considered as a single phase. ❑ Each polymorphic form constitutes a separate phase. Classical examples of polymorphism are the pair of minerals calcite and aragonite, both forms of calcium carbonate. Perhaps the most famous example is that of the polymorphs of carbon: graphite and diamond.  Component (C) The term component is defined as “the smallest number of independent variable constituents, 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” For example”: (1) In water system Ice (s) Water (l) Vapour (g) The chemical composition of all the three phases is H2O. Hence it is one component system. (2) 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. 8 (3) (a) In the dissociation of NH4Cl: (only NH4Cl is heated) in a closed vessel NH4Cl(s) NH4Cl(g) NH3(g) + HCl(g) The proportions of NH3 and HCl are equivalent [[NH3] = [HCl]] and hence, the composition of both phases (solid and gaseous) can be expressed in terms of NH4Cl alone. No. of Components (C) = No. of Constituent – [No. of Equations relating to concentration of constituents] = 3 (NH4Cl, NH3, and HCl) – 2 = 1 Hence the number of component is one. (b) When NH4Cl is heated in a closed vessel along with NH3 or HCl, At equilibrium: Keq = [NH3][HCl] ……………..(i) But [NH3] ≠ [HCl] …………(ii) 9 however, if NH3 or HCl is in excess (i.e. 1 NH3 + 4 HCl or 4 NH3 + 1 HCl) [see eqn (ii)] Only one equation (i) relates the concentrations of constituents No. of component, (C) = 3 - 1 = 2, i.e. under the above conditions, the system has two-components (4) The thermal decomposition of CaCO3 CaCO3 (s) CaO(s) + CO2(g) The composition of each of the three phases can be expressed in terms of at least any two of the independently variable constituents, CaCO3, CaO and CO2. Suppose CaCO3 and CaO are chosen as the two components, then the composition of different phases is represented as follows: CaCO3 solid phase CaCO3 = CO2 + CaO CaO solid phase CaO = CaCO3 - CO2 CO2 gaseous phase CO2 = CaCO3 - CaO Thus, it is a two-component system. (5) (6) Number of Components of a system may alternatively be defined as the number of chemical constituents/species of the system minus the number of equations relating to those constituents in an equilibrium state. For example 2KClO3(s) 2KCl(s) + 3O2(g) Number of constituents = 3 [KCl]2[O2]3 Keq= = [O2]3 [KClO3]2 No. of equations relating the concentration of constituents = 1 No. of component = no. of constituents - no. of equations relating the concentration of constituents Hence, number of components = 3 - 1 = 2 i.e., it is a two-component system.  Degrees of Freedom (or Variance) (F) The term degrees of freedom or variance of a system denoted by F is defined as the minimum number of independently variables factors such as temperature, pressure, concentration, which must be arbitrarily fixed in order to define the system completely. F (degrees of freedom; variance): Number of attributes of a system (T, P, phase composition) that can be changed independently without creating or destroying a phase, or... Number of parameters (T, P, system composition) that need to be described to completely define the composition and identity of each phase. F=3 : trivariant F=2 : divariant F=1 : univariant F=0 : invariant if F < 0 then there must be disequilibrium. The phase rule is a generalization given by Willard Gibbs (1874), which seeks to explain:  The equilibrium existing in the heterogeneous system.  It is useful to understand the effect of intensive variables, such as temperature, pressure, or concentration, on the equilibrium between phases as well as between chemical constituents.  It is used to deduce the number of degrees of freedom (F) for a system. It is stated that: “provided the equilibrium between any number of phases is not influenced by gravity electrical or magnetic forces or by surface action and only by temperature, pressures and concentration, then the number of degrees of freedom (F) of the system is related to the number of components (C) and phases (P) by the phase rule equation: F=C–P+2 For any system at equilibrium at definite temperature and pressure.”  If we consider the water system, at a specific temperature and pressure, three phase of water- ice, liquid and vapour are, in equilibrium Ice (s) Water (l) Water vapour (g) hence, degree of freedom = 0 Water has three phases (solid, liquid, gas) and one component (H2O). Phase (P) = 3, Component (C) = 1, F = C – P + 2 = 1 – 3 + 2 = 0 Similarly, equilibrium of liquid water (l) vapour (g) has two-phases and hence, F = 1 When the degree of freedom (F) of a given system is one, it is referred to as univariant system. Water has two phases (liquid and vapour) and one component (H2O). Phase (P) = 2, Component (C) = 1, F = C – P + 2 = 1 – 2 + 2 = 1 If the system containing liquid water, pieces of ice are added and this system with 2 phases is allowed to come to equilibrium, then it is an univariant system. Phase (P) = 2, Component (C) = 1, F = C – P + 2 = 1 – 2 + 2 = 1 Only one variable, either temperature or pressure need to be specified in order to define the system. If the pressure on the system is maintained at 1 atm, then the temperature of the system gets automatically fixed at 0oC, the normal melting point of ice. For the reduction of Nickel Oxide, NiO, NiO(s) + CO(g) = Ni(s) + CO2(g) There are four constituents. There are now two constraints on the composition of the phases of the system, the first as a result of the overall stoichiometry of the chemical equation, and the second because the amount of CO and CO2 in the gas phase are related. Therefore, only C=N-R=4-2=2 independent components are necessary to specify the composition of each phase. If, however, additional CO was artificially added to the system, the constraint imposed by the balance of CO and CO2 in the gas phase would be lost and the composition of each phase could instead only be specified by C=N-R=4-1=3 independent components. Component (C): The independent chemical species (element, compound) in terms of which the composition of a system is specified are called components. In Cu-Ni system: components are Cu and Ni. Some examples System Components Phases Water H2 O Liquid Water + Ice H2 O Liquid + Solid Brine NaCl+H2O Liquid Solution (Salt water) Mild Steel Fe, C α, Fe3C Types of Phase Diagrams based on number of components Unary Diagram: Single Component (C =1) Binary Diagram: Two Components (C =2) Ternary Diagram: Three Components (C =3) Examples of Heterogeneous Equilibria Liquid – Vapour (vapourization) Solid – Vapour (sublimation) Solid – Liquid (fusion) Solid 1 – Solid 2 (transition) Solubility of Solids, Liquids and Gases in each other Vapour pressure of Solutions Chemical reaction between Solids or Liquids and Gases Distribution of solutes between different phases  Phase diagram Phase diagram is a graphical representation of the physical states of a substance under different conditions of temperature and pressure. A typical phase diagram has pressure on the y-axis and temperature on the x-axis. As we cross the lines or curves on the phase diagram, a phase change occurs. In addition, two states of the substance coexist in equilibrium on the lines or curves. Triple point – the point on a phase diagram at which the three states of matter: gas, liquid, and solid coexist. Critical point – the point on a phase diagram at which the substance is indistinguishable between liquid and gaseous states. Fusion(melting) (or freezing) curve – the curve on a phase diagram which represents the transition between liquid and solid states. Vaporization (or condensation) curve – the curve on a phase diagram which represents the transition between gaseous and liquid states. Sublimation (or deposition) curve – the curve on a phase diagram which represents the transition between gaseous and solid states. How many intensive variables can be independently specified at the triple point of water ? Read : At the triple point, all three phases exist in equilibrium. This is the unique aspect of the triple point and this problem. Given : Number of chemical species present: C 1 Number of phases present at equilibrium: P 3 Equation : Gibbs Phase Rule : DOF (oFree) = C – P + 2 Solve : oFree 0 No intensive variables can be independently specified at the triple point ! This means that there is just one triple point and All of the properties of all of the phases are fixed ! The triple point is unique.  Water (H2O) Phase Equilibria Ice (s) Water (l) Water vapour (g) Since H2O is the only chemical compound involved, therefore, it is single or one-component system. From the phase rule, when C = 1, F=C–P+2 =1–P+2 =3–P i.e, the degree of freedom depends on the number of phases present at equilibrium. Three different case are possible : (i) P = 1 ; F=2 (bivariant system) (ii) P = 2 ; F=1 (univariant system) (iii) P = 3 ; F = 0 (invariant system)  Ice (s) Water (l) Water vapour (g) From the above , it is clear that for any one-component system, the maximum number of degrees C Solid Liquid of freedom is two. A Therefore, such a system can be Pressure represented completely by a two-dimensional O The most convenient variable A’ are the pressure and the B temperature. The water system is --273 shown in the diagram consisting Temp 100 of (1) Areas : AOB, AOC, and BOC are the fields of existence of vapour, liquid and ice phase respectively. Within these single-phase areas, the system in bivariant, because to locate any point in an area, temperature as well as pressure coordinates need to be know. This also following from phase rule equation : F = 3 – P = 3 – 1 = 2. 29 2. Boundary lines: separating the areas are lines OA, OB, and OC, connecting the point at which two phases can coexist in equilibrium. In order to locate any point on a particular line, either temperature or pressure co-ordinate should be known, because for fixed value of one coordinate, the second is automatically fixed, In other words, any point on boundary lines has one degree of freedom or is univariant. This also follows from phase rule equation: F=3–P=3–2=1 The curve OA, dividing the liquid from the vapour region, is called vapour pressure curve of liquid water or vaporization curve. At any given temperature, there is one and only one pressure at which water vapour is in equilibrium with liquid water. Similarly, at any given pressure, there is one temperature at which water vapour is in equilibrium with liquid water. In other words, the system is univariant. i.e, has one degree of freedom. The curve OA has a natural upper limit at +374ᵒC. which is the critical-point, beyond which the phase merges into vapour phase and they are no longer distinguishable from each other. The curve OB is the sublimation curve of ice. It gives the conditions under which water vapour is in equilibrium with solid ice. The point B has a natural limit at -273oC, beyond which the two phases merge into each other. The curve OC, which divies the solid–ice region from the liquid–water region, is called melting curve, because it indicates how the melting temperature of ice or the freezing tempereture of water varies with the pressure. The slope of OC towards the pressure axis shows that the melting point of ice is decreased by increasing pressure. 3. Triple point: The three curves OA, OB, and OC meet at O, at which solid, liquid and vapour are simultaneously at equilibrium. This point at 273.16 k is called a triple – point. Since three phases co-exist, the system is invariant (F=3-3=0). In other words, there is no degree of freedom at O, i.e., neither pressure nor temperature can be altered, even slightly, without causing the disappearance Super- of one of the phase. critical Pcr Fluid 4. Metastable curve OA’: As water does not always freeze at 0 oC, so if the vessel containing water and vapour is perfectly clean and free from dust, it is possible to super – cool water several degrees below its freezing point 0. The dotted curve OA’, Ptp a continuation of vaporization curve AO, represents the pressure curve of super cooled water. This curve represents a metastable system. On slight disturbance, the super cooled water at once changes to Ttp Tcr solid ice. It may be noted that metastable vapour pressure of supper cooled water is higher than the vapour pressure of ice. 5. Polymorphism: Timman and Bridgman showed that water under high pressure (up to 5 X103 atm), exists in six other forms, besides ordinary ice (called ice I), which are stable under different conditions of temperature and pressure. These polymeric forms of ice (called ice I to ice VII) differ in crystalline structure, density and other physical properties. The slope of OC towards the pressure axis shows that the melting point of ice is decreased by increasing pressure. The melting curve or fusion curve of ice/water is very special. It has a negative slope (or tilted towards pressure axis) due to the fact that when ice melts, the molar volume decreases. Ice actually melt at lower temperature at higher pressure. Example: The liquid formed between the skate and ice act as a lubricant so that the skater moves gracefully across the ice. The skate apply a very high pressure on to the ice. Liquid H2O Solid H2O  The Sulphur System Sulphur solid exists in two crystalline forms. ❑ Orthorhombic. S8 or S (rh) ❑ Monoclinic. S4 or S(mo) Yellow sulphur of the orthorhombic (or rhombic) crystalline form. It is the form that commonly exists under normal conditions.  Phase Diagram of Sulphur Phase = P = 4 Component (C) = 1 F=C–P+2 E (151ᵒC, 1288mm) =1–4+2 = -1 If F < 0 then there must be disequilibrium. Sulphur has three triple points G, C, and B. 1 atm = 760 mmHg 0ᵒC = 273K  Reduced (or Condensed) Phase Rule In a two-component system, when P = 1 degree of freedom (F) has the highest value: F = C – P + 2 = 2 - 1 + 2 = 3. Since the maximum number of degrees of freedom (F) in a two- component system is three. So, the phase behavior of any binary system may be represented by a three-dimensional diagram of pressure, temperature and composition. A solid-liquid equilibrium of an alloy 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 pressure is not considered, is known as condensed system. It will reduce the degrees of freedom of the system by one and for such a system, the phase rule becomes: F = C – P + 1 This is known as the reduced (or condensed) phase rule, having two variables, namely, Temperature and Concentration (or Composition) of the constituents.  Eutectic system A eutectic system is a mixture of chemical compounds or elements that have a single chemical composition that solidifies at a lower temperature than any other composition made up of the same ingredients. This composition is known as the eutectic composition and the temperature at which it solidifies is known as the eutectic temperature. On a phase diagram the intersection of the eutectic temperature and the eutectic composition gives the eutectic point. Non-eutectic mixtures will display solidification of one component of the mixture before the other.  Phase Diagram of Lead-Silver System 961oC 327oC 303oC (2.6 mass % Ag) 1. Liquid + solid Pb and 2. Solid Pb + eutectic  Description of the phase diagram for Lead-Silver system. A (327oC) Freezing point of lead C=1, P=2, F=0 Fixed T (Pb) C (961oC) Freezing point of silver C=1, P=2, F=0 Fixed T (Ag) B (303oC, 2.6 mass Eutectic point C=2, P=3, F=0 Fixed T and % Ag) composition AB Crystallization of lead C=2, P=2, F=1 T or composition (Pb) Begins BC Crystallization of silver C=2, P=2, F=1 T or composition (Ag) begins Area above ABC Liquid phase C=2, P=1, F=2 T and composition Area below DBE Solid mixture C=2, P=2, F=1 T or composition Area ADBA Solid lead (Pb) in C=2, P=2, F=1 T or composition equilibrium with liquid having composition given by the 42 curve AB Area CEBC Solid silver in C=2, P=2, F=1 T or composition equilibrium with liquid having composition given by the curve BC DBE Both lead and silver C=2, P=3, F=0 Fixed T separate from liquid of composition B Pattinson’s Process for the Desilverisation of Argentiferous Lead The process of heating argentiferous lead containing a very small quantity of silver (~ 0.1 mass%) and cooling to get pure lead (Pb) and liquid richer in silver (Ag) is known as the Pattinson’s process. This process can be understood by following the phase diagram of the lead-silver system. The argentiferous lead is melted and heated to a temperature above the melting point of pure lead (Pb). Let the point a represent this system on the diagram. This system is then allowed to cool slowly and the temperature of the melt decreases along a-b. At b, solid lead (Pb) starts separating. As the system further cools, more and more lead separates and the liquid in equilibrium with the solid lead (Pb) gets richer in silver (Ag). The lead (Pb) that separates floats and is continuously removed by ladles. When the temperature of the liquid reaches ‘a’ on the curve, the eutectic temperature, solid lead (Pb) is in equilibrium with the liquid having the composition B (Ag). After removing the lead (Pb) that separates, the liquid is cooled further when it solidifies to give a mixture of lead (Pb) and silver (Ag) having the eutectic composition of 2.6 mass % of silver (Ag). This solid mixture of lead (Pb) and silver (Ag) is subjected to other processes for the recovery of silver (Ag).  Phase Diagram of Salt Water 47 Merits of Phases Rule 1. It is applicable to both physical and chemical equilibria. 2. It require no information regarding molecular/ micro-structure, since it is applicable to macroscopic system. 3. It is a convenient method of classifying equilibrium states in terms of phases, components and degrees of freedom. 4. It helps us to predict the behaviour of a system, under different sets of variables. 5. It indicates that different systems with same degree of freedom behave similarly. 6. It does not take into cognizance of either the nature or quantities of component present in the system. 7. It helps in deciding whether under a given set of condition: (a). various substances would exist together in equilibrium or (b). some of the substances present would be interconverted or (c). some of the substances present would be eliminated. Limitations of Phase Rule (1) Phase rule is applicable for only those systems which are in equilibrium. Consequently, it not much use for those systems which attain the equilibrium state very slowly. (2) It applies only to a single equilibrium system; and provides no information regarding any other possible equilibria in the system. (3) It requires utmost care in deciding the number of phases existing in an equilibrium state, since it considers the number of phases, rather than their amounts. Thus, even if a trace of a phase is present, it accounts towards the total number of phases. (4) It conditions that all the phases of the system must be present simultaneously, under the identical conditions of temperature and pressure. (5) It conditions that solid and liquid phases must not be in finely- divided state; otherwise, deviations occur.