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PHASE RULE The phase rule is a generalization given by Williard Gibbs (1876) which seeks to explain the equilibria existing in heterogeneous systems. With the application of phase rule it is possible to predict qualitatively by means of a diagram the effect of changing pressure, temperature and concentration on a heterogeneous system in equilibrium. The phase rule is a relation between the number of components (C), the number of phases (P) and the number of degree of freedom (F) of a heterogeneous system in equilibrium. It is expressed as : F= C-P+ 2 PHASE A phase may be defined as any homogeneous and distinct part of a system which is bounded by a surface and is mechanically separable from the other part of the system. For example: ➢ At freezing point, water consists of three phases : Ice (s) Water (l) Water Vapour (g) ➢ A pure substance (solid, liquid or gas ) made of one chemical species , is considered as one phase. Thus oxygen(O2), benzene(C6H6) and ice (H2O) are all one-phase system. ➢ Mixture of gases: All gases mix freely to form homogeneous mixtures. Therefore any mixture of gases , say O2 & N2 is a one phase system. ➢ Decomposition of calcium carbonate: When calcium carbonate is heated in a closed vessel, we have : CaCO3(s) CaO(s) + CO2(g) There are two solid phases and one gas phase. Hence it is a three phase system. ➢ Mixture of solids: Sulphur is a mixture of rhombic and monoclinc sulphur. These allotropes of sulphur consists of same chemical species but differ in physical properties. Thus a mixture of two allotropes is a two-phase system. COMPONENT The term component may be defined as the least number of independent chemical constituents by which the composition of every phase of the system can be expressed directly in term of equations or indirectly. ➢ In the water system Ice (s) Water (l) Vapour (g)

The chemical composition of all the three phases is H2O. Hence it is one component system . ➢ The sulphur system: It consists of four phases; rhombic, monoclinc, liquid and vapour, the chemical composition of all phases is S. Hence it is one component system. ➢ Dissociation of NH4Cl in a closed vessel: NH4Cl (s) NH3 (g) + HCl (g) [NH3] = [HCl] Keq = [NH3] [HCl] / [NH4Cl] = [NH3] [HCl] [Because the active mass of NH4Cl (s) is constant ] Now, the number of components = No. of constituents – no. of equation relating to concentration of constituents = 3(NH4Cl, NH3, HCl) – 2 = 1 i.e ; it is a single component system. When NH4Cl is heated in a closed vessel along with NH3 or HCl then : [NH3] ≠ [HCl] Keq = [NH3] [HCl] Therefore, only one equation relates the concentration of constituents Hence, no. of components ( C ) = 3 – 1 = 2 Therefore it is a two component system. ➢ In 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 & CO2. Thus it is a two component system. ➢ Sodiun chloride solution: Phase = 1, Component = 2 ➢ Sucrose (s) Sucrose (aqueous sol.) Phase = 2, Component = 2 ➢ Aqueous Solution of mixture of NaCl & KCl No of Constituents = 3 (NaCl, KCl & H2O) There is no relation that can control their concentration, So, No. of Components = 3 ➢ Aqueous Solution of KCl & NaBr An equllibrium is maintained: KCl + NaBr NaCl + KBr The above equilibrium is maintained when a mixture of KCl & NaBr is dissolved in water. No. of Constituents = 5 (KCl, NaCl, KBr, NaBr and H2O)

So, No. of Components = 5-1 = 4 ➢ Mixture of NH4Cl(s), NH4Cl(aq.), Cl-(aq.), H2O(liq.), H3O+(aq.), H2O(g), NH3(g), OH-(aq.), NH4OH(aq.) No. of Constituents = 8 No. of restrictions = 5 i) Conditions of electroneutrality ii) NH4Cl NH4+ + Cliii) NH4+ + H2O NH3 + H3O+ iv) NH3 + H2O NH4OH v) 2H2O H3O+ + OHSo, No. of Components = 8-5 = 3 Degree of freedom The least number of variable factors (concentration, pressure & temperature) which must be specified so that the remaining variables are fixed automatically and the system is completely defined. ❖ A system with F=0, is known as nonvariant or having no degree of freedom. ❖ A system with F=1, is known as univariant (having one degree of freedom) ❖ A system with F=2, is known as bivariant (having 2 degrees of freedom) Consider some examples: ➢ In case of water system (triple point): Ice (s) water (l) Vapour (g) Here, the three phases can be in equilibrium only at a particular temperature & pressure. If any of the variable, i.e., temp & pressure is altered, three phases will not remain in equilibrium and one of the phases disappears. Therefore the system is nonvariant (F=0) ➢ For a system consisting NaCl (s) NaCl (aq sol.) Water vapor (g) P = 3, C= 2, F = 1 Since the saturation solubility is fixed, at a particular temperature & pressure, hence the system is univariant (F=1) ➢ For a system consisting NaCl (s) NaCl water(l) water vapour(g) We must state either the temperature or pressure because the saturation solubility is fixed at a particular temperature or pressure. Hence the system is univariant.(F=1). ➢ For pure gas: From gas law, PV = RT, if the values of Pressure (P) and Temperature (T) be specified, Volume (V), the third variable is fixed automatically. Hence degree of freedom (F) = 2.

Advantages of Phase Rule: Phase Rule is applicable to both physical and chemical equilibria. Phase Rule is applicable to macroscopic system and hence no information is required regarding molecular/ microstructure. Phase Rule helps us to predict the behavior of a system under different conditions. It is a convenient method of classifying equilibrium states in terms of phases, components and degree of freedom. Limitations of Phase Rule Phase rule is applicable only for those systems which are in equilibrium. It is not of much use for those systems which attains the equilibrium state very slow. Only Three degrees of freedom i.e, temperature, pressure and composition are allowed to influence the equilibrium systems. Under the same conditions of temperature and pressure , all the phases of the system must be present. It considers only the number of phases , rather than their amounts. Derivation of phase Rule Consider a heterogeneous system in equilibrium , having C components in which P phases are present. According to the definition of the degree of freedom (F), is the minimum number of independent variables which must be fixed arbitrarily to define the system completely. No. of independent variables = Total no. of variables – no. of relations between them at equilibrium Now let us calculate total no. of independent variables: (1) Temperature: At equilibrium ,temperature of every phase is same, so there is only one temperature variable of the entire system. (2) Pressure: At equilibrium , each phase has the same pressure, so there is only one pressure variable of the entire system. (3) Concentration: Concentration of each components is generally expressed in terms of mole fractions For example , if there are two components A & B in one phase and if we know the concentration of one (say A), the concentration of other (i.e.,B) can be automatically found because sum is unity. Similarly, if we have three components and if the composition of two is known , then the composition of third can be easily found out. Thus , if we have C components , we must know the concentrations of C – I components . So for P phases the total composition variables are P(C – I). Hence, total number of variables = 1 (for temperature) + 1(for pressure) + P(C - 1) (for composition) = P(C – 1) + 2 When P phases are present , (P – 1) equations are available for each component & for C component , the total no. of equations are C(P – 1).

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