Phase equilibria by Meenakshi

Phase equilibria is a topic of physical chemistry. It involves the study of equilibrium between two or more phases of heterogeneous system.

1. Phase Equilibria 1 Presented by: Meenakshi khatkar M.Sc. Previous year 180000701029

2. Content 2 Introduction Definition of phase ,component and degree of freedom Equilibrium and it’s type Conditions for phase equilibrium Gibbs phase rule One component system Conculsion References

3. Introduction 3 Phase equilibrium is the study of the equilibrium between two or more phases of heterogeneous systems. The number of phases that can exist together at equilibrium depends upon the temperature,pressure,and composition of various phases J.W.Gibbs gave a generalization which applicable to all heterogeneous equilibria known as phase rule. It is mathematically defined as: F = C-P+2 Where F = number of degrees of freedom C = number of components P = number of phases

4. Phase 4 Phase is defined as any homogeneous and physically distinct part of a system which is separated by a well defined boundary, physically and chemically different from other parts of system. A system may contain one or more than one phases. For example a system containing ice, Liquid water and water vapour is a three Phase system

5. Component 5 For a system in equilibrium it is the minimum number of independent chemical constituents in terms of which the composition of each phase can be expressed either directly or in terms of a chemical equation. The independent chemical constituents is the one whose concentration can be varied independent of other constituent of the system. For example : NaCl solution it contain solid NaCl and water.There are two component NaCl and water. The composition of each phase can be expressed in terms of two constituent NaCl and water. Note: The number of components may or may not be equal to the actual number of constituents present in the system

6. Degree of freedom 6 Degree of freedom is defined as the number of variables, such as temperature, pressure and concentration, which can be varied independently without changing the number of phases. The degree of freedom in phase rule equations is given by F = C-P+2 For example a system containing two component gaseous mixture have three degree of freedom. Same result is obtained by phase rule equation F = C-P+2 = 2-1+2 = 3

7. Equilibrium 7 A system is said to be in the state of equilibrium if the properties like temperature, pressure and composition etc. of the various phases do not under go any change with time. Equilibrium is of two types: True equilibrium : A system is said to be in a state of true equilibrium if the same state can be obtained by approach from either direction.For example, the following equilibrium This equilibrium can be attained from either side i.e. By melting of ice or by freezing of water. Hence,it is a true equilibrium.

8. 2 Metastable equilibrium: 8 A system is said to be in a state of metastable equilibrium if the same state can be approached only from one direction and that too by very careful change of conditions. For example, water at -2°C can be obtained by careful cooling of water without appearance of ice but it is not possible to obtain it by melting of ice.Hence, water at -2°C is said be in a state of metastable equilibrium. In this figure curve OA` represents the metastable equilibrium between liquid water and vapour phase. If a small crystal of ice is added to the supercooled liquid , the liquid at once solidifies and changes into Ice and curve OA` merges into curve OB.

9. Condition for phase equilibrium 9 A system having more than one phase is in equilibrium if following conditions are satisfied. Thermal Equilibrium: In this state the temperature of all the phases must be same. If temperature is not same than heat will flow from one part of system to another part. Mechanical Equilibrium: In this condition ,all the phases of system are under the same pressure . Otherwise , the volume change from one phase to another phase. Chemical Equilibrium: In the state of chemical equilibrium, the chemical potential of a component must be same in all phases.

10. Gibbs Phase Rule 10 J. Willard Gibbs gives a relationship between the number of phases,P, the number of components,C, and the number of degree of freedom F . This relationship is known as phase rule. F=C-P+2 Derivation of phase rule Consider a heterogeneous system having P phases (P 1, P2,P3,....Pn) and components C (C1,C2,C3,….Cn). Then degree of freedom F is given by F = (Total no. Of variables)- ( No. Of relationship between variables at equilibrium)

11. Cont... 11 The total number of of variables 1. one is temperature and one is pressure variable for whole system. 2. P(C-1) are composition variables. Total number of variables = P(C-1) +1+1 = P(C-1)+2 . Number of relationship between variables at equilibrium C(P-1) Thus degree of freedom = [P(C-1)+2]-[C(P-1)] = PC-P+2-PC+C = C-P+2 This Is the Gibbs phase rule.

12. One component system 12 Under nomal conditions water exists in phases namely liquid water, ice and water vapour. All these phases can be represented by single constituent ‘Water’ so it is one component system. The number phases that can exists at any time depends on the conditions of temperature and pressure.

13. Phase diagram of water system 13

14. 14 Phase diagram of water consists the following three curves 1 Curve OA: It gives the equilibrium between liquid water and water vapours .it is called vapour pressure curve of water. The degree of freedom for this curve is given by: F =C-P+2 =1-2+2 = 1 2 Curve OB: It is the curve which represents the equilibrium between the ice and water vapours. This is sublimation curve of ice. The degree of freedom for this curve is given by: F= C-P+2 =1-2+2 =1 3 Curve OC: It is the curve which represents the equilibrium between ice and liquid water. This is the melting point curve of ice.Degree of freedom for this curve is given by: F = C-P+2 =1-2+2 = 1 4 Curve OA’ : This is the metastable curve for supercooled liquid. It is seen in the phase diagram curve OA’ lies above the curve OB. Hence ,vapour pressure of metastable system is higher than of the stable system at same temperature.

15. Areas AOC,AOB and BOC 15 The areas AOC, AOB and BOC in the phase diagram show the conditions of temperature and pressure at which a single phase ice,water or vapours can exist. It is necessary to specify both temperature and pressure to define a system in these areas. The degree of freedom for these areas is given by: F =C-P+2 = 1-1+2 = 2 So these areas are bivariant system. Triple point: The point ‘O’ in the phase diagram represents triple point of water system The curve oA ,OB and OC meets at triple point ‘O’ . At this point all the three phases are exist in equilibrium . Only one such point is possible. The degree of freedom at this point is given by: F =C-P+2 = 1-3+2 = 0 So the system is invariant or non-variant at this point.

16. Conclusion: 16 Phase equilibria gives the conditions that must be specified for a system to exist in equilibrium. A generalization is given by J.W.Gibbs which predict the conditions that a must specified for a system to exhibit equilibrium. This generalization is known as phase rule. This rule is mathematically given as: F= C-P+2 The degree of freedom is calculated by this rule.

17. References 17 ^ Gibbs,J.W., Scientific Papers (Daver , New York,1961) ^Atkins ,P.W. ; de Paula, J.(2006) Physical chemistry (8 th ed.). Oxford University Principles of physical chemistry by B.R.Puri ,L.R.Sharm, Madan S.Pathania. Physical chemistry by S.Kiran.

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