Phase Rule and Phase Equilibria

• Phase (p): A form of matter that is homogeneous in

chemical composition and physical state. Typical phases are solid, liquid and gas. , Two immiscible liquids separated by a distinct boundary are counted as two different phases.

• Homogeneous phases: pure liquids or solutions

• Two phases systems: immiscible liquids (or solutions) , since there is a definite boundary between them.

• One phase system: a mixture of gases, because the mixture is homogeneous and there are no bounding surfaces between the different gases in the mixture.

One phase systemTwo phase system

Number of components of a system (C):

• Is the smallest number of constituents by which the composition of each phase in the system at equilibrium can be expressed in the form of a chemical formula or equation.

• Ice , water , water vapor (3-phase system) the number of components is 1 (formula is H2O).

• A mixture of salt and water is a two component system

since both chemical species are independent & different .

Phase Equilibria and the Phase RuleThe Phase Rule: Relation between the effect of the least number of independent variables (temperature, pressure and concentration). upon

various phases (solid, Liquid and gaseous) that exist in an equilibrium system.

Degrees of freedom ( f ):

• Number of degrees of freedom is the number of variable conditions i.e. (temperature, pressure & concentration) that must be known, so that the condition of the system at equilibrium may be completely defined.

• The relationship between the number of phases (P), components (C) and degrees of freedom (F) for equilibria that are influenced only by temperature, pressure and concentration is given by equation (the phase rule):

F = C - P + 2• The application depends on the number of

components present in separate systems.

Phase diagrams:

• Represent the effects of temperature, pressure and composition on the phase equilibria , showing the variation of transition temperature such as boiling or melting point with pressure or compression.

• Representation of the effect of three variables would require three axes. This can be achieved with three-dimensional models but if one variable is fixed the resulting planar diagram can be regarded as a section through such a model.

Systems Containing One Component

• The difficulties associated with the representation of 3 variables do not arise in systems containing 1 C.

• The areas each correspond to a single P. The no. of degrees of F is therefore given from the equation :

F = 1 - 1 + 2 = 2

• (2) means that temperature & pressure can be varied independently within these areas.

t

t

System corresponding to a point that lies on one of the

lines AO , BO, or CO,

The number of degrees of freedom is reduced because from equation (1)

F = 1 - 2 + 2 = 1

This means that a single variable exists when equilibrium is established between 2 phases.

Melting Point:

The boundary BO represents the coexistence of liquid water in solid ice at various temperature and pressures.

BO therefore indicates the effect of pressure on m.p of ice(-ve slope of BO) the m.p as the pressure .

To maintain equilibrium conditions between the two phases, the temperature & pressure must not be varied independently of each other.

Triple Point :

Point O , which is the only point in the diagram where three phases may coexist in equilibrium. F = 1 - 3 + 2 = 0

The system is therefore invariant , i.e. any change in pressure or temperature will result in an alteration of the number of phases that are present.

Sublimation and Sublimation Drying (Freeze Drying):

CO the sublimation pressure curve for ice (coexistence of vapour and solid phases in equilibrium).

A mass of ice water vapour by

heating on condition pressure is

< triple point pressure.

Important in drying compounds that are sensitive to the higher temperature usually associated with drying techniques.

Lyophilization, Gelsiccation, Freeze drying 1-It is drying by sublimation from the frozen condition , i.e. (drying of blood plasma, blood serum and penicillin). 2-Freezing the solution of the material (-l0o C to -30o C ) in suitable containers connected to a high vacuum system (0.1 - 0.3 mm Hg). 3-A partial pressure of water vapour, less than that of the material being dried, is attained. 4-water sublimes from the frozen mass until the material is desiccated.