UNITIII PHASE EQUILLIBRIA Derivation of the phase rule

UNIT-III PHASE EQUILLIBRIA • Derivation of the phase rule • The water System • The Sulphur System • Lead Silver System • Desilverisation of Lead • Incongruent Melting points

Phase Rule When a heterogenous system in equilibrium at a definite tenperature and pressure the number of degrees of freedom is equal to by 2 the difference in the number of components and the number of phases provided the equilibrium is not influenced by external factors such as gravity, electrical or magnetic forces, surface tension etc.

Derivation of Phase Rule Gibbs Phase Rule is expressed by the simple formulation: F = C-P+ 2, where P is the number of phases in the system. C is the minimum number of chemical components required to constitute all the phases in the system. F is the number of degrees of freedom in the system (also referred to as the variance of the system). The integer in the Gibbs Phase Rule is related to the number of intensive parameters (i. e. those that are independent of mass; such as pressure and temperature)

Water System Water is a one component system Which is chemically a single compound involved in the system. The three possible phases in this system are ice(solid phase), water(liquid phase), vapour(gaseous phase). Hence, water constitutes a three phase, one component system. Since water is a three phase system. It can have the following equilibria Ice------ Water Ice------Vapour Water-----Vapour

The phase diagran consist of 1. Curves: There are three curves 2. Areas: Three curves divide the diagram into three areas 3. Triple ponit: The above three curves meet at one point and tha point is called triple point 4. Metastable equilibrium: The one curve represent the metastable equilibrium

Sulphur System Sulphur is a one component system and it can exist in two solid forms: rhombic and monoclinic. The rhombic form is stable at ordinary temperatures while the monoclinic form is stable at higher temperatures.

Substances that can exist in more than one crystalline form are said to display the phenomenon of polymorphism. There are two types of polymorphism, enantiotropy and monotropy. Enantiotropy is a more common form of polymorphism – exhibited by sulphur, tin, ammonium nitrate, carbon tetrachloride among other substances. Enantiotropy is the crystalline modifications of the same substance in which one form is stable above a definite temperature and the other stable below it, so that the forms can change reversibly one into the other. Invariant states are represented by points on phase diagrams. Systems with one degree of freedom, F = 1, are univariant and those with two degrees of freedom, F = 2, are bivariant.

For a one-component system such as sulphur, the coexistence of three phases in equilibrium corresponds to an invariant state since F = C – P + 2 = 1 – 3 + 2 = 0 This state is called a triple point; the point where it corresponds to the coexistence of solid, liquid and vapour phases at a particular temperature and particular pressure. In the sulphur system four possible triple points exists for the four phases: rhombic sulphur (solid), monoclinic sulphur (solid), sulphur (liquid) and sulphur (vapour).

Lead – Silver system: It is a two – component system with four possible phases – solid Ag, solid Pb, solution of Ag + Pb and its vapour. The two metals are completely miscible with each other in liquid state and do not form any chemical compound. There is almost no effect of pressure on equilibrium, the temperature and composition are considered to construct the phase diagram at constant atmospheric pressure.

Desilverisation of lead The Parkes process is a pyrometallurgical industrial process for removing silver from lead during the production of bullion. It is an example of liquid extraction. The process takes advantage of two liquid-state properties of zinc. The first is that zinc is immiscible with lead, and the other is that silver is 3000 times more soluble in zinc than it is in lead. When zinc is added to liquid lead that contains silver as a contaminant, the silver preferentially migrates into the zinc. Because the zinc is immiscible in the lead it remains in a separate layer and is easily removed. The zinc-silver solution is then heated until the zinc vaporizes, leaving nearly pure silver. If gold is present in the liquid lead, it can also be removed and isolated by the same process.

Incongruent Melting point Incongruent melting occurs when a solid substance does not melt uniformly. During melting a new solid (of different composition) forms. For example, melting of orthoclase (KAl. Si 3 O 8) produces leucite(KAl. Si 2 O 6) in addition to a melt. The melt produced is rich in silica (Si. O 2) so that the proportions of leucite and melt created can be recombined to yield the bulk composition of the starting feldspar. Another mineral that melts incongruently is enstatite (Mg 2 Si 2 O 6), which produces forsterite (Mg 2 Si. O 4) in addition to a melt (if melting at low pressure). Enstatite melts congruently between pressures of 2. 5 and 5. 5 kilobars.