Phase Rule

Phase Rule

Phase Rule

Phase Rule

Phase rule was deduced by the American physicist J. Willard Gibbs and stated as "If the equilibrium between any number of phases is not influenced by gravity, electrical, magnetic forces or by surface action but are influenced only by temperature, pressure and concentration , then the number of degrees of freedom (F) of the system is related to the number of components (C) and number of phases (P) by the following equation"-
F = C − P + 2

Phase (P)

A phase is defined as an homogeneous, physically distinct and mechanically separable portion of system, which is separated from other such parts of the system by definite boundary surfaces.

Solid Phase
Each solid forms a separate phase. The number of solid phase depends on the number of solids present in it.
Example- Many forms of sulphur can exist together, but these are all separate phases.
Liquid Phase
If two liquids are immiscible, they will form two separate liquid phases.
Examples- Water and Oil.

If two liquids are miscible they will form one liquid phase only.
Water and Ethyl alcohol
Gaseous phase
Since a gaseous mixture are completely miscible in all proportions so, it will form one phase only. Example : a mixture of N2 and H2 forms one phase only.

A solution of a substance in a solvent consists of one phase only, e.g. NaCl solution.

A heterogeneous mixture like CaCO3(s) ⇌ CaO(s) + CO2(g)consists of three phases (i.e., two solids and one gaseous).

At freezing point, water consists of three phases
Ice(S) ⇌ Water(L) ⇌ Water Vapour(G)
The chemical component of all the three phases is H2O and therefore it is one component system.
A homogeneous solid solution of a salt forms a single phase.
Example- Mohr’s salt [ FeSO4. (NH4)2SO4.6H2O] solution has a single phase.

Component (C)

It is defined as the smallest number of independently variable constituents by means of which the composition of each phase can be expressed in the form of a chemical equation.
Ice(S) ⇌ Water(L) ⇌ Water Vapour(G)
The chemical component of all the three phases is H2O and so it is an one component system.
Sulphur exists in four phases namely rhombic sulphur, monoclinic sulphur, liquid sulphur and vapour sulphur, but the chemical composition of all phases is S. So, it is an one component system.

Degree of Freedom (F)

It is defined as the minimum number of independent variable factors such as temperature, pressure and concentration of the phases, which must be fixed in order to define the condition of a system completely.
A system having 1,2,3 or 0 degrees of freedom is called univariant, bivariant, trivariant and nonvariant respectively.
It is calculated by formula
F = C − P + 2
Ice(S) ⇌ Water(L) ⇌ Water Vapour(G)
The three phases can be in equilibrium only at particular temperature and pressure. Therefore, when all the three phases are present in equilibrium, then no condition need to be specified. The system is therefore zero variant or invariant or has no degree of freedom.
F = C − P + 2
In the water system-
C = 1 and P = 3
So, F = 1 − 3 + 2 = 0. So, it is a zero variant or invariant or has no degree of freedom.
In this system, if pressure or temperature is altered , three phases will not remain in equilibrium and one of the phases disappears.
If we consider a system consisting of water in contact with its vapour,
Water(l) ⇌ Water vapour(g)
we must state either the temperature or pressure Thus degree of freedom is one and the system is univariant.
If we consider a system consisting of water vapour phase only, we must state the values of both the temperature and pressure in order to define the system completely. Hence the system is bivariant or has two degrees of freedom.

Merits of the Phase Rule

Followings are the main merits of phase rule-
1. It is applicable to both physical and chemical equilibria.
2. It is applicable to macroscopic systems, so it requires no information regarding molecular/microstructure.
3. It is a convenient method of classifying equilibrium states in terms of phases, components and degrees of freedom.
4. It helps 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 helps in deciding whether various substances would exist together in equilibrium or some of the substances present would be interconverted or some of the substances present would be eliminated.

Limitations of Phase Rule

Followings are the main limitations of phase rule-
1. It can be applied only for system in equilibrium. So, it is less important in case of very slow equilibrium state attaining system.
2. It applies only to a single equilibrium system; and provide no information regarding any other possible equilibria in the system.
3. It requires at most care in deciding the number of phases existing in an equilibrium state, since it considers only the number of phases, rather than their amounts. Thus even if a trace of phase is present, it accounts towards the total number of phases.
4. It limits that all phases of the system must be present simultaneously under the identical conditions of temperature and pressure.
5. It limits that solid and liquid phases must not be in finely-divided state; otherwise deviations occurs.


Reduced Phase Rule or Condensed Phase Rule

In some systems, an equilibrium exists between solid- liquid phases and gaseous phase is practically absent. Hence the effect of pressure on such system can be neglected. Then it is necessary to take into account only two variables viz. temperature and concentration. Such system showing solid-liquid equilibrium. So, the system in which only solid and liquid phase are considered and gas phase is neglected is called condensed system and the phase rule reduces to-
F= C – P + 1.
This is called Reduced Phase Rule or Condensed Phase Rule.

Thermodynamic Derivation of Phase Rule

Phase Diagram