Phase Rule

PHASE RULE

If the equilibrium between any number of phases is not influenced by gravity, or electrical, or magnetic forces but is influenced only by pressure, temperature and concentration, then the number of degree of freedom (F) of the system is related to number of components (C) and number of phases (P) by the following phase rule equation.

F = C – P + 2

1. Definition of terms with examples

1. Phase (P)

Phase is defined as, “any homogeneous physically distinct and mechanically separable portion of a system which is separated from other parts of the system by definite boundaries”.

Examples

(a) Gaseous phase

All gases are completely miscible and there is no boundary between one gas and the other.

Example

Air, which is a mixture of O₂, H₂, N₂, CO₂ and water vapour, etc., constitutes a single phase.

(b) Liquid phase

The number of liquid phases depends on the number of liquids present and their miscibilities.

(i) If two liquids are immiscible, they will form three separate phases two liquid phase and one vapour phase.

Example

Benzene - Water.

(ii) If two liquids are completely miscible, they will form one liquid phase and one vapour phase.

Example

Alcohol - Water.

(c) Solid phase

Every solid constitutes a separate phase.

Example

Decomposition of CaCO₃

CaCO₃(s) ⇌ CaO(s) + CO₂(g)

It involves three phases, solid CaCO₃, solid CaO and gaseous CO₂.

(d) Consider a water system consisting of three phases.

Ice(s) ⇌ Water(1) ⇌ Vapour(g)

Each phase is physically distinct and homogeneous and there are definite boundaries between phases. So this forms three phases.

(e) A solution of a substance in a solvent consists of one phase only.

Example

Sugar solution in water.

(f) An emulsion of oil in water forms two phases

(g) MgCO₃ (8) → MgO_(s) + CO_2(g)

It involves three phases, solid MgCO₃, solid MgO and gaseous CO₂

(h) Rhombic sulphur (s) → Monoclinic sulphur (s)

It forms two phases.

(i) Consider the following heterogeneous system.

CuSO_4(s)  + 5H₂O₍₁₎ ⇌ CuSO₄ . 5H₂O_(s)  

Number of phase = 3; Number of component = 2

2. Component (C)

Component 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”.

Examples

(a) Consider a water system consisting of three phases.

Ice(s) ⇌ Water(1) ⇌ Vapour(g)

The chemical composition of all the three phases is H₂O, but are in different physical form. Hence the number of component is one.

(b) Sulphur exists in 4 phases namely rhombic, monoclinic, liquid and vapour, but the chemical composition is only sulphur. Hence it is a one component system.

(c) Thermal decomposition of CaCO₃

CaCO₃(s) ⇌ CaO(s) + CO₂(g)

The system consists of three phases namely, solid CaCO₃, solid CaO and gaseous CO₂. But it is a two component system, because the composition of each of the above phases can be expressed in terms of any two of the three components present. When CaCO₃ and CaO are considered as components.

This system has three phases, but the number of component is only two.

(e) An aqueous solution of NaCl is a two component system.

The constituents are NaCl and H₂O.

(f) CuSO₄.5H₂O(s) ⇌ CuSO₄ . 3H₂O(s) + 2H₂O(g)

It is also a two component system.

(g) In the dissociation of NH₄C1, the following equilibrium occurs.

NH₄Cl(S) ⇌ NH₃(g) + HCl(g)

The system consists of two phases namely solid NH4Cl and the gaseous mixture containing NH₃ + HCl. When NH₃ and HCl are present in equivalent quantities the composition of both the phases can be represented by the same chemical compound NH₄Cl and hence the system will be a one component system.

3. Degree of freedom (F)

Degree of freedom is defined as, "the minimum number of independent variable factors such as temperature, pressure and concentration, which must be fixed in order to define the system completely”.

A system having 1, 2, 3 and 0 degrees of freedom is called univariant, bivariant, trivariant and nonvariant respectively.

Examples

(a) Consider the following equilibrium

Ice(s) ⇌ Water(1) ⇌ Vapour(g)

These three phases will be in equilibrium only at a particular temperature and pressure. Hence, this system does not have any degree of freedom, so it is non variant or zero variant.

(b) Consider the following equilibrium

Water(1) ⇌ Water vapour(g)

Here liquid water is in equilibrium with water vapour. Hence any one of the degrees of freedom such as temperature or pressure has to be fixed to define the system. Therefore the degree of freedom is one.

(c) For a gaseous mixture of N₂, and H₂, we must state both the pressure and temperature. Hence, the system is bivariant.