# Phase, Component, and Degree of freedom

Phase rule is a theoretical quantitative approach for predicting the effect of change in
temperature, pressure, and concentration on a heterogeneous system in equilibrium. This relationship was given by American physicist Josiah Willard Gibbs, and hence the rule is popularly known as Gibb’s Phase Rule. It deals with the stability of phases present in the material at equilibrium conditions. According to Gibb’s phase rule, if the heterogeneous equilibrium system is not affected by gravity, electric or magnetic forces, or surface action, but gets influenced by temperature, pressure, and concentration, then the number of degree of freedom (F) of the system is given by

F = C – P + 2

where, F = degree of freedom, P = phase, and C = component

Thus, Gibb’s phase rule relates the degree of freedom (F), number of components (C), and number of phases of the system (P). Each of these terms has a special significance in the description of the heterogeneous system in equilibrium.

## Phase

A phase is any homogenous part of a system that has the same physical and chemical properties that are separated from other parts by distinct boundary. Phases may either be pure compounds or mixtures such as solid or aqueous solutions, and a system can have one or more phases. For example, a system that contains liquid water, water vapor, and solid ice is a three-phase system.

• A system containing two immiscible liquids has two-phase.
• Two completely miscible liquids are one-phase systems.
• Gaseous mixtures constitute one phase system.
• Number of phases for a pure compound (solid, liquid, or gas) made up of single chemical species is one.
• The mixture of two allotropes is a 2-phase system.

## Component

Component of a system is defined as the minimum number of constituents required to define all of the phases present in a system.

• The number of individual gases present determines the number of components in a gaseous mixture. For example, the mixture of oxygen and nitrogen gases is a one-phase system but has two components.
• A one-component system has all of its phases represented in terms of one chemical individual. For example, a system containing liquid water (H2Ol), water vapor (H2Og), and solid ice (H2Os) is a one-component system.
• An aqueous solution of any solute is a two-component system. For example, sodium chloride solution in water is a 2-component system as it is composed of two chemical components i.e. sodium chloride (NaCl) and water (H2O).
• Decomposition of CaCO3 (s) ⇌ CaO(s) + CO2(g) is a three-phase, but two-component system. It can be described as: CaCO3 = CaO + CO2; CaO = CaCO3 – CO2; CO2 = CaCO3 – CaO
• The dissociation of ammonium chloride, NH4Cl (s) ⇌ NH3(g) + HCl (g) is a one-component system since both the constituents NH3 and HCl are in a gaseous state in equal proportion, the composition of which is expressed in the same chemical component, NH4Cl.

## Degree of Freedom

Degree of freedom is defined as the minimum number of the independent variables that are to be arbitrarily fixed so that the remaining variables are automatically fixed and the system is well-defined.

• If F = 0, then a system is nonvariant, while univariant and Bivariant for F= 1, and 2 respectively.
• A system consisting of a pure gas has two degrees of freedom (F = 2), while a mixture of gases has three degrees of freedom (F = 3).
• The degree of freedom for the ice-water-vapor system is zero.
• The system has one degree of freedom for saturated NaCl solution.

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