Component | Phase | Degree of freedom

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Explain (i) Component; (ii) Phase; (iii) Degree of freedom.

Phase:

It defines a phase as the part of the heterogeneous system which comprises two or more homogeneous parts which are separated from each other by definite boundaries.

Examples:  Phase, Phase, Phase, Phase

(i) CaCO 3CaO + CO2

Phase I II III

This system has three phases i.e. solid (CaCO 3 ) , solid (CaO) , gas (CO 2 ).

(ii) A system comprising water and ice: All the pieces of ice form one phase and the water another phase. Thus, there are two phases.

• A mixture of gases such as helium, hydrogen and argon makes up a single-phase since gases are completely miscible.
• Liquids may or may not form a single phase. It depends upon their miscibility. Completely miscible liquids make up one phase system. For example, water and alcohol.

 

Component:

The component of a system in equilibrium is defined as the minimum number of independently variable constituents chosen, by which the composition of any phase of the system can be expressed either directly or as a chemical equation.

The term component actually refers to ‘’chemical constituents’’ which are present in the phases of a heterogeneous system.

Example of one component system :

•  Consider the case of system ice‐water‐vapour. At the freezing point of water, three phases are in equilibrium.

ice_{( s)}water_{( l )}vapour_{( g )}

Since, the chemical composition of all the phase is H₂O, hence it is one component system.

• At the boiling point of water, the liquid and vapour are in equilibrium.

^H 2 ^O ( l )    ^H 2 ^O( v )

So in this case, a number of phases are two, viz. liquid phase and vapour phase but because the chemical constituents present in either of the liquid or vapour phase is H ₂ O only. So this system is also a “one component system”.

Example of two component system :

•  Consider the decomposition of CaCO₃ into CaO and CO₂

CaCO _{3 ( s )}   CaO _{( s )} + CO_{2 ( g )}

The composition of any phase can be expressed in terms of at least any two of the independently variable constituents: CaCO₃, CaO and CO₂. Thus, it is a two component system.

Example:

CaCO₃  solid phase : CaCO ₃ = CaCO ₃ + 0 CaO

CaO solid phase : CaO = 0 CaCO ₃ + CaO

CO₂  gaseous phase : CO ₂  = CaCO ₃ – CaO

• Consider a system comprising a solution of sugar in water. In this case, the solution contains two constituents, namely sugar and water. Thus, this is a two‐component system.

Degree of freedom or variance :

Degree of freedom or variance of a system is defined as the minimum number of the independently variable factors such as temperature, pressure and concentration of the components which must be arbitrarily fixed in order to define the system completely.

 Examples :

1.  Consider a gaseous mixture of two gases, CO₂ and N₂  in equilibrium. To define this system, three variables viz. Composition (35% CO₂ & 65% N₂ ), temperature ( 40 ^o C ) and pressure (760 mm) are required to be arbitrarily fixed. Hence the system has three degrees of freedom.
2. From the definition, a gas or vapour may be completely defined by fixing two variables P and T or V because the third variable may be calculated from the equation PV = RT and will have a certain definite value (R is a constant), hence the degree of freedom of the system is two.
3. Consider a system of two phases viz. water in equilibrium with its vapour. The vapour pressure of water will have only one fixed value at a given temperature. Thus, if temperature is arbitrarily fixed, the pressure is automatically determined and vice versa. The system will have one degree of freedom.
4. For ice‐water vapour system: In the system, ice-water vapour, the three phases coexist at the freezing point of water. As the freezing temperature of the water has a fixed value, the vapour pressure of water also has a definite value. The system has two variables (T and P) , both of which are already fixed. The system is completely defined automatically and there is no need to specify any variable. It has no degree of freedom.

Systems having the degree of freedom three, two, one or zero are known as trivariant, bivariant, uni variant (or mono variant) and nonvariant systems, respectively.  Phase