Phase Equilibria B.Sc. 1st Year Notes

Phase Equilibria

Phase Equilibria MCQs

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

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.

Sodium chloride solution is an one component system while saturated solution of sodium chloride is two component system. Explain.

What is the number of phases and components present in the following reaction ?
MgCO₃(solid) ⇌ MgO(solid) +CO₂ (Gas)
1. 3, 2
2. 1, 3
3. 2, 3
4. 1, 2

Answer: We have two solids and one gaseous component in the above reaction. So, we have 3 phases. Under equilibrium, the gaseous component may evaporate, we have only two components.

What is the number of phases and components in the following reaction ?
NH₄Cl(solid) ⇌ NH₃ (Gas) + HCl (Gas)
1. 1, 2
2. 2, 1
3. 3, 1
4. 3, 2

What is the number of phases and components in an aqueous solution of glucose ?
1. 2, 1
2. 3, 2
3. 1, 3
4. 1, 2

What is the number of phases and components in the following reaction ?
Fe(Solid) + H₂O (Gas) ⇌ FeO (Solid)+ H₂(Gas)
1. 3, 3
2. 2, 3
3. 1, 3
4. 2, 2

Calculate the degree of freedom for the following reaction.
N₂O₄(Gas) ⟶ 2NO₂(Gas)
1. 1
2. 2
3. 3
4. 0

Eutectic system

A binary system in which two components are miscible in all proportion in the liquid state but do not react chemically is known as Eutectic system.
Example- A mixture of Pb and Ag comprises of such a system.
(The word 'Eutectic' came from Greek word 'eutectos' which means easy melting)

Eutectic Point

It is the lowest freezing point that can be reached for a eutectic combination (which means lowest melting point).
In the solid-liquid system where all three phases, namely the liquid melt of the two metals and the solid phases of each of the components, are in equilibrium at eutectic point.
The melting point of the mixture corresponding to the eutectic point is the lowest. At this stage, the system is invariant (i.e., the degrees of freedom or variance are zero) and has a fixed temperature and composition.

Phase Diagram

It is a graph obtained by plotting one degree of freedom against another. If the phase diagram is plotted between temperature against pressure, the diagram is called P-T diagram. P-T diagram is used for one component system.
If the phase diagram is drawn between temperature against composition, the diagram is called T-C diagram. T-C diagram is used for two component system.
From the phase diagram, it is possible to predict whether an eutectic alloy or a solid solution is formed on cooling a homogeneous liquid containing mixture of two metals. Phase diagrams are useful in understanding the properties of materials in the heterogeneous equilibrium system.

Phase Diagram of Water System

Water is an 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) and vapour(gaseous phase).
Hence, water constituetes a three phase and one component system. Since water is a three phase system, it can have the following three equilibria-
Ice ⇌ Vapour
Ice ⇌ Water
Water ⇌ Vapour
i.e. Ice ⇌ Water ⇌ Vapour
Each equilibrium involves in two phases. The nature of these phases which exist in equilibrium at any time depends on the conditions of temperature and pressure. These conditions have been determined and summarized in the pressure-temperature diagram in which pressure is treated as independent variable.

The phase diagram consists of-
1.Curves: There are three curves OA, OB and OC
2.Areas: Three curves OA , OB and OC divide the diagram into three areas AOB, AOC and BOC.
3.Triple point: The above three curves meet at the point O and is known as triple point.
4.Metastable equilibrium: The curve OA represents the metastable equilibrium.
Curve OA
The curve OA is called vapourisation curve and represents the equilibrium between water and vapour. At any point on the curve the following equilibrium will exist-
Water ⇌ Water vapour
Applying phase rule equation on this curve-
F = C – P + 2
or, F = 1 – 2 + 2
or, F = 1
The degree of freedom of the system is one, i.e, univariant.
Curve OB
The curve OB is called sublimation curve of ice and represents the equilibrium between ice and vapour. At any point on the curve the following equilibrium will exist-
Ice ⇌ Vapour Applying phase rule equation on this curve-
F = C – P + 2
or, F = 1 – 2 + 2
or, F = 1
The degree of freedom of the system is one, i.e., univariant.
Curve OC
The curve OC is called melting point curve of ice and represents the equilibrium between ice and water. At any point on the curve the following equilibrium will exist-
Ice ⇌ Water
The curve OC is slightly inclined towards pressure axis. This shows that melting point of ice decreases with increase of pressure. The degree of freedom of the system is also one. i.e., univariant.
Areas
Area AOC, BOC , AOB represents water, ice and vapour respectively. In order to define the system at any point in the areas, it is essential to specify both temperature and pressure.
Applying phase rule equation on the area-
F = C – P + 2
or, F = 1 – 1 +2
or, F = 2
So, the degree of freedom of the system is two. i.e., Bivariant.
Triple point (Point 'O')
At triple point all the three phases (i.e. ice, water and vapour) coexist. Thus the value of Phase(P) is 3. Applying phase rule equation, the degree of freedom at this point is zero. It means that three phases can coexist in equilibrium only at a definite temperature and pressure.
At this triple point, neither pressure nor temperature can be altered even slightly without causing the disappearance of one of the phases.
Curve OA' ( Metastable equilibrium)
The curve OA' is called vapour pressure curve of the super-cool water or metastable equilibrium. The following equilibrium will exist-
Super-cool water ⇌ Vapour
Supercooled water is unstable and it can be converted into solid by slight disturbance.

Summary of Water System

Curve/Area/Point	System Name	Phases in Equilibrium	Number of Phases	Degree of Freedom
Curve OB	Vaporization	Liquid & Vapour	2	1
Curve OA	Sublimation	Solid & Vapour	2	1
Curve OC	Fusion	Solid& Liquid	2	1
Curve OA'	Metastable	Liquid & Vapour	2	1
Area AOC		Ice	1	2
Area BOC		Water	1	2
Area AOB		Vapour	1	2
Point O		Ice, Water & Vapour	3	0

Phase Diagram of KI–H₂O System
KI–H₂O System has four phases- Solid KI, Solution of KI in water, Ice and Vapour. Only two chemical constituents KI and H₂O being necessary to depict the composition of all the four phases. So, it is a two-component system.
Since the conditions for the existence of the various phases are studied at atmospheric pressure, the vapour phase is ignored and the system KI-H₂O is regarded as a condensed system. Pressure being constant, the two variables, temperature and concentration will be considered. The T-C diagram of the system is shown below.


KI–H₂O System consists of-
1. Curves AO and OB
2. Eutectic Point O
3. The area above AOB and the areas below the curves OA and BO

Curve AO
The point A represents the freezing point of water or the melting point of ice (0ºC) under normal conditions. The curve AO shows that the melting point of ice falls by the addition of solid KI. As more and more of KI is added, the concentration of solution and the melting temperature changes along the curve AO. The phases in equilibrium along the curve AO are ice and solution.
Applying the reduced phase rule equation to the condensed system ice/solution, we get the degree of freedom-
F = C – P + 1
or, F = 2 – 2 + 1
or, F = 1
Thus the system is monovariant.
Curve BO
At O, the solution is saturated with KI. Thus the curve BO depicts the effect of temperature on the concentration of saturated solution or the solubility of KI. The phases in equilibrium along the curve are solid KI and solution.
Applying the reduced phase rule equation, we get the degree of freedom-
F = C – P + 1
or, F = 2 – 2 + 1
or, F = 1
Thus the condensed system solid KI/solution is monovariant.
Eutectic point
The lowest point attainable by the addition of KI along the curve OA is O. Here the solution becomes saturated with KI and the solid KI appears as the third phase. This point is termed the Eutectic Point or Cryohydric Point as one of the components in the system is water.
Applying the reduced phase rule equation to the system ice/solid KI/solution at point O.
F = 2 – 3 + 1
or, F = 0 Hence the system is nonvariant. That is, both the temperature are fixed.
The Area above AOB
It represents the single phase system 'solution'.
Applying the phase rule equation-
F = C – P + 1
or, F = 2 – 1 + 1
or, F = 2
Therefore the system is bivariant.
As labelled in the diagram, the area below AO shows the existence of ice and solution, while the area below BO depicts the presence of solid KI and solution. Below the eutectic temperature line, there can exist ice and solid KI only.

Phase Diagram of Lead –Silver system

It is a two component system. The two metals are completely miscible in liquid state and does not form any compound. There is almost no effect of pressure on this system. The temperature composition (T-C) phase diagram is shown below-

Lead –Silver system contains-
1. Curve AC
2. Curve BC
3. Eutectic Point C
4. Area
Curve AC
The curve AC is the freezing point curve of pure lead. The melting point of lead decreases gradually along the curve AC, with the continuous addition of silver. Thus, the curve AC is showing the effect of addition of silver on the melting point of pure lead. All along the curve AC two phases – solid lead and liquid are in equilibrium.
Applying the Reduced Phase rule equation-
F = C – P + 1
or, F = 2 – 2 + 1
or, F = 1
or, F = 1
Thus, it is a univariant system.
Curve BC
Curve BC is the freezing point curve of pure silver and represents the effect of addition of pure lead on the melting point of pure silver. All along the curve BC two phases – solid silver and liquid are in equilibrium. Applying the Reduced Phase rule equation-
F = C – P + 1
or, F = 2 – 2 + 1
or, F = 1
or, F = 1
Thus, it is a univariant system.
Point C
Point C is the eutectic point where solid silver, solid lead and their solution coexist. The curves AC and BC meet at point C. Since the experiment is carried out at constant pressure.
Applying the Reduced Phase rule equation-
F = C – P + 1
or, F = 2 – 3 + 1
or, F = 0
Thus, it is a non-univariant system and the number of degree of freedom for the system at the eutectic point C is zero.
Areas
The area above the line ACB has a single phase (molten Pb+Ag). Applying the Reduced Phase rule equation-
F = C – P + 1
or, F = 2 – 1 + 1
or, F = 2
Thus, the system is bivariant.
Both the temperature and composition have to be specified to define the system completely.
The area below the line AC ( solid Ag + liquid melt), below the line BC ( solid Pb +liquid melt) and below the eutectic point 'C' have two phases and the system is univariant.
Applying the Reduced Phase rule equation-
F = C – P + 1
or, F = 2 – 2 + 1
or, F = 1
Thus, the system is univariant.