Phase Rule for BTech class.pptx

By
Dr. Indu Chopra
Scientist, Division of Soil Science and Agricultural Chemistry, ICAR- Indian Agricultural Research
Institute, New Delhi-110012
Phase rule and its application
in one and two component
systems

Phase rule
Objectives:
• To understand the concept of phase, components and degree of freedom
• To study practical examples of Phase systems
• To understand phase system in chemical reaction
• To understand phase diagrams and their applications in one and two component
systems

Phase
It is defined as “ Physically distinct, homogenous and mechanically separable part of a
system ”.
(i) A gaseous mixture constitutes a single phase since gases are completely
miscible.
example : Air
(ii) Two or more liquids which are miscible with one another constitute a single phase as there is no
bounding surfaces separating the different liquids.
example : water and alcohol, chloroform and benzene constitute one phase system.
(iii) A system consisting of a liquid in equilibrium with its vapour constitute a two phase system
example : H2O(l) H2O(g)
Terms

Component
It is defined as “Minimum number of independent variable constituents which are required
to express the composition of each phase in the system”.
In a chemically reactive system, the number of components is given by
C = N - E
Where, C - components.
N - Number of chemical species
E - Number of independent equations relating to the
concentrations of the species.
 Each independent chemical equilibrium involving the constituents count as one equation.
 The condition that a solution be electrically neutral also counts as one equation if ions are considered as
constituents.

Examples
(i)Sulphur system
(a)monoclinic sulphur, (b)rhombic sulphur (c)liquid sulphur
(d) sulphur vapour. (C = 1; P=4)
(ii) Water system
solid,liquid and vapour
(C=1 ; P = 3)
.
(iii) Salt + water system
 Certain salts are capable of existing as hydrates with different number of water molecules of crystallization.
The system is a two component.(C=2 , P = 1)
 The composition of each phase of the hydrates is completely described in terms of the anhydrous salt and water
alone. e.g.,
Na2SO4 + water

Degree of freedom (F)
• It can be defined as the least number of variable factors (concentration, pressure and
temperature) which must be specified so that the remaining variables get fixed and the
system can be explained.
• A system with F = 0 (nonvariant), F=1 (univariant) and F = 2 (bivariant).
• Examples of degree of freedom:
 In case of pure gas (F =2) because PV =RT in this case when any two variables are fixed
third will automatically get fixed.
 For mixture of gases (F=3) in this case another component comes into picture apart
from P, V and T (i.e. mixture composition). When any of the three variables get fixed
fourth variable will automatically get fixed. Hence degree of freedom is 3

Continued:
 In case of water and water vapour (F=1): Here, in this case, the two variables are T and
P. When one is fixed the other one will automatically gets fixed.
 For saturated sugar solution (F=1): The saturated sugar sugar solution is in equilibrium
with solid sugar and water vapour. In this case, system can be completely defined by
fixing temperature only. The remaining two variables solubility and vapour pressure
have a definite value at a particular temperature.
 For ice-water-water vapour system (F=0): In this ice ⇌ water ⇌ water vapour coexist
simultaneously at the freezing point. Since value of freezing temperature and vapour
pressure of water are fixed. Therefore, both variables( T and P) are fixed and no need
to specify any variable. Hence, in this case F=0

Summary
• Phase: any homogeneous part of system having same physical and chemical properties
throughout
• Components: least number of independent chemical constituents in terms of which the
composition of every phase can be expressed by means of a chemical equation
• Degree of freedom: least number of variable factors (concentration, pressure and
temperature) which must be specified so that the remaining variables are fixed
automatically and the system is completely defined.
• Phase diagrams: Plots showing the conditions of pressure and temperature under which
two or more physical states can exist together in a state of dynamic equilibrium.

Phase and phase rule
• A phase can defined as any homogeneous and physically distinct part of a system
bounded by a surface and is mechanically separable from other parts of the system.
• A phase may be gaseous , liquid or solid.
• Definite boundary present between any two phases is called an interface.
• The homogeneous reversible reactions can be studied using the law of mass action. But,
for studying heterogeneous reversible reactions, phase rule is used.
• Therefore, phase rule deals with the behavior of heterogeneous systems.

Examples of some common terms in phase system
• One phase system: system containing only liquid water
• Two phase system: system containing water in liquid and vapour form
• Three phase system: system containing water in solid, liquid and vapour form
• Homogeneous system: System consisting only of one phase
• Heterogeneous system: System consisting of two or more phases
• Continuous phase: Ex. Ice as one single block
• Non-continuous phase: Ice in many pieces

“ In a heterogeneous system in equilibrium not affected by gravity or by
electrical and magnetic forces, the number of degrees of freedom(F) of the
system is related to the number of component(C) and the number of phases(P)
existing at equilibrium”.
It is expressed by mathematically,
F = C – P + 2
where,
F - number of degrees of freedom
C - number of components
P - number of phases
2-additional variables of temperature and pressure
Gibbs Phase Rule

Phase rule
• In cases, where equilibrium between different phases is not influenced by
gravity, electric/magnetic forces or through 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 phase rule
equation :
• It gives qualitative prediction which suggests the effect of change in
pressure, temperature and concentration in a heterogeneous system.

Practical examples of Phase systems?
• Pure substances: made up of one chemical species only e.g. ice, benzene, oxygen
• Mixture of gases: All gases mix freely to form homogeneous mixture Therefore, mixture of gases O2
and N2 is a one phase system.
• Miscible liquids: Ex. Completely miscible liquids like ethanol and water forms one phase system
• Non-miscible liquids: Mixture of two non-miscible liquids will form separate layers e.g. mixture of
hexane and water will form 2 phase system.
• Aqueous solutions: e.g. sugar solution is uniform throughout therefore it will form 1 phase system.
However, when already saturated sugar solution comes in contact with sugar it will form 2 phase
system.
• Mixture of solids: Ex. as the physical properties of allotropes is different, they form 2 phase system

Understanding phase system in chemical reaction
• Ex. Decomposition of Calcium carbonate at equilibrium
CaCO3 (solid) ⇌ CaO (solid) + CO2 (gas)
• There are two solid phases and one gaseous phase. Each phase has different physical and
chemical properties. Therefore, it is a 3 phase system.
• However, the Dissociation of ammonium chloride at equilibrium is a two phase system.
NH4Cl (solid) ⇌ NH3 (gas) + HCl (gas)
• This is because gaseous mixture of NH3 and HCl forms uniform system.

Phase Diagram
• Phase diagram 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.

Uses of Phase diagram
• 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.
• The phase diagrams are useful in understanding the properties of materials in the
heterogeneous equilibrium system.
• The study of low melting eutectic alloys, used in soldering, can be carried out
using phase diagrams.

Merits of the Phase rule
• Applicable to both physical and chemical equilibria.
• Requires no information related to molecular/micro-structure, because it is
applicable to macroscopic systems.
• Convenient method to classify equilibrium states in terms of phases, components
and degrees of freedom.
• Helps to predict the behavior of a system, under different sets of variables.

Limitations of Phase rule
• Can only be applied to system in equilibrium.
• Deals with single equilibrium system and provide no information about any other
possible equilibria existing in the system.
• As it considers only the total number of phases, rather than their amounts. Therefore,
even if a trace of phase is present, it accounts towards the total number of phases.
• All phases of the system must be present simultaneously under the identical conditions
of temperature and pressure.

Applications of Phase rule to one
component system (water system)
• The water system is a one component system
Ice ⇌ Water ⇌ Vapour
(Solid) (liquid) (gas)
• Water can exist in three possible phases i.e. solid, liquid and vapour. Therefore three forms of
equilibria may exist (i.e. Liquid – vapour , solid vapour and solid liquid)
• Each equilibrium involves 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 and is
plotted along y – axis whereas temperature is plotted along x-axis in Fig 1.

Fig 1. Water system

• The phase diagram for the water system is shown in Fig 1.
• The phase diagram consists of following:
 Curves: three curves OA, OB and OC.
 Areas: Three curves OA , OB and OC divide the diagram into three areas AOB, AOC
and BOC.
 Triple point: The above three curves meet at the point O and is known as triple
point.
 Metastable equilibrium: The curve OA represents the metastable equilibrium.

Curve OA
• The curve OA is called vapourisation curve, it represents the equilibrium between water
and vapour. At any point on the curve the following equilibrium will exist.
Water ⇌ Water vapour
• The degree of freedom of the system is one, i.e, univariant. Thus applying phase rule
equation,
F = C – P + 2; F= 1 – 2 + 2; F = 1
• This equilibrium (i.e, line OA ) will extend upto the critical temperature. Beyond the
critical temperature the equilibrium will disappear and water vapour will exist solely.

Curve OB
• The curve OB is called sublimation curve of ice, it represents the equilibrium
between ice and vapour. At any point on the curve the following equilibrium will
exist.
Ice ⇌ Vapour
• The degree of freedom of the system is one, i.e., univariant. Therefore on
applying phase rule:
F = C – P + 2; F = 1 – 2 + 2; F = 1
• This equilibrium line will extend upto the absolute zero (0 K) point at which no
vapour can exist and ice will exist as sole form of water.

Curve OC
• The curve OC is called the melting point curve of ice, it 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 1.

Triple point (Point ‘O’)
• At triple point all the three phases i.e. ice, water and vapour coexist. Therefore, the
value of P is 3. Hence, upon application of phase rule, the degree of freedom at this
point will come as zero.
• This means that three phases can coexist in equilibrium only at a definite temperature
and pressure. The values are 0.0075 °C and 4.58 mm respectively.
• At triple point, neither pressure nor temperature can be altered even slightly without
causing the disappearance of one of the phases.

Curve OB ( Metastable equilibrium)
• The curve OB is called vapour pressure curve of the super-cool water or
metastable equilibrium.
• At this curve following equilibrium will exist:
Super-cool water ⇌ Vapour
• Sometimes water can be cooled below 0 °C without the formation of ice, this
water is called super-cooled water.

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.
• Therefore, the degree of freedom of the system is 2 (i.e., bivariant).
• This is predicted by the phase rule
F = C – P + 2; F = 1 – 1 +2; F = 2

Summary of salient features of phase diagram of water system

Phase rule in Two component system
Reduced phase rule or condensed phase rule
• We know the phase-rule equation,
F = C – P +2 (eq.1)
• For a two component system, C = 2 and hence the above equation becomes,
F = 2 – P + 2 = 4 – P (eq. 2)
• The minimum number of phases in any system at equilibrium is one. It is clear from the eq. 2, the
maximum number of degree of freedom is three.
• Thus, three variables – pressure, temperature and composition of one of the components must be
specified to describe the system.
• This will lead to three dimensional figures which are difficult to represent on paper. Therefore, to
simplify this one of the three variables is kept constant.

Reduced phase rule or condensed phase rule
• In solid-liquid equilibrium of an alloy , practically there is no gaseous phase and
the pressure will not have much influence. In the case of solid-liquid equilibrium,
the experiments are generally carried out at constant pressure.
• Thus the system in which only the solid and liquid phases are considered and the
gas phase is ignored is called a condensed system. This reduces the degree of
freedom of the system by one. The phase rule equation then can be written as:
F = C – P + 1 (eq. 3)
• This equation is called reduced phase rule or condensed phase rule.

Types of solid-liquid equilibria
• Those equlibria in which the components are completely miscible with one another in liquid state. They do not form
any compound on solidification. They give rise to merely an intimate mixture known as eutectic . Examples of this
system are
 lead-silver system
 Lead-Antimony system
 Zinc-cadmium system
 Potassium iodide- water system
• Those equilibria in which the components enter into chemical combination . They give rise to one or more compounds.
Examples of this system are :
 Zinc-magnesium system
 Calcium chloride – Potassium chloride system
 Gold-Tellurium system.

Classification of two component system
The two component systems are classified into the following types :
• Simple eutectic formation
• Formation of compound with congruent melting point.
• Formation of compound with incongruent melting point.
• Formation of solid solution.

Simple eutectic formation
• A system with two substances which are completely miscible in the liquid state ,
but completely immiscible in the solid state is known as eutectic system. In this
system the substances do not react chemically.
• Among the mixtures of different proportions of two substances, the mixture
which has the lowest melting point is known as the eutectic mixture.
• The temperature and composition corresponding to the point eutectic point is
called eutectic temperature and eutectic composition respectively.

Formation of compound with congruent melting point
• In this type of binary alloy system the two substances form one or more
compounds with definite proportions. Of the compounds, a compound is said to
possess congruent melting point, if it melts exactly at a constant temperature into
liquid, having the same composition as that of the solid.
Formation of compound with incongruent melting point
• Of the above compounds, a compound is said to possess incongruent melting
point, if it decomposes completely at a temperature below its melting point
yielding a new solid phase with a composition different from that of the original.

Formation of solid solution
• In this type, when two substances, especially metals, are completely miscible in
both the solid and liquid states, they form solid solutions where mixing takes
place in the atomic levels.
• A solid solution can be formed only when the difference between the atomic
radius of two metals is not greater than 15%.

Lead –Silver system
• It is a two component system.
• The two metals are completely
miscible in liquid state and do not
form any compound.
• There is almost no effect of
pressure on this system.
• The temperature- composition
phase diagram is shown in Fig 2. It
contains lines, areas and the
eutectic point.
Fig 2. Lead-silver system

The 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.
• Therefore, the curve AC exhibit the impact 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.
• According to reduced phase rule equation
F = C – P + 1; F = 2 – 2 + 1; F = 1
• Hence, the system is univariant.

The 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.
• According to reduced phase rule equation.
F = C – P + 1; F= 2 – 2 + 1 F = 1
• Hence, the system is univariant.

Point C ( Eutectic point)
• 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, the number of degree of freedom for the system at the
eutectic point C is zero on the basis of reduced phase rule.
F = C – P + 1; F = 2 – 3 + 1 = 0; F = 0
• Hence, the system is non-univariant.
• Eutectic composition is 2.6% silver and 97.4% lead and the corresponding
temperature is 576 K.

• The area above the line ACB has a single phase (molten Pb+Ag).
• According to reduced phase rule equation,
• F = C – P + 1; F = 2 – 1 + 1; F = 2
• Hence, 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.

• Behl, A., Behl, B. S. and Tuli G.D. (2010) Essentials of Physical Chemistry. S. Chand
Publishing. ISBN: 81-219-2978-4
• Puri, B.R., Sharma, L.R. and Pathania M.S. (2008) Principles of Physical Chemistry.
Vishal Publishing Company. ISBN: 8188646652
• https://ncert.nic.in/textbook.php?lech1=0-9
References

Phase Rule for BTech class.pptx

More Related Content

What's hot

Similar to Phase Rule for BTech class.pptx

Recently uploaded

Phase Rule for BTech class.pptx