Sunny gupta phase_rule_ppt

TOPIC : PHASE RULE
- Sunny gupta

 Phase :It is defined as “ Physically distinct,
homogenous and mechanically separable part of a
system ”.
 A System may consist of one or more than one phase
 A System consisting of only one phase throughout the
system is known as Homogeneous System .
For ex. : pure water, pure carbon etc.
 A System consisting of more than one phase is known
as Heterogeneous System .
For ex. : mixture of water and chloroform etc
.

1.Pure Substance :A Pure substance is made up of one chemical
species and is considered as one phase .
For ex- O2 , Benzene etc.
2. Mixture of gases :Gases mix freely to form homogeneous
mixture and considered as one phase system.
3. Miscible liquid :Two miscible liquid forms a complete
homogenous system therefore called as one phase system
4. Mixture of solid: A mixture of allotrope of sulphur is two-
phase system. For ex- Mixture of Srhombic & Smonoclinic
5. Non miscible liquid : A mixture of two non-miscible liquid
form two separate layer and is considered as two-phase
system. For ex- Mixture of water and CHCl3

The least number of independent chemical constituent in terms
of which the composition of each phase can be expressed by
means by chemical equation.
 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 conc. of 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.

For Non-Reactive System.
1.SULPHUR SYSTEM : Sulphur has four different phases i.e.
SRhombic , SMonoclinic , Sliquid, Svapour .
Number of Phases = 4 but these 4 phases are made up of the
single chemical identity and is considered as 1- Component System
2.WATER SYSTEM : Water has 3 phases i.e. solid (ice), liquid
water, water vapour . All these 3 phases are made up of the
single chemical identity and is considered as 1- Component
System
3.MIXTURE OF GASES : Mixture of gases is a one phase
system but it contains different chemical species. So the no.
gases in a mixture is equal to the number of the component .
For Ex- the mixture of O2 and N2 is one phase system but
there is two different chemical species hence it is a 2-
component system.

For Reactive System.
1. DECOMPOSITION OF CaCO3
CaCO3 (s) CaO(s) + CO2 (g)
 The composition of all the three phases can be
expressed in terms of the either of the two components.
 It is a two component system
CASE 1:
When CaCO3 and CaO are present as 2 components.
CaCO3 = CaCO3 + 0.CaO
CaO = 0. CaCO3 + CaO
CO2 = CaCO3 - CaO

CASE 2:
When CaCO3 and CO2 are present as 2 components.
CaCO3 = CaCO3 + 0. CO2
CO2 = 0. CaCO3 + CO2
CO2 = CaCO3 - CaO
CASE 3:
When CaO and CO2 are present as 2 components.
CaCO3 = CaO +CO2
CO2 = 0. CaO + CO2
CaO = CaO + 0. CO2
From the above three cases it is clear that only the
constituent are needed to be express the composition
of the each of the phases .Hence it is a two-
Component System.

1 . A solution containing Na+ , Cl- , Ag+ , NO3
-AgCl(s)and H2O.
Soluion: Reactions taking place in the given solution.
NaCl Na+ + Cl-
NaNO3 Na+ + NO3
-
AgCl Ag+ + Cl-
AgNO3 Ag+ + NO3
-
NO.of independent chemical reaction taking place, R=5
No. of species , S=11
x Na+ + x Ag+ = xNO3
- + xCl-
xH+ = xOH-
Condition of electro neutrality , Z=2
No. of component in the system, C= S – R - Z
= 11 – 5 – 2= 4
total number of component in given system = 4

 “It is defined as the minimum number of independent
variables such as temperature, pressure and
concentration which should be specified in order to
define the system completely”.
It is denoted by ‘F’
For Examples
(i) State of a pure gas can be specified by two variables P and
T or P and V , third variable can be calculated. Hence pure gas
has degree of freedom two (F = 2)
(ii) H2O(l) H2O(g)(F=1)Monovariant
(iii) A gaseous mixture say N2 and O2 gases is completely
defined when three variables(T,P and C).
(F=3) Trivariant.

 Water At Triple Point .
ICE WATER WATER VAPOUR
This system has three phases and all are coexisting at
freezing point of the water.
Since the freezing point of water has one fixed value,
therefore vapour pressure of water have definite
value ,So we can say that system has two variables
which are already fixed, therefore system is
completely defined therefore degree of freedom at
this point is zero .Thus system is invariant.

 “Phase rule” is an important tool used for the quantitative
treatment of systems in equilibrium.
 It enables us to predict the conditions that must be specified
for a system to exhibit equilibrium.
 It is very useful to understand the effect of intensive
variables, such as temperature, pressure, or concentration,
on the equilibrium between phases as well as between
chemical constituents.
 J. Willard Gibbs enunciated the phase rule in 1876 on the
basis of Thermodynamic principles
 Two or more different phases are present in equilibrium to
form a “heterogeneous system”. Such system are studied by
phase rule.

Gibbs phase rule : “ In a heterogeneous system in
equilibrium is 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

 The greater the number of components in a
system, greater is the degree of freedom for a given
number of phases.
The greater the number of phases, the smaller is the
number of degree of freedom
The number of phases is maximum, the number of
degrees of freedom = Zero, for a given number of
components.
For
One component system P = 3
Two component system P = 4
Three component system P= 5

 Provides convenient method of classification of equilibrium
states of system
 Predict the behavior of system with changes in the intensive
variables.
 The phase rule confirms that the different systems having
the same number of degrees of freedom behave in same
manner.
 It is applicable only to macroscopic systems and not
concerned with molecular structure.
 It predicts that, under a given conditions whether a number
of substances taken together would remain in equilibrium
 It takes no account of nature of reactant and products in
phase

 The phase rule is applicable to heterogeneous systems in
equilibrium, hence it is not applicable for the systems which
are slow to attain the equilibrium state
 It Considers only no. of phases not quantity of phases
It is applicable to a single equilibrium state. . It never
gives information about the other possible state
equilibrium in the system
All the phases in the system must be present under the
same Temperature, Pressure and Gravitational force .
 Solid or liquid phases are not finely divided, If it
happens , deviation must occurs.

# Application of Gibbs Phase Rule
One Component System
From the mathematical expression of phase rule
F = C – P + 2
When C = 1, P = 1
F= 1-1+2 =2
All one component systems can be completely described
graphically by stating only two variables such as pressure
and temperature on appropriate axis.

Clapeyron equation: In system of a pure substance if
several phases are present at equilibrium under a
given set of conditions , there is always a
possibility of transition of a substance from one
phase to another phase by altering any of the
variables
A thermodynamic relation between the change of
pressure and change of temperature of a system at
equilibrium is called clapeyron equation.
(dp/dt )= ∆Hm/(T∆Vm)

Case 1
FOR SOLID LIQUID EQUILIBRIUM
The integrated Clausius clapeyron equation for this is given by
∆P=(∆Hm,f/ ∆Vm,f)(∆T/T)
Case 2
FOR SOLID VAPOUR EQUILIBRIUM
ln(P2/P1) = (∆Hm,sub/R)(1/T1 – 1/T2 )
Case 3
FOR LIQUID VAPOUR EQUILIBRIUM
ln(P2/P1) = (∆Hm,VAP/R)(1/T1 – 1/T2 )

1. It is a convenient graphical representation formed by
plotting the values of intensive variables for
equilibrium conditions between two phases.
2. It shows the properties such as mp, bp, phase
transition point and triple point.
3.The complex city of phase diagram increase with
increase in number of component in the system.
4.For a simple substance (one component system) phase
diagram is two dimensional plot where P & T are
independent variables.
5.The phase diagram of a two component system is a
three dimensional plot, where third axis is for
composition

6. Three dimensional plot can also converted into
two dimensional plot by keeping one variable
constant.
• Isobaric
• Isothermal
7. When one of the variable kept constant then
phase rule equation is reduced to :
F = C – P + 1
8. This is known as reduced phase rule.

http://www.ques10.com/p/7239/what-is-a-condensed-phase-systems-draw-
the-phase-1

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the-phase-1

1.Water exist in three possible phases: ice, water, vapors
2.It is a one component system so maximum degrees of freedom is
two, when one phase is stable at equilibrium.
F= C-P+2 = 1-1+2=2
3. Phase diagram of water is two dimensional plot where P & T are
taken as axes.
Phase diagram is divided into three areas:
Area BOC – where ice has stable existence
Area COA – where water has stable existence
Area BOA – where water vapors has stable existence
Phase Rule for this system:
F = C-P+2 = 2
Degrees of freedom is two hence bivariant system.

1.Melting point Curve (Curve OC)
2.Vaporization curve or vapor pressure curve (Curve OA)
3.Metastable equilibrium (Curve OA’)
4.Sublimation Curve (Curve OB)
5.Triple point O
Melting point Curve (Curve OC)
1.Also known as melting point curve or freezing point curve
or fusion curve.
2.Represents equilibrium between ice & water
3.It is enough to know either T or P because other variable
gets automatically fixed.
e.g. At atmospheric pressure, ice & water can be in
equilibrium only at one temperature i.e. at freezing point
of water.
4. Thus ice- water equilibrium line (Curve OC) has only one
degree of freedom (Univariant system).
Phase Rule: F = C- P +2 = 1-2+2 = 1

Vaporization Curve or vapor pressure curve (Curve OA)
1.Represents the equilibrium between two phases water & vapor..
2. It enough to know either T or P because other variable gets automatically fixed.
3. Because at any temperature, Pressure of vapor in equilibrium is fixed in value.
4. Thus water & vapor equilibrium line OA has only one degree of freedom so
univariant system.
5.Phase Rule: F = C- P +2 = 1-2+2 = 1
6. At higher end, curve OA terminates at point A which is critical temperature
(374C) and Pressure (218atm.) of water.
7.At this point liquid & vapor phases become indistinguishable & merge into
single fluid phase.
8.Under normal conditions terminus point is O where water freezes to form
ice.

Vaporization Curve or vapor pressure curve (Curve OA’)
1.Curve OA’ represents the meta-stable equilibrium.
2.Under some special conditions pure water may be cooled down much below
the freezing point without forming ice.
3.Thus it is possible to extend vapor pressure curve even below freezing point
of water.
4.This equilibrium can be approached by cooling liquid water and not by
heating ice.
5. Metastable vapor pressure of super cooled liquid is higher than the vapor
pressure of ice.
Sublimation Curve (Curve OB)
1.Represents the condition for equilibrium between ice and vapors.
2.Shows vapor pressure of ice at different temperature
3.In order to describe the system along line OB either value of T or P need to
bespecified.
4.Because at any temperature, value of vapor pressure of ice is fixed.

▶ If we start a liquid phase and allow it to cool in steady surrounding the
graph line obtained between temperature and time is known as cooling
curve .

1. In two component system with P=1, the number
of degrees of freedom are highest order is three.
2. In two component system phase diagram may be
represented by three dimensional diagram of P,
composition and T.
3. In this diagram two axes represents two variables
while third variable is held constant.
4. Phase Diagram may be constructed as :
1. P-T diagram keeping conc. Constant
2. P- Conc. Diagram T constant
3. T-C diagram keeping P constant.

• When P is kept constant, vapour phase of system is
not considered. In this case system is said to be
condensed and phase rule reduced to
• F = C – P +1
• This is called condensed phase rule or reduced phase
rule.
• T vs. Composition diagrams are shown to represents
the solid- Liquid equilibria.
• Two component system is to be classified depending
upon miscibility of two components in molten state
and also on basis of solid phases that separates out on
cooling.

When two components that are completely miscible in
liquid state are allowed to cool at low Temperature
and components begin to separate out as solid in any
of following three forms:
1. Components are not miscible in solid state and form
eutectic mixture. Pb-Ag alloy, Cd- Bi alloy
2. Components form a stable solid compound which
melts at constant temperature to give a liquid with
same composition. Such compounds are said to have
congruent melting points.: Zn-Mg system
3. Components form a solid compound which is unstable
and decomposes below its mp to give a new solid
phase and liquid that is different in composition from
original compound. Such compounds have
incongruent mp e.g. : Na-K system

• Two component system in which both the
components are completely miscible in liquid phase
but do not react chemically is called a eutectic system
e.g. Ag-Pb System
• Eutectic Temperature and composition: for a pure
substance A, the freezing point is higher and upon
increasing the conc. of B freezing point decreases to
lowest value. This is called eutectic temperature and
composition at this state is called eutectic
composition.
• Eutectic Point: (easily melted) is defined as the lowest
melting point attained by the mixture

• Congruent melting : occurs during melting of a
compound when the composition of the liquid that
forms is the same as the composition of the solid.
• It can be contrasted with incongruent melting.
• A binary system is said to be possess a congruent
melting point when it melts at sharp temperature to
give a liquid of the same composition as that of
solid.
• This generally happens in two-component systems.
• e.g. Zn-Mg System

 We have rounded maximum in case of
congruent melting point because the
component is not much stable at its melting
point it partially dissociates and the product
of dissociation is the liquid phase disperses
the actual melting point of the compound
with the result that the curve has a flattened
maximum but not a peak.

“Always do the things with
+ve intent”
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Sunny gupta phase_rule_ppt

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