Phase Equilibrium
B. Sc. VI Semister
Physical Chemistry
By
Dr. Anjali Acharya
Institute for Excellence in Higher
Education
Bhopal

Contents
•Phase equilibrium
•Statement and meaning of terms C,P, F
•Darivation of Gibb’ s Phase Rule
•One component system,

Phase Transformation
प्रावस्था रूपाांतरण
1. For Heterogeneous System ववषमाांग तांत्रां
2. Transfermation of phases रूप पररवततन
3. Diagramatic reprepresentation प्रावस्था आलेख़

Phases - प्रावस्था
Solid ठरस
Liquid तरल
Gaseous गैस

Tools
Variables-
Temperature ताप
Pressure दाब
Composition सांध्रता
Volume आयतन

Gibb’s Phase Rule
F = Degree of Freedom स्वांत्ता की करवि
Diagrammatic representation आलेख वित्
F = C – P + 2
C = Component घिक
P = Phase प्रावस्था

Definition – पररभाषा
Phase – Physically distinct and
mechanically separable part of
Heterogeneous system
भौवतक रूप से सुस्पष्ट एवां याांवत्क वववि
से अलग हरने वाले भाग कर प्रावस्था कहते
है.

Definition – पररभाषा
Component – minimum number of phases
required to explain composition of each phase
chemically is known as the component.
घिक - प्रावस्थाओ की कमतर
सांख्या विस से प्रत्येक अवस्था कर
एक रासायवनक सूत् वदया िा
सक
े , घिक कहलाता है.

Definition – पररभाषा
Degree of freedom – minimum number
of variables to explain phase diagram is
called as degree of freedom.
स्वतांत्ता की करवि - पररवती अवयव की
आवश्यक सांख्या विस से पूणत प्रावस्था
आलेख समझाया िा सक
े स्वतांत्ता की
करवि कहलाता है .

Phase Equilibrium
Example
Water system
Sulphur system
Carbondioxide System
Calcium Carbonete
Ammonium Chloride
Alloys – Pb-Ag
Zn- Mg

Example - Water system
Number of component = 1 = H2O
Number of phases 3
Ice
Liquid
Vapour

Sulphur system
Number of phases – Four
SR
SM
Sl
Sv
Component = 1 i.e. S

Calcium Carbonate
Phases –3
Solid CaCO3
Solid CaO
Gaseous CO2
CaCO3 CaO + CO2
Number of component = 2 because at least
two phases required to give chemical formula
for each phase

Darivation of Gibb’s Phase Rule
For heterogeneous system if components
represented by 1,2,3 and phases are a,b,c
Chemical potential (µ ) for each phase is
given by –
(µ1a ) , (µ2a ) , (µ3a ) , (µ1b ), (µ2b) , (µ3b )
, (µ1c) , (µ2c ) , (µ3c )

Darivation of Gibb’s Phase Rule
According to Gibb’s Duhem Equation ∑ µ dn = 0
(µ1a ) = (µ1b ) = (µ1c) = (µ1P)
(µ2a =(µ2b) = (µ3c ) = µ2P
(µ3a = (µ3b ) = (µ3c ) = µ3P
= µcP
number of independent equation = C ( P – 1)

Darivation of Gibb’s Phase Rule
Each phase contain all the C components.
To define composition of each phase C – 1 concentration
should be specified at constant P and T .
Total number of variable = P ( C – 1) + 2 -----------( eq.1)
Number of equations = C ( P -1) ------------------------ ( eq 2)
F = eq.1 – eq.2
F = P ( C -1 ) +2 – C (P -1)
F = PC –P + 2 – CP + C
F= C – P + 2 -------------------- Phase Rule

One Component sustem
एक घिक का तांत्
Water system िल तांत्
Phases / प्रावस्था–
•Ice बर्
त
•liquid द्रव H2O
•Vapours वाष्प
F = C – P + 2 Phase Rule प्रावस्था वनयम
C = 1 P = 1
Therfore 1 – 1 + 2 = 2

0oC T 100oC
A
O
B
C
Critical T
Critical P
Vaporization curve
Sublimation curve
217.5 Atm
374oC
.0075oC
Tripal point
4.58mm
Supersublimation curve
Melting point curve
P
P-T Diagram
Water system
प्रावस्थ आलेख Phase rule digram –
P – T Diagra

0oC T 100oC
A
O
B
C
Critical T
Critical P
Vaporization curve
Sublimation curve
217.5 Atm
374oC
.0075oC
Triple point
4.58mm
Super sublimation curve
Melting point curve
P
P-T Diagram
Water system
प्रावस्थ आलेख Phase rule digram –
P – T Diagra
A’
Vapours
Liquid
Ice
Super cool

प्रावस्थ आलेख Phase rule digram –
P – T Diagrame
S.No. Curve Name Phases F = C – P +2 D.F. = F
1 AO Sublimation
curve
ICE and
Vapours
= 1 – 2 + 2 1, Mono
variant, uni
variant
2 BO Vaporisation
curve
Liquid and
Vapours
= 1 – 2 + 2 1, Mono
variant, uni
variant
3 CO Melting
point curve
of water
Ice and liquid = 1 – 2 + 2 1, Mono
variant, uni
variant
4 A. O Super
sublimation
curve
Ice and super
cold water
= 1 – 2 + 2
Curve s

प्रावस्थ आलेख Phase rule digram –
P – T Diagram
S.No. Point Name Phases Temperatu
re
Pressure D.F.
1 O Triple
Point
Ice, liquid
Vapours
.0075 0 C 4.58 mm F = 1 -
3 + 2 =
0
Invaria
nt
Point

प्रावस्था आलेख Phase rule digram –
P – T Diagram
S.No
.
Name Phases D.F.( F = C
– P +2)
D.F.
1 Out side
AOC
Ice F = 1 -1 +2 2, Bivariant
2 BELOW
AOB
Vapours F = 1 -1 +2 2, Bivariant
3 Above
COB
Liquid, water F = 1 -1 +2 2, Bivariant
4 AOA’ Super cooled
liquid, water
F = 1 -1 +2 2, Bivariant
Areas

Carbon dioxide System
No. of Phases
Solid ice
Liquid
Gas

Carbon dioxide System
1. त्रिक त्र िंदु पर कौन सी प्रावस्था होगी ?
2. प्रावस्था आलेख में वकतने वक्र है एवां उनक
े F का मान हरगा ------
3. वत्क वबांदु वकस ताप और दाप पर है एवां F का मान ------?

One component एक घिक का तांत्
Sulphur system सल्फर तांत्
Phases - प्रवास्थाये
Sm Sulphur monoclinic
SR Sulphur Rhombic
Sl Sulphur Liquid
SV Sulphur Vapour
Example Polymorphysim
S – S Tronsformation
Meaning – in solid phase two types
of crystalline structure

Components
All the four phases can be represented by the only
chemical individual “ SULPHUR” itself.
Hence an one component system -
Phase Rule
F = C – P + 2

Phase Transfermation
368.5 K
SR Sm
388 K 393 K
Sl
717.7 K
Sv

0.03mm
0.04mm
1288 atm
.0006mm
A
B
C
D
E
M.P. curve of SR
F
SR
G
SM
SL
368.5OK
388OK
393OK
428OK
S Vapor
T
P
P-T Diagram
Sulphur System

0.03mm
0.04mm
1288 atm
Transition curve
Vapor pressure curve of SR
.0006mm
A
B
C
D
E
Sublimation curve of SM
Vapor pressure curve of SL
M.P. curve of SM
M.P. curve of SR
F
SR
G
SM
SL
368.5OK
388OK
393OK
428OK
S Vapor
T
P
P-T Diagram
Sulphur System

Sulpher system सल्फर तांत्
Curves / वक्र
S. No Curve Name Phases Degree of
Freedom ( F)
1 A B vapour presure curve of SR
SR का वाष्पदाब वक्र
SR and SV 1 univariant
एक िर
2 BC Sublimation curve of SM
उर्ध्तपातन वक्र
SM and SV 1 univariant
एक िर
3 CD vapour pracure curve of SL
वाष्प दाब वक्र
SL and SV 1 univariant
एक िर
4 BE transition curve of SR
रूपाांतरण वक्र
SR and SM 1 univariant
एक िर
5 CE Melting point curve of SM
SM का गलनाांक वक्र
SM and SL 1 univariant
एक िर
6 EF Melting point curve of SR
SR का गलनाांक वक्र
SR and SL Melting point
curve of SM
SM का गलनाांक
वक्र

Sulpher system सल्फर तांत्
S. No Point
s
Name Phases Tempratu
re
Pressure D.F.( F)
1 B Triple Point
वत्क वबांदु
SR- SM-SV 368.5 K .0006
mm
0
invariant
अिर
2 C TriplePoint
वत्क वबांदु
SM- SL –SV 393 K 0.04 mm 0
invariant
अिर
3 E Triple Point
वत्क वबांदु
SR-SM –SL 428 K 1288
mm
0
invariant
अिर
4 G Meta StableTriple
Point
वत्क वबांदु
SM – SL –SV 388 K 0.03 mm 0
invariant
अिर
Triple Points / वत्क वबांदु

Sulpher system सल्फर तिंि
S. No Area क्षेत् phase F = C – P
+2
D.F ( F)
1 Below
ABCD
SV 1-1+2 = 2
2 Above ABEF SR 1-1+2 =2
3 Between
DCEF
SL 1-1+2 =2
4 Inside BCE SM 1-1+2 =2
Area क्षेत्

Expected Questions
1. पाररभावषत कीविए –a . प्रावस्था b घिक c. स्वतांत्ता की करवि
2. एक घिक का तांत् िल अथवा सल्फर का प्रावस्था
आलेख बनाएां .
3. वगब्स’ क
े प्रावस्था वनयम की उत्पवि कीविये .
4. वकसी प्रावस्था आलेख में F का वनिातरण क
ै से
वकया िाता है ?
5. वक्र, वबांदु एवां क्षेत् की स्वतांत्ता की करवि क्या
हरती है ?

Dr. Anjali Acharya
Email-
anjaliacharya2007@rediffmail.com