1. Phase Equilibrium UNIT-III Topics of Chapter:
Statement and meaning of Phase, component and degree
of freedom.
Derivation of Gibbs phase rule.
Phase equilibrium of one component systems-water,
cabon dioxide and sulphur System.
Phase equilibrium of two component systems-Bi-Cd
system, Pb-Ag system, desilverisation of lead.
Solid Solutions- compound formation with congruent
melting point(Mg-Zn) and incongruent melting point (NaCl-
H2O) system.

2. Phase Equilibrium For a heterogeneous system in equilibrium
F = C- P +2
F = number of degree of freedom
C = number of components
and P = number of phases
Phase : Any homogenous, physically distinct and
mechanical separable portion of a system which is separated
from other such part of a system by definite boundary
surface.

3. Phase Equilibrium A system may contain one or more than one phase
i) A system containing only liquid water is a one component
system or P =1
ii) a system containing liquid water and water vopour is a two
component system or P =2
iii) A system containing ice, liquid water and water vapour is
a three component system or P =3
Component: The minimum number of independent
phase can be expressed either directly or in form of chemical
equation, negative or zero sign being permitted.

4. Phase Equilibrium Examples: i) Water system consists of equilibrium
Ice Water Vopour
(solid) (Liquid) Gaseous)
It is a one component system because the composition of the
three phases can be expressed as water.
ii) Sulphur System consists of four phases- monoclinic(s),
Rhombic(s), liquid(l) and vapours(g) is also one component
system
iii) Decomposition of CaCO3 by heat can be expressed
CaCO3(s) CaO (s) + CO2(g)

5. Phase Equilibrium There are three different constituents forming three
different phases. But the composition of each phase can be
expressed in terms of two of constituents.
Degree of Freedom:
the smallest number of independently
variables such as pressure , temperature and concentration
that can be varied without disturbing the number of phases
present in equilibrium
For examples:
i) Ice ,water and vapour system: This system has no degree
of freedom or in other word it is invariant i.e. F=o

6. Phase Equilibrium
ii) Water – Vapour system: This system has only one degree
of freedom or in other words, it is invariant i.e. F=1.
ii) For a gas : This system has two degree of freedom or it is
bi variant.
Equilibrium:
A system is said to be in equilibrium if the
properties like temperature, composition etc of various
phases do not under go any change with time. These
equilibrium may be of two types
True Equilibrium: Which is obtained from either direction
For example: the equilibrium between ice and water at I atm.

7. Phase Equilibrium pressure and Oo C is a true equilibrium
Metastable Equilibrium : a state of system which can be
obtained only from one direction and too very careful change
of conditions. For e.g. Water at -20 C.
Derivation of Gibbs Phase Rule:
The degree of freedom , F of a system
is given by the difference of total number of variables
required to specify the system and number of independent
equations available to define the system at equilibrium. Thus
Degree of freedom = Total number of variables - Number of
variables defined by the system because of its being in
equilibrium ……………..i

8. Phase Equilibrium
A simple phase containing C components can be completely
by defined by C-1 concentration terms.
For P phase having C components then the number of
concentration required will be P(C-1). Besides
concentration variables, there are two more variables i.e.
temperature and pressure of the system
Thus total number of variables = P(C-1) +2 …………….ii
For a system of three phases , two equation are required to
define each component.

9. Phase Equilibrium F=C-P+2
For a system having P phase, P-1 equations are required for
each component. If there are C component present in P
phases, then
The number of independent equations + C (P-1) ………iii
Putting equation (ii) and (iii) in equation (i), we get
F= [P(C-1) +2] – [C(P-1)]
F=C-P+2

10. Phase Equilibrium Phase Diagrams :
The diagram representing conditions of
temperature, pressure and composition at which one or more
phase exit together.
Application of Phase Rule to One component system:
As C=1 and minimum P=1 therefore maximum F=C-P+2=2
The two degree of freedom chosen on the plot are
temperature versus pressure
A. Phase Diagram of Water System:
Phase diagram of water as shown in fig.

11. Phase Equilibrium

12. Phase Equilibrium Some important features of Water System:
(i) Possible phases : Ice (s), Water(l), Vapour (g)
(ii) Curves: three stable curves (a) OA ( Vapour pressure
curve, Water Vapour)
(b) OB ( Sublimation Curve, Ice Vapour)
(c) OC ( Melting point curve, Ice Water )
iii) One metastable curve OA’ (Vapour pressure curve of
super cooled water)
(iv) Areas : Three areas representing ice, water and vapour.

13. Phase Equilibrium (v) Triple point (O):
Where all the three phases are in
equilibrium(0.0098oC and 4.58 mm pressure).
The melting point curve OC slopes towards pressure axis
has negative slope ,showing that the melting point of ice
decreases with increase of pressure

14. B. Phase Diagram Of Carbon dioxide System:
Phase Equilibrium
B. Phase Diagram Of Carbon dioxide System:

15. Phase Equilibrium Phase diagram of Carbon dioxide:
Some Important Features :
(i) Possible phases: Solid CO2,liquid CO2 and gases CO2
(ii) Curves: Three stable curves OA(vaporization
curve),OB(sublimation curve ) and OC (melting curve).
(iii) Areas: Three areas representing solid CO2,liquid CO2
and gases CO2 respectively.
(iv)Triple point(O): Where all the three phases exist
together(-56.4o C and 5 atm pressure)

16. C. Phase Diagram Of Sulphur System :
Phase Equilibrium
C. Phase Diagram Of Sulphur System :

17. Phase Equilibrium Sulphur system (one component system):
Some Important Features:
(i)Possible phases: Rhombic Sulphur (SR),mono clinic
Sulphur(SR), Sulphur vapour (SV) and Sulphur liquid(SL).
(ii) Maximum phases: If P=4, then F=C-P+2=1-4+2=-1
Which is meaning less. Hence all the four phases cannot exist.
(iii) Areas : Four areas containing one phase each
(iv) Curves: There are six stable curves.
a) Sublimation curve of SR
b) Sublimation curve of SM

18. Phase Equilibrium c) Vapour pressure curve of SL
d) Transition curve of SR
e) Melting curve of SM
f) Melting curve of SR
Meta stable curves: There are four metastable curves
a) Sublimation curve of SR
b) Sublimation curve of SM
d) Melting curve of SR

19. Phase Equilibrium Triple points:
There are three stable triple points SR-SM-SV,
SM-SL-SV, SR-SM-SL and one metastable triple point SR-SL-SV.
Application of phase rule to two component system:
As C =2,minimum P=1 and hence minimum F=C-P+2=3
Thus there are three variables (pressure, temperature and
composition) should be plotted .But for convenience, two
dimension diagram are plotted by keeping the third variable
constant. Hence we have p-t, c-p or t-c diagrams. Generally
pressure kept constant at atmospheric pressure and we have
t-c diagram

20. Phase Equilibrium Reduced Phase Rule:
If pressure is kept constant then vapour phase neglected
in system involving solids and liquid. The degree of freedom
is reduced by one and hence the phase rule equation
becomes C-P+1
Types of two component systems:
a) System in which components do not react but simply mix
for example, Bi-Cd, Pb-Ag and KI-H2O system.
b) System in which components react to form compounds
e.g, Mg-Zn system forming MgZn2, Na2SO4- H2O,
FeCl3-H2O and NaCl- H2O system forming hydrate.

21. Phase Equilibrium Two component system: A) Bismuth Cadmium system:
These are further of two types:
a)Those which form compound with congruent melting
point e.g, Mg-Zn and FeCl3-H2O systems.
b)Those which form compound with incongruent melting
point e.g,Na2SO4-H2O and NaCl- H2O systems.
Two component system:
A) Bismuth Cadmium system:

22. Phase Equilibrium

23. Phase Equilibrium Some Important Features of Bi-Cd System:
i)Possible Phases: Bi(s),Cd(s) ,their solution in each other, vapour neglected.
ii) Melting points: Bi=271oC and Cd=321oC.
iii) Curves: Freezing point curve of Bi to which increasing amount of Cd are added and freezing point curve of Cd to which Bi is being added .
iv)Eutectic point: It is a point where two curves intersect. It corresponds to a temperature of 144oC and a composition of
40% Cd +60% Bi.

24. Phase Equilibrium

25. Phase Equilibrium Some special features of Pb-Ag system:
i)Possible phases: Pb(s),Ag(s) their solution in each other, vapour neglected.
ii)Melting points: Ag=961oC and Pb=327oC.
iii)Curves: Freezing point curve of Ag to which increasing amount of Pb are added and freezing point curve of Pb to which Ag is being added .
iv)Eutectic point: It is a point where two curves intersect. It corresponds to a temperature of 303 oC and a composition of 97.4% Pb +2.6% Ag

26. Phase Equilibrium C. Phase Diagram of Mg –Zn system:
Mg and Zn reacts to form stable compound MgZn2 with congruent melting point.
i)Possible phases: Mg(s),Zn(s),MgZn2 (s),liquid/melt and vapour .
ii)Melting points: Mg=650oC and Zn=420oC.
iii)Curves and point: Freezing point curve of Zn to which increasing amount of Mg are added .The lowest temperature reached is 380oC(eutectic point) below which Mg Zn2 is formed.

27. Phase Equilibrium

28. Phase Equilibrium
iv)Freezing point curve of solid MgZn2 to which increasing amount of Mg are added. The freezing point keeps on increasing till is maximum at 590oC which represents congruent melting point. On further adding MgZn2 ,its freezing point decreases and is lowest at 347oC which is the another eutectic point. v)Freezing point curve of Mg to which increasing amount of Zn are added. The freezing point decreases still the lowest freezing point of 347oC is obtained.

29. Phase Equilibrium
D. Phase Diagram of NaCl-H2O system:
Sodium chloride and water react to form stable compound NaCl.2H2O with incongruent melting point(o.15oC)
i)Possible phases: NaCl (s), NaCl.2H2O(s),ice solid, solution and water vapour.
ii)Curves and point: a)Freezing point curve of H2O to which increasing amount of NaCl are added .The lowest temperature reached is -21.2oC(23% NaCl). At this point NaCl.2H2O starts separating . Hence it is eutectic point.

30. Phase Equilibrium
By B.K Choudhary

31. Phase Equilibrium
b) Solubility curve of NaCl.2H2O (s): It rises with increase of temperature till at 0.15oC .it starts decomposing to give anhydrous NaCl. c) Solubility curve of anhydrous NaCl : Which increases with increase of temperature.