1. Gibbs Phase Rule
• The number of degrees of freedom or variance of a
system, F, is related to the number of components(C)
and number of phases(P).
•F = C - P + 2
2.
3. Phase(P)
• A phase is a Homogenous, physically distinct &
mechanically separable portion of the heterogeneous system.
which is separated from other parts of the system by well defined
boundary surfaces.
• IT IS DENOTED BY `P’.
• Each phase is separated by a phase boundary known as
Interface.
4. • For e.g. water exists in three forms:
• Ice water water vapour
(s) (l) (g)
P =?
5. -
• Solid
• Various allotropes [e.g. diamond; graphite] or compositions
like NaCl, NaCl.2H2O
• Alloys
• Liquid
• Miscible liquids (solutions) are one phase
• Immiscible liquids are multiple phases (P>1)
• Gas
• Systems consisting of gases can have only one phase
6. -
• A mixture of Rhombic sulphur and monoclinic sulphur
• P =
CaCO3 (s) CaO (s) + CO2 (g)
• P =
Fe (s) + H2O (g) FeO (s) + H2 (g)
• P =
An emulsion of oil in water at 2 atm and 70 degree c.
• P =
• Water system at 4.578 mm of Hg and at 0.0098 degree c.
7. • Component (C)
• Independently chemical constituents of a system by means
of which the composition of all the phases in the system
can be expressed.
• Examples: water system
• Ice water water vapour
(s) (l) (g)
P =? C=?
8. DEGREE OF FREEDOM(F)
• It is defined as the minimum no of independent variable
factors such as temp., pressure and conc. which must be
specified in order to define the system completely.
• When
• F =0 non varient system
• F =1 uni varient system
• F=2 bi varient system
• F=3 tri varient system
9. -
• For pure gases;
• PV =nRT
• If the value of any two variables (P,V,T) is fixed, the third
variable will have fixed by the above condition itself. Thus the
system is Bivariant system.
10. Phase Rule
• It was given by J.W.GIBBS.
• Derivation of Gibbs phase rule:
• Consider a heterogeneous system of p phases at eqm containing
in all c components,
• phases are (Pa, Pb, Pc, …………Pp )
• Components are (C1, C2 ,C3 , ……….. CC
11. • Degree of Freedom or Variance =
• [total no of variable that need to be specified]- [tot no of
restricting condition that are imposed by interdependent
variables]
• (a) To find out the total no of Variables :
(I) Temperature: same for all phases =1 variable
(ii) pressure: same for all phases =1 variable
(iii) concentration: conc. term for 1 phase=C
conc. term for P phase=PC
Total no of variable= PC+2
12. • (b) To find out total no of relationship between variables:
• (i) Thermodynamic criteria:
• At equilibrium the chemical potential of any component in
each phase must be equal,
• for component 1 μ1(a)= μ1(b)= μ1c=…. μ1(p)
• for component 2 μ2(a)= μ2(b)= μ2c=…. μ2(p)
• for component 3 μ3(a)= μ3(b)= μ3c=…. μ3(p)
• For 1 component there are P-1 such equations
• Since there are C components, equilibrium requires that
there are C(P-1) equations linking the chemical potentials
in all the phases of all the components.
13. -
• F = total required variables - total restraining conditions
• F = P(C-1) + 2 - C(P-1) = PC - P + 2 -CP + C = C- P + 2
14. For systems, which are in equilibrium
C = S – R
• 2KClO3 (s) ↔ 2 KCl (s) + 3 O2 (g)
C =
• KCl-NaCl-H2O C =
• KCl - NaBr - H2O C =
• NH3 at 42 °C
• MgCO3 (s) ↔ MgO (s) + CO2 (g) in closed vessel
15. • KCl-NaCl-H2O system consist of six species:
KCl, NaCl, H2O, K+, Na+ and Cl-
S = 6
The no of independent equilibrium reactions are Two
NaCl ↔ Na+ + Cl-
KCl ↔ K+ + Cl-
Thus R = 2
When ions are present in the system, then the condition of
electroneutrality , the modified equation would be:
C = S – (R+1) = 6 – (2+1) = 3
• KCl - NaBr - H2O 9 species S = 9 R=4 C = 4
