The Gibbs phase rule relates the number of degrees of freedom (F) of a system to the number of components (C) and phases (P) present, given by the equation F = C - P + 2. A phase is a homogeneous, physically distinct portion of a heterogeneous system separated by well-defined boundaries. The number of components is the number of independently varying chemical constituents that can describe the composition of all phases. The degrees of freedom represent the minimum number of variables needed to specify the system.

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

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

16. Water system