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Derivation of The Phase Rule

The document describes the derivation of the phase rule. It states that for a heterogeneous system with C components in P phases at equilibrium, the degrees of freedom are calculated as F = C - P + 2, where F is the number of variables like temperature and pressure that can be independently varied. This is derived by determining that there are P(C-1) concentration variables and P - 1 equations per component, for a total of C(P - 1) equations. The number of variables is then the total variables (P(C-1) + 2) minus the number of equations (C(P - 1)).

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Dipto Kumer Sarker
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196 views3 pages

Derivation of The Phase Rule

The document describes the derivation of the phase rule. It states that for a heterogeneous system with C components in P phases at equilibrium, the degrees of freedom are calculated as F = C - P + 2, where F is the number of variables like temperature and pressure that can be independently varied. This is derived by determining that there are P(C-1) concentration variables and P - 1 equations per component, for a total of C(P - 1) equations. The number of variables is then the total variables (P(C-1) + 2) minus the number of equations (C(P - 1)).

Uploaded by

Dipto Kumer Sarker
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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DERIVATION OF THE PHASE RULE

 A heterogeneous system in equilibrium of C components in which P phases are present.


 We have to determine the degrees of freedom of this system.
 Since the state of the system will depend upon the temperature and the pressure, these
two variables are always there.
 The concentration variables depend upon the number of phases.
 Independent concentration variable for one phase with respect to the C components =C-
1 (Since Conc. Of the last component is independent)
 Independent concentration variable for P phase with respect to the C components = P(C-
1)
 Total number of variables = P(C-1) + 2
 On thermodynamic consideration when a system is in equilibrium, the partial molal free
energy of each constituent of a phase is equal to the partial molal free energy of the same
constituent in every other phase.
 Since the partial molal free energy of the constituents of a phase is a function of the
temperature, pressure and (C – 1) concentration variables,
 it follows that if there is one component in two phases, it is possible to write one equation
amongst the variables and if there is one component in three phases, this fact may be
written with the help of two equations.
 In general, therefore, when P phases are present, (P – 1) equations are available for each
component and for C components, the total number of equations or variables are
C (P -1).

F = No. of variables – Number of equations

= [P (C – 1) + 2] – [C (P – 1)]

= PC – P + 2 – PC + C
=C–P+2
F=C–P+2
POLYMORPHISM

 The occurrence of the same substance in more than one crystalline forms is

known a Polymorphism.

 In the case of elements the term allotropy is often used.

 The individual crystalline forms of an element are referred to as polymorphs or

allotropes.

Enantiotropy

 one polymorphic form (or allotrope) can change into another at a definite

temperature

 When the two forms have a common vapour pressure.

 This temperature is known as the transition temperature

 One form is stable above this temperature and the other form below it.

 When the change of one form to the other at the transition temperature is

reversible, the phenomenon is called enantiotropy and the polymorphic forms

enantiotropes.

 α-Sulphur to β-Sulphur

Monotropy

 It occurs when one form is stable and the other metastable

 The metastable changes to the stable form at all temperatures and the change

is not reversible.

 There is no transition temperature as the vapour pressures are never equal.

 White phosphorus ⎯⎯→ Red phosphorus


Dynamic allotropy

 Resembles enantiotropy in that it is reversible but there is no fixed transition

point.

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