PHASE RULE

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Introduction:

In practice there can be observed many different types of systems. For example consider ice in a glass of water and the same ice in water closed in a bottle. Now, the system tries to gain equilibrium by changes in the variables like temperature, pressure and so on.
In the first case, the melting of ice depends on the temperature of the water, the water in turn evaporates into vapour, however, the glass being open to atmosphere allows for the vapours to escape and hence there is a constant change in the volume of the water and the system as a whole. Therefore, it can never achieve an equilibrium state.
In the second case, since the bottle is a closed environment, it does not allow the vapours to escape, the melting of ice depends on the temperature of water, and since the volume remains constant, pressure may also come into picture.
Thus, in order to define a particular system, to define the state of each phase in the system, we have to know about some fixed number of variables. The phase rule was formulated by J. Williard Gibbs to do this!

The phase rule:

The phase rule is a relationship for determining the least number of intensive variables (independent variables that do not depend on the volume or size of the phase) that can be changed without changing the equilibrium state of the system
or
The least number of intensive variables required to define the state of the system.

F = C-P+2

Where 'F' is called number of degrees of freedom of the system
'C' is the number of components in the system
'P' is the number of phases in the system

Definitions:
1. Phase: A phase is defined as a homogenous, physically distinct portion of a system that is separated from other portions of the system by bounding surfaces. E.g.: Water and its vapour is a two phase system.
2. Components: A component is the smallest number of constituents by which the composition of each phase can be expressed in the form of a chemical equation or chemical formula.
3. Degrees of freedom: The number of degrees of freedom is the least number of intensive variables that must be known or fixed to define a system completely.

One- Component System (2):

Consider
the following three systems
(3):

System

Number
of phases

Degrees
of freedom

Explanation

Gas, solid or liquid

1

F= C-P+2

=
1-1+2 = 2

We must fix two variables to define the
system. E.g.: pressure (p2) and temperature (t2); represented by D

Gas-liquid, liquid-solid, or gas-solid

2

F= C-P+2

=
2-1+2 = 1

We must fix one variable to define the
system. E.g.: pressure (p1) or temperature (t2); represented by E

Gas-solid-liquid

3

F= C-P+2

=
3-1+2 = 0

System can lie on the point of
intersection of the lines bounding the three phases; represented by O

Applications:

* The phase rule is used to describe systems of one component as well as multi-component systems.
* For one component system of water, the phase rule is applied and the phase diagram gives a lot of information like the triple point, sublimation temperature, boiling point and freezing point. The phase diagram of solvents can be used to determine the parameters useful distillation procedures.
* For two component liquid containing systems like phenol-water, which are partially miscible, the equilibrium temperature at which these two phases are completely miscible called 'critical solution temperature' can be determined. Also, the phase diagram gives the exact data regarding the various concentrations at which the two phases are miscible and at what temperatures.
* For two component systems like salol-thymol system, which shows four regions in the phase diagram, many observations can be made, the melting point of pure salol and thymol can be noted. The most important use of such a phase diagram is the determination of the 'eutectic point' which is the "point at which the liquid and solid phases have the same composition". It is of critical importance, because the eutectic point is at a temperature lower than the melting points of either of the individual components. Thus, a eutectic mixture can be melted at a temperature lower than the temperature required to melt one of the components.
* The tertiary and ternary phase diagrams provide comprehensive and accurate data of the various composite component systems which are applied in many areas of pharmacy like the formulation of micro-capsules, polymer coating methods and many other processes.

Reference:
1) Essentials of Physical chemistry; B.S. Bahl, G.D. Tuli, Arun bahl; S. Chand and company; pg: 558-562. [access date: 12th September, 2010]
2) http://serc.carleton.edu/research_education/equilibria/phaserule.html [Accessed on 12th september 2010]
3) Physical pharmacy and pharmaceutical sciences,5th edition, Patrick J. Sinko; Lippincott Williams and Wilkins, pgs:47-49 [access date: 12th September, 2010]

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About the Author

Prof. J. Vijaya Ratna's picture

Dr. Vijaya Ratna Jayanthi serving Andhra University College of Pharmaceutical Sciences as Chairman, Pharmaceutical Technology Department.

Dr. J. Vijaya Ratna did her B.Pharm (1977), M.Pharm (1979), PGDAS (1981) and Ph.D (1998) at Andhra University Campus and won "M.L. Khorana Gold Medal" for standing University FIRST in graduation.

Comments

A.R.Khan's picture

Thanks for sharing great knowledge in simple way.. If i learn this rule ...where can i apply in "real" world ? I mean this knowledge is useful when i formulate suspensions or syrups or some thing else ? I will appreciate if you can explain real life applications...
Prof. J. Vijaya Ratna's picture

Dear Khan Sir Phase rule finds uses in a number of situations such as preparation of suspension and emulsions. But it is especially applicable in finding the right concentrations of the different ingredients in the preparation of microcapsules and self emulsifying drug delivery systems. vijaya Ratna

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