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Transcript and Presenter's Notes

The Phase Rule

The Degrees of Freedom is the number of intensive

variables such as temperature, pressure, and/or

concentration of the components of a phase which

must be arbitrarily fixed in order that the

condition of the system may be perfectly defined.

Algebraic Analogy It is commonly known that a

system of two equations can be used to solve a

maximum of two unknowns. However, if the system

contains three unknowns yet only two equations,

one of these independent variables must be

defined in order to solve for the other two

variables. In this case the system has one

Degree of Freedom. In other words, the Degrees

of Freedom equals the number of variables minus

the number of equations.

Click to continue.

The Phase Rule - cont.

F variables - equations

Variables The variables involved in phase

diagrams are temperature, pressure, and the mole

fraction of each component within each phase.

Since the mole fractions of the components of a

single phase add to one, it is possible to

determine the mole fraction of one component if

the rest are known. Therefore, each phase has a

number of independent variables equal to the

number of components minus one. As a result the

entire system has a number of independent

variables equal to the number of phases x (number

of components -1) temperature pressure or

variables P(C-1) 2.

Equations The equations used are a direct

result of Gibbs free energy relationship. If

three phases are in equilibrium the total change

in free energy of each component of the phases is

zero. For example a binary system of components

A and B, consider a point at which the three

phases ?, ?, ? are in equilibrium together. The

resulting equations for component A are dGA ?

dGA ? and dGA ? dGA ? . Notice that the number

of equations for component A is one less than the

number of phases. Therefore the total number

equations equals the number of components x (the

number of phases - 1) or equations C(P-1).

F variables - equations F P(C-1) 2 -

C(P-1) F PC - P 2 - PC C F C - P 2

MENU

Note If pressure is held constant then the

phase rule becomes F C - P 1

Click to repeat.

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