The Phase Rule

1
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.
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2
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
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Note If pressure is held constant then the
phase rule becomes F C - P 1
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