In general the change of *Gibbs* free energy for a phase equilibrium
(*Δ**G*(*P, T)*)
at pressure *P* and temperature *T* is given by

where νi is
the stoichiometric coefficient of the *i ^{ th}* phase component,

Further consideration requires the definition of standard states and
reference conditions. Solids are considered to be in standard state if they
are of pure end member composition (pure phase component) and reference
conditions are 0.1 MPa and 298 K. Fluids are treated as pure hypothetical
ideal gases at a reference pressure of 0.1 MPa (1 bar) and temperature *T*.* Δ**G**(P, T)*
is then given by

where* Δ* designates an equivalent
relationship for each parameter or function except for

where *f°j**(P, T)*
is the fugacity of the *j*^{ th}
pure fluid phase component, ν is total
number of fluid phase components, and *a**i* are
the activities of the *i*^{ th}
phase component.

In the case that the heat capacitiy of a phase is only available in intervals, the following relationship is used:

or in the case of a phase transition the following relationship is applied:

where

The molar volumes of solids at elevated pressure
and temperature are evaluated with the compressibility coefficient *β* and the
thermal expansion coefficient *α*.

The combination and integration with the assumption that* α* and* β* are not a function of pressure
and temperature leads to:

Although* α* and* β* are treated as constants, this relationship mimics the real volume change
as a function of pressure and temperature. With this equation the second
integral of the main equation is calculated
for *n* solid phase components involved in the phase equilibrium:

The last three terms of the main equation
can be combined to form the reduced equilibrium constant ln *K**red*

which leads to:

Evaluation of the right hand side leads to the following conditions:

reactants stable equilibrium products stable

In evaluating the ln *K**red* term for each available
experimental result, the heat capacities for all components,
the molar volumes and the coefficients of the
thermal expansion and compressibility of the
solids are required. If any fluids are involved, their functions
of state are also required. If mixed phases are considered, activity models must be taken into account. Lastly,
some phases show phase transitions as a function of *P* and *T*, while others
reveal a continuous change in the degree of order,
all of which must be considered thermodynamically.

last modified: 8.8.1997 by Matthias Gottschalk