Page 174 - Chemical equilibria Volume 4

150 Chemical Equilibria
In the case of a very abundant solvent which does not participate as a
component in an equilibrium, and therefore whose Gibbs energy is
practically constant, it is not included in the list of components. The
consequence of this is that the sum of the molar fractions in that solvent shall
not be equal to 1, but instead equal to the sum of the molar fractions of the
solutes. This method avoids simultaneously using very high values of molar
fractions (very close to 1) and very low values (very close to 0).

Thus, the problem at hand is finally to find the series of values of
variables x 1, x 2, … x N which minimize the function (, ,...Gx x 2 x N ) subject to
1
certain constraints. This is a classic mathematical problem which can be
solved by a variety of algorithms – such as the Lagrange multiplier method
with several variables.

The software tools available on the market usually come with their own
databanks, and hence are often fairly specialized in a particular domain, such
as petrochemistry, interphase equilibria in materials, thermodynamics of
plasma projection, etc. The use of such software has become extremely
commonplace; developers have invested a huge amount of effort in
simplifying and clarifying in the ergonomics of the man–machine interfaces,
in particular.