Page 173 - Chemical equilibria Volume 4

Determination of the Values Associated with Reactions – Equilibrium Calculations 149
4.10.4. Method of minimization of the Gibbs energy function
Modern numerical methods are built upon the fact that, at equilibrium,
the Gibbs energy of the system should be zero. In fact, it is extremely
difficult, a priori, to obtain a value of zero, so calculation software tends to
use the minimization of the Gibbs energy function.

Consider a system containing n chemical elements (in the sense of the
periodic classification) divided between N components. The Gibbs energy of
the system will be given by the weighted sum of the molar fractions of the
Gibbs energies of each of the N components, as follows:

N
G = ∑ n G j [4.53]
j
j= 1
The quantities n j are such that:

N
∑ n = n t [4.54]
j
j= 1
For each component, its molar Gibbs energy is such that:

– if it belongs to a gaseous phase, it is given by:

f
*
G = g + Rln j [4.55]
T
j
j
P 0
– if it belongs to a liquid or solid solution, we write:
G = g + Rln x j [4.56]
γ
0
T
j
j
j
– if it is pure of phase, we have:
G = g 0 j [4.57]
j
Note that, of the N components of the system, the same chemical species
present in several phases is counted as one component in each of those
phases.