Page 185 - Chemical equilibria Volume 4

As this property is extensive, it has corresponding partial molar values,
relating to each component of the solution, defined by: Appendix 1 161
⎛ J ⎞ ∂ xs
J xs = ⎜ ⎟ [A1.26]
⎝ n ∂ i ⎠ PT n
,, j i≠

We can divide this definition for the Gibbs energy.

A1.3.2. Excess Gibbs energy

Consider a solution. The excess Gibbs energy, according to the
definition, will be:

−
G = G G * [A1.27]
xs
However, the molar Gibbs energy of the solution can be written:

N N
m ∑
G = x μ i ∑ = ⎣ x ⎡ i ( g + Rln x + R lnγ (I) ) ⎤ ⎦ [A1.28]
0
T
T
i
i
i
i
i= 1 i= 1
Similarly, for a perfect solution, this molar Gibbs energy would be:
m ∑
G = N ⎣ x ⎡ i ( g + Rln x ⎤ T i ) ⎦ [A1.29]
0
*
i
i= 1
From this, we deduce the molar excess Gibbs energy of the solution at
hand:
N
G = RT ∑ x i lnγ i (I) [A1.30]
xs
m
i= 1
If the excess Gibbs energy is known, the solution is completely
characterized: if we add the term of the Gibbs energy of the perfect solution,
we obtain the Gibbs energy of the solution, which is the characteristic
function with our choice of variables P, T and composition.