Page 186 - Chemical equilibria Volume 4

162 Chemical Equilibria
By applying relation [A1.26] to the Gibbs energy, then immediately for
the partial molar excess Gibbs energy of the component:
⎛ N ∂ lnγ (I) ⎞
G = RT ⎜ ⎜ lnγ i (I) + ∑ x j j ⎟ ⎟ [A1.31]
xs
i
⎝ i= 1 n ∂ i ⎠
However, the Gibbs–Duhem relation enables us to write:

N
∑ x j ∂ lnγ (I) = 0 [A1.32]
j
i= 1 n ∂ i

Thus, ultimately, the partial molar excess Gibbs energy of the component
is:

G = Rlnγ i (I) [A1.33]
T
xs
i
Relation [A1.33] forms the link between the description of the solutions
by the Lewis activity coefficients method, and that by the excess Gibbs
energy. The two methods, therefore, are equivalent.