Page 179 - Chemical equilibria Volume 4

Appendix 1 155
A1.2.1. Activity coefficients of reference states
0
Expression [A1.7], in fact, introduces two functions: μ , known as the
i
reference chemical potential, and the activity coefficientγ . Therefore, this
i
introduction requires another given. We choose the definition of the
reference state by way of a convention.
In practice, we have seen the introduction of several conventions; three
are frequently used, and we refer to these as conventions (I), (II) and (III).
Each of these have a corresponding reference chemical potential. We denote
those respectively as μ i 0(I) , μ i 0(II) and μ i 0(III) . Each convention also has a
corresponding activity coefficient, written as γ i (I) , γ i (II) and γ i (III) , and an
activity, written as a i (I) , a i (II) and a i (III) . Whenever an expression is valid
irrespective of the reference used, we omit the distinguishing sign (I), (II) or
(III).

It goes without saying that the value of the chemical potential of a
component of the solution does not depend on the reference chosen, but
instead, as the chemical potential is the partial molar Gibbs energy, the
Gibbs energy of the solution would depend on that reference, which would
be absurd.

A1.2.2. Convention (I)

Convention (I) takes as a reference the components in the pure state in the
same state of aggregation as the solution (this is known as the pure-
substance reference). In these conditions, the chemical potential of the
reference state is the molar Gibbs energy of the pure component and the
chemical potential is then written as:

0
μ i = g + Rlnγ i (I) x i [A1.9]
T
i
This referenceis primarily used when all the components of a solution
play the same role, and in particular have comparable molar fractions. For
example, this convention is chosen when a given covers a broad spectrum of
compositions, possibly spanning from one pure substance to another.