Aspen Physical Property System - Physical Property Models

zi = Charge of ion i
Subscripts c, c', and a, a' denote cations and anions of the solution. B, C, �,
and � are interaction parameters. f(I) is an electrostatic term as a function of
ionic strength. The cation-anion parameters B and C are characteristic for an
aqueous single-electrolyte system. These parameters can be determined by
the properties of pure (apparent) electrolytes. B is expressed as a function of
� (0) and � (1) , or of � (0) , � (2) , and � (3) (see equations 11 through 15).
The parameters � and � are for the difference of interaction of unlike ions of
the same sign from the mean of like ions. These parameters can be measured
from common-ion mixtures. Examples are NaCl + KCl + H2O or NaCl + NaNO3
+ H2O (sic, Pitzer, 1989). These terms are discussed in detail later in this
section.
Fürst and Renon (1982) propose the following expression as the Pitzer
equation for the excess Gibbs energy:
The difference between equations 3 and 4 is that Pitzer orders cation before
anions. Fürst and Renon do not. All summations are taken over all ions i and j
(both cations and anions). This involves making the parameter matrices Bij,
Cij, �ij, and �ijk symmetric, as follows:
Second-order parameters are written Bij if i and j are ions of different sign. Bij
= 0 if the sign of zi = sign of zj, and Bii = 0. Since cations are not ordered
before anions, Bij = Bji. This eliminates the 2 in the second term in brackets in
Pitzer's original expression (equation 3). Second-order parameters are written
�ij if i and j are ions of the same sign. Thus �ij = 0 if the sign of zi is different
from the sign of zj, and �ii = 0 with �ij = �ji.
Third-order parameters are written Cij if i and j are ions with different signs.
Cij = 0 if the sign of zi = sign of zj, and Cii = 0 with Cij = Cji. The factor of 2 in
the fifth bracketed term in Pitzer's original expression (equation 3) becomes
1/2 in equation 4. The matrix C is symmetric and is extended to all
ions to make the equation symmetric.
2 Thermodynamic Property Models 139
(3)
(4)