Thermodynamic consistency and reference scale conversion in multisolvent electrolyte solutions

doi:10.1016/S0167-7322(00)00117-3

Journal of Molecular Liquids

Volume 87, Issues 2–3, September 2000, Pages 129-147

https://doi.org/10.1016/S0167-7322(00)00117-3 Get rights and content

Abstract

The conversion of activity coefficients and osmotic coefficients between the McMillan-Mayer (MM) framework (comprising most electrolyte theories) and the the Lewis-Randall (LR) framework (including most experimental data) is carefully investigated. Two methodologies are presented: (1) the conversion based on the Kirkwood-Buff solution theory, and (2) thermodynamic principles (e.g., the Poynting correction). We pay special attention to conversion in multisolvent electrolyte solutions, since its theoretical status is not clearly known, and the industrial importance is great. We clarify the relation between the single-solvent case and the multisolvent case. Formulas valid in the former may not be valid in the latter. We develop molecular interpretations whenever possible. The Gibbs-Duhem relation, basis of thermo-dynamic consistency, is analyzed in both the Lewis-Randall and the McMillan-Mayer frameworks. A new hybrid formula is derived that allows the proper intrusion of MM quantities into the LR picture. Furthermore, we propose the use of the affinity principle (halophilia and halophobia) regarding the solvents to construct useful equations for solvent activity calculations.

References (27)

L.L. Lee
AIChE J
(1988)
B.A. Pailthorpe et al.
J. Chem. Soc. Faraday Trans. 2
(1984)
P. Debye et al.
Z. Phys.
(1923)
W.G. McMillan et al.
J. Chem. Phys.
(1945)
K.S. Pitzer
J. Phys. Chem.
(1973)
J.G. Kirkwood et al.
J. Chem. Phys.
(1951)
J.P. O'Connell
H.L. Friedman
J. Chem. Phys.
(1960)
H.L. Friedman
J. Solution Chem.
(1972)
H.L. Friedman
J. Solution Chem.
(1972)
H.L. Friedman
J. Solution Chem.
(1972)
R.L. Perry et al.
Mol. Phys.
(1988)
R.J. Wooley et al.
Fluid Phase Equil.
(1991)
H. Cabezas et al.
Ind. Eng. Chem. Res.
(1993)
J.P. O'Connell
Fluid Phase Equil.
(1993)
J.P. O'Connell
Fluid Phase Equil.
(1995)
E. Matteoli et al.
J. Phys. Chem.
(1982)
E. Matteoli et al.
J. Chem. Phys.
(1984)
L. Lepori et al.
J. Phys. Chem.
(1988)
L. Lepori et al.L. Lepori et al.

E.Z. Hamad et al.

J. Chem. Phys.

(1987)

E.Z. Hamad et al.

J. Phys. Chem.

(1990)

E.Z. Hamad et al.E.Z. Hamad et al.

L.L. Lee

Molecular Thermodynamics of Nonideal Fluids

(1988)

J.G. Kirkwoor

J. Chem. Phys.

(1935)

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As discussed recently by Vafaei et al. [22] who are attempting to change that trend, the observed usage disparity between the two formalisms might be in part because the original MM manuscript is “hard to read” and the formalism reduces the analysis of the solution to a solute-only form, i.e., where the solvent degrees of freedom in the corresponding partition function are integrated out. Moreover, because the MM formalism delivers thermodynamic properties as power series of the solute concentrations, whose higher order coefficients are difficult to interpret, the formalism has been useful only for dilute solutions [23–25]. In contrast, the KB formalism involves all species correlation functions where certain combinations of their configurational integrals (i.e., the so-called KB integrals) can be related directly to macroscopic properties including the solution compressibility, the ion osmotic susceptibilities and corresponding partial molar volumes [6,26].
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Extension of COSMO-RS for monoatomic electrolytes: Modeling of liquid-liquid equilibria in presence of salts
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Although giving a contribution to the Gibbs excess energy of the solution, the Pitzer Debye–Hückel term is derived from a primitive model developed in the McMillan–Mayer framework [27]. Simple conversion terms to the Lewis–Randall framework are given by Lee [28]. Nevertheless, in this work conversion between both frameworks has been neglected due to the lack of necessary information on the partial molar volumes of the species in the mixture.
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Thermodynamic consistency and reference scale conversion in multisolvent electrolyte solutions

Abstract

AIChE J

J. Chem. Soc. Faraday Trans. 2

Z. Phys.

J. Chem. Phys.

J. Phys. Chem.

J. Chem. Phys.

J. Chem. Phys.

J. Solution Chem.

J. Solution Chem.

J. Solution Chem.

Mol. Phys.

Fluid Phase Equil.

Ind. Eng. Chem. Res.

Fluid Phase Equil.

Fluid Phase Equil.

J. Phys. Chem.

J. Chem. Phys.

J. Phys. Chem.

J. Chem. Phys.

J. Phys. Chem.

Molecular Thermodynamics of Nonideal Fluids

J. Chem. Phys.