Unified Thermodynamics for All Concentrations of Electrolytes Based on Hydration and Partial Dissociation (Without Activity Coefficients, 1995-)
Authors: Heyrovska Raji 
Published: February 2020

Twenty years ago in the ECS meeting at Reno, May 1995, the author presented her breakthrough paper on the partial dissociation and hydration of NaCl from ‘zero to saturation’. This totally replaced the idea of complete dissociation and the activity coefficient corrections in thermodynamics and confirmed the theory of electrolytic dissociation founded over a century ago by Svante Arrhenius for which he was awarded the Nobel Prize in 1903. According to his original theory (1884 - ), a fraction (α
) mole of an electrolyte like NaCl dissociates in water into 2α moles of ions, the rest (1-α)being in the undissociated form:

NaCl (1-
α
) ↔ Na+(
α
) + Cl- (
α
) (1)

Thus every mole of salt increased to (1-α) + 2α = (1+α) = i ( >1) moles of solute on dissolving in water. With the ratio of the equivalent conductivity at any concentration (L) to that at infinite dilution (Lo) as a measure of the degree of dissociation (α),this factor, i, called van't Hoff factor, explained the increase in osmotic pressure as observed by van't Hoff. This theory was greatly successful in explaining many other properties of dilute electrolyte solutions.
While attempts were in progress to extend the theory to concentrated solutions, the thermodynamics of solutions was replaced (Lewis and Randall, 1921) by that of the empirical concepts of activity and activity coefficients. Since the Debye-Huckel theory of interionic interaction for completely dissociated electrolytes, as shown:

NaCl
→
Na+ + Cl- (2)

was able to nearly explain the concentration dependence of activity coefficients for very dilute solutions, the latter equations based on complete dissociation were gradually extended to higher concentrations until they resulted in extremely elaborate equations (Pitzer, 1973) without physical significance.
The author became aware of the complexity of the theory of simple electrolytes like NaCl (aq) during her doctoral work on strong electrolytes. In the following years, she abandoned this theory and started reinvestigating the available experimental data on the properties of electrolytes (Heyrovska, 1979, 1980). Gradually it became clear that, with the degrees of dissociation (α)and the hydration numbers evaluated by the author from the vapor pressure (or osmotic coefficient) data (instead of from the conductivity ratio), the original idea of partial dissociation due to Arrhenius, as per equation (1), and of 'free water' (Bousfield, 1917), could explain quantitatively the non-ideal properties of electrolytes over a large range of concentrations (Heyrovska, 1987, 1988).
Further advance was made by the author in 1995 on realizing that the molalities of ‘free’ water in the "surface and bulk of solution" are different. This made a breakthrough in the theory of electrolytes, which could then be extended to the whole range of concentrations from "zero to saturation" (Heyrovska, 1995, 1996) for the first time. Many thermodynamic properties of solutions could thus be explained quantitatively in terms of simple mathematical relations involving the degrees of dissociation, hydration numbers and volumes of ions and ion pairs, without any empirical parameters. For review papers on the subject, see Heyrovska, 1998, 2003, 2006, 2011 and 2013. For a complete list of references and Table of equations, see Refs. 11,12 below and the literature therein. Full list of all publications are in: www.jh-inst.cas.cz/~rheyrovs. Some selected references pertaining to the ‘whole concentration range’ are given below.

References

1. R. Heyrovska, 187th Mtg of the Electrochemical Society, USA, Reno, USA, Vol. 95-1 (1995) abstract no. 662.
2. R. Heyrovska, Journal of Electrochemical Society, 143 (1996) 1789-1793.
3. R. Heyrovska, Croatica Chemica Acta, 70 (1997) 39 - 54.
4. R. Heyrovska, Journal of Electrochemical Society, 144 (1997) 2380-2384.
5. R. Heyrovska, Invited article: Chemicke Listy, 92 (1998) 157-166.
6. R. Heyrovska, Invited contribution in Chapter 11, Book: "Ionic Equilibrium", Ed.: J. N. Butler (Harvard Univ.) (John Wiley and Sons, New York, (1998), pp. 477-481.
7. R. Heyrovska, Journal of Molecular Liquids81 (1999) 83-86.
8. R. Heyrovska, Marine Chemistry, 70 (2000) 49-59, Dedicated to Frank J. Millero on the occasion of his 60th birthday
9. R. Heyrovska, Invitation Plenary Lecture: "Symposium Svante Arrhenius", Uppsala, Sweden, 27 – 29 November, 2003, commemorating the 100th Anniversary of the award of the Nobel Prize to Arrhenius in 1903. Full text in: www.jh-inst.cas.cz/~rheyrovs; http://almaz.com/nobel/chemistry/1903a.htmland in: Special Issue of Electroanalysis, 18 (2006) 351 - 361.
10. R. Heyrovska, http://precedings.nature.com/documents/6416/version/1
11. R. Heyrovska, Invited article: Current Topics in Electrochem., 16, 47-56, 2011.
12. R. Heyrovska, Invited article: Structural Chem. (2013) 24: 895-1901.