Editing Activity coefficient (section)

==== Stokes–Robinson model ====
For concentrated ionic solutions the hydration of ions must be taken into consideration, as done by Stokes and Robinson in their hydration model from 1948.<ref>{{Cite journal |doi = 10.1021/ja01185a065|pmid = 18861802|title = Ionic Hydration and Activity in Electrolyte Solutions|journal = Journal of the American Chemical Society|volume = 70|issue = 5|pages = 1870–1878|year = 1948|last1 = Stokes|first1 = R. H|last2 = Robinson|first2 = R. A}}</ref> The activity coefficient of the electrolyte is split into electric and statistical components by E. Glueckauf who modifies the Robinson–Stokes model.

The statistical part includes [[solvation shell|hydration index number]] {{mvar|h}}, the number of ions from the dissociation and the ratio {{mvar|r}} between the [[apparent molar property|apparent molar volume]] of the electrolyte and the molar volume of water and molality {{mvar|b}}.

Concentrated solution statistical part of the activity coefficient is:
:<math>\ln \gamma_s = \frac{h- \nu}{\nu} \ln \left (1 + \frac{br}{55.5} \right) - \frac{h}{\nu} \ln \left (1 - \frac{br}{55.5} \right) + \frac{br(r + h -\nu)}{55.5 \left (1 + \frac{br}{55.5} \right)}</math><ref name="Glueckauf1955">{{Cite journal |url=https://pubs.rsc.org/en/content/articlelanding/1955/tf/tf9555101235 |doi = 10.1039/TF9555101235|title = The influence of ionic hydration on activity coefficients in concentrated electrolyte solutions|journal = Transactions of the Faraday Society|volume = 51|pages = 1235|year = 1955|last1 = Glueckauf|first1 = E.|url-access = subscription}}</ref><ref name="Glueckauf1957">{{Cite journal |url=https://pubs.rsc.org/en/content/articlelanding/1957/TF/tf9575300305 |doi = 10.1039/TF9575300305|title = The influence of ionic hydration on activity coefficients in concentrated electrolyte solutions|journal = Transactions of the Faraday Society|volume = 53|pages = 305|year = 1957|last1 = Glueckauf|first1 = E.|url-access = subscription}}</ref><ref name="Kortüm1960">{{cite journal|last1=Kortüm|first1=G.|title=The Structure of Electrolytic Solutions |publisher=Herausgeg. von W. J. Hamer; John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd. |location=London |url=https://onlinelibrary.wiley.com/doi/10.1002/ange.19600722427 |year=1959 |journal=[[Angewandte Chemie]]|volume=72|issue=24|page=97|issn=0044-8249|doi=10.1002/ange.19600722427|author1-link=Gustav Kortüm|url-access=subscription}}</ref>

The Stokes–Robinson model has been analyzed and improved by other investigators.<ref name="Miller1956">{{Cite journal |last= Miller|first = Donald G. |url=https://pubs.acs.org/doi/pdf/10.1021/j150543a034 |doi = 10.1021/j150543a034 |title = On the Stokes-Robinson Hydration Model for Solutions |journal = The Journal of Physical Chemistry|volume = 60|issue = 9|pages = 1296–1299|year = 1956|url-access = subscription}}</ref><ref>{{Cite journal |last=Nesbitt |first=H. Wayne |doi=10.1007/BF00649040 |url=https://link.springer.com/article/10.1007/BF00649040 |title = The stokes and robinson hydration theory: A modification with application to concentrated electrolyte solutions |journal =[[Journal of Solution Chemistry]] |volume = 11 |issue = 6 |pages = 415–422 |year=1982 |s2cid= 94189765|url-access=subscription }}</ref> The problem with this widely accepted idea that electrolyte activity coefficients are driven at higher concentrations by changes in hydration is that water activities are completely dependent on the concentration of the ions themselves, as imposed by a thermodynamic relationship called the Gibbs-Duhem equation. This means that the activity coefficients and the corresponding water activities are linked together fundamentally, regardless of molecular-level hypotheses. Due to this high correlation, such hypotheses are not independent enough to be satisfactorily tested.