Editing Activity coefficient (section)

=== Ionic solutions ===
{{anchor|Mean activity coefficient}}

Knowledge of activity coefficients is particularly important in the context of [[electrochemistry]] since the behaviour of [[electrolyte]] solutions is often far from ideal, even starting at low densities due to the effects of the [[ionic atmosphere]].  Additionally, they are particularly important in the context of [[soil chemistry]] due to the low volumes of solvent and, consequently, the high concentration of [[electrolytes]].<ref>{{cite book | first1= Jorge G. |last1=Ibáñez|first2=Margarita |last2=Hernández Esparza|first3=Carmen |last3=Doría Serrano|first4=Mono Mohan |last4=Singh| title= Environmental Chemistry: Fundamentals| year= 2007| publisher= Springer| isbn= 978-0-387-26061-7}}</ref>

For solution of substances which ionize in solution the activity coefficients of the cation and anion cannot be experimentally determined independently of each other because solution properties depend on both ions. Single ion activity coefficients must be linked to the activity coefficient of the dissolved electrolyte as if undissociated. In this case a mean stoichiometric activity coefficient of the dissolved electrolyte, ''γ''<sub>±</sub>, is used. It is called stoichiometric because it expresses both the deviation from the ideality of the solution and the incomplete ionic dissociation of the ionic compound which occurs especially with the increase of its concentration.

For a 1:1 electrolyte, such as [[sodium chloride|NaCl]] it is given by the following:

:<math> \gamma_\pm=\sqrt{\gamma_+\gamma_-}</math>

where <math>\gamma_\mathrm{+}</math> and <math>\gamma_\mathrm{-}</math> are the activity coefficients of the cation and anion respectively. <!-- "This definition involves a [[tacit assumption]] of a degree of 100% ionic dissociation of the electrolyte." No it does not. the activities in the expression are activities of ions, irrespective of whether ion association is also occurring. (signed) petergans-->

More generally, the mean activity coefficient of a compound of formula <math>A_\mathrm{p} B_\mathrm{q}</math> is given by<ref>{{cite book|last1=Atkins|first1=Peter|last2=dePaula|first2=Julio|title=Physical Chemistry|date=2006|publisher=OUP|isbn=9780198700722|chapter=Section 5.9, The activities of ions in solution|edition=8th}}</ref>

:<math> \gamma_\pm=\sqrt[p+q]{\gamma_\mathrm{A}^p\gamma_\mathrm{B}^q}.</math>

The prevailing view that single ion activity coefficients are unmeasurable independently, or perhaps even physically meaningless, has its roots in the work of Guggenheim in the late 1920s.<ref name="Guggenheim1928">{{cite journal|last1=Guggenheim|first1=E. A.|title=The Conceptions of Electrical Potential Difference between Two Phases and the Individual Activities of Ions|journal=The Journal of Physical Chemistry|volume=33|issue=6|year=1928|pages=842–849|issn=0092-7325|doi=10.1021/j150300a003}}</ref> In this view, the partitioning of the physical [[electrochemical potential]]s into an activity contribution and a [[Galvani potential]] contribution is arbitrary, thus nonidealities in ion activities can be remapped to nonidealities in Galvani potential and vice versa. Nevertheless, certain products of activities (such as <math> \gamma_\pm</math>) reflect a charge-neutral stoichiometry that is anyway insensitive to this partitioning, so these products are physically meaningful even if the single-ion activities are not.<ref name="Guggenheim1928"/> However, chemists have never been able to give up the idea of single ion activities, and by implication single ion activity coefficients. For example, [[pH]] is defined as the negative logarithm of the hydrogen ion activity. If the prevailing view on the physical meaning and measurability of single ion activities is correct then defining pH as the negative logarithm of the hydrogen ion activity places the quantity squarely in the unmeasurable category. Recognizing this logical difficulty, [[International Union of Pure and Applied Chemistry]] (IUPAC) states that the activity-based definition of pH is a notional definition only.<ref>{{GoldBookRef|title=pH| file = P04524}}</ref> Despite the prevailing negative view on the measurability of single ion coefficients, the concept of single ion activities continues to be discussed in the literature.<ref name="Rockwood2015">{{cite journal|last1=Rockwood|first1=Alan L.|title=Meaning and Measurability of Single-Ion Activities, the Thermodynamic Foundations of pH, and the Gibbs Free Energy for the Transfer of Ions between Dissimilar Materials|journal=ChemPhysChem|volume=16|issue=9|year=2015|pages=1978–1991|issn=1439-4235|doi=10.1002/cphc.201500044|pmid=25919971|pmc=4501315}}</ref><ref>{{Cite journal |last=May |first=Peter M. |last2=May |first2=Eric |date=2024 |title=Ion Trios: Cause of Ion Specific Interactions in Aqueous Solutions and Path to a Better pH Definition |url=https://pubs.acs.org/doi/10.1021/acsomega.4c07525 |journal=ACS Omega |volume=9 |issue=46 |pages=46373–46386 |doi=10.1021/acsomega.4c07525|pmc=11579776 }}</ref>