Editing Thermodynamic activity (section)

==Measurement==
The most direct way of measuring the activity of a volatile species is to measure its equilibrium partial [[vapor pressure]]. For water as solvent, the [[water activity]] ''a<sub>w</sub>'' is the equilibrated [[Humidity|relative humidity]]. For non-volatile components, such as [[sucrose]] or [[sodium chloride]], this approach will not work since they do not have measurable vapor pressures at most temperatures. However, in such cases it is possible to measure the vapor pressure of the ''solvent'' instead. Using the [[Gibbs–Duhem relation]] it is possible to translate the change in solvent vapor pressures with concentration into activities for the solute.

The simplest way of determining how the activity of a component depends on pressure is by measurement of densities of solution, knowing that real solutions have deviations from the additivity of (molar) volumes of pure components compared to the (molar) volume of the solution. This involves the use of [[partial molar volume]]s, which measure the change in chemical potential with respect to pressure.

Another way to determine the activity of a species is through the manipulation of [[colligative properties]], specifically [[freezing point depression]]. Using freezing point depression techniques, it is possible to calculate the activity of a weak acid from the relation,
:<math>b^{\prime} = b(1 + a)\,</math>
where {{mvar|b′}} is the total equilibrium molality of solute determined by any colligative property measurement (in this case {{math|Δ''T''<sub>fus</sub>}}), {{mvar|b}} is the nominal molality obtained from titration and {{mvar|a}} is the activity of the species.

There are also electrochemical methods that allow the determination of activity and its coefficient.

The value of the mean ionic activity coefficient {{math|''γ''<sub>±</sub>}} of [[ion]]s in solution can also be estimated with the [[Debye–Hückel equation]], the [[Davies equation]] or the [[Pitzer equations]].

===Single ion activity measurability revisited===
The prevailing view that single ion activities are unmeasurable, or perhaps even physically meaningless, has its roots in the work of [[Edward A. Guggenheim]] in the late 1920s.<ref>{{cite journal|first=E. A. |last=Guggenheim |title=The Conceptions of Electrical Potential Difference between Two Phases and the Individual Activities of Ions |journal=[[J. Phys. Chem.]] |volume=33 |issue=6 |date=1929 |pages=842–849 |doi=10.1021/j150300a003}}</ref> However, chemists have not given up the idea of single ion activities. For example, [[pH]] is defined as the negative logarithm of the hydrogen ion activity. By implication, if the prevailing view on the physical meaning and measurability of single ion activities is correct it relegates pH to the category of thermodynamically unmeasurable quantities. For this reason the [[International Union of Pure and Applied Chemistry]] (IUPAC) states that the activity-based definition of pH is a notional definition only and further states that the establishment of primary pH standards requires the application of the concept of 'primary method of measurement' tied to the Harned cell.<ref>{{GoldBookRef|file=P04524|title=pH}}</ref>  Nevertheless, the concept of single ion activities continues to be discussed in the literature, and at least one author purports to define single ion activities in terms of purely thermodynamic quantities. The same author also proposes a method of measuring single ion activity coefficients based on purely thermodynamic processes.<ref>{{cite journal|first=A.L. |last=Rockwood |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 |date=2015 |pages=1978–1991 |doi=10.1002/cphc.201500044 |pmid=25919971 |pmc=4501315 }}</ref> A different approach <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> has a similar objective.