symbols: $x_{+}$, $x_{-}$
synonyms: ionic amount fraction, species amount fraction, species mole fraction
https://doi.org/10.1351/goldbook.15335
- For an ionized salt \(\ce{B}\) in solution, \[x_{+\rm{B}} = \frac{\nu_{+\ce{B}}x_{\ce{B}}}{1 + \sum \limits_{i=1}^{s} \left(\nu_{i} - 1 \right)x_{i}},x_{-\ce{B}} = \frac{\nu_{-\ce{B}}x_{+\ce{B}}}{\nu_{+\ce{B}}}\] where the summation is over all $s$ solute components \(i\) and \(\nu_{i} = \nu_{+i} + \nu_{-i}\) is the sum of the stoichiometric numbers of the ions formed from salt \(i\).
- For a single solvent \(\ce{A}\) in an ionic solution, \[x'_{\ce{A}} = \frac{x_{\ce{A}}}{1 + \sum \limits_{i=1}^{s} \left(\nu_{i} - 1 \right)x_{i}}\] Note 1: These are generalizations of terms and are used in formulating fitting equations for solubility of salts, in defining activity coefficients on the mole fraction scale, and in discussing salt effects on solubilities of gases.
Note 2: Note that \[\sum \limits_{i=1}^{s} \left(x_{+i} - x_{-i} \right) + x'_{\ce{A}} = 1\]