Abstract
A. Ferse and H.O. Müller have recently presented a mathematical method aimed at subdividing the activity coefficients of electrolytes into functions of individual ionic species; these functions are suggested to be the ionic activity coefficients. By examining the method, it is possible to verify that the peculiar mathematical structure of the functions in question really guarantees a unique result, unlike the usual subdivisions of electrolyte activity coefficients, which admit infinite possibilities for the ionic activity coefficients. But the subsequent step of the reasoning, i.e., that these functions have to be the activity coefficients of the ionic species, is an illation. And indeed, another kind of subdivision in individual functions can be exemplified, whose mathematical structure also guarantees results that are unique and perfectly compatible with all theoretical properties of the ionic activity coefficients. It is concluded that it is impossible to rely on mathematical method to pull the activity coefficients of ions out of the mean activity coefficients of the electrolytes. And hence, the individual functions for the ionic species determined by Ferse and Müller do not represent the ionic activity coefficients and do not have any particular utility.
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Notes
\( \begin{array}{*{20}{c}} {{C_{\text{1a}}} = \left[ {{q_{{1}}} + {{\left( {q_1^2 - {4}{q_{{2}}}} \right)}^{{{1}/{2}}}}} \right]/{2} }{{C_{\text{1b}}} = {C_{\text{2a}}}} \\ {{C_{\text{2a}}} = \left[ {{q_{{1}}} - {{\left( {{q_{{1}}}^{{2}} - {4}{q_{{2}}}} \right)}^{{{1}/{2}}}}} \right]/{2}}{{C_{\text{2b}}} = {C_{\text{1a}}}} \\ {{B_{\text{1a}}} = \left( {{A_{\text{DH}}}{q_{{1}}} + {p_1}} \right)/{2} + \left( {{A_{\text{DH}}}q_1^2 + {p_{{1}}}{q_{{1}}}--{2}{p_{{2}}}} \right)/\left[ {{2 }{{\left( {{q_{{1}}}^{{2}} - {4}{q_{{2}}}} \right)}^{{{1}/{2}}}}} \right]}{{B_{\text{1b}}} = {B_{\text{2a}}}} \\ {{B_{\text{2a}}} = \left( {{A_{\text{DH}}}{q_{{1}}} + {p_{{1}}}} \right)/{2} - \left( {{A_{\text{DH}}}{q_{{1}}}^{{2}} + {p_{{1}}}q1--{2}{p_{{2}}}} \right)/\left[ {{2 }{{\left( {{q_{{1}}}^{{2}} - {4}{q_{{2}}}} \right)}^{{{1}/{2}}}}} \right]}{{B_{\text{2b}}} = {B_{\text{1a}}}} \\ \end{array} \)
Reference
Ferse A, Müller HO (2011) Factorizing of a concentration function for the mean activity coefficients of aqueous strong electrolytes into individual functions for the ionic species. J Solid State Electrochem. doi:10.1007/s10008-011-1413-9
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Malatesta, F. Comment on “Factorizing of a concentration function for the mean activity coefficients of aqueous strong electrolytes into individual functions for the ionic species” by A. Ferse and H.O. Müller. J Solid State Electrochem 15, 2169–2171 (2011). https://doi.org/10.1007/s10008-011-1527-0
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DOI: https://doi.org/10.1007/s10008-011-1527-0