Single-Ion Activity: Experiment versus Theory

Abstract

The almost century-old dispute over the validity of the experimentally derived activity of a single ion, a(i), is still unsettled; current interest in this issue is nourished by recent progress in electrochemical cell measurements using ion-specific electrodes (ISEs) and advanced liquid junctions. Ionic solution theories usually give expressions for a(i) values of the positive and negative ions, that is, the respective a(+) and a(-), and combine these expressions to compute the mean ionic activity, a(±), that is indisputably a thermodynamically valid property readily derivable from experiment. Adjusting ion-size parameters optimizes theory's fit with experiment for a(±) through "optimizing" a(+) and a(-). Here I show that theoretical a(i) values thus obtained from the smaller-ion shell treatment of strong electrolyte solutions [Fraenkel, Mol. Phys. 2010, 108, 1435] agree with a(i) values estimated from experiment; however, theoretical a(i) values derived from the primitive model, the basis of most modern ionic theories, do not agree with experiment.

Chapter 27 The Activity of Individual Ions Measuring and Modeling

“…Hence, it is remarkable that in the case of the individual Hurlen [47] activity of ions, the situation has been the inverse. Another comparison of theoretical predictions versus experimental data can be found in [56], but the reported discrepancies between the theory and experiment are much greater than those presented in [54,55]. In this case, the theory is confirming the validity of the experimental measurements.…”

Ion transfer of weak acids across liquid|liquid interfaces

“…Activity coefficients Electrolyte solutions are non-ideal, with an increasing shift from the ideal behaviour by increasing the concentration [79][80][81][82][83][84][85][86]. Local electrostatic effects are generally considered to be the major source of non-ideality in electrolyte solutions and they are taken into account by using activity coefficients, γ i , that can be calculated according to classical Debye-Hückel (DH) theory [87,88] or by Fraenkel's smaller-ion shell (SiS) model [89][90][91][92][93]. The latter model is a fundamental generalization of the DH theory that takes into account the different sizes of spherically symmetric charged species to calculate their activity coefficients.…”

“…The latter model is a fundamental generalization of the DH theory that takes into account the different sizes of spherically symmetric charged species to calculate their activity coefficients. The activity coefficients for the different species are given by [91]:…”

“…(16) and (17). Recently, the activity coefficients of individual ions using an ionic liquid salt bridge inserted in a Harned cell have been experimentally determined by the group of Prof. Kakiuchi [94,95] and successfully contrasted with the theory of NIES developed by Prof. Fraenkel [89][90][91][92][93].…”

“…In this sense, the expressions of the activity coefficients given by the DH theory are obtained [88,91]:…”