Unraveling the Behavior of the Individual Ionic Activity Coefficients on the Basis of the Balance of Ion–Ion and Ion–Water Interactions

Abstract

We investigate the individual activity coefficients of pure 1:1 and 2:1 electrolytes using our theory that is based on the competition of ion-ion (II) and ion-water (IW) interactions (Vincze et al., J. Chem. Phys. 133, 154507, 2010). The II term is computed from Grand Canonical Monte Carlo simulations on the basis of the implicit solvent model of electrolytes using hard sphere ions with Pauling radii. The IW term is computed on the basis of Born's treatment of solvation using experimental hydration free energies. The two terms are coupled through the concentration-dependent dielectric constant of the electrolyte. With this approach we are able to reproduce the nonmonotonic concentration dependence of the mean activity coefficient of pure electrolytes qualitatively without using adjustable parameters. In this paper, we show that the theory can provide valuable insight into the behavior of individual activity coefficients too. We compare our theoretical predictions against experimental data measured by electrochemical cells containing ion-specific electrodes. As in the case of the mean activity coefficients, we find good agreement for 2:1 electrolytes, while the accuracy of our model is worse for 1:1 systems. This deviation in accuracy is explained by the fact that the two competing terms (II and IW) are much larger in the 2:1 case so errors in the two separate terms have less effects. The difference of the excess chemical potentials of cations and anions (the ratio of activity coefficients) is determined by asymmetries in the properties of the two ions: charge, radius, and hydration free energies.

Activity coefficients of individual ions in LaCl3from the II+IW theory

“…4 for La 3+ and Cl − , respectively, in LaCl 3 . This figure explains why the qualitative agreement for La 3+ is so valuable (the corresponding figure for Ca 2+ can be found in our previous papers [24,25]). The II term goes down to −20kT and the IW term goes up to 20kT at concentrations close to saturation.…”

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.…”

Poisson-Fermi modeling of ion activities in aqueous single and mixed electrolyte solutions at variable temperature

“…Note that the shell volume depends not only on O w i but also on the bulk void fraction Γ B , namely, on all salt and water concentrations (C B k ). As discussed in [25], the solvation free energy of an ion i should vary with salt concentrations and can be expressed by a dielectric constant ǫ(C B i ) that depends on the bulk concentration C B i of the ion. Therefore, the Born energy…”

“…We refer to our previous papers and references therein for a historical account of the literature of this theory. In [19], we proposed a PF model for calculating activity coefficients of individual ions in aqueous single NaCl and CaCl 2 electrolyte solutions at the temperature 298.15 K. The model is further tested in this paper for eight 1:1 electrolytes (LiCl, LiBr, NaF, NaCl, NaBr, KF, KCl, and KBr), six 2:1 electrolytes (MgCl 2 , MgBr 2 , CaCl 2 , CaBr 2 , BaCl 2 , and BaBr 2 ), one mixed electrolyte (NaCl + MgCl 2 ), one 1:1 electrolyte (NaCl ) at various temperatures from 298.15 to 573.15 K, and one 2:1 electrolyte (MgCl 2 ) at various temperatures from 298.15 to 523.15 K, for which the experimental data were compiled by Valiskó and Boda in [25] and Rowland et al in [13] from various experimental sources in [26][27][28][29][30][31][32][33][34][35].…”