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Fraenkel D.,Eltron Research & Development Inc.
Journal of Chemical Theory and Computation | Year: 2015

A recent Monte Carlo (MC) simulation study of the primitive model (PM) of ionic solutions (Abbas, Z. et al. J. Phys. Chem. B 2009, 113, 5905) has resulted in an extensive mapping of real aqueous solutions of 1-1, 2-1, and 3-1 binary electrolytes and a list of recommended ionic radii for many ions. For the smaller cations, the model-experiment fitting process gave much larger radii than the respective crystallographic radii, and those cations were therefore claimed to be hydrated. In Part 1 (DOI 10.1021/ct5006938) of the present work, the above study for the unrestricted PM - dubbed MC-UPM - has been confronted with the Smaller-ion Shell (SiS) treatment (Fraenkel, D. Mol. Phys. 2010, 108, 1435), or DH-SiS, by comparing the range and quality of model-experiment fits of the mean ionic activity coefficient as a function of ionic concentration. Here I compare the ion-size parameters (ISPs) of best fit of the two models and argue that since ISPs derived from DH-SiS are identical with (or close to) crystallographic or thermochemical ionic diameters for both cations and anions, and they do not depend on the counterion - they are more reliable, as physicochemical entities, than the PM-derived recommended ionic radii. © 2014 American Chemical Society. Source


Fraenkel D.,Eltron Research & Development Inc.
Journal of Physical Chemistry B | Year: 2012

In part 1 of this study, I reported that the Debye-Hückel limiting law and the smaller-ion shell (SiS) model of strong electrolyte solutions fit nicely with the experimental mean ionic activity coefficient (γ±) of aqueous sulfuric acid as a function of concentration and of temperature when the acid is assumed to be a strong 1-3 electrolyte. Here, I report that the SiS-derived activity coefficient of H +, γH +, of the 1-3 acid is comparable to that of aqueous HCl. This agrees with titration curves showing, as well-known, that sulfuric acid in water is parallel in strength to aqueous HCl. The calculated pH is in good accord with the Hammett acidity function, H 0, of aqueous sulfuric acid at low concentration, and differences between the two functions at high concentration are discussed and explained. This pH-H0 relation is consistent with the literature showing that the H0 of sulfuric acid (in the 1-9 M range) is similar to those of HCl and the other strong mineral monoprotic acids. The titration of aqueous sulfuric acid with NaOH does not agree with the known second dissociation constant of 0.010 23; rather, the constant is found to be ∼0.32 and the acid behaves upon neutralization as a strong diprotic acid practically dissociating in one step. A plausible reaction pathway is offered to explain how the acid may transform, upon base neutralization, from a dissociated H4SO 5 (as 3H+ and HSO5 3-) to a dissociated H2SO4 even though the equilibrium constant of the reaction H+ + HSO5 3- ↔ SO 4 2- + H2O, at 25 °C, is 10-37 (part 1). © 2012 American Chemical Society. Source


Fraenkel D.,Eltron Research & Development Inc.
Journal of Physical Chemistry B | Year: 2012

The almost century-old dispute over the validity of the experimentally derived activity of a single ion, ai, 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 ai 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 ai values thus obtained from the smaller-ion shell treatment of strong electrolyte solutions [Fraenkel, Mol. Phys.2010, 108, 1435] agree with ai values estimated from experiment; however, theoretical ai values derived from the primitive model, the basis of most modern ionic theories, do not agree with experiment. © 2012 American Chemical Society. Source


Fraenkel D.,Eltron Research & Development Inc.
Journal of Physical Chemistry B | Year: 2012

According to the literature, when H2SO4 dissolves in water, (1) it retains its molecular formula and tetrahedral structure of two O atoms and two OH groups bonded to a central S atom, and (2) it ionizes partially, as a 1-1 electrolyte, to H+ (H3O+) and HSO4 -; the latter ion further dissociates at low concentrations (<0.1 M) to H+ and SO4 2-. Using the Debye-Hückel (DH) limiting law at very low concentration, and the smaller-ion shell (SiS) model of strong electrolyte solutions-an extension of the DH model for ion size dissimilarity-up to moderate concentration, I examine the theory-experiment fit of the mean ionic activity coefficient (γ±) of the acid as a function of concentration (at 0 to ∼6 m) and of temperature (at 0-60 °C). The fit is impossible if H 2SO4 in water is assumed to be a 1-1 or 1-2 electrolyte, but is excellent when the acid is treated instead as a strong 1-3 electrolyte; that is, aqueous sulfuric acid behaves as a fully dissociated H3A acid. At 25 °C, the SiS best fit is achieved with the H+ diameter being 1.16 Å (as obtained for strong mineral 1-1 protonic acids) and with the A3- ionic diameter being 5.77 Å. On the basis of the present study, H2SO4 in water may be H4SO 5 (dubbed "sulfoxuric", or parasulfuric acid) completely ionized to 3H+ and the ("bisulfoxate", or parabisulfate) anion HSO5 3-. The calculated standard potential of a newly proposed half-cell reaction, H2 + HSO5 3- ↔ H+ + SO4 2- + H2O + 2e -, at 25 °C, is -1.0933 V. © 2012 American Chemical Society. Source


Fraenkel D.,Eltron Research & Development Inc.
Journal of Chemical Thermodynamics | Year: 2014

The calculation of thermodynamic properties of many strong electrolytes in solution, including aqueous sulfuric acid, has been performed over the past four decades using so-called thermodynamic models, such as the well-known Pitzer model. I have recently pointed out (Fraenkel, 2012) [15,16] that H 2SO4 in water appears to follow the mean ionic activity pattern of a strong 1-3 electrolyte, and postulated that this H3A acid may be H4SO5 fully ionizing to 3H+ (3H3O+) and HSO53-. This contrasts with the traditional view of the aqueous acid - claimed to be supported by thermodynamic models - according to which H2SO4 retains its molecular structure in water and dissociates primarily to H+ and HSO4-, and at <0.1 M, HSO4- dissociates further to H+ and SO42-. I now show that a good fit of Pitzer model with the activity coefficients reported by Hamer and Harned can be obtained for the "1-3 H2SO4" even by using the simple 3-parameter equation of the model; the best-fit Pitzer parameters are β(0) = 0.240, β(1) = 4.30 and CMX = -0.0134, and the standard deviation, σ is 0.0152. With the corrected activity coefficients as proposed in the first reference above, the best-fit parameters are β(0) = 0.230, β(1) = 3.60 and CMX = -0.0120, and σ = 0.0081. σ of the analysis of the "1-3 acid" is in both cases considerably lower than that of the "1-2 acid" (σ = 0.049) that provides a best-fit β(1) value of -3.000; a negative β(1) is inappropriate since it is parallel to a negative ion-ion distance of closest approach in Debye-Hückel-type expressions of the activity coefficient. © 2014 Elsevier Ltd. All rights reserved. Source

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