Effect of Solvent Permittivity on the Thermodynamic Behavior of HCl Solutions: Analysis Using the Smaller-Ion Shell Model of Strong Electrolytes

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Abstract
The recently introduced smaller-ion shell (SiS) treatment of strong binary electrolyte solutions [Fraenkel, D. Mol. Phys.2010, 108, 1435] that extends the Debye–Hückel theory to size-dissimilar ions is very effective for many electrolytes of various families up to moderate ionic concentration. The (molal) mean ionic activity coefficient, γ±, as a function of the reciprocal screening length, κ, hence ionic strength, I, is given by an analytic mathematical expression that incorporates the three ion-size parameters (ISPs). Experimental γ± data are fitted with calculated values derived from ISPs that seem to adequately represent the relevant mean effective ionic sizes. The SiS analysis has been lately shown effective for aqueous HCl, HBr, HI, and HClO4 at 25 °C, at which the solvent permittivity, ε, is 78.4 [Fraenkel, D. J. Phys. Chem. B2011, 115, 557]. In this paper, the behavior of HCl in solvents ranging in ε between approximately 10 and 80 is analyzed and discussed. The SiS treatment is found again suitable for computing γ± values that agree with experiment. Within the concentration range of the available experimental data, ion pairing is not indicated and, contrary to literature claims, HCl appears fully ionized even at 0.5 m (molal) with ε < 10. ISPs do not seem to be affected by temperature, but co-ion ISPs increase linearly with 1/ε. The chemical nature of the solution has no observable effect on γ± and on ISPs. The present analysis supports the view that electrolyte theories in which the solvent is considered at the McMillan–Mayer level can be successful and valuable.

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