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

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 HClO(4) at 25 °C, at which the solvent permittivity, ε, is 78.4 [Fraenkel, D. J. Phys. Chem. B 2011, 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.

Ion strength limit of computed excess functions based on the linearized Poisson–Boltzmann equation

“…Indeed, in nature, cations and anions always have FULL PAPER different size; furthermore, in many cases, ISPs exhibit considerable nonadditivity. [14][15][16]19,21]…”

“…Previous articles on the DH-SiS theory have shown its widespread agreement with experiment. [14][15][16][17][18][19][20][21] Therefore, factors in DH-SiS, such as dQ/dr, or A* and A*' (e.g., in Fig. 3A), are inherently "correct" in being building blocks or derivatives of the theoretical process that leads to a "correct" c 6 .…”

“…The analytic mathematical expressions of DH-SiS for the activity coefficients of electrolyte solutions as functions of ion strength, I, afford excellent fit with experiment, in a systematic manner, for electrolytes of almost all ion-valence families (i.e., 1-1, 1-2, 2-2, etc.). The emerging importance of DH-SiS, as demonstrated in my recent articles [15][16][17][18][19][20][21] calls, however, for more scrutiny of its physico-mathematical foundations. Because DH-SiS, like the parent DH theory, is an electrostatic-only theory within the MM level of modeling, the following conditions are required:…”

Thermodynamics of primitive model electrolytes in the symmetric and modified Poisson-Boltzmann theories. A comparative study with Monte Carlo simulations

“…Fraenkel [31,32] took this idea further and developed the Smaller ion Shell (SiS) theory, which is based on an improved DH type theory with different ion sizes, and gives a better representation of the HCl experimental individual activity coefficients [28]. The SPB and MPB activities using ionic radii from Fraenkel's theory [31] are given in figure 2. Although MC data are not available at these ionic radii, from the consistency of the simulation data with the theories for all the 104 cases for which the MC data are available, it is a fair conjecture that the SPB and MPB curves in this figure will be very close to the "exact" results for the model.…”

“…(Colour online) Experimental and theoretical (SPB and MPB) decadic logarithm of individual and mean activity coefficients of HCl solution as functions of electrolyte concentration. In the SPB and MPB calculations, the ionic radii are r H + = 0.58 × 10 −10 m, r Cl − = 1.81 × 10 −10 m, and are taken from the SiS theory of Fraenkel[31].…”