C. V. Krishnan

Models having the thermodynamic properties of aqueous solutions of tetraalkylammonium halides

The hypernetted-chain integral-equation-approximation method is used to calculate the ion-ion pair correlation functions and the thermodynamic properties of models of the kind previously studied,(1) which are based on an ion-ion pair potential having four terms: the usual Coulomb term, a core repulsion term, a term to represent a well-known dielectric repulsion effect, and a “Gurney” term to represent the effect of the overlap of the structure-modified regions, solvation shells or “cospheres,” when the ions come close together. The coefficientAij of the last term for each pairi,j of ionic species is the only parameter that is adjusted to fit the solution data. It is determined by fitting excess-free-energy (osmotic-coefficient) data. It is scaled to represent the molar free-energy change of water displaced from the cospheres when they overlap. The corresponding entropy changeSij and volume changeVij are determined by fitting, respectively, excessenthalpy and excess-volume data. Problems of finding a uniquely “best” set of parameters are discussed together with many examples of variations of the model, most of which require further investigation. A consistent set of these parameters, which represents much of what is known about the thermodynamic excess functions of these solutions at concentrations up to about 0.5M, is interpreted as far as possible in terms of the data for thermodynamic solvation functions for the same systems.

Model calculations for Setchenow coefficients

The calculations of Setchenow coefficients reported earlier [H. L. Friedman, C. V. Krishnan, and C. Jolicoeur,Ann. N.Y. Acad. Sci.204, 79 (1973)] have been extended to aqueous solutions of various nonelectrolytes mixed with alkali or alkylammonium halides. A few data for Setchenow coefficients in methanol have also been treated. The GurneyAij parameters for nonelectrolyte-ion interactions in models which fit the data are mostly negative, and more so the larger the solute molecules. A value ofAij near-100 cal-mole−1 seems to characterize hydrophobic bonding. In several systems these is evidence that some nonsolvation contribution to theuij pair potential which is not explicitly accounted for in the models is important in the real systems. Quite possibly this contribution is due to dispersion forces or to the chargepolarizability interaction. On the whole, theAij parameters do not seem to depend upon the charges on solute particlesi andj; this is evidence that the model is fairly realistic.

IONIC INTERACTIONS IN WATER

By comparing the accurately calculated thermodynamic properties of solution models with the thermodynamic excess functions of real aqueous solutions, it is possible to reach detailed conclusions about the contribution of solvation to ion-ion forces and to other solute-solute forces as well. While there are some ambiguities that remain to be resolved by comparison with other types of experimental data, it seems clear that the data used here are consistent with models in which the ions are not rigidly hydrated; rather the hydration layers, even of Li+ and Mg++, seem to be penetrated in collisions with other solute particles in solution. This study includes alkali halides, alkaline earth halides, tetraalkyl ammonium halides, some nonelectrolytes, and various mixtures, all at concentrations of up to about 1 M. Once the solvation parameters in the models are adjusted to fit the data, one gets good agreement of model and experiment for the osmotic and activity coefficients, the heats of dilution, and the apparent molal volumes over this range. The theory necessary to calculate Setchenow coefficients from pair correlation functions that are derived from a model is also given in this paper. The result provides some striking examples of the effect of Coulomb (COUL) forces on the concentration dependence of the zeroth moments J(g l )d3r of the pair correlation functions.