J. Phys. Chem. 1982, 86,2491-2494
2491
Dielectric Properties of Electrolyte Solutions. 2. Alkali Halides in Methanol Paul Winsor, I V , and Robert H. Cole' Chemistry Department, Brown University, Providence, Rhode Island 029 12 (Received: September 23, 198 1; I n Final Form: January 7, 1982)
Static permittivities obtained by time domain reflectometry (TDR) measurements are reported for KI, NaI, LiI, NaC1, and LiCl at concentrations from 0.06 to 0.32 M in methanol at 25 "C. Decrements proportional to specific conductance increase with decreasing ion sizes. Specific ion decrements derived from the salt values are in reasonably good agreement with predictions of the Hubbard-Colonomos-Wolynes theory for ions at infinite dilution, thus providing further evidence for kinetic depolarization produced by molecular dynamics of ion-dipole interactions rather than static solvation effects.
I. Introduction
decrements from the equations
In the preceding paper (part 1),l it was found that the dielectric decrements produced in seven solvents by addition of sodium iodide were only partially accounted for by the Hubbard-Onsager (HO) the0ry~9~ of kinetic depolarization. In this theory, the solvent is represented by a dielectric continuum and no provision is made for including interactions of ions with neighboring solvent dipole molecules. Prior to the development of the HO theory, traditional interpretations of the observed decrements were in terms of static effects of the intense ionic fields at short range, described by a saturated dielectric permittivity near the ion or by formation of solvated or "irrotationally bound" clusters of solvent molecules around the ions. In paper 1of this series, we indicated the difficulties in accounting for the decrements produced by NaI in excess of the HO predictions as additive effects described by such models, and we return to these questions later in this paper. For all but one of the solvents studied, the approach just described was the best available, but recently Hubbard, Colonomos, and Wolynes4 (HCW) have developed a molecular dynamic treatment of static and kinetic effects with ion-dipole interactions specifically included and have given results of numerical calculations for atomic ions in methanol. These predict specific ionic decrements as a function of bare ion radius which reduce to the HO result for large ions are smaller for radii down to about 2.2 A and increase rapidly for smaller ions to values as much as three times the HO result in the case of Li+. The predictions of the HCW theory4 are clearly in the right direction for NaI in methanol, with the excess decrement attributed to the sodium ions, but for a quantitative comparison one needs measurements on a series of salts in order to calculate experimental ionic decrements. This is readily seen from the form of the HCW prediction that the observed permittivity decrement AcMX for a salt MX = M+ + X- is given by
t+(MX)A(M+)+ [l - t+(MX)]A(X-)= A(MX) (2) In the work reported here, we obtained AMx values for the salts NaI, LiC1, NaC1, LiI, and KI. Together with the results for NaI in methanol reported in paper 1, these suffice to calculate experimental ionic decrements AM+and AX- for the five ions given the transference numbers t+-
-At(MX)
+ K~A(MX)K(MX) =
K,[A(M+)K(M+)A(x-)~(x-)] (1)
where K , = 9 X 1 0 % ~(ps), with 7 D the Debye solvent relaxation time, and K(MX),K(M+),and K ( X - ) are specific conductances for the salt and ions. As contributions from the reduced ion decrements A(M+) and A(X-1 to the salt decrements are weighted by ion conductances, one needs transference numbers t+(MX) to obtain experimental ion (1) Winsor, IV,P.; Cole, R. H. J.Phys. Chem. Preceding article in this issue. (2) Hubbard, J. B.; Onsager, L. J . Chem. Phys. 1977, 67,4850. (3) Hubbard, J. B. J . Chem. Phys. 1978, 68,1649. (4) Hubbard, J. B.; Colonomos, P.; Wolynes, P. G. J . Chem. Phys. 1979, 71,2652.
(MX).
In section 11,we describe the method and give our experimental results. The analysis of these and comparison with the HCW theory is presented in section 111, and in sections IV and V difficulties with static solvation models and general conclusions are discussed. 11. Experimental Method and Results
The TDR method used to obtain the desired permittivity data for the solutions measured here and the details of all design and temperature control are described in paper 1. The frequency range of E*calculated from the time domain data was from 0.2 to 8 GHz for all the methanol solutions. Measurements were made for three concentrations of each salt: 0.06,0.10, and 0.16 M for NaC1, and 0.06,0.16, and 0.32 M for the other salts. The methanol used was Fisher certified reagent grade (maximum impurity
