COMMUNICATIONS TO THE EDITOR
2097
az = 3.26 X cm3 (from Heydweiller’s5 molecular refractions) gives ep = 111 for KC1, thus predicting that KC1 should have an association constant some 8 times larger than TlCl from these effects. This larger (10) To whom inquiries regarding this work should be addressed. value arises from the much smaller value of n for KCI, despite the larger ro and smaller polarizabilities. It L. PRATT CHEMICAL ENGINEERING DEPARTMENT GRAHAM appears that the major failure of the procedure arises STANLEY H. LANGER‘~ UNIVERSITY OF WISCONSIN MADISON, WISCONSIN53706 from the choice of close-range dielectric constant, which is identified with n2 for the solid (extrapolating n to RECEIVED MARCH 24, 1969 infinite wavelength). If it is assumed that the closerange dielectric constant should be the same for TlCl and KC1 then a value for this (to be compared with n2) of about 3.4, using the same polarizabilities and internuclear distances as above, would reproduce the factor of 13 difference between TlCl and KC1 while Comment on “Conductance of Thallous Chloride allowing polarizability of ions and dielectric saturation in each case. This value for the close-range dielectric in Dioxane-Water Mixtures at 25”” constant is not unreasonable. Sir: D’Aprano and Fuossl have recently determined However, the D’Aprano and Fuoss procedure would the association constants for thallium(1) chloride in still fail to account for the observed trend in association dioxane-water mixtures from conductance measureconstants for TlC1, TIBr, and T1I in water at 25”. ments at 25”. Their figure in water, 5.2 f 0.5 1. mol-’, This trend is K T E L< K T ~ < B ~K T ~ I Using .~ data is as close as can be expected to our figures2 from solufrom the sources given above we get e p values of 15.0, bility and spectrophotometric measurements, since 8.6, and 4.2, respectively, for these halides. (Our we have shown that the values obtained depend on the ep value for TIC1 is slightly different from that of mean ionic activity coefficients used and D’Aprano D’Aprano and Fuoss as we have rounded off the exand Fuoss use the Debye-Huckel limiting law. trapolated value of n to 2.1.) Again the majorcontriI n discussing the well-known finding that thallium(1) bution to these differences comes from the differences in chloride has a higher association constant than most extrapolated refractive indices (2.1, 2.2, and 2.4, reother 1: 1 salts, D’Aprano and Fuoss propose that this spectively), these increases, and increases in ro, offcan be accounted for by assuming mutual polarization setting increases in a2. But in this case, even if the of TI+ and C1- ions. They give an expression for the same value for the close-range dielectric constant is association constant assumed for each halide, the order of e p values remains the same. Since eb values in eq 1 are also in this order, the D’Aprano and Fuoss procedure predicts the trend K A = KoebeP (1) of association constants to be opposite to that observed, where K Ois an excluded volume factor, eb is a factor unless it is assumed that the close-range dielectric arising from chargecharge interactions, and ep is a constant decreases along the series. This is an unlikely factor allowing for polarization and dielectric saturaassumption, as noted below. tion effects. p is given by their model, after matheA previous’ thermodynamic analysis of association matical approximations and allowing for dielectric of TIC1 and TlBr suggests a reason for the failure found saturation, as above. This analysis shows that the reversal of stability of these salts in water, compared with the gas phase, arises from a fine balance of enthalpy and entropy terms in which, among other factors, the greater with symbols as in their paper. The factor e p (with the value 13.0 for TlCl with their choice of parameters) is claimed to account for the increased association of (1) A. D’Aprano and R. M. Fuoss, J . Amer. Chem. Soc., 91, 279 (1969). TlCl compared with that of a salt with the same size (2) J. B. Macaskill and M . H. Panckhurst, Aust. J . Chem., 22, 317 ions but whose charges remain fixed at the centers.” (1969), and earlier papers. It is shown that this factor is consistent with the differ(3) “Landolt-Bornstein Tabellen,” 6th ed, Vol. 11, Part 8, “Opences in association between TIC1 and KC1. However, tische Konstanten,” Springer-Verlag, 1962. (4) “Interatomic Distances,” Special Publications No. 11, 1958, D’Aprano and Fuoss do not consider the effect of and No. 18, 1965, The Chemical Society, London. polarization and dielectric saturation in the KC1 case. (5) A. Heydweiller, Phys. Z.,26, 526 (1925). Using their procedure we get n = 1.5 (extrapolated (6) “Stability Constants,” Special Publication No. 17, The Chemical from data listed in Landolt-Bornstein3) which, toSociety, London, 1964. gether with ro = 2.67 a1 = 1.07 X cma, and (7) M. H. Panckhurst, Aust. J . Chem., 15, 194 (1962).
Acknowledgment. The authors thank the Petroleum Research Fund, administered by the American Chemical Society, for an International Award (G. L. P.).
Volume 79, Number 6 June 1989
2098 hydration enthalpy for C1- than Br- more than overcomes the greater bond strength of TIC1 over TlBr. Thus detailed allowance for ion-solvent interactions is important in accounting for stability trends. While continuum models, such as that of D’Aprano and FUOSS, could be claimed to allow for ion-solvent interactions by introducing dielectric saturation, this does not seem to us to be a satisfactory alternative. To account for the stability trend for any series of halides in which stability increases with halide size it would be necessary to assume that saturation effects (as reflected by the close-range dielectric constant) become more important with increasing size. This is the opposite of that usually a ~ s u m e d ,saturation *~~ effects being assumed to
The Journal of Physical Chemistry
COMYUN~CATIONS TO THE EDITOR decrease with increasing size whatever detailed model is used. The applicability of continuum models in general has also been questioned.lo (8) E. Glueckauf, “Chemical Physics of Ionic Solutions,” B. E. Conway and R. G. Barradas, Ed., John Wiley & Sons, Inc., New York, N. Y., 1966, p 67. (9) R. Fernhdez-Prini and J. E. Prue, Trans. Faraday SOC., 62, 1257 (1966). (10) See comments by S. Levine and E. Glueckauf in ref 8, pp 106 and 107, and the paper by 5 . Levine and D. K. Rozenthal in ref 8, p 119.
CHEMISTRY DEPARTMENT M.H. PANCKHURST OF OTAGO UNIVERSITY DUNEDIN, NEW ZEALAND RECEIVED APRIL I, 1969
