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moves more NaCl than it moves itself. These results were quite uncxpected. This surprisingly large D , , underscores the fact that a cross-term cocfficient need not be small and can exceed one or both main-term cocflicients. contrary to commonly held opinions. Clearly, models of diffusion processes that ignore cross terms can often be substantiall) inaccurate, as discussed in ref 12. Moreover, the large D I 2at high concentrations simply cannot be predicted from the infinitc dilution value calculated from the Nernst-Hartley c q u ; i i i o n ~ . ~ ~Inclusion . ~ ~ . ~ ~ of thermodynamic gradients and vibcoaity factors in Nernst-Hartley estimates improves matters somewhat up to about 1 mol dm-3, as both we (unpublished) and Leaist' have found. However, other types of ionic interaction have a major influence on the values of D , even in moderately concentrated electrolyte solutions, and good approximations a t high concentrations have yet to be found. These issues will be discussed elsewhere. after we present the D, extrapolated to C, = 0 and c2= 0. W e have made preliminary calculations of the Onsager reciprocal relations ( O R R ) for ternary d i f f ~ s i o nusing ~ ~ ,our ~ ~D, ~~~ (38) Gosting, L. J. Adcances in Protein Chemistry: Academic Press: New York, 1956; Vol. XI. pp 429-554. (39) Wendt. R . P. J. Phys. Chem. 1965, 69, 1227.
and derivatives of activity data;6 the O R R were found to be satisfied with reasonable estimates of experimental errors. These results, plus estimates of the D,, based on ionic Onsager coefficients 1,,,13,'4 will be reported elsewhere. It is interesting that the partial molal volumes of these systems appear to be linear in the square root of ionic strength (see Figure 1 ) . However, it is noted that the ratio of concentrations of the solutes is not constant in this series of experiments, so care should be taken in interpreting this linearity.
Acknowledgment. This work was primarily performed under the auspices of the U S . Department of Energy a t the Lawrence Livermore National Laboratory under Contract W-7405-ENG-48. J.A.R. and D.G.M. thank the Office of Basic Energy Sciences (Geosciences) for support. D.G.M., L.P., and J.G.A. thank Dr. Christopher Gatrousis for C R R support. J.G.A. also thanks TCU for research fund Grant No. 5-23824. R.M. thanks T C U for supporting him through a research fellowship. The research published here is based in part on the Ph.D. dissertation of R.M., TCU. Registry No. NaCI, 7647- 14-5; MgCI,, 7786-30-3 (40) Miller, D. G. J . Phys. Chem. 1959. 63, 570
Structure, Dynamics, and Molecular Association of LIAsF, and of LiCIO, in Methyl Acetate at 25 OC Mark Salomon,* Michelle Uchiyama, Army Power Sources Laboratory, Fort Monmouth, New Jersey 07703-5000
Meizhen Xu, and Sergio Petrucci* Weber Research Institute and Department of Chemistry, Polytechnic University, Farmingdale, New York I I735 (Received: August I I , 1988; I n Final Form: November 14, 1988)
The nature of ion solvation and complex formation of LiAsF, and LiCIOI in methyl acetate (MA) at 25 OC has been studied over the concentration range of to 0.5 mol dm-). The properties of these electrolyte solutions were studied by infrared and microwave relaxation spectroscopy and by audio frequency electrolytic conductance. The infrared spectra of LiAsF6 solutions over the concentration range 0.1-0.5 mol dm-3 suggest the existence of contact ion pairs, and solvent separated ion pairs, and possibly dimers. Microwave complex permittivities for LiAsF, m d L i C Q solutions over this same concentration range confirm the existence of both contact and solvent separated ion pairs and indirectly confirm the existence of contact apolar dimers. The audio frequency electrolytic conductivity data obtained in dilute solutions ( to 0.03 mol dm-3) reveal a minimum in the molar conductances of both salts at around 0.01 mol dm-3. Simultaneously we have found that the solution permittivity and viscosity both increase as concentration increases. These results are interpreted in terms of alternative models either involving triple ions or neglecting triple ions. The analyses suggest that the effect of increasing solution permittivity and viscosity as concentration increases is not an important factor leading to the appearance of conductivity minima. Instead, the important factor may be attributed to either ion-dipole and/or dipole-dipole interactions that result in nonelectrolyte activity coefficients significantly less than unity.
Introduction The search for a new electrolyte-solvent system that could give the best suitable combination for the construction of secondary lithium batteries is a problem of pragmatic importance in the area of portable power sources. On the theoretical side, the knowledge of the structure and dynamics of the species in solution is a prerequisite for a nonempirical approach to the selection of electrolyte solutions for use in lithium batteries. It was with these ideas in mind that we investigated the properties of LiAsF, and LiC104 in methyl acetate. The methods selected for these studies were infrared spectroscopy, and audio frequency electrolytic conductance. Since various species (ions, ion pairs, and higher agglomerates) may predominate over specific concentration ranges, the advantage of combining the above three 0022-3654/89/2093-4374$01.50/0
experimental techniques is that we were able to investigate electrolyte solutions over the extremely wide concentration range of to 0.5 mol dm-3. For example, in dilute solutions (0.1 mol dm-3), there is no doubt that neutral complexes form, as revealed by the infrared and microwave relaxation experimental data. When the anion is used as a probe, infrared spectra can detect both contact ion pairs and solvent separated ion pairs and solvent separated dimers (if present), and in which case we designate "spectroscopically free AsF,-" simply as a "noncontact" AsF6- species. Thus the IR band a t 703 cm-' was assigned to either a solvent separated ion pair or a solvent separated dimer. The bands a t 717 and 677 cm-' are assigned, respectively, to a contact species (e.g. LiAsF6) and a combination band. In view of the complexity of this band structure, equilibrium constants cannot be calculated. These analyses of the infrared spectra do, however, identify both solvent
TABLE VI: Concentration c (mol/dm3), Ion Pair Concentration c, = c ( 1 - a),Fuoss-Hsia K,, Using Either the Solution Permittivities c = c(c) or eo of the Solvent, ylw= K,/K;, 7:" by the Xu-Obeid Dipole-Dipole Theory," and Distance Parameter d , 104c, M 104cp,M 10"Kp yns IO*^,, cm LiAsF,, c = c(c), K.0 = 1 . O I 7 X 10, 1.14 f.00 0.4619 0.3962 0.5754 1.13 1.00 0.6557 0.9993 0.8970 1.12 1.00 1.8863 1.7382 1.08 1.00
0.9162 6.82 2.7303 0.932 0.9164 0.8842 7.00 6.2688 0.899 0.8840 12.102 0.848 0.8338 0.8326 7.10 0.772 0.7591 0.7570 7.17 22.261 0.653 0.6421 0.6425 7.20 40.062 75.924 0.495 0.4867 0.4880 7.22 0.3034 7.17 0.311 0.3058 137.17 7.07 0.1499 0.150 0.1475 229.22 LiAsF,: c = co = 6.66; K: = 1.045 X 10, 1.143 1.00 0.4619 0.3962 1.132 1.00 0.6557 0.5754 0.999 0.8970 1.1 I6 1.00 1.8863 1.7382 1.080 1.00 0.8910 6.73 2.9345 2.7303 0.932 0.8918 6.94 6.5954 6.2688 0.901 0.8622 0.8634 0.8141 7.07 12.582 12.0986 0.851 0.8144 0.777 0.7435 0.7443 7.18 22.973 22.260 0.662 0.6334 0.6322 7.25 41.144 40.061 77.724 75.916 0.507 0.4852 0.4834 7.34 7.39 0.3028 140.41 137.08 0.314 0.3005 7.31 235.67 227.32 0.104 0.09952 0.09958 LiC104: t = c(c); K: = 8.25 X IO7 0.2801 0.2749 10.75 1.00 1.00 0.3714 0.3652 10.40 0.5119 0.5044 9.886 1.00 0.9933 0.9824 9.173 1.00 0.9501 5.03 3.1350 7.840 0.9501 3.1563 0.9199 4.93 3.3807 3.3582 7.580 0.9195 6.1761 6.1450 7.397 0.8964 0.8937 5.00 7.255 0.8792 0.8773 4.98 6.6262 6.5936 0.8691 5.15 13.873 7.171 0.8690 13.920 6.914 0.8379 0.8363 5.09 14.270 14.220 6.608 0.8008 0.7986 5.19 26.345 26.275 6.872 0.8328 0.8352 5.27 27.388 27.318 6.110 0.7404 0.7387 5.25 44.894 44.797 5.24 49.593 5.866 0.7109 0.7100 49.698 5.948 0.7208 0.7183 5.39 78.814 78.681 0.6072 5.33 5.038 0.6105 106.05 105.88 0.5512 5.29 114.54 4.580 0.5551 114.73 5.32 0.5037 155.09 154.86 4.179 0.5064 5.28 199.23 198.93 3.270 0.3963 0.4021 0.3705 5.26 3.070 0.3720 208.46 208.14 0.3014 5.24 259.67 2.482 0.3008 260.07 5.20 0.2122 344.73 344.18 1.796 0.2176 LiC104: c = eo = 6.66; K: = 8.24 X IO7 0.2801 0.2749 10.76 1.00 0.3652 10.37 1.00 0.3714 1.00 0.5044 9.89 0.5119 9.17 1.00 0.9933 0.9824 0.9514 5.04 3.1350 7.84 0.9515 3.1563 0.9222 4.94 3.3582 7.59 0.921 1 3.3807 5.02 6.1450 7.40 0.8981 0.8996 6.1761 0.8841 5.OO 6.5936 7.26 0.8811 6.6262 0.8731 5.17 13.872 7.18 0.8714 13.920 6.92 0.8398 0.8414 5.1 I 14.270 14.220 0.8050 5.22 26.274 6.62 0.8034 26.345 6.89 0.8362 0.8351 5.29 27.388 27.318 6.13 0.7439 0.7441 5.29 44.894 44.797 5.89 0.7148 0.7135 5.28 49.593 49.698 5.99 0.7269 0.7258 5.46 78.814 78.681 5.09 0.6177 0.6190 5.42 105.88 106.05 4.64 0.5631 0.5602 5.38 114.54 114.73 155.09 154.86 4.25 0.5158 . 0.5144 5.44 0.4061 5.42 3.35 0.4066 199.23 198.93 5.41 208.14 3.15 0.3823 0.3795 208.46 5.42 2.57 0.31 19 0.3085 260.07 259.67 0.2282 5.44 0.2294 1.89 344.73 344.18 "The series expansion was truncated at n = 23. The calculated yi",cd were evaluated in steps of d, of 0.01 X IO-* cm, approximating to the nearest ync. 2.9345 6.5954 12.582 22.973 41.144 77.724 140.41 235.67
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separated and contact ion pairs, and possibly a solvent separated dimer (the solvent separated ion pair and dimer are spectroscopically indistinguishable as explained above). Microwave spectra which reflect differences in moments of inertia of dipolar species are particularly sensitive to the presence of apolar species, and in fact the present results suggest the existence of dimers at concentrations above 0.1 mol dm-3. The relaxation spectra analyzed above confirm the existence of both contact and solvent separated ion pairs and indirectly confirm the
Salomon et al. existence of contact dimers. An order of magnitude value for Kq can be extracted from the microwave spectral data.
Acknowledgment. This work was supported by the Army Office for Scientific Research, Durham, N C under Grant No. DAAG29-85-KO051. The authors express their gratitude for generous support. Registry No. LiAsF,, 29935-35- 1; LiCI04, 7791-03-9; MeOAc, 7920-9.
COMMENTS Reply to Comments on “The Kinetic Mass Action Law Revisited by Thermodynamics” Sir: In a Comment’ by Garcia-Colin about our paper,* two arguments were developed. First, it was claimed, quoting ref 1, that ”the statement that the kinetic mass action law (KMAL) can be derived by appealing to a minimum number of assumptions, implying by this that those used are only of thermodynamic nature, is untenable”. Second, it is argued by Garcia-Colin that, still quoting him, “the derivation proposed in ref 2, is at best equivalent to the standard one given in several well-known monographs on the s ~ b j e c t ’ ’ . ~We , ~ show briefly in this reply that neither of these two arguments is well founded. 1. We never have asserted that KMAL can be derived by using exclusively thermodynamic arguments. Anyone working in thermodynamics is fully aware that the complete knowledge of a constitutive equation requires in addition experimental observations and complementary information from other theories, such as statistical mechanics and quantum mechanics. This was furthermore explicitly written in ref 2 at the end of section 3. It is also claimed by Garcia-Colin that expression 3.17 in ref 2 cannot be considered as the kinetic mass action law since it ( I ) Garcia-Colin, L. J . Phys. Chem. 1988, 92, 3017. (2) Lebon, G.; Torrisi, M.; Valenti, A. J . Phys. Chem. 1987, 91, 5103. ( 3 ) de Groot, S. R.; Mazur, P. ”+equilibrium Thermodynamics; Dover: New York, 1984; Chapter IO. (4) Haase, R. Thermodynamics of Irreversible Processes; Addison-Wesley: Reading, M A , 197 I ; Chapter 2.
cannot be shown that w(T,p,$)is equal to the quantity kpr(@JJ”a. As stated above, it is clear that we cannot establish such a result. We need for that what Garcia-Colin calls a mechanistic assumption, but it is worth noticing that the coefficient w ( T,p,s) is perfectly compatible with an expression like Garcia-Colin’s eq 8 in ref I . Moreover, and this is shown in section 4 of the Lebon et al. paper,* the only property that is provided by thermodynamics concerns the sign of w . 2. The second criticism mentioned by Garcia-Colin is that “the results of ref 2 are a t best equivalent to those already given in the l i t e r a t ~ r e ” . The ~ , ~ latter references concern the classical theory of irreversible thermodynamics which predicts a linear relation between the rate of advancement of the reaction E and the affinity A. As stated explicitly in ref 3 and 4, such a result is only valid in the close vicinity of equilibrium. In ref 2 , we have obtained a result that is valid in the nonlinear regime, Le., far from equilibrium.
Institute of Physics LiPge University B 4000 LiPge, Belgium
G . Lebon*
Dipartimento di Matematica Uniuersita di Catania Catania, Italy
M. Torrisi A. Valenti
Receiced: January 9, 1989; In Final Form: January 31, 1989
