1666
J. Phys. Chem. 1990, 94, 1666-1669
be of great value in demonstrating that these conditions are satisfactory for the problem a t hand. When engaged in the analysis of real data pertaining to potentially heterogeneous systems, one may be tempted on the basis of low-precision data to espouse a simple model that predicts the two or three components observed in the analysis of the decay data. It is important to collect data to high precision in order to examine critically the proposed model. Even then, it may not be possible to rule out the presence of an underlying distribution of lifetimes since the success of the MEM and ESM in differentiating the discrete case from the continuous distribution is critically dependent on the separation of lifetimes. The great danger lies in attaching physical significance to the discrete components recovered in the study of complex heterogeneous systems. If the system in fact is described by a continuous distribution of lifetimes, then a two- or three-component fit merely provides an empirical
representation based on what is in fact an inadequate fitting function and the parameters are in general physically meaningless. It perhaps should be mentioned that we find the four-component model to be in general indistinguishable from a continuous distribution unless the components are widely separated in lifetime space. High-precision data will in general not reveal the fact that the four-component exponential function is not a good model, nor will the MEM or ESM resolve four closely spaced discrete components. Simulations are required to establish whether the separation between lifetimes required for resolution is present. Acknowledgment. The authors acknowledge the financial support of the Natural Science and Engineering Research Council of Canada. Registry No. SDS,151-21-3;pyrene, 129-00-0;3-methylindole, 8334-1; CU", 15158-11-9.
Solubltity of CoCI, in Molten NaCI-AICI, Chien Wai: Ira Bloom, Deanna Caveny,l and Milton Blander* Argonne National Laboratory, Chemical Technology Division/Materials Science Program, 9700 South Cass Avenue, Argonne, Illinois 60439-4837 (Received: May 15. 1989)
Measurements of the solubility of CoCl, (in mole fraction units) in molten NaCI-AlC13 solutions ranged from 2.2 X IO-" to 6.1 5 X lo-, in solvent compositions ranging from a mole fraction of A1Cl3 (XAlcl,)of 0.502-0.669. The steep increase in the solubility of CoCl2 as a function of XNcb is well-represented by the coordination cluster theory. A solubility product (in ion fraction units) for CoC1, of 4.7 X IS deduced from the measurements. The insolubility of CoClz near the 50-50 solvent composition is a consequence of the fact that the complexing of solid CoCl, by AIC13 to form Co(AlCl,), in solution is considerably weaker than the complexing of 2NaCl(I) to form 2NaAIC14(1).
Introduction Molten chloroaluminates are ordered liquids and have striking physicochemical properties.'" For example, at the 50-50 mol % NaCI-AlCI, composition, one can describe the ordering phenomenon in the melt in terms of the formation of a very stable tetrahedral A1Cl4- anion to form molten NaA1CI4. Charge ordering of this 1:l salt leads to the high probability that the Na+ cations are nearest neighbors of the AICl, anion and, hence, the next-nearest neighbor of an AI3+ cation. Thus, charge ordering leads to the type of physical ordering of the cations described in one dimension by ABABAB .... This phenomenon can be correlated with both chemical and physical One of the most striking properties observed is the very sharp minimum in solubility and maximum in activity coefficients of solutes at the 50-50 mol % composition. Activity coefficients are very large and can change by more than 1 order of magnitude going from 50 to 60 mol % A l a 3 . In fact, solutes, which interact with NaCl and AIC13 more weakly than these two solvent components interact with each other, are often insoluble at the 50-50 mol % composition because of a large maximum in the activity coefficients of the solute. This property of the activity coefficients is general for ordered liquids, and the magnitude of the effect is larger the stronger the interaction between the monovalent chloride and AIC1, (Le., the more negative is the excess free energy of mixing of the solvent components). In this paper we describe the influence of ordering on the solubility of CoCI, in NaCI-AICI, melts as a function of composition. Since the solvent can be 'Present address: Department of Chemistry, University of Idaho, Moscow, ID 83843. 'Summer 1985 Student Research Participant from University of Southern Mississippi, Hattiesburg, MS 39401.
0022-3654/90/2094- 1666$02.50/0
described by both physical and chemical models, we will examine both types of models. It is well-known that the tetrachloroaluminate ion, A1C14-, disproportionates very little at the 50-50 mol % composition of the NaCI-AlCl, system.'-" Values of this disproportionation constant for the reaction
+
2AlC14- s A12C17- CI-
(1)
range from 1.06 X at 175 OC to 5.83 X 10" at 355 0C.4 In physical terms, the disproportionation constant is a measure of the disorder in this ordered system; the larger this constant, the greater the disorder. This disproportionation reaction can be redefined in physical terms. Because of charge ordering, the nearest neighbors of anions are predominantly cations. Thus, the species AIC14-, Al,Clf, and CI- all have sodium cations as nearest neighbors. If Na+ is A and A13+ is B, then AICl, designates AB next-nearest-neighbor pairs, AI2Cl7- designates BB next-nearest-neighbor pairs, and C1- designates AA next-nearest-neighbor pairs where the two A's are Na+ cationic nearest neighbors of C1-. Consequently, eq 1' is a chemical way of expressing this physical 2AB
$
BB + AA
(1')
( I ) Tremillon, B.; Letisse, G. J. Electrocmnal. Chem. 1968, 17, 371. (2) Torsi, G . ;Mamantov, G . Inorg. Chem. 1971, I O , 1900. (3) Fannin, Jr., A. A.; King, L. A.; Seegmiller, D. W. J . Electrochem. Soc. 1972, 119, 801. (4) Boxall, L. G.; Jones, H.L.; Osteryoung, R. A. J . Electrochem. Sot. 1913, 120, 223. ( 5 ) Cyvin, S . J.; Klaeboe, P.; Rytter, E.; 0ye, H. A. J . Chem. Phys. 1970, 52, 2116.
( 6 ) Saboungi, M.-L.; Rahman, A.; Blander, M . J . Chem. Phys. 1984,80, 2 141-50.
0 1990 American Chemical Society
The Journal of Physical Chemistry, Vol. 94, No. 4, 1990 1667
Solubility of CoCI2 in Molten NaCI-AICI,
TABLE I: Mole Fractions of Melt Components Saturated with Solid
I
CoCI, at 175 OC XNaCl
xAICl,
0.498 0.486 0.464 0.453 0.428
0.502 0.5 13 0.533 0.541 0.560 0.575 0.628
0.405 0.31 1
XCOCI, 2.2 x 10-4 7.2 X 10-4 3.2 x 10-3 5.1 x 10-3 1.2 x 10-2 2.0 x 10-2 6.15 X IO-'
XAlcl, (in solvent) 0.502 0.514
0.535 0.544 0.567 0.587 0.669
process. The advantage of the chemical approach is that the ordering phenomenon can be expressed in terms of an additive solution of NaCI, NaAICI,, and NaA12C17. Because of the near ideality of mixtures of three salts with a common cation and different anions, such a description of ordering can be very precise. This melt is a relatively simple molten salt. Upon addition of AICI,, the AICI4- ions react to form AlzC17- ions4s5 AICl4-
+ AIC13 F! A12C1,-
(2)
with a formation constant (using anion fractions for AIC1,- and AlzC17-and mole fractions for AICI,) that ranges from 2.4 X lo4 a t 175 O C to 3.8 X IO2 at 355 0C.4 Consequently, at 175 "C, over 99% of the AICI, added to NaAICI, is present as A12C17-ions with XAI,-I, = 0.51, well over 90% with X A I C I ,= 0.63, and about 80% with XAIcI,= 0.67. This property greatly simplifies the chemical description of these melts, which can be described as additive ternary solutions of NaCI, NaAICI,, and NaAlZCl7with some Al2CI6species that is negligible (
