COMMUNICATIONS TO THE EDITOR
2137
Electrical Conductance of Concentrated Aqueous Solutions and Molten Salts:
Correlation through Free Volume Transport Model
Sir: Following a successful correlation of electrical conductance data for nitrate melts,l both glass-forming and otherwise, by means of the equation A
=
AT-”z exp(-k/(T
- To))
(1)
(derived from the free volume transport model of Cohen and Turnbull,2 Tobeing the temperature below which the liquid contains no free volume, A and k are constants), we have investigated the possibility of extending this type of interpretation of transport phenomena to concentrated aqueous solutions. Such an extension is strongly suggested by reports that, e.g., hot Mg(N03)2-H20solutions, when sufficiently concentrated, yield glassy solids on ~ o o l i n g . ~ . ~ We have measured the electrical conductance of Mg(N03)2-Hz0solutions as a function of temperature and water content in the range Mg:H2O = 1:6 to 1:2.9, and of molten Ca(NOJ2.4Hz0as a function of temperature, and find eq. 1 is satisfied within experimental error with the same limitations found in the case of the water-free Ca(N03)z-KN03me1ts.l The To values (theoretical glass transition temperatures) obtained are, not surprisingly, dependent on the charge concentration, ranging from 201’K. for Ca(NOa)z.4Hz0to 244OK. for Mg(N03)~.2.9H20;cf. 306-330’K. for KN03-Ca(N0J2 glasses. The important finding, however, is that one can predict To for the 1:4 liquids,6 to within experimental error ( f5’), from the To 21s. cation charge-to-radius-ratio plot obtained experimentally for the water-free Ca(NO&KN03 melts by making the reasonable assumption that the predominant cations in the liquid at this compo& t i o n are quasi-spherical M(H20)2+ (M2+ = Mg2+, Ca2+) species with effective radii ( 2 ~ ~ ~ rMa+). 0 Furthermore, the constant k of eq. 1 for the aqueous nitrates is the same within experimental error as for the Ca(N03)z-KN03 melts. Finally, plots of E , vs. T (e.g., Figure 6 (ii) of ref. 1) for the water-free eutectic melts Li, Na, K, NOS6and Na, K, NOZ, NO8 form a natural extension to higher temperatures for E, os. T plots of the aqueous melts of about the same To value, thus linking the temperature dependence of conductance of the aqueous and nonaqueous glassforming liquids and emphasizing the lack of distinction between them. Thus, despite some ambiguity arising from the treatment of M(H20)d2+ species as spherical ions, these
+
observations strongly imply that both the electrical conductance behavior and the glass-forming ability of these solutions may best be interpreted by regarding the aqueous melts as molten salts of large (;.e., weak field) cations. This appears to be a fruitful concept, as it leads one to predict tetrahedral NiC12- complexes in, e.g., hot (100-150’) highly concentrated MgClz solutions by analogy with NiCLZ- in molten CsC1.’ The existence of these complexes, previously unobserved in aqueous systems, is readily demonstrated by test tube experiments and has now been verified by spectroscopic methods.*S9 The free volume approach offers an interpretation of both the temperature dependence of liquid transport properties and the phenomenon of glass formation, and, as glass-forming ability is apparently quite common among concentrated aqueous solutions, this approach may provide a useful new view of concentrated electrolyte solutions in general. (1) C. A. Angell, J. Phys. Chem., 64, 218, 1917 (1964). (2) M. H. Cohen and D. Turnbull, J . Chem. Phys., 31, 1164 (1959). (3) J. W. Mellor, “Comprehensive Treatise on Inorganic and Theoretical Chemistry,” Vol. IV, Longmans, Green and Co., London, 1940, p. 380. (4) We now 6nd that many solutions of highly soluble salts have concentration ranges which are glaa,+forming on sufEcient cooling (e.g., quenching into liquid nitrogen) although it seems that only concentrated Mg(N0s)rHzO solutions have high enough glass transition temperatures to yield brittle glasses at room temperature. (5) The 1:4 compositions are the simplest to treat since the higher water content solutions were not glass-forming and thus TOcould not be determined experimentally, and for lower water contents the choice of species and their effective radii raises difficulties. (6) L. A. King, C. C. Bissell, and F. R. Duke, J. Electrochem. Soc., 111, 720, (1964). (7) D. M. Gruen and R. L. McBeth, J . Phys. C h m . , 63, 393 (1959). (8) C. A. Angell and D. M. Gruen, to be published. (9) NiCl2- complexes are not found in concentrated CaClz solutions, however, because the Ni2+ competes successfully with the Ca*+for the hydration sheath. (10) Currently on leave at Argonne National Laboratory, Argonne, Ill.
DEPARTMENTOF METALLURGY UNIVERSITYOF MELBOURNE PARKVILLE N.2. VICTORIA AUBTRALA RECEIVED APRIL 9, 1965
Concerning the Reaction NO2
NO
+ Oz
C. A. A N G E L L ~ ~
+ NO* +
Sir: Kistiakowski and co-workers1s2have postulated this reaction as a result of their studies of the flash photolysis of nitrogen dioxide and the reaction of nitrogen atoms with nitrogen dioxide. Volume 69, Number 6 June 1966
