CALCIUM NITRATETETRAHTDRATE-CADMIUN NITRATETETRAHYDRATE
2287
Conductance, Viscosity, Density, Proton Magnetic Resonance Spectra, and Glass Transition Temperatures of Calcium Nitrate Tetrahydrate-Cadmium Nitrate Tetrahydrate Melts. An Ideal Fused Salt System by C. T. Moynihan, C. R. Smalley, Department of Chemistrg, Calijornia State College at Los Angeles, LOEAngeles, Calijornia 90052
and C. A. Angell, and E. J. Sare Department of Chemistry, Purdue University, Lafayette, Indiana 47907
(Received November 11, 1968)
Conductance, viscosity, density, pmr spectra, and glass transition temperature measurements have been performed for the binary hydrate melt system calcium nitrate tetrahydrate-cadmium nitrate tetrahydrate. Chemical shift us. composition plots for the water proton resonance indicate that in these melts the Ca2+ and Cd2+ ions are equally hydrated. Glass transition temperatures are a linear function of cation fraction of Cd2+ and decrease from 222 to 210" as X w + increases from 0 to 1. Both conductance and fluidity exhibit a non-Arrhenius temperature dependence for all compositions and have been described in terms of threeparameter equations of theformsA = AAT-''~ exp[--ka/(T - TO,A)] and @ = A+T-'/' exp[-k+/(T - TO,,)]. It is shown that the parameters in these equations have a simple dependence on composition such that To,a = To,+for each composition, k~ and JG, are composition independent, and In Ah and In A, show identical linear us. X w + parallel similar plots for the glass transition dependences on composition. Plots of T0.a and TO,+ temperature, T,. Both conductance and fluidity isotherms show negative deviations from additivity as a function of composition, primarily as a result of the composition dependence of the To,aand To,,parameters.
I n the past few years a number of physical-chemical investigations of the properties of molten calcium nitrate tetrahydrate systems have been carried out. These include studies of cond~ctance,'-~viscosity,' density,l83,4 acid-base and electrochemical reactions,516 proton magnetic resonance ~ p e c t r aultrasonic ,~ absorption,899 Cd2+ diffusion coefficients,'O hydration and association equilibria," and glass transition temperature12 in Ca(N03)2.4HzO and its solutions with other anhydrous nitrates. Much of the interest in calcium nitrate tetrahydrate melts stems from the fact that they may be considered quasi-fused salts in which the hydrated calcium ions are taken as a fundamental component of the melt. Pmrj7c o n d ~ c t a n c e and , ~ , ~density4 studies have shown the utility of this concept and indicate that in solutions of Ca(N0&.4H20 with salts whose cations have low charge : radius ratios, e.g., KN03, virtually all of the waters of hydration are retained in the coordination sphere of the more polarizing Ca2+ ion. An even more interesting aspect of molten calcium nitrate tetrahydrate solutions is that they exhibit extremely low stable or metastable (undercooled) liquidus temperatures for molten salts of their ionic strength. Hence they allow exploration of molten salt properties at corresponding temperatures quite low in comparison to those attainable in most anhydrous melts. A direct consequence of these low liquidus temperatures is that the temperature dependence of the transport properties
of calcium nitrate tetrahydrate melts is not Arrhenius. Rather, the temperature dependence of conductance and fluidity is well described by equations of the form A = AAT-'/'exp[-kk,/(T
-
TO,^)]
(1)
and
4 =
1
- =
?I
A,T-"'exp[-k+(T
- To,,)]
(2)
where A is equivalent conductance, 4 is fluidity, 7 is viscosity, T is absolute temperature, and AA,A,, kA, k,, To,a,and To,, are empirical parameters. Equations of (1) C. T.Moynihan, J . Chem. Phgs., 70, 3399 (1966). (2) C. A. Angell, J. Electrochem. Soc., 112, 1224 (1965). (3) C. A. Angell, J. Phys. Chem., 70, 3988 (1966). (4) J. Braunstein, L. Orr, and W. Macdonald, J . Chem. Eng. Data, 12, 415 (1967). (5) R.-P. Courgnaud and B. Trerhillon, BUZZ. Sac. Chim. Fr., 752 (1965). (6) R.-P. Courgnaud and B. Trehillon, ibid., 758 (1965). (7) C. T.Moynihan and A. Fratiello, J . Amer. Chem. Soc., 89, 6546 (1967). (8) S. Petrucoi and F. Fittipaldi, J . Acoust. Soc. Am., 42, 517 (1967). (9) G.8 . Darbari and S. Petrucci, J . Phys. Chem., 73, 921 (1969). (10) J. Braunstein, L. Orr, A. R. Alvarez-Funes, and H. Braunstein, J.Electroanal. Chem., 15, 337 (1967). (11) J. Braunstein and H. Braunstein, paper presented at 156th National American Chemical Society Meeting, Atlantic City, N. J., Sept 8-13, 1968. (12) C.A. Angell, E. J. Sare, and R. D. Bressel, J. Phys. Chem., 71, 2759 (1967). Volume 78, Number 7 J u l y 1969
2288
C. T. MOYNIHAN, C. R. SMALLEY, C. A. ANGELL, AND E. J. SARE
the form of 1 and 2 can be derived from theories which the same temperature agreed within 0.5 cps (0.008 take the free volume or the configurational entropy as ppm) or better. the important quantities in setting the temperature Glass transition temperatures, Tg,were determined ~ ~ molten mixtures quenched to the glassy state in dependence of the liquid transport p r o p e r t i e ~ . ~ v l ~ -for The To parameters have been interpreted14as theoretical liquid nitrogen by the DTA method described preglass transition temperatures at which the configuraviously.12 Sample compositions were determined by tional entropy of the liquid would vanish via a seconddirect weighing. Heating rates between 9 and 21'/ order thermodynamic transition for equilibrium cooling min were employed, and a doubling of the heating rate of the liquid on an infinite time scale. For finite coolwas found to increase the measured value of Tg by ing rates the experimental glass transition inevitably about 2". Tg values determined at constant heating intervenes at temperature Tg( T , > To) as a kinetically rate were reproducible t o within f0.5". Pure cadmium imposed reflection of the reversible transition which nitrate tetrahydrate melts could not be quenched to would occur at TO. Equations 1 and 2 have been apthe glassy state, but glasses could be formed from of transplied e x t e n ~ i v e l y l - ~ ~ ' ~t ,o~the 6 - ~description ~ Cd(NOa)z-HzO solutions with concentrations on either port properties in fused salts and aqueous solutions. side of the tetrahydrate composition. Consequently, Empirically it is found that the non-Arrhenius behavior the T, result reported below for pure cadmium nitrate implicit in these equations is observed in the temperatetrahydrate was interpolated (to within f0.5") from ture interval TO- ZTO. a plot of T, us. composition for Cd(KO&-HzO solutions Reported here are conductance, viscosity, density, in this concentration range. pmr, and glass transition temperature studies of binary Conductivity, viscosity, and density measurements solutions of molten calcium nitrate tetrahydrate (mp were carried out in a 20-1. water bath whose tempera42.7') and cadmium nitrate tetrahydrate (mp 59.4'). tures were measured with an NBS-calibrated platinum The near equivalence of the ionic radii of Ca2+ and resistance thermometer and a Leeds and Korthrup Cd2+ (0.99 us. 0.97 A), which is in turn reflected in the Mueller bridge. The conductivity cell was a Pyrex Unear equality of the equivalent volumes of the two tube with the arms connected by a length of 2-mm i.d. suggests that melts (68.0 us. 67.4 cma/equiv at 40°)19820 capillary and with platinized Pt electrodes dipping into the Ca2+ and Cd2+ions should be equally hydrated in the two arms. The cell constant was 56.70 cm-1 as mixtures of the two tetrahydrates. Hence, it was determined by calibration with 0.1 demal KC1 solution expected that mixtures of the two tetrahydrates should at 25". Conductivity measurements were carried out be nearly ideal, save for the mass difference between the at 1000 cps with a Leeds and Northrup Jones conductwo hydrated cations, and that the transport studies tivity bridge. Three Cannon-Ubbelohde dilution viswould furnish an assessment of the composition decometers of cell constants 0.04962,0.2498,and 2.871 cSt/ pendence of the parameters in eq l and 2 for a nearly sec were used for the viscosity measurements. Densities ideal binary mixture. were measured in a dilatometer of approximately 26-cm3 capacity described previous1y.l Melt compositions Experimental Section for conductivity, viscosity, and density studies were determined by directly weighing the two components Reagent grade Mallinckrodt calcium nitrate tetrainto an erlenmeyer flask. The flask was then tightly hydrate and cadium nitrate tetrahydrate were used capped, the components melted and mixed in a hot without further purification. Comparison of the water bath at about 60', and the conductivity cell, density data for the two pure melts used for the conviscometers, and dilatometer filled with the molten ductance and viscosity measurements with the precise mixture. The conductivity, viscosity, and density density us. composition data of Ewing and Mikovksy'e measurements were all carried out simultaneously in the and Ewing and Herty20 showed that the actual H20/Ca same water bath. and H20/Cd mole ratios were 4.09 f 0.01 and 4.07 f 0.01, respectively. Results Samples for proton magnetic resonance spectra The results of the pmr measurements as a function measurements were prepared by weight directly in 5of Cd2f cation fraction are shown in Figure 1 for several mm nmr tubes; 0.005 cation fraction of tetramethylammonium nitrate was added to each sample as an (13) M. H. Cohen and D. Turnbull, J . Chem. Phys., 31, 1164 (1959). internal chemical shift standard, and the sample tubes (14) G. Adam and J. H. Gibbs, ibid.,43, 139 (1965). were tightly capped. Before running the spectra the (15) C. A. A.ngel1, J. Phys. Chem., 68, 1917 (1964). samples were melted in a hot water bath and agitated t o (16) C. A. Angell, L. J. Pollard, and W. Strauss, J . Chern. Phys., 43, 2899 (1966). dissolve the tetramethylammonium nitrate and mix the (17) C. A. Angell, J. Phys. Chem., 70, 2793 (1966). two major components. The pmr spectra were run on a (18) C. A. Angell, J . Chem. Phys., 46, 4673 (1967). Varian A-60 spectrometer as described previously.' (19) W. W. Ewing and R. J. Mikovsky, J . A m . Chem. Soc., 72, Duplicate chemical shift measurements performed at 1390 (1950). different times on samples of the same composition at (20) W. W. Ewing and C. H. Herty, J . Phys. Chem., 57, 245 (1953). T h e Journal of Physical Chemistry
2289
CALCIUM NITRATETETRAHYDRATE-CADMIUM NITRATETETRAHYDRATE
-2,0
-.
t
000
025 0.50 0.75 Cation Fraction Cd+2
1.00
Figure 1. Chemical shifts of the water proton resonance in calcium nitrate tetrahydrate-cadmium nitrate tetrahydrate melts with respect to the internal standard tetramethylammonium ion resonance at 60 Mc. The (CH3)rN+ peak occurs upfield from the HnO peak.
temperatures. Only one water proton peak was observed for all compositions and temperatures. The ordinate of Figure 1 is the chemical shift of water protons in parts per million with respect to the internal standard (CHs)hN+ protons. The tetramethylammonium ion resonance occurs at higher fields than the water resonance. The chemical shift isotherms are linear with composition within the limits of experimental reproducibility, 0.5 cps (0.008 ppm). The glass transition temperatures, T,, for heating rates of S0/min are shown in the upper portion of Figure 2. Within experimental error T , appears to be a linear function of Cd2+cation fraction. Densities were linear functions of temperature within experimental error (0.05%) and are given in Table I
'9.0Cation Fraction Cdt2 0;2
04
d6
68
3
Figure 2. Glass transition temperatures (T,) and transport for constant k h and k+ values us. parameters (T0.h and To,+) composition in calcium nitrate tetrahydrate-cadmium nitrate tetrahydrate melts. The T, result for XCd2+ = 1.0 is interpolated from T , measurements on more and less concentrated solutions of Cd(NO& in water.
in equation form. The equivalent volumes exhibit slight (0.2-0.3% at X C d n t = 0.5) negative deviations from additivity. Equivalent conductance and viscosity results are presented in the form of Arrhenius plots in Figures 3 and 4. Below 20-25" the undercooled melts rich in cadmium nitrate tetrahydrate tended to crystallize spontaneously, so that it was not possible to obtain data over as extensive a temperature range as for the melts rich in calcium nitrate tetrahydrate. The conductance and viscosity data have been computer fitted by a least-squares procedure t o equations of the form of 1 and 2 to the nearest 0.5" in TO. The best fit parameters are given in Table 11. The parameters for pure Ca(SO& 4.09H20 have been calculated from those determined' for Ca(KO&.4.04H20 by a method described p r e v i o ~ s l y , ~where ~ ~ ~ J it* was shown empirically that to a very good approximation the isothermal dependence of the conductance and fluidity on the water content in Ca(NOa)2 solutions could be described by varying the To parameter alone, such that dTo/diV = 12.9" l./equiv. I n this case the difference in the H20/Ca ratio of 0.05 can be compensated for by lowering TOby 1.2". The data presented in Figures 3 and 4 for X C d l r = 0 are likewise those determined for Ca(NO& e4.04HZO corrected to the composition Ca( N O B *4.09H20a )~ I
Table I: Parameters for Density Equations and Equivalent Volumes at 40' for Ca(NOs)z.4.09Hn0-Cd(NOs)z .4.07H20 Melts. Density Equation: p (g/cm3) = a - bt ("C) Cation
-
fraction
Cd2'
0.000 0.253 0.501 0.750 1,000
a
1.765 1.908 2.045 2.191 2.322
b
0.00088 0,00088 0,00098 0.00114 0.00114
Ve a t 40°, cma/equiv
68.70 68.35 68.27 68.00 68.06
Volume 73, Number 7 July 1969
C. T. MOYNIHAN, C. R. SMALLEY, C. A. ANGELL, AND E. J. SARE
2290
Table I1 : Best Fit Parameters for Eq 1 and 2 for the Equivalent Conductance and Fluidity of Ca(NOs)a~4.09H~0-Cd(N03)n.4.07H~0 Melts
_---
Cation fraction CdP +
0.000" 0.253 0.501 0.750 1,000 a
-Fluidity, P-1
Equivalent conductance, cma/ohm equiv
Ah
kA
3600 3281 3773 4282 3825
625.12 585.63 603.30 619.35 587.86
Std dev in lnh
TO,^
199.8 202.5 198.5 195,O 194.5
0.002 0.002 0.002
0.003 0.003
7
A+
k4
Tot4
Std dev in In 4
8 428 8 295 14 ,000 7,523 6,410
676.51 654.25 766.78 600.07 554.07
203.8 204.5 192.0 204.5 205.5
0.002 0,001 0 004 0.001 0.003 ~
Parameters calculated from data for Ca(NOs)z.4.04HzO, ref 1.
Also given in Table I1 are the standard deviations of In A or In 9 from the best fit curves of the form of eq 1 or 2 for each composition. These standard deviations are in turn approximately equal to the fractional deviations of the experimental points from the best fit curves (A In x = Ax/x) and show that the internal precision for the temperature dependence of A or 9 for each composition is of the order of 0.1-0.401,. Isotherms of A and 9 as a function of composition at 20" are shown in Figure 5. The scatter of the points in the isotherms from smooth curves drawn through them is of the order of 1-2% and is indicative of the accuracy of the A and 9 determinations. The reason for the relativity poor accuracy in comparison to the precision of the data is the difficulty of controlling exactly the water content of the melts and the very high sensitivity of A and I$ to small changes in water content at these high concentra-
3x0-
Figure 4. Arrhenius plots of viscosity in calcium nitrate tetrahydrate-cadmium nitrate tetrahydrate melts.
tions.av18 At 20" in calcium nitrate tretrahydrate, for instance, a change in the H20/Ca ratio of only 0.01 gives rise to a change of about 2% in A and 9.
Discussion
O'i
a@
0 003 .02 29
30
3.1
3,2
3.3
3.4
55
1031 T PK)
Figure 3. Arrhenius plots of equivalent conductance in calcium nitrate tetrahydrate-cadmium nitrate tetrahydrate melts. T h e Journal of Physical Chemistry
36
One may assume that the observed position of the water proton peak in the pmr spectrum of the calcium nitrate tretrahydrate-cadmium nitrate tetrahydrate melts is a weighted average due t o rapid water molecule and/or proton exchange of the chemical shifts of the water protons in the hydration spheres of the Ca2+and Cd2+ions. Since the water/total cation mole ratio is constant in these melts, the linearity of the chemical shift vs. composition plots in Figure 1 indicates that the Ca2+and Cd2+ions are equally hydrated. The experimental uncertainty of 0.008 ppm in the chemical shift measurements corresponds to an uncertainty in the relative hydration numbers of k O . 1 mol of HzO at the
CALCIUM NITRATETETRAHYDRATE-CADMIUM NITRATETETRAHYDRATE
02
Q4
0.6
0.8
Cation Fraction Cd+2 Figure 5. Equivalent conductance and fluidity isotherms a t 20” for calcium nitrate tetrahydrate-cadmium nitrate tetrahydrate melts.
0.5 composition. Hence our assumption that from a structural viewpoint the calcium-cadmium nitrate tetrahydrate melts should be fairly ideal is supported by the equal hydration numbers found from the pmr measurements. (An alternative explanation has been suggested for the pmr results, namely, that when Cd(XO& .4Hz0 is added to Ca(NO3)2.4H20,water in the hydration shell of Cd2+ is displaced by T\To3-, giving rise to “free” water in the melt. This would presumably account for the increase in the conductance and fluidity of the melts with increasing cadmium concentration: “free” water would exist in a nitrate ion environment and could be expected to have a proton chemical shift similar to that found in concentrated KN03 or (CH&NN03 solutions. Results cited in an earlier publication,’ however, show that in concentrated KN03 or (CH&NNO3 solutions the water proton resonance occurs well upjield (by about 0.6 ppm) from that in calcium nitrate tetrahydrate. Hence the production of “free” water in the melts would be expected to result in a concentration induced change in 6 opposite in direction to that shown in Figure 1 or a t least to cause the 6 vs. X C d n + plots to exhibit a XCd2+ =
229 1
marked departure from linearity in the positive direction.) The glass transition temperature results show a decrease in T , of around 12” in going from pure calcium t o pure cadmium nitrate tetrahydrate. This decrease may be explained in terms of the correlation that has been noted by Ange1112r21and o t h e r P between T , (or To)and the characteristic Debye temperature, 013, for a substance. This correlation has been rationalizedz1 by postulating that cooperative rearrangements are induced among the particles of an amorphous, glassy phase by the interaction of energetic, Brillouin zone boundary phonons. These interactions become important in the region of OD, and the induced rearrangements are manifested by the glass transition and the appearance of fluid properties in the amorphous phase. The Debye temperature, 033, is directly proportional to characteristic Debye frequency, VD, and hence is expected to show an r n - ’ I 2 dependence on the effective masses of the component particles of the amorphous phase. Consequently one predicts the decreases in T, observed here with increases in the average cationic mass. Normally one would expect to find for a system like calcium-cadmium nitrate tetrahydrate a fairly monotonous variation with composition in the empirical parameters of eq 1 and 2 used to describe the transport properties. Inspection of the best fit parameters in Table 11, however, fails to reveal such a trend, save perhaps that AA, A,, kA, IC,, To,*, and To,, are for the most part all, respectively, of about the same magnitude and do not seem to vary greatly with composition. The reason for this apparent lack of a trend is that there is a high correlation among the parameters in eq 1 and 2, so that if the transport data do not cover too extensive a range in magnitude and the Arrhenius plots (cf. Figures 3 and 4) do not show too marked a curvature, one finds that there are a number of A-k-To sets which will give an adequate description of the data. As an example, one can fit the conductance data shown in Figure 3 for X C d l i = 0.501 to within a standard deviation in In A of 0.004 (twice that for the best fit) with T o , A values anywhere in the range 195.0-201.5. The corresponding ranges in An and kA are 4548-3214 and 644-569, respectively. It appears likewise, from this example, that the Toparameters are the ones most precisely determined by the curve fitting procedure and that small variations in To will produce much larger variations in A and k . Consequently, it is not surprising that for the systems under consideration, where in light of the composition dependence of Tg one does not expect a large composition dependence of TO(vide infra), no meaningful trends are apparent in the composition dependences of the A and k terms. (21) C.A. Angell, J. Amer. Ceram. SOC.,51, 117 (1968). (22) R. H. Cole and D. W. Davidson, J. Chem. Phys., 20, 1389 (1952).
Volume 79, Number 7 July 1960
C. T.MOYNIHAN, C . R. SMALLEY, C. A. ANGELL,A N D E. J. SARE
2292
An empirical r ~ l e ~ that ~ ~ hasJbeen ~ found ~ ~ ~ to hold J ~ for a large variety of fused nitrates and chlorides and concentratcd aqueous solutions states that the kA and k , terms are composition independent for systems in which the composition changes do not alter the melt structure in too radical a fashion. According to the Adam-Gibbs derivation14 of eq 1 and 2, the k terms are given by
k=- N A p S , * RAG‘, where N is Avogadro’s number, S,* is the minimum configurational entropy per particle required for a mass transporting rearrangement, A p is a free-energy barrier opposing the rearrangements, and AC, is the change in heat capacity of the liquid at the glass transition. Adam and Gibbs suggest that changes in A p from system to system may be off set partially by parallel changes in AC,. If one couples this with the fact that the value of k may be varied over fairly wide limits and still be consistent with an acceptable fit to eq 1 and 2, the ability to define a “universal” k term which describes the Iowtemperature transport properties of a large variety of systems is not difficult to understand. I n the derivations of eq 1 and 213,14the To term emerges as a thermodynamic rather than a kinetic parameter. Hence, values of Toderived from measurements of different transport properties of the same liquid should be identical. This prediction of equal To’s for different transport properties has been tested only in a few cases for concentrated aqueous solutions’ and organic l i q ~ i d s ~ ~ but ~ ~appears ~ - ~ 6to hold fairly well. One obvious way to order the A , k, and To parameters for the conductance and fluidity of calcium-cadmium nitrate tetrahydrate systems is to invoke the empirical rule that the kA and k, terms should be composition independent. To do so it is necessary to select a value of To for one composition, determine the corresponding A and k terms, and match the A , TO, and IC terms for other compositions to this under the constraint of composition invariant k,, and k,. For our conductance and fluidity data, a table was constructed for each composition by computer selection of TOvalues in the range 190-205 at Tointervals of 0.5 and calculation of the corresponding A and k parameters which gave the best fit to the data for each particular Tovalue. Because the data for pure Ca(NOa)2.4.09H20 cover a fairly extensive temperature range, this composition was chosen to fix the comparison values of kA and k,. I n light of the above discussion, we selected the comparison values 202.5, of kA and k, for the same value of To,,, and TO,,, which falls in between the best fit values for this composition. For the other compositions the values of A and To were chosen from the tables of A-k-To sets to correspond to the k,, and k, values for the pure Ca(N03)z.4.09H20for TO= 202.5. The results of this data treatment are shown in Table 111. Although the standard deviations for the The Journal of Phyaical Chemistry
fits with equal k A and IC, terms are larger than the best fit standard deviations, the parameters in Table I11 with one exception still describe the data within 1% or better. The real justification for the somewhat arbitrary construction of Table 111, however, lies in the empirical and theoretical correlations that can be achieved in this fashion. The first of these correlations is that within 2’ or better TO,h = To,,for each composition, as required by the theoretical derivations of eq 1 and 2. P\/lore important, the TOvalues in Table 111 show an approximately linear variation with composition that within the uncertainities in T,, T o , A , and To>, parallels the composition dependence of the experimental glass transition temperatures, as is shown in Figure 2. Since the glass transition temperature, Tg, may be taken as an isoviscous point (7 at T , .u 1013P), eq 2 predicts that for systems with the same k, terms the composition dependence of T , must parallel that of To, if one ignores small differences in the A , terms.26 The k,/k, ratio for the data in Table I11 is 1.18, the significance of which has been discussed previously. The ordering of the A-k-To parameters in Table I11 also reveals a definite trend with composition in the preexponential terms, corresponding to an increase of about 30% in both A , and A , between pure calcium and pure cadmium nitrate tetrahydrate. Plots of In Ah and In A , vs. X C d z + are h e a r and parallel within the uncertainties of 1-275 in the absolute magnitudes of the transport properties as a function of composition (cf. Figure 5 ) ) showing that the same factors determine the composition dependence of the pre-exponential terms for both conductance and fluidity. At the moment we are not able to explain why Ah and A , should increase with increasing X C d 2 + , for one would expect the larger mass of the Cd2+ ion to lead to the reverse of the observed effect.13 It may be that the composition dependence of the Ah and A , terms is related to differences in the lability of water or nitrate ions in the coordination shells of Ca2+and Cd2+. The differences in the proton chemical shifts for water coordinated to Ca2+and to Cd2+shown in Figure 1 indicates a difference in the strength of the interactions between the water and the respective cations. This effect may manifest itself in the transport properties which depend on short time scale rearrangements in the liquid, although it is apparently not Iarge enough to cause a departure from randomness in the average (23) D. J. Denney, J . Chem. Phys., 30, 159 (1959). (24) D. J. Denney, ibid., 27, 259 (1957). (25) D. W. Davidson and R. H. Cole, ibid., 19, 1484 (1951). (26) An alternative method of ordering the A-k-To parameters as a function of composition would be to pick a To value for one composition and choose the To values for the other compositions on the basis of the variation of Tgwith composit*ion. Treatment of the calciumcadmium nitrate tetrahydrate transport data in this fashion, again using To = 202.5 for; X C d r + = 0, gives a set of parameters with standard deviations of the same magnitude as those in Table 111 and ~ C Aand kg terms which are constant to within &5%.
CALCIUM KITRATETETRAHYDRATE-CADMIUM NITRATETETRAHYDRATE
2293
-
Table 111: Parameters for Eq 1 and 2 for the Equivalent Conductance and Fluidity of c a ( R ’ 0 ~4.09HzO-Cd(NOa)z~4.07H20 )~ Melts Selected to Give Constant k~ and kg Values. The k~ and k g Values for Cation Fraction Cd2+ = 0.000 for TO,A= TO,,= 202.5 Were Selected As the Standard Values to Be Matched at Other Compositions Cation fraction Cdz +
0.000 0.253 0.501 0.750 1,000
Equivalent conductance, cms/ohm equiv------
Fluidity, p -1
7 -
AA
3063 3377 3577 3790 3911
kA
591.86 591.51 591.87 591.92 593.03
TO,A
Std dev in In
202.5 202.0 199.5 197.5 194.0
0.007 0.002 0.002 0.004 0.003
distribution of water molecules between the two cations. As shown in Figure 5 , both the A and qi isotherms for the calcium-cadmium nitrate tetrahydrate system show negative deviations from additivity of about 11% at 20”. These negative deviations become more pronounced at lower temperatures and less pronounced a t higher temperatures, so that above 60” the A and qi isotherms are very nearly those predicted on the basis of additivity. The negative deviations from additivity in this system can be analyzed in terms of the functional forms used to express the temperature dependence of the transport properties (eq 1 and 2) and the variation with composition in the empirical parameters tabulated in Table 111. More particularly, it may be shown that the linear decrease in Towith increasing cation fraction of Cd2+is primarily responsible both for the relatively large changes in A and qi as a function of composition and for the negative deviations from additivity of the isotherms. The linear dependence of In Ah and In A, on X C d l l . accounts for only about 30% of the total change in A and qi between the extremes of the isotherms and leads to a predicted composition dependence of A and qi at constant temperature which itself is nearly linear in XCdZ+.
Our findings here underscore the necessity of understanding the transport behavior of fused-salt systems at low temperatures where eq 1 and 2 apply if we are to gain insight into the details of these transport processes a t higher temperatures, above 2To. I n this case, analysis of the composition dependence of the conductance of the reasonably “ideal” calcium-cadmium nitrate tetrahydrate system in terms of the composition dependence of the parameters in eq l has revealed that negative deviations from ideality extremely reminiscent of those observed a t higher temperatures for most anhydrous binary monovalent cation nitrate systerns’s ,27-31 can occur in the face of a very simple composition dependence of these parameters (constant k,; TO,^ and In A , linear functions of Xcd2+). The empirical utility of eq 1 for expressing composition dependences of equivalent conductance is likewise clear. These same anhydrous binary nitrate melts, however, reveal positive deviations from additivity in their
4
9,197 10,405 10,548 11 , 519 12 ,220
__--___-__-
k@
TO>,
Std dev in In
694.51 697.92 698.93 697.46 697.10
202.5 201.5 197.5 196.0 193.0
0.004 0,009 0,005 0,005 0.012
+
fluidity isotherm^,^^*^* in contrast to the negative deviations observed for the system considered here. This contrast between the conductance and fluidity isotherms for the higher temperature melts serves to point up the difficulties inherent in any attempt to explain totally the transport properties of most fused salts. It appears that most of these systems display their liquidus regimes in a temperature range intermediate between the low-temperature extreme in which transport behavior is described well by eq l and 2 and the hightemperature extreme in which the melt begins to assume the properties of a molecular liquid, and conductance, but not fluidity, decreases with increasing temperat ~ r e . ~Fortunately, ~ - ~ ~ some of the characteristics of the low-temperature transport behavior do seem to be carried over into the normal liquidus regions of some fused salts, and analysis of the composition dependence of the parameters of eq 1 and 2 has yielded useful qualitative correlations in the case of the monovalent nitrates.18 It is hoped that future studies of model systems which have stable or metastable liquidus regions in the interval To-2To will continue to yield insight into the perplexing problem of fused salt transport properties.
Acknowledgment. This work was supported in part by a National Science Foundation Institutional Grant (California State College a t Los Angeles) and in part by a grant from the Office of Saline Water (Purdue). (27) L. A. King and F. R. Duke, J . Electrochem. Soc., 111, 712 (1964). (28) B. De Nooijer and J. A. A. Ketelaar, Rec. Trav. Chim., 83, 573 (1964). (29) H. C. Cowen and H. J. Axon, Trans. Faraday SOC., 5 2 , 242 (1956). (30) J. Byme, H. Fleming, and F. E. W. Wetmore, Can. J . Chem., 30, 922 (1952). (31) 5. Forcheri, V. Wagner, and E. Berra, Electrochim. Metall., 3, 123 (1968). (32) G. Murgulescii and S. Zuca, Electrochim. Acta, 11, 1383 (1966). (33) L. F. Grantham and S. J. Yosim, J . Chem. Phys., 45, 1192 (1966). (34) L. F. Granthnm and S. J. Yosim, J . Phys. Chem., 72, 762 (1968). (36) J. D. Kellner, ibid., 71, 3254 (1967). (36) J. D. Kellner, ibid., 72, 1737 (1968).
Volume 73, Number 7 July 1989
