2384
A. S. DWORKIN, H. R. BRONSTEIN, AND M. A. BREDIG
The Electrical Conductivity of Solutions of Metals in Their Molten Halides.
VIII, Alkaline Earth Metal Systems1
by A. S. Dworkin, H. R. Bronstein, and M. A. Bredig Chemhtry Diviswn, Oak Ridge National LabOTatOTg, Oak Ridge, Tennessee
(Received February 11, 1966)
~~
In the alkaline earth metal-metal halide systems MX2-M (M = Ca or Sr, X = C1, Br, or K, is similar to that in the sodium systems where the value of dK/dNM decreases as the metal Concentration increases. For explanation, an equilibrium 2M2+ 2e S (M2)2+is assumed similar to 2Na+ 2e s Na2 for the sodium systems. The doubly charged alkaline earth molecule ions ( M z ) 2 + contain M in a dimer of oxidation state I rather than zero (Na2). The species (I\12)2+ are analogous in electronic structure to the neutral Na2 molecules. Their equilibrium with the F-center-like electrons is concentration dependent. The systems BaBr2-Ba and BaIz-Ba, on the other hand, are similar to the potassium systems. They give an increasing slope of specific conductivity with increasing metal concentration. This is attributed to the much lower stability of the dimer traps K2 and (Ba2)2+. As a result, electron orbital overlap occurs at lower metal concentration. Observed salt freezing point depressions agree with this interpretation if solubility of the metal in the solid is considered.
I), the concentration dependence of the specific conductivity,
+
Introduction The specific electrical conductivity K of solutions of calcium in calcium chloride was found to increase as the metal concentration, N M ,is increased.2 However, as in the sodium-sodium halide melts, dK/dNM decreases as N M increases. This was attributed to the gradual trapping, in pairs, of the single relatively mobile, probably F-center- or anion-like, electrons3 by the reaction 2e2Ca2+ e ( C Z ~ ~ )Le., ~ + , through formation of molecule ions, (Ca2)2+(cf. HgZ2+ and Cd22+). These represent the dimeric form of the otherwise uncommon oxidation state (I) of calcium. Their equilibrium with the mobile electrons and the normal cations Ca2+ depends on metal concentration. The explanation for the observed conductance behavior was thus analogous to that proposed earlier4 for solutions of sodium metal in molten sodium halides. There the “single bond” of the neutral group I metal molecules, Na2 (oxidation state zero, M O ) , presumably of similar electronic structure as the proposed group I1 metal molecule ions, ( C S ~ ~ was )~+, proposed to represent the state in which the electrons are trapped in pairs. Preliminary measurements in the Sr-SrCh solutions2 indicated a situation intermediate between that of the Na-NaX and K-KX sys-
+
The J O I L T of ~Physical ~~ ChemistTy
+
t e m ~ . The ~ K-KX systems exhibit an accelerating rise in conductivity with increasing metal concentration. This is consistent with the assumption that in the solution K2 molecules are less stable than Naz molecules as they are known to be in the vapor state. The conductivity of the Ba-BaX2 systems, which like the K-KX systems exhibit far greater metal solubility than the Na-NaX and Ca-CaX2 systems, was predicted2 to behave similarly to that of the K-KX systems. In the present study, we have measured the specific conductivity of solutions of Ca, Sr, and Ba in their respective bromides and iodides and made additional conductivity measurements in the Sr-SrC12 system. These measurements allow a comparison with the alkali and rare earth metal-halide sy~tems.2~~~6 Freez(1) Research sponsored by the U. S. Atomic Energy Commission under contract with Union Carbide Corp. (2) A. 5. Dworkin, H. R . Bronstein, and M. A. Bredig, Discussions F a r d u y SOC.,32, 188 (1961); see also M. A. Bredig, ibid., 32, 257 (1961). (3) (a) M. A. Bredig, J. W. Johnson, and W. T. Smith, Jr., J . A m . Chem. Soc., 7 7 , 307 (1955); (b) K. S. Piteer, ibid., 84, 2025 (1962). (4) H. R. Bronstein and hl. A. Bredig, ibid., 80, 2077 (1958); J . Phys. Chem., 65, 1220 (1961).
ELECTRICAL CONDUCTIVITY OF METALS IN THEIR MOLTEN HALIDES
2385
ing-poin t depression measurements were also made in an attempt to derive from the activity of the solvent salt thus obtained further information on the nature of the solute species. Previous data were incomplete and based mainly on gross phase diagrams of doubtful reliability.
I
I
I
I
I
Experimental Section The molybdenum parallel electrode assembly used to measure the conductivity of the metal-metal halide solutions, the sapphire capillary cell used with the pure salts, and the experimental procedure have been described in detail previously.2 The freezing-point depression measurements were made in a manner also reported earlier7 except that the solutions were held in tantalum metal capsules about 3 in. in length and 0.63 in. in diameter with a thermocouple well protruding about 0.75 in. into the sohtion. The capsules were filled and welded in a drybox under helium. The salts were prepared from reagent alkaline earth carbonates or hydroxides which were dissolved in the appropriate aqueous acids. The hydrates were crystallized, crushed, and vacuum-desiccated at room temperature over Pz06for 2 days after which they were dehydrated by gradual heating to about 400" over a period of 3 days. The chlorides and bromides were then melted in quartz in an atmosphere of their respective dry halogen gases, purged with Ar, and filtered into a quartz bulb. The iodides were melted under vacuum in a molybdenum boat. All of the salts and metals were free of foreign metals as determined spectrographically. The halides showed no alkalinity from pyrohydrolysis.
Ca-CaBrZat 790" 0 1.53 0.65 1.86 0.95 1.94 1.45 2.02 1.70 2.05 1.85 2.10 2.1 2.14 2 . 3 (satd) 2.16
Results and Discussion
Ca-CaIz at 830'
600'
u 1
2 3 mole % Ca
4
f 2 3 mole % Sr
4
I
2
I
I
3 4 5 mole % Ba
I
O
6
7
8
Figure 1. Specific conductivity in molten alkaline earth halides as a function of metal solute concentration. (For the SrClrSr and the barium systems, measurements extended beyond data shown, cf. Table I.)
Table I: Specific Conductivity, Metal-Halide Systems
K,
in Alkaline Earth
Mole
X,
Mole
XI
Mole
X,
metal
ohms-' om-'
metal
ohms -1 em-'
metal
ohms -1 em -1
%
%
Sr-SrClz at 900" 2.05 2.63 3.36 3.6 5.4
0 1.05 3.1 3.6 7 . 2 (satd)
Sr-SrBrz at 700'
The specific conductivity of the pure salts as measured with the sapphire capillary cell agreed with the measurements of Bockris, et to within f1%. The results of the specific conductivity measurements for the solutions of the metal in the salt are given in Table I and Figure 1. Measurements were discontinued in the barium systems at metal concentrations far below saturation when the electrical resistance of the solution became so low that a large experimental error was introduced by the greatly increased relative contribution of the electrode resistance to the total resistance. (The Ba-BaClz system could not be measured in the present apparatus because of the high melting temperature of BaCI2, 960"). Saturation of the salt solution with metal was determined in samples taken from the liquid salt phase after excess metal had been added. This concentration agreed well in most cases
I
1
1.24 1.35 1.38 1.44 1.48 1.54 1.57 1.61 1.64 3.8(satd) 1.71 0 0.70 0.90 1.15 1.50 1.95 2.25 2.7 3.0
0 0.6 1.05 2.25 2.5(satd)
0.99 1.50 1.71 2.22 2.32
Sr-SrIz at 600" 0 0.7 1.4 2 . 0 (saM)
0.63 0.82 0.89 0.93
%
Ba-BaBrz at 870" 1.24 2.16 4.13 6.9 ...
0 1.0 2.8 5.2 24.0 (satd)
Ba-BaIz at 740" 0 0.75 0.62 0.91 1.32 1.5 2.14 3.1 6.3 4.0 11.6 9.2 16.2 18.8 f 1 19.8 33.0 f 3 22.0 (satd) ...
(5) A. S. Dworkin, R. A. Sallach, H. R. Bronstein, M. A. Bredig, and J. D. Corbett, J . Phys. Chem.,67, 1145 (1963). (6) A. 8. Dworkin, H. R. Bronstein, and M. A. Bredig, ibid., 67, 2715 (1963). (7) J. W.Johnson and M. A. Bredig, ibid., 62, 604 (1958). (8) J. O'M. Bockris, E. H. Crook, H. Bloom, and N. E. Richards, Proc. Roy. SOC.(London), A255, 558 (1960).
Volume 70,Number 7 July 1966
2386
A. S. DWORKIN, H. R. BRONSTEIN, AND M. A. BREDIG
with that concentration at which the conductivity retype of crystal structure most likely interferes with the mained constant despite further additions of metal. simple interpretation of the melting-point depression. As can be seen in Figure 1, the rate of increase of the On the basis of vapor pressure measurements for the specific conductivity with increasing metal concentrasystems M-MC12 (M = Ca, Sr, and Ba), van Westention decreases in the calcium and strontium systems. burg and Peterson13recently proposed that the dissociaThe conductivity in the barium systems shows an action (ionization) of the dissolved alkaline earth metal celerating rise as predicted2 which is thought to be caused according to M + &I2+ 2e- was complete. (Alterby a relatively lower stability of (Ba2)2+ions, leading to nately but less l i k e l ~ , ~the , ’ ~oxidation-reduction reaction M hf2++.2M+ would also produce two “new” much higher concentrations of single, less localized mobile electrons and also slightly higher concentrations particles, Le., particles not present in the pure solvent of metal ions, from the equilibrium (Baz)2+S 2Ba2+ salt.) This method has the great advantage of giving 2e-. The results for the Sr-SrCl2 solutions are slightly directly the activity of the solute and is of course not different from the preliminary data2 in that above 2 affected by the problem of solid solutions. No tendency to electron interaction such as formation of (M22+) mole % metal a reversal in curvature is now observed, is shown in these measurements below 3, 7, and 5 mole similar to that in the ?;a-NaBr and Na-NaI systems at % metal in the Ca, Sr, and Ba systems, respectively. similarly high metal concentrations and temperature^.^ Our conductivity and cryoscopic measurements on the This reversal was attributed to the increasing imporCa and Sr chloride solutions do not seem to suggest tance of the general orbital overlap of the metal electrons much more electron interaction than might be com(beginning formation of a “conduction band”) as compatible with a reasonably limited sensitivity of the pared with the trapping of electrons in localized twovapor pressure measurements to such interaction. A electron bonds. comparison of the bromide systems which show intenIt is quite reasonable to assume that even the prosive curvature of the conductivity us. concentration posed alkaline earth molecule ions Ca22+and Srt2+are curves (Figure 1) , but for which vapor pressure measurenot very stable but in dilute solution dissociate into ments are not available as yet, will be more significant. M2+ and two mobile, F-center-like electrons which are The eutectic compositions obtained from the freezresponsible for the conductivity increase. This type of ing-point data are in good agreement with those deelectrons would be expected to behave thermodynamirived from our conductivity and solubility measurecally as more or less distinctly separate particle~.~*~b. ments at slightly higher temperatures. Agreement is As a result, measurements of the depression of the also good with available data reported by Staff a n ~ o n ~ ~ freezing points of the salts on the first additions of metal and by Peterson and Hinkebein.15 On the other hand, should yield a cryoscopic number n of 2, from n = various data of the older literature, and more recent [(Tm- T)/Nmetal](ASm/RTm). With increasingN,,t,l, n phase diagrams proposed by Emons, et aZ.,16and includshould decrease from 2 toward 1 with a rate depending 2M2+ $ (M2)2+, ing the suggestions that ions such as Cas2+and even mainly on the equilibrium 2eSr2+ occur, are totally at variance with our results as ie., the liquids should be convex to the concentration well as with those of the other investigators mentioned. axis. Unfortunately, much supercooling coupled with The phase diagrams of the alkaline earth metal-metal the short concentration range available for measurement weakened the reliability of the observed freezingpoint lowering. This and the possibility of heat-ofmixing effects as well as of metal solubility in the solid (9) A. S.Dworkin and M. A. Bredig, J. Phys. Chem., 67, 697 (1963). salt prohibits a detailed quantitative evaluation of the (10) A. S. Dworkin and M. A. Bredig, J. Chem. Eng. Data, 8 , 416 liquidus curvature in terms of the equilibrium proposed (1963). above. However, as can be seen from the example (11) B. D . Lichter and M. A. Bredig, J. Electrochem. SOC.,112, 506 (1965). shown in Figure 2, while the existence of this equilibrium (12) E, Mollwo, Nachr. Wissensch. Ges. G6Ltingen II, 1 (6), 79 as suggested by the conductivity results is not clearly (1934). supported, it is not contradicted by the cryoscopic meas(13) J. A. van Westenburg, Iowa State University of Science and Technology, Abstracts of Doctoral Theses, pp 1129-1 130; University urements. For Sr-SrC4 (ASm = 3.39 eu/mole), n Microfilms, Inc., Ann Arbor, Mich., Order No. 64-9291. appeared to be slightly less than unity. (Earlier,2 we (14) L. Staffansson, Ph.D. Thesis, London, 1960. had obtained n = 2 on the basis of ASm = 7 eu/mole, (15) D. Peterson and J. A. Hinkebein, J . Phys. Chem., 63, 1360 estimated previous to our calorimetric measurementsQ (1959); J. A. Hinkebein, Ph.D. Thesis, Iowa State College, Dissertation Abstr., 19, 1932 (1958), University Microfilms, Inc., Ann Arbor, and discovery of the solid-state transition.1° In this Mich,, Card No. 58-7557. case, as in the system Ca-CaF2,11 high solubility of the (16) H. H. Emons, et al., 2.Anorg. AZZgem. Chem., 323, 114 (1963); metal in the solid salt SrC1212which also has the fluorite 2. Chem.,2, 313, 377 (1962).
+
+
+
+
~~
The Journal of Physical Chemistry
ELECTRICAL CONDUCTIVITY OF METALS IN
THEIR
MOLTEN HALIDES
2387
740
Table I1 : Estimated Metal Solute Equivalent Conductance at Infinite Dilution, AM- (mho cmz), in Molten Halide Solutions, M-MXZ and hf-MX
735
OC
730
+ EUTECTIC
7250
I
I
I
...
-04
.02
.03
'
I
.i2
Figure 2. Salt melting point depression in the calcium-calcium bromide system.
halide systems will shortly be discussed by us in greater detail elsewhere on the basis of our own measurements. It is of considerable interest to consider the behavior of the mobile electrons in the most dilute solutions where their mutual interaction is minimal. Figure 1 shows a steeper increase in conductivity on the addition of metal to the salt to occur in the bromide systems of calcium and strontium than in either the chloride or iodide systems. Table I1 shows this in a slightly different fashion, namely, through the values of the equivalent conductance of the solute metal AM (or, at infinite dilution, AM-). As first defined el~ewhere,~ AM = (KsolnVsoln - (1 - NM)KsaltVsalt)/NM (Or AMdK/WM (lim NM+ 0) X Vsalt), where V is the equivalent volume. The values of AM- for the bromide solutions far exceed those of both the corresponding chloride and iodide solutions. A much weaker but qualitatively somewhat similar effect had been found in the alkali metal systems also listed in Table 11, the main difference being that for the alkali metals Alllm in the iodide systems is still larger than AM- in the corresponding bromide ~ y s t e m s . ~However, there the increase to the iodides is not nearly as large as the trend for the change from the fluoride to the bromide systems would lead one to expect (for NaI-Na: -16,000 instead of an extrapolated value of at least 25,000 and for KBr-K: 8100 instead of at least 15,000 ohm-1 cm2 equiv -I).
M
F
c1
Br
I
Ca Sr Ba Na K
... ... ...
890 1600
...
6000 2800
4,200 5,100 2,830 13,000 6,500
860 1,570 1,300 16,000 8,100
800
...
The occurrence of the maximum of electron mobility in the bromide systems, or of the lag in the iodide systems, is probably of rather complex origin. Conceivably, it is mainly connected with the divergent influences, upon the electron mobility, of the size and of the polarizability of the halide ion. With increasing atomic number of the halide ion, its size is thought to inhibit increasingly the motion of electrons by increasing their jump distance, while its simultaneously increasing polarizability facilitates such motion. That the effect is so much stronger in the alkaline earth than in the alkali metal systems may be due to the much higher ratio of the number of halide ions to that of the metal ions. Another effect is apparent from Table I1 and Figure 3. In the alkaline earth bromide and iodide systems, there is a drop of AM- in going from the strontium to the barium solutions after a rise in going from the calcium to the strontium systems. (A similar effect would probably have been observed for the barium chloride solutions, had they been accessible to measurement.) This behavior of the alkaline earth solutions may be considered similar to that of the alkali metal systems. Here AM" was also found to decrease in going from the Xa (corresponding to Sr) to the K (corresponding to Ba) systems. However, the possible correspondence of the lithium to the calcium solutions with respect to a low AM- has not been accessible to measurement because of the low solubility of Li in its halides. As in the case of the effect of the halide ion above, a tentative explanation may be given. The size of the cation may influence the electron mobility in two opposing ways thus leading to the conductivity maximum at Na or Sr. For larger cations, the average distance for electron jumps from cation to cation is greater. Greater distance means smaller jump pr~bability.'~-'~ On the other hand, the tighten-
(17) W. F. Libby, J . Phys. Chem., 5 6 , 863 (1952). (18) S. A. Rice, Discussions Faraday soc., 32, 188 (1961). (19) D. 0. Raleigh, J . Chem. Phys., 38, 1677 (1963).
Volume 70, Number 7
J u l y 1966
A. S. DWORKIN, H. R. BRONSTEIN, AND M. A. B R E D ~ G
2388
F
CI
Br
I
Figure 3. Estimated metal solute equivalent conductance at infinite dilution, AMm(mho eme), in molten halide solutions, M-MXs and M-MX.
ing of the electron shell of the anion in the field of the larger cations is smaller; i e . , the anion polarizability
The Journal of P h y s h l Chemistry
which controls the bridging action of the anion in electron transfer" is greater. Finally, a comparison of our results with a very recent attempt to study the electrical conductance of calcium solutions in molten calcium chloride by Emons and Richterz0shows their results to be considerably different from ours, more so, in fact, than their Figure 4 which includes but misrepresents our early data2 would seem to indicate. For instance, for Acam one obtains from their data at 850" the value of only 200 mho cm2/equiv of calcium metal, not very much larger than some ionic equivalent conductances in molten salts, and only onefifth of our value of nearly 1000 (Table 11). Their apparatus did not permit sampling the solution during the measurements. The use of an inert gas flow from an inlet immediately above the crucible suggests that considerable losses of somewhat volatile calcium metal from the melt to colder parts of the apparatus may have occurred.
Acknowledgment. Our thanks are due to D. E. Lavalle for the preparation of the pure anhydrous salts used in our measurements. (20) H.H. Emons and D. Richter, 2. Anorg. Allgem. Chem., 339, 91 (1965).
