Relative Cation Mobilities in Potassium Chloride-Lithium Chloride Melts1"Sb
by Cornelius T. Moynihan and Richard W. Laity F ~ i c k(,'hemica1 I,uhorntor?j, Princeton ~.'niceruity,I'rinceton,
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(Received .Ifuy 19, tBGk)
I-littorf-typo transforcnce cxporiiiicnts have been used to dcteriiiine the relative rnobilitics of I,i- arid Ifound to he c ~ l u s l (within ut)oiit 15!&) at, all conc:ciit,rat,ioiis. It will be seen iti t h c prctscliit coiiitii~itiicatiori that, this "rule'! no longer
applies to KC1-LiC1 whcri the experiments are extendcd bcyotid 50 iiiole yo IICI and a correction is inade in one of our earlictr results. Instead, it iiiust be replaced by a less restrictive generalization, whose implications are nonetheless significant arid will be discussed herein. Some results showing the effect of ternpcrature will also bc included. We bcgin, however, with a fuller cxplariatiori of the rnethod used in the experiments. Iiittorf Method in Fused Salts. The proccdurc employed in this investigation rescrribles the Hittorf tnethod for determining transference nunibers in clectrolytic solutions, providing a measure of mobilitics of ionic species relative to components of the electrolyte. It should not be confused with experiments in which a porous disk or other external reference is used to dejine the trarisference numbers.fi In our experimerits a binary fused salt niixture initially having uniform composition throughout the cell is electrolyzed ~~~~~~
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(1) (a) Part of a paper presented at the Symposium on Electrolytic Solutions and Fused Salts, 145th National Aleeting of t h e American Chemical Society, New York, N. Y . , September, 1963; (b) this work is supported through a contract with the U. 8. Atomic Energy Commission. l.'inancial aysistance from an NSF predoctoral fellowship is also gratefully acknowledged. (2) 15. 11. Van Artsdalen and I . S. Yal'fe. .J. P h y s . Chem., 59, 118 (1955). (3) Ixplsin th(>ot)scrwd heats the other. This seetiis to he a less restrictive version of niixing in binary alltali halidc systclins. Imrisdtn of our earlier generalization that the inobi1itic.s of statcd that whcn all t h e cations arc thc satiie. the both like-charged ions are equal a t all conccntrati~ris.~ environnicnt of the anion is on the average syiiiinetrical. In the present form it covers all of the cxatiiples citvd \i'hcn cations of utiqual size are tiiiwd, h o w v w , sonic in that c~otiinnunication,as well ab the exceptions subof the anions (consid(.ring for thc tnonicnt a coliricar sequently noted by Jkrlin and c o - ~ o r k e r s . ' ~At first group like Lit (:l-K+) find thcwsolves hct\wcn clcctric sight the steady decrease in the niobilities of both I,i+ fields of diffrring intensitic~s. In such circumstmces and Kt relative. to C1 - may appmr iricorisisterit with the electron (*loud of a largc anion likc ('I - t m d s to the existence of a niininnuni in the isothcrni of equivabecome polarized iii thc. direction of the stiiallcr of the lent conductance .i for the melt as a whole. Equation two rations. I,utnsdt~n pointed out that this effect 8 shows that t h c v is no inconsistency when the effect gives a riet stability to the iiiixturv which is consistent of concentration is taken into account. In other with thc csotherinic nature of thc. mixing process. words, the lithium iori is such a poor conductor in This siiiiplc niodcl \vas fouiid to givc rctinarltably quannearly pure KC1 that the primary d'fect of adding titative correlation of c.xpclriiricmtal data with ralculaLiCl to the melt is simply to dilute it, thereby lowering tions based solely on ioiiic siw and anion polarizability its total conductance. parameters. We note further that changing the cornposition has It is difficult to apply the Tmnisdcn tnodcl quantitatively to any transport process. Qualitatively, a much greater effect 011 the inobility of Li+ than on that of Kf. Such behavior niay also turii out to be however, it is apparetit that a strmgthcwing of the rathcr general in mixtures of this type. When the attractive force brtwccw a cation and an anion should concentration effect is large enough, it lcads to the lower the mobility of the forincr relative to the latter. nnobility cross-over shown in l'ig 3 and citc.d above The addition of a single potassiiiiii ion to pure LiCI can for two other alkali halide systcms. In addition to affect a substaiitial nutither of lithiuin ions in this way, thesc examples, an extcnsivr SPI irs of mobility results for binarv niixtures of alkali nictal nitrates recentlv Figure 3. Relative roriductanceu of K + and Id ions in KCI- IiC1 rneltti at 640'. +
RELATIVE CATIONMOBILITIESIN KC1-LiC1 MELTS
by inducing polarization in each of the chloride ions in its immediate coordination sphere. Hence the very rapid initial drop in lithium ion mobility as KC1 is added. At higher concentrations of KC1, it is clear that the additional asymmetry introduced by addition of further potassium ions is somewhat smaller, and the lithium ion mobility falls less rapidly. As for the potassium ion itself, its attraction to chloride is weakened by addition of lithiiirm ions. The weakening of its attachment to just one chloride in its coordination sphere does not greatly increase its ability to move, however. Hence, starting from pure KC1, we see thak the potassium ion mobility rises only slowly until a substantial fraction of chlorides in the neighborhood of each potassium have become polarized by having also a lithium neighbor. If changes in relative mobility are to be attributed to changes in the cation-anion bond energy, it is reasonable to expect a corresponding change in the activation energy for conducta,nce. Although accurate evaluations of activation energy are not permitted by the uncertainties in our data, we have combined the results of runs 5-8 and those of runs 11 and 13 with the conductance data of Van Artsdalen and Yaffe2 to obtain the rough estimates listed in Table 11. The heats
Table 11: Approximate Heats of Activation for Relative Cation Conductances in KC1-LiC1 AH*KCL
AH*LiCIv
EK
cal. mole-'
cal. mole-)
0.000 0.310 0.650 1,000
... 3500 3500 3700
2000 2800 5100
...
of activation AH* were calculated from the equations X K C ~ = A K exp(-AaHKcI/RT) and X ~ i c l= A L exp~ ( A H L c I I R T ) . The apparent increase in AH* for each cation with increasing KC1 concentration is consistent with the model, as is the greater rate of increase for Li+.
3317
It is appropriate to consider the concentration dependence of other transport properties in the light of this model. It is known that the viscosity of KC1LiCl mixtures actually shows a negative deviation from additivity of the pure salt values.16 I n view of the behavior of A, this is the opposite of what would be predicted by Walden's rule. A microscopic picture of viscous flow in fused salts, however, does not require cations and anions to move relative to one another, so long as there are some bonds weak enough to permit relative motion of adjacent layers. Specifically, the strengthening of the Li-C1 bond need not inhibit flow substantially, since the two ions can move along together. The weakening of the K-C1 bond does enhance the flow process, nevertheless, by providing points a t which successive layers can shear. Thus the polarization of the anion in fused mixtures also accounts qualitatively for the behavior of viscosity. Similar predictions can be anticipated for the case of self-diffusion, where again, in contrast with electrical mobility, cations are not required, by the definition of the transport property, to move relative to their anion neighbors in order to contribute to the total observed flux. Hence, the diffusioh mobility of lithium ion in this system would not be expected to show such a strong decrease with increased potassium ion concentration. Experiments are under way in this laboratory to test this hypothesis. Some indication of its validity is provided by the self-diff usion results in molten IVaNO3-KNO3 mixtures reported by Lantelme and Chemla. l7 The concentration dependencies of both cation diffusion mobilities appear to be linear, while the electrical conductance of the system shows the usual negative deviation from additivity. The effects in these nitrate mixtures are too small to be unambiguous, however, so that further confirmation of the applicability of the Lumsden model in explaining transport phenomena should be sought in other systems. (16) S. V. Karpachev, A. Stromberg, and V. N. Podchainova, Zh. Obshch. Khim., 5 , 1517 (1935). (17) F. Lantelme and M . Chemla, Bull. sot. chim. France, 969 (1963).
Volume 68, Number 11
November, 1,964
