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Isotope effects in countercurrent electromigration in molten metal halides
J. inorg, nucl.Chem., 1971,Vol. 33, pp. 1561to 1568. PergamonPress. Printedin Great Britain
ISOTOPE EFFECTS IN COUNTERCURRENT ELECTROMIGRATION IN MOLTEN METAL HALIDES H. K A N N O D e p a r t m e n t of Chemistry, T h e University of T o k y o , Bunkyo-ku, T o k y o , Japan
(Received 13 August 1970) A b s t r a c t - T h e mass effects of Li +, K ~, and Rb ÷ in molten LiBr, KBr, RbBr and Rbl have been measured. N e w empirical formulae presented by Saito and Kanno, which correlated the cationic m a s s effects of metal halides with the ionic radius ratio r+/r of the salt, have been developed and interpreted qualitatively in terms of ionic intities in the melt.
INTRODUCTION COUNTERCURRENT electromigration in molten salts has the interesting features that this is one of the most promising methods for high enrichment of metal isotopes in the laboratory scale and that the isotope effect (mass effect) determined in electromigration experiment is a useful key parameter for interpreting the transport mechanism in molten salts. Up to recently, theories of the transport processes of pure molten salts have been discussed in connection with such properties as electrical conductance, self-diffusion and transport number. The term defined by Klemm[1] as mass effect has become recognized as an important parameter in ionic migration. Klemm e t al. as well as Lund6n e t al.[2, 3] have contributed considerably to our knowledge of the transport properties of molten salts by the determination of the mass effects. The semi-empirical formulae derived by Klemm e t al.[4, 5] relating the mass effect with the ratio of the cationic and anionic masses m + / m - have been widely used for attempts of the theoretical interpretation of the isotope effect and for the estimation of the experimentally undetermined value. These formulae, however, have been shown by recent works[6, 7] to be inaccurate for some halides and lacking in generality. As alternatives to these formulae, Saito and Kanno[7] have deduced new empirical formulae to the cationic mass effects of molten halides, which give better applicabilities to the experimental data than Klemm's formulae. The purposes of the present paper are two-fold-to give the experimental results of the mass effects of cations in molten LiBr, KBr, RbBr and Rbl, and to I. 2. 3. 4. 5. 6. 7.
A. Klemm, Z. Naturf. 1,252 (1946). A. Klemm, E. Lindholm and A. Lund6n, Z. Naturf. 7a, 560(1952). A. Lund6n, S. Christofferson and A. Lodding, Z. Naturf. 13a, t034 (1958). A. Klemm, Z. Naturf 6a, 687 ( 1951 ); A. N e u b e r t and A. Klemm, Z. Naturf. 16a, 685 ( 1961 ). S. Jordan and A. Klemm, Z. Naturf. 21a, 1581 (1966). J. R o m a n o s and A. K l e m m , Z. NaturJ~ 19a, 1000 (1964). N. Saito and H. Kanno, Bull. ('hem. Soc. Japan 42, 2409 (1969). 1561
1562
H. K A N N O
develop new empirical formulae by correlating the mass effects with the transport numbers of the molten salts. EXPERIMENTAL
Electromigration cell. In all the experiments, cells of quartz glass were used (Fig. 1). The separation columns had an inner diameter of about 4 mm and were packed with quartz powder (q5 = 0.1 0.2 mm). Materials. LiBr and KBr were of commercial reagent grade. These salts were dried to anhydrous form and used for the electromigration. RbBr and Rbl were prepared from crude RbCI by using the purification method of lshibashi et al.[8]. After electrolysis of the aqueous solution of purified RbCI, the resulted RbOH solution was converted into RbBr and Rbl by adding hydrobromic or hydroiodic acid and subsequent drying. Procedure. The whole cell packed with quartz powder in the part of separation column was on a vertical electric oven. When the cell was electrically heated up to appropriate temperature (for LiBr: 630 or 650°C, KBr: 800°C, RbBr: 750°C, RbI: 730°C), the salt was slowly poured into the cell and was melted. When the melt penetrated to reach the anode, the electromigration was begun. During the electrolysis, bromine gas (in the case of Rbl, iodine gas) was introduced into the cathode compartment, thus suppressing the electrodeposition of alkali metal at the anode. The transported charge was measured with a copper coulometer and the reading of the current during the run. The oven-temperature was controlled and adjusted to pre-determined value by use of an automatic temperature regulator in conjunction with a chromel-alumel thermocouple. After electrolysis and quenching, the electromigration cell was taken out of the furnace and the separation column was cut into a several number of fractions for the chemical and mass-spectrometric analyses. Each fraction was dissolved in distilled water and the resultant solution was filtrated with a filter paper to remove quartz powder, then diluted to 100 ml in a volumetric flask. Chemical analysis. LiBr. The amount of lithium in each fraction was determined by the titration of Br- with standardised AgNO3 solution, using 5% KzCrO4 solution as an indicator. KBr and RbBr. The two methods, the titrimetry of Br- with AgNO3 solution and the gravimetry of potassium ion (or rubidium ion) as potassium (or rubidium) tetraphenylborate, were used. Anode
~
,
Cothode
Br2
Br2~
Corbon
electrodes
/Molten salt
Fig. I. Electromigration cell. 8. M. lshibashi, T. Yamamoto and T. Hara, Bull. Inst. chem. Res. Kyoto Univ. 37, 153 (I 959).
Isotope effects in molten metal halides
1563
Rbl. The same gravimetric procedure as in the RbBr experiment was employed for quantitative analysis of rubidium ion in the sample solution. Isotope ratio measurement.The measurements of isotope ratio were carried out with a solid source mass spectrometer (Atlas CH4 mass spectrometer) by means of surface ionization technique. As a working material, an aliquot of each sample solution was directly used without further chemical treatment. Each analysis consisted of 10-15 determinations. RESULT
The conditions and results of the experiments are summarized in Table 1. As typical examples of the electromigrations, analyses of the experiment Nos. 1,3, 5 and 7 are given in Tables 2-5. F o r calculating the mass effect (IX), the usual well-known equation was used ( 1 ) A u / u = tx ( A m / m )
(I)
= -- { ( N i / N f l ) -- ( N j / N f l ) } ( F ' N ) / Q
where Au is the mobility difference between two isotopic ions, u is the mean mobility of the cations relative to the anions, N , N i ° and N~ are total molar amount of cations and those of cationic isotope (i) before and after the electrolysis in the enriched region near the anode, i a n d j are two cationic isotopes of mean mass (m) and mass difference (Am), F is Faraday constant and Q is the transported charge. LiBr. The mean value of the mass effect* of Li ion in molten LiBr obtained in this work is -0.145. This value is a little smaller in its absolute value than that obtained by Lund6n et a/.[3], but considering the differences of experimental conditions and errors, the result agrees fairly well with that of Lund6n. In Lund6n's experiment, the fused salt chain was cathode (carbon r o d ) + Brz/PbBrJLiBr/anode (carbon rod) or c a t h o d e ( c a r b o n r o d ) + BrJPbBrJLiBr/PbBr2/anode ( c a r b o n r o d ) whereas ours was cathode (carbon rod)+ BrJLiBr/anode
(carbon rod).
The mass effect in a binary system so far investigated is larger than that in a Table 1. Conditions and results of the experiments
Experiment No. 1 2 3 4 5 6 7 8
Salt
Temp. (°C)
LiBr 650 ± 10 LiBr 630-- 10 KBr 800± 10 KBr 800± 10 RbBr 750±10 RbBr 750± 10 Rbl 730-+-10 Rbl 730± 10
Duration (hr) 20 4 25 21 33.5 30 21-5 26-5
Average Sep. column current length (mA) (cm) 88 218 50 75 115 87 168 208
15 12 15 15 12 15 15 15
Transported charge
(× 104C)
Mass effect --p.
0.636 0.314 0.455 0.569 1.384 0.936 1.305 1.967
0.138 ± 0.009 0.153 ±0.010 0.102±0.010 0.094±0-009 0.075±0.008 0-078±0.010 0-085___0.008 0.089±0-008
*The mass effect is generally referred to as large or small in its absolute value.
H. K A N N O
1564
Table 2. Experiment No. 1
Frac. No. 1 2 3 4 5 6 7 8 9 Initial
Frac. length (cm)
LiBr (m-equiv.)
0.9 1.5 1.8 1.7 1,8 1.9 1,6 1-7
1 '326 1.350 1 "562 1 '732 1 '684 1 "932 2"11,z 1 "703 1 '804
7Li/GLi 16-05 ± 0.04 15.04 ± 0.04 14.85 ± 0.04 13-57±0.03 13.22 ± 0.04 12'99 ± 0.04 12.76±0.03 12.55 ± 0 . 0 4 12.31 ± 0 . 0 4 12.31 ± 0 . 0 3
M a s s e f f e c t - t~ = 0.138±0.009.
Table 3. Experiment No. 3
Frac. No. 1 2 3 4 5 6 7 8 Initial
Frac. length (cm)
KBr (m-equiv.)
1.5 1.0 1.3 1.5 1.8 1.9 2-3
1 '658 1 '788 1"103 1 "405 1-207 1 "428 2.072 2.50~
39K/41K 13.20 ± 0.03 13.45 _+0.04 13.55 ± 0.04 13.56 ± 0.04 13.74 ± 0.03 13.78 ± 0.04 13.81 ± 0 - 0 3 13.85 ± 0-03 13.91 ± 0.04
M a s s effect-- I.L = 0-102±0.010.
Table 4. E x p e r i m e n t No. 5
Frac. No. 1 2 3 4 5 6 7 Initial
Frac. length (cm)
RbBr (m-equiv.)
1.6 1.4 1 '3 1.3 1 '0
0"388 1-734 1-909 1 "501 1 "584 1"982 1 "068
M a s s effect - - t t = 0.075 +0.008.
85Rb/S~Rb 2-464 ± 0,006 2-458 ± 0-007 2'513 -+-0.008 2.543 ± 0 - 0 0 9 2.570 ± 0-007 2.581 ± 0 - 0 0 4 2.595 ±0-008 2.597 -----0.008
Isotope effects in molten metal halides
1565
Table 5. Experiment No. 7
F Fac. No.
Frac. length (cml
1 2 3 4 5 6 7 8 Initial Mass effect
1.8 1.7 1.7 1-4 2-3 2.3
Rbl Im-equiv.) 1.10~, t .78~, 1.90z 1.48,2 0.99~ 1.54~ 1.32~ 1.83._,
~'~Rb/~TRb 2"523 ± 0-009 2"523 +0.011 2.516 + 0.005 2-516+0.010 2.517 ± 0.010 2-543 + 0.005 2,575 ±0.010 2.598 +_0,009 2.597 + 0.008
p, -- 0.085 ±0.008.
corresponding simple system. It was observed by Monse and Klemm[9] that the mass effect of Li + in the binary system L i C l + PbCI.,, in which initial lithium content was 5.3 per cent in mole fraction, is - 0 . 3 0 . This value is much larger than that of the corresponding simple system, i.e. pure molten LiCI. T h e y explained that this phenomenon is caused by "mixing effect". In Lund6n's experiments the boundary between LiBr and PbBr2, where the mixing of LiBr and PbBr., had occurred and the mixing effect should affect the mobility of lithium ion, consequently, the mass effect of Li + ion, was used for the calculation of the mass effect. It is, however, not yet established to what extent the measured fractionation is affected by the direct result of the mixing effect. Comparison of the experimental results of Lund6n and the present work indicates that in the case of molten L i B r + PbBr.2 the mixing of the salts had no appreciable effect on the mass effect of lithium ion. KBr. The results obtained in this experiment give the mass effect of K* ion in molten KBr to be -0.098. Jordan and Klemm [9] determined the mass effect of K + ion in molten KCI and obtained for value o f - 0 . 0 7 3 . Therefore, the general tendency of the decrease of the mass effect with decreasing in the radius r+/r Ior mass ratio m+/m -) is also observed in potassium halide series. In molten KNO3 system, Lund6n et a/.[10] measured the mass effect of K ÷ ion to be --0-040. The trend that the mass effect of cation in metal halide is much larger than that in the corresponding metal nitrate also exists for lithium, rubidium and thallium salts [11-13]. RbBr and RbI. As the results of molten RbBr are --0.075 and -0-078, they agree fairly well with those reported by Jordan and Klemm [5]. In the experiments for Rbl, two runs were carried out and the mean value of the mass effect is given to be --0-087. So Rbl is the most efficient among rubidium halides for the production of enriched rubidium isotope S7Rb so far as the mass effect is concerned. 9. 10. 11. 12. 13.
E. U. Monse and A. Klemm, Z. NaturJ~ 12a, 318 (1958). A. Lund6n, C. Reutersward and N. Sj/3berg, Z. NaturJ~ 10a, 279 11955). A. Lund6n, E. U. Monse and N. G. Sj6berg, Z. Natmf. lla, 75 (1956). A. Lund6n,Z. Naturf. 21a, 1581 11966). 1. Okada and N. Saito, Bull. chem. Soc. Japan 43,394 ( 19701.
1566
H. K A N N O
However, Rbl is rather thermally unstable and when melted it slowly decomposes into oxide. This thermal unstability is a large weak point to a long run of electromigration which is necessary for high enrichment. Taking account of all other properties of these halides, e.g. melting point, electric conductance, RbBr may be said to be most appropriate for the long run of electromigration and high enrichment. DISCUSSION
In attempt of finding the relation between the mass effect and other physical constants of molten salt, Klemm e t al.[4] found that between the mass effects and the structures of the salts exists the following coincidence: the mass effects of the monovalent metal halides and of the divalent metal halides which on crystallization form layer lattices belong to one group, while those of the divalent metal halides which on crystallization do not form layer lattices belong to the other. From this fact, they proposed the semi-empirical formula for each group. However, as already mentioned[7], the mass effects recently determined have often shown large deviations from the ones expected by the formula. The deviations have been also observed in the present experiments for molten KBr, RbBr and Rbl. In fact the applicability of new semi-empirical formula derived by Jordan and Klemm[5] for alkali halides is good. Nevertheless, the model, from which the new empirical formula is derived, cannot be applied to divalent metal halides. Accordingly the model can hardly be regarded as adequate. Although isotope effect is the property that stems from the mass difference between isotopic ions, mass effect is not necessary to be the function of the masses of cation and anion because it is a reduced parameter. Success of the attempted correlation of mass effect with ionic radius ratio [7] suggests that the ionic radius is the significant parameter characterizing the ionic migration in molten salt. Many thermodynamic properties of molten salts are successfully explained in terms of ionic radii of the component. Stillinger [ 14] and Mayer [ 15] have shown that the surface tensions, compressibilities and thermal expansibilities of alkali halides are represented by the function of a length parameter, the sum of cation and anion radii. Reiss and his coworkers [ 16] applied the theory of corresponding state with success to the melting points of alkali halides and alkaline earth oxides by correlating the melting point with the anion-cation distance. Probably the reason why the ionic radius is a successful correlating parameter for molten salts is that as a first approximation the potential of interaction between the particles in ionic liquid is pairwise additive and is represented fairly well by a Coulomb potential z~z~ e z ti~3 - - _ _
kro
where zi, zj are valences of ions i and j, rij is the distance between ions of i and j, and k is a dielectric constant. This treatment can be further simplified by adopting 14. F. H. Stillinger, J. c h e m . P h y s . 35, 1581 (1961). 15. S.W. Mayer,J. c h e m . P h y s . 40, 2429 (1964). 16. H. Reiss, S. W. Mayer and J. Katz. J. c h e m . P h y s . 36, 144 (1962).
Isotope effects in molten metal halides
1567
the average cation-anion distance or the sum of cation and anion radii as a unit parameter. In this approximation, the thermodynamic and transport properties can be expressed by the function of the variables r(= r + + r I, ~;, xj, m;, mj and/, T. At present, the empirical formulas presented by Saito and K a n n o have no definite theoretical foundation and it is unable to connect them directly with above mentioned simple model. Their validities, however, may be regarded as a verification of the model as a first approximation. In K l e m m ' s interpretation he considered that the crystal structure of the sah is retained to some extent in liquid state, giving the reflection of its effect upon the mass effect of cation and anion. His consideration may be true in some degree. H o w e v e r , it is improbable that the surrounding of the cation in the liquid Zn('l., resembles more to the one in molten LiC1 than in molten CaCI.,. Rather, the fact that the mass effects are classified into two groups may be mainly ascribed to the difference of the ionic entities, which participate in ionic migration, between the molten monovalent halides and the molten divalent halides. Markov and Delimarskii[17] proposed that in a molten divalent metal halide MX., the following two equilibria exist MX., ~ M X + + X
M)( + ~ M 2 + 1 ( whereas in a molten monovalent metal halide M X only one equilibrium MX ,~ M++X
.
So in a molten monovalent metal halide there are the sole mobile cations M ~, but the situation is different for a molten divalent metal halide~ where it is reasonably expected that two kinds of cationic entities, M X ~ and M z+, take part in ionic migration. Bockris et al.[18], analyzing theoretically the data of conductance and transport number for molten divalent metal halides, have shown that the dominant mobile cations in molten MX,, are M X +. This is in consistence with the facts that cationic mass effects of molten metal halides are classified into two groups: monovalent metal halide group and divalent metal halide group, and that the mass effect of MX,_, is smaller than that of M X because of the relative mass difference of two isotopic ions M X + being smaller than that of M z-. By the way, Borucka et a/.[19] proposed that the transport numbers of the molten salt can be represented with good accuracy as follows, for a monovalent molten salt t+=r-/(r +f). t =r+/(r++r ) and for a divalent molten salt t+=r
/ ( r + + 2 r ),
t = (r++r)/(r++2r
).
H e r e dominant mobile ions in a molten divalent metal halide are assumed to be M X + and X , the radius of M X + is assumed to be the sum of the radii of M ''+ and 17. B. F. Markov and Yu. K. Delimarskii, Ukrain. Khim. Zh. 19,255 ( 19531. 18. ,I. O'M. Bockris, E. H. Crook, H. Bloom and N. E. Richards, Proc. Roy. Soc. Lond. A225. 55S 11960L 19. A. Z. Borucka, J. O'M. Bockris and J. A. Kitchner, Proc. Roy. Soc. Lond. A241. 554 ( 1957 L
1568
H. K A N N O
Table 6. Transport numbers in molten metal halides
Salt
Temp. (°C)
t+ (Obs.)
tl (Calc.)
Ref.
LiC1 KCI RbC1 MgCI2 CaCI~ SrCI, PbBF2
600 830 785 730-920 780-1100 880-1165 500
0.75 -+-0.03 0-62 + 0.04 0.58 ± 0-04 0.48 + 0-04 0.42 ± 0 - 0 9 0.26±0.09 0.357±0.013
0.74 0.58 0.55 0.43 0.39 0.37 0-38
* * * t t t $
*F. R. D u k e and A. L. B o w m a n , J. electrochem. Soc. 106,626 (1959). tE. D. Wolf and F. R. D u k e , U . S . A . E . C . Rep. 1S-344 (May, 1961). SR. W. Laity and F. R. D u k e , J. electrochem. Soc. 105, 97 (1958).
X - , and t+ and t_ are the cationic and anionic transport numbers of the molten salt, respectively. Using these relations, our empirical formulae can be rewritten as p~ = 0.181 (t_/t+) - 0 . 2 0 3 tx = 0 . 2 3 3 ( t _ / t + ) - 0 . 4 1 8
(for monovalent metal halides) (fordivalent metalhalides).
(2) (3)
By this refinement, we can know that the salt having large cationic transport number will show large isotope effect in ionic migration and that if anions did not carry electricity, i.e. t_ = 0, the cationic mass effect would be maximum. The fact that the cationic mass effects of solids NaCI[20] and AgCl[21] are larger than those of molten salts may be regarded as the qualitative agreement with the fact above mentioned because the transport numbers of the negative ions are negligibly small in these solid crystals [22, 23]. If the cationic mass effect of molten halide is measured, transport number can be estimated by the formulae (2) and (3). Table 6 gives the calculated transport numbers of the molten salts for which the experimental data are available. Although the experimental data are not so accurate, the agreement between the observed and calculated values is good. Acknowledgement-The author wishes to express his gratitude to Professors N. Saito and I. Tomita, Drs. 1. Okada and T. Morimoto for their assistance and helpful suggestions during the course of this study. 20. 21. 22. 23.
M. Chemla and P. Siie, C.r. hebd. SOance. Acad. Sci. Paris 236, 2397 (1953). A. Klemm, Naturwissenschaften 32, 69 (1944). C. T u b a n d t , H. Reinhold and G. Liebold, Z. anorg, allg. Chem. 197,225 ( 1931 ). C. Tubandt, Handbuch der Experimentalphysik, Vol. 12. p. 283 (I 932).
ISOTOPE EFFECTS IN COUNTERCURRENT ELECTROMIGRATION IN MOLTEN METAL HALIDES H. K A N N O D e p a r t m e n t of Chemistry, T h e University of T o k y o , Bunkyo-ku, T o k y o , Japan
(Received 13 August 1970) A b s t r a c t - T h e mass effects of Li +, K ~, and Rb ÷ in molten LiBr, KBr, RbBr and Rbl have been measured. N e w empirical formulae presented by Saito and Kanno, which correlated the cationic m a s s effects of metal halides with the ionic radius ratio r+/r of the salt, have been developed and interpreted qualitatively in terms of ionic intities in the melt.
INTRODUCTION COUNTERCURRENT electromigration in molten salts has the interesting features that this is one of the most promising methods for high enrichment of metal isotopes in the laboratory scale and that the isotope effect (mass effect) determined in electromigration experiment is a useful key parameter for interpreting the transport mechanism in molten salts. Up to recently, theories of the transport processes of pure molten salts have been discussed in connection with such properties as electrical conductance, self-diffusion and transport number. The term defined by Klemm[1] as mass effect has become recognized as an important parameter in ionic migration. Klemm e t al. as well as Lund6n e t al.[2, 3] have contributed considerably to our knowledge of the transport properties of molten salts by the determination of the mass effects. The semi-empirical formulae derived by Klemm e t al.[4, 5] relating the mass effect with the ratio of the cationic and anionic masses m + / m - have been widely used for attempts of the theoretical interpretation of the isotope effect and for the estimation of the experimentally undetermined value. These formulae, however, have been shown by recent works[6, 7] to be inaccurate for some halides and lacking in generality. As alternatives to these formulae, Saito and Kanno[7] have deduced new empirical formulae to the cationic mass effects of molten halides, which give better applicabilities to the experimental data than Klemm's formulae. The purposes of the present paper are two-fold-to give the experimental results of the mass effects of cations in molten LiBr, KBr, RbBr and Rbl, and to I. 2. 3. 4. 5. 6. 7.
A. Klemm, Z. Naturf. 1,252 (1946). A. Klemm, E. Lindholm and A. Lund6n, Z. Naturf. 7a, 560(1952). A. Lund6n, S. Christofferson and A. Lodding, Z. Naturf. 13a, t034 (1958). A. Klemm, Z. Naturf 6a, 687 ( 1951 ); A. N e u b e r t and A. Klemm, Z. Naturf. 16a, 685 ( 1961 ). S. Jordan and A. Klemm, Z. Naturf. 21a, 1581 (1966). J. R o m a n o s and A. K l e m m , Z. NaturJ~ 19a, 1000 (1964). N. Saito and H. Kanno, Bull. ('hem. Soc. Japan 42, 2409 (1969). 1561
1562
H. K A N N O
develop new empirical formulae by correlating the mass effects with the transport numbers of the molten salts. EXPERIMENTAL
Electromigration cell. In all the experiments, cells of quartz glass were used (Fig. 1). The separation columns had an inner diameter of about 4 mm and were packed with quartz powder (q5 = 0.1 0.2 mm). Materials. LiBr and KBr were of commercial reagent grade. These salts were dried to anhydrous form and used for the electromigration. RbBr and Rbl were prepared from crude RbCI by using the purification method of lshibashi et al.[8]. After electrolysis of the aqueous solution of purified RbCI, the resulted RbOH solution was converted into RbBr and Rbl by adding hydrobromic or hydroiodic acid and subsequent drying. Procedure. The whole cell packed with quartz powder in the part of separation column was on a vertical electric oven. When the cell was electrically heated up to appropriate temperature (for LiBr: 630 or 650°C, KBr: 800°C, RbBr: 750°C, RbI: 730°C), the salt was slowly poured into the cell and was melted. When the melt penetrated to reach the anode, the electromigration was begun. During the electrolysis, bromine gas (in the case of Rbl, iodine gas) was introduced into the cathode compartment, thus suppressing the electrodeposition of alkali metal at the anode. The transported charge was measured with a copper coulometer and the reading of the current during the run. The oven-temperature was controlled and adjusted to pre-determined value by use of an automatic temperature regulator in conjunction with a chromel-alumel thermocouple. After electrolysis and quenching, the electromigration cell was taken out of the furnace and the separation column was cut into a several number of fractions for the chemical and mass-spectrometric analyses. Each fraction was dissolved in distilled water and the resultant solution was filtrated with a filter paper to remove quartz powder, then diluted to 100 ml in a volumetric flask. Chemical analysis. LiBr. The amount of lithium in each fraction was determined by the titration of Br- with standardised AgNO3 solution, using 5% KzCrO4 solution as an indicator. KBr and RbBr. The two methods, the titrimetry of Br- with AgNO3 solution and the gravimetry of potassium ion (or rubidium ion) as potassium (or rubidium) tetraphenylborate, were used. Anode
~
,
Cothode
Br2
Br2~
Corbon
electrodes
/Molten salt
Fig. I. Electromigration cell. 8. M. lshibashi, T. Yamamoto and T. Hara, Bull. Inst. chem. Res. Kyoto Univ. 37, 153 (I 959).
Isotope effects in molten metal halides
1563
Rbl. The same gravimetric procedure as in the RbBr experiment was employed for quantitative analysis of rubidium ion in the sample solution. Isotope ratio measurement.The measurements of isotope ratio were carried out with a solid source mass spectrometer (Atlas CH4 mass spectrometer) by means of surface ionization technique. As a working material, an aliquot of each sample solution was directly used without further chemical treatment. Each analysis consisted of 10-15 determinations. RESULT
The conditions and results of the experiments are summarized in Table 1. As typical examples of the electromigrations, analyses of the experiment Nos. 1,3, 5 and 7 are given in Tables 2-5. F o r calculating the mass effect (IX), the usual well-known equation was used ( 1 ) A u / u = tx ( A m / m )
(I)
= -- { ( N i / N f l ) -- ( N j / N f l ) } ( F ' N ) / Q
where Au is the mobility difference between two isotopic ions, u is the mean mobility of the cations relative to the anions, N , N i ° and N~ are total molar amount of cations and those of cationic isotope (i) before and after the electrolysis in the enriched region near the anode, i a n d j are two cationic isotopes of mean mass (m) and mass difference (Am), F is Faraday constant and Q is the transported charge. LiBr. The mean value of the mass effect* of Li ion in molten LiBr obtained in this work is -0.145. This value is a little smaller in its absolute value than that obtained by Lund6n et a/.[3], but considering the differences of experimental conditions and errors, the result agrees fairly well with that of Lund6n. In Lund6n's experiment, the fused salt chain was cathode (carbon r o d ) + Brz/PbBrJLiBr/anode (carbon rod) or c a t h o d e ( c a r b o n r o d ) + BrJPbBrJLiBr/PbBr2/anode ( c a r b o n r o d ) whereas ours was cathode (carbon rod)+ BrJLiBr/anode
(carbon rod).
The mass effect in a binary system so far investigated is larger than that in a Table 1. Conditions and results of the experiments
Experiment No. 1 2 3 4 5 6 7 8
Salt
Temp. (°C)
LiBr 650 ± 10 LiBr 630-- 10 KBr 800± 10 KBr 800± 10 RbBr 750±10 RbBr 750± 10 Rbl 730-+-10 Rbl 730± 10
Duration (hr) 20 4 25 21 33.5 30 21-5 26-5
Average Sep. column current length (mA) (cm) 88 218 50 75 115 87 168 208
15 12 15 15 12 15 15 15
Transported charge
(× 104C)
Mass effect --p.
0.636 0.314 0.455 0.569 1.384 0.936 1.305 1.967
0.138 ± 0.009 0.153 ±0.010 0.102±0.010 0.094±0-009 0.075±0.008 0-078±0.010 0-085___0.008 0.089±0-008
*The mass effect is generally referred to as large or small in its absolute value.
H. K A N N O
1564
Table 2. Experiment No. 1
Frac. No. 1 2 3 4 5 6 7 8 9 Initial
Frac. length (cm)
LiBr (m-equiv.)
0.9 1.5 1.8 1.7 1,8 1.9 1,6 1-7
1 '326 1.350 1 "562 1 '732 1 '684 1 "932 2"11,z 1 "703 1 '804
7Li/GLi 16-05 ± 0.04 15.04 ± 0.04 14.85 ± 0.04 13-57±0.03 13.22 ± 0.04 12'99 ± 0.04 12.76±0.03 12.55 ± 0 . 0 4 12.31 ± 0 . 0 4 12.31 ± 0 . 0 3
M a s s e f f e c t - t~ = 0.138±0.009.
Table 3. Experiment No. 3
Frac. No. 1 2 3 4 5 6 7 8 Initial
Frac. length (cm)
KBr (m-equiv.)
1.5 1.0 1.3 1.5 1.8 1.9 2-3
1 '658 1 '788 1"103 1 "405 1-207 1 "428 2.072 2.50~
39K/41K 13.20 ± 0.03 13.45 _+0.04 13.55 ± 0.04 13.56 ± 0.04 13.74 ± 0.03 13.78 ± 0.04 13.81 ± 0 - 0 3 13.85 ± 0-03 13.91 ± 0.04
M a s s effect-- I.L = 0-102±0.010.
Table 4. E x p e r i m e n t No. 5
Frac. No. 1 2 3 4 5 6 7 Initial
Frac. length (cm)
RbBr (m-equiv.)
1.6 1.4 1 '3 1.3 1 '0
0"388 1-734 1-909 1 "501 1 "584 1"982 1 "068
M a s s effect - - t t = 0.075 +0.008.
85Rb/S~Rb 2-464 ± 0,006 2-458 ± 0-007 2'513 -+-0.008 2.543 ± 0 - 0 0 9 2.570 ± 0-007 2.581 ± 0 - 0 0 4 2.595 ±0-008 2.597 -----0.008
Isotope effects in molten metal halides
1565
Table 5. Experiment No. 7
F Fac. No.
Frac. length (cml
1 2 3 4 5 6 7 8 Initial Mass effect
1.8 1.7 1.7 1-4 2-3 2.3
Rbl Im-equiv.) 1.10~, t .78~, 1.90z 1.48,2 0.99~ 1.54~ 1.32~ 1.83._,
~'~Rb/~TRb 2"523 ± 0-009 2"523 +0.011 2.516 + 0.005 2-516+0.010 2.517 ± 0.010 2-543 + 0.005 2,575 ±0.010 2.598 +_0,009 2.597 + 0.008
p, -- 0.085 ±0.008.
corresponding simple system. It was observed by Monse and Klemm[9] that the mass effect of Li + in the binary system L i C l + PbCI.,, in which initial lithium content was 5.3 per cent in mole fraction, is - 0 . 3 0 . This value is much larger than that of the corresponding simple system, i.e. pure molten LiCI. T h e y explained that this phenomenon is caused by "mixing effect". In Lund6n's experiments the boundary between LiBr and PbBr2, where the mixing of LiBr and PbBr., had occurred and the mixing effect should affect the mobility of lithium ion, consequently, the mass effect of Li + ion, was used for the calculation of the mass effect. It is, however, not yet established to what extent the measured fractionation is affected by the direct result of the mixing effect. Comparison of the experimental results of Lund6n and the present work indicates that in the case of molten L i B r + PbBr.2 the mixing of the salts had no appreciable effect on the mass effect of lithium ion. KBr. The results obtained in this experiment give the mass effect of K* ion in molten KBr to be -0.098. Jordan and Klemm [9] determined the mass effect of K + ion in molten KCI and obtained for value o f - 0 . 0 7 3 . Therefore, the general tendency of the decrease of the mass effect with decreasing in the radius r+/r Ior mass ratio m+/m -) is also observed in potassium halide series. In molten KNO3 system, Lund6n et a/.[10] measured the mass effect of K ÷ ion to be --0-040. The trend that the mass effect of cation in metal halide is much larger than that in the corresponding metal nitrate also exists for lithium, rubidium and thallium salts [11-13]. RbBr and RbI. As the results of molten RbBr are --0.075 and -0-078, they agree fairly well with those reported by Jordan and Klemm [5]. In the experiments for Rbl, two runs were carried out and the mean value of the mass effect is given to be --0-087. So Rbl is the most efficient among rubidium halides for the production of enriched rubidium isotope S7Rb so far as the mass effect is concerned. 9. 10. 11. 12. 13.
E. U. Monse and A. Klemm, Z. NaturJ~ 12a, 318 (1958). A. Lund6n, C. Reutersward and N. Sj/3berg, Z. NaturJ~ 10a, 279 11955). A. Lund6n, E. U. Monse and N. G. Sj6berg, Z. Natmf. lla, 75 (1956). A. Lund6n,Z. Naturf. 21a, 1581 11966). 1. Okada and N. Saito, Bull. chem. Soc. Japan 43,394 ( 19701.
1566
H. K A N N O
However, Rbl is rather thermally unstable and when melted it slowly decomposes into oxide. This thermal unstability is a large weak point to a long run of electromigration which is necessary for high enrichment. Taking account of all other properties of these halides, e.g. melting point, electric conductance, RbBr may be said to be most appropriate for the long run of electromigration and high enrichment. DISCUSSION
In attempt of finding the relation between the mass effect and other physical constants of molten salt, Klemm e t al.[4] found that between the mass effects and the structures of the salts exists the following coincidence: the mass effects of the monovalent metal halides and of the divalent metal halides which on crystallization form layer lattices belong to one group, while those of the divalent metal halides which on crystallization do not form layer lattices belong to the other. From this fact, they proposed the semi-empirical formula for each group. However, as already mentioned[7], the mass effects recently determined have often shown large deviations from the ones expected by the formula. The deviations have been also observed in the present experiments for molten KBr, RbBr and Rbl. In fact the applicability of new semi-empirical formula derived by Jordan and Klemm[5] for alkali halides is good. Nevertheless, the model, from which the new empirical formula is derived, cannot be applied to divalent metal halides. Accordingly the model can hardly be regarded as adequate. Although isotope effect is the property that stems from the mass difference between isotopic ions, mass effect is not necessary to be the function of the masses of cation and anion because it is a reduced parameter. Success of the attempted correlation of mass effect with ionic radius ratio [7] suggests that the ionic radius is the significant parameter characterizing the ionic migration in molten salt. Many thermodynamic properties of molten salts are successfully explained in terms of ionic radii of the component. Stillinger [ 14] and Mayer [ 15] have shown that the surface tensions, compressibilities and thermal expansibilities of alkali halides are represented by the function of a length parameter, the sum of cation and anion radii. Reiss and his coworkers [ 16] applied the theory of corresponding state with success to the melting points of alkali halides and alkaline earth oxides by correlating the melting point with the anion-cation distance. Probably the reason why the ionic radius is a successful correlating parameter for molten salts is that as a first approximation the potential of interaction between the particles in ionic liquid is pairwise additive and is represented fairly well by a Coulomb potential z~z~ e z ti~3 - - _ _
kro
where zi, zj are valences of ions i and j, rij is the distance between ions of i and j, and k is a dielectric constant. This treatment can be further simplified by adopting 14. F. H. Stillinger, J. c h e m . P h y s . 35, 1581 (1961). 15. S.W. Mayer,J. c h e m . P h y s . 40, 2429 (1964). 16. H. Reiss, S. W. Mayer and J. Katz. J. c h e m . P h y s . 36, 144 (1962).
Isotope effects in molten metal halides
1567
the average cation-anion distance or the sum of cation and anion radii as a unit parameter. In this approximation, the thermodynamic and transport properties can be expressed by the function of the variables r(= r + + r I, ~;, xj, m;, mj and/, T. At present, the empirical formulas presented by Saito and K a n n o have no definite theoretical foundation and it is unable to connect them directly with above mentioned simple model. Their validities, however, may be regarded as a verification of the model as a first approximation. In K l e m m ' s interpretation he considered that the crystal structure of the sah is retained to some extent in liquid state, giving the reflection of its effect upon the mass effect of cation and anion. His consideration may be true in some degree. H o w e v e r , it is improbable that the surrounding of the cation in the liquid Zn('l., resembles more to the one in molten LiC1 than in molten CaCI.,. Rather, the fact that the mass effects are classified into two groups may be mainly ascribed to the difference of the ionic entities, which participate in ionic migration, between the molten monovalent halides and the molten divalent halides. Markov and Delimarskii[17] proposed that in a molten divalent metal halide MX., the following two equilibria exist MX., ~ M X + + X
M)( + ~ M 2 + 1 ( whereas in a molten monovalent metal halide M X only one equilibrium MX ,~ M++X
.
So in a molten monovalent metal halide there are the sole mobile cations M ~, but the situation is different for a molten divalent metal halide~ where it is reasonably expected that two kinds of cationic entities, M X ~ and M z+, take part in ionic migration. Bockris et al.[18], analyzing theoretically the data of conductance and transport number for molten divalent metal halides, have shown that the dominant mobile cations in molten MX,, are M X +. This is in consistence with the facts that cationic mass effects of molten metal halides are classified into two groups: monovalent metal halide group and divalent metal halide group, and that the mass effect of MX,_, is smaller than that of M X because of the relative mass difference of two isotopic ions M X + being smaller than that of M z-. By the way, Borucka et a/.[19] proposed that the transport numbers of the molten salt can be represented with good accuracy as follows, for a monovalent molten salt t+=r-/(r +f). t =r+/(r++r ) and for a divalent molten salt t+=r
/ ( r + + 2 r ),
t = (r++r)/(r++2r
).
H e r e dominant mobile ions in a molten divalent metal halide are assumed to be M X + and X , the radius of M X + is assumed to be the sum of the radii of M ''+ and 17. B. F. Markov and Yu. K. Delimarskii, Ukrain. Khim. Zh. 19,255 ( 19531. 18. ,I. O'M. Bockris, E. H. Crook, H. Bloom and N. E. Richards, Proc. Roy. Soc. Lond. A225. 55S 11960L 19. A. Z. Borucka, J. O'M. Bockris and J. A. Kitchner, Proc. Roy. Soc. Lond. A241. 554 ( 1957 L
1568
H. K A N N O
Table 6. Transport numbers in molten metal halides
Salt
Temp. (°C)
t+ (Obs.)
tl (Calc.)
Ref.
LiC1 KCI RbC1 MgCI2 CaCI~ SrCI, PbBF2
600 830 785 730-920 780-1100 880-1165 500
0.75 -+-0.03 0-62 + 0.04 0.58 ± 0-04 0.48 + 0-04 0.42 ± 0 - 0 9 0.26±0.09 0.357±0.013
0.74 0.58 0.55 0.43 0.39 0.37 0-38
* * * t t t $
*F. R. D u k e and A. L. B o w m a n , J. electrochem. Soc. 106,626 (1959). tE. D. Wolf and F. R. D u k e , U . S . A . E . C . Rep. 1S-344 (May, 1961). SR. W. Laity and F. R. D u k e , J. electrochem. Soc. 105, 97 (1958).
X - , and t+ and t_ are the cationic and anionic transport numbers of the molten salt, respectively. Using these relations, our empirical formulae can be rewritten as p~ = 0.181 (t_/t+) - 0 . 2 0 3 tx = 0 . 2 3 3 ( t _ / t + ) - 0 . 4 1 8
(for monovalent metal halides) (fordivalent metalhalides).
(2) (3)
By this refinement, we can know that the salt having large cationic transport number will show large isotope effect in ionic migration and that if anions did not carry electricity, i.e. t_ = 0, the cationic mass effect would be maximum. The fact that the cationic mass effects of solids NaCI[20] and AgCl[21] are larger than those of molten salts may be regarded as the qualitative agreement with the fact above mentioned because the transport numbers of the negative ions are negligibly small in these solid crystals [22, 23]. If the cationic mass effect of molten halide is measured, transport number can be estimated by the formulae (2) and (3). Table 6 gives the calculated transport numbers of the molten salts for which the experimental data are available. Although the experimental data are not so accurate, the agreement between the observed and calculated values is good. Acknowledgement-The author wishes to express his gratitude to Professors N. Saito and I. Tomita, Drs. 1. Okada and T. Morimoto for their assistance and helpful suggestions during the course of this study. 20. 21. 22. 23.
M. Chemla and P. Siie, C.r. hebd. SOance. Acad. Sci. Paris 236, 2397 (1953). A. Klemm, Naturwissenschaften 32, 69 (1944). C. T u b a n d t , H. Reinhold and G. Liebold, Z. anorg, allg. Chem. 197,225 ( 1931 ). C. Tubandt, Handbuch der Experimentalphysik, Vol. 12. p. 283 (I 932).