57%
A. S. DWORKIN, R. B. ESCTJE AND E. R. VANARTSDALEN
T'ol. 64
the data on the U02C1+complex to the UOzOH+ion TABLE I1 in the kinetic situation, it would appear that the E Q U I L I B R I U M DATAFOR THE UOyCl' COMPLEX 1N 60 VOLeffect of the solvent on the stability of the UOzXf UME yo ETHANOL SOLVEXT ion is a principal factor in the influence of the sol- x or bi ai bn K X 10-1 vent on the rate of the electron exchange reaction 424 0.040 0.040 0.0085 0.1915 5.36 between U(IS7)and U(T-I) ions. 450 .040 .040 .0085 ,1918 5.36 The data for the equilibrium constants mere 466 ,040 .010 ,0087 ,1915 4.57 neither as precise nor as accurate as those for the A V . 5.10 empirical formulas as is illustrated for 60 volume ethanol solvent in Table 11. The values of the The lack of relatively high accuracy and precision constants given in Table I are average values for in the case of the equilibrium data arose perhaps all the wave lengths used in t h e case of a particular from the fact that dilutions of the solutions had to solvent. be made and optical densities read from graphs prepared originally for obtaining empirical formuTABLE I las of the U02C1+complex. The data for the U02C1+and U02C13-complexes EQUILIBRIUM CONSTANTS A S D FREEEXERGY O F DISSOCIAsubstantiate the assumption of their existence made T I O N AT 25" O F THE uoZclT COMPLEX IX VARIOUS SOLVENTS by Mathews, Wear and .4mis6 based on transferVOl. % HClOI, Ionic AFO ethanol pH .Ma strength K X 10-8 cal./rnhe ence data. 0 0.50 1.238 22.8 2240 Acknowledgment.-The authors are indebted t o 30 0.1411 1.238 165 1070 the United States iltomic Energy Commission for a grant under Contract AT-(40-1)-2069, which GO .I411 1.238 510 400 made this research possible. J.D.H. is also indebted 90 .0088 0.078 1.47 3880 to the National Science Foundation for a Cotiperaa In alcohol containing solvents the molarity of the acid tive Fellowship which gave him financial support. rather than the pH of the solution is given.
SELF-DIFFUSION I N MOLTEX XITRATES' BY A. S. DWORKIN,R. B. ESCUE AND E. It. VANARTSDALEX Contribution from the Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee Received J a n u a r y 8, 1960
The self-diffusion coefficients D for the ions in molten LiYOa, NaN03, KNOJ, CsN03 and have been measured as a function of temperature by the capillary method. The results are expressed in the form of the equation D = A exp( -AH */ RT). The values for the energy of activation for diffusion, AH for the cation and anion, respectively, in kcal. are: LiN03, 5.49 and 6.34: NaXOl. 4.97 and 5.08: KKO,. 5.53 and 5.76: CsNOt. 5.61 and 6.28: and .4eNO*. 3.73 and 3.84. The values for t h e diffusion'coefficients, ( D X 106): for the cation'and anion, respectively,'in cm.* iec.'i a t 350' are: LiNOo, (2.93) and (1.15); XaNO?, 2.33 and 1.48; K1;Od, 1.52 and 1.35; &NO3, (1.22) and (l.!l); and AgNO?, (2,40) and (1.40). The results indicate that the diffusion coefficients of the cation vary inversely with ion size. The Nernst-Einstein relationship is shown not to hold for molten nitrates. Values for phenomenologicalfriction coefficients as proposed by Laity are all positive and all but those for LiSOI are of the same order of magnitude. The friction coefficients for the relative motion of anion and cation and for cation and cation increase with increasing cation size while those for anion-anion motion decrease with increasing cation size.
*,
As prtrt of our program t o elucidate the mechanism of transport in molten salts, we have measured the self-d:ffusion coefficients of the individual ions in molten Lixo3, N a S 0 3 , KNOs, Csh'O3 and XgSOa as a function of temperature. The method emnloyed involved a determination of the rate at, which a tracer ion diffused from a capillary tube into a stirred bath of pure untagged nitrate. The method was originally used by Anderson and Saddington? in aqueous solution and has since been emploped by many ot8hem3n4 We have reported previously the results of our measurements in NaN03.5 The only ot'her published work on self-diffusion in (1) Work performed for the U. 5. Atomic Energy Commission a t the Oak Ridge Xational Laboratory, operated b y the Union Carbide Cornoration. Oak Ridge, Tennessee. (2) J . S. Anderson and K. Saddington, J . C h e m . Soc., 5381 (1949). (3) J. H. K a n g and J. W. Kennedy, J . Am. Chem. Soc., 72, 2080 (1950):J. H.Wang, ibid.. 74, 1182 (1952). 14) R . hlills, ibid., 77, 6116 (1955), and previous papers. ( 5 ) E. R . Van .4rtrdalen, D. Brown, A . S. Dworkin and F. J. Miller, ibid., 78, 1772 (1956).
molten salts appears t o be that of measurements in T1C1,6 NaC17 and ZnBr2,8and only for NaCl are data available for both cation and anion diffusion. The nitrates were chosen for study because their relatively low melting temperatures made it experimentally feasible to study the self-djffusion in a group of compounds therebv permitting one to nnte the effect of change in cation size and mass on the diffusion process. The nitrates also lend themselves to the use of a combination of readily available stable and radioactive isotopes as tracers, enabling one to follow both the cation and anion diffusion in one experiment. The equation used to calculate the self-diffusion coefficient D of a tracer in a pure salt -
L
1
-
(6) E. Berne and A. Klernm. 2. Mnturforsch., 8 8 , 400 (1953). (7) -4. Z.Boriicka, J . O'M. Rorkris and J. A . Kitchener, Proc. R o y . SOC.( L o n d o n ) , A241, 554 (1957). (8) L. Wallin and A. Lunden, Z. Naturforach., 14A,262 (1959).
SELF-DIFFUSION I S MOLTEN
July, 1960
has been derivedg from a solution of Fick’s law of diffusion of a tracer from a uniform tube of length E, closed at one end, into a bath containing zero coiicentration of tracer. Po is the initial concentration of tracer in the tube and C,,, is the average concentration of tracer in the tube after time t. This simplified form of the equation is good to better than 0 2% under the conditions of our experiment.
873
NITRATES Tn
Experimental Apparatus.--The capillary tubes which contained the tagged salt were of transparent fused silica and were specially selected for uniformity of bore. They ranged in length from 3-5 cm. (measured on a micrometer stage to =k 0.02 mm.) and had an external diameter of about 5 mm. with an internal diameter of less than 0.7 mm. They were closed a t one end with a flat seal. The extremely small bore tubes made the filling operation more difficult. Nevertheless, it was considered desirable to use them in order to eliminate uncertainties due to convection which would have been encountered with larger bore tubes. The capillaries were filled in the apparatus shown in Fig. 1 in the following manner. Molten salt from the reservoir G was drawn into the filling tube E by means of a screw syringe. The filling tube then was maneuvered into the silica capillary D. The salt was forced into the capillary, filling i t from the bottom as the filling tube was raised, thereby preventing the trapping of gas bubbles. Some insulation around the Pyrex tube A was necessary to attain the somewhat higher temperature necessary for the CsN03 experiment, but not enough to obscure the view of the filling operation. Pyrex capillary holders were used in many of the experiments as well as the platinum capillary holder, C. It was possible to fill as many as three capillaries t o be used concurrently in the same bath. R h e n the salts used were more dense than fused silica, the capillaries were secured in the holder to prevent their floating to the surface of the bath. The diffusion experiments were carried out in a 3.5 in. bore Marshall tube furnace 16 in. long, having ten external taps for the attachment of shunt resistors to reduce the temperature gradient. A heavy-walled Inconel liner waa placed in the furnace and an aluminum shield was used as a cover. The furnace was controlled by a chromcl-alumel thermocouple n-hich operated a Leeds and Northrup recorder-controller in conjunction with a Leeds and Korthrup “DAT” controller. The temperature of the salt bath remained constant to rtO.3’ during the course of the diffusion period. The baths, made up of from 400 to 800 g. of salt, were contained in either Pyrex tubes or platinum crucibles depending upon which salt was being measured. The baths were stirred Rith Pyrex or silica spiral stirrers powered by 100 r.p.m. constant speed motors. The temperature of the bath was measured with a platinum, 90% platinum-lO~o rhodium thermocouple by means of a Rubicon precision potentiometer. The thermocouple was placed in a silica tube which in turn was inserted in the salt bath close to the diffusion capillaries. Materials.-The nitrates used were reagent grade materials which were dried in an oven a t 120”. They were heated slowly in situ under dry argon to the temperatures a t which the measurements were made. The radioactive and stable isotopes used as tracers were obtained from the Oak Ridge National Laboratory The radioactive isotopes used were NaZ2,C S ’ and ~ ~ Ag”0. The stable isotopes were Lis, K41,W a n d 0 ’ 8 . Experimental Procedure.-The capillaries were filled with tagged salt in the manner described above. The molten salt was allowed to overflow slightly and cover the top of the capillary tube to allow for contraction during the transfer operation. The capillaries were transferred from the filling apparatus to the furnace containing the untagged salt bath without allowing the salt to freeze. This prevented the formation of gas bubbles in the capillary. The capillaries were partially submerged in the salt-bath until temperature equilibrium was reached a t which time they were completely submerged and the diffusion period was begun. (9) A, C . Wahl and N. A . Bonner, “Radioactivity Applied to Chemistry,” John ’Tiley a n d Sons, Inc., Kew York, N. Y.,77, 1951, p.
507.
H
Fig. 1.-Capillary filling device: A, Pyres tube; B, nichrome heating ribbon; C, platinum capillary holder; D, silica capillaries; E, silica filling tuhe drawn to fine capillary a t end; F, Pyrex tube-cup holder and thermocouple tube; G, platinum cup-salt reservoir; H, aluminum top: I, tridimensional control for filling tuhe; J, three-position plug for capillary holder. When sufficient time was allowed for about 60-70% of the tracer to diffuse out of the capillary (about two to five days), the diffusion period was ended by removing the capillaries from the bath. The capillaries then were cleaned on the outside and dried. If they contained radioactive tracer, they were weighed and then placed in a 47 high pressure ion chamber and counted. The activities were obtained in terms of a reading on a Brown chart. Since a ratio was all that was required, (Ca,&” in eq. 1) no conversion to actual counts was made. R h e n the capillaries contained stable isotope tracers, the salt was washed into a small beaker by a stream of distilled water from a fine silica capillary, transferred to the silica tubes in which the analysis was to be made, and evaporated to dryness. The salt then was analyzed for isotopic abundance with a G.E. mass spectrometer. The initial isotopic concentration of the salt could not be measured during an actual diffusion run, thereby necessitating separate calibration determinations. These were made in the same manner as were the diffusion runs except that the capillaries were held under the surfam of the saltbath only momentarily. By determining Coin this mannrr, any errors inrurred by the entry of the capillaries into and their removal from the bath should be cancelled. When stable isotopes were employed, the Concentration of isotope in the “normal” salt bath, CN,as well as the initial concentration of isotope in the capillary was obtained. It was necessary to subtract CN from both the numerator and denominator in the term ( C.,,/CO ) in equation 1 to account for back diffusion of the stable isotope from the normal bath into the capillary. Ten to fifteen calibration runs were made for each salt which gave values for Cu good to =kO.51.0%.
-1.S.DTVOKKIN, R.R. Escm
8'71
. ~ N DE.
R. T7.4x ARTSDALFS
Results The effect of a number of variables on the selfdiffusion coefficient D was studied during the course of the measurements in NaN03. It was found that D did not change, within experimental error, with a change in the length of capillaries (from 3-5 cm.) or duration of the diffusion period (from 2-4 days). This indicated that the stirring rate was sufficient to prevent accumulation of tracer at the mouth of the capillary but slow enough to prevent an appreciable amount of liquid from being dragged out of thtl capillary due to stirring. The rate was somewhat lower than that used by Klemni.6 It was approximately the same as that discussed by Mills4 and found to be satisfactory within the experimental error of our measurements. Borucka, Rockris, and Kitchener' used a much slower rate and also applied a correction for the stirring effect. Their larger bore and rather short capillaries may have led to the more serious stirring problem which they encountered. A series of twenty diffusion runs m:de 11-ith larger bore silica capillaries (approximately 1 111111. bore) led to values of D for Na+ S a S 0 3 approximately 37, higher than those obtained from forty runs made with the smaller bore capillaries. -1 very definite loss in precision was also noted. This certainly can be ascribed to a greater iiifluence of convection currents with largerbore capillarie* in which case the stirring rate has greater effect than with the smaller bore capillarie.. S a S 0 3 wa\ the only salt for which a separate series of runs was made for the cation and anion. 018w.as uhed iiiitially to follow the nitrate diffusion. However, it was shown that the self-diffusion coefficients of the nitrate ion as determined with N15as the tracer agreed very well with those determined using 0'" (Table I). Since S15could be obtained a t a much higher enrichment than 018and could be incorporated 117 the salts more easily, it was used in all subsequent measurements. The .elf-diffusion coefficients D may be expressed hy an eqnation nf the form U
=
A exp(-AH+IRT)
(2)
where A is a eonstant, AH* is a temperature coefficient factor generally considered to represent the energy of activation for the diffusion, R is the molar gas constant, and 7' is absolute temperature. The parameters of this equation for the ions in the five nitrates meawred, as derived by the method of least squares, are given in Table 11. Table I1 also includes the applicable temperature ranges for each equation (60-70" ahove the melting points of the salts) and the probable errors in D and AH*. The experimental values of D are given in Table I.
288 5 296.3 309.7 320.5
1.66 1.72 1.78 1.92 1.93 2.16 2.16 2.39
344.8
349.1
357.13
264.0 271.3
0.510 .52 .60
360.0 368.4
.53 279.0
.59
.60 288. .5 296.3 309.7 320.5
,60 .65 .70 ,72 .81 .82 .94
Xa+ in NaT\'03 313.5 1.79 1.77 1.82 314.5 1.73 315.5 1.93 1.83 1.81 1.85 320.5 1.91 1.97 1.94
428.7
2.02
443.8
'.18 2 40 2.36 2.70 2.55
456.5
477 9
428.7 443.8 456.5
1.90 2 21 2.37 2.35 477.9 2.67 2.54 a N15used as tracer.
475.3
375.8
5'01. 64 2.13 2.18 2.16 2.26 2.32 2.30 2.22 2.38 2.46 2.43 2.42 2.52 2.54 2.65 2.66 2.60 2.61 2.70 2.60 2.76 2.70 2.70 2.75 2.64
KO3- in N a N O t 320.6
328.7
350.9
359.4
366.2 377.4
1.21 1.21 1.25 1.21 1.27 1.27 1.27 1.48 1.49 1.51 1.56 1.57 1.59 1.54 1.62 1.63 1.78 1.80
h g T in AgXO8 219 5 1 09 1 07 1 19 233 0 1 23 1.30 244 0 1 40 255 3 1 58 274 5
K + in KSOa 344.8
345.5 352.9 359.0 363.3 367.3 368.7 375.0 381.2 389.0
1.51 1.51 1.44 1.49 1.48 1.53 1.54 1.57 1.67 1.66 1.66 1.70 1.74 1.71 1.70 1.78 1.75 1.88 1.90 2.06 2.01
303- in KSO," 345.5 1.33 1.29 352.9 1.32 1.35 359, 0 1.53 1.49 967.3 1.54 1.49 375.0 1.61 1.58 389.0 1.80 1.77
503in AgS03a 219 5 233 0 244 0 255 3 274 5
288.5
0.64 .59 .62 .73 . 72 .82 90 .86 I 08 1 08
0 ' 8 used as tracer. TABLEI SELF-DIFFUSIOS COEFFICIEATS FOR MOLTEN SITRATES The probable error in D as derived from the devia-
D
t, "C.
X 105, cm.2 sec.-l
x
D
t , OC.
X 106, cm.2 eec.-l
t. O C .
D
106, om.2 sec.-l
Li+ in L i S 0 3 N a + in ?;ax03 (cont'd.) NO,- in NaN03" 264 0 1 -46 X24 6 1 97 332 5 1 30 1 43 1 98 1 33 1 59 890 0 2 04 343 4 1 40 271 3 1 53 334 6 2 16 1 43 279 0 1 66 2 10 364 9 1 67
tions from the calculated least squares log D z's. 1lT lines is in general about f1.5%. The uncertainty in AH* (the slope of the lines) is in general =t24v0 although it is somewhat higher for the ions in C s S O s and the nitrate in iigIT0~. Discussion It appears that the energy of activation for diffwion, AH*, for each of the ions measured is tem-
July. 1960
SELF-DIFFUSIOS IS ~ I O L T E ?;ITRATES N
Probable error in D ,
dpplicable temp. range, T.
1.5 2.5
264-320
1 5
313-376
1.0 1 5 1. 5
344-389
1.5 I
428-478
1.0 4.0
219-289
, t i
perature independent over the rather short teniperature range of these investigations. The energy of activation for cation and anion in each salt is approximately equal within experimental error (Table 11). L i s 0 3 is the exception, in which case AH* for the nitrate is somewhat larger. (Xlthough C s S 0 3 :Ippears to be an exception. it should be noted that thtx experimental errors involved in the CsT\‘Os measurements were somewhat larger than those with the other nitrates.) I t may also be noted that AH* for both of the ions in AgKO8 is sign$cantly lower than those found for the alkali-metal nitrates. The observation was made at the conclusion of the discussion of the K a y o 3 measurement^,^ that the ratio of the self-diffusion coefficients of the two ions is approximately proportional to the inverse square roots of their masses. The data for the five nitrates reported in this work, however, show that the abox-e relationship is not a general one. On the other hand, a relationship between the diffusion coefficients and ion size does appear to exist. Table I11 lists self-diffuion coefficients for the nitrates at : 3 j o o . To compare the results at this temperature, it was necessary to extrapolate the L i S 0 3 and .\ gSOa \.slues above the actual measured temperature range and the CsSOg below its melting point, ‘l’he Cc;?;03 values, therefore, are hypothetical and nrr included merely for the purpose of comparison. Since the AH* 1 alues are all approximately equal, a compariioii a t ally reasonable temperature would lead t o approximntelp the same relative cation to union value9 for each salt and the same relative ration to cation values among the alkali-metal nitrates as those shown in Table 111. As can be seen from Table 111, the self-diffusion coefficient of the cation is larger than that for the anion in each salt. The self-diffusion coefficient of the cation is highest for the Li+ in LiK03 and decreases with increasing cation size. The product of the cation diffusion voefficient and cation radius (DTr+)is given for each salt in Tabk 111. The constancy of this quantity suggests that the cation diffusion coefficients
875
vary inversely with the cation radius. AglL’03does not fit in this order. However, since Afl* for the ions in hgN03 is significantly different from that for the alkali-metal nitrates, the extrapolated diffusion coefficients in AgN03 at 350’ are not indicative of the relative values at all temperatures. Thr data for the anion diffusion coefficients indicate that the D- for the YO$- in LiX03 is homewhat lower than would be expected. The above considerations seem to indicate that the migration of the ions is affected more by the ion size or core repulsions than by the attractive forces which are mainly coulombic. If the latter were the most important factor, one would expect Li+ in L i s 0 3 to have the smallest diffusion coefficient. One must be careful not to ascribe too much importance to any correlations of radius with diffusion coefficients, such as the relative constancy of D+T+,or to any speculation which follows from such correlations. The effective radii of the ions in the melt may yery well differ from the crystal radii used in the above correlations. In this connection, it may be significant to note that at 350°, the molar volume of AigKO?i q TABLE
111
sELF-DIFFCSIOX COEFFICIESTS .4T 350” B+ x IW, B- x 100, cm.?aec.-’ crn.Zsee.-l D+rl
a
1 I5h 1 91) 2 93* 2.33 1 48 L 21 1 52 1 35 2 01 ] 2.‘h I llh L 04 csso, 2 40b 1 40* .i02 AgKO1 a The following ionic radii (in A.) were used to calculate D+r+:Li+, 0.68; Na+, 0.95; Ag+, 1.26; K + , 1.33; Ce+ 1.67. * Extrapolated.
LiSO, SaXO, KSO,
Iess than that of S-aS03 although the radius of the silver ion as given by Pauling is considerably larger than that of the sodium ion. There has been some discussion7lo c*oiicerning the applicability of the Xernst-Einstein re1at’ionship in molten salts. This relation between the equivalent conductance (A) of the medium and the self-diffusion coefficients of the cation and anion (D+and D - ) for a uni-univalent electrolyte is given by the equation A
FZ
= -
(D+ + D - )
(3)
where F is faraday’s constant. R is the gas constant, and T is the absolute temperature. Although this relation is valid for electrolyte solutions at infinite dilution and in some cases for ionic crystals, the equivalent conductance of molten salt? as d c u l a t e d from equation 3 is always higher than the experimental value. A(ca1culated) is higher than -i(exp.) for S a C P by about 40% and, for the nitrates, by about 307, for LiKO, to about for CsNO?. Borucka, Bockris and Kitc3hener’ apparently har-e assumed that the Sernst-Einstein relation is applicable in molten salts and that discrepancies are due entirely to “molecule” or “vacancy-pair” diffusion. On this basis, they have calculated self-diffusion coefficients for the ions and “mo1eciile”iii molten NaC1 which agree very well with those calculated from the Stokes-Einstein relationship. Yangl“ has (10) I. Yang J
Chem P h p s , ‘27, 801 (19.57)
also done this using our previously published values ance measurements given with the friction cofor NaN0s6 and again obtained good agreement for efficients in Table IV. ill1 of the friction coefthe ions (although not for the molecule). When ficients are positive and except for LiN03, r+-, this treatment is applied t o the remaining nitrates r++. and r-- for each salt are of the same order the agreement is in general poor. However, the of magnitude indicating, according to Laity, that a calculations from which the three “true” self-dif- high degree of association need not be postulated fusion coefficients (ie., cation, anion and molecule) in the melt and that the choice of the ions as the are derived are based on a fallacy. -4s Laity’l has mobile species is probably a proper one. It can pointed out, (‘. . . . in the calculations from the con- be noted that for the alkali-metal nitrates the ductance and self-diffusion data no account has r+- and r++ values increase with increasing been taken of the relative concentrations of ions cation size while the r-- value decreases with inand molecules, a factor which has a controlling ef- creasing cation size. For each salt, r++ is always For the alkali-metal fect on the values calculated for the three ‘true’ less than r+- and r--. self-diffusion coefficients.” In light of the above, nitrates, the friction coefficient for the relative the apparent corroboration of the hypothesis of motion of unlike ions is always larger than that for Borucka, Bockris and Kitchener when applied to like ions except in the case of LiN03 where r-is larger. LiTu’O3 is also the only salt in which NaCl and NaP\’03must be considered fortuitous. Laity” has proposed a method of writing phe- AH* for the nitrate is larger than that for the nomenological equations for the description of elec- cation, the others all showing approximately equal trical and mass transport which give rise to a set of d u r s of AH+ for cation and anion. This seems t o friction coefficients. These quantities relate the indicate that in the latter cases, migrations of results of such measurements as electrical conduct- both anion and cation are complementary interance, transference numbers and diffusion coefficients actions while for the nitrate in LiNO3, the anionin such a way that a single type of physical con- anion interaction is the important factor. cept can be applied in interpreting the results of all TABLEIV three. For a pure molten salt, equations (4), (5) FRICTION COEFFICIEKTS FOR MOLTEN KITRATES and (6) can be derivedll (assuming only two ionic A, r++ x 10-8 species). ohms-’ t. r+(joules/ A
p
= I(z+
= (z+
+
+
cm.*
(4)
2-)/7+-1
and
$+
Z-)/(Z+T+-
+
Z-T++)
(5)
and D--RT- -
(z+
+ z-)/(z-~+- + z + ~ - - )
(6)
where r + - , t’++ and r-- represent the friction coefficients for the relative motion of unlike and like ions, respectively, and z is the ionic charge. (The symbols a++and D-- are used by Laity in the same sense as D+ and D- are used in this work.) It can be shown that the Nernst-Einstein relationship (equation 3) is a very special case of equations 4,5 and 6. l 1 The friction coefficients for the nitrates were calculated using equations 4, 5 and 6 from values of D+ and D- (some of which are extrapolated) and from the equivalent conduct(11) R. W. Laity, J . Chem. Phvs.. 30, G82 (195
LiN03 n’aT\TO3 KNO,
OC.
350 350 450 350 450 42.414 450 ~ 5 5 . 7 ’ ~ 350 53.01* 52.713 72.3 35.014 54.8
X 10-8
cm.*/sec.)
r-- X 10-8
3.51 3.53 2.57 5.19 3.39 4.39 3.34
0.03 .92 .39 1.63 0.78 .87 .98
5.50 3.47 2.03 2.48 1.28 0.99 4.06
As is t’he case with the diffusion coefficients, other correlations of radius with friction coefficients are obvious, but are too speculative to make at the present stage of development of the theory of transport processes. Further application of the apparently useful hypothesis advocated by Laity toward the derivation of a quantitative t>heoryto explain t,ransport properties in molten salts awaits the availability of more experimental data (e.g., inter-diffusion Coefficients in mixtiires). (12) F. M. Jaeger and B. Kapma, Z . anorg. Chem., 113, 27 (1920). (13) J. Byrne, H. Fleming and F. E. \V. Wetmore, Can. J . Chem..
30, 922 (1952). (14) D. F. S m i t h a n d E. R. Van Artsdalen. unpublished data.
