Conductance Studies of the Alkali Metal Chlorides
2521
(31) G. Astarita. Ind. Eng. Chem., Fundam., 4,236 (1965). (32) S. B. Clough, H. E. Relad, A. 8. Metzner. and V. C. Behn, AlChEJ., 8, 346 (1962). (33) A. B. Metzner. Nature (London),208, 267 (1965). (34) J. L. Gainer and A. B. IMtzner, AlChE lnst. Chem. Eng. Symp. Ser., No. 6, 74 (1965). (35) C. R. Wilke an13 P. Chang, AIChEJ., 1, 264 (1955).
(36) (37) (38) (39) (40) (41) (42)
H. Eyring, J. Chem. Phys., 4, 283 (1936). R. J. Bearman, J. Phys. Chem., 85, 1961 (1961). A. Huq and T. Wood, J. Chem. Eng. Date, 13,256 (1968). J. L. Duda and J. S. Vrentas. A s h € J., 15,351 (1969). M. Cable and D.J. Evans, J. Appl. Phys., 38,2899 (1967). D. W. Readey and A. R. Cooper. Chem. Eng. Sci., 21,917 (1966). W. Y. Ng and J. Walkley, Can. J. Chem., 47, 1075 (1969).
Conductance Studies of the Alkali Metal Chlorides in Aluminum Chloride-Propylene Carbonate Soluition Jacob JornbX1and Charles W. Tobias Inorganic Materials Research Division, Lawrence Berkeley Laboratory and Department of Chemical Engineering, University of California. Berkeley, California 94720 (Received February 19, 1974) Publication costs assisted by the University of California
Conductance of the alkali metal chlorides, LiCl, NaCl, KCl, RbCl, CsC1, in unit molality solution of Ale13 in propylene carbonate was measured a t 25 and 3 5 O . The measurements were performed in order to characterize the new process for the electrodeposition of the alkali metals a t ambient temperature. The results have been interpreted in terms of solvation, ionic equilibrium, and the structure making-breaking ability o f the alkali metals in AlCl3 propylene carbonate solution.
Propylene carbonate (PC) is a polar aprotic solvent which exhibit&many useful properties for electrochemical applications. Since the early research on PC was oriented toward the development of high-energy batteries, most of the work was concerned with emf measurements, electrodeposition, stability tests, and conductance at high concentration range. Recently, conductance measurements were performed in the dilute range in order to gain better understanding about the solvent-solute interaction^.^-^ The feasability of the electrodeposition of all the alkali metals from their clilorides in AlC13-propylene carbonate solution has hieen demonstrated.'j Lithium, sodium, potassium, rubidium, and cesium were electrodeposited at ambient temperature showing stable and reversible behavior.7>8 The alkali metal chlorides are practically insoluble in PC, however, in the presence of AlC13 a complex is formed between the chloride and AlClz MCl t AlC1,
--t
M'
+
AlC1,-
(1)
where M represents the alkali metal. The electrodeposition of the alkali metals from their chlorides in AIC13-PC solution is proposed as a new process for the electrodeposition and refining of the alkali metals at ambient temperature.'j In order to characterize such a process, thermodynamic7 and kinetics measurements were performed. This paper presents the results of conductance studies of the alkali metal chlorides in unit molality A1C13 solution in PC, at 25 and 3 5 O , over a wide concentration range of up to 1 n ;alkali metal chloride. The role of AlC13 is discussed in the light of earlier and a general evaluation of the results is given.
Previous Work Most of the data on solubilities and conductivities in PC are summarized in Jasinski's re vie^,^ and the reader is referred to Table XI11 and XIX in that review. Conductance measurements in dilute solutions were performed in order to obtain the equivalent conductance a t infinite dilution. The equivalent conductances a t infinite dilution, no, were obtained in most cases by extrapolation of a plot of A us. c to infinite dilution. HarrislO obtained Kohlrusch plots for NaI and KI in PC, and the equivalent conductances were 28.3 and 31.0 ohm-l cm2 equiv-l, respectively. The slopes of the straight lines were in good agreement with the Onsager limiting law equation. Fuoss and HirschZa studied the conductance of tetra-n- butylammonium tetraphenylboride in PC and concluded that ion association was negligible. Wu and Friedman2binvestigated the conductances and heats of solution of several alkali metal iodides, perchlorates, trifluoroacetates, and tetraphenylborates in PC. The perchlorates were found to be strong electrolytes, whereas the trifluoroacetates showed considerable ion association. Keller, et al. 3 measured the equivalent conductance of LiC104, LiC1, LiBr, TBABR, and TMAPFG in PC, and obtained the equivalent conductance at infinite dilution. Mukherjee and Boden4 made conductance and viscosity measurements of LiC1, LiBr, LiC104, Et4NC1, Et4NC104, n-Bu4NBr, and nBu4NC104 in PC. The method of Fuoss and Accascinall was used to obtain A0 and the individual ion conductances A+O and A-O. LiCl and LiBr were found to be associated, whereas no association could be detected for the other salts. The Journalof Physical Chemistry, Vol. 78, No. 24, 1974
2522
Jacob Jorne and Charles W. Tobias
TABLE I: Equivalent Conductance and Ionic Conductance in 'PIC (ohm-1 ern2 equiv-1) 1 1 1 1
Salt
A
x+
A-
Ref
. l _ l
25.6 26.2 27.5 26.2 27 36 25 6 26.2 26.08 26.3 28.2 28.3 30.75 31 .0
LiCl LiBr
LiCIOI
Na I NaClOa
Rr
KCIQa Et,EJC18* n-Ru,NClOa n-BudNP3r (i-Am)&"i-Am)*B (i-Am)4N.I
30.15
32.06 28.17 28.65 16.37 26.95
3 3
7.30
20.20
4
7.30
20.05
4
7.30
3
18.78
3 12,13 3 14 10
11.97 11.97 13.28 9.39 9.39 8.185 8.185
18.78 18.78 18.78 18.78
19.26 8.185 18.675
2b 5
10 5
5 5 5 5 5
Table I presents the equivalent conductances and ionic conductances at infinite dilution for several electrolytes in PC. The ionic conductance of Lis is the lowest, which means that thp ion has a large effective size. The ionic conductance of CliD4-, I -,Br and C1- are approximately the same. Anions are poorly solvated in PC, and their ionic conductance is higher than the conductance of the cations. -$
Conductance ~ ~ ~ ~ ~ rof~Ale13 m ein nPCt s AQ, a strong Lewis acid which is very soluble in PC (3.2 M ) , increases the solubility of salts that are insoluble in pure PC by farming complex ions with the anions of these salts. AE13 in combination with LiCl was investigated as an electrolyte for high-energy batteries (ref 3 and 14-19). Conductance measurements and nmr studies were performed in order to understand the transport properties and the species present in A1C13 solutions in PC. Boden14 measured the epecific conductance of AlC13 in PC over a wide concentrakion r,snge. The maximum specific conductance of approximately 1 W 2 ohm--' cm-l occurs a t an AlC13 concentration of 1.2 M. The specific conductance falls off a t higher cojicentrati~)~s because of the increasing viscosity of the solution and due to ion association at high concentrations. Breivogel arid Eisenbergl5 measured the equivalent conduclaace of dilute solutions of AlCl3 and LiC1AlC13 in PC, using a dc conductivity method. The results were interpreted through the Onsager equation, after being corrected for viscosity effect using the Walden rule. The limiting equivalent conductance of LiAlC14 was estimated to be 34.5 ohm-l equiv-l, although the extrapolation was somewhat uncertain. l5 The experimental slope in the case of LiAI614 did not agree with the calculated Onsager slope. Breivogel and IEi~enberg~~ attempted to explain the anomalous minimum in the equivalent conductance of AlCl3 by the presence of different ionic species in different concentration regions. The rapid increase in the equivalent Conductance WLRSexplained as being caused by an increase in the numbier of ions per mole of solute as the concentration increases. The following equilibrium reactions were proposed as being able to explain such an increase in the equivalent conductance 3AICB3 -*AIC1," + AIzC1,'IAlICl, =F:& AEC1,- -I AI,C1,* The JournalofPhysical Chemistry, Val. 78, No. 24, 1974
(2 1
(3)
Although either of the equations can explain qualitatively the anomalous behavior, further work is required to confirm this hypothesis. A dif€erent approach was proposed by Keller, et al.,3 who found the same anomalous behavior of AE13 at low concentrations. The minimum in the plot of A0 us. C1I2 was explained by the hydrolysis of AIC13 with traces of water to give aluminum hydroxide and HCI. Keller, et al., also studied directly the ionic equilibria of AlCl3 in PG using nmr techniques. From the 27Al spectra, Keller concluded that the main species are Al(PC),3+ and AlCl*-, similar to the species present in an AlCI3 solution in acetonitrile. Nigh-resolution IN spectra of 1 M AIC13-PC indicate peaks due to coordinated PC as well as bulk PC. From the IN and the 27Alspectra, Keller showed that the A1 coordination number ( n ) is six. Therefore, the dissolution of AICl3 in PC proceeds according to Furthermore, it was observed that the a d d ~ t ~ oofn LiC1 to an AlC13-PC solution reduces the concentration of the coordinated A1 species, and a t the saturation point, where the LiClA1C13ratio is 1:1,the coordinated Al species disappears. Such observations can be explained by the reaction between Licl and A1(PC),j3+to give AICld-. Keller3 discusses the complexing strength of AI3+ toward several aprotic solvents and chloride ion. The complexing strength of AI3* toward 61- is stronger than toward PC, AN, and water, but weaker than toward DMF. This ionic equilibria analysis of AlC13 in PC, according t o Keilier, et al., is in contrast to the analysis of Brievogel and Eisenberg.15 Neither of these workers succeeded in explaining quantitatively the minimum in the e q u ~ ~ aconductance ~~nt plot of AlC13 in PC. Experimental Section Conductivities of the alkali metal chloride in AlC13-PC solutions were measured a t 25 and 3 5 O using an ac bridge. Sinusoinal signals at 20 kHz and amplitude of around 15 V were generated by an ac generator detector, Model 861 A, Electro Scientific Industries, Portland, Oreg. The cell resistance and capacitance were balanced with an impedance bridge, Model 290 A, Electro Scientific Industries, Portland, Oreg., and with variable decade capacitors, Models CDA-2 and CDA-3, Cornell-Dubilier Electronic Division, Federal Pacific Electric Division. The conductance cell consisted of two parallel bright platinum disk electrodes. Because of the relatively low conductivities of the nonaqueous solutions, the cell was designed to give a relatively low cell constant, 0.439 cm-t? which was determined using 0.1 and 0.01 N aqueous KCl solution. All electrical wires were shielded. At the frequency of 20 kHz the results were independent of the frequency. The solutions were prepared in an argon drybox by dissolving weighed amounts of the alkali metal chlorides in 1 m AlC13 solution in PC. The volumetric concentrations in moles per liter were calculated from the measured densities of the solutions. The alkali metal chloride concentration varied from 0 to 1 m, all in the presence of AIC13 (1rn 1. The preparation of the solutions was similar to the procedure described for the potential r n e a ~ u r e m e n t sThe .~~~ AICl3 salt was added very slowly to PC to prevent heating and darkening of the solution. Propylene carbonate (Jefferson Chemical Co., Houston, Tex.) was distilled a t 0.5 mm pressure by means of a commercially available distillation column (Semi-CAL series
Conductance Studies of the Alkali Metal Chlorides
2523
TABLE VI: Specific Conductance of CsC1 in AICI, (1 m)-PC Solution at 26 a n d 36"
TABLE PI: Speciffic Conductance of LiCl in AlCl ( I m)-PC S o h tion at 25 and 35 O m, mol/lg of PC 0.02 0.1 1 .o
-
e,--__
_-
lo%, ohm-' cm-l
25 O
35 O
25 O
35 O
11.0251 0.1262 1.2594
0.0250 0.1253 1.2512
6.708 6.741 6.700
8.315 8.442 8.434
TABLE 111: Specific Conductance of NaCl in A1CI3 (1 rn)-PC Solution a t 25 and 95" _.___l___l m, 6, M l O 3 ~ ,ohm-' cm-l
c,
lo3,, ohm-' cm-l
m, mol/ kg of PC
25 O
35 O
0.0025 0.01 0.10 0.25 0.50 1.oo
0.0031 0.0126 0.1264 0.3238 0.6597 I .3597
0.0031 0.0125 0.1259 0.3215 0.6555 1.3481
25 O 6.848 6.732 6.173 7.910 9.070 1 3 257
35 O 8.508 8.410 8 676 9 756 I1 171 13 806
l _ l l l l _
~ _ _ _ _ _ -
mol/kg of PC
25 O
35 O
25 O
35 O
0.01 0.10 0.25 0.50
0,0126 0 . 9264 0 .3I63 0.6350
0.0125 0.1253 0,3138 0.6279
6.971 6.955 6.910 7.119
8.702 8.693 8.662 8.941
__
TABLE I V Specific Conductance of KCl in AlCk m, mol/ kg of PC 0,0025 0.01 0.10 0.25 0 "50 1.oo
c,
1 0 3 ~ohm-' , cm-l
~----1__
25
35 O
25 O
35 O
0.0031 0,0126 0.12B'I 0.316'7 0.6390 1.300
0,0031 0.0125 0,1254 0,3143 0.6330 1.2920
6.915 6.994 7.278 7.754 8.516 10.210
8.591 8.763 9.108 9.649 10.630 12.725
TABLE V: Specific Conductance of RbCl in AlCl, (1m)-PC Sdriltfon at 25 a n d 35"
c,
ohm-' cm-1
l O 3 ~
_ I
25O
35 O
25 O
0.0031 0.0126
0.0632 0.1272 0.319,4
E.319i5
0.0031 0.0125 0.0626 0.1261 0.3168 1.3091
7.157 7.041 7.242 7.294 8.022 11.003
m, mol/kg of PC
p
(25O), g/ml p (35O), g/ml
~ I _ _ _ - I _ _ _ _ _ _ _
LiCl
0.5
NaCl
0.01 0.10 0.25 0.50 0.0025 0 .os 0.10 0.25 0.50 0.01 0.05 0.10 0.25 1.OO 0.0025 0.01 0.50 1.oo
KCI
RbCl RbCl
1. o
1.262 1.261 1 ,259 1.262 1.263 1.265 1.266 1.261 1.262 1.261 1 266 1.278 I .263 P .265 1.272 9 277 1.319 1,265 1.263 1.319 1.359
1.252 1.218 1 251 1.252 1.253 1.255 1.255 1 252 1.252 1 254 1.257 1.267 1.253 1.253 1.261 1.267 1.309 1.253 1.310 1.348
35 O ~
0.0025 0.01 0.05 0.10 0.25 1.oo
Salt
CSCI
_ _ . l _ _ l l _ . _ l l -
m, mol/ kg of PC
TABLE VII: Densities of t h e AlkaE Metal Chorides in AlCh (1 m)-PC at 25 and 35'
~~
~~
8.914 8.743 9.020 9.101 9.950 13.799
3650, Podbielniak, Franklin Park, Ill.) packed with stainless steel helices. The reflux ratio was 60 to 100 and the head temperature 66". The first 10% and the last 25% of the solvent wefe discarded. The "as received" solvent contains a few tenths of a per cent of the following impurities: water, propyleae glycol, propion aldehyde, and propylene oxideegGas chromatographic analysis of the product performed in this ~ a ~ Q r i ~ t showed O r y the water content to be always below 50 ppmefi The salts were dried in a vacuum oven (Hotpack, Philadelphia, Pa.) a t 200" and approximately 50 p pressure for at least 24 hr. The find solutions were treated with molecular sieves (Linde 4A) in order to remove traces of water. The molecular sievea were treated before use by heating (300"),high vacuum, and several flashes with argon. easurenierrts were made a t 25 and 35 f 0.01". Densif solutions of different alkali metal chloride molalities were measured using R pycnometer a t 25 and 35". Its
The specific conductance of the alkali metal chlorides in 81613 (1m)--P@ solution at 25 and 35" is given in Tables 11VI. The concentration is given on molarity basis (mole/
liter) and was transferred from the molality basis by multiplying by the density of the solution. Densities of different molalities of the alkali metal chlorides in AIC13 (1m)-PC solution at 25 and 35" are presented in Table VI1.
Discussion The specific conductance of the alkali metal chlorides in AIC13 (1 m)-PC solution is presented in Figures 1 and 2 at 25 and 35", respectively. The general trend, with the exception of LiC1, is that the specific conductance increases with an increase in the concentration of the alkali metal chloride, MCl. In the case of WaCl, the specific conductance is almost constant over the entire concentration range. A steady increase in the specific conductance can be observed for KCI, RbC1, and CsC1 solutions in AIC13 (1 m)-PC. Small minima can be observed at low concentrations of LiCl and CsC1. A comparison of the specific conductance o i the alkali metal chlorides shows that the specific conductance increases as we pass along the alkali metal series from Li to Cs. Despite the fact that Li i s the smallest ion, its chloride solutions have the lowest conductance, while Rb and Cs, which are large ions, have the highest. These observations can be explained on the basis of ionic equilibrium, solvation, and viscosity considerations. Our measurements yield a value of 6.9 X 10-3 ohm-1 cm-l for the specific conductance of a 1 m, i.e., 1.263 M ,solution of AlC13, as compared to BodenV4 law-frequency value of 9 X ohmd1 cm-1 for a 1A4 solution of AlClz in PC. However, the present results are in better agreement The Journalof Physical Chernishy, Val. 78, No. 24, 1974
Jacob Jorne and Charles W . Tobias
2524
'
*
o-LiCl
6O
-
l
-
r
----
w-L
0
Flgure 2. ( I rn)-PC
-
~
1.2
14
the alkali metal chlorides in AIC13
restricted to concentrations of up to 0.6 M. However, crude extrapolation of their data to 1 M gives a value of approximately 7 X lov3ohm-' cm-I at 25'. The temperature coefficient of the specific conductance of AIC13 (1 m ) solution in PC can be calculated from the data at 25 and 35'. Our value of 0.15 X ohm-l cm-' 'K-l is in reasonable agreement with d d d T = 0.17 X loW3,calculated after Kelier, et al. The temperature coefficient of the specific conductance of LiAlC14 (1 m ) in PC is 0.17 X ohm-' cm-l 'K-l, again in good agreement with a value of 0.18 X after Keller, et ~ 1 In. general, ~ good agreement was found between the present results of AlCl3 and LiAIC14 solutions in PC, and the corresponding results found in the literature. This agreement also should lend credibility to the data obtained for the rest of the alkali metal chloride-AlCb system. Unfortunately, the latter results cannot be compared to earlier results obtained elsewhere; previous work was restricted to the LiC1-AlC13 system. The addition of x moles of alkali metal chloride, MCI, to AlC13 (1 m ) solution in PC is accompanied by the following reaction xMCl t 1,$Al(PC)63+ + 3/,A1C1,xM+
0
8
r
04 06 0.8 I O MCI CONCENTRATION (mOleA1
02
figure 1. Specific conductance of (1 m)-PC solution at 25'. l4
-
d 01
1
t
I
I
I
LICI
I)
-
06 08 IO MCI CONCENTRATION fmole/ll
0.4
12
14
Specific conductance of the alkali metal chlorides in AICI, solution at 35'.
with the value 6.96 X ohm-I cm-l reported by Keller3 for 1 A4 AlC13 solution in PC a t 25'. Extrapolation of the conductance curve of Rreivogel and Eisenberg15results in a somewhat smaller value of approximately 6 X ohm-l cm-l. Chilton and Cook16 report a specific conductance of approximately 7.1 X for AlC13 (1 M ) at 25'. The specific conductance of LiAlC14 (I m ) a t 25' was measured in the present work as 6.7 X ohm-l cm-'. The molarity of this solution i s 1.26 M. Keller, et al.,3 reports a value of 6.58 X for saturated solution of LiCl in AlC13 (1 M ) in PC at 25', in1 good agreement with the present results. In addition, Keller's data confirm the present observation that the addition of LiCl to AlC13 (1 m ) solution reduces the conductance of the resultant solution. Eisenberg, et al. 's, conductance measurements of LiAlC14 in PC15 were The Journal of Physical Chernistry, VoI. 78, No. 24, 1974
+
----D
t1-r)/4Al(PC)63++ '3+X'/,A6GX4~4 3y/2PC (5)
The number of charge carriers increases by 0.5 x mol, and therefore, purely on this basis, the specific conductance should increase. The equivalent conductances of all the species are not known. The equivalent conductance of LiAIC14 in PC is reported as 34.5 ohm-l cm2 equiv-I.l5 The equivalent ionic conductance of Li+ in PC is 7.30 ohm-' cm2 equiv-l. Hence the estimated equivalent conductance of AlC14- is relatively quite high: 27.2 ohm-' em2 equiv-l (see Table I for comparison). The equivalent ionic conductances of the alkali metal ions in PC increases from Li+ to Cs+, despite the fact that the ionic crystal radius of Li+ is the smallest, and that of Cs+ the largest. This reversed trend was observed in most aprotic solvents as well as in water, and is caused by the tightly held sheath of solvent molecules attracted by the intense electric field of the small ion. The equivalent ionic conductances of Li+, Na+, and K+ in PC are 7.30,9.40, and 12.0, respectively (see Table I), and it is expected that the equivalent ionic conductances of Rb+ and Cs+ are even higher. The solvated radius of ions in nonaqueous solvents is discussed by Della Monica and Senatore.20The radii of the solvated metal ions increase from Li+ to Cs+ in most solvents (methanol, formamide, N,Ndimethylformamide, dimethylacetamide, pyridine, acetonitrile, and sulfolane). The same trend was observed by Yao and Bennion21 in DMSO. Mukherjee, Boden, and Lindauer5 report equivalent conductances for Li+ and K+ in PC of 7.30 and 11.97, respectively. The addition of MC1 to AlCl3 solution in PC results in two effects: addition of M+ ions, and a conversion of Al(Pc)63+to ions. On the basis of the discussion so far, both effects tend to increase the conductance, and the increase is larger as we move along the alkali metal series from Li to Cs. The equivalent conductance of Al(PC)63+ is not known since extrapolation to infinite dilution of AlC13 in PC is tenuous (because of the minimum at low concentrations) and therefore quantitative analysis is not possible. Viscosities of electrolytic solutions haw been used as an indication of the degree of structure within the solvent. In aqueous solutions the effects are generally ascribed to the
Conductance Studies of the Alkali Metal Chlorides
ability of the various ions to increase or decrease the structure of water over that of the pure solvent. Small ions, such as lithium, are structure makers, while large simple ions, such as cesium, are structure breakers. This i s the reason why the viscosities of aqueous alkali metai solutions decrease as the cations change along the series from Ei+ to Cs’. According to this consideration, the effect should not be observed for solvents exhibiting only a small tendency for structuring. However, Criss and MastroisaniZ2discuss this aspect, and show that even in s t r ~ ~ c t ~solvents, r~~~s the €3 coefficients in the Jones-Dole equatior i23 decrease with an increase in the size of the ion persumably because of structuring of the solvent By t h e smaller cations. In the present system, the original solut! or) is AlCh (1m)PC and not pure PC. This solution posses%:s a large degree of order to begin with. The addition of LiCt to this solution destroys the previous order by converting Al(PC&3+ to A E 4 - , but the small Li+ ion is a %+xwturemaker, and therefore the viscosity increases. On the other hand, the addition of CsCl, for example, destroys the initial order, but the large Cs+ ion is a poor order maker, and it is predicted, therefore, that the increase in the viscosity with concentration will be small or ever, reversed in the case of RbCl and CsCl solutions in AlC13-PC. Evidence that in PC viscosity varies with the size of the cation can be found in the viscosity measurements of Mukherjee and Boden4 The B , coefficient decreases in the order LiC104 > n-Bu4NCl04 > EtdNC104, in agreement with the size of the solvated cations. The minimum in the conductance curve for LiCl in AK13 (1 m)-PC can be the result of ionic association of LiC1 in PC.4,24-26The association constant for LiCl was estimated tQbe 557 from conductance measurements: and as 59 from emf m e a ~ u r e m e n t s The . ~ ~ minimum in the conductance curve of CsCl in AIC13 (1m)-PC can be the result of a corn. bination of the opposing factors which determine the conductance of the solution. The minimum in the plot Qf the equivalent conductance of AlC13 in PC was observed by several ~ o r k e r s . ~ There J~J~ is no conclusive explanation for this behavior a t low concentration. An attempt to explain the minimum on the basis of the water content of the solvent seems questionable because the minimum was observed by three independent laboratories and the water contents were probably dif-
2525
ferent. Moreover, if we assume that the minimum is the result of the water content, we can extrapolate to infinite dilution, neglecting the minimum, and obtain the molar conductance at infinite dilution, A0 = 18 ohm-1 cm2 mol-l. ‘The equivalent conductance of AlC14- was estimated before a t 24.2, and according to this, the equivalent ionic conductance of A ~ ( P C ) Gwould ~ + be s
- 3 . 2 ohm‘’ cm2 equiv-‘
(7)
Thus it seems that the minimum in the equivalent conductance of AlC13 is not due t o impurities, but is probably a genuine featurs associated with multiple ionic equilibria. Acknowledg auspices of t h e References
wg was conducted under the a e r g y Commission. ~
a
(1) Address cori
%or at the Department of Chemical Engineering , Wayne State University, Detroit, Mich. 48202 (2) (a) R. Fuoss CI Chem. SOC., 82, 1013 (1968); (b) Y. Wu and H. Fi ?020 (1966). (3) R. Keller. et al !o. NAS 3-8521, Dec 1969. (4) L. Mukherjee art,. hem., 73, 3965 (1969). (5) L. Mukherjee, D. UL- ,
