Conductance of Some 1:1 Electrolytes in N,N-Dimethylacetamide at 25°C

P1: FHD/FNV P2: FZN/FNV QC: FJQ

Journal of Solution Chemistry [josc] pp529-josl-375136 June 7, 2002 11:27 Style file version June 5th, 2002

Journal of Solution Chemistry, Vol. 31, No. 5, May 2002 (C© 2002)

Conductance of Some 1:1 Electrolytesin N,N-Dimethylacetamide at 25◦C

Debasish Das,1 Bijan Das,1,2,∗ and Dilip K. Hazra 1

Received November 6, 2001

Precise conductance measurements of solutions of lithium chloride, lithium bromide,lithium iodide, lithium perchlorate, lithium tetrafluoroborate, lithium hexafluoroarsen-ate, tetrabutylammonium bromide, and tetrabutylammonium tetraphenylborate inN,N-dimethylacetamide are reported at 25◦C in the concentration range 0.005–0.015 mol-dm−3. The conductance data have been analyzed by the 1978 Fuoss conduc-tance equation in terms of the limiting molar conductance (30), the association constant(Ka), and the association diameter (R). The limiting ionic conductances have been esti-mated from an appropriate division of the limiting molar conductivity of the “referenceelectrolyte” Bu4NBPh4. Slight ionic association was found for all these salts in thissolvent medium. The results further indicate significant solvation of Li+ion, while theother ions are found to be unsolvated inN,N-dimethylacetamide.

KEY WORDS: Electrical conductance; electrolytes; lithium ion;N,N-dimethylaceta-mide; reference electrolyte; limiting molar conductance; association constant; associa-tion diameter; ionic association; solvation.

1. INTRODUCTION

Lithium has been used for many years as an anode material for nonaqueousbatteries.(1) In such systems, the choice of electrolyte solution and optimization ofits salt concentration are two important factors. An electrolyte possessing high spe-cific conductivity and, hence, minimal ion–ion interaction is required to maintainthe cell at low resistance. Knowledge of the state of association of the electrolytesand their interaction with solvent molecules is essential for the optimal choice ofsolvent and electrolyte.

Recently, we have initiated a comprehensive program to study Li+ ion solva-tion in different nonaqueous solvents from the measurements of various transport,

1Department of Chemistry, North Bengal University, Darjeeling 734430, India.2Present address: Polymer-Institut, Universit¨at Karlsruhe (TH), Kaisersrtasse 12, 76128 Karlsruhe,Germany; email: [email protected]

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426 Das, Das, and Hazra

thermodynamic, and spectroscopic properties.(2−9) In this paper, an attempt ismade to unravel the nature of various types of interactions prevailing in solutionsof some lithium salts—lithium chloride LiCl, lithium bromide LiBr, lithium iodideLiI, lithium perchlorate LiClO4, lithium tetrafluoroborate LiBF4, and lithium hex-afluoroarsenate LiAsF6 in N,N-dimethylacetamide—from precise conductivitymeasurements. Conductance measurements have also been performed on twoother electrolytes, tetrabutylammonium bromide Bu4NBr, and tetrabutylammo-nium tetraphenylborate Bu4NBPh4, in order to obtain the limiting single-ion con-ductivities in this solvent medium.

2. EXPERIMENTAL

N,N-Dimethylacetamide (G.R.E. Merck, India,>99.5%) was distilled twicein an all-glass distillation set immediately before use and the middle fraction col-lected. The purified solvent had a density of 0.93652 g-cm−3, a coefficient of vis-cosity of 1.2244 mPa-s, and a specific conductance of about 1.01× 10−6 S-cm−1

at 25◦C. These values are in good agreement with literature values.(10)

The salts were of Fluka purum or puriss grade. Lithium chloride, lithiumbromide, lithium iodide, lithium tetrafluoroborate, and lithium hexafluoroarsenatewere dried under vacuum at high temperature for 48 h and were used withoutfurther purification. Lithium perchlorate was recrystallized three times from con-ductivity water and then dried under vacuum for several days. Tetrabutylammo-nium bromide was purified by recrystallization and was driedin vacuoat elevatedtemperature for 12 h. Tetrabutylammonium tetraphenylborate was prepared bymixing equimolar quantities of sodium tetraphenylborate (NaBPh4) and tetrabuty-lammonium bromide in aqueous medium. The salt was driedin vacuoat 80◦Cfor 48 h.

To avoid moisture pickup, all solutions were prepared in a dehumidified roomwith utmost care.

Conductance measurements were carried out on a Pye-Unicam PW 9509 con-ductivity meter at a frequency of 2000 Hz using a dip-type cell of cell constant1.14 cm−1 and having an accuracy of 0.1%. Measurements were made in an oilbath maintained within 25± 0.005◦C. The details of the experimental procedurehave been described earlier.(4,11) Solutions were prepared by mass for the conduc-tance runs, the molalities being converted to molarities using densities measuredwith an Ostwald–Sprengel type pycnometer of about 25-cm3 capacity. Severalindependent solutions were prepared and runs were performed to ensure the re-producibility of the results. Correction was made for the specific conductance of thesolvent.

The relative permittivity ofN,N-dimethylacetamide (ε = 37.78) at 25◦C wastaken from the literature.(10)



N,N-Dimethylacetamide 427

3. RESULTS AND CALCULATION

The measured molar conductance3 of electrolyte solutions, as a function ofmolar concentrationc at 25◦C, are given in Table I.

The conductance data have been analyzed by the 1978 Fuoss conductance-concentration equation.(12,13) For a given set of conductivity values (cj , 3j ; j =1, . . . , n), three adjustable parameters, the limiting molar conductivity30, asso-ciation constantKa, and the cosphere diameterR, are derived from the followingset of equations:

3 = p[30(1+ RX)+ EL] (1)

p = 1− α(1− γ ) (2)

γ = 1− Kacγ2 f 2 (3)

−ln f = βκ/2(1+ KR) (4)

β = e2/εkBT (5)

Ka = KR/(1− α) = KR(1+ KS) (6)

whereRX is the relaxation field effect,EL is the electrophoretic countercurrent,ε is the relative permittivity of the solvent,e is the electronic charge,kB is theBoltzmann constant,γ is the fraction of solute present as an unpaired ion,c is themolarity of the solution,f is the activity coefficient,T is the temperature in abso-lute scale, andβ is the twice the Bjerrum distance. The computations were per-formed on a computer using the program as suggested by Fuoss. The initial30

values for the iteration procedure were obtained from the Shedlovsky extrapola-tion(14) of the data. Input for the program is the set (cj,3j ; j = 1, . . . , n), n, ε, η,T , initial value of30, and an instruction to cover a preselected range ofR values.

In practice, calculations are made by finding the values of30 andσ , whichminimize the standard deviation,σ ,

σ 2 =n∑

j=1

[3j (calc)−3o

j (obs)]2/

(n− 2) (7)

for a sequence ofR values and then plottingσ againstR; the best-fitR corre-sponds to the minimum inσ vs. R curve. However, since a rough scan using unitincrement ofR values from 4 to 20 gave no significant minima in theσ (%) vs.Rcurves, theR value was assumed to beR= a+ d, wherea is the sum of the ioniccrystallographic radii andd is given by(13)

d = 1.183 (M/ρo)1/3 (8)

whereM is the molecular weight of the solvent andρo its density.




Table I. Equivalent Conductances and Corresponding Molaritiesof Electrolytes inN,N-Dimethylacetamide at 25◦Ca

104 c 3 104 c 3

LiCl LiBr149.961 50.67 150.418 51.70138.853 51.36 140.390 52.33127.745 52.12 130.362 52.90116.636 52.90 120.334 53.58105.528 53.73 110.307 54.1994.420 54.59 100.278 54.7083.312 55.56 90.251 55.4872.204 56.52 80.223 55.1861.095 57.59 70.493 55.84

60.715 57.60LiI LiClO 4

129.606 41.34 141.250 47.70120.180 41.75 131.987 48.09109.969 41.35 122.725 48.4699.757 42.88 113.463 48.8989.546 43.30 104.201 49.2378.549 43.89 94.938 49.6869.909 44.45 85.676 50.1559.691 45.02 76.414 50.6152.766 45.43 67.151 51.1047.032 45.87 57.889 51.69

LiBF4 LiAsF6

140.241 51.34 149.511 30.63129.810 51.85 139.543 31.01120.538 52.44 129.576 31.51110.107 52.96 119.608 31.8999.675 53.59 109.641 32.3790.403 54.22 99.674 32.9079.972 54.91 89.707 33.3969.541 55.67 79.739 33.9360.209 56.2749.837 57.22

Bu4NBr Bu4NBPh4

138.937 47.52 163.589 34.20129.013 48.22 151.471 34.66119.089 49.00 139.353 35.06109.165 49.71 127.236 35.5499.241 50.54 115.118 36.0589.317 51.49 103.000 36.5279.393 52.39 90.883 37.0969.469 53.35 78.765 37.6259.545 54.42 66.647 38.25

aUnits:c, mol-dm−3; 3, S-cm2-mol−1.




Table II. Conductivity Parameters of Electrolytes inN,N-Dimethylacetamide at 25◦Ca

Salt 30 Ka R σ%

LiCl 69.79± 0.20 45.76± 0.82 7.93 0.10LiBr 67.35± 0.26 33.14± 0.96 8.09 0.15Lil 51.97± 0.15 30.09± 0.78 8.33 0.15LiClO4 58.16± 0.06 22.33± 0.23 8.14 0.05LiBF4 65.08± 0.12 30.03± 0.46 8.31 0.09LiAsF6 43.26± 0.19 52.05± 1.28 9.26 0.09Bu4NBPh4 44.47± 0.09 30.97± 0.44 14.50 0.08Bu4NBr 69.27± 0.20 45.63± 0.88 12.10 0.08

aUnits:30, S-cm2-mol−1; Ka, dm3-mol−1; R, A.

The values of30, Ka, and R obtained by this procedure are reported inTable II.

4. DISCUSSION

The association constantsKa of these electrolytes (cf., Table II) indicate thatthese salts are slightly associated inN,N-dimethylacetamide. This implies thata preponderant portion of each salt remains dissociated in this solvent medium.This is quite expected because of the medium relative permittivity of the solventmedium. TheKa values of the lithium salts are, in general, found to decreasewith increasing size of the anion; LiAsF6 is, however, an exception, which hasthe highestKa value though the crystallographic radius of AsF−6 ion is maximumamong the anions investigated.

In order to investigate the specific behavior of the individual ions comprisingthese electrolytes, it is necessary to split the limiting molar electrolyte conductancesinto their ionic components. In the absence of accurate transport number data forthese systems, we have used the “reference electrolyte” method for the divisionof 30 into their ionic components. Bu4NBPh4 has been used as the “referenceelectrolyte.”(15) Bu4NBPh4 was also used as the reference electrolyte by Fuoss andHirsch(16) to evaluate the limiting ionic conductances in several organic solvents.We have divided the30 values of Bu4NBPh4 into ionic components using a methodsimilar to that proposed by Krumgalz(17) for division of viscosityB coefficients:

λo(Bu4N+)/λo(Ph4B−) = r (Ph4B−)/r (Bu4N+) = 5.35/5.00= 1.07 (9)

Ther values have been taken from the works of Gillet al.(18,19) The limitingion conductances calculated from the above equation are recorded in Table III.

It is seen from Table III that for the halide ions, theλ0 values decrease inthe following order: Cl− > Br− > I− i.e., the limiting ionic conductivity valuesdecrease with increasing size of these anions.




Table III. Limiting Ionic Conductances and Ionic Stokes’Radii in N,N-Dimethylacetamide at 25◦Ca

Ion λo± rs Ion λo± rs

Li+ 21.07 3.18 ClO−4 37.09 1.81Bu4N+ 22.99 2.81 BF−4 44.01 1.52Cl− 48.72 1.37 AsF−6 22.19 3.02Br− 46.28 1.45 Ph4B− 21.48 3.12I− 30.09 2.23

aUnit: λo±, S-cm2-mol−1; rs, A.

This is also found to be true for the molecular anions,i.e., theλ0 values ofthese ions decrease in the order: BF−

4 > ClO−4 > AsF−6 > Ph4B−.This observation indicates that all these anions remain unsolvated inN,N-

dimethylacetamide solutions. Had these ions been solvated inN,N-dimethylaceta-mide, their limiting ionic conductivity values would have been in the reverse or-der, since the smaller ions with higher surface charge density could associate agreater number of solvent molecules to form a larger solvodynamic entity withlower mobility. This is, obviously, not the case here.

The starting point for most evaluations of ionic conductances is Stokes’ lawthat contends that the limiting Walden product (the limiting ionic conductance-solvent viscosity product) for any singly charged, spherical ion is a function onlyof the ionic radius and, thus, under normal conditions, is a constant. In Table IIIwe have collected the Stokes’ radii (rS) of the ions inN,N-dimethylacetamide.For lithium ion, the Stokes’ radius is much higher than its crystallographic ra-dius, suggesting that this ion is significantly solvated in this solvent medium. TheStokes’ radii of the other ions are, however, found to be either very close to orsmaller than their corresponding crystallographic radii. This observation indicatesthat these ions are scarcely solvated inN,N-dimethylacetamide solutions. Thisalso supports our earlier contention derived from the order of the limiting ionicconductivity values (cf., the preceding paragraph).

It may thus be concluded that all these lithium salts remain slightly associ-ated inN,N-dimethylacetamide solutions apparently due to the medium relativepermittivity of the solvent. Lithium ion is found to be significantly solvated in thissolvent medium, while the other ions remain scarcely solvated.

REFERENCES

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6. B. Das, P. K. Muhuri, and D. K. Hazra,Acoust. Lett.18, 69 (1994).7. B. Das and D. K. Hazra,J. Phys. Chem.99, 269 (1995).8. P. K. Muhuri, B. Das, and D. K. Hazra,J. Phys. Chem.101, 3329 (1997).9. P. J. Victor, P. K. Muhuri, B. Das, and D. K. Hazra,J. Phys. Chem. B104, 5350 (2000).

10. Y. Marcus,Ion Solvation(Wiley, New York, 1985).11. D. Dasgupta, S. Das, and D. K. Hazra,J. Chem. Soc. Faraday Trans. 184, 1057 (1988).12. R. M. Fuoss,Proc. Natl. Acad. Sci. U.S.A.75, 16 (1978).13. R. M. Fuoss,J. Phys. Chem.82, 2427 (1978).14. R. M. Fuoss and T. Shedlovsky,J. Amer. Chem. Soc.71, 1496 (1949).15. B. S. Krumgalz,J. Chem. Soc. Faraday Trans. 179, 571 (1983).16. R. M. Fuoss and E. Hirsch,J. Amer. Chem. Soc.82, 1013 (1960).17. B. S. Krumgalz,J. Chem. Soc. Faraday Trans. 176, 1275 (1980).18. D. S. Gill,Electrochim. Acta24, 701 (1979).19. D. S. Gill and M. B. Sekhri,J. Chem. Soc. Faraday Trans. 178, 119 (1982).

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Conductance of Some 1:1 Electrolytes in N,N-Dimethylacetamide at 25°C