Z. Phys. Chem.218 (2004) 341–348 by Oldenbourg Wissenschaftsverlag, München

Electrical Conductances of Some Alkali-MetalSalts in N,N-Dimethylacetamide–WaterMixture at 25 ◦C

By Debashis Das, Bijan Das, and Dilip K. Hazra∗Department of Chemistry, North Bengal University, Darjeeling 734 430, India

(Received October 6, 2003; accepted in revised form December 17, 2003)

Electrical Conductance / Alkali-Metal Salts / N,N-Dimethylacetamide /Limiting Molar Conductance / Ionic Association / Solvation

Precise measurements on electrical conductances of the solutions of lithium chloride(LiCl), lithium bromide (LiBr), lithium iodide (LiI), lithium perchlorate (LiClO4),lithium tetrafluoroborate (LiBF4), sodium bromide (NaBr), sodium tetraphenylborate(NaBPh4), potassium bromide (KBr), rubidium bromide (RbBr), cesium bromide (CsBr)and tetrabutylammonium bromide (Bu4NBr) in N,N-dimethylacetamide+ water (50% v/v)mixture have been reported at 25◦C in the concentration range 0.02–0.05 mol dm−3.The conductance data have been analyzed by the 1978 Fuoss conductance–concentrationequation in terms of the limiting molar conductance (Λ0), the association constant(KA) and the association diameter (R). The limiting ionic conductances (λ0

±) havebeen estimated from the appropriate division of the limiting molar conductivity valueof the “reference electrolyte” tetrabutylammonium tetraphenylborate (Bu4NBPh4). Theelectrolytes investigated here are found to be significantly dissociated in this solventmedium and all ions remain unsolvated inN,N-dimethylacetamide+ water (50% v/v)mixed solvent system with exception of the lithium ion where significant solvation hasbeen noticed. The results have been interpreted in terms of the specific constitutional andstructural factors of the solvent and of the solute ions.

1. IntroductionStudies of the transport properties of electrolytes in different solvent me-dia are of great importance to obtain information on the behavior of ions insolution. The conductometric method is well-suited to investigate the ion–solvent and ion–ion interactions in electrolyte solutions [1, 2]. Recently, wehave initiated a comprehensive program to study the solvation and associ-ation behavior of several 1:1 electrolytes in different nonaqueous solvents

* Corresponding author. E-mail: dkhazra@rediffmail.com

342 D. Daset al.

from the measurements of various transport, thermodynamic, and spectro-scopic properties [3–7]. As a part of a series of investigations, we have veryrecently reported [8, 9] the conductances of a number of alkali-metal andtetraalkylammonium salts in the pure solventN,N-dimethylacetamide at 25◦C.Now, we have extended the work to study the conductometric behavior of somealkali-metal salts inN,N-dimethylacetamide+ water (50% v/v) in an attemptto unravel the nature of various types of interactions prevailing in these solu-tions and to study the effect of addition of water toN,N-dimethylacetamide onthe ion association and solvation behaviour of these electrolytes.

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 frac-tion was collected. The purified solvent had a specific conductance of about10−6 S cm−1 at 25◦C. The properties of the purified solvent agree well withthe literature values [10]. Triply distilled water with a specific conductanceof less than 10−6 S cm−1 at 25◦C was used for the preparation of the mixedsolvent. The mixed solvent system (50%N,N-dimethylacetamide+ water v/v)had a density of 0.99877 g cm−3 and a coefficient of viscosity of 0.03318 mPa sat 25◦C.

The salts were of Fluka’s purum or puriss grade. Lithium perchlorate wasrecrystallized three times from conductivity water and then dried under vacuumfor several days. Sodium tetraphenylborate was recrystallized from acetone anddriedin vacuo at 80◦C for 72 h. Tetrabutylammonium bromide was purified byrecrystallization from conductivity water, dried for 3–4 h at 100◦C. The othersalts were dried under vacuum for a long time immediately prior to use andwere used without further purification.

In order to avoid moisture pickup, all solutions were prepared in a dehu-midified room with utmost care.

Conductance measurements werecarried out on a Pye-Unicam PW 9509conductivity meter at a frequency of 2000 Hz using a dip-type cell of cell con-stant 1.14 cm−1 and having an accuracy of 0.1%. Measurements were madein an oil bath maintained within 25±0.005◦C. The details of the experimen-tal procedure have been described earlier [11, 12]. Solutions were prepared bymass for the conductance runs, the molalities being converted to molarities bythe use of densities measured with an Ostwald-Sprengel type pycnometer ofabout 25 cm3 capacity. Several independent solutions were prepared and runswere performed to ensure the reproducibility of the results. Due correction wasmade for the specific conductance of the solvent.

The relative permittivity ofN,N-dimethylacetamide+ water (50% v/v)mixture (ε = 59.92) at 25◦C was obtained using the equations as described inthe literature [13].

Electrical Conductances of Some Alkali-Metal Salts. . . 343

3. Results and calculationThe measured molar conductance (Λ) of electrolyte solutions as a function ofmolar concentration (c) at 25◦C are given in Table 1.

The conductance data have been analyzed by the 1978 Fuoss conductance–concentration equation [14]. For a given set of conductivity values (cj , Λ j ,j = 1, . . . , n), three adjustable parameters – the limiting molar conductivity(Λ0), association constant (KA) and the cosphere diameter (R), are derivedfrom the following set of equations:

Λ = p[Λ0(1+ RX)+ EL] (1)

p = 1−α(1−γ) (2)

γ = 1− KAcγ 2 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 isthe molarity of the solution,f is the activity coefficient,T is the temperaturein absolute scale, andβ is twice the Bjerrum distance. The computations wereperformed on a computer using the program as suggested by Fuoss. The initialΛ0 values for the iteration procudure were obtained from Shedlovsky extrapo-lation [15] of the data. Input for the program is the set (cj , Λ j ; j = 1, . . . , n),n, ε, η, T , initial value ofΛ0, and an instruction to cover a preselected range ofR values.

In practice, calculations are made by finding the values ofΛ0 andσ whichminimize the standard deviation,σ ,

σ 2 =∑ [

Λ j (calcd) −Λ0j (obsd)

]2/(n −2) (7)

for a sequence ofR values and then plottingσ againstR; the best-fitR corres-ponds to the minimum inσ vs. R curve.

The values ofΛ0, KA and R obtained by this procedure are reported inTable 2.

4. DiscussionThe association constants (KA) of these electrolytes (cf. Table 2) – whichare always less than 10 – indicate that these salts are significantly dissoci-ated inN,N-dimethylacetamide. This implies that these salts remain mainly

344 D. Daset al.

Table 1. Equivalent conductances and corresponding molarities of electrolytes inN,N-di-methylacetamide+ water (50% v/v) at 25◦C.

104 c/mol dm−3 Λ/S cm2 mol−1 104 c/mol dm−3 Λ/S cm2 mol−1

LiCl LiBr512.95 22.41 470.01 21.01477.58 22.61 437.59 21.17442.20 22.79 405.18 21.29406.83 22.99 372.76 21.43371.45 23.19 340.35 21.60336.07 23.40 307.93 21.76300.70 23.60 275.52 21.93265.32 23.86 243.10 22.10

Lil LiClO 4

444.92 17.75 433.95 19.18414.24 17.85 404.02 19.30383.55 17.93 374.09 19.41352.87 18.02 344.17 19.54322.18 18.12 314.24 19.68291.50 18.22 284.31 19.83260.82 18.32 254.38 20.00230.13 18.47 224.46 20.12

LiBF4 NaBr420.05 21.85 438.72 31.41391.09 21.98 406.60 31.59362.12 22.13 376.48 31.78333.15 22.24 346.36 31.95304.18 22.39 316.24 32.14275.21 22.56 286.12 32.33246.24 22.70 256.01 32.55217.27 22.88 225.89 32.78

KBr RbBr437.36 35.34 472.68 36.01407.20 35.48 440.08 36.12377.03 35.59 407.48 36.22346.87 35.70 374.88 36.35316.71 35.82 342.29 36.47286.55 35.99 309.69 36.60256.38 36.10 277.09 36.71226.22 36.26 244.49 36.85

CsBr NaBPh4432.99 35.06 436.50 20.00403.13 35.22 406.40 20.10373.27 35.41 376.29 20.20343.40 35.59 346.19 20.29313.54 35.79 316.09 20.40283.68 36.00 285.98 20.50253.82 36.20 255.88 20.62223.96 36.43 225.78 20.75

Electrical Conductances of Some Alkali-Metal Salts. . . 345

Table 1. continued.

104 c/mol dm−3 Λ/S cm2 mol−1

Bu4NBr435.90 21.14405.84 21.33375.78 21.55345.72 21.77315.65 21.98285.59 22.13255.53 22.42225.47 22.68

Table 2. Conductivity parameters of electrolytes inN,N-dimethylacetamide+ water (50%v/v) at 25◦C.

salt Λ0/S cm2 mol−1 KA/dm3 mol−1 R/Å σ%

LiCl 26.61±0.03 5.19±0.06 14.0±0.5 0.04LiBr 24.40±0.03 4.58±0.06 9.5±0.5 0.04Lil 20.25±0.03 2.47±0.08 12.5±0.5 0.05LiClO4 22.30+0.03 4.77±0.10 6.5±0.5 0.06LiBF4 25.19±0.03 4.47±0.10 6.5+0.5 0.04NaBr 35.76±0.02 3.88±0.04 8.0±0.5 0.02NaBPh4 25.52±0.01 3.12±0.03 6.0±0.5 0.03KBr 38.50±0.03 1.99±0.04 8.5±0.5 0.04RbBr 38.81±0.02 1.68±0.02 12.0±0.5 0.02CsBr 39.50±0.01 3.45±0.02 8.0±0.5 0.01Bu4NBr 25.54±0.08 6.86±0.19 16.0±0.5 0.01

in the form of free ions in this solvent medium. A comparison of the avail-able association constant values [15, 16] in pureN,N-dimethylacetamide withthose obtained in theN,N-dimethylacetamide+ water system in the presentstudy reveals that the addition of water to pureN,N-dimethylacetamide re-sults in a lower level of ionic association. This may be attributed to the in-creased relative permittivity of the mixed solvent medium compared to the pureN,N-dimethylacetamide.

In order to investigate the specific behavior of the individual ions com-prising these electrolytes, it is necessary to split the limiting molar electrolyteconductances into their ionic components. In the absence of accurate trans-port number data for these systems, we have used the “reference electrolyte”method for the division ofΛ0 into their ionic components. Tetrabutylammo-nium tetraphenylborate (Bu4NBPh4) has been used as the “reference elec-trolyte” [16]. Bu4NBPh4 was used as the “reference electrolyte” also by Fuoss

346 D. Daset al.

Table 3. Limiting ionic conductances, Walden products and Stokes radii inN,N-dimethyl-acetamide+ water (50% v/v) at 25◦C.

ion λ0±/S cm2 mol−1 λ0

±η0/S cm2 mol−1 Pa s rS/Å

Li + 6.76 0.022 3.66Na+ 18.13 0.060 1.36K+ 20.87 0.069 1.18Rb+ 21.18 0.070 1.17Cs+ 21.87 0.072 1.13Bu4N+ 7.81 0.026 3.12Cl− 19.85 0.066 1.24Br− 17.63 0.058 1.40I− 13.49 0.044 1.83ClO4

− 15.53 0.051 1.59BF4

− 18.42 0.061 1.34BPh4

− 7.39 0.024 3.35

and Hirsch [17] to evaluate the limiting ionic conductances in several organicsolvents. We have divided theΛ0 values of Bu4NBPh4 into ionic componentsusing a method similar to that proposedby Krumgalz [18] for division of vis-cosity B coefficients:

Λ0(Bu4NBPh4) = λ0(Bu4N+)+λ0(Ph4B−) (8)

λ0(Bu4N+)

λ0(Ph4B−)= r(Ph4B−)

r(Bu4N+)= 5.35

5.00. (9)

The r values have been taken from the works of Gillet al. [19, 20]. Therelevant limiting molar conductance of the electrolyte tetrabutylammoniumtetraphenylborate Bu4NBPh4 was obtained from the limiting molar conduc-tivity values of Bu4NBr, NaBPh4 and NaBr by the method of additivity. Thelimiting ion conductances calculated from the above equations are recorded inTable 3.

The limiting ionic equivalent conductivities of the alkali-metal and halideions in the present solvent system are substantially lower than those observed inaqueous solutions [21]. It is generally accepted that the alkali-metal and halideions possess an excess mobility in aqueous medium owing to their ability tobreak the hyrogen bonds in their immediate vicinity and thereby reduce thelocal viscosity.

It is seen from Table 3 that for the halide ions, theλ0 values decrease in thefollowing order:

Cl− > Br− > I−

i.e., the limiting ionic conductivity values decrease with increasing size of theseanions.

Electrical Conductances of Some Alkali-Metal Salts. . . 347

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

BF4− > ClO4

−> Ph4B

−.

This observations indicate that allthese anions remain unsolvated inN,N-dimethylacetamide+ water solvent system investigated here. Had these ionsbeen solvated in the mixed solvent medium, their limiting ionic conductivityvalues would have been in the reverse order since the smaller ions with highersurface charge density could associate greater number of solvent molecules toform a bigger solvodynamic entity with lower mobility. This is, obviously, notthe case here.

The starting point for most evaluations of ionic conductances is Stokes’ lawthat contents that the limiting Walden product (the limiting ionic conductance–solvent viscosity product) for any singly charged, spherical ion is a func-tion only of the ionic radius and thus, under normal conditions, is a con-stant. In Table 3 we have collected the Stokes’ radii (rS) of the ions inN,N-dimethylacetamide+ water solvent system. For lithium ion, the Stokes’ radiusis much higher than its crystallographic radius suggesting that this ion is sig-nificantly solvated in this solvent medium. The Stokes’ radii of the other ionsare, however, found to be either very close to or smaller than their correspond-ing crystallographic radii [10]. Thisobservation indicates that these ions arescarcely solvated in the mixed solvent medium. This also supports our ear-lier contention derived from the order of the limiting ionic conductivity values(cf. the proceeding paragraph). Similar behaviour has also been observed inpureN,N-dimethylacetamide solutions [8].

It may thus be concluded that all these alkali-metal salts remain signifi-cantly dissociated inN,N-dimethylacetamide+ water solvent system appar-ently due to the high relative permittivity of the solvent medium. Lithium ionis found to be significantly solvated in this solvent medium while the other ionsremain scarcely solvated.

Acknowledgement

The authors are thankful to the University of North Bengal for financial assis-tance.

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