J. CHEM. SOC. FARADAY TRANS., 1991, 87(21), 3511-3513 351 1

Electrical Conductances for some Tetraalkylammonium Bromides, Lithium Tetrafluoroborate and Tetrabutylammonium Tetrabutylborate in Propylene Carbonate at 25 OC

Prakash K. Muhuri and Dilip K. Hama* Department of Chemistry, North Bengal University, 734 430 Darjeeling , India

Conductance measurements are reported for several symmetrical tetraalkylammonium bromides, lithium tetra- fluoroborate (LiBF,) and tetrabutylammonium tetrabutylborate (Bu,NBBu,) in propylene carbonate (PC) at 25 "C. The data have been analysed by the 1978 Fuoss conductance equation in terms of the limiting molar conductivi- ty, A', the association constant, K, , and the association distance R. The single-ion conductances have been determined from the A' value of Bu,NBBu, using it as a 'reference electrolyte'. The results indicate that with the exception of LiBF, to some extent, other salts are almost unassociated in this solvent medium. The evalu- ation of Stokes radii of the ions indicate that Li+ is extensively solvated while the other ions remain almost unsolvated. The results have been discussed in terms of the ion-solvating ability of PC and also compared with the previous values in this system.

Propylene carbonate (PC) has drawn much attention in recent years as a solvent medium for electrochemical studies' relating to high-energy batteries2v3 and free-radical species., It is a stable solvent of moderately high relative permittivity5 (64.40 at 25°C) and has good solvent properties6*' for a variety of organic and inorganic salts. Hence, it is of much interest to study the behaviour of electrolytes in such a solvent medium. The conductometric method is well known' to give valuable information regarding ion-solvent inter- actions of electrolytes in non-aqueous and mixed solvents. Although conductance measurements on alkali-metal iodides9-' and quarternary ammonium perchlorates6*' ' have been reported in PC, no such experimental data for tetraalkylammonium bromides (except tetrabutylammonium bromide) and lithium tetrafluoroborate are available in the literature. Conductance measurements on tetra- butylammonium tetrabutylborate have been reported by Takeda and co-workers,12 but this compound has been further investigated by us in order to maintain an internal consistency amongst the derived values with these electro- lytes.

We have therefore repeated a few of the earlier measure- ments and have also measured the electrical conductances of several additional tetraalkylammonium bromides, R,NBr (R = methyl to heptyl), LiBF, and Bu,NBBu, in PC at 25 "C. Single-ion conductances have been derived using Bu,NBBu, as the 'reference electrolyte' in an effort to provide reliable values of the ionic mobilities for these ions in this medium.

Experimental PC (Merck >99% pure) was dried over freshly ignited quick- lime for several hours13 and then distilled three times under reduced pressure under nitrogen, the middle fraction being taken each time. The purified sample had a density of 1.1988 g cm-3, viscosity of 2.471 CP and a specific conductance of ca. 0.73 x S cm-' at 25°C; these values are in good agreement with the literature values.' ',14

Tetraalkylammonium bromides were of purum or puriss grade (Fluka) and were purified as described in the liter- ature.' 5*16 The salts were purified by recrystallization and the higher homologues were recrystallized twice to ensure maximum purity. The recrystallized salts were dried in uacuo at elevated temperatures for 12 h.

Lithium tetrafluoroborate (Fluka, puriss) was dried under vacuum at high temperature for ca. 48 h immediately prior to use and was used without further purification.

Tetrabutylammonium tetrabutylborate (Alfa Products) was purified as suggested in ref. 17.

Conductance measurements were made using a Pye- Unicam PW 9509 conductivity meter at a frequency of 2000 Hz using a dip-type immersion cell of cell constant 0.751 cm-' and having an accuracy of +0.1%. The cell constant was checked frequently using standard KCI solutions. Mea- surements were made in an oil bath maintained at 25 0.005"C. Details of the experimental procedure have been described previously. " Several independent solutions were prepared and measurements were made with each of these to ensure the reproducibility of the results. All data were corrected with the specific conductance of the solvent. The corrected values were analysed by means of the Fuoss conductance e q ~ a t i o n . ' ~ . ~ '

Results The measured equivalent conductances and the correspond- ing concentrations, C , in molarities are given in Table 1. The data were analysed with the Fuoss conductance equation ' 9 * 2 0

which can be expressed as

( 1 )

(2)

(3)

- Inf= /?k/2(1 + kR) (4)

A = P[(Ao(l + R,) + EL]

P = [l - a(l - r)] 7 = 1 - KAcy2f2

e2 EkB T

p=- (5)

where R , and EL are relaxation and hydrodynamic terms, respectively, and the other terms have their usual meanings. The parameters A', K A and R were obtained by solving the above equations. Initial A' values for the iteration procedure were obtained from Shedlovsky extrapolation of the data.

In practice, calculations were made by finding the minimum values of A' and a for a sequence of R values and then plotting

o2 = [Ajcalc.) - Ajobs.)I2/(n - 2) j

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3512 J. CHEM. SOC. FARADAY TRANS., 1991, VOL. 87

Table 1 Equivalent conductances and corresponding molarities of the tetraalkylammonium bromides, tetrabutylammonium tetra- radii of the ions in PC at 25 "C butylborate and lithium tetrafluoroborate in propylene carbonate at 25 "C ion A:/s cm2 mol-l n:qo/S cmz rno1-l P r$nm

c/10-4 A/S cmz c/104 A/S cm2 Me,N + 12.85 0.319 0.26 mol dm-3 mol-' mol dm-3 mol-' Et,N+ 1 1.70 0.290 0.28

Pr,N+ 10.33 0.255 0.32

Table 3 Limiting ionic conductances, Walden products and Stokes

Me,NBr 13 1.702 100.094 84.861 60.056 50.047 40.037 24.760 10.536

444.474 375.533 300.067 226.398 159.916 100.621 75.466 50.059 25.155

Pr,NBr

Pen,NBr 5 19.858 348.875 199.279 100.506 90.109 74.513 60.304 45.027 30.152

Hep,NBr 523.988 399.977 300.450 200.862 99.558 75.105 60.084 45.063 30.042

Bu,NBBu, 206.727 149.532 120.59 1 89.582 74.422 60.364 39.692 24.807 9.923

27.18 27.67 27.97 28.44 28.73 28.95 29.40 29.99

22.85 23.31 23.84 24.54 25.04 25.79 26.10 26.49 27.07

19.30 20.19 21.29 22.1 1 22.33 22.6 1 22.82 23.10 23.45

18.12 18.68 19.05 19.73 20.5 1 20.93 21.00 21.55 2 1.80

15.38 15.85 16.17 16.48 16.64 16.85 17.18 17.54 18.00

Et,NBr 90.445 73.080 62.226 44.137 36.540 29.304 18.089

Bu,NBr 622.737 498.190 400.628 298.9 14 201.352 100.261 79.874 60.156 40.104 20.052

506.841 349.720 199.357 99.679 89.542 74.337 60.097 45.073 30.048 10.016

529.635 398.992 300.127 199.496 100.631 90.038 74.149 60.025 45.019 30.01 3 10.004

Hex,NBr

LiBF,

26.67 27.03 27.26 27.7 1 27.89 28.12 28.53

20.5 1 21.34 21.99 22.75 23.54 24.74 25.04 25.35 25.76 26.28

18.63 19.54 20.63 21.69 21.85 22.16 22.16 22.50 22.80 23.36

19.64 20.73 21.70 23.06 24.66 24.90 25.21 25.59 26.01 26.39 27.39

B U ~ N +

Pen,N+ Hex,N+ Hep,N+ Li +

Br- BBu, BF,

9.44 6.86 6.14 5.17 8.89

18.24 9.44

19.59

0.234 0.170 0.152 0.128 0.220 0.452 0.234 0.486

0.35 0.48 0.54 0.64 0.37 0.18 0.35 0.17

a(%) = 100a/Ao against R ; the best-fit R corresponds to a minimum of the a(%) us. R curve. First, approximate runs over a fairly wide range of R values were made to locate the minimum and then a fine scan around the minimum was made. Finally, with this minimized value of R, the corre- sponding Ao and a were calculated.

The values of A', K , and R obtained by this procedure are recorded in Table 2. The limiting ionic conductances (2;) based on the value of Bu,NBBu, are given in Table 3. The 2: value for the Li' ion was taken from ref. 11 to calculate the single-ion mobility for BF, ion, assuming that the rule of additivity holds in this case.

Discussion Table 2 shows that the limiting equivalent conductances (Ao) of the tetraalkylammonium bromides decrease as the alkyl chain-length increases. This is in agreement with earlier find- ings for tetraalkylammonium bromides in other aprotic sol- vents.21 The size and structure-forming effect decrease as the alkyl chain-length increases and consequently the mobility is in the reverse order. A' for Bu,NBr was reported by Jansen and Yeager." A comparison of the limiting equivalent con- ductance for Bu,NBr as obtained by us with that of ref. 11 shows a difference of ca. 0.4%, indicating the closeness of our values with theirs. Also, a comparison of the reported Ao value of Bu,NBBu, by Takeda and co-workers12 with ours shows a difference of ca. 1%. Takeda and co-workers'2 reported the Ao value directly from the extrapolation of A us. JC plots, while our value was determined by the Fuoss method,20 hence the observed difference.

The association constants in Table 2 show that these salts are essentially unassociated with the minor exception of LiBF, . Presumably this salt shows slight ion-pairing though the association constant is much less than that of LiC16 and LiBr.6 This may be due to the: very large size of the tetra- fluoroborate ion which has a lower affinity for the lithium ion

Table 2 PC at 25 "C

Conductance parameters of tetraalkylammonium bromides, lithium tetrafluoroborate and tetrabutylammonium tetrabutylborate in

~~~ ~

salts Ao/S cm2 mol- ' K,/dm3 mol- ' Walden product R/nm 0

Me,NBr Et,NBr Pr,NBr Bu,NBr Pen,NBr Hex,NBr Hep,NBr Bu,NBBu, LiBF,

~ ~~

31.09 k 0.02 29.94 0.01 28.57 k 0.02 27.68 f 0.01 25.10 f 0.03 24.38 f 0.03 23.41 & 0.03 18.88 f 0.01 28.48 & 0.02

6.82 +_ 0.1 1 8.15 f 0.10 4.20 f 0.07 5.00 f 0.04 3.92 f 0.12 4.71 f 0.16 3.65 f 0.10 5.79 * 0.12

10.09 f 0.11

0.768 0.740 0.706 0.684 0.620 0.602 0.578 0.467 0.704

1.40 1.70 1.33 1.23 0.83 1.30 1.05 1.31 1.32

0.06 0.03 0.12 0.07 0.20 0.27 0.19 0.10 0.15

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J. CHEM. SOC. FARADAY TRANS., 1991, VOL. 87 3513

than the smaller C1- and Br- ions. The decrease in the association constant with increasing anion size agrees with the theories of Denison and Ramsey,22 and G i l k e r ~ o n . ~ ~ The higher A' value of LiBF, than that of LiCl and LiBr also corroborates the above viewpoint. However, for R4N+ ions, the general decrease in the association constant with increas- ing cation size is in agreement with the charge density values of these ions.

The single-ion conductances were evaluated from the divi- sion of A' value of Bu,NBBu, using the r e l a t i ~ n s h i p : " ~ ~ ~

&(Bu,N+) = A,(Bu,B-) (7) The reason behind the choice of Bu,NBBu, as the reference electrolyte is in the fact that the cation and anion in this case are symmetrical in shape and have almost equal van der Waals volumes.

The 2, values of the ions thus obtained are presented in Table 3. Kay and co-workers' previously analysed the con- ductance data of several workers and calculated the best esti- mate of limiting ion conductances in PC at 25°C. Comparison of our results with theirs reveals that in the case of Me,N+, Et,N+ and Pr,N+ ions, the A0 values obtained by us are 1-11% lower, and for Bu,N+ the value is 5% higher than the values proposed by Kay and co-workers. This discrepancy is due to the different procedures

for the calculation of A' values and also on the choice of the 'reference electrolyte','*" which was also differ- ent for calculating the limiting ion conductances in non- aqueous solvents.

The Walden products (E,:qo) and Stokes radii (r,) of the ions are reported in Table 3. Walden products are usually employed to discuss the interactions of the ions with the solvent medium. From Table 3, we see that for large R4N+ ions, i : q o increases from the tetraheptylammonium ion to the tetramethylammonium ion and for the electrolyte taken as a whole it follows the same sequence (Table 2). This leads to the fact that electrostatic ion-solvent interaction is very weak in these cases. On the other hand, the alkali-metal ions are small enough to possess high charge density, resulting in strong ion-solvent interactions." From Table 3, it can be seen that the Stokes radii increase with increasing size of the tetraalkylammonium ions and this is most likely due to the lower ionic mobilities of these cations. For Li+, however, the Stokes radius was much greater than its crystallographic radius (0.93 A),25 indicating that it was substantially solvated in this solvent medium. On the other hand the higher mobil- ity of the Br- ion than the cations relative to its crystallo- graphic size (1.80 indicates that it is poorly solvated in this medium. The slight difference in limiting ionic conduc- tance values of Br- and BF, ions seems to indicate that the effective sizes of these anions in PC are almost the same and

thus very little solvation, if any, is involved. On the other hand, the very low mobility of the tetrabutylborate ion has been attributed to its very much larger size. Thus, it appears that the large sizes of R4Nf ions, their low charge densities and the high relative permittivity of PC render these ions to be free, unassociated and almost unsolvated in this medium.

P. K. M. thanks the University of North Bengal for the award of a junior fellowship.

References 1

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5 6

7

8

9 10

1 1 12

13 14 15

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Paper 1/01635K; Received 9th April, 1991

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