J . Chem. SOC., Faraday Trans. 1, 1982,78, 119-125

New Approach to the Evaluation of Single-ion Conductances in Pure and Mixed Non-aqueous Solvents

[Part 21

BY D I P SINGH GILL* A N D M A D H U BALA SEKHRI

Department of Chemistry, Himachal Pradesh University, Simla- 17 1005, India

Received 9th December, 1980

Equivalent conductances of tetrabutylammonium tetraphenylborate (Bu,NBPh,) in acetonitrile (AN) and in several acetonitrile+ benzene (AN + BN) mixtures covering the dielectric constant range 12.3 < E < 36.0 have been measured at 25 OC. Limiting ion conductances ,I: for Bu,N+ and Ph,B- have been determined by the method of Fuoss and coworkers; the ion conductances thus obtained are in quantitative agreement (within an average of +2%) with the values predicted by an empirical equation already proposed from our laboratory. These investigations thus provide further positive support for our new method for the evaluation of limiting ion conductances.

In a previous paper, we have proposed an equation for the evaluation of limiting ion conductances dp in pure and mixed non-aqueous so1vents.l This equation predicts limiting ion conductances of Bu,N+, Pr,N+ and Et,N+ in pure and mixed non-aqueous solvents in quantitative agreement with the experimentally determined values. In the present paper we report some conductance measurements of Bu,NBPh, in pure acetonitrile (AN) and in several acetonitrile + benzene (AN + BN) mixtures covering the dielectric constant range 12.3 < E < 36.0 at 25 O C to provide further positive support for the usefulness of our equation for evaluating limiting ion conductances in pure and mixed non-aqueous solvents.

E X P E R I M E N T A L Acetonitrile (E. Merck, 99 % purity) was purified by fractional distillation (two times) over

P,O, through a long vertical column. The purified solvent with density 0.7766 g ~ m - ~ , viscosity 0.341 x kg m-' s-l (cP), dielectric constant 36.0 and specific conductance (1-4) x lo-* S2-l cm-l (all at 25 "C) was used. These physical constants agree well with the literature2 and also with our previously reported value^.^ The water content of the solvent was found to be < 50 ppm. The purified solvent was used immediately after distillation.

Benzene (B.D.H. AnalaR of 99.5% purity) was refluxed over sodium metal for 8-10 h and was then slowly fractionated through a long vertical column. The purified solvent had a density of 0.8735 g C M - ~ and viscosity of 0.608 kg m-ls-l (cP), values which agree well with the literature values.,

Bu,NBPh, was prepared by the method of Accascina et aL5 Conductances were measured with a calibrated Toshniwal conductance bridge model

CL10/02A at a frequency of 3000 Hz. A conductance cell similar in design to that reported by Shedlovsky6 with bright platinum electrodes was used. The cell constant was determined following the method of Fuoss and coworkers7 using aqueous potassium chloride solutions in the concentration range (3-70) x lo-, mol dm-3. All measurements were carried out at

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120 S I N G LE-ION C O N D U C T A N C ES

TABLE 1 .-EQUIVALENT CONDUCTANCES, A, AND MOLAR CONCENTRATIONS, c, OF Bu,NBPh4 IN ACETONITRILE AND ACETONITRILE + BENZENE MIXTURES AT 25 O C

c/ 10-4 A c/ 10-4 A c/ 10-4 A

100% AN 88% A N 56% AN

9.744 110.1 1 21.02 104.39 28.30 102.02 35.40 99.50 42.32 97.47 49.08 97.04 55.67 94.99 62.10 93.60

94% AN

9.299 16.38 23.33 30.09 36.67 43.07 49.3 1 61.29

106.00 103.02 99.66 97.70 95.5 1 94.03 92.78 91.29

22.77 94.52 28.69 93.05 34.49 90.22 42.06 88.27 47,60 86.65 54.83 85.49 61.87 84.24

74% A N

5.610 96.26 17.76 90.9 1 28.01 87.57 32.97 86.44 37.78 84.37 44.82 82.83

66% AN

5.150 80.10 8.930 76.85

23.42 69.45 29.3 1 65.25 33.01 64.53 37.85 62.42

51% A N

82.16 1.442 4.350 78.43 8.67 1 74.14

13.47 71.87 15.06 69.72 19.41 67.62 21.63 65.88

45% AN

5.400 88.80 10.60 84.92 14.53 82.63 19.70 79.90 23.30 78.31 26.90 76.79

3.856 71.97 13.98 63.32 16.03 62.25 18.69 59.38 21.30 58.1 1 23.83 56.65

TABLE DERIVED CONDUCTANCE PARAMETERS FOR Bu4NBPh, IN ACETONITRILE AND ACETONITRILE + BENZENE MIXTURES AT 25 *C BY SHEDLOVSKY'S METHOD

100 94 88 74 66 56 51 45

36.0" 33.3b 29.7b 22.9b 19.4b 1 5.7b 14.0b 12.3b

0.341" 0.355b 0.367b 0.395b 0.414b 0.43gb 0.450b 0.466b

1 19.96 1 15.69 11 1.40 105.74 99.28 91.96 89.25 84.32

11 9

13 13 21 31 25 52

a Ref. (3); ref. (11).

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D. S. G I L L A N D M. B. S E K H R I 121

25.00+0.01 O C . AN+BN mixtures were prepared by weight and in each case a range of concentrations of the salt was produced by adding stock solutions of appropriate concentrations from a weight burette to a known quantity of the solvent mixture taken in the conductance cell. In all cases the measurements were repeated with different stock solutions to obtain reproducible results. The reproducibility of the conductance measurements is ca. 0.2%.

R E S U L T S A N D DISCUSSION

The measured equivalent conductances, A, and the corresponding molar concen- trations, c, of Bu,NBPh, in AN and in AN+BN mixtures at 25 O C are reported in table 1. The association constant, KA and the limiting equivalent conductance (A,) in all cases have been iteratively calculated by a least-squares treatment with an IBM 1620 computer using Shedlovsky’s rnethods-lo which involves the following set of equations

- 1 SA -

S =

D =

and a =

8.204 x 105A, 82.5 +--- (&T)$ 7](ET)*

1.8246 x lo6 ( c a ) i / ( ~ T ) i 1 + 50.29 x los R (ca)l/(&T)t

-

For the analysis of conductance data, values of the dielectric constant ( E ) and viscosity ( r ) for AN and AN + BN mixtures were taken from the literature3. l1 and are also reported in table 2.

Justice12 has suggested that the Bjerrum critical distance,

e2 q = - 2 ~ k T

should be used for the calculation of mean-ion activity coefficients from eqn (4). Our derived conductance parameters reported in table 2 have also been obtained after setting R = q in eqn (4) . The standard deviations in A, and K A values of table 2 obtained by applying standard’statistical equations13 were found to be always less than +0.2% and lo%, respectively.

The root mean-square deviations oA calculated from the standard deviations of the individual points in no case exceeded the experimental uncertainty of the present conductance measurements, i.e. 0.2 %. This shows the good applicability of Shedlovsky’s equation to our conductance data.

The conductance measurements in the present work have been made over a wide range of dielectric constant (36.0 2 e 2 12.3) and the precision of our conductance data is ca. +0.2%. The use of all other conductance equations which demand a

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122 S I N G LE-ION C O N D U C T A N CES

precision in the conductance data much better than +0.1% were not thought appropriate for the analysis of the present data. Fuoss and c o - w ~ r k e r s ~ ~ ~ ~ ~ also preferred to analyse their conductance data for a number of solvent mixtures where the measurements were made over a wide range of dielectric constant by the Fuoss meth0d,~7 l6 which is closely similar to Shedlovsky's method. Fuoss and Shedlovsky9

TABLE 3.-EXPERIMENTAL AND THEORETICALLY CALCULATED LIMITING ION CONDUCTANCES FOR Bu,N+ AND Ph,B- IN ACETONITRILE AND ACETONITRILE + BENZENE MIXTURES AT 25 "C

mol % RP(Bu,N+) % A N & 1.4% AZ(BU,N+)~ difference

100 94 88 74 66 56 51 45

62.26 60.04 57.82 54.88 51.53 47.73 46.32 43.76

63.62 60.63 58.12 53.04 49.76 46.94 45.49 43.74

- 2.2 - 1.0 - 0.6

3.4 3.5 1.7 1.8 0.1

mol % RP(Ph,B -) % AN & I % Az(Ph,B-)b difference

100 94 88 74 66 56 51 45

57.70 55.65 53.58 50.86 47.75 44.23 42.93 40.56

58.24 - 55.57 53.27 48.68 46.06 43.16 41.84 40.24

.1.0 0.2 0.6 4.3 3.6 2.5 2.6 0.8

a For the calculation of these values from eqn (6), ri was taken as 5.00 A and r y as 0.85 A For the calculation of these values from eqn (6), ri was taken as 5.35 A and ;

have shown that the two treatments yield the same values of A. and slightly different values of association constant; in the range lo3 >, KA >, 1 Shedlovsky's treatment should be preferred for extrapolation. As our KA values for Bu,NBPh, lie in this range, we have thus preferred to analyse our conductance data by Shedlovsky's method and not by the Fuoss method.

To give an indication of the precision of the present conductance measurements, our A, value, 119.96 i2-l cm2 molt1 for Bu4NBPh, in pure AN from table 2, can well be compared with the A. value of 119.7 C2-I cm2 mol-l reported by Coetzee and Cunningham.17 These values are in agreement with each other within +0.2%, i.e. the claimed accuracy of the present measurements.

LIMITING I O N C O N D U C T A N C E S

Using the assumption of Fuoss and c o ~ o r k e r s ~ ~ ~ l5 (which is claimed to be valid within 1 %) that the limiting transference number of Bu,N+ in Bu,NBPh, is 0.519 and is independent of the so1vent,l49 l5 limiting ion conductances 2; for Bu,N+ and

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D. S. G I L L A N D M. B. SEKHRI 123

Ph,B- in pure AN and in AN + BN mixtures have been calculated from the A,, values of Bu,NBPh, from table 2. These values are reported as A:(Bu,N+) and Ay(Ph,B-) in table 3. The validity of the assumption of Fuoss and coworkers can be checked from a comparison of the limiting ion conductances of Bu,N+ and Ph,B- in pure AN from table 3 with such values obtained from direct transference-number measurements in AN. The limiting ion conductances of 62.26 and 57.70 0-l cm2 mol-1 for Bu,N+ and Ph,B- in AN in table 3 are within 1.4 and 1 .Ox, respectively, in agreemenf with the values 61.4 and 58.3 0-l cm2 mol-l reported by Springer et al.lS from direct transference-number measurements in AN.

P R E D I C T I O N OF L I M I T I N G I O N C O N D U C T A N C E O F Bu,N+ I N A C E T O N I T R I L E

In a previous paper1 we have proposed an equation which theoretically predicts limiting ion conductances of Bu,N+, Pr,N+ and Et4N+ in pure and mixed non-aqueous solvents within an average uncertainty of +2%. This equation can be written in the form

A N D ACETONITRILE+BENZENE MIXTURES

27 = I Z I F 2 / ( 6 ~ N ~ ) [ r i - ( 0 . 0 1 0 3 &+ry)] (6)

TABLE 4.-LIMITING ION CONDUCTANCES AP(Ph,B-) AND ri VALUES FOR Ph,B- IN SOME NON- AQUEOUS SOLVENTS AT 25 "C

solvent & VlCP AP(Ph,B-) riIA

acetoni trile i-butyronitrile n-butyronitrile nitromethane nitrobenzene acetone NN-dimethylformamide ethyl methyl ketone dimethylsulphoxide propylene carbonate methanol ethanol

36.0a 23.8lC 24.26d 36.7a 34.3h 20.7j 37.6a 18.014" 46.6a 65.0a 32.6a 24.3a

0.341" 0.48Y 0. 553d 0.61 18f 1 .839i 0.304 0. 796a 0.3774" 1 .990a 2.48a 0.545" 1.084"

58.3b 39.3OC 34. 50d 31.57f.g 10.79f. 62.65k 24.5l 50.1 6"3 10.6lng 8.26*

37.054 19.34'

5.34 5.40 5.40 5.48 5.33 5.37 5.44 5.37 5.48 5.52 5.53 5.29

a Ref. (3); ref. (18); ref. (14); A. D'Aprano and R. M. Fuoss, J. Solution Chem., 1974, 3,45 ; calculated from (i-Am),BuNBPh, assumption; f ref. (1 7) ; based on (i-Am), NB(i-Am), as a reference electrolyte: E. Hirsch and R. M. Fuoss, J . Am. Chem. SOC., 1960,82,1018;i R. A. RobinsonandR. H. Stokes, Electrolyte Solutions (Butterworths, London, 1959), p. 458; D. F. Evans, J. Thomas, J. A. Nadas and M. A. Matesich, J. Phys. Chem., 1971, 75, 1714; ' V . M. Tsentovskii, V. P. Barabanov, N. K. Mochalov and N. A. Tumasheva, Zh. Obshsch. Khim., 1974,44,1938; " S . R. C. Hughes and D. H. Price, J. Chem. SOC. A , 1967, 1093; D. E. Arrington and E. Griswold, J . Phys. Chem., 1970,74, 123; P A,, value for Bu,NBPh, reported by R. M. Fuoss and E. Hirsch, J . Am. Chem. Soc., 1960, 82, 1013 was corrected for a viscosity ratio of 2.55312.48 and from the resulting A. value RP(Ph,B-) was calculated by combining this A. value with the ionic conductance of Bu,N+ from L. M. Mukherjee, D. P. Boden and R. Lindauer, J. Phys. Chem., 1970, 74, 1942; Q calculated by combining A?(Bu,N+) = 38.94 from the results of R. L. Kay, C. Zawoyski and D. F. Evans, J. Phys. Chem., 1965, 69, 4208 with the A. value 75.99 for Bu,NBPh, reported by M. A. Coplan and R. M. Fuoss, J. Phys. Chem., 1964, 68, 1177; ' S. Schiavo and G. Marrosu, Z . Phys. Chem. (N.F. ) , 1977, 105, 157.

R. H. Boyd, J . Chem. Phys., 1961, 35, 1281;

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124 SINGLE-ION C O N D U C T A N C E S

where ri is the crystallographic radius of the ion and ry is the empirical constant 0.85 A for dipolar non-associated s01vents.l~~ 2o The validity of eqn (6) for Bu,N+ in AN and AN + BN mixtures has been tested by calculating A: values theoretically, using eqn (6) and substituting ri and r y values equal to 5.00 and 0.85 A, respectively.' The theoretically calculated A: values for Bu4N+, which are recorded as AE(Bu,N+) in table 3, are in excellent agreement (within an average uncertainty of Ifr 1.8%) with the AP(Bu,N+) values in the same table.

TABLE 5.-LIMITING ION CONDUCTANCES A:(Ph,B-) AND ri VALUES FOR Ph,B- IN SOME MIXED NON-AQUEOUS SOLVENTS AT 25 "C

solvent mixture & q/cP Ay(Ph4B-)d ri/A

AN + carbon tetrachloride" 19.87 17.18 13.92 11.16

1-BN + chlorobenzeneb 20.98 16.26 11.99 9.90

i-BN + o-dichlorobenzeneb 20.86 15.85 11.76 9.99

i-BN + 1,2-di~hloroethane~ 18.46 14.63 12.61 10.34

i-BN + benzeneC 19.04 14.79 10.38

i-BN + dioxanc 18.98 13.95 10.31

0.4676 0.5042 0.5566 0.5992 0.527 0.596 0.661 0.696 0.638 0.916 1.184 1.317 0.659 0.735 0.768 0.795 0.477 0.482 0.503 0.541 0.630 0.720

40.90 37.70 33.69 30.87 36.60 32.27 29.00 27.06 30.79 21.09 15.86 14.56 29.40 26.17 25.04 24.12 39.24 38.24 36.34 34.94 30.01 26.17

5.34 5.34 5.36 5.39 5.32 5.28 5.25 5.30 5.23 5.25 5.34 5.23 5.27 5.26 5.24 5.24 5.43 5.44 5.45 5.38 5.34 5.30

a D. S. Berns and R. M. Fuoss, J . Am. Chern. Soc., 1960, 82, 5585; ref. (15); ref. (14); A:(Ph,B-) in all mixed solvents were obtained from the A,, values of Bu,NBPh, using the

assumption of Fuoss and coworkers, ref. (14) and (1 5).

TEST O F T H E V A L I D I T Y O F EQN (6) FOR Ph,B- I N P U R E A N D M I X E D N O N - A Q U E O U S S O L V E N T S

Eqn (6) contains the ri parameter which is equal to the crystallographic radius of the ion.' The crystallographic radius of Ph,B- is not accurately known in literature, therefore, the validity of eqn (6) for A:(Ph,B-) can not be tested as such. AP(Ph,B-), however, can be accurately determined both in pure and mixed non-aqueous solvents from the conductance data available in the literature. Therefore, for a test of the validity of eqn (6) for Ph,B- it would be meaningful to evaluate first the ri values by using the literature value of iZP(Ph,B-) and examining whether ri in pure and mixed non-aqueous solvents remains constant. If it remains constant within experimental uncertainty this constant value of ri can then be used to calculate AP(Ph,B-)

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D. S. G I L L A N D M. B. SEKHRI 125 theoretically in AN and AN+ BN mixtures; these values can then be compared with our experimental values of table 3.

Taking accurate values of Ap(Ph,B-) in various pure and mixed non-aqueous solvents from the literature (as reported in tables 4 and 5 ) and the corresponding E

and values for the pure solvents or the solvent mixtures, ri values have been calculated using eqn (6) and substituting ry = 0.85 Al. These ri values are reported in tables 4 and 5.

A careful examination of tables 4 and 5 shows that ri values for Ph,B- in pure non-aqueous solvents (table 4) and in mixed non-aqueous solvents (table 5 ) calculated using eqn (6) remain constant and equal to 5.35 A within the average uncertainty of ca. 2%.

P R E D I C T I O N O F L I M I T I N G I O N C O N D U C T A N C E O F Ph,B- I N A C E T O N I T R I L E A N D ACETONITRILE+BENZENE MIXTURES

Using ri = 5.35 A for Ph,B- in eqn (6) , limiting ion conductances of Ph,B- in pure AN and in AN + BN mixtures have been theoretically calculated. These values have been reported as A:(Ph,B-) in table 3 for comparison with our experimental values. The agreement between the AE(Ph,B-) and AP(Ph,B-) values of table 3 is very good (within an average uncertainty of *2%), thereby showing that eqn (6) predicts limiting ion conductances for Ph,B- also in quantitative agreement with the experi- mental values.

M. B. S. thanks the C.S.I.R., New Delhi for a Junior Research Fellowship.

D. S. Gill, J. Chem. Soc., Faraday Trans. I, 1981, 77, 751. J. A. Riddick and W. B. Bunger, Organic Solvents (Wiley-Interscience, New York, 1970). D. S. Gill, J. Solution Chem., 1979, 8, 691. I. N. V’yunnik, A. M. Zholnovach and A. M. Shkodin, Zh. Obshch. Khim., 1977, 47, 1681 F. Accascina, S. Petrucci and R. M. Fuoss, J. Am. Chem. Soc., 1959, 81, 1301.

ti T. Shedlovsky, J . Am. Chem. Soc., 1932, 54, 141 1. J. E. Lind, Jr., J. J. Zwolenik and R. M. Fuoss, J. Am. Chem. Soc., 1959, 81, 1557. T. Shedlovsky, J . Franklin Inst., 1938, 255, 739. R. M. Fuoss and T. Shedlovsky, J . Am. Chem. Soc., 1949, 71, 1496.

lo R. M. Fuoss and F. Accascina, Electrolytic Conductance, (Interscience, New York, 1959). l 1 I. N. V’yunnik, A. M. Zholnovach and A. M. Shkodin, Elektrokhimiya, 1976, 12, 1334. l 2 J-C. Justice, Electrochim. Acta, 1971, 16, 701. l3 W. J. Youden, Statistical Methods for Chemists (John Wiley, New York, 1951), p. 42. l4 C. J. James and R. M. Fuoss, J . Solution Chem., 1975, 4, 91. l 5 A. D’Aprano and R. M. Fuoss, J . Solution Chem., 1975, 4, 175. l6 R. M. Fuoss, J . Am. Chem. Soc., 1935, 57,488. l 7 J. F. Coetzee and G. P. Cunningham, J. Am. Chem. Soc., 1965,87, 2529.

l9 D. S. Gill, Electrochim. Acta, 1977, 22, 491. 2o D. S. Gill, Electrochim. Acta, 1979, 24, 701.

C. H. Springer, J. F. Coetzee and R. L. Kay, J . Phys. Chem., 1969, 73, 471.

(PAPER O/ 1905)

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