r

Indian Journal of ChemistryVol. 17A. February 1979. pp. 126-129

Applicability of Fuoss-Onsager Equation to Electrical Conductances ofDilute Solutions of Triethyl-n-propylammonium Iodide

N. ISLAM*, M. R. ISLAM & M. AHMAD

Department of Chemistry, Aligarh Muslim University. Aligarh 202001

Received 13 July 1977; revised and accepted 18 December 1978

The electrical conductances of triethyl-n-propylammonium iodide (Et3PrNI) recorded inwater (dielectric constant, D = 78), nitrobenzene (D = 34), acetic anhydride (D = 20), t-butano l(D = 17), and benzyl alcohol (D =,13) at 30° have been analysed in terms of Fuosa-Onsagerequation. The limiting equivalent conductance, Ao' the ion-size parameter, aO, and the asso-ciation constant, KA have been computed. The ion-size parameter is found to be independentof the dielectric constant of the medium; the association constants, however, show an exponen-tial relationship whereas walden products show no regular variation. Besides the dielectricconstant. the viscosity of the medium has also been found to affect significantly the value of Ao.

STUDIES in the equivalent conductances oftetraalkylammonium salts have extensivelybeen made in aqueous and non-aqueous

solvents':". It has been found that in water andalcohols, salts with large anions such as perchlo-rate and iodide ions are more associated than thosewith small anions. On the other hand, salts withlarge cations", such as cesium and rubidium ions,have also been found to be associated more thanthose with small cations. These observations seemto be in conflict with the ionic association theories",However, Evans and coworkers+" discussed thediscrepancy in terms of the difference in the extentof solvation and suggested the formation ofsolvent-separated ion pairs and contact ion pairs.They also evaluated the solute-solvent interactionsystematically from the viewpoint of transportproperties.

In the present study, the electrical conductanceof triethyl-s-propylammonium iodide has been mea-sured as a function of concentration in severalsolvents of varying dielectric constants. The inter-actions of this salt with the solvents have beenvisualized in the light of the limiting equivalentconductance, Ao• The ion-size parameter. aO, andthe ionic association constant, KA. The latterquantity being dependent on the dielectric constantof the medium helped in selecting water (D = 78),nitrobenzene (D = 34), acetic anhydride (D = 20),I-butanol (D = 17), and benzyl alcohol (D = 13)for such an investigation.

Materials and MethodsTriethyl-s-propylammonium iodide used was a

Eastman Kodak product. All the solvents, benzylalcohol (PhCH20H), I-butanol (BuOH), acetic anhy-dride (Ac20), nitrobenzene (PhN02) and waterwere distilled? and purified before use. The solu-tions were prepared by weight in a dry box underpurified dry N2 atmosphere. The· conductances(± 0·2%) of dilute solutions of EtaPrNI were mea-

126

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sured at 30° with a conductivity bridge of Philipstype PR 9500 at a frequency of 50 Hz. The pyrexconductivity cell (cell constant = 1·0459 cm-I)-Philips type PV 9055 with lightly platinized electrodeswas standardized with a decinormal potassiumchloride solution at 30° using the constants reportedby Lind et al.10•

Density (±0·3%) and viscosity (±0·1%) ofmeasurements were made with a calibrated pykno-meter of 0·02 ml divisions and a Cannon-Ubbelohdeviscometer, respectively. These measurements weremade in a relay-controlled thermostated water-bathof ± 0·02° thermal stability. The densities andthe viscosities of the organic solvents employed aregiven in Table 1.

TABLE 1 - DENSITIES AND VISCOSITIES (AT 30°) OFORGANIC SOLVENTS

Solvent Density Viscositygjcc poise

Nitrobenzene 1-1936 0·0122Acetic anhydride 1'0686 0·0080I-Butanol 0'8053 0·0220Benzyl alcohol 1'0379 0'0470

Results and Discussion

The meas~red equivalent conductances of EtaPrNI(Table 2) 111 the solvents under investigation arefound to follow the order. H20> (Ac20) > PhN02> BuOH> PhCH20H. The interchanged order inthe values of A in the last two pairs suggests therole of the solvent properties especially the viscositybesid~s the dielectric constant in determining themagnitude of A of the added solute. Relativelyhigher value~ of conductance for EtaPrNI in A~Omay be ascnbed to the dissociation of the solventmolecules which furnish additional ions to thesolution.

r

ISLAM et al.: CONDUCTANCE OF EtaPrNI IN DIFFERENT SOLVENTS

TABLE 2 - CONDUCTANCEDATA OF TRIETHYL-n-PROPYLAMMONIUMIODIDE IN SEVERAL SOLVENTSAT 30°

Solvent A (em" equiv ? ohm'") at [electrolyte] x 10' (mol/litre)

100·0 80·0 40·0 10'0 6·0 2·0

100·990 100'850 107-350 109·240 125·43026·894 27'162 30'186 33·633 34'873 37'00749·562 53·498 58'845· 74·297 78'435 88·281

6·418 7·060 8'828 13'447 19'583 25'6794·350 4'555 5'650 8'475 10·005 14·868

WaterNitro benzeneAcetic anhydrideI-ButanolBenzyl alcohol

TABLE 3 - COMPUTEDPARAMETERSOF EQs. (1) AND (2) FOR EQUIVALE_'TCONDUCTANCESOF TRIETHYL-n-PROPYLAMMONIUMIODIDE AT 30°C

WaterNitrobenzeneAcetic anhydrideI-ButanolBenzyl alcohol

Ao S E ] J(A aO Av. dev;

112'25 92'56 35'67 159·99 0'00 3'03 4·810038'34 96-71 160·50 955'16 70'78 8'80 0·000995·32 298·24 2561'70 6616·70 271'82 5'45 0·006030·58 120-45 1352'20 2025·00 1858'34 2·10 0'174021'08 97·81 2195'50 5799·70 4455'90 6'50 0·0290

Solvent

According to Fuoss et al.ll the long-range inter-actions between ions not in contact are best describedby the equationA = Ao-S(1/2+EC log C+ l(a)C '" (1)while the short-range interactions which create ionpairs are best described by the equationA = AO-SCl/2yl/2+ECY log CY+ ICY -KACYAji

.. , (2)where the terms have their usual significances. Re-cently, "Paracond" has been designed for the para-metric analysis of conductance data for the symme-trical electrolytes.

In view of the inability of our data to be analysedby the Paracond=, Eqs. (1) and (2) were employedfor explaining the concentration dependence ofthe un associated and the associated electrolytes,respectively. The viscosity correction was not madeas Ao and KA are found to be unaffected by such acorrection while aO shows a small effect.

The initial values of Ao were obtained from theFuossShedlovsky-s-w extrapolation of the equiva-lent conductance data by the method of least squaresfitting. The Ao values thus obtained were employedin such an analysis. The parameters computedare listed in Table 3.

The computed values of Ao are found to dependon the dielectric constant in a manner similar tothose of the equivalent conductances. The singleion conductances (Table 4) of triethyl-n-propyl-ammonium ion in all these solvents were calculated withthe help of Walden rule based on the Stoke's lawl5

using the crystallographic radiit" of the iodide ion.The ionic Walden products, Ao"IJ, have been

found to increase with a decrease in the dielectricconstant and is consistent with the Fuoss-" andZwanzig's-" view. According to them, the depen-dence of the ionic Walden product on the solventproperties may be given asA~"IJ=F2IN(61tr+Blr3) ... (3)where B is a function of the dielectric constant aswell as the viscosity and explains the increase in

(

TABLE 4 - SINGLE ION CONDUCTIVITIESOF TRIETHYL-n-PROPYLAMMONIUMION AND THE IONIC WALDEN PRODUCT

IN DIFFERENT SOLVENTS

Solvent A; Att) Aot)

Water 32-86 0·261 0'879Nitrobenzene 25·21 0·307 0'468Acetic anhydride 47'21 0·378 0'763I-Butanol 21·26 0'467 0'673Benzyl alcohol 13'04 0·613 0'991

A; (for I-) in H20 = 76'98; PhNO. = 13'3, (AcO).O =48'11; BuOH = 9·32; PhCH20H = 8'04. -

the ionic Walden product with decreasing dielectricconstant. The fact !hat the values of this productare almost constant in alcohols where the dielectricrange is 32·6-17·5 appears to denote that B remains.constant in those alcohols.

The ~ald~n :product, Ao1J for triethyl-n-propyl-a~momum lOdI~e has ~e~n plotted against ut:(FIg. 1) and a typical variation of Ao1J with dielectricconstant of the medium is observed. The plotp~sses ~hrough the maxima corresponding to thedlelectr.Ic constants of benzyl alcohol and aceticanhydnde and through the minima at the dielectricconstants of butanol and nitrobenzene. Such atyp.ical ?ehavio~r of Walden product may be ex-plain ed m the ~Ight. of the limiting equivalent con-ductance, the VISCOSItyand the dielectric constantof the medium. Mainly, the ion-ion and the ion-?olvent interactions play important role in deterrnin-m.g the n.ature. of variation in Walden productWIth t~e dielectric constant. Therefore, a detailed~n~lysI~ of such a variation in Ao"IJ demands a clearinsight mto the nature of interactions in the system.The concept of structure making and structurebreaking electrolytes suggested by Evans and Kay+m~y be employed for this purpose. In the case oftnethyl-n-propylammonium ions possessing largehydr~phobic. side chains, the solvent molecules maybe slightly influenced by the ionic charge of the

127

INDIAN J. CHEM., VOL. 17A, FEBRUARY 1979

6.0,.......-------------.

0·8

OJ,

0-2

2·0 6·0 so 10.010cYo .

12.0'·0

Fig. 1 - Walden product of Et3PrNI as a function ofdielectric constant

In

r-soIII IV1·9

1·8 1·60

1-7

1-6

1·50

III 1·5

IV 1-4

11 1-3 HO

I Benzyl alcoholII 1-Butanal

II I Acetic Anhydride) V Nitrobenzene

1-23 5 7 9 IV

o 20 £0 60 80CX103(mole II itra )

Fig. 2 - Log (A'fj/'fjo) versus concentration for Et3PrNIin several organic solvents

100 I-m

unit hydrophobic side chain on the surface of theseions. Hence, the solvent molecule on the hydro-'phobic surface may be oriented in such a manneras to form a cage about the hydrocarbon side chains.The clathrate thus obtained as a result of solvationincreases the size of the entity which in turn decreasesthe mobility and increases the local viscosity. Onthis basis the triethyl-n-propylammonium ion isa structure breaker in water, butanol and benzylalcohol thereby showing abnormality in their Ao'YJbehaviour. The behaviour of log (A'YJI'YJo) withchange in concentration (Fig. 2) seems to be rathersimilar to that of the equivalent conductance.This implies that A dominates over the viscositychange throughout the concentration range.

The plot of log KA versus liD shown in Fig. 3indicates that the association constant of Et3PrNI

128

(

'.0::J:.4.

'"o-' 2·0

2·0 8·0'·0 6.0100/0

Fig. 3 -. Log KA versus Yl D for Et3PrNI at 30°

in the solvents under investigation is an exponen-tial' function of dielectric constant,KA = K~ exp(e2IDKT) ... (4)where the terms have their usual significances.The evaluation of the ion-size parameters usingdifferent conductance equations shows a significantdifference in the a" values for a definite electrolytein a particular dielectric medium. For example,the reported values of aO for various tetraalkyl-ammonium salts in ethanol and propanol'? are4·2± 0·2 A and 5·0± 0·5 A, respectively, and arebased on the Fuoss-Onsager equation. Instead, theFuoss-Hsia20,21 analysis of the same data gave com-parable but constant values of aO which appearedto be independent of the dielectric constant as isthe case with several other solvents--".

An examination of Table 3 shows that the ion-size parameter, aO for Et3PrNI increases from BuOHto PhN02• This seems to imply that the ion-pairformation decreases from BuOH to PhN02• More-over, the aO value is found to be small compared tothe sum of the crystallographic radii of the cationand the anion. Therefore, the association ofEt3PrN+ ion to the solvent molecules may presumablydecrease the contact distance parameter. Consi-dering the insignificant influence of the nature ofthe solvent on the aO values, this quantity may, onthe average, be taken as 5·15 ± 1·03 A in thesolvents under discussion.

AcknowledgementThe authors thank Prof. W. Rahman for provid-

ing necessary facilities. Professors R. M. Fuossand R. L. Kay are thanked for sending us theParacond and the Fortran Programmes, respectively.The financial assistance to one of them (M.A.)from the UGC, New Delhi, is gratefully acknow-ledged.

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cu«; 69 (1965), 3878.2. KAY, R. L., ZAWOYSKI, C. & EVANS, D. F., J. phys.

Chem., 69 (1965),4208.3. KAY, R. L. & EVANS, D. F., J. phys. cu-«, 69 (1965),

4216.4. EVANS, D. F. & KAY, R. L., J. phys. cs-«, 70 (1966),

366; 2325.5. KAY, R. L., EVANS, D. F. & CUNNINGHAM,G. P., J. phys.

Chem., 73 (1969), 3322.6. KAY, R. L., HALES, B. J. & CUNNINGHAM,G. P., J. phys.

cs-«, 71 (1967), 3925.7. Fuoss, R. M., J. Arn. chem, Soc., 80 (1958), 5059.8. EVANS, D. F. & GARDAM,P., J. phys. Chem., 73 (1969),

158.

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ISLAM et al.: CONDUCTANCE OF EtaPrNI IN DIFFERENT SOLVENTS

9. VOGEL, A. 1., Text book of practical organic chemistry(Longrnans, London), 1924.

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16. NIGHTINGLE, E. R (Jr), J. phys. Chem., 63 (1959),1381-

17. Fuoss, R M., Froc. nail Acad, Sci., U.S.A., 45 (1959),807.

18. ZWANZIG,R, J. chem . Phys., 38 (1963), 1603; 52 (1970),3625.

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20. Fuoss, R. M. & HSIA, K. L., Proc. nail. Acad su., U.S.A.,57 (1967), 1550.

21. PRINI, R F., Trans. Faraday Soc., 65 (1969), 3311.

129