Indian Journal of ChemistryVol. 20A, September 1981, pp. 879-882

Excess Partial Molal Volume of Tetra-n-butylammonium Bromidein Water at 25°C

K. J. PATIL* & A. B. WAZALWARDepartment of Chemistry, Institute of Science, Nagpur-440 001

Received 15 December 1980; revised and accepted 31 January 1981

The isothermal compressibility values for tetra-x-butylammonium bromide water binary system of differentcompositions have been calculated at 25°C using literature data of adiabatic compressibility, density and specific heat.The variation of internal pressure has been studied, using Tammann- Tait-Gibson model. It is found that isothermalcompressibility, apparent molal isothermal compressibility (q,Klso) of so/ute and the effective internal pressure (B +P.)exhibit minima at certain salt concentrations. The results are discussed in terms of cation-cation induced struc-tural interactions with solvent water. Excess partial molal volumes of this salt have been calculated using Gibson-Tait equation and the values compared with those reported by Wen and Nara. The agreement between thevalues obtained using these two approaches is satisfactory.

AQUEOUS solutions of tetraalkylammoniumhalides have been investigated by a variety

, of techniques viz. density, viscosity, NMRspectroscopy, dielectric relaxation etc.' The physi-cal properties of these salts seem to offer a strongsupport to the notion that in aqueous solutions, thepeculiarities of the tetraalkylammonium ions aredue not only to their large ionic size but also to thesignificant modification of water struture around thecations. The apparent and partial molal volumes ofthese salts have been studied by several workersv+,It has been established that some of these salts showsubstantial negative deviations from the Debye-Huckel Iimiting law at relativity low concentrations.Wen and Nara" made measurements of volume ofmixing in ternary systems and calculated the excessvolume of a pure salt (V~) in solution applyingFriedeman's method. The present paper deals withthe calculation of vf of tetra-z-butylammoniumbromide (TBuABr)· in aqueous solution applyingTammann-Tait-Gibson (TTG) equation to thevolume and compressibility data.

TheoryThe TTG model has been nicely summarised by

Harned and Owens. It has been applied to calculateparameters which are related to the fundamentalthermodynamic, crystallographic and other properties of the solutes involved", Recently Leyenderk-kers=" used it to calculate refractive index and vis-cosity of sea water. Tammann's hypothesis stat~sthat in the presence of an ionized solute, the water III

aqueous solution behaves as though it has been su?-jected to a constant electrostatic pressure .(Pe) III

addition to the atmospheric pressure. The Tait equa-tion for water may be written" as

~o(P) V~ = O:3~3 pC ... (1)

where fio is the isothermal compressibility, Vo is thespecific volume, P is the pressure while Band Carethe positive constants. C;Vo varies very little withcomposition and is also independent of temperature.The constant B represents the difference between theexpansive pressure due to thermal energy and thecohesive pressure, due to temperature-independentattraction between the molecules. Therefore, Bdecreases with increase in temperature upto 30-40°Cand increases with the intermolecular forces.Gibson modified Eq. (1) for aqueous solutions ofelectrolytes and gave the expression (2)

A _ 0.4343 XIC X d'Y2 (2)I'.v. - B+P+Pe - 2· dP ...

where ~ and V represent isothermal compressibilityand specific volume of solution respectively, Xland X2 represent the mole-fraction of solvent andsolute respectively and 'Y 2 is the specific volume ofthe pure solute (as a liquid). Equation (2) can berewritten as :

V~1')-M2'Y2= B~4~~~e .il!(B+Pe) ... (3)

where V2 is the partial molar volume of solute andm is the molality of solution at a given temperature.It is clear that excess partial molar volume of solute'1 (= V2: ~ M, 1/12 = V 2 - ~) is governed by t~ofators; (i) (B + Pe) the rate of change of effectiveinternal pressure with concentration and (ii)Cf(B + Pe-l- P) which is related to the compressibili-ty of the solvent at the pressure (P+ Pe) which is in-dependent of solute. Many workers='? have assumedB as a constant but we feel that since sa Its like tetra-alkylammonium halides significantly affect waterstructure, B-parameter, must get affected by soluteor the interactions therein. This is also evident fromthe values of apparent molal compressibilities of

879'

INDIAN J. CHEM., VOL. 20A, SEPTEMBER 1981

8

,

8

360

&+ 3200~

5600

4600

E~3600Q.-

2600

3S~ ~~ ~ -7~ ~~ ~o 0.5 1.0 1.5 2.0

mFig. 1 - Variation of various thermodynamic parameters with concentration (molality) of tetra-n-butylammoniumbromide (TBuABr) in water at 2$OC [(a) isothermal compressibility (~I.o); (b) apparent molal isothermal compressi-bility of solute (~K'I.O); (c) internalpressure (PI); (d) Gibson-Tait parameter (B + Po); and (e) excess partial molal volume

of TBuABr (V~)].

880

PATIL & WAZALWAR : EXCESS PARTIAL MOLAR VOLUME OF (n-Bu)4NBr

water in aqueous solutions of tetraalkylammoniumbromides as reported by Schiavo et a/.ll

ResultsThe calculationsof V~ as a function of concentra-

tion using Eq. (3) require the data of isothermalcompressibility (~ISO)'and internal pressure due toelectrostriction (Pe) as a function of concentrationof electrolyte. ~lso values have been calculatedusing Eq. (4)

, cx2T '~so -~ad = - ...(4}a

where ~ad is the adiabatic compressibility, exthe co-efficient of thermal expansion and a the volumetricspecific heat at temperature T for solutions. Theadiabatic compressibility data were directly takenfrom Schiavo et al.ll while at values were computedfrom the density data of Schiavo et al.12• The specificheat data were obtained from Desnoyer and Philip-P(below 0.3 m) and Frank and Wen14 (upto == 2 m):'The variation of ~ISOas a function of concentrationat 25"C is shown in Fig. 1 (curve a). The internalpressure (PD was calculated using the thermodyna-mical equation :

PI = ( ~~ )T = ~:o.T ... (5)

and assuming atmospheric pressure (P) to be negligi-ble. The variation of PI as a function of conentrationis shown in Fig. 1 (curve c). The effective electro-static pressure (Pe) due to ions was calculated by sub-tracting the internal pressure of pure solvent from thetotal internal pressure of solution. The parameter-B was calculated at various concentrations usingEq.

(2)and assuming that the factor X2 ~~2is.negligible.

The mole-fractions of solute and solvent were calcu-lated by the method given by Robinson and Stokes=for electrolytes. The variations of tPK(ISO)B + P,and V~ are also shown in Fig. 1 (curves, b, d and ereSPectively). Finally excess partial molal volumeV~ for the salt was computed using Eq. (3) and divid-ing the value by 2 since the number of ions involved

are two .''The parameter :m (B + Pe) was estimated

by drawing the slopes at different concentrations bytangent method. Apparent molal isothermal coin-pressibilities (tPk180)were calculated using Eq. (5)

1000tPKtso = m.d

o(~- (30) + f3·tPv •.. (6)'"

where do is the density of solvent and tPv is the appa-rent molal volume of solute. The various calculatedparameters are collected in Table 1.

DiscussionIt is evident from Fig. la that f31so passes through

minimum at about 1.Tm, This is significant since1 : I electrolytes generally do not show such a ,behaviour, although many aqueous-nonelectrolytesystems are characterised by such a behaviour-e. It ~has been established that aqueous amine solutionsexhibit I : I correspondence in volumetric and.compressibility behaviour", The partial .molalvolume of TBuABr also goes through minimum atabout the same concentration 2indicating the simi- ~1arity between the two parameters. The negativeslopes of the plots of partial volume and compressibi-'lity parameter versus concentration have been inter-.preted as due to hydrophobic hydration of the solutein water while the positive slope after minimum hasbeen attributed to usual structure breaking effect ofsolute on water. The apparent molal isothermalcompressibility (4)K,ISO)of T BuABr (Fig. 1) alsovaries uniquely in the studied concentration range.This is the first example of an electrolyte wheretPKISOgoes through a minimum. Conway andVenall= have shown that 4>K,adexhibits a positiveslope inthe concentration range below 0.1 M forTBuABrat25"Cwitha4>k = -18>< 1O-4cm5 atrrr?mol-I; As the values of tPK'lS~obtained in thisstudy are all positive and the plot of 4>K,ls0versusconcentration has a negative slope, one can say thatbelow 0.1 m solute-solvent effect predominates andwith further increase in concentration solute-solute(cation-cation) effect predoininates leading to dec-rease in tPKlsOand resulting in a minimum at 0.4-0.6 m. The minimum in case of 4>K,adis morepronounced. It is believed that tPkexhibits a mini-

TABU! 1 - VARIOUSTHERMODYNAMICPARAMETERSFOR TETRA-n-BUIYLAMMONWMBROMIDE-WATER, SYSTEMSAT 25°C

_EConcentration ~ISOXlOG PI B II+Pe V2 Pe ,pK .180 X 10'

(m) (atm'<) (atm) (atm) (atm) (ml. mol=") (atm) (cm'.atm-Imor-')

0.00 45.23 1681 3014 3014 00.10 44.08 1779 2988 3086 -10.6 98 21.50

0.20 43.02 2055 2785 3159 -10.4 374 18.5

0.30 41.98 2352 2564 3235 -10.4 671 18.00.40 41.07 2598 2388 3305 -10.2 917 17.6

0.64 39.08 3122 2009 3450 -9.2 1441 18.50.92 37.65 3752 1476 3547 -2.8 2071 29.01.73 36.49 5193 114 3626 -2.2 3512 57.2

2.20 36.62 5555 -449 3425 +11.7 3874 69.1

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INDIAN J. CHEM., VOL. 20A, SEPTEMBER 1981

mum at about 0.4 to 0.6 m and may show a maxi-mum in low concentration region (0 to 0.1 m).

The plot in Fig. 1(curve c) indicates that the totalinternal pressure increases with concentration whichis as expected. The calculation of B + Pe parameterindicates (Table 1and Fig. 1 d) that (B + Pe) passesthrough a maximum at about 1.7m while B decreasesmonotonously but has positive values upto 1.7 mand becomes negative thereafter.

Since B is the measure of cohesion in liquid state,one can visualise the negative B-value as the completebreakdown of water structure and the state of waterin such a situation may resemble micelle. The maxi-mum in B + P, may indicate maximum structuremaking effect on solvent water through cation-cationinduced structural interactions. Wen and Saitohave interpreted their volumetric results for(TBuABr) in terms of formation of clathrate-likestructure in solution. We feel that our observationsand tentative interpretations are consistent withearlier views. The decrease in c/>k values indicatesa lower compressibility value for the salt, and alsosuggests a rigid clathrate-like structure in solution.

The hydrophobic interactions are always charac-terised by loss in volume-s, The calculations ofexcess volume of mixing in case of electrolytes aredifficult as the intrinsic volume of pure crystallinesolid in solution is difficult to assess although manyempirical attempts have been made using crystallo-graphic radii'". We feel that the Gibson-Tait equa-tion (Eq. 1) although empirical in origin, shouldgive excess partial molal volume of a solute as afunction of concentration. When one compares Wenand Nara's values of excess partial molal volume ofTBuABr(-11.5, -9.2 and -7.3 ml/mol at 0.2,0.5and 1.0 m respectively at 25°C) with the values ob-tained in the present study by applying the TTGmodel (Table 1) , a fair agreement is apparent. Webelieve that the excesspartial molal volume of electro-

882

lytes can be studied with more ease using the internalpressure parameters, as evident in the present study.

AcknowledgementThe authors are thankful to Prof.A. Gopalkrishna

and Dr O. B. Thakare for the encouragement.

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