Indian Journal of ChemistryVol. 33A, December 1994, pp. 1075-1082

Partial molar volume studies of ion-solvent interactions in some mixedsolvent media

(Late) Prem P Singh & Vibha"Department of Chemistry, Maharshi Dayanand University, Rohtak 124 00 1

Received} September 1993; revised 11 May 1994; accepted 16 June 1994

Partial molar volumes ;v of sodium chloride, sodium acetate, sodium formate, hydrochloric acid,acetic acid and formic acid have been determined dilatometrically in some quasi-isodielectric [water(W)+cosolvent (aprotic dioxane (0), dipolar aprotic (DMF) and protic (FO)] media at 308.15 K andthe same have been analysed to evaluate their limiting ;'; values. These values have been coupledwith the corresponding limiting values in W to compute 11;'; data which suggest that for a particu-lar HA or NaA, the 11;'; values generally vary as FO<OMF<O as required by the Gutmann'sdonor and the electron pair acceptance indices of formamide (FO), N,N-dimethylformamide (OMF)and l,4-dioxane (0) cosolvents in the present mixed solvent media. The variation of 11;'; (HA orNaA) within the same mixed solvent media suggest that while the chemical effects of protons of ac-ids on the cosolvent have a dominant influence (based on Ben-Naims approach) on their AJ'; data,the electrostriction effects of CH)COO-, HCOO- and Cl- on W play an important role in deter-mining the values of 11;'; of their sodium salts.

Ion-ion and ion-solvent interactions play an im-portant role in the solution chemistry":" of so-lutes. Most of such studies have been carried outin water (W) which is a structured solvent par ex-cellence. If the nature of W can be modified by acosolvent in such a way that the electrostatic ef-fects arising from dielectric constant remain al-most the same, then the chemical effects of thecosolvent should play an important role in influ-encing ion-solvent interactions. As partial molarvolume of a solute reflects the cumulative effects 7

of ion-ion and ion-solvent interactions, it wouldbe of interest to study partial molar volumes ofsome strong electrolytes (containing anions ofweak acids) in W+cosolvent (aprotic D, dipolaraprotic DMF or protic FD) systems. Such dataare expected to highlight the role of the cationand of the anion of an electrolyte in influencingits partial molar volume at infinite dilution inmixed solvent systems. These considerationsprompted us to undertake the present study.

Materials and Methodsl,4-Dioxane (D) (Merck, AR) was purified as

suggested by McGlashan and Rastogi", N,N-Dimethylformamide (DMF) (Ranbaxy, AR) andformamide (FD) (Merck, AR) were purified bystandard methods".

Deionized water was mixed with some solid

NaOH and a pinch of solid KMn04 and doublydistilled from an all-glass assembly.

D (dielectric constant E308.15K= 2.039)10(a) andDMF (E30S.15K=34.93)lIl(a)were mixed individuallywith appropriate quantities of doubly distilled W(E30S.15K= 74.8)10(8)to yield mixed solvent systemshaving Emix(308.15K) of 70, it being assumed'?'!"that Emix= waEa+ (1- Wa)Eh(where a = W, b = D orDMF or FD and Wa is the weight fraction of a).

h'

The validity of the assumption Emix= I Wa e, was

checked by calculating Emixfor (W + D) mixed sol-vent system containing 20 weight per cent of Dand it was found that the Emixof this solvent sys-tem was within 4% of the value reported for it inthe literature'I'". We expect the relation Emix=b

I WIEo to hold for other W+ cosolvent (CS) sys-•terns (containing a small proportion of CS) also;the relevant E data were taken from the litera-turelO(a).

FD (E308.15K = 102.8)10(0)was mixed with appro-priate quantities of doubly distilled W to yield amixed solvent system having Emix(308.I~K)= 78.4.The weight fraction (x 102) of D, DMF and FDin the various (W+ CS) systems were 6.6, 12.03and 12.42 respectively.

1076 INDIAN J CHEM, SEC. A, DECEMBER 1994

Table l=-Apparent molar volumes tA and degrees of dissociation a at 308.15K of various solutes in different quasi-isodielectricmedia as function of solute molarity

C ;. a Ac C ;. a Acmol l'! ml mol "! mol l " ' mlmol-1

Formic acid (D +H2O)

0.6540 25.08 0.3347 5.89 0.1610 25.10 0.5102 8.980.5961 25.01 0.3511 6.18 0.1181 25.11 0.5614 9.880.5783 25.00 0.3540 6.23 0.1092 25.11 0.5750 10.120.5342 24.98 0.3739 6.58 0.0861 25.11 0.6131 10.790.5071 24.96 0.3852 6.78 0.0463 25.13 0.6920 12.180.2674 25.08 0.4097 7.21 0.0243 25.14 0.8449 14.870.2270 25.09 0.4540 7.99 0.0175 25.14 0.9080 15.98

Acetic acid

0.7912 48.82 0.1511 1.36 0.3541 48.40 0.2544 2.29

0.740 48.80 0.1544 1.39 0.3523 48.40 0.2556 2.30

0.6924 48.74 0.1567 1.41 0.3012 48.31 0.2767 2.49

0.5712 48.66 0.1767 1.59 0.2421 48.29 0.320 2.880.5220 48.60 0.1811 1.63 0.2000 48.23. 0.3567 3.21

0.4631 48.54 0.2100 1.89 0.090 48.20 0.5678 5.110.3940 48.47 0.2333 2.10 0.0442 48.14 0.7878 7.09

Sodium acetate

0.7921 2.89 0.2601 4.62

0.640 3.32 0.2116 4.81

0.5776 3.78 0.1444 5.11

0.4624 3.97 0.0787 5.64

0.360 4.10 0.0256 6.02

0.3481 4.32 0.0056 6.22

Sodium formate

0.9216 27.89 0.2809 2952

0.8464 28.00 0.160 30.00

0.7744 28.02 0.1369 30.10

0.6724 28.41 0.09 30.30

0.5929 28.82 0.0441 30.78

0.4761 28.98 0.0196 30.89

0.4096 29.11 0.0081 31.10

Hydrochloric acid

1.00 7.91 0.4229 6.25

0.8836 7.50 0.3136 5.80

0.7744 ; 7.25 0.2025 5.56

0.6724 7.00 0.1369 4.75

0.5929 6.75 0.0484 4.25

0.5041 6.60 0.0144 3.60

Sodium chloride

0.8649 19.32 0.3481 18.50

0.1569 19.10 0.2116 18.25

0.1056 18.94 0.1089 18.01

0.640 18.82 0.0729 17.90

0.5329 1~.69 0.0441 17.74

0.4489 18.60 0.01 17.49

SINGH et al.: ION-SOLVENT INTERACTION IN MIXED SOLVENT MEDIA 1077

Hydrochloric acid (Loba Chemicals, 35-38%)was diluted with the appropriate mixed solventsystem to the required concentration and standar-dized by conductance method 12. Sodium hydro-xide solutions in the appropriate mixed solventswere standardized against hydrochloric acid (inthe appropriate mixed solvent). Stock solutions offormic acid (FA) and acetic acid (AA) in the ap-propriate mixed solvents were prepared by dilu-tion of purified acid and were standardizedagainst the sodium hydroxide solutions.

Solutions of sodium formate (NaFor) were pre-pared from the solid salt (Sarabhai, 98%). Anhy-drous sodium formate contained heavy metalsetc., so it was recrystallized twice from water andwashed with alcohol and acetone. After first dry-ing in air, the salt was heated to 110ce.

Solutions of sodium acetate (NaA) were pre-pared using solid sodium acetate trihydrate (BDH,AR Grade) whose purity was checked by titrationwith standard hydrochloric acid.

MeasurementsDensities of concentrated stock solutions were

measured at 308.15 K by a densimeter':' that wascalibrated with water (density of water 0.99406glml at 308.15 K). The densimeter was rinsedthrice with solutions. Temperature of the ther-mostate was maintained at 308.15 ± 0.01 K andthe density of the solution was calculated as de-scribed in the Iiterature '"; at least two determin-ations of density were made at each concentra-tion.

Concentrated stock solutions were diluted withtheapropriate mixed solvent in a V-shaped dila-tometer" to obtain apparent molar volume datain the manner described elsewhere".

Conductance of the various solutions of FA andAA were determined at 308.15 K by a digitalconductivity meter (Century, India):

Calculation and ResultsThe apparent molar volume <Pvrof the final so-

lution was obtained from the apparent molar vo-lume <Pviof the initial stock solution utilizing therelationship 15

<Pvr=<Pvi+ ~v/n2 ... (1)

where ~ v denotes the volume change accompany-ing dilution of the initial stock solution to yield afinal solution containing n2 moles of the solute.The <PViof the stock solution of molarity C, how-ever, was calculated from the density p of the so-

lution and that of the solvent p* via the relation-ship!",

- M~ 1000 [p- P*]A. ----'('vi- * C *p p

... (2)

where M, denotes the molar mass of the solute.Such data for the various electrolytes in the var-ious quasi-isodielectric media are recorded as <Pvin Table 1.

The ¢v data of sodium formate, sodium acetate,sodium chloride and HCl in the present quasi-iso-dielectric media were expressed' as

¢~=<Pv-kco5=¢:+BC ... (3)

where the limiting slope k for 1:1 electrolytes inwater is approximately II (h)0.667 S, and

SIl;c) = 1.1515 vRTSf I3 a~:f- f3] ... (4)

sllid) = (1.29 X 106) V - I (~Vj ZJ)( e'T r IS ..•. (5)

All the terms have their usual significance'v-"Since the dependence of e on P has been studiedfor water'l'" as a solvent only (and even in thiscase the results are not too reliable"), one has to

(aInf )make a reasonable guess about 3 -ap - f3 for

present quasi-isodielectric media. As the maxi-mum proportion of the cosolvent in W is about12% by weight, it would be reasonable to assume

that the value of (3 a~:f - (3) for the present

mixed media would not be significantly differentfrom that of pure W. With this crude assumption,when no other method is available to compute

value of (Ja~ f - f3), the limiting slope k was

found to have a theoretical value of 2.11 cm ' I-OS

mol- 15 in solvent systems with fmix = 70 at 308.15K and a value of 1.79 cm ' 1-05 mol':": 5 in me-dia with fmix = 78.4 at 308.15 K. The limiting va-lue <P': of the apparent molar volume at infinitesi-mal concentration of the solute was found fromthe intercept of the linear plot of <P~ against e.Such ¢': data of HCl, NaCl, NaA and NaFor inthe present quasi-isodielectric media are recordedin Table lA.

Since the weak molecular acids, formic acidand acetic acid, would undergo incomplete ioniza-

1078 INDIAN J CHEM, SEe. A, DECEMBER 1994

Table lA-Apparent molar volumes tPv and degree of dissociation a at 308.15K of various solutes in different quasi-isodielec-tric media as function of solute molarity

(Dirntthy/fomwmide + Water)Formic acid

0.870 24.71 0.1876 9.21 0.302 24.08 0.2261 11.10

0.773 24.62 0.1904 9.35 0.230 23.94 0.2489 12.220.702 24.55 0.1935 9.50 0.144 23.76 0.3055 15.000.576 24.42 0.1992 9.78 0.090 23.64 0.3914 19.220.5261 24.35 0:2057 10.10 0.058 23.55 0.4908 24.100.4343 24.24 0.2143 10.52 0.026 23.41 0.6517 32.000.3621 24.14 0.2236 10.98 0.010 23.32 0.7898 38.78

0.0025 23.21 0.9053 44.45

Acetic acid

0.941 46.38 0.2041 1.98 0.250 45.82 0.3072 2.980.810 46.30 0.2165 2.10 0.2025 45.78 0.3515 3.41

0.7056 46.22 0.2258 2.19 0.1521 45.72 0.4124 4.010.4761 46.02 0.2392 2.32 0.0529 45.51 0.6278 6.090.3844 45.98 0.2474 2.40 0.0324 45.46 0.7062 6.850.3025 45.92 0.2763 2.68 0.0081 45.35 0.8887 8.62

Sodium acetate

0.8464 -0.40 0.260 • -2.51

0.722 -1.25 0.161 -3.25

0.640 -1.39 0.124 -3.43

0.5329 -1.72 0.096 -3.69

0.468 -1.85 0.056 -4.14

0.392 -2.42 0.0324 -4.28

Sodium formate

0.8836 27.11 0.2916 26.41

0.7569 26.96 0.247 26.12

0.627 26.81 0.2025 26.320.5476 26.74 0.1425 25.51

0.468 26.57 0.064 25.94

0.40 26.48 0.04 25.800.0121 25.66

Hydrochloric acid

0.9409 3.91 0.360 2.28

0.8?81 3.62 0.213 1.92

0.745 3.38 0.207 1.58

0.64 3.17 0.108 1.13

0.566 2.92 0.02 0.220.443 2.61 0.029 0.35

Sodium chloride

0.870 18.60 0.435 18.05

0.810 18.56 0.363 17.89

0.773 18.47 0.2025 17.71

0.703 18.43 0.141 17.66

0.577 18.26 0.0256 17.14

0.526 18.18 0.0025 16.90

(Contd)

SINGH et al.: ION-SOLVENT INTERAcnON IN MIXED SOLVENT MEOlA 1079

Table lA-Apparent molar volumes ;, and degree of dissociation a at 308.15K of various solutes in different quasi-isodielec-tric media as function of solute molarity - Contd

(Formamide+ Water)Formic acid

0.963 15.23 0.4169 84.21 0.277 13.52 0.5615 113.430.825 14.96 0.4335 87.56 0.221 13.26 0.5940 119.990.7225 14.70 0.4455 89.99 0.149 12.97 0.6448 130.24

0.640 14.52 0.4593 92.78 0.105 12.70 0.6840 138.16

0.548 14.31 0.4765 96.26 0.060 12.41 0.7541 152.320.458 14.12 0.4950 100.00 0.040 12.22 0.8075 163.120.375 13.80 0.5237 105.78 0.0196 12.00 0.8878 179.34

0.0081 11.81 0.9629 194.50

Acetic. acid

0.845 45.76 0.2876 32.84 0.230 45.31 0.3822 43.650.740 45.71 0.2882 32.91 0.160 45.26 0.4378 50.00

e.612I

45.62 0.3019 34.48 0.1163 45.20 0.4841 55.280.533 45.58 0.3027 34.57 0.0820 45.14 0.5373 61.36

0.457 45.51 0.3.118 35.61 0.0416 45.07 0.6785 77.480.380 45.44 0.3305 37.74 0.0225 45.01 0.7749 88.49

0.293 45.38 0.3618 41.32 0.0064 44.95 0.9322 106.46

Sodium acetate

0.9216 - 11.81 0.322 -14.780.7921 -12.32 0.250 -15.390.6561 - 12.94 0.187 - 15.550.5776 - 13.46 0.135 -16.550.468 -13.97 0.0889 -16.910.3919 -14.36 0.050 -17.76

0.0169 -18.31

Sodium formate

0.9025 28.74 0.266 28.030.7056 28.63 0.226 28.070.605 28.51 0.152 27.850.552 28.38 0.135 27.640.4356 28.27 0.09 27.550.346 28.09 0.037 27.32

0.0121 27.14

Hydrochloric acid

0.9025 0.05 0.2715 -2.110.7396 -0.41 0.2025 -2.620.640 -0.72 0.164 -2.660.528 -1.22 0.0966 -3.40

0.4055 -1.63 0.041 -4.230.3481 -1.89 0.01 -4.50

Sodium chloride

0.8281 18.00 0.1849 17.290.627 17.78 0.1225 17.200.512 17.68 0;784 17.080.369 17.50 0.040 16.950.3136 17.48 0.0225 16.890.260 17.39 0.01 16.80

1080 INDIAN J CHEM;SEC A, DECEMBER 1994

Table 2-Limiting value of apparent molar volume at 30B.15 K for various solutes in some quasi-isodielectric media; also re-corded are the fj.¢:' values for the various solutes (based on their ¢:' values in W at 29B.15K) in these media

Solute D+W DMF+W FD+W

¢:' fj.¢:' ¢:' fj.¢:' rp~ fj.¢:'(ml mol :') (mlmol I) (mlmol-I)

HCOONa 30.0 4.94 25.0 -0.06 27.0 1.94CH,COONa 5.4 - 33.H3 -4.0 - 43.23 -17.7 - 56.93NaCI 17.33 0.93 16.8 0.40 16.6 0.2HCI 4.05 -14.05 0.45 -17.75 -4.20 -22.3HCOOH 32.2 -2.49 31.0 -3.69 20.8 -13.89

CH3COCH 74.1 22.17 76.0 24.07 91.5 39.57

tion in the present solvent systems, their ~: datawere next considered, as a first approximation, tobe made up of independent contributions fromthe ions ~i' and molecules ~u and wereexpressed'l'" as:

~v = aL ~ + (1 - a) ~u

where

~~= ~7 + k (ac f' + biac~:= ~: + bu(1- a) c

and b, and bu are empirical constants",A proper combination of Eqs 6-8 yields 7

~"= ~v - all.yo - ka(ac)(j·5 = ~: + bia2c

+ bu(l- a)2c

... (6)

... (9)

However, evaluation of ~: from Eq. 9, when noinformation is available about the relative magni-tudes of the various terms, is subject to consider-able speculation. To obviate this problem we fol-lowed Geffeken and Price's method 17 as describedelsewhere'l'" The method envisages that Eq. 6can be expressed ll(f) in the form,

~u = ~v - all.~v

where

... (10)

... (11)ll.~v= '2:.~- ~u

and

L~ = ~v(HCI)+ ~v(NaAor NaFor)- ~v(NaCI)... (12)

The apparent molar volume ~u at a certain specif-ic concentration of the undissociated weak acidwas then obtained by successive approximationsin the manner described in the literature'Iv', Such~u data were next plotted against (1 - a)2C andthen interpolated linearly to obtain ~:, and arerecorded for formic acid and acetic acid in Table2. The necessary a data were obtained from the

(7)

(8)

conductance data of the solutions of these weakelectrolytes by first evaluating 18(.) A 0 from the Avs Co, plot (such plots were- found to be linearup to C = 0.25 m) in a particular medium whichwas then combined with the A data at any specif-ic concentration in that medium to obtain the avalue. Such an approach was necessitated by thefact that no precise activity co-efficient data ofthese electrolytes in the present quasi-isodielectricmedia are available (or could be computed) andthe evaluation of KA from Fuoss's and other con-ductance equations 18 - 23 is quite involved. More-over, the above procedure has been utilised tocalculate'r''" a data for weak electrolytes.

DiscussionWe are unaware of any ~: data of 1:1 electro-

lytes in the present mixed solvent systems withwhich to compare our results. It is, however, in-teresting to note that while the ~: data of AA,FA and HCI vary as AA> FA> HCI, the ~: dataof their sodium salts vary as NaFor > NaCl > Na-AC in these mixed solvent systems; The reported?~: data at 298.15 K of these electrolytes vary inwater as AA> FA> HCI; andNaAc > NaFor > NaCl.

Since ~: reflects ion-solvent interactions, ll.~:(HA or NaA) =~: (HA or NaA) in [W+ coso 1-vent (cs)] ~: (HA or NaA) in W. These datashould highlight the role of the cosolvent (cs) inmodifying ion-solvent interactions of these elec-trolytes with water (in W + CS systems) in a situa-tion where the electrostatic effects arising fromdielectric constant remain almost the same. As-suming that ~: data of these electrolytes in W donot change drastically'I's' with a 10° rise of tem-perature (or change by a constant fixed propor-tion), we employed the reported tfJ: data? at298.15 K of these electrolytes in water to com-

SINGH et al.: ION-SOLVENT INTERACTION IN MIXED SOLVENT MEDIA 1081

pute D.(r: (HA or NaA) data. Such data are re-corded in Table 2 and show that, for a particular HAor NaAj; D.f: values generally vary asFD < DMF < D. This is understandable.

Gutmann's donor number DN (detined/" as thenegative of the molar enthalpy of reaction of thesolvent in a dilute -solution in 1,2-dichloroethanewith antimony pentachloride) of FD, DMF and DislO(c)36, 26.6 and 14.8 kcal mol-1 respectivelywhile the corresponding electron pair acceptanceindex25 ET values'P'" are 56.6, 43.9 and 36 kcalmol-1 respectively. Both the DN and ET valuesof FD, DMF and D would then require that ionsof the present electrolytes should undergo maxi-mum ion-W interactions when FD is a cosolventcompared to the situation when D is a cosolvent.Furthermost, the variation of the D.tjJ;' (HA or NaA)within the same (W+CS) sysem, however, suggeststhat it is the interaction of the cation and or anion withco-solvent thatinfluences ion-W interactions. Thisseems reasonable.

Water is a structured solvent and the pair pot-ential energy U of the molecules in pure W canbe attributed " to non-structural and structural in-teractions. The non-structural part of U owes itsorigin to hard core repulsions and also to attrac-tions due to dispersion forces, dipole-dipole in-teractions etc., while the structural part of Uarises from the hydrogen bond formation. If thestructural part is described in terms of an interac-tion energy Uhb and a geometric factor g (R;, ~)(which determines the mutual configuration of thetwo molecules) then for a system of N watermolecules U may be expressed'? as,

U (RN)= Unon-slr (RN)+ u., g (RN)N

where g(RN)= L: g (R;, R) and is a measure of thei"j

extent of hydrogen bonding in a particular confi-guration RN. The probability factor D. < g > = exp(- U [RN]/kT) then determines'? the extent ofstructure inherrent in pure W. If now a solute ionY is introduced at a fixed point Ro in W then< g > y= < g > y- < g > would determine thechange produced by ion Y in the structure of W.If W, however, contains a cosolvent in the initialstate, then the pair potential energy U' (RN) maylikewise be expressed as,

U'(RN)= U~on,Slr. (RN)+ Ubb g'(RN)

so that (Uhb A < g > )= Uhb g' (RN)- u,g(RN}

should then (if Unon-slr. = U~on-slr., which is morelikely to be true in the present situation as the

proportion of the cosolvent in (W+ CS) systems isvery small) represent(Uhb D. <g>}y= exp [-(D.G~oln (Y in (W+ CS))

- D.G~oln (Y in W))/ RT]

For an infinite dilute situation (Uhb D. < g > )A +

(U hb D.< g > )B - ) = D should then express

D= exp [- (D.G~oln. (AB in (W+ CS))- D.GO(AB in W)jR1]

= exp [ - XIRT]

Now all the present cosolvents have great chemi-cal affinity for the protons of HCI, AA and FA. Ifthis chemical effect outweighs any other effect onW by the anionic part of these acids then an acidyielding large proportion of protons (as dictatedby its dissociation constant) would bring out largechanges in the structure of W in a W + CS systemso that D. < g > for that acid in a given W + CSsystem should increase. D values for HCI, FA andAA in a given W + CS solvent system should thenvary as HCl > FA> AA. Since D.tjJ'; for an acidwould be a function of X and as the X values ofthe present acids would vary as HCl < fA < AA,the above treatment would require that D.tjJ'; forthese acids in a given mixed solvent systemshould vary as HCI < FA < AA; the relevant D.tjJ';data support it.

On the other hand, the variation:" of electro-striction effect" of CH,COO ". HCOO - and Cl"in the order CH3COO- >CI- >HCOO- wouldrequire that D values for NaAc, NaFor and NaCIin a given mixed solvent system should vary asNaAC> NaFor > NaCl. The D.f: for these saltsin a given mixed .solvent system should then varyas NaAC < NaCI < NaFor; as is indeed the case.

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1082 INDIAN J CHEM, SEC. A, DECEMBER 1994

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