Indian Journal of ChemistryVol. 24A. March 1985. pp. 191-194

Ionization Constants of Water & Related Transfer Free Energies ofHydroxide Ion in Aqueous Acetonitrile & Dimethylformamide Based on TATB

Assumption

URMILA MANDAL. SWAPAN BHATTACHARYA & KIRON K KUNDU'

Department of Chemistry. Jadavpur University. Calcutta 700032

Receired 21 May 1984: rerised and accepted 26 September 1984

The ionization constants (,Kw) of water have been determined in aqueous mixtures (20.40.60 wt ~.~)of acetonitrile anddimethylformamide at 25 C from emf measurements of cells comprising glass and Ag-AgCl electrodes. Transfer free energies.~G?(OH ) have been evaluated therefrom using ~G?{H ") values based on TATB assumption. These are explained in the lightof ion-solvent interactions as guided by physicochemical properties of the solvents.

The rates of nucleophilic reactions including base-catalyzed reactions, are often dramatically enhancedon the addition of dipolar aprotic solvents to proticsolvents like water, alcohols, glycols etc. I -). It isbelieved since long that nucleophiles and the Brenstedbases like OH - etc. get increasingly 'activated' due tothe decreased solvation of the ions in these solvents.These views are substantiated by the observedincreasingly positive magnitudes of transfer freeenergies, L1G, of nucleophiles like halide ions (X ),OH ...etc. from water to some aqueous dipolar aproticsolvents'':". as recently determined using widelyknown't'' tetraphenylarsonium tetraphenylboride(TATB) assumption: L1G, (Ph4As +) = L1~XPh4B -)= tL1G~(Ph4AsPh4B).

Although L1G~'(i)values of various ions based onTATB assumption are known in aqueous mixtures ofsome aprotic and dipolar aprotic solventst" includingacetonitrile (ACN)5c and N,N-dimethylformamide(DMF)5d, those for OH - are known only in a limitednumber of solvents, other than ACN and DMF. Aspart of our studies on the rates of alkaline hydrolysis ofcrystal violet cation (CV +) in aqueous mixtures ofvarious protic, aprotic and dipolar aprotic solventsincluding ACN and DMF7, it was considered essentialto determine L1G~(OH ") values in the latter twocosolvent systems. In this communication we reportthe L1G~(OH-) values by measuring the ionizationconstants (sKw)of water in aq. ACN and aq. DMF (20,40 and 60 wt (~;)and then evaluating L1G~(OH") usingL1G~(H+) values based on TATB assumption", asreported earlierkd

Materials and MethodsSince Pt, H 2 (g, I atm)/H + electrode was found to

behave irreversibly in these solvent systems, cell (A)

GE-H+ /NaOH(ml), NaCl(m2)' solvent/AgCl-Ag... (A)

was used for the determination of .K; values in thesesolvents. In cell (A) GE - H + stands for H + -reversibleglass electrode. The E~cll values of cell (A). weredetermined using the cell (B)GE - H + /HCl(m), solvent/AgCI- Ag ... (8)

in an auxiliary experiment for each of the solventmixtures before the use of cell (A) in the correspondingsolvent mixtures.

The reagent grade sovents were purified as describedearlier5c.d. All other chemicals were of AR grade andused after usualpretreatment. Concentrations of theelectrolytes were determined by standard procedures.GE - H + electrodes used were of Elico model EI-52.Ag-AgCI electrodes were prepared by the methoddescribed earlier'.'. K iethley digital electrometer(model 616) was used for measuring the emf of the cells.Other experimental details were essentially the same asdescribed earlier". Emf values were correct to±.OOI V.

ResultsThe emfs of the cells (A) and (B) are given by

... (1)

where k = 2.303 RT; F and sE~cll represents thestandard emfs of the cells (A) and (B). Assumingcomplete ionization ofHCI, an extrapolation function.EO'cell defined by Eq.(2)

E~:ll= EB+ 2 k log aHC) - 2 kSfCI i2 = sE~c1)+ bw: ... (2)

was constructed, where Sf is the Debye-Huckelconstant (values were taken from earlier papers v?')and ha is an empirical constant depending upon thenature of the solute, solvent and temperature. Theplots of EO'cell versus ('He) were linear which onextrapolation to C= 0 furnished E~c11values on molarscale .

191

INDIAN J. CHEM., VOL. 24A, MARCH 1985

Table \- Values of p,K':.., and Related Transfer Free Energies Accompanying Ionization of Water in Aqueous Mixtures ofACN and DMF at 25cC

wr, p.K'; 6(IlG?on) llG?(H +)* llG?(OH -),pp ~G?(H20) llG?(OH -)cosolvent (kJ mol 'I) (kJ mol-I) (kJ mol-I) (kJ mol' I) (kJ mol-I)

ACN +water mixtures

20 14.33 1.10 -3.1 4.2 0.56 4.840 15.05 4.30 -4.8 9.1 0.83 9.960 16.68 12.57 -4.9 17.5 0.96 18.5

DMF + water mixtures

20 12.95 -6.80 -3.0 -3.8 0.15 -3.640 13.06 -7.14 -9.4 2.3 0.38 2.760 13.04 -8.44 -16.5 8.1 0.78 8.9

*IlG?(H +) values were taken from references 5c and 5d. but slightly modified due to the involved computational errors in the previouslyreported data.

The emf, EA of cell (A), given by Eq. (I), can. becorrelated with .r; (= aWGOW/GH.O)· On replacing Gwby KwGH,o/GOH' one has the usual extrapolationfunction p.K'; defined by" Eq. (3)

p,K~=(E-sE~cIlJik+logjcCl/COH )

=psK~+logaH,o YeI'/YOH" =PsK~+f{)I) ... (3)

As in previous studiesHa'c the standard state is sochosen that at infinite dilution in a given solvent yCI-= YOH= GH0 = I. PsK~ values were computed usingsE~cll values obtained from the data for cell (B) andemploying Eq. (2). The plotsPsK~ versus ionic strength(J1) were linear which on extrapolation to J1 = 0furnished psK~ on molar scale. This shows that as inaqueous dioxane'?'. THF8a, DME8a and DMS08b

, theterm-log GH,o YCi-lYow in dilute solutions of eachsolvent is directly proportional to J1 and so at J1 = 0, theactivity term vanishes. The values of PsK~ arepresented in Table 1. The estimated uncertainties inPsK~ values are of the order ± 0.02 unit.

The solvent effects, 6(~G~n)' on the ionization ofwater were computed on mole fraction scale usingEq. (4)

b(tlGi~n) = stlGi~n- wtlGi~n= 2.303 RT[PsK~ - PwK;]+ 2.303 RT 10gjdsM w/dwMJ " .(4)

where the subscripts sand w refer to the solvent and thereference solvent water respectively, and other termshave usual significance. These values are given inTable I.

Since the solvent effects on p.K; are related totlG?(H +), ~G?(OH -)'pp and tlG?(OH -) byEq. (5)5b.8b -d,

6(tlG?on)= tlG?(H +) + tlG?(OH -)app= tlG?(H +)+ tlG?(OH-) - tlG?(H 20) (5)

tlG?(OH -)app values were computed by subtractingtlG?(H +) values based on TATB assumption for thesesolvent mixtures, as reported by us earlier ":".

192

tlG?(OH -) values were estimated by adding - RT InsGH.O totlG?(OH -)app in the case of ACN + watermixtures" and - RT In xH,o in the case of DMF+ water mixtures", as the corresponding sGH.Odataactivity of water in the solvent) to the best' of ourknowledge are not known; xH,o is the mol fraction ofwater and can approximately be equated to SQH,O'Allthese values are listed in Table 1. It is evident fromTable 1 that the contributions of RT InosGH.oor RT InxH,o are rather small compared to tlG( (Ol-l-)app andhence tlG(o(OH ") values differ slightly from thecorresponding ~G(o(OH -)app' Similar is the case inDMSO-water mixtures'", although experimentalvalues of sQH,owere used.

DiscussionInterestingly enough, while b(tlG?on)-wt 'Yo profile for

ACN-water mixtures (Fig. l) becomes increasinglypositive that for DMF-water mixtures (Fig. 2) exhibitsa sharp downward trend upto 20 wt % DMF followedby a slight 'roller-coaster' type behaviour in 20-60 wt %aq DMF. Since these profiles are chiefly guided by thecombined effects of transfer free energies of H + andOH - from water to the respective solvents, theobserved opposing behaviour of b(tlG?oJ obviouslyreflects the involved nature of the relative behaviour ofthese two ions in the two solvent systems.

The tlG?(H+)-composition profile in DMF-watermixtures becomes increasingly negative with a slighthump around 20 wt % DMF (Fig. 2), which is chiefly "due to the combined effects of intrinsic protophilicityof DMF and the possible hydrates of DMF10

-13 atlower compositions where the basicity is lyingintermediate between pure water and DMF5d and theBorn-type electrostatic interactions. Similarly, inACN-water mixtures the observed slight minimum in~G?(H +)-composition profile (Fig. 2), is the result ofthe possible breakdown of three dimensional (3D) ice-like water structures releasing more basic monomeric

20r------------------------------,

MANDAL et al.: IONISATION CONSTANTS OF WATER

15,-aE

o

-5

-10L-----------oi2;;-0--------4-;!;0,-------'6:'1i0--J

wl·/. ACN

Fig. 1 - Variation ofb(~G~on)and ~G~(i) for H +, OH - and CI withwt "0 ACN in ACN + water mixtures

15

10

CI~/

/./

.//

//

~/

//

//

//

/

~/

.//--'0 5

E

OHLY./

".//

//

./

/

):f./

././

',-- /..... -...... /

"'_-'v. ,,/--0-<, -,

<, -, -,----"c..---Q-- __ c6( ~Gion)-,

V'- ,"-

"- ,,',H+,

~,

~.x:--.....-= 0

0<5-o.•.•......

~-50<5-o"<0

-10

-15

-20

20 40wl% DMF

Fig.2 Variation of b(~G?on)and ~G~(i) for H + ,OH and CI withwt "" DMF in DMF+water mixtures

60

water molecules5c.!3.14, and formation of possiblehydrates of ACN 15, as shown in (A) and (B)5c.On the other hand, the observed upward trend ofdG~(OH -) profile in ACN-water mixtures is the resultof increasing destabilizing effect of the aproticity ofACN hydrates (A) and (B) and of pure ACN whichbecomes all the more aprotic with the possibleformation of dimers+?'! 7 as shown in (C)5c,besides thesuperimposed Born-type electrostatic effect. Butsignificantly enough, the dG?(OH -)-composition

6+ 6-H3C-S"'~

N"C-CH36- 6+

A B C

/O~...HH-C~ +6-1}

/N, ... O <, H6+H3C CH3

o

profile in DMF-water mixtures exhibits a distinctminimum around 20 wt % DMF and then assumes anincreasingly positive trend, as is expected from thedestabilizing effect of the aproticity of DMF, besidesthe Born-type electrostatic effect. The observed initialminimum or increased stabilization ofOH - comparedto pure water is possibly indicative of the effect of thepossible stable hydrates of'DMf l'' -13 imparting moreproticity, HH, to the H-bonded intercomponentcomplex as shown in (D),Thus (D) is likely to be more effective for solvation ofprotophilic anions like OH - which can undergo'localized hydrolysis' type interaction 18 as in (E) tnanthat for non-protophilic anion like CI - as in (F), This isalso evident from the parallel behaviour of both OH -and Cl " in this solvent system (vide Fig. 2). Thisexplains why dG~(OH -)-composition profile is lyingbelow that for CI - in the solvents. On the contrary, asin DMSO-water mixtures" the observed reversebehaviour of CI - and OH - in ACN-water mixturesseemingly results from the combined effects of largerBorn-type electrostatic effect of OH - compared toCI - and the opposing soft-soft interactions 19 on thesoft Cl ". Besides, because of the structural akinness ofOH ~ in pure water, OH - gets more stabilized in purewater than does CI -, thus augmenting moredestabilization of OH - than CI -.

AcknowledgementThanks are due to the C~IR, New Delhi for financial

assistance,

References1 Bowden K, Chern Rev, 66 (1966) 119 and relevant references

therein.2 Ritchie C D, in Solute-solvent interactions edited by J F Coetzee

and C D Ritchie (Marcel Decker, New York), 1969 andrelevant references therein.

3 Parker A J, Chern Rev, 69 (1969) I, and relevant referencestherein.

4 Marcus Y, Rev anal Chern, 53(1980) 473, and relevant referencestherein.

5 (a) Das A K & Kundu K K, J soln Chern, 8 (1979) 259.(b) Datta J & Kundu K K, Can J Chern, 59 (1981) 3141.(c) Das K, Das A K & Kundu K K, Electrochirn Acta, 26(1981)

47\.(d) Das K, Bose K & Kundu K K, Electrochirn Acta, 26 (198:)

479.

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INDIAN 1. CHEM., VOL. 24A, MARCH 1985

(e) Bhattacharya A, Datta 1, Das K & Kundu K K, Indian JChern, 21A (1982) 9.

6 Cox BG, Hedwig G R, Parker A J& Watts D W, Aust J Chern, 27(1974) 477.

7 (a) Mandai U, Sen S, Das K & Kundu K K, J chem Soc PerkinTrans ll-communicated.

(b) Mandai U, Bhattacharya S& Kundu K K, J chem Soc PerkinTrans ll, communicated,

8 (a) Datta 1 & Kundu K K, Can J Chern, 89 (1981) 3141.(b) J chem Soc Faraday Trans I, (1973) 730.(c) J phys Chern, 71 (1975) 2604.(d) Harned H S & Fallon L D, J Arn chem Soc, 61 (1939) 2374.

9 Vierk V A, Zfur anorg Chern, Band 261 (1950) 283.

194

10 Rohdewald P & Moldner M, J phys Chern, 72 (1968) 2710.II DeVissar C & Somsen G, Z phvs Chern, 92 (1974) 159.12 Bougard 1& lodot R, J chem Thermod, 7 (1975) 1165.13 Saito M, Analyt Chern, 47 (1975) 1784.14 Robertson R E & Sugumari S E, Can J Chern, 50 (1972) 1353and

relevant references therein.15 Le Nauvon A, Gentric E & Soumagre p, Can J Chern, 45 (197 I)

1533.16 Zukhova E L, Opt Spectrosk, 4 (1958) 750.17 Saum AU, J po/yrn sa, 42 (1960) 57.18 Robinson R A & Harned H S, Chern Rei', 28 (1941) 419.19 Pearson R G, J Am chern So(', 85 (1963) 3533.