Indian Journal of ChemistryVol. 25A, January 1986, pp. 26-30

Solubility & Dissociation Constant of Benzoic Acid inIsopropanol +Water Mixtures

A PAL & S C LAHIRI*Department of Chemistry, University of Kalyani, Kalyani 741235

Received 16 February 1983; revised and accepted 4 June 1985

The thermodynamic dissociation constants of benzoic acid and free energies of transfer of benzoic acid in isopropanol+ water mixtures have been determined from pH-metric and solubility measurements. The free energies of transfer of benzoateion have been determined using /';.G ~ values thus determined and /';.G ~H+J values previously determined. The free energies oftransfer of benzoate ion have been found to be positive in going from aqueous to aquo-organic mixtures.

Accurate solubility data have diverse applications indifferent branches of science and technology'. Thisprompted us to determine the accurate solubility dataof benzoic acid, an antifungal preservative widely usedin lotions and ointments, in waterand mixed solvents.Recently, Das et al.' determined the solubility ofbenzoic acid in different solvents over a wide range oftemperatures. However, their data are limited to a fewpercentages. Though limited data are available' on thesolubility values of benzoic acid in isopropanol-watermixtures, the values of the thermodynamic di-ssociation constants of benzoic acid in these solventsare lacking. We, therefore, report in this paper thesolubilities and the thermodynamic dissociationconstants of benzoic acid in isopropanol + watermixtures.

The study is expected to enable us to determine theeffect of solvents on the dissociation constants and findout the "free energy" of transfer of benzoic acid andbenzoate ion in different mixed solvents.

Materials and MethodsBenzoic acid (G.R.E. Merck) was used as such.

Isopropanol (AR, B.D.H)was distilled and the middlefraction was used without further purification. NaOHsolution (G.R.E. Merck) was standardized in the usualway. The chemicals were of guaranteed quality (E.Merck). For the determination of the solubility ofbenzoic acid at 298 K in mixed solvents, saturatedsolutions of benzoic acid were prepared in theappropriate solvents at about 303 K and filtered. Thesolution was taken in the Campbell solubilityapparatus) fitted with a sintered disc and a fine tube.The solutions were then allowed to equilibrate in athermostat maintained at 298 K (± 0.01) for 24 hr.After equilibration, the solutions were filtered byinverting the apparatus keeping it in the thermostat.The benzoic acid content of the filtered solution wasdetermined by titration at 298 K against a standard

26

Table I-Dissociation Constants of Benzoic Acid in Waterand Isopropanol-Water Mixtures at 298 K

Isopropanol A Total benzoic pH pA pKT(wt %) acid concen- (corrected)

tration (CT)(mol dm -3)

0.0 0.509 0.0284 2.89 4.18 4.218.0 0.568 0.0595 2.90 4.38 4.42

16.3 0.650 0.0628 2.92 4.63 4.6825.1 0751 0.1797 2.87 5.00 5.0734.3 0.899 0.5290 2.77 5.26 5.3343.9 1.101 0.9728 2.70 5.39 5.4954.0 1.417 1.4344 2.77 5.69 5.8164.6 1.9334 1.7663 2.84 5.93 6.0875.8 2.697 2.2466 2.95 6.25 6.6387.5 3.633 2.7083 3.01 6.45 6.68

NaOH solution. The process was repeated severaltimes for each set of measurements. The solubilityvalues of benzoic acid in water and mixed solvents arerecorded in Table 1. The errors involved in thesolubility measurements are in the range 0.2-0.5~~.

The density values of isopropanol + water mixtureswere determined with the help of an accuratepycknometer, previously calibrated.

For the determination of the dissociation constantsof benzoic acid, the hydrogen ion concentrations of thesaturated solutions of benzoic acid were measuredusing a systronics digital pH-meter having an accuracyof ±0.01 pH unit.

The weight percentages of the organic solvents weredetermined in the same way as described earlier, thedielectric constant values were taken from the datagiven by Akerlof and Short".

ResultsThe thermodynamic dissociation constant (HBz) for

the reactionHBz¢H+ +Bz- ... (1)(HBz = benzoic acid)

PAL & LAHIRI: SOLUBILITY & DISSOCIATION CONSTANT OF BENZOIC ACID

is ... (2)

Since, CH, = CBz-' we can write

... (3)

where [Ch = total benzoic acid concentration and CH,= concentration of H + in the saturated experimentalsolution, determined pH-metrically. Appropriatecorrections" -10 were applied to the pH meter readingsto get the true H + ion concentrations in the mixedsolvents. The method, initiated by Uitert et al.5, hasbeen extensively studied and verified by differentworkers" -10. Though the 'correction factors' for themixed solvents were known, we considered it desirableto find the 'correction factor' with each set ofmeasurements to avoid any error resulting from (i)changes in the asymmetry potential of the glasselectrode and (ii) liquid-junction potential of uncertainmagnitude which may change from solution tosolution. Since the solutions are extremely dilute(~10 -3M), the activity coefficients of ions can beregarded as unity. But, to get the accuratethermodynamicvalue of the dissociation constants, weused the proper activity corrections. The values of theactivity coefficient of the ion were calculated usinglimiting Debye-Hiickel equation,

-logJi = Ad JIi ... (4)

with appropriate A-values in each solvent takingintoaccount the changed dielectric constants of the mixedsolvents. The [H + J values in water were determinedfrom pH readings and the/H, values calculated usingEq. (4). The activity coefficients of uncharged benzoicacid can be regarded to be unity in the saturatedsolutions of benzoic acid in the respective solvents.

The pK; values of benzoic acid before and aftercorrections are recorded in Table 1.

The free energies of transfer for the dissociation ofbenzoic acid have been calculated using the usualrelation,

ddG;'(1) = - 2.303 RT[Iog Ka(s)-log Ka(w,J ... (5)

The free energies of transfer of neutral benzoic acid aregiven by Eq.6,

dG~(HBz) = dG~(HBz'- dG~(HBZ'

~ ~H~ 23 ~= -2.303RT log-- x----~ - . 03RTlog--Cw /W(HBz, ~~ (6)

where cs and Cw are the molar solubilities of thesaturated solutions of benzoic acid in the solvenns) andwater Iw) respectively. Since the benzoic acid is present

in its standard state (saturated) in the respectivesolvents, the activity coefficient of neutral benzoic acidcan be regarded as unity in aqueous and mixedsolvents. The assumption may be a gross over-simplification. Attempts have been made to calculatethe activity coefficients of benzoic acid theoreticallyfrom the available data. For ideal solutions where thesolubility is not affected by the nature of the solvent,the solubility at a desired temperature can beaccurately calculated using the relation 11.12,

... (7)

where Tm = melting point, and dHmF is the heat offusion at the melting point. It can be calculated usingthe relations, 11

dHF =dHmF-dCp(Tm-1) (8)

and dCp=C~-O (9)

The values of dHF (heat of fusion at temperature 1)C~ and C~ for benzoic acid have been taken from theliterature':'.

The value of X 2 has been found to be 0.1327 forbenzoic acid in water at 298 K, which is obviouslymuch higher than the actual value. We, therefore,calculated the activity coefficients of benzoic acid (y 2)in different solvents using the relation, 11.12, 14015

- 6 6 2 V2<1>ilogY2-( 1- 2) 2.303RT ... (10)

where V2 is the molar volume of (supercooled) liquidsolute and <1>1is the volume fraction of the solvent, 61

and 62 are the solubility parameters of the solvent andthe solute respectively. The 6 value of isopropanol hasbeen calculated from the cohesive energy density!" as 6=(c.e.d.)1I2.

The value of the molar volume of benzoic acid hasbeen calculated to be 113.88 ml-1 from the-relation V2

Mbenzoicacid(d densi hi' . h= d-. m = ensity at t e me ting point of t e

benzoic acid 1.0713 g/ml ':').Assuming the mixed solvent to be an 'assorted'

solvent of molecular weight Ms,

Ms =(1 OO)/{wt % of org. solvent + ~t~)nof water 1Morganic 18.016 S

... (11)

the molar volume (VI) of the mixed solvent has beendetermined from the density values (determined by us)and molecular weights.

27

INDIAN J. CHEM .. VOL. 25A, JANUARY 1986

Table 2-Calculation of the Activity Co-efficients ofBenzoic Acid in Isopropanol-Water Mixtures at 298 K

Isopropanol X2 bm x' V, <1>, Y2,(wt %)

0.0 0.001 23.40 0.998 18.00 0.0179 1.0098.0 0.025 23.10 0.997 19.46 0.0104 1.010

16.3 0.055 22.74 0.996 21.01 0.0209 1.01125.1 0.091 22.32 0.989 23.04 0.0228 1.01834.3 0.135 21.79 0.967 25.56 0.0247 1.01343.9 0.190 21.14 0.939 28.80 0.0270 1.01454.0 0.260 20.31 0.911 32.98 0.0300 1.01464.6 0.354 19.19 0.888 38.52 0.0342 1.01475.8 0.485 17.63 0.860 46.27 0.0398 1.01287.5 0.678 15.33 0.832 57.79 0.0481 1.007

The solubility parameters of the mixed solvents havebeen calculated using the relation,

<5mixedsolvents= Xl <51+ X 2<52 ... (12)

where Xl' <51and X2, <52represent the mole fractionand the solubility parameters for the first and secondsolvents respectively. <1>1' the volume fraction of thesolvent, is given by Eq. 13,

<1> Xl VI1 = 1000 ... (13)

where Xl represents the mole-fraction of the solvent ofmolar volume VI in the saturated solutions of benzoicacid.

Using these data, we have calculated the r, values ofbenzoic acid in isopropanol-water mixtures. Thevalues are presented in Table 2.

DiscussionIt is to be noted that the activity coefficient values of

benzoic acid in mixed solvents have been found to beclose to unity. It is apparent that the insertion of the }'2

values (a=X2}'2) does not improve the results. It is tobe noted that the Eq. (10) is applicable to regularsolutions which exhibit positive deviations fromRaoult's law. But if negative deviations from Raoult'slaw arise, when specific interactions like solvation andassociation occur, Eq. (10) fails. In the case of benzoicacid solution, both dimerization of benzoic acid andinterlinking of water molecules to benzoic acid byhydrogen-bonding are possible. These may lead to thechange in }'2 values and result in lower solubility ofbenzoic acid in water and in mixed solvents. Due tolow ionic strengths of the solutions, the pKa valuesreported here can be regarded as the idealthermodynamic values. The results agree very wellwith the values determined conductometrically usingFuoss-Kraus method 17. As expected, the solubilityvalues of benzoic acid increase with increase in[organic solvent]' It is seen that the solubility values

28

are greater than those in the methanol + water orethanol +water mixtures due to greater hydrophobiccharacter of the isopropanol + water mixtures.

The pK-values of benzoic acid increase continuouslywith increase in organic solvent content and show alinear relationship when plotted against 1/D at lowpercentages but deviations occur near '" 60 wt % oforganic solvents. Obviously the solute-solventinteractions of varied nature are responsible for thedeviations.

In view of the limitations of Born equation 18 anduncertainty regarding the radii values of H + ion andunsymmetrical benzoate ion, we have not divided!::J.pKT into !::J.pKT(el) and !::J.pKT(non e l} as done by Batesand Robinsorr'".

However, since the free energies of transfer of ionsgive the relative magnitudes of the differences in theion-solvent interactions of ions, which are thedominating forces in dilute solutions where ion-ioninteractions are absent, we tried to determine the freeenergies of transfer of benzoate ion in the presentstudy. One of the advantages of determiningpK-valuesof weak acids like benzoic acid by the solubilitymethod is that the solutions are extremely dilute andthe ions are in their respective standard states insolutions of the different solvents, an essentialcondition for the determination of medium effects ofions.

The free energies of transfer of benzoate ion havebeen determined utilising the well-known relation?",!::J.G~(ion)= !::J.G~(neut)+ !::J.G~(el) ... (14)

where !::J.G~(neut)has been assumed to be equal to itsuncharged analogue.Since !::J.G~(Bz-)=!::J.G~(HBz)+!::J.G;(el)'

We have,!::J.!::J.G~(1)= !::J.G~(1)- !::J.G~(1)= !::J.G~(H+)

+!::J.G~(Bz-)-!::J.G~(HBz) ... (15)

or !::J.G~(Bz-) = !::J.!::J.G~(1)- !::J.G~(H+) + !::J.G~(HBz)... (16)

!::J.G~(HBz) values have been determined fromsolubility measurements. Corrections for the di-ssociation of benzoic acid in different solvents, thoughvery small, have been made. !::J.G~(Bz-) values inisopropanol + water mixtures have been calculatedusing !::J.G~(H+) values determined in our laboratory'".The values are recorded in Table 3.

There is a wide divergence in the reported !::J.G~(H+)values in different mixed solvents and in most cases thevalues are limited to a few percentages only.

The !::J.G~(H+) values in isopropanol + watermixtures have been relatively less investigated.However, the different extrathermodynamic methodsof evaluation of !::J.G~(H+) have inherent limitations.

PAL & LAHlRI: SOLUBILITY & DISSOCIATION CONSTANT OF BENZOIC ACID

Table 3-Solubility & Free Energy of Transfer Data of Benzoic Acid in Isopropanol +Water Mixtures at 298 KIsopropanol I/D x 102 Solubility Solubility tJ.G~neUI) AG4oeut) AG;reac. 1) AG~(rUC' 1) ~G~(H')

AGOt(A-)

(wt %) (moldm -3) (molal) (kl/mole) (kJ mol-I) (kJ mol ") (kJ mol-I) (kl mol ") (kl mol ")

0 1.27 0.0284 0.0285 8.82 24.62(0.0271)* (8.94)·

8.0 1.37 0.0395 0.0403 8.01 -0.81 25.22 1.20 -1.16 1.51(0.0382) (8.09) ( -0.85)

16.3 1.50 0.0628 0.0649 6.86 -1.96 26.70 2.68 -2.03 2.68(0.0616) 6.91 ( -2.03)

2.51 1.65 0.1797 0.1894 4.25 -4.57 28.93 4.91 -3.60 3.84(0.1784) (4.27) ( -4.67)

34.3 1.86 0.5290 0.57022 1.58 -7.24 30.41 6.39 -4.31 3.35(0.5273) (1.59) ( -7.35)

43.9 2.13 0.9728 1.0771 0.07 -8.75 31.32 7.30 -5.15 3.58(0.9,.708) (0.07) ( -8.87)

54.0 2.52 1.4344 1.6328 -0.89 -9.71 33.15 9.13 -5.50 4.80(1.4327) ( -0.89) ( -9.83)

64.6 3.10 1.7883 2.0938 -1.44 -10.26 34.69 10.67 -5.63 5.34(1.7869) ( -1.44) ( -10.94)

75.8 3.87 2.2466 2.7077 -2.00 -10.82 37.83 13.81 -5.08 7.95(2.2455) ( -2.00) ( -10.94)

87.5 4.72 2.7083 3.3645 -2.47 -11.29 38.11 14.09 -3.25 5.93(2.7073) (-2.47) ( -11.4l)

"Corrected for dissociation of benzoic acid~G~(H +) was determined in our laboratory

AG~(H +) values obtained from simultaneousextrapolation method+' are always more negative.The limitations of the Well's method/" and theferrocene ferricinium method have been dis-cussed2o

•24. However, no AG~(H+) values inisopropanol +water mixtures based on widelyadvocated Ph4AsBPh4 or TABBPh4 methods areavailable. The values of AG~(H +) determined by us inethanol +water mixtures compare very favourably(both qualitatively and quantitatively) with thosereported by Popovych and Dill using TABBPh4

method+'. Thus, we consider our values of AG~(H+) inisopropanol + water to be reliable, but it is difficult topredict the error range in view of the uncertainty in theelectrostatic contributions to AG~(H+).

It is seen that AG~(benzoate ion), cannot becalculated using Eq. (14) as there is considerableuncertainty in calculated values of AG~~el)due to thelimitations of the Born equation! and non-availability of reliable value of radius of unsymmetri-cal benzoate ion. The radius (r = 0.275 nrn) calculatedby us using bond distance values is greatly differentfrom the value (r=0.055 nm) used by Robinson andBates 1 9 in the calculation of ApK T(nonel)of benzoicacid. Moreover, ion-dipole, ion-quadrupole anddispersion forces are likely to be large in the case ofbenzoate ion. We, therefore, prefer to use Eq.(16) tocalculate AG~)(benzoate ion) utilizing the determinedvalues of AG~(HBz) and AG~(H "), AG~(Bz -) valueshave been found to be fairly consistent. The values are

predominantly positive, in-agreement with the fact thatAG~ of anions are usually positive26

•27

•

The AG~(Bz -) shows two maxima around 25 and 75wt% of isopropanol. These may reflect thecharacteristic changes in solvent properties in theseregions though the structural changes of the solventsare not usually reflected in AG~(ion) values due toknown but not complete compensation in AH~ andAS~ values26

•27

. It is unfortunate that most of thestudies are limited to low organic content region andusually one maximum or minimum is noted in thisregion. It is to be noted that the addition of alcoholfirst strengthens the three dimensional polymericstructure of water molecules. The structure formationof water becomes maximum at about -25 wt%beyond which depolymerization of water moleculesbegins with the addition of alcohol. The de-polymerization process continues up to -75 wt% andsubsequently structure formation characteristic ofalcohol molecules takes place. Thus, the structuralchanges may result in two maxima for AG~(Bz -). Theresults are not unusual and are in accord with theobservation that the structural changes are pro-nounced in the regions 20-30 and 75-90 wt% of organicsolvents/" .

It is possible to analyse AG~(Bz -) in the waysuggested by Treiner28•31 as,

AG~(Bz --)= AG~(cav)+AG~(specific)

+AG ~(structural)+AG ~(el)

29

INDIAN J. CHEM., VOL. 25A, JANUARY 1986

LlG~(cav)'representing the free energy change due tocavity formation, may be calculated using the scaledparticle theory as used by Treiner29

,3o and recently by

Kundu et al.31 However, in view of the limitations inthe calculation of LlG~(el)'we do not expect the methodto give more information regarding the (specific andstructural) effects.

We can calculate LlG~(el) from Eq. (14) usingLlG~(Bz -) and LlG~(HBz). The LlG~(el)values thusobtained would be in qualitative agreement with thecalculated LlG~(el)values using Born equation butquantitative agreement is quite poor. Moreover, if weanalyse LlG~(HBz) and LlG~(Hz -), we have,

LlG~(HBz) = LlG~(cav)1 +LlG~(specific)1+ LlG~(structural)1 and

LlG~(Bz -) = LlG~(cavh + LlG~(specifich+ LlG~(structural)2 + LlG~(el)

Though LlGt~cav)(Bz-) ~ LlG~(cav)(HBz),the specific andstructural effect would be different for Bz - and HBz.Thus, an uncertainty is inherent in the LlG~(Bz-)values. The calculations of LlG~(cav)also involve anelement of uncertainty. It is to be noted that LlG~(ion)values are based on extra-thermodynamic assum-ptions with their inherent limitations; therefore, weconsider that LlG~(ion) values should be calculatedusing different methods to have a consistent set ofvalues before deriving positive conclusions from theresults.

It is clear that more values of the 'medium effect' ofions are required to get a clear picture regarding the ionsolvent interactions.

AcknowledgementThe authors wish to thank the UGc, New Delhi for

a Research Fellowship to A.P.

References1 Kertes A S, in Solubility data series (Pergamon Press, Oxford,

New York), vii, 1979.2 Das K, Das A K, Bose K & Kundu K K, J phys Chern,82(1978)

1242.

30

3 Campbell A N, J chern Soc, (1930) 179.4 Akerlof G & Short a A, J Arn chern Soc, 58 (1936) 1241.5 Van Uitert L G & Haas C C, J Arn chem Soc, 75 (1953) 451.6 Bhattacharyya U C & Lahiri S C, Z physik Chern, (N.F.), 50

(1966) 451.7 Lahiri S C & Aditya S, J Indian chem Soc, 51 (1974) 319.8 Gentile P S, Cefola M & Celiano A V, J phys Chern, 67 (1963)

1447.9 Irving H M N & Manhot V S, J inorg nucl Chern,30 (1968) 1215.

10 Bates R G, Deterrnination of pH, theory and practice, (WileyInterscience, New York) 1973,276-77.

11 Hildebrand J H & Scott R L, The solubility of nonelectrolytes(Reinhold, New York) 1950, Chapter 1,2,23.

12 Moelwyn-Hughes E A, Physical chemistry, 2nd Edn (PergamonPress, London) 1965, Chapter 17.

13 Internationalcriticaltables, Vol. III (McGraw Hill, New York &London) 1928.

14 Hildebrand J H & Wood J E, J chem Ph),s, 1 (1933) 817.15 Martin AN, Swarbrick J & Cammarata A, Physical pharmacy

(Lea & Febiger, Philadelphia), 1969, Chapter 12.16 Dack M R J, Chern Soc Rev, 4 (1975) 211.17 Pal A & Lahiri S C (unpublished data).18 Born M, Z physik, 1 (1920) 45.19 Bates R G & Robinson R A, in Chemical physics in IOniC

solutions, edited by B E Conway & R G Barradas (JohnWiley, New York) 1966, Chapter 12.

20 Lahiri SC & Aditya S, J Indian chem Soc, 56 (1979) 1112 andreferences cited therein.

21 Chakraborty S K, Sengupta D & Lahiri S C, Z physik Chern(Leipzig) (in press).

22 Bose K, Das K, Das A K & Kundu K K, J chernSoc Faraday I, 74(1978) 1061.

23 Wells C F, J chem Soc Faraday I, 70 (1974) 694.24 Sengupta D, Pal A & Lahiri S C, J chernSoc, Dalton Trans, (1983)

2685.25 Popovych a & Dill A J, Analyt Chern, 41 (1969) 456.26 Wells C F, J chem Soc, Faraday Trans I, 69 (1973) 984.27 Feakins D, Physico-chemical process in rnixed aqueous solvents,

edited by F Franks (Heinemann, London) 1967, 71.28 Amis E S & Hinton F, Solvent effects on chernicalphenomena,

Vol. I (Academic Press, New York and London) 1973,Chapter 4.

29 Treiner C, Can J Chern, 55 (1977) 682.30 Treiner C, La Beanerais A & Micheletti C, in Advances in

chemistry series, edited by W F Furter (American ChemicalSociety, Washington) 1979, 109.

31 Bhattacharyya A, Dutta J, Das K & Kundu K K, Indian J Chern,21A (1982) 9.