rNOTES

4. KRISHNA, V. G. & CHOWDHURY, M., J. phys. Chem., 67(1963), 1067.

5. KRISHNA, V. G. & BHOWMIK, B. B., J. Am. chem. Soc.,90 (1968), 1700.

6. BENESI, H. A. & HILDEBRAND, J. H., ]. Am. chem,s«; 71 (1949), 2703.

7. KATZlN, L. T., J. chem. Phys., 21 (1953), 490.8. SLlFKIN, M. A., Spectrocbim, Acta, 20 (1964), 1543.9. AWTREY, A. D. & CONNICK, R. E., J. Am. chem, s«.,

73 (1951), 1842.10. WATENABE, K., J. chem, Phys., 26 (1957), 542.11. BHOWMIK, B. B., Spectrochim. Acta, 27A (1971), 321.

Combining Rules for Intermolecular PotentialParameters & Excess Thermodynamic Func-

tions of Liquid-Liquid Mixtures

D. D. DESHPANDE

Department of Chemistry, Indian Institute of TechnologyPowai, Bombay 400076

andS. L. OSWAL*

Department of Chemistry, South Gujarat UniversitySurat 395007

Received 10 April 1978; accepted 4 July 1978

The validity of combining rules for interactionparameters and distance parameters in relation tothe excess thermodynamic functions has been Inves'ti-~ated. The excess functions based on van der Waalsequation of state and average potential model havebeen calculated for equimolar composition of elghtliquid-liquid mixtures. It is observed that the excessvolume is very sensitive to changes in rlB and thusthe theory could be used to predict all the three excessfunctions GE, HE and VE by adjusting E1B and r :B.However, the results show that the geometric meanrule of distances proposed by Good and Hope[J. chern. Phys., 53 (1970), 540] is invalid.

A NUMBER of statistical molecular theories forsolutionsv? of liquid-liquid mixtures are avail-

able which give explicit expressions for excess thermo-dynamic functions in terms of molecular andphysical properties of a reference substance. Inthe development of these theories a few assumptionshave been made and if any simple mixture deviatesfrom anyone or more of these assumptions, it leadsto a considerable disagreement between theory andexperiment.

For a sufficiently good agreement between thetheory and the experimental results on all the threeexcess functions GE, HE and VE, an empirical adjust-ment of one or two of the interaction parametersis usually necessary. Many authors6-10 have justifiedthe empirical adjustments of these parameters onthe ground that the combining rules are not rigo-rously valid. In this paper, therefore, we presentour results of excess thermodynamic functionsfor eight binary systems (Table 1) calculated onthe basis of different combining rules, and an analysisof geometric mean (GM) rule of distances proposedby Good and Hopev.

Combining rules and equation of state - For abinary mixture, coordinates of Lennard-jones+P

I

potential are related to those of pure componentsthrough the Lorentz-Berthelot combining rules(1) and (2).

'" (1). .. (2)

Many authors=" have assumed the validity of Eq.(2) and have attempted to adjust the value of €A'k

to fit the excess functions. It is observed thatrequired €AoB is less than that given by GM rule.Good and Hope+ have shown that Eq. (2) fordistances is inconsistent with the form of potentialand that the assumption of GM rule for interactionwould necessarily imply the assumption of GM rulefor distances. To test this, Eqs. (1) and (2) canbe modified as follows:

° t( ° O)~€AB = 'o,€AA€BB

rAoB = 4>(rAoA+rBOB)/2° J.I( ° o)lrAB = 't' rAArBB .

where 1; and fs are empirical coefficients close tounity and Eqs. (4) and (5) are based on arithmeticand geometric mean rule for distances.

Prigogines' average potential model (APM)3 andvan der Waals equation of state (VdW)6,9 are usedfor testing the suitability of the combining rules.Explicit expressions for excess functions GE, HE andVE based on APM theory- and VdW9 correspondingto two fluid van der Waals approximations can befound elsewhere3,6.9,13,14.

The results of these calculations for eight binarysolutions comprising Ar, Kr, N2, °2, CO, CH4,are reported in Table 1, and have been comparedwith experimental=", LRS theory'' and APM theoryreported by Bellemans". The critical constantsneeded for these calculations were taken fromHougen et a».

From the present computation some generalobservations can be made: (i) A decrease of thecoefficient 1; from 1·0 causes an increase in all thethree excess functions and comparatively the func-tions GE and HE are more sensitive than VE to suchchanges.

(ii) An increase of the coefficient 4> from 1·0causes a considerable increase in VE and a verysmall decrease in GE while HE is almost unchanged.Variation of 1% in coefficient 4> of Eq. (4) changesthe value of VE by 0·48 to 0·60 cm'' mole-! in VdWcalculations and by 0·8 to 1·0 em" mole= in APMtheory.

(iii) The value of 1; needed in the APM theoryis greater than unity to bring calculated valuescloser to experimental ones for some of the systems.This is unrealistic for such systems of nonpolarcomponents.

For these systems VE obtained from 4> = 1 and~ fitted to GE is always less than the experimentalresults except for N2+CO, and CO+CH4• There-fore, it necessarily needs 4>>1·0 for bringing VEclose to the experimental data. For systems I toVI, 4> needed an adjustment of 1·0 to 1·0022 whereasfor VII and VIII it is slightly less than unity forVdWequations. Agreement of HE data for N2+Ozis very good whereas for other systems it is moderate.

... (3)

... (4)

... (5)

87

INDIAN J. CHEM .• VOL. 17A. JANUARY 1979

TABLE 1 - COMPARISONOF THEORYAND EXPERIMENTFOR EIGHT BINARYMIXTURESAT X = 0·5

~ 4> GE HE VE(J mole-I) (J mole-t) (ern" mole-t)

(I) Ar+Kr AT 116 K

Experiment 0·99 84 103 -0'53LRS 0·990 1'0 84 -0·44APM 1·027 1·0 84 63 -0·87APM (This work) 1·025 1'0033 85 72 -0'53VdW (This work) 0'969 1·0 84 60 -0,58VdW (This work) 0·968 1·0007 84 63 -0·53

(II) Ar+N. AT 84 K

Experiment 1·00 34 51 -0·18LRS 0·997 1'0 34 38 -0·23APM 1·014 1'0 34 45 -0·20APM (This work) 1·014 1·0002 34 45 -0·18VdW (This work) 0·987 1·0 34 40 -0'18

(III) Ar+O. AT 84 K

Experiment 0'99 37 60 +0·14LRS 0·988 1·0 37 52 +0·14APM 0·988 1·0 36 55 +0·14VdW (This work) 0·978 1'0 37 50 +0'12VdW (This work) 0·978 1'0004 37 50 +0'14

(IV) Ar+CO AT 84 K

Experiment 0·99 57 +0'10LRS 0'985 1'0 57 -0'07APM 1·005 1'0 57 +0'04APM (This work) 1·005 1'0008 57 +0·10VdW (This work) 0'968 1'0 57 79 +0'06VdW (This work) 0·968 1'0007 56 79 +0'10

(V) Ar+CH. AT 91 K

Experiment 0·99 74 103 +0'17LRS 0·979 1'0 74 85 -0'13APM 1·034 1'0 73 103 +0'15APM (This work) 1'034 1·0002 73 103 +0'17VdW (This work) 0·962 1'0 74 88 +0'04VdW (This work) 0·961 1'0022 74 92 +0'17

(VI) N2+O. AT 78 K

Experiment 43 46 -0'21LRS 0·997 1'0 42 45 -0,24APM 1·010 1'0 44 44 -0·21VdW (This work) 0·984 1'0 43 48 -0·22VdW (This work) 0'984 1·0000 43 48 -0·21

(VII) N2+CO AT 84 K

Experiment 0·99 23 +0'13LRS 0·992 1·0 23 +0'10APM 0·991 1·0 23 +0'14APM (This work) 0·991 0·9999 23 +0'13VdW (This work) 0·983 1'0 23 35 +0·17VdW (This work) 0·983 0·9994 24 35 +0'13

(VIII) CO+CH. AT 91 K

Experiment 1'00 115 105 -0·32LRS 0·987 1·0 115 103 -0,50APM 0'997 1·0 115 95 -0'47APM (This work) 0·996 1'0014 115 99 -0'32VdW (This work) 0·957 1'0 115 119 -0'25VdW (This work) 0·958 0·9990 114 117 -0,32

88

I

r

Sinee ~ of Eq. (4) is an adjustable coefficient toarithmetic mean rule of distances, and its valueneeded is greater than unity, hence, it is obviousthat if Eq. (5) based on geometric mean rule ofdistances is used, VE 'obtained would be far lowerthan the experimental one. Therefore it can be com-mented that the geometric mean rule of distancesproposed by Good and Hopet! is unsuitable for thesesimple systems.

One of the authors (S.L.O.) is thankful to theeSIR, New Delhi, for the. research fellowship.

References1. PRIGOGINE, I., The molecular theory of solutions (North

Holland, Amsterdam), 1957.2. RawLINsoN, J. S., Liquid and liquid mixtures (Butter-

worth, London), 1971.3. BELLEMANS, A., MATHOT, V. & SIMON, M., Ado, chem,

Phys., 11 (1967), 117.4. ARAKAWA,K. & KIYOHARA,0., Bull. chem, Soc. Japan,

43 (1970), 975.5. DESHPANDE, D. D. & OSWAL, S. L., J. phys. Chem., 76

(1972), 3005.6. MCGLASHAN,M. L., Trans. Faraday Soc., 66 (1970), 18.7. LELAND, T. VV., ROWLINSON, J. S. & SATHER, G. A.,

Trans. Faraday Soc., 64 (1968), 1447.8. LELAND, T. W., ROWLINSON, J. S., SATHER, G. A. &

WATSON, I. D., Trans. Faraday Soc., 65 (1969), 2034.9. MARSH, K. N., MCGLASHAN,M. L. & CHRISTINAWARR,- Trans. Faraday Soc., 66 (1970), 2543.

10. MARSH, K. N., J. chem, Thermodynamics, 3 (1971), 355.11. GOOD, R. J. & HOPE, C. J., J. chem, Phys., 53 (1970),

540.12. LONGUET-HIGGINS,H. C. & WIDOM, B., Mol. Phys., 8

(1964), 549.13. HOUGEN, O. A., VVATSON,K. M. & RAGATZ, R. A.,

Chemical process principles, Vol. 1 (Wiley, New York),1959.

Excess Volumes for Binary Solutions ofm-, 0- & p-Xylenes in Tetrahydrofurant

S. L. OSWAL*t & G. V. BAKOREDepartment of Chemistry, University of Udaipur

Udaipur 313001

Received 13 March 1978; accepted 4 July 1978

The excess volumes (VE) for three binary solutionsof tetrahydrofuran (THF) with m-, 0- and p-xyleneshave been computed at 35° from the density data.The excess volumes for all these three systems arenegative and follow the order: p-xylene+THF <o-xylene-c T'Hf"< m-xylene+THF.

TETRAHYDROFURAN is a very useful solventdue to its strong proton accepting ability.

In addition, this solvent either alone or with ahydrocarbon is used as solvent for several polymers.This prompted us to determine excess volumes forbinary solutions of tetrahydrofuran with 0-, m- andp-xylenes at 35°± 0·010. Although the excess volumesVE, of tetrahydrofuran solutions in cyclohexane, n-heptane, benzene, toluene, carbon tetrachloride,chloroform and water are available in the Iiterature=+.No such data are available with xylenes.

t Presented at Convention of Chemist, Madurai, 1974.tPresent address: Department of Chemistry, South

Gujarat University, Surat 395007.

I

NOTES

The densities were determined with a Lipkin'sbicapillary pycnometer with a bulb volume of 14ems and a capillary bore diameter of about 0'1 em.The temperature of the water thermostat Was con-trolled to ± 0'01 0. The liquid level in the two armsof the pycnometer was measured with respect toreference mark by a travelling microscope readingto 0'001 em. The pycnometer was calibrated withtriply distilled water and benzene. The temperatureWas noted on calibrated Beckmann thermometers.All the chemicals used Were of Riedel (Germany)AR grade and were further purified by standardprocedures-e. Only triply distilled samples Were usedfor the measurements. The densities of purifiedsamples agree closely with the literature data".

The measurements of density Were made in thetemperature range 29° to 40° at intervals of about2°e. At each composition the temperature-densitydata were fitted to an equation of type y = a+b(t) by the least squares method and the densitiesat 35° calculated therefrom. The densities so ob-tained, are correct to 1 parts in 104.

Excess volumes Were calculated at 35° from thedensity data using the relation (1)VE = (MIXl +M2X2)/dI2-MIXl/dl-M2X2/d2 ... (1)where M, x and d represent molecular weight, molefraction and density respectively. Subscripts 1, 2and 12 refer to pure components and the mixturerespectively. The excess volumes thus obtainedare recorded in Table 1.

The excess volumes for all the three systems arenegative and their magnitude increases in the order:p-xylene + THF <o-xylene + THF <m-xvlene + THF.

A comparison of VE of these systems with otheravailable data1.2 seems worthwhile. Values of excessvolumes of equimolar binary solutions of cyclohexane,n-heptane, benzene, toluene, m-xylene, o-xylene andp-xylene in THF are 0'552, 0'405, -0'275, -0'342,-0·26,-0'28 and-0'31 ems mc le< respectively. VEvalues for the systems cyclohexane + THF andn-heptane+ THF is positive whereas for systemsbenzene + THF, toluene + THF, o-xylene + THFm-xylene + THF p-xylene + THF are negative.

TABLE 1- EXCESS VOLUMESFORXYLENES+TETRAHYDROFURANSYSTEMSAT 35°

(x is the mole fraction of tetrahydrofuran)

x VE x VE VE VEem" mole-! em" mole-! ems mole-s

(1) m-Xylene (2) o-Xylene (3) p-Xylenes+THF +THF +THF

0'0702 -0,05 0'0948 -0'04 0'1048 -0'070'1520 -0'09 0'1832 -0'12 0'2552 -0'210'2301 -0'15 0'2472 -0'16 0'3528 -0'260'3229 -0'20 0'3623 -0'25 0'4432 -0,300·4613 -0,25 0'4286 -0·28 0'5386 -0'310'5298 -0'26 0'5032 -0·28 0'5498 -0'320'6020 -0'25 0·6072 -0'27 0'6248 -0,320'6602 -0'21 0'7063 -0'26 0'7396 -0'280'7713 -0'19 0'7901 -0·22 0'7739 -0'240'8322 -0'16 0'8714 -0'15 0'8422 -0'200·8784 -0,09 0'9314 -0'08 0'9679 -0'060·9583 -0'06

89

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