Topological and thermodynamic investigations of binary mixtures: Molar excess volumes, molar excess enthalpies and isentropic compressibility changes of mixing

Fluid Phase Equilibria 235 (2005) 42–49

Topological and thermodynamic investigations of molecularinteractions in binary mixtures: Molar excess volumes

and molar excess enthalpies

Sanjeev Makena,∗, Bal Raj Deshwalb, Renu Chadhac, Anud,Krishan Chander Singhd, Hwayong Kime, Jin-Won Parka

a Department of Chemical Engineering, Yonsei University, Seoul 120-749, Republic of Koreab Korea Institute of Energy Research, Daejon 305 600, Republic of Korea

c Department of Pharmaceutical Science, Punjab University, Chandigarh, Indiad Department of Chemistry, M. D. University, Rohtak 124001, Haryana, India

e School of Chemical Engineering, Seoul National University, Seoul 151-744, Republic of Korea

Received 18 November 2003; received in revised form 8 June 2005; accepted 22 June 2005

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Molar excess volumes and molar excess enthalpies of butyl acetate (i) with cyclohexane or benzene or toluene oro-, m- or p-xylene (j)inary mixtures have been measured dilatometrically and calorimetrically over the entire composition range at 308.15 K. The obsave also been analyzed in terms of graph theoretical approach. The analysis ofVE data by graph theoretical approach suggests thatcetate in pure state exists as associated entity and (i + j) mixtures are characterized by the presence of (i–j) molecular entity. It has furtheeen observed thatVE andHE values calculated by this approach agree well with the corresponding experimental values. The preolecular entity is further confirmed by IR study of (i + j) mixture.2005 Elsevier B.V. All rights reserved.

eywords:Molar excess volume; Molar excess enthalpy; Butyl acetate; Aromatics; Graph theoretical approach

. Introduction

A number of experimental as well as theoretical stud-es on thermodynamic properties for alkyl ester withlkanes [1–9], aromatic hydrocarbons[8–17], alcohols

18,19], chloroalkane[20] and acetonitrile[16,21]have beeneported in literature. Among them, systemic data for alkylster + aromatic polar solvent are relatively rare[10–17].lkyl esters are characterized by dipole–dipole interac-

ions in the pure state[1–3]. The degree and strength ofipole–dipole interactions decreases with the increasing sizef alkyl group in the esters. The additions of inert solvents

ike alkane generally break the orientation order of pure

∗ Corresponding author. Tel.: +82 2 364 1807.E-mail address:[email protected] (S. Maken).

alkyl esters to give the positive value of excess thermnamic functions like excess molar volume,VE, excess molaenthalpy,HE, and excess molar Gibb’s free energy,GE [4,5].However, these values become very less and eventive in the mixtures of alkyl esters + aromatic hydrocarb[10,11,14,15]. Specific interactions of dipole–induce diptype are postulated to account for such behavior[14,15].

Moreover, it has been revealed[22–26]that that graph theoretical approach, based on molecular connectivity param[27] of third degree, could be of great use not only in euating theirVE andHE but also in understanding the natof molecular interactions between the components of bmixtures. These considerations prompted us to carrysystemic study on the thermodynamic properties of aesters with aromatic hydrocarbons. In first paper ofseries, we report the measuredVE andHE data for buty

378-3812/$ – see front matter © 2005 Elsevier B.V. All rights reserved.oi:10.1016/j.fluid.2005.06.011

S. Maken et al. / Fluid Phase Equilibria 235 (2005) 42–49 43

Table 1Densities,ρ, and refractive indices,nD, of the pure components at 308.15 K

Substance ρ (kg m−3) nD

This work Literature This work Literature

Butyl acetate 865.45 865.4a 1.3908 1.3910a

Cyclohexane 764.43 764.46b 1.4205 1.4201c

Benzene 862.93 862.95b 1.4921 1.49170d

Toluene 852.80 852.85b 1.4885 1.48870d

o-Xylene 867.41 867.38b 1.5031 1.50295e,f

m-Xylene 851.53 851.57b 1.4946 1.49464e,f

p-Xylene 847.91 847.87b 1.4879 1.4881d

a Ref. [21].b Ref. [31].c Ref. [32].d Ref. [33].e Ref. [28].f At 298.15 K.

acetate + cyclohexane or benzene or toluene oro-, m- or p-xylene at 308.15 K and their interpretation in terms of graphtheoretical approach.

2. Experimental

Butyl acetate (BA) (Merck) was dried over anhydrousmagnesium sulphate and then fractionally distilled[28]. Themiddle fraction of distilled BA was then dried over type0.3 nm molecular sieves (Merck) in an amber colored bottlefor several days before use. Cyclohexane, benzene, tolueneand xylenes (Merck) were purified with standard procedure[28,29]. The purities of the purified samples were checked bymeasuring their densities and refractive indices at 308.15 Kas described earlier[30] and these compared well with theliterature values[21,28,31–33]as shown inTable 1.

Molar excess volumes,VE, for the binary mixtures havebeen measured dilatometrically at 308.15 K in the mannerdescribed elsewhere[34]. The temperature of the thermostatwas controlled within±0.01 K. The uncertainties in the mea-suredVE values are±0.5%.

Molar excess enthalpies (HE) were determined with a heatflux calorimeter (model C-80, Setaram, France) at 308.15 Kas described elsewhere[35]. The uncertainties in the mea-s E −1

3

ort n,xF tere

X

Fig. 1. Excess volumes (VE) for butyl acetate (i) + benzene (j) (♦) or toluene(�) or o-xylene (�) or m-xylene (�) or p-xylene (�) or cyclohexane (©)at 308.15 K as a function of mole fraction of butyl acetate (xi ). The curvesrepresent the values calculated from Eq.(1).

wherexi is the mole fraction of BA andXn (n= 0–3) areadjustable parameters. These parameters were evaluated bymethod of least squares and are given along with standarddeviations,σ(X), in Table 4. TheVE values for BA + benzeneat 308.15 K have been reported by Oswal[14]. Our experi-mental curve for BA + benzene system is in agreement withthat reported by him.VE values ofo-,m- orp-xylene systemsat 303.15 K have also been reported by Ramachandran et al.[15]. Our experimental values for these systems are lowerthan their values at each mole fraction because reported val-ues are at lower temperature. However, the general shape ofthe curves is same. We are unaware of any previously pub-lishedHE data for the present systems at 308.15 K with whichto compare our results. TheHE values for all the binary sys-tems are negative over the entire composition range except

F(3r

uredH values are about±0.1 J mol .

. Results and discussion

The VE and HE for BA + cyclohexane or benzeneoluene oro-, m-, p-xylene as a function of mole fractioi , at 308.15 K are reported inTables 2 and 3and shown inigs. 1 and 2. The results were fitted to the Redlick-Kisquation

E(X = V orH) = xi(1 − xi)3∑

n=0

Xn(1 − 2xi)n (1)

ig. 2. Excess enthalpies,HE, of butyl acetate (i) + benzene (j) (�), toluene�), o-xylene (�), m-xylene (�), p-xylene (�) or cyclohexane (©) at08.15 K as a function of mole fraction of butyl acetate (xi ). The curvesepresent the values calculated from Eq.(1).

44 S. Maken et al. / Fluid Phase Equilibria 235 (2005) 42–49

Table 2ExperimentalVE data for butyl acetate (i) + aromatic hydrocarbons or cyclohexane (j) mixture at 308.15 K

Butyl acetate (i) + benzene (j) Butyl acetate (i) + toluene (j) Butyl acetate (i) +o-xylene (j)

xi VE (cm3 mol−1) xi VE (cm3 mol−1) xi VE (cm3 mol−1)

0.0901 0.042 0.0550 −0.019 0.1121 −0.280.2214 0.070 0.1581 −0.060 0.1983 −0.0630.3662 0.076 0.2744 −0.082 0.2744 −0.0820.4623 0.069 0.4420 −0.100 0.3652 −0.0970.5430 0.060 0.5243 −0.103 0.4665 −0.1090.6504 0.044 0.6231 −0.102 0.5691 −0.1080.7052 0.036 0.7619 −0.089 0.6060 −0.1060.7601 0.028 0.8490 −0.069 0.7502 −0.0900.8505 0.017 0.9052 −0.051 0.8041 −0.0830.9370 0.006 0.9032 −0.056

Butyl acetate (i) +m-xylene (j) Butyl acetate (i) +p-xylene (j) Butyl acetate (i) + cyclohexane (j)

xi VE (cm3 mol−1) xi VE (cm3 mol−1) xi VE (cm3 mol−1)

0.1509 −0.077 0.0881 −0.080 0.1062 0.3470.1651 −0.083 0.1630 −0.159 0.1575 0.4350.2243 −0.094 0.3140 −0.247 0.2230 0.5210.3140 −0.127 0.3481 −0.281 0.3004 0.6040.3921 −0.142 0.5001 −0.316 0.4851 0.6740.5651 −0.144 0.6164 −0.318 0.4863 0.6850.6690 −0.131 0.7380 −0.282 0.5412 0.6540.8091 −0.097 0.7871 −0.264 0.6489 0.6070.8816 −0.052 0.8758 −0.221 0.7350 0.4980.9052 −0.043 0.9179 −0.171 0.7661 0.406

0.8854 0.195

Table 3ExperimentalHE data for butyl acetate (i) + aromatic hydrocarbons or cyclohexane (j) mixture at 308.15 K

Butyl acetate (i) + benzene (j) Butyl acetate (i) + toluene (j) Butyl acetate (i) +o-xylene (j)

xi HE (J mol−1) xi HE (J mol−1) xi HE (J mol−1)

0.1269 −7.5 0.1520 −29.2 0.0707 −9.00.2523 −14.0 0.1873 −36.0 0.1859 −12.40.4029 −20.9 0.2873 −50.0 0.2214 −20.00.4575 −22.7 0.3922 −57.1 0.3134 −26.00.4958 −24.5 0.4465 −60.0 0.3539 −27.30.5619 −26.4 0.5020 −61.8 0.4773 −29.00.6599 −27.4 0.5430 −63.0 0.5868 −30.00.7279 −26.0 0.6000 −62.0 0.6462 −29.10.7714 −24.5 0.7435 −52.0 0.8002 −22.00.8714 −20.4 0.8705 −36.0 0.8364 −19.0

0.8898 −32.0

Butyl acetate (i) +m-xylene (j) Butyl acetate (i) +p-xylene (j) Butyl acetate (i) + cyclohexane (j)

xi HE (J mol−1) xi HE (J mol−1) xi HE (J mol−1)

0.1568 9.9 0.0722 −14.9 0.1409 816.90.1886 13.9 0.1892 −35.8 0.1975 1071.40.2879 17.1 0.3182 −47.9 0.2672 1286.50.4265 21.9 0.3590 −51.1 0.3389 1392.10.4818 22.1 0.4828 −57.6 0.4035 1385.80.5375 23.2 0.6364 −57.0 0.4961 1254.20.6365 23.4 0.6512 −57.0 0.5517 1120.10.7881 19.1 0.7888 −44.8 0.6466 858.20.8286 18.0 0.8394 −36.9 0.7965 470.40.9169 11.9 0.9169 −22.8 0.8311 396.2

0.9061 236.4

S. Maken et al. / Fluid Phase Equilibria 235 (2005) 42–49 45

Table 4Adjustable parametersXn (X=V orH) of Eq.(1) along with standard deviation,σ(XE)

System V0 V1 V2 V3 σ(VE)

Butyl acetate (i) + benzene (j) 0.259 0.232 0.071 0.008 0.008Butyl acetate (i) + toluene (j) −0.411 0.040 −0.154 0.0894 0.002Butyl acetate (i) +o-xylene (j) −0.435 0.004 −0.039 0.326 0.002Butyl acetate (i) +m-xylene (j) −0.592 0.077 0.063 −0.172 0.009Butyl acetate (i) +p-xylene (j) −1.226 0.214 −0.493 0.694 0.012Butyl acetate (i) + cyclohexane (j) 2.721 0.176 −0.047 1.497 0.015

H0 H1 H2 H3 σ(HE)

Butyl acetate (i) + benzene (j) −97.5 55.2 −39.5 33.1 0.7Butyl acetate (i) + toluene (j) −248.0 24.2 −43.8 66.8 0.9Butyl acetate (i) +o-xylene (j) −120.1 16.7 −19.2 −1.2 0.7Butyl acetate (i) +m-xylene (j) 90.9 −18.0 31.1 −37.2 0.8Butyl acetate (i) +p-xylene (j) −233.0 41.2 −44.9 3.3 0.9Butyl acetate (i) + cyclohexane (j) 4978.7 4251.1 −417.8 −2853.9 2.0

Vn, σ(VE) are in cm3 mol−1 andHn, σ(HE) are in J mol−1.

for cyclohexane andm-xylene systems. At equimolar com-position,HE values vary in the order:

cyclohexane> m-xylene> benzene> o-xylene

> p-oxylene> toluene.

On the other hand, whileVE values for BA + toluene oro-,m-orp-xylene systems are negative over the whole compositionrange, these are positive for BA + cyclohexane or benzenesystems. At equimolar composition,VE values follow thesequence:

cyclohexane> benzene> toluene≈ o-xylene

> m-xylene> p-xylene.

At the simplest qualitative level, the observedHE andVE

values may be attributed to the resultant of two opposingeffects. The positive contribution toHE andVE values arisesfrom the breaking and stretching of dipole–dipole interac-tions in self-associated BA and negative contribution arisesdue to the formation of attractive interactions between polarcarboxyl group of BA and�-electrons of aromatic hydro-carbons. As theHE and VE values for cyclohexane + BAmixture are highly positive, it indicates the dissociation ofdipole–dipole interactions and absence of attractive interac-tions. When cyclohexane is replaced by benzene,HE andVE E es alsot and� isi nsityo omesm es ofH oft ausef nd itse the

presence of steric hindrance between the two methyl groupsof xylenes and the alkyl groups of BA, which restrict theproper orientation of these molecules and obstruct the acetatetoward the ring thus making interactions weaker. Among thexylenes,p-xylene is symmetrical molecule, thus it offers leaststeric hindrance. TheHE andVE values for this system aremost negative[12]. The substitution of methyl group inmeta-position seems to be most sterically hindered and thusHE isslightly positive for this system.

3.1. Conceptual aspects of graph theoretical approachand results

According to mathematical discipline of graph theory[36], if the atoms in a structural formula of a molecule arerepresented by vertices and bonds joining them by edges,then the resulting graph describes the totality of informationcontained in that molecule[27,36–39]. Consequently, ifδv

m,δvn, etc. represent the degrees ofmth andnth vertices of the

graph of a molecule (shown inFig. 3 around atoms), thenconnectivity parameters of third degree,3ξi , is defined[39]by Eq.(2) and shown inFig. 3:

3ξi =∑

m<n<o<p

(δvmδv

nδvoδ

vp)−0.5 (2)

wm ,Zb

δ

F ard-i d bye

tso s

values decrease considerably andH becomes negativhowing the breaking of dipole–dipole interactions andhe formation of interactions among polar ester groups-electrons on benzene ring[12]. When a methyl group

ntroduced in benzene (as in toluene), the electron def �-electron cloud increases and these interactions becore stronger and this should lead to more negative valuE andVE than benzene + BA mixture. The introduction

wo methyl groups in benzene (as in xylenes) should curther enhancement of these attractive interactions ahould further yield more negative values ofHE andVE. How-ver, it is not observed experimentally. It may be due to

hereδvm, etc. reflect explicitly the valency ofmth vertex in

olecular graph ofi and is related[39] to maximum valencym, and number of H-atoms,hm, attached tomth, etc. vertexy the relation:

vm = Zm − hm (3)

urther, Kier[27] has suggested that the information regng effect of branching in the molecules can be obtainevaluation of3ξi of molecules.

SinceVE of an (i + j) mixture reflects interactional effecn the packing of molecules and as (3ξi)−1 of i determine

46 S. Maken et al. / Fluid Phase Equilibria 235 (2005) 42–49

Fig. 3. Structures of various components of binary mixture along with3�′ values.

[23] the effectiveness with which the molecular surface ofiinteracts with that of anotheri molecule, the interactional partof the molar volume of purei has been taken to (3ξi)−1. Theideal interactional molar volume of an (i + j) mixture would

then be proportional to∑

xi(3ξi)−1

, wherexi and (3ξi) denotemole fraction and connectivity parameter of third degree,respectively, ofi. The interactional molar volume of an (i + j)mixture should also be proportional to 1/(3ξ)m of the mix-ture. If (3ξ)m of the real mixture in the molecular graph isexpressed by

∑{x1(3ξi)m}, where (3ξi)m denotes3ξ of i in

the mixture and if the proportionality constantαij is assumeto be the same for the mixture and its pure components then,

VE may be expressed by[23]

VE = αij

[{∑xi(

3ξi)m}−1 −

∑ xi

3ξi

](4)

whereαij is the constant characteristic of the (i + j) mixtureand can be evaluated using equimolar experimentalVE value.

As the degree of association ofi andj is not known in themixture and pure state, we regarded (3ξi) and (3ξi)m (i = i orj) as adjustable parameters and evaluated them by employingVE data to Eq.(4). Only those values of (3ξi) and (3ξi)m wereretained that best reproduced theVE data. Various (3ξi) or(3ξi)m (i = i or j) parameters along withαij are recorded in

S. Maken et al. / Fluid Phase Equilibria 235 (2005) 42–49 47

Table 5Comparison of smoothenedVE andHE values with their corresponding values calculated from graph theory along with the various3ξ values, interaction energyparametersχ′

ij andαij , and standard deviationσ(VE) andσ(HE)

Mole fraction (xi )

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Butyl acetate (i) + benzene (j)VE (experimental) 0.045 0.066 0.075 0.076 0.065 0.051 0.036 0.023 0.011VE (graph) 0.031 0.051 0.062 0.067 0.065 0.058 0.048 0.035 0.039HE (experimental) −6.5 −12.0 −17.0 −21.1 −24.4 −27.0 −26.5 −23.5 −16.6HE (graph) −5.2 −10.6 −16.6 −21.1 −24.4 −27.0 −27.0 −23.0 −15.0

(3ξi ) = (3ξi )m= 1.261; (3ξj ) = (3ξj )m= 0.666;αij =−0.5943;χ∗ij =−50.6;χ12 =−0.17;σ(VE) = 0.015;σ(HE) = 1.0

Butyl acetate (i) + toluene (j)VE (experimental) −0.050 −0.073 −0.089 −0.098 −0.103 −0.103 −0.096 −0.082 −0.055VE (graph) −0.044 −0.074 −0.093 −0.101 −0.103 −0.094 −0.079 −0.058 −0.032HE (experimental) −19.50 −37.50 −51.00 −58.6 −62.0 −62.00 −58.02 −52.00 −39.00HE (graph) −20.28 −36.86 −49.51 −58.6 −62.0 −61.16 −55.09 −43.27 −25.14

(3ξi ) = (3ξi )m= 1.261; (3ξj ) = (3ξj )m= 0.840;αij = 2.5610;χ∗ij =−125.8;χ12 =−9.44;σ(VE) = 0.014;σ(HE) = 7.5

Butyl acetate (i) +o-xylene (j)VE (experimental) −0.030 −0.064 −0.087 −0.102 −0.109 −0.109 −0.099 −0.85 −0.067VE (graph) −0.041 −0.072 −0.094 −0.105 −0.109 −0.102 −0.088 −0.066 −0.037HE (experimental) −11.00 −18.50 −25.00 −28.2 −30.0 −28.50 −27.51 −22.00 −12.54HE (graph) −13.53 −21.01 −26.48 −28.2 −30.0 −29.87 −24.87 −20.24 −11.51

(3ξi ) = (3ξi )m= 1.661; (3ξj ) = (3ξj )m= 1.426;αij = 28.5985;χ∗ij =−69.7;χ12 =−4.03;σ(VE) = 0.006;σ(HE) = 3.3

Butyl acetate (i) +m-xylene (j)VE (experimental) −0.051 −0.093 −0.125 −0.142 −0.148 −0.140 −0.123 −0.097 −0.046VE (graph) −0.054 −0.095 −0.124 −0.141 −0.148 −0.139 −0.121 −0.091 −0.051HE (experimental) 8.49 14.50 18.51 −21.2 −22.7 23.50 22.00 19.00 12.01HE (graph) 7.18 13.21 17.92 −21.2 −22.7 22.56 20.35 15.99 9.27

(3ξi ) = (3ξi )m= 1.261; (3ξj ) = (3ξj )m= 1.174;αij = 139.070;χ∗ij = 59.9;χ12 = 0.86;σ(VE) = 0.066;σ(HE) = 1.5

Butyl acetate (i) +p-xylene (j)VE (experimental) −0.092 −0.180 −0.246 −0.300 −0.306 −0.321 −0.298 −0.252 −0.181VE (graph) −0.130 −0.224 −0.285 −0.316 −0.306 −0.299 −0.254 −0.189 −0.103HE (experimental) −19.00 −32.50 −43.00 −54.4 −58.2 −54.00 −50.51 −41.00 −23.00HE (graph) −17.52 −32.88 −45.57 −54.4 −58.2 −61.34 −56.69 −45.65 −27.14

(3ξi ) = (3ξi )m= 1.666; (3ξj ) = (3ξj )m= 1.250;αij =−22.4577;χ∗ij =−125.1;χ12 =−7.18;σ(VE) = 0.081;σ(HE) = 6.0

Butyl acetate (i) + cyclohexane (j)VE (experimental) 0.270 0.480 0.600 0.650 0.680 0.590 0.410 0.380 0.180VE (graph) 0.226 0.408 0.544 0.632 0.680 0.654 0.582 0.452 0.259HE (experimental) 583.5 1081.2 1359.2 1389.4 1244.7 979.6 709.6 484.3 288.6HE (graph) 144.1 251.5 324.1 1389.4 1244.7 351.5 302.4 226.6 125.4

(3ξi ) = (3ξi )m= 1.261; (3ξj ) = (3ξj )m= 1.500;αij =−112.513;χ∗ij = 3632.0;χ12 = 0.00;σ(VE) = 0.012;σ(HE) = 354

αij andσ(VE) are in cm3 mol−1; χ∗ij , χ12 andσ(HE) are in J mol−1.

Table 5along withVE values obtained from Eq.(4) for thevarious binary mixtures as a function ofxi and are also com-pared with their experimental values. Examination ofTable 5reveals thatVE values agree well with their correspondingexperimental values and thus (3ξi) or (3ξi)m (i = i or j) valuescan be relied upon to extract information about the state ofpure components as well as their mixture.

A number of structures (I–VIII ) were then assumed fori andj and their (3ξ′

i) values were calculated from structuralconsiderations of Eq.(2). These values were then comparedwith corresponding values, (3ξi) obtained from Eq.(4). Anystructure or combination of structures that yielded (3ξ′

i) valueswhich compared well with the corresponding (3ξi) obtained

from Eq. (4) were considered as representative structure ofthat component. It was assumed that BA exists as molec-ular entitiesI and II . The calculated values of (3ξ′

i) forthese molecular entities were 0.889 and 1.880, respectively.The (3ξi) values for BA in BA (i) + cyclohexane or benzeneor toluene oro-, m- or p-xylene (j) mixtures from Eq.(4)are 1.261, 1.261, 1.261, 1.661, 1.261 and 1.666, respec-tively (Table 5). It suggests that BA exists as a mixture ofmonomer and dimer (average (3ξ′

i) = 1.384). Further, (3ξ′i)

values of 0.666, 0.840, 1.426, 1.174, 1.250 and 1.500 forbenzene, toluene,o-, m-, p-xylene and cyclohexane (molec-ular entitiesIII –VIII in Fig. 3) suggest that they exist asmonomers.

48 S. Maken et al. / Fluid Phase Equilibria 235 (2005) 42–49

Fig. 4. IR spectra of butyl acetate,p-xylene and their equimolar mixture.

(3ξi)m values were next evaluated to see the postulationof BA in aromatic hydrocarbons (Fig. 3). For this purpose, itwas assumed that if BA (i) in benzene or toluene or xyleneis assumed to exist as molecular entityIX (3ξ′

i = 1.20), then(3ξi)m values of 1.261–1.666 (Table 5) for these mixturessuggest that BA (i) + aromatic hydrocarbons (j) mixtures con-tain molecular entityIX . For calculating (3ξ′

i)m value, it isassumed that molecular entityIX is characterized by inter-actions between�-electrons spilling over O–C–O of BA anddelocalized�-electrons cloud of aromatic hydrocarbon. Thepresence of molecular entityIX in the studied mixtures thensuggests that addition of BA to aromatic hydrocarbons shouldhave influenced symmetric vibrations of carbonyl group ofBA and also the ring vibrations of aromatic hydrocarbons.In view of this, we analyzed IR spectra of pure BA and itsequimolar mixture withp-xylene. It was observed from theIR spectra (Fig. 4) that BA andp-xylene in their pure stateshowed characteristic vibrations at 1744 cm−1 (C O stretch-ing), 1069 and 1034 cm−1 (C O stretching) and 1516, 1460and 1382 cm−1 (ring vibrations)[41]; while their mixtureshowed characteristic vibrations at 1686, 1103, 1063 and1541, 1470, 1370 cm−1, respectively. Thus, IR spectra pro-vide an additional support to the presence of molecular entityIX (Fig. 3) in these mixtures.

To study the energetic of the interactions operatingb umedt

((

(

np e top

�

whereSj is the surface fraction ofj involved in (i–j) contactand is defined[42,43]by:

Sj = xjVj∑xiVi

(6)

So that Eq.(5) reduces to

�Ha = xixjχijVj∑xiVi

(7)

Further, ifχii andχ12 are molecular interaction parametersfor (i–i) and specific interactions betweeni andj components,then enthalpy change due to processes (b) and (c) are[42–44]given by:

�Hb = x2i xjχiiVj∑

xiVi

(8)

�Hc = xix2jχ12Vj∑xiVi

(9)

The total enthalpy change due to processes (a–c) is given by:

HE =[

xixjVj∑xiVi

][χij + xiχii + xjχ12] (10)

SinceVj /Vi = (3ξi /3ξj), Eq.(10) then reduces to:

H

FE

H

E

ppwx

ap hisg n ofEc

H

E

w( lyuH yi

nsb

etween the components of these mixtures, it was asshat (i + j) mixtures formation involves:

a) the formation of unlike contact betweeni andj;b) unlike contact then leads to depolymerization of (i) to

yield monomer;c) monomer ofi andj then formi–j molecular entity.

Consequently, ifχij is the molar enthalpy interactioarameter of (i–j) contacts, then change in enthalpy durocess (a) is expressed[42,43]by:

Ha = xiχijSj (5)

E =[

xixj(3ξi/3ξj)

xi + xj(3ξi/3ξj)

][χij + xiχii + xjχ12] (11)

or these mixtures, if it is assumed thatχij = χii = χ∗ij, then

q.(11) reduces to:

E =[

xixj(3ξi/3ξj)

xi + xj(3ξi/3ξj)

][(1 + xi)χ

∗ij + xjχ12] (12)

q.(12)contains two unknown parametersχ∗ij andχ12. These

arameters were calculated employingHE data at two com-ositions (xi = 0.4 and 0.5) for various (i + j) mixtures andere subsequently used to evaluateHE at other values ofi . Such values ofHE along with parametersχ∗

ij and χ12

re recorded inTable 5and calculatedHE found to com-are well with their corresponding experimental values. Tives additional support to assumptions made in derivatioq.(10)–(12). For BA (i) + cyclohexane mixture (j), χ12 = 0,onsequently Eq.(12) for this mixture reduces to:

E =[

xixj(3ξi/3ξj)

xi + xj(3ξi/3ξj)

][(1 + xi)χ

∗ij] (13)

q. (13) contains only one unknown parameterχ∗ij and it

as calculated employingHE data only at one compositionxi = 0.5) for various (i + j) mixtures and were subsequentsed to evaluateHE at other values ofxi . Such values ofE were tabulated inTable 5and comparison was not ver

mpressive.Values ofχ12, a measure of extent of specific interactio

etweeni andj for BA + benzene or toluene orp-xylene are

S. Maken et al. / Fluid Phase Equilibria 235 (2005) 42–49 49

−0.17,−9.44 and−7.18 J mol−1 which again indicate theincrease in interactions with increase in electron donatingtendency due to addition of methyl groups to benzene, slightlyless negative (−7.18 J mol−1) value forp-xylene may be dueto steric hindrance offered by its two methyl groups.

List of symbolsBA butyl acetateGE molar excess Gibb’s free energyhm number of H-atomsHE molar excess enthalpyHn adjustable parameters of Eq.(1)Sj surface fraction ofjth componentVE molar excess volumeVi , Vj molar volume ofith andjth componentsVn adjustable parameters of Eq.(1)xi , xj mole fraction ofith andjth componentsZm maximum valency

Greek lettersαij constant characteristic of (i + j) mixture in Eq.(4)δvm degree ofmth vertex of the graph of a molecule

σ standard deviation3ξi , (3ξi)m, (3ξ′

i) connectivity parameters of third degree ofith component in pure state, mixture from Eqs.(4)

χ er-

A

nksK ita-t AjitM ov-e tateC

R

004)

.

her-

004)

ieu,

2001)

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New

[ urth

[ d.,

[ Han,

[ 9.[ 98)

[ ata

[[ . 29

[ 9.[ mic

[[ ug

[ Aca-

[[[ 989)

and(2)ii, χij, χ

∗ij, χ12 molecular interaction parameters for diffent binary interactions in Eqs.(10)–(12)

cknowledgement

Bal Raj Deshwal and Sanjeev Maken (S.M.) thaorean Federation of Science and Technology for inv

ion under Brain Pool program, and S.M. also thanks. Sharon (IAS), Commissioner, Technical Education, Grnment of Haryana, for award of study leave from C.R. Sollege of Engineering, Haryana, India.

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