J. Chem. Thermodynamics 43 (2011) 1583–1590

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J. Chem. Thermodynamics

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Application of ERAS-model and Prigogine–Flory–Patterson theory to excessmolar volumes for ternary mixtures of (2-chlorobutane + butylacetate + isobutanol)at T = 298.15 K

K. Khanlarzadeh, H. Iloukhani ⇑Department of Physical Chemistry, Faculty of Chemistry, University of Bu-Ali Sina, Hamedan, Iran

a r t i c l e i n f o

Article history:Received 14 December 2010Received in revised form 4 May 2011Accepted 11 May 2011Available online 18 May 2011

Keywords:2-ChlorobutaneButylacetateIsobutanolExcess molar volumePFP theoryERAS-model

0021-9614/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.jct.2011.05.017

⇑ Corresponding author. Tel./fax: +98 811 8282807E-mail address: iloukhani@basu.ac.ir (H. Iloukhani

a b s t r a c t

Densities of the ternary mixture consisting of {2-chlorobutane (1) + butylacetate (2) + isobutanol (3)} andrelated binary mixtures were measured over the whole range of composition at T = 298.15 K and ambientpressure. Excess molar volumes VE

m for the mixtures were derived and correlated as a function of molefraction by using the Redlich–Kister and the Cibulka equations for binary and ternary mixtures, respec-tively. From the experimental data, partial molar volumes, Vm;i excess partial molar volumes, VE

i partialmolar volumes at infinite dilution V0

m;i and apparent molar volumes Vu;i were also calculated. For all bin-ary mixtures over the entire range of mole fractions VE

m data are positive. The experimental results of theconstituted binary mixtures have been used to test the applicability of the extended real associated solu-tion (ERAS-model) and Prigogine–Flory–Paterson (PFP) theory.

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1. Introduction

This paper is a continuation of our earlier work related to thestudy of thermodynamic properties of binary and ternary mixtures[1–4]. Study of room temperature polar liquids (RTPLs) as solventshave received an increasing attention in the last years from funda-mental and applied points of view. As for thermodynamics of RTPLsin solution with other compounds, there are many experimentaland theoretical studies which deal on the behavior of thermody-namic properties of mixtures of RTPL + common organic solvent.However, due to the enormous number of possible binary systems,a lot of work remains to be done. Polar compounds present goodsolubility with other liquids. Therefore, there are several worksthat study the thermodynamic properties of polar compoundextensively studied due to its importance for supercritical extrac-tion [5–7]. Esters are one of the best candidates that exist as dipo-lar associates in their pure liquid state, available with not onlyaliphatic, aromatic and even acrylic nature but also with a varietyof general structures with molecular formulas, R(CH2)u�1COOR0

where u = 1, 2, 3, 4, 5, 7, . . . , 11, 13, R = –H, –CnH2n +1 (n = 1, 2, 3,4, 5, 6, . . . , 8) and R0 = –CH3 or –CnH2n+1 (n = 1, 2, 3, 4, . . . , 6). Theexcess molar enthalpies excess molar volumes, of (alkyl alkano-ates + n-alkanes) were reported to study the effects due to varia-tions in the length of R or R0. On the other hand, much effort in

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.).

this field has been devoted to the study of (RTPLs + alcohol) binarymixtures, mainly motivated by their solubility with RTPLs as wellas their low environmental impact. Besides, investigation of thethermo-physical properties of esters, due to their widespread usein industrial processes has increased. Esters are used in flavoring,perfuming, artificial essences, cosmetics, and also they are impor-tant solvents in pharmaceutical, paint, and plastic industries. Thethermodynamic properties of RTPLs with other polar compoundshave been studied in some extent, especially volumetric properties,but there are few works that study their thermodynamic behaviorconsidering ERAS-model or Prigogine–Flory–Patterson theory.

The present work analyzes the excess molar volumes, partialmolar volumes Vm;i excess partial molar volumes, VE

i partial molarvolumes at infinite dilution V0

m;i and apparent molar volumes Vu;i

of ternary and constituted binary mixtures of 2-chlorobutane,butylacetate, and isobutanol by means of the ERAS-model [8] andPFP theory [9–11]. The RTPLs were selected in order to be able tostudy the effect of changing the chemical structure of the cationand/or the anion on thermodynamic properties. The derived prop-erties provide valuable information for qualitatively analyzing themolecular interactions between molecules. In fact the excess func-tions of binary and ternary mixtures are complex properties be-cause they depend not only on solute–solute, solvent–solventand solute–solvent interactions, but also of the structural effectsarising from interstitial accommodations. So these are very impor-tant from theoretical points of view, to understand liquid theory.Esters, haloalkanes, and alkanols, and their binary mixtures find

TABLE 1Experimental and literature values of densities, q, and refractive indices, nD of purecomponents at T = 298.15 K.

Compound q/(g � cm�3) nD

Exp. Lit.a Exp. Lit.a

2-Chlorobutane 0.86721 0.86710 1.3999 1.4001Butylacetate 0.87620 0.87636 1.3919 1.3918Isobutanol 0.79784 0.79780 1.3939 1.3939

a Reference [12].

1584 K. Khanlarzadeh, H. Iloukhani / J. Chem. Thermodynamics 43 (2011) 1583–1590

applications as solvent in chemistry and modern technology. Theexcess quantities of binary mixtures have been fitted to the Red-lich–Kister equation to determine the coefficients. For correlatingthe ternary data, the Cibulka equation was used. As far as we know,no data are available for the mixtures investigated in the openliterature.

2. Experimental

2.1. Materials

2-Chlorobutane (w > 0.99), butylacetate (w > 0.99), isobutanol(w > 0.99), where w is mass fraction were purchased from Merckand used without further purifications. The experimental densitiesand refractive indices of the pure materials are presented atT = 298.15 K in table 1 along with the corresponding literature val-ues [12]. Compounds were stored in brown glass bottles and frac-tionally distilled immediately before use.

2.2. Apparatus and procedure

The density of the compounds and their binary and ternarymixtures were measured with an Anton Paar digital densimeter(Model DMA-4500), operated in the static mode and the uncer-tainty of the density measurement was estimated to be within±1 � 10�5 g � cm�3. The temperature in the cell was regulated to±0.01 K with solid-state thermostat. The apparatus was calibratedonce a day with dry air and double-distilled freshly degassedwater. Airtight stoppered bottles were used for the preparationof the mixtures. The mass of the dry bottle was first determined.The less volatile component of the mixture was introduced in thebottle, and the total mass was recorded. Subsequently, the othercomponent was introduced, and the mass of bottle along withthe two components was determined. Ternary mixtures were pre-pared by mixing of three components. A total of 40 compositionswere measured at T = 298.15 K for the ternary system of {2-chloro-butane (1) + butylacetate (2) + isobutanol (3)}. Each mixtures wasimmediately used after it was well-mixed by shaking. All theweightings were performed on an electronic balance (AB 204-NMettler) accurate to 0.1 mg. The uncertainty in the mole fractionis estimated to be lower than ±2 � 10�4.

3. Results and discussion

3.1. Binary mixtures

Excess molar volumes for all mixtures were calculated fromdensity results at T = 298.15 K and at ambient pressure using thefollowing equation:

VEm ¼

XN

i¼1

xiMiðq�1 � q�1i Þ; ð1Þ

where q is the density of the mixture, qi, is the density of pure com-ponent, xi, is the mole fraction, Mi, is the molar mass of componenti, and N stands for the number of components in the mixture. Theexcess molar volumes uncertainties are estimated to±1 � 10�3 cm3 �mol�1. The corresponding VE

m, values of binary mix-tures at T = 298.15 K are presented in table 2 and plotted againstmole fraction x, in figure 1. The experimental results for all binarymixtures were fitted by the least squares method with all pointsweighted equally to Redlich–Kister polynomial equation [13]:

VEm ¼ xð1� xÞ

XN

k¼0

Aið1� 2xÞk; ð2Þ

where x is the mole fraction of solvent, Ai are adjustable parametersobtained by fitting, and N is the degree of the polynomials. The re-sults are given in table 3 together with corresponding standarddeviations. For none of the systems does the precision warrantthe use of more than three parameters. In each case, the optimumnumber of coefficients was ascertained from an examination ofthe variation of the standard deviation r, with

r ¼X VE

m;exp � VEm;cal

� �2

n� p

264

375

1=2

; ð3Þ

where VEm;exp and VE

m;cal are the experimental and calculated valuesof the excess molar volumes, respectively, and n and p are the num-ber of experimental points and number of parameters retained inthe respective equations.

VEm is the results contribution from several opposing effects.

These effects may be divided arbitrarily into three types, namely,the physical, chemical, and structural. Physical contributions, thatis, nonspecific interactions between the real species present inthe mixture, contributes a positive term to VE

m. The chemical orspecific intermolecular interactions results in a volume decreaseand these effects include charge-transfer type forces and othercomplex-forming interactions. This effect contributes to the nega-tive values to VE

m. The structural contributions are mostly the}neg-ative and arise from several effects, especially from interstitialaccommodation and changes of free volume}.

Excess molar volume of for all binary mixtures containing (2-chlorobutane + butylacetate), (2-chlorobutane + isobutanol), and(+butylacetate + isobutanol) are positive over the whole range ofmole fractions. Positive values would indicate that molecular inter-actions between different molecules are weaker than interactionsbetween molecules in the same pure liquid and that repulsiveforces dominate the behavior of the solutions. For (2-chlorobu-tane + isobutanol) and (butylacetate + isobutanol), intensity attrac-tive interactions between unlike species decrease because ofbreaking H-bonding and repulsive interactions predominate, lead-ing to positive excess molar volumes values. The specific interac-tions of alkyl acetate with alcohols can be visualized due topresence of ion pair of electrons on the oxygen atom of alkyl ace-tate on account of which it can act as a strong proton-acceptorfrom the alkanol. Further these system are also an ideal choice toexamine ideal associated solution models with Flory’s interactionterm to predict and analyze theoretically the excess molar volume[14–17].

The partial molar volumes, Vm;i were evaluated using the fol-lowing equation [18]:

Vm;i ¼ VEm þ V�m;i þ ð1� xiÞð@VE

m=@xiÞT;P ð4Þ

where V�m;i is pure molar volumes of component i. The excess partialmolar volumes VE

1 ¼ ðV1 � V�1Þ and VE2 ¼ ðV2 � V�2Þ from VE

m and themolar volumes of the pure components are also calculated. The val-ues of partial molar volumes and the excess partial molar volumes

TABLE 2Densities, q, excess molar volumes, VE

m , partial molar volumes, Vm;i , excess partial molar volumes, VEi , and apparent molar volumes, Vu;i , for binary mixtures at T = 298.15 K.

x q/(g � cm�3) VEm=ðcm3 �mol�1Þ Vm;1/(cm3 �mol�1) Vm;2/(cm3 �mol�1) VE

1/(cm3 �mol�1) VE2/(cm3 �mol�1) Vu,1/(cm3 �mol�1) Vu,2/(cm3 �mol�1)

2-Chlorobutane + butylacetate0.0000 0.87620 0.000 106.87 132.57 0.114 0.000 99.560.0787 0.87555 0.011 106.87 132.57 0.109 0.001 104.97 99.550.1618 0.87483 0.024 106.86 132.57 0.101 0.002 104.96 99.530.2330 0.87420 0.034 106.85 132.58 0.093 0.004 104.96 99.510.3250 0.87336 0.047 106.84 132.59 0.080 0.014 104.96 99.490.3861 0.87280 0.053 106.83 132.60 0.070 0.024 104.96 99.470.4512 0.87220 0.058 106.82 132.61 0.060 0.039 104.97 99.450.5060 0.87170 0.060 106.81 132.63 0.051 0.053 104.98 99.440.5902 0.87094 0.058 106.79 132.65 0.038 0.079 105.00 99.420.6656 0.87027 0.052 106.78 132.68 0.027 0.105 105.02 99.400.7352 0.86965 0.044 106.77 132.70 0.018 0.128 105.04 99.390.7862 0.86919 0.037 106.77 132.72 0.012 0.144 105.05 99.380.8516 0.86860 0.027 106.76 132.73 0.006 0.161 105.07 99.380.8961 0.86819 0.019 106.76 132.74 0.003 0.169 105.08 99.370.9458 0.86773 0.010 106.76 132.75 0.001 0.175 105.09 99.381.0000 0.86721 0.000 106.76 132.75 0.000 0.174 105.10

2-Chlorobutane + isobutanol0.0000 0.79782 0.000 108.04 92.90 1.280 0.000 99.560.0579 0.80182 0.068 107.87 92.91 1.116 0.004 103.93 99.490.1152 0.80577 0.127 107.72 92.92 0.967 0.016 104.00 99.410.2274 0.81351 0.218 107.47 92.96 0.712 0.057 104.14 99.280.3166 0.81967 0.268 107.30 93.01 0.541 0.107 104.25 99.170.4235 0.82701 0.307 107.13 93.09 0.371 0.191 104.38 99.020.4896 0.83153 0.320 107.04 93.16 0.284 0.260 104.45 98.930.5564 0.83612 0.321 106.97 93.25 0.210 0.344 104.53 98.830.6097 0.83979 0.313 106.92 93.33 0.159 0.426 104.59 98.760.6872 0.84508 0.296 106.86 93.47 0.099 0.572 104.67 98.610.7523 0.84959 0.263 106.82 93.63 0.061 0.724 104.75 98.500.8090 0.85354 0.225 106.79 93.79 0.035 0.883 104.82 98.380.8487 0.85633 0.191 106.78 93.91 0.022 1.011 104.88 98.290.8975 0.85977 0.143 106.77 94.09 0.010 1.191 104.94 98.160.9293 0.86205 0.104 106.76 94.23 0.005 1.322 104.99 98.080.9638 0.86455 0.057 106.76 94.38 0.001 1.478 105.04 97.991.0000 0.86721 0.000 106.76 94.56 0.000 1.658 105.10

Butylacetate + isobutanol0.0000 0.79782 0.000 136.52 92.90 3.952 0.000 92.900.0589 0.80241 0.217 136.06 92.92 3.489 0.014 128.88 92.670.1065 0.80612 0.372 135.71 92.95 3.137 0.046 129.08 92.490.1907 0.81270 0.599 135.13 93.05 2.562 0.146 129.43 92.160.2720 0.81903 0.765 134.64 93.20 2.064 0.293 129.76 91.850.3894 0.82820 0.912 134.01 93.49 1.442 0.590 130.23 91.410.4427 0.83234 0.946 133.77 93.66 1.198 0.758 130.44 91.210.5277 0.83896 0.953 133.43 93.97 0.857 1.069 130.77 90.890.6070 0.84514 0.913 133.16 94.31 0.591 1.409 131.07 90.580.6829 0.85107 0.830 132.96 94.69 0.383 1.782 131.36 90.290.7405 0.85558 0.738 132.83 95.00 0.256 2.098 131.58 90.060.8166 0.86157 0.578 132.70 95.46 0.127 2.561 131.87 89.750.8700 0.86579 0.438 132.64 95.82 0.064 2.918 132.07 89.530.9312 0.87067 0.249 132.59 96.27 0.018 3.364 132.30 89.281.0000 0.87620 0.000 132.57 96.82 0.000 3.914 132.57

K. Khanlarzadeh, H. Iloukhani / J. Chem. Thermodynamics 43 (2011) 1583–1590 1585

are presented in table 2 and latter were plotted against mole frac-tion in figures 2 and 3.

The partial molar volumes, V0m;j at infinite dilution appear to be

of particular interest. In the limit of infinite dilution, solute–soluteinteractions disappear. Thus the values of the partial molar vol-umes at infinite dilution provide insight into solute–solventinteractions.

Setting x = 0 and x = 1, respectively, in equation (4) leads to:

V0j ¼ V�j þ

Xi¼0

Aið�1Þi ð5Þ

{+1 for j = 1 and �1 for j = 2}.All partial molar volumes at infinite dilution were calculated

using the Redlich–Kister coefficient, Ai, in equation (5) listed intable 4.

Apparent molar volumes, Vu,i which may be more convenientand accurate can be calculated as followings [19]:

Vu;i ¼ V0i � ðV

Em=xiÞ; ð6Þ

where V0i is molar volume of the pure component. The values of

apparent molar volumes are also reported in table 2.

3.2. Ternary mixtures

Excess molar volumes for ternary mixtures of {2-chlorobutane(1) + butylacetate (2) + isobutanol (3)} at T = 298.15 K were calcu-lated using equation (1) and the results were listed in table 5and graphically shown in figure 4. The excess molar volumes forthe ternary system were correlated using the Cibulka equation[20]:

DQ123 ¼ DQ bin þ x1x2x3D123 ð7Þ

and

v mE

/(cm

3 . m

ol-1

)

x

FIGURE 1. Excess molar volumes, VEm at T = 298.15 K for the binary systems: (�) {2-

chlorobutane (1) + butylacetate (2)}, (N) {2-chlorobutane (1) + isobutanol (3)}, (�){butylacetate (2) + isobutanol (3)}. x1 is the mole fraction of the first component ineach binary. Solid line calculated with Redlich–Kister equation.

TABLE 3Coefficients of Redlich–Kister equation, Ai and standard deviations, r for binarymixtures at T = 298.15 K.

System A0 A1 A2 r

(cm3 �mol�1)

2-Chlorobutane + butylacetate 0.236 –0.03 –0.092 0.00052-Chlorobutane + isobutanol 1.276 –0.189 0.193 0.0015Butylacetate + isobutanol 3.827 0.019 0.106 0.0004

v m,1

E /(

cm3 .

mol

-1)

x

FIGURE 2. Excess partial molar volumes, VEm;1 at T = 298.15 K for the binary

systems: (�) {2-chlorobutane (1) + butylacetate (2)}, (N) {2-chlorobutane (1) + iso-butanol (3)}, (�) {butylacetate (2) + isobutanol (3)}. x1 is the mole fraction of the firstcomponent in each binary system.

v m,2

E /

(cm

3 .m

ol-1

)

x

FIGURE 3. Excess partial molar volumes, VEm;2 at T = 298.15 K for the binary

systems: (�) {2-chlorobutane (1) + butylacetate (2)}, (N) {2-chlorobutane (1) + iso-butanol (3)}, (�) {butylacetate (2) + isobutanol (3)}. x1 is the mole fraction of the firstcomponent in each binary system.

TABLE 4The partial molar volumes at infinite dilution V0

m;i of the binary mixtures atT = 298.15 K.

System �V0m;1=ðcm3 �mol�1Þ �V0

m;2=ðcm3 �mol�1Þ

2-Chlorobutane + butylacetate 106.87 132.752-Chlorobutane + isobutanol 108.04 94.56Butylacetate + isobutanol 136.52 96.82

1586 K. Khanlarzadeh, H. Iloukhani / J. Chem. Thermodynamics 43 (2011) 1583–1590

DQ bin ¼X3

i¼1

X3

j>i

DQij; ð8Þ

where DQ123 refers to VEm for the ternary system and

x3 = 1 � x1 � x2. DQij in equation (8) is the binary contribution ofeach i–j pair to the VE

m given by equation (2) with the parametersof Ai, reported in table 3. The ternary contribution term D123 wascorrelated using the expression suggested by Cibulka:

D123 ¼ B0 þ B1x1 þ B2x2: ð9Þ

The ternary parameters, B0, B1, and B2, were determined withthe optimization algorithm similar to that for the binary parame-ters. The fitting parameters and the corresponding standard devia-tions are given in table 6.

Excess molar volumes for studied ternary system were also pre-dicted using four geometrical solution models [21–24]. These mod-els use binary contributions evaluated by Redlich–Kister equation.

1. Jacob–Fitzner Model [21]

VE123 ¼ VE

12x1x2=½ðx1 þ x3Þ=2Þðx2 þ x3Þ=2�VE13x1x3=

½ðx1 þ x2Þ=2Þðx3 þ x2Þ=2� þ VE23x1x3=

½ðx2 þ x1Þ=2Þðx3 þ x1Þ=2�: ð10Þ

2. Kohler Model [22]

VE123 ¼ VE

12ðx1 þ x2Þ2 þ VE13ðx1 þ x3Þ2 þ VE

23ðx2 þ x3Þ2: ð11Þ

3. Rastogi Model [23]

VE123 ¼ ½V

E12ðx1 þ x2Þ þ VE

13ðx1 þ x3Þ þ VE23ðx2 þ x3Þ�=2: ð12Þ

4. Radojkovic Model [24]

VE123 ¼ VE

12 þ VE13 þ VE

23: ð13Þ

Standard deviations presented in table 7, were determined for allmodels as:

S ¼ 1n

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXn

i¼1

ðVE123ðexpÞi � VE

123ðcalÞiÞ2

vuut : ð14Þ

TABLE 5Experimental densities, q and excess molar volumes, VE

m for the ternary mixture of {2-chlorobutane (1) + butylacetate (2) + isobutanol (3)} at T = 298.15 K.

x1 x2 q/(g � cm�3) VEm/(cm3 �mol�1)

0.0506 0.0526 0.80556 0.2240.0577 0.1739 0.81574 0.5290.0628 0.3414 0.82938 0.7550.0751 0.5398 0.84588 0.7330.0756 0.8665 0.87160 0.1100.0699 0.6048 0.85058 0.6860.0601 0.3798 0.83219 0.7830.0584 0.2121 0.81883 0.6000.0547 0.0658 0.80691 0.2640.1028 0.0327 0.80767 0.1960.1115 0.1775 0.82003 0.5080.1260 0.3440 0.83437 0.6590.1313 0.5533 0.85113 0.5900.1434 0.7953 0.87069 0.1290.2218 0.1750 0.82787 0.4450.2412 0.3457 0.84297 0.4910.2612 0.5462 0.85981 0.3300.2770 0.6672 0.86987 0.1240.2495 0.4439 0.85120 0.4430.2293 0.2587 0.83520 0.4930.5385 0.2722 0.85773 0.1830.7449 0.0721 0.85531 0.1960.5630 0.2974 0.86125 0.1440.5164 0.3852 0.86469 0.1330.4555 0.4357 0.86447 0.1580.4002 0.5463 0.86890 0.1180.4558 0.0291 0.83165 0.3400.4431 0.1752 0.84345 0.3150.4784 0.3456 0.85932 0.1970.5051 0.4407 0.86792 0.1070.4624 0.2556 0.85130 0.2660.4390 0.1004 0.83682 0.3330.5525 0.1758 0.85100 0.2360.6282 0.3219 0.86713 0.0810.6605 0.1782 0.85851 0.1420.6900 0.2565 0.86634 0.0670.7740 0.1755 0.86580 0.0450.8649 0.0316 0.86014 0.1410.9176 0.0329 0.86419 0.0492

0.0 0.1 0.2 0.3 0.4 0.5

butylaceta

1.0

isobutanol

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.8

0.70.6

0.5

0.40.3

0.30.20.1

FIGURE 4. Isolines at constant excess molar volume VEm for ternary mixtures of {2-chl

K. Khanlarzadeh, H. Iloukhani / J. Chem. Thermodynamics 43 (2011) 1583–1590 1587

Ternary predictions using the Jacob–Fitzner [21], Kohler [22] Rast-ogi [23], and Radojkovic [24] models show good agreement withexperimental data for this system. Although this standard deviationis beyond to experimental error, both models present the advantageof using exclusively binary data, which are easily available in theliterature.

4. The theoretical models

4.1. PFP theory

The Prigogine–Flory–Patterson (PFP) theory [9–11] has beencommonly employed to analyze excess thermodynamic properties.This theory has been used to interpreting the results of measure-ments of the excess properties of a number of binary systemsformed by molecular species which differ in size and shape.Although in the development of the theory hydrogen bonds andinteractions of strong electrostatic nature are specifically excluded,a purely empirical application of the Flory formalism can still pro-vide an interesting correlation between the excess molar volumesof more complex mixtures. In fact, and despite the ionic characterof the PL systems, the use of Flory-type theories has proven suc-cessful in predicting and modeling both the excess propertiesand fluid-phase behavior of PL-containing mixtures [25,26].ThePFP theory considers a molecule to be made up of equal segments(isomeric portions), specified by the effective number. Each seg-ment has intermolecular contact sites capable of interacting withneighboring sites. According to the PFP theory, VE

m calculations in-clude three contributions: (i) interactional, which is proportionalto the (v12) parameters; (ii) the free volume contribution whicharises from the dependence of the reduced volume upon the re-duced temperature as a result of the difference between the degreeof expansion of the two components, and (iii) the (P⁄) contribution,which depends both on the differences of internal pressures anddifferences of reduced volumes of the components. The VE

m was cal-culated by means of the PFP theory using the following equationwith the three contributions.

2-chlorobutane0.6 0.7 0.8 0.9 1.0

te

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.2 0.10.08

0.05

orobutane (1) + butylacetate (2) + isobutanol (3)} correlated by Cibulka equation.

TABLE 6Ternary coefficients of Cibulka equation, Bi for VE

m and standard deviations, r, at T = 298.15 K.

System B0 B1 B2 r/(cm3 �mol�1)

2-Chlorobutane + butylacetate + isobutanol �4.7443 �1.9767 �2.2710 0.018

TABLE 7Standard deviation, S=ðVE

mÞ in the prediction of VEm with

different models for the ternary mixture at T = 298.15 K.

Model S (VEm/(cm3 �mol�1)

Jacob–Fitzner 0.03Kohler 0.04Rastogi 0.02Radojkovic 0.02

TABLE 8Parameters of pure components used in Flory theory. Reduction parameters forpressure, P⁄ molar hard core volumes, V⁄ reduction parameters for temperature, T⁄ atT = 298.15 K.

Component P⁄/(J � cm–3) V⁄/(cm3 �mol�1) T⁄/K

2-Chlorobutane 494.694 81.583 4450.39Butylacetate 513.001 105.313 5045.43Isobutanol 436.253 70.997 5296.04

Vm

E/(

cm 3 .m

ol -

1)

x

FIGURE 5. Excess molar volumes VEm at T = 298.15 K for the binary systems: (�)

{2-chlorobutane (1) + butylacetate (2)}, (N) {2-chlorobutane (1) + isobutanol (3)},(�) {butylacetate (2) + isobutanol (3)}. x1 is the mole fraction of the first componentin each binary. Solid line calculated with PFP theory.

1588 K. Khanlarzadeh, H. Iloukhani / J. Chem. Thermodynamics 43 (2011) 1583–1590

VEm=ðx1V�1 þ x2V�2Þ ¼

ð~V1=3 � 1Þ~V2=3W1h2v12

ðð4=3Þ~V�1=3 � 1Þ=P�1�

ð~V1 � ~V2Þ2ðð14=9Þ~V�1=3 � 1ÞW1W2

ðð4=3Þ~V�1=3 � 1Þ~Vþ

ð~V1 � ~V2ÞðP�1 � P�2ÞW1W2

P�1W2 þ P�2W1: ð15Þ

The ~V of the solution is obtained through the Flory’s theory. Thecharacteristic parameters V⁄and P⁄ are obtained from thermalexpansion coefficient ai, and isothermal compressibility, bT. Thethermal expansion coefficient ai, is used to calculate the reducedvolume by equation:

eV i ¼ ð1þ ðð4=3ÞaiTÞ=ð1þ aiTÞÞ3: ð16Þ

Here, the molecular contact energy fraction is calculated by:

W1 ¼ u1P�1=ðu1P�1 þu2P�2Þ ð17Þ

with the hard-core volume fractions defined by:

u1 ¼ x1V�1=ðx1V�1 þ x2V�2Þ: ð18Þ

The values of pure parameters for the pure liquid components andthe mixture are obtained by Flory theory. The pure compounds andthe mixtures parameters values obtained by Flory theory areshowed in table 8.

The values of thermal expansion coefficient ai, and isothermalcompressibility bT, for the pure components were obtained fromthe literature. In order to obtain VE

m it is necessary to find the inter-actional parameter, v12, which was obtained by fitting the theoryto experimental values of VE

m for each one of the binary system.Table 9 presents the calculated equimolar values of the threecontributions to VE

m according to equation, together with the inter-actional parameter, v12. An analysis of each of the three contribu-tions to VE

m shows that, the interactional contribution is ‘‘alwayspositive in all binary mixtures; this contribution seems importantto explain the VE

m behavior for system studied’’. The free volume ef-fect is negative and it seems to have little significance for the sys-tem studied. Figure 5 shows the excess molar values predicted byPFP theory for binary systems.

TABLE 9Calculated values of contributions of the PFP theory. Interactional parameters, v12 reducti

System v12=ðJ � cm�3Þ

2-Chlorobutane + butylacetate 8.52-Chlorobutane + isobutanol 14.5Butylacetate + isobutanol 52.5

4.2. ERAS-model

The ERAS-model [8] has been utilized to interpret quantitativelythe thermodynamic properties of mixtures and combines the lin-ear-chain association model with Flory’s equation of state. TheERAS model was successfully applied to describe simultaneouslyHE, GE, and VE of (alkanol + alkane) mixtures as well as activity coef-ficients and apparent molar volumes. The ERAS model, originallydeveloped for (alkanol + alkane) mixtures, has been extended tobinary (alkanol + amine/ester) mixtures [27]. The ERAS model hassubsequently being successfully applied by many investigators todescribe the excess properties of (alkanol + ester) mixtures. Theprocedure for calculation of reduction parameters and their corre-sponding values for associated liquids are different than that fornon-associated components as originally adopted by Flory andco-workers [5,28]. We have also examined the ERAS-model to ana-lyze the present volumetric properties of three introduced binary

on parameters for pressure, P⁄ for binary mixtures at T = 298.15 K.

Interactional Free volume P⁄

0.1689 –0.0733 502.8950.2523 –0.1192 464.8190.9115 –0.0105 472.134

TABLE 10Properties and parameters of pure components used in the ERAS-model, thermal expansion coefficients, a, isothermal compressibility, bT self-association constants, KA reductionparameters for volume, V⁄ reduction parameters for pressure, P⁄ self-association enthalpies, Dh� and self-association volume, Dv� at T = 298.15 K.

Component 104a/(K�1) 104bT=ðMPa�1Þ KA V⁄/(cm3 �mol–1) P⁄/(J � cm–3) Dh⁄/(kJ �mol�1) Dv⁄/(cm3 �mol�1)

2-Chlorobutane 13.13 13.55 0 81.62 495.39 0 0Butylacetate 10.69 9.89 0 105.07 513.13 0 0Isobutanol 9.78 10.33 16.46 77.88 310.39 –25.6 –5.6

TABLE 11ERAS-model binary mixture parameters, van der Waals interaction parameters, v12 cross association constant, KAB cross association volume, Dv� and standard deviations, r atT = 298.15 K.

System v12/(J � cm–3) KAB Dv⁄/(cm3 �mol�1) r

2-Chlorobutane + butylacetate 8.52 0 0 0.0042-Chlorobutane + isobutanol 1.79 35.05 –4.78 0.005Butylacetate + isobutanol 2.73 12.52 –2.95 0.003

v mE

/(c

m3 .m

ol-1

)

x

FIGURE 6. Excess molar volumes VEm at T = 298.15 K for the binary systems: (�)

{2-chlorobutane (1) + butylacetate (2)}, (N) {2-chlorobutane (1) + isobutanol (3)},(�) {butylacetate (2) + isobutanol (3)}. x1 is the mole fraction of the first componentin each binary. Solid line calculated with ERAS-model.

K. Khanlarzadeh, H. Iloukhani / J. Chem. Thermodynamics 43 (2011) 1583–1590 1589

systems at T = 298.15 K. The assumption made in frame of the ERASmodel includes the self-association of isobutanol and polarity ofchloroalkane and butylacetate according to the following reactionscheme:

Am þ A!KAAmþ1; ð19Þ

Bn þ B!KABnþ1; ð20Þ

where m or n are the degree of self-association, ranging from 1 to1.The cross-association between A and B molecules are representedby:

Am þ Bn !KAB

AmBn: ð21Þ

The association constants Ki (i = A, B, AB) are assumed to be inde-pendent of the chain length. Their temperature dependence is givenby

Ki ¼ K0 exp½�ðDh�i =RÞð1=T � 1=T0Þ�; ð22Þ

where K0 is the equilibrium constant at the standard temperatureT0 = 298.15 K, R the gas constant and Dh�i , enthalpy for the reactionsgiven by equations (26)–(30), which corresponds to the hydrogenbonding energy. These reactions are also characterized by the vol-ume change Dv�i , related to the formation of the linear chains.

The essential property of the ERAS-model is that the excessfunction VE

m is split into a chemical and a physical contribution.The expression for VE

m of the ERAS-model extended to the two-block approach of cross-association are given by [27,29]

VEc ¼ ~VM xAKADv�AðuA1 �u0

A1Þ þ xBKBDv�BðuB1 �u0B1Þ þ xAKABDv�AB

�� uB1ð1� KAuA1ÞðVB=VAÞð1� KBuB1Þ þ KABuB1

�; ð23Þ

VEp ¼ ðxAv�A þ xBv�BÞðeV M �uA

eV A �uBeV BÞ; ð24Þ

VE ¼ VEp þ VE

c ; ð25Þ

wherein KA and KB are the equilibrium constants of chain self-asso-ciation of alkanol and/or ester, respectively. KAB, and Dh�AB, are theassociation constants and hydrogen bond energy from the cross-association. uA1 and uB1 are the hard core volume fraction of thebutylacetate and isobutanol in the mixture, respectively. They haveto be calculated numerically from the solution of the following cou-pled equations.

uA ¼ uA1=ð1� KAuA1Þ2½1þ VAKABuB1=VBð1� KBuB1Þ�; ð26Þ

uB ¼ uB1ð1� KBuB1Þ2½1þ ðKABuA1=1� KAuA1Þ�: ð27Þ

Here uA and uB are the stoichiometric hard-core volume fractionsof components.

The physical contribution VEp in ERAS-model is derived from Flo-

ry’s equation of state which is assumed to be valid not only forpure components but also for the mixture

~Pi~Vi

~Ti

¼~V1=3

i~V1=3

i � 1� 1

~Vi~Ti

; ð28Þ

where i = A, B. In equation (28), ~Vi ¼ Vi=V�i ; ~Pi ¼ Pi=P�i ; ~Ti ¼ Ti=T�iare the reduced volume, pressure, and temperature, respectively.All the reduction parameters V�i ; P�i ; T�i of pure components canbe determined knowing the experimental data for molar volumeV, thermal expansion coefficient a, isothermal compressibility bT ,provided suitable association parameters Ki, Dv�i ; Dh�i are known.The reduction parameters for the mixture P�M ; T�M and V�M are calcu-lated from mixing rules [30,31].

P�M ¼ uAP�A þuBP�B � XABuAhB; ð29Þ

T�M ¼P�M

uAP�A=T�M þuBP�B=T�M; ð30Þ

V�M ¼ xAV�A þ xBV�B: ð31Þ

1590 K. Khanlarzadeh, H. Iloukhani / J. Chem. Thermodynamics 43 (2011) 1583–1590

XAB is an interaction parameter characterizing the difference of dis-persive intermolecular interaction between A and B, ui and hi arehard-core volume fraction and the surface fraction of the compo-nent i [32].

The mixture parameters appearing in the theoretical expressionof excess molar volume are: XAB; KA; KB; KAB; Dh�A; Dh�B; Dh�AB;

Dv�A; Dv�B; Dv�AB. All the parameters can be obtained by adjustingthem to VE

m of binary systems.The properties and parameters as equilibrium constant K, ther-

mal expansion coefficient a, isothermal compressibility bT molarvolume Vm characteristic volume V⁄ and characteristic pressureP⁄ for pure component are listed in table 10 and the ERAS-modelparameters for binary mixture are listed in table 11. The resultsof fitting experimental data with ERAS-model are shown in figure6. The values of calculated VE

m for all binary mixtures are in goodagreement with experimental data.

5. Conclusions

Excess molar volumes VEm of binary and ternary mixtures of {2-

chlorobutane (1) + butylacetate (2) + isobutanol (3)} were calcu-lated by using measured densities at T = 298.15 K. The experimen-tal VE

m of binary systems were fitted by Redlich–Kister polynomialequation and ternary system results were fitted by Cibulka equa-tion. VE

m for ternary mixtures were also predicted by many empir-ical expressions using data for the corresponding binary mixtures.Excess molar volume of for all binary mixtures containing (2-chlo-robutane + butylacetate), (2-chlorobutane + isobutanol), and(+butylacetate + isobutanol) are positive over the whole range ofmole fractions. Positive values would indicate that molecular inter-actions between different molecules are weaker than interactionsbetween molecules in the same pure liquid and that repulsiveforces dominate the behavior of the solutions. Excess molar vol-umes for binary mixtures are described qualitatively for all rangesof mole fractions by the PFP and ERAS-models. The standard devi-ations between experiment and models are satisfactory for mix-tures under study. The ERAS-model parameter calculation ismore complex, although suitable for the property representation,as can be observed in figure 6 which show that the ERAS-modelis better to reproduce the experimental data rather than PFPtheory.

Acknowledgments

The authors thank the University authorities for providing thenecessary facilities to carry out the work.

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JCT 10-425