J. Chem. Thermodynamics 78 (2014) 241–253

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J. Chem. Thermodynamics

journal homepage: www.elsevier .com/locate / jc t

Excess molar volumes and excess isentropic compressibilities of binaryand ternary mixtures of o-chlorotoluene with cyclic ether and amidesor cyclohexane at different temperatures

http://dx.doi.org/10.1016/j.jct.2014.06.0300021-9614/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +91 9729071881.E-mail address: v_sharmachem58@rediffmail.com (V.K. Sharma).

V.K. Sharma a,⇑, Rajni Dua a, Dimple Sharma b

a Department of Chemistry, M.D. University, Rohtak 124001, Haryana, Indiab Department of Chemistry, Hindu College, Sonepat 131001, Haryana, India

a r t i c l e i n f o a b s t r a c t

Article history:Received 18 April 2014Received in revised form 25 June 2014Accepted 29 June 2014Available online 9 July 2014

Keywords:DensitySpeed of soundExcess molar volumeExcess isentropic compressibilityGraph theory

Densities and speeds of sound data for ternary o-chlorotoluene (i) + tetrahydropyran (j) + N-methylfor-mamide or N,N-dimethylformamide or cyclohexane (k) and their sub-binary o-chlorotoluene or (tetrahy-dropyran + cyclohexane) mixtures have been measured at temperatures (298.15, 303.15, 308.15) K and0.1 MPa. The excess molar volumes, VE

ijk, VE and excess isentropic compressibilities, ðjESÞijk, jE

S for ternaryand binary mixtures respectively have been determined from the experimental densities, speeds of soundvalues and fitted to Redlich–Kister equation to calculate ternary and binary adjustable parameters alongwith standard deviations. The excess properties, VE

ijk and ðjESÞijk have been tested in terms of (i) Graph;

and (ii) Prigogine–Flory–Patterson (PFP) theories.� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Thermodynamic properties of multi-component liquid mixturesare essential for process designing as well as for understandingstructural and packing changes in mixtures. The design and opera-tion of processes that involve non-electrolyte mixtures requireknowledge of rigorous models or experimental data to representthe non-ideality of mixtures. The highest quality of density andspeed of sound data and their analysis provide informationrequired for improving the parameters for the predictive modelswhich in turn are also used in simulation packages, design pro-cesses in chemical and biological industries [1–3]. o-Chlorotolueneis used as an intermediate in the chemical industry and as a sol-vent for chemical processing as well as a solvent for the formula-tion of agricultural pesticides. o-Chlorotoluene breaks down tointermediates such as cresols, 2-chlorobenzaldehyde, mixeddichlorotoluenes, 2-chlorobenzoic acid, 2-chlorobenzonitrile and2-chlorobenzylchloride which are further used in the productionof coloring agents, agrochemicals, and pharmaceuticals [4,5].Tetrahydropyran is used as a reaction medium solvent for organicand biological processes, a solvent for plastics and polymers and asa dispersing agent for textile processes [6]. N-methylformamide

(NMF) a polar and protic solvent is used in the pharmaceuticalindustry and organic synthesis. Anticancer properties have alsobeen credited to N-methylformamide molecule. N,N-dimethyl-formamide (DMF) a polar and aprotic solvent is used in the indus-try of synthetic fibers, leathers, films and during the coatingprocesses [7]. Cyclohexane is a main ingredient among medicinesand chemical waste liquids. It is widely used as a solvent, polaradditive, dilution initiator, structure regulator, and active additivein the synthesis of copolymer, resins and rubber [8]. Consequently,densities and speeds of sound data of o-chlorotoluene with tetra-hydropyran and N-methylformamide or N,N-dimethylformamideor cyclohexane mixtures may be of vital importance for industries.Further, survey of literature has shown that the densities andspeeds of sound of o-chlorotoluene (i) + tetrahydropyran (j) + N-methylformamide or N,N-dimethylformamide or cyclohexane (k)mixtures are not available in literature. This prompted us to mea-sure densities and speeds of sound of the present mixtures.

2. Experimental

o-Chlorotoluene (o-CT) (Fluka, mass fraction, 0.993; GC),tetrahydropyran (THP) (Fluka, mass fraction, 0.996; GC), N-methyl-formamide (NMF) (Fluka, mass fraction, 0.994; GC), N,N-dimethyl-formamide (DMF) (Fluka, mass fraction, 0.998; GC), cyclohexane(Fluka, mass fraction, 0.996; GC) were purified by standardmethods [9–11]. The source of chemicals, their purification and

242 V.K. Sharma et al. / J. Chem. Thermodynamics 78 (2014) 241–253

analysis methods along with final purity are listed in table 1. Thedensities and speeds of sound values of the purified liquids atT = (298.15, 303.15, 308.15) K are recorded in table 2, where theyare compared with literature [7,9,12–39] values.

The density and sound analyzer apparatus (Anton Paar DSA5000) was used to measure densities and speeds of sound valuesof the purified liquids and their mixtures as described elsewhere[40,41]. The equipment was calibrated at T = 293.15 K with doublydistilled, deionized and degassed water. The various mole fractionsof binary or ternary liquid mixtures were prepared by measuringmasses of the components in air tight glass bottle of capacity�5 ml using an electric balance (Model: Mettler AX-205 DeltaRange) with a sensitivity of ±10�5 g. The uncertainty in mole frac-tion is 1 � 10�4. The uncertainties in the density and speed of soundmeasurements are 0.5 kg �m�3 and 0.1 m � s�1, respectively. Theuncertainty in VE values calculated from density results is 0.1%and uncertainty in the temperature measurement is ±0.01 K.

3. Results

The measured densities, qijk;q and speeds of sound, uijk, u of ter-nary o-CT (i) + THP (j) + NMF or DMF or cyclohexane (k) and theirsub-binaries o-CT or THP (i) + cyclohexane (j) at (298.15, 303.15,308.15) K are listed in tables 3 and 4 respectively. The excess molarvolumes, VE

ijk;VE; isentropic compressibilities, ðjSÞijk;jS; and

excess isentropic compressibilities ðjESÞijk;jE

S for the ternary andbinary mixtures respectively were calculated using the equations

VEijk ¼

Xk

i¼i

xiM�i ðqijkÞ

�1 �Xk

i¼i

xiM�i ðq�i Þ

�1; ð1Þ

VE ¼Xj

i¼i

xiM�i ðqÞ

�1 �Xj

i¼i

xiM�i ðq�i Þ

�1; ð2Þ

ðjSÞijk ¼ ðqijku2ijkÞ�1; ð3Þ

jS ¼ ðqu2Þ�1; ð4Þ

jES

� �ijk ¼ ðjSÞijk � jid

S ; ð5Þ

jES ¼ jS � jid

S ; ð6Þ

where xi, M�i and q�i are the mole fraction, molar mass and density of

pure component (i), respectively. The qijk, q and uijk, u are the densi-ties and speeds of sound of ternary and binary mixtures respectively.

The ideal isentropic compressibilities, jidS values for ternary and

binary mixtures were calculated using Benson and Kiyohara [42]equation

jidS ¼

Xj or k

i¼i

/i jS;i þTVm;ia�2i

C�p;i

" #� T

Xj or k

i¼i

xiVm;i

! Pj or ki¼i /ia�i

� �2

Pj or ki¼i xiC

�p;i

� � : ð7Þ

TABLE 1Details of chemical source, purification method, final purity and analysis method.

Chemical name Source Purification met

o-Chlorotoluene Fluka Fractional distilTetrahydropyran Fluka Vacuum distillaN-methylformamide Sigma Aldrich Vacuum distillaN,N-dimethylformamide Sigma Aldrich Vacuum distillaCyclohexane Fluka Fractional distil

GCa = Gas chromatography.

The /i;jS;i, Vm;i, a�i , T and C�p;i (i = i or j or k) are the volume frac-tion, isentropic compressibility, molar volume, thermal expansioncoefficient, temperature and molar heat capacity of pure compo-nent (i). The a�i values for various liquid were calculated usingexperimental density data in the manner described elsewhere[16]. The C�p;i values for o-CT, THP, NMF, DMF and cyclohexane weretaken from literature [43–45]. The VE

ijk; ðjESÞijk and VE;jE

S values forternary and binary mixtures are given in tables 3 and 4 respec-tively. Using Redlich–Kister [46] equations

XEijkðX ¼ V or jSÞ

¼ xixj

X2

n¼0

XðnÞij

� �ðxi � xjÞn

" #þ xjxk

X2

n¼0

XðnÞjk

� �ðxj � xkÞn

" #

þ xixk

X2

n¼0

XðnÞik

� �ðxi � xkÞn

" #

þ xixjxk

X2

n¼0

XðnÞijk

� �ðxj � xkÞnxn

i

" #; ð8Þ

XEðX ¼ V or jSÞ ¼ xixj Xð0Þ þ Xð1Þð2xi � 1Þ þ Xð2Þð2xi � 1Þ2h i

; ð9Þ

excess molar volumes and excess isentropic compressibilities datafor the present ternary and binary mixtures were fitted by leastsquares optimization method. The XðnÞijk (X = V or jS) (n = 0 to 2)and XðnÞij , XðnÞjk , XðnÞik (n = 0 to 2) etc. are parameters characteristic of(i + j + k) ternary and sub-binaries (i + j), (j + k), (i + k) of (i + j + k)mixtures. The XðnÞij (X = V or jS) (n = 0 to 2) etc. for o-CT + THP orNMF or DMF; THP + NMF or DMF were taken from literature[43,44,47,48]. The standard deviations, r(VE

ijk), r(VE) and rðjESÞijk,

r(jES) of the fit defined by

r XEijk

� �ðX ¼ V or jSÞ

¼X

XEijk

� �exp t� XE

ijkðcalc equation 8Þ

� �2,ðm� nÞ

( )0:5

;

ð10Þ

rðXEÞðX ¼ V or jSÞ

¼XðXEÞexp t � XE

ðcalc equation 9Þ

h i2�ðm� nÞ

0:5

; ð11Þ

{where m, n are the number of experimental points and number ofadjustable parameters of equations (8) and (9)} along with ternaryand binary parameters are recorded in tables 5 and 6. The varioussurfaces generated [49] by VE

ijk and ðjESÞijk values {computed by

employing equation (8)} for the ternary mixtures at T = 298.15 Kare shown in figures 1–6 respectively. In figure 1 VE

ijk values (corre-sponding to i–j axis) were obtained by keeping xk constant andvarying the values of xi and xj (shown as blue line); VE

ijk values(corresponding to j–k axis) were obtained by keeping xi constantand varying the values xj and xk (shown as red line).

hod Final purity (mass fraction) Analysis method

lation 0.993 GCa

tion 0.996 GCtion 0.994 GCtion 0.998 GClation 0.996 GC

TABLE 2Comparison of densities, q�i speeds of sound, u�i of pure liquids with their literature values at T/K = (298.15, 303.15, 308.15) and 0.1 MPa.

Components T/K q�i /kg �m�3 u�i /m � s�1

(Expt.) (Lit.) (Expt.) (Lit.)

o-Chlorotoluene 298.15 1077.3 1076.44 [12]1077.40 [9]

1298.7 1299.06 [14]

303.15 1072.5 1072.60 [9] 1280.7 1279.33 [14]1282.00 [15]

308.15 1067.6 1068.24 [13] 1262.7 1261.82 [15]1266.00 [13]

Tetrahydropyran 298.15 879.13 878.85 [16]877.23 [17]879.05 [18]878.91 [19]879.16 [18]

1269.8 1269.3 [23]1270.00 [24]1272 [17]

303.15 873.99 873.95 [20]874.2 [21]

1246.8 1246.4 [25]

308.15 868.83 868.80 [22]869.2 [21]868.81 [16]

1224.4

N-methylformamide 298.15 999.00 998.83 [26]999.19 [7]

1431.6 1431.5 [27]

303.15 994.65 994.48 [26]994.75 [7]

1417.4 1415.93 [28]

308.15 990.30 990.33 [7] 1402.2 1400.71 [28]

N,N-dimethylformamide 298.15 944.60 944.60 [29]944.7 [30]

1458.5 1457.81 [32]

1458.5 [27]303.15 939.83 939.7 [31]

940.10 [29]1440.2 1438.38 [32]

1448.80 [29]308.15 935.05 934.64 [28]

935.6 [29]1420.8 1419.04 [32]

1421.95 [33]Cyclohexane 298.15 773.94 773.68 [16,26]

773.94 [17]773.90 [34]

1253.6 1254.0 [37]1255 [17]

303.15 769.21 769.20 [35] 1229.1 1228.0 [36]1230.0 [38]1225.7 [25]

308.15 764.45 764.40 [36] 1205.1 1205.3 [39]

Standard uncertainties u are u (T) = ±0.01 K, u(xi) = ±1 � 10�4, u(q) = ±0.5 kg �m�3, u(u) = ±0.1 m � s�1, u (P) = ±100 Pa.

V.K. Sharma et al. / J. Chem. Thermodynamics 78 (2014) 241–253 243

4. Discussion

The VE data of o-CT or THP (i) + cyclohexane (j) binary mixturesat T = (298.15 and 308.15) K and jE

S data of (THP (i) + cyclohexane(j)) binary mixture at T = 308.15 K are reported in literature[50,16–18]. The comparison between experimental densities, qand speeds of sound, u of (THP (i) + cyclohexane (j)) mixture atT = (298.15 and 308.15 or 308.15) K with literature values [16–18] is presented in Figures 7 and 8. The results suggest that qvalues compare well with literature values. However, there is adifference of ’4 m � s�1 in u values of (THP (i) + cyclohexane (j))mixture. It is due to the reason that the speeds of sound valuesof pure THP and cyclohexane reported by us (1269.8,1253.6 m � s�1) differ from literature values (1272, 1255 m � s�1)[17]. However, both are comparable with values reported by otherresearchers [23–25,36–39]. However, our VE and jE

S values forthese mixtures are in agreement with literature values (shown infigures 9–11). We have measured VE and jE

S values of (THP(i) + cyclohexane (j)) mixtures (already reported in literature atT = (298.15, 308.15 and 308.15) K respectively) to estimate binaryadjustable parameters of the said mixture which in turn arerequired to fit VE

ijk and ðjESÞijk data to Redlich–Kister equation to

predict ternary adjustable parameters and standard deviations atthe studied temperatures. The VE

ijk and ðjESÞijk data of the studied

(i + j + k) mixtures are not available in literature for comparisonwith measured results. The VE data for o-CT or (THP (i) + cyclohex-ane (j)) mixtures are positive over entire composition range.

However, while jES data of o-CT (i) + cyclohexane (j) are negative;

those for THP (i) + cyclohexane (j) are positive over full range ofcomposition. The VE data for o-CT or (THP (i) + cyclohexane (j))mixtures suggest that cyclohexane gives relatively more closedpacking in THP as compared to o-CT. This may be due to highdipole moment of THP (l = 1.63) [10] in comparison to o-CT(l = 1.43) [10] which in turn leads to strong dipole-induced dipoleinteraction in (THP + cyclohexane) mixtures.

The densities of o-CT (i) + THP (j) + NMF or DMF or cyclohexane(k) mixtures at T = (298.15, 303.15, 308.15) K vary linearly withincreasing temperature. However, there is a remarkable changein densities of (o-CT (i) + THP (j) + NMF (k)) mixture atxi P 0.4506. The deviation suggests that measured ternary mixturedensities do not agree with the sub-binary mixtures. The VE

ijk of(o-CT (i) + THP (j) + NMF or DMF (k)) mixtures are negative overentire values of xi and xj. However, for (o-CT (i) + THP (j) + cyclo-hexane (k)) mixture, sign of VE

ijk values is dictated by the relativeproportion of components in mixed state. Further, while ðjE

SÞijk ofo-CT (i) + THP (j) + DMF or cyclohexane (k) mixtures are negative;those for (o-CT (i) + THP (j) + NMF (k)) mixture changes sign withthe change in mole fraction of components. The VE

ijk and ðjESÞijk data

suggest that NMF gives relatively more closed packing with o-CT:THP molecular complexity as compared to DMF or cyclohexane.This may be due to the presence of –CH3 groups in DMF which inturn restrict the approach of DMF molecules towards o-CT: THPmolecular entity. The lower VE

ijk (o-CT (i) + THP (j) + cyclohexane(k)) mixture than those of (o-CT (i) + THP (j) + NMF or DMF (k))

TABLE 3Measured densities, qijk, excess molar volumes, VE

ijk, speeds of sound, uijk, isentropic compressibilities, ðjSÞijk and excess isentropic compressibilities, ðjESÞijk data compared with

theories for (i +j + k) mixtures as a function of mole fraction, xi of component (i) and xj of component (j) at T / K = (298.15, 303.15, 308.15) and 0.1 MPa.

xi xj qijk /kg �m�3

VEijk Expt. /

cm3 �mol�1

VEijk Graph /

cm3 �mol�1

VEijk PFP /

cm3 �mol�1

uijk /m � s�1

ðjSÞijk /TPa�1

ðjESÞijk Expt./

TPa�1

ðjESÞijk Graph/

TPa�1

ðjESÞijk PFP/

TPa�1

o-Chlorotoluene (i) + tetrahydropyran (j) + N-methylformamide (k) T/K = 298.150.0988 0.8213 910.15 �0.150 �0.148 �0.059 1283.0 667.5 �5.3 �5.4 �81.30.1132 0.7961 914.59 �0.163 �0.163 �0.065 1284.9 662.3 �5.9 �5.9 �80.30.1334 0.7621 920.70 �0.180 �0.175 �0.074 1287.4 655.3 �6.8 �6.5 �79.10.1508 0.7327 925.96 �0.191 �0.193 �0.080 1289.6 649.3 �7.4 �6.9 �78.00.1713 0.7004 931.94 �0.203 �0.202 �0.087 1291.9 642.9 �8.1 �7.3 �76.80.1905 0.6712 937.44 �0.214 �0.213 �0.092 1293.9 637.1 �8.7 �7.6 �75.70.2105 0.6428 942.94 �0.222 �0.223 �0.096 1295.8 631.6 �9.3 �7.9 �74.70.2358 0.6118 949.34 �0.226 �0.224 �0.098 1297.5 625.7 �10.1 �8.3 �73.60.2509 0.5936 953.12 �0.231 �0.236 �0.100 1298.4 622.4 �10.4 �8.6 �73.00.2816 0.5655 959.74 �0.230 �0.239 �0.099 1299.2 617.3 �11.3 �9.2 �72.20.3296 0.5387 968.08 �0.231 �0.227 �0.090 1298.1 613.0 �12.7 �10.8 �71.80.3608 0.5267 972.87 �0.242 �0.241 �0.082 1296.5 611.5 �13.6 �12.3 �71.80.4018 0.5187 978.32 �0.275 �0.275 �0.067 1293.5 610.9 �14.9 �14.9 �72.10.4506 0.2646 1020.2 �0.969 �0.964 �0.108 1315.2 566.6 �7.1 �5.1 �59.90.4815 0.2418 1026.2 �1.004 �1.011 �0.102 1314.2 564.2 �6.5 �4.9 �59.70.5106 0.2204 1031.6 �1.030 �1.043 �0.097 1313.3 562.1 �5.8 �4.6 �59.50.5307 0.2078 1034.7 �1.023 �1.056 �0.093 1312.5 561.1 �5.3 �4.4 �59.50.5568 0.1864 1039.8 �1.056 �1.056 �0.088 1311.5 559.1 �4.2 �3.7 �59.20.5781 0.1717 1043.2 �1.050 �1.045 �0.083 1310.7 558.0 �3.4 �3.2 �59.10.6018 0.1565 1046.5 �1.020 �1.020 �0.078 1309.8 557.0 �2.6 �2.6 �59.10.6238 0.1423 1049.5 �0.985 �0.982 �0.073 1308.9 556.2 �1.8 �2.0 �59.00.6426 0.1313 1051.7 �0.938 �0.942 �0.070 1308.3 555.5 �1.2 �1.5 �59.00.6928 0.1012 1057.2 �0.789 �0.781 �0.058 1306.6 554.1 0.8 0.3 �59.00.7113 0.0925 1058.6 �0.712 �0.717 �0.054 1306.0 553.9 1.4 0.8 �59.20.7324 0.0812 1060.5 �0.628 �0.625 �0.050 1305.4 553.4 2.0 1.6 �59.20.7534 0.0711 1062.0 �0.537 �0.531 �0.045 1304.8 553.1 2.6 2.3 �59.30.7762 0.0618 1063.5 �0.440 �0.435 �0.040 1304.1 552.9 3.1 2.8 �59.50.8078 0.0508 1065.3 �0.313 �0.313 �0.034 1303.2 552.7 3.3 3.3 �59.8

T/K = 303.150.0988 0.8213 905.08 �0.155 �0.153 �0.060 1261.7 694.1 �6.5 �6.6 �83.80.1132 0.7961 909.53 �0.169 �0.169 �0.067 1263.7 688.5 �7.2 �7.2 �82.90.1334 0.7621 915.65 �0.186 �0.180 �0.075 1266.4 681.0 �8.1 �8.0 �81.60.1508 0.7327 920.93 �0.198 �0.199 �0.082 1268.8 674.6 �8.8 �8.5 �80.40.1713 0.7004 926.92 �0.211 �0.208 �0.088 1271.1 667.7 �9.4 �9.0 �79.20.1905 0.6712 932.42 �0.221 �0.219 �0.093 1273.3 661.5 �10.1 �9.4 �78.10.2105 0.6428 937.94 �0.230 �0.229 �0.097 1275.2 655.7 �10.6 �9.8 �77.00.2358 0.6118 944.35 �0.235 �0.230 �0.100 1277.0 649.4 �11.3 �10.3 �75.90.2509 0.5936 948.13 �0.238 �0.243 �0.101 1278.0 645.8 �11.6 �10.5 �75.30.2816 0.5655 954.76 �0.238 �0.245 �0.100 1277.6 641.7 �11.2 �12.5 �74.40.3296 0.5387 963.10 �0.239 �0.234 �0.092 1278.1 635.7 �14.1 �12.8 �74.00.3608 0.5267 967.89 �0.250 �0.248 �0.084 1276.8 633.8 �15.3 �14.3 �74.00.4018 0.5187 973.35 �0.286 �0.286 �0.068 1274.1 632.9 �17.1 �17.1 �74.20.4506 0.2646 1015.9 �1.038 �1.031 �0.110 1297.2 584.9 �8.5 �7.7 �61.80.4815 0.2418 1021.9 �1.074 �1.083 �0.104 1296.5 582.1 �8.0 �7.5 �61.50.5106 0.2204 1027.4 �1.104 �1.118 �0.099 1295.9 579.7 �7.5 �7.1 �61.30.5307 0.2078 1030.5 �1.095 �1.132 �0.095 1295.2 578.5 �7.1 �6.8 �61.30.5568 0.1864 1035.7 �1.136 �1.134 �0.089 1294.6 576.1 �6.2 �6.0 �61.00.5781 0.1717 1039.1 �1.128 �1.122 �0.085 1294.0 574.8 �5.4 �5.3 �60.90.6018 0.1565 1042.4 �1.096 �1.096 �0.080 1293.2 573.7 �4.6 �4.6 �60.80.6238 0.1423 1045.3 �1.059 �1.055 �0.075 1292.4 572.7 �3.7 �3.8 �60.80.6426 0.1313 1047.5 �1.008 �1.012 �0.071 1291.7 572.2 �3.0 �3.1 �60.80.6928 0.1012 1052.9 �0.847 �0.839 �0.060 1289.9 570.8 �0.6 �0.8 �60.80.7113 0.0925 1054.2 �0.764 �0.771 �0.056 1289.2 570.8 0.1 �0.1 �60.90.7324 0.0812 1056.0 �0.675 �0.672 �0.051 1288.3 570.5 1.1 0.9 �60.90.7534 0.0711 1057.5 �0.578 �0.570 �0.046 1287.6 570.4 1.9 1.9 �61.00.7762 0.0618 1058.9 �0.473 �0.467 �0.041 1286.6 570.5 2.7 2.6 �61.20.8078 0.0508 1060.6 �0.336 �0.336 �0.035 1285.3 570.7 3.3 3.3 �61.5

T/K = 308.150.0988 0.8213 899.97 �0.158 �0.157 �0.061 1240.5 722.1 �7.5 �7.6 �86.30.1132 0.7961 904.44 �0.173 �0.173 �0.068 1242.7 716.0 �8.3 �8.3 �85.30.1334 0.7621 910.57 �0.192 �0.186 �0.076 1245.6 707.8 �9.3 �9.1 �84.00.1508 0.7327 915.87 �0.205 �0.205 �0.083 1248.1 700.9 �10.1 �9.8 �82.80.1713 0.7004 921.89 �0.219 �0.215 �0.090 1250.8 693.4 �10.9 �10.3 �81.50.1905 0.6712 927.41 �0.231 �0.226 �0.095 1253.0 686.8 �11.4 �10.8 �80.40.2105 0.6428 932.93 �0.239 �0.236 �0.099 1255.1 680.5 �12.0 �11.2 �79.30.2358 0.6118 939.36 �0.246 �0.237 �0.102 1257.1 673.7 �12.8 �11.6 �78.10.2509 0.5936 943.15 �0.250 �0.249 �0.103 1258.1 669.8 �13.2 �11.9 �77.50.2816 0.5655 949.78 �0.248 �0.249 �0.102 1259.1 664.2 �13.9 �12.5 �76.60.3296 0.5387 958.04 �0.240 �0.231 �0.094 1258.2 659.4 �15.5 �13.9 �76.20.3608 0.5267 962.76 �0.246 �0.240 �0.085 1256.8 657.6 �16.5 �15.4 �76.1

244 V.K. Sharma et al. / J. Chem. Thermodynamics 78 (2014) 241–253

0.4018 0.5187 968.11 �0.270 �0.270 �0.069 1254.1 656.8 �18.3 �18.3 �76.40.4506 0.2646 1011.2 �1.069 �1.045 �0.112 1282.3 601.5 �12.7 �11.6 �63.60.4815 0.2418 1017.2 �1.103 �1.095 �0.106 1281.7 598.4 �12.2 �11.4 �63.30.5106 0.2204 1022.6 �1.126 �1.128 �0.100 1281.2 595.8 �11.5 �11.0 �63.10.5307 0.2078 1025.7 �1.116 �1.141 �0.097 1280.5 594.6 �11.0 �10.7 �63.10.5568 0.1864 1030.8 �1.148 �1.141 �0.091 1280.1 592.1 �10.0 �9.8 �62.70.5781 0.1717 1034.1 �1.136 �1.128 �0.086 1279.4 590.8 �9.2 �9.0 �62.60.6018 0.1565 1037.4 �1.100 �1.100 �0.081 1278.5 589.8 �8.1 �8.1 �62.50.6238 0.1423 1040.3 �1.058 �1.058 �0.076 1277.5 589.0 �6.9 �7.0 �62.50.6426 0.1313 1042.5 �1.007 �1.015 �0.072 1276.6 588.6 �5.8 �6.1 �62.50.6928 0.1012 1047.9 �0.843 �0.840 �0.061 1274.2 587.8 �2.7 �2.9 �62.50.7113 0.0925 1049.2 �0.760 �0.770 �0.057 1273.1 588.0 �1.7 �1.9 �62.60.7324 0.0812 1051.0 �0.669 �0.670 �0.052 1272.0 588.1 �0.3 �0.5 �62.60.7534 0.0711 1052.5 �0.573 �0.568 �0.047 1270.8 588.3 1.0 0.9 �62.70.7762 0.0618 1053.9 �0.467 �0.464 �0.042 1269.5 588.7 2.1 2.1 �62.90.8078 0.0508 1055.7 �0.333 �0.333 �0.036 1267.7 589.4 3.3 3.3 �63.2

o-Chlorotoluene (i) + tetrahydropyran (j) + N,N-dimethylformamide (k) T/K = 298.150.0782 0.8613 901.71 �0.101 �0.109 �0.056 1279.8 677.2 �3.6 �4.0 �81.60.1132 0.7961 912.01 �0.150 �0.150 �0.077 1283.7 665.4 �3.7 �3.7 �78.50.1305 0.7706 916.65 �0.169 �0.171 �0.080 1285.1 660.6 �4.1 �4.5 �77.50.1717 0.7134 927.42 �0.213 �0.216 �0.085 1288.5 649.5 �5.4 �6.5 �75.10.1908 0.6871 932.34 �0.231 �0.233 �0.086 1290.2 644.4 �6.1 �7.1 �74.10.2115 0.6602 937.54 �0.250 �0.250 �0.086 1292.0 639.0 �7.0 �7.8 �73.00.2606 0.6112 948.67 �0.279 �0.284 �0.079 1295.8 627.8 �10.6 �11.6 �71.60.2841 0.5829 954.23 �0.292 �0.295 �0.078 1297.7 622.3 �11.4 �11.9 �70.60.3121 0.5514 960.63 �0.304 �0.304 �0.076 1299.6 616.3 �12.3 �12.3 �69.60.3413 0.5207 967.05 �0.312 �0.310 �0.072 1301.2 610.7 �13.1 �12.9 �68.70.3648 0.5064 971.39 �0.311 �0.313 �0.067 1303.0 606.4 �15.7 �15.3 �68.70.4098 0.4642 980.60 �0.313 �0.311 �0.061 1304.7 599.1 �16.6 �16.1 �67.80.4349 0.4438 985.39 �0.309 �0.307 �0.057 1305.5 595.4 �17.3 �16.9 �67.40.4687 0.4203 991.45 �0.300 �0.298 �0.052 1306.7 590.7 �18.9 �18.6 �67.30.4932 0.4125 995.07 �0.287 �0.287 �0.048 1308.3 587.2 �22.2 �22.2 �67.70.5327 0.3709 1003.0 �0.277 �0.270 �0.044 1307.0 583.6 �19.1 �19.8 �66.60.5409 0.3508 1005.4 �0.277 �0.269 �0.043 1305.3 583.8 �15.2 �16.2 �65.70.5666 0.3272 1010.2 �0.266 �0.257 �0.040 1304.6 581.6 �13.9 �15.2 �65.20.5922 0.2946 1015.5 �0.252 �0.247 �0.035 1303.1 579.9 �10.1 �11.7 �64.20.6123 0.2705 1019.6 �0.241 �0.238 �0.031 1302.5 578.2 �7.9 �9.2 �63.50.6323 0.2504 1023.3 �0.227 �0.229 �0.027 1302.5 576.1 �6.9 �7.6 �63.10.6578 0.2337 1027.3 �0.211 �0.213 �0.024 1302.8 573.6 �7.3 �7.6 �63.00.6906 0.2138 1032.3 �0.190 �0.191 �0.021 1303.1 570.5 �7.9 �8.0 �63.00.7021 0.2067 1034.0 �0.183 �0.183 �0.021 1303.2 569.5 �8.1 �8.1 �63.00.7212 0.1898 1037.2 �0.169 �0.172 �0.017 1303.6 567.4 �7.7 �6.8 �62.70.7587 0.1687 1042.6 �0.145 �0.143 �0.016 1303.6 564.4 �8.2 �7.5 �62.80.7885 0.1483 1047.0 �0.125 �0.123 �0.014 1303.7 561.9 �8.1 �6.9 �62.70.8199 0.1298 1051.4 �0.106 �0.097 �0.012 1303.4 559.9 �7.9 �7.1 �62.6

T/K = 303.150.0782 0.8613 896.60 �0.104 �0.109 �0.063 1258.1 704.7 �4.8 �5.0 �84.10.1132 0.7961 906.88 �0.150 �0.150 �0.087 1262.5 691.8 �5.0 �5.0 �81.00.1305 0.7706 911.51 �0.168 �0.169 �0.090 1264.0 686.7 �5.4 �5.9 �79.90.1717 0.7134 922.24 �0.207 �0.209 �0.095 1267.6 674.8 �6.8 �7.9 �77.50.1908 0.6871 927.15 �0.223 �0.224 �0.097 1269.4 669.3 �7.5 �8.5 �76.40.2115 0.6602 932.32 �0.239 �0.239 �0.097 1271.3 663.6 �8.3 �9.2 �75.30.2606 0.6112 943.42 �0.263 �0.267 �0.089 1275.3 651.8 �12.0 �12.9 �73.80.2841 0.5829 948.97 �0.275 �0.277 �0.088 1277.2 646.0 �12.8 �13.2 �72.80.3121 0.5514 955.36 �0.285 �0.285 �0.085 1279.2 639.7 �13.6 �13.6 �71.80.3413 0.5207 961.77 �0.291 �0.290 �0.081 1280.9 633.7 �14.3 �14.1 �70.90.3648 0.5064 966.11 �0.291 �0.292 �0.075 1282.6 629.2 �17.0 �16.5 �70.90.4098 0.4642 975.33 �0.292 �0.290 �0.068 1284.4 621.5 �17.8 �17.3 �69.80.4349 0.4438 980.13 �0.288 �0.287 �0.064 1285.3 617.6 �18.5 �18.1 �69.50.4687 0.4203 986.21 �0.281 �0.279 �0.058 1286.5 612.6 �20.1 �19.9 �69.30.4932 0.4125 989.86 �0.271 �0.270 �0.053 1288.1 608.9 �23.5 �23.5 �69.70.5327 0.3709 997.75 �0.260 �0.256 �0.049 1287.1 605.0 �20.3 �21.1 �68.60.5409 0.3508 1000.2 �0.258 �0.254 �0.048 1285.4 605.1 �16.2 �17.3 �67.70.5666 0.3272 1005.0 �0.249 �0.243 �0.044 1284.9 602.7 �14.7 �16.3 �67.20.5922 0.2946 1010.4 �0.236 �0.233 �0.039 1283.5 600.8 �10.7 �12.5 �66.10.6123 0.2705 1014.4 �0.225 �0.224 �0.034 1283.0 598.9 �8.4 �9.8 �65.40.6323 0.2504 1018.1 �0.213 �0.214 �0.029 1283.1 596.6 �7.3 �8.1 �64.90.6578 0.2337 1022.2 �0.199 �0.200 �0.026 1283.5 593.8 �7.8 �8.1 �64.90.6906 0.2138 1027.2 �0.181 �0.181 �0.024 1284.0 590.5 �8.5 �8.6 �64.90.7021 0.2067 1028.9 �0.174 �0.174 �0.023 1284.1 589.4 �8.7 �8.7 �64.90.7212 0.1898 1032.2 �0.161 �0.164 �0.019 1284.6 587.1 �8.3 �7.3 �64.60.7587 0.1687 1037.6 �0.140 �0.139 �0.017 1284.8 583.8 �8.9 �8.0 �64.60.7885 0.1483 1042.1 �0.123 �0.120 �0.015 1285.1 581.1 �8.8 �7.4 �64.50.8199 0.1298 1046.5 �0.105 �0.099 �0.014 1284.9 578.8 �8.6 �7.8 �64.4

T/K = 308.150.0782 0.8613 891.49 �0.109 �0.110 �0.063 1236.2 734.0 �5.2 �5.4 �86.60.1132 0.7961 901.74 �0.151 �0.151 �0.087 1240.9 720.2 �5.5 �5.5 �83.4

(continued on next page)

V.K. Sharma et al. / J. Chem. Thermodynamics 78 (2014) 241–253 245

TABLE 3 (continued)

xi xj qijk /kg �m�3

VEijk Expt. /

cm3 �mol�1

VEijk Graph /

cm3 �mol�1

VEijk PFP /

cm3 �mol�1

uijk /m � s�1

ðjSÞijk /TPa�1

ðjESÞijk Expt./

TPa�1

ðjESÞijk Graph/

TPa�1

ðjESÞijk PFP/

TPa�1

0.1305 0.7706 906.36 �0.167 �0.168 �0.090 1242.5 714.7 �6.0 �6.5 �82.30.1717 0.7134 917.03 �0.200 �0.201 �0.095 1246.4 701.9 �7.5 �8.7 �79.80.1908 0.6871 921.91 �0.212 �0.214 �0.097 1248.4 696.0 �8.2 �9.3 �78.60.2115 0.6602 927.07 �0.225 �0.226 �0.097 1250.4 689.9 �9.1 �10.1 �77.50.2606 0.6112 938.12 �0.245 �0.246 �0.089 1254.6 677.2 �13.0 �13.9 �76.00.2841 0.5829 943.65 �0.253 �0.254 �0.087 1256.7 671.0 �13.8 �14.2 �75.00.3121 0.5514 950.01 �0.260 �0.260 �0.084 1258.8 664.3 �14.7 �14.7 �73.90.3413 0.5207 956.41 �0.265 �0.264 �0.080 1260.7 657.9 �15.5 �15.3 �72.90.3648 0.5064 960.76 �0.264 �0.264 �0.074 1262.5 653.1 �18.3 �17.8 �72.90.4098 0.4642 969.98 �0.264 �0.263 �0.067 1264.5 644.8 �19.1 �18.6 �71.90.4349 0.4438 974.79 �0.261 �0.260 �0.063 1265.5 640.6 �19.9 �19.4 �71.50.4687 0.4203 980.90 �0.256 �0.254 �0.057 1266.8 635.3 �21.6 �21.3 �71.30.4932 0.4125 984.58 �0.249 �0.249 �0.053 1268.4 631.3 �25.1 �25.1 �71.70.5327 0.3709 992.49 �0.239 �0.238 �0.048 1267.6 627.1 �21.7 �22.6 �70.50.5409 0.3508 994.94 �0.235 �0.235 �0.047 1266.1 627.0 �17.5 �18.7 �69.60.5666 0.3272 999.75 �0.226 �0.226 �0.044 1265.7 624.4 �15.9 �17.6 �69.10.5922 0.2946 1005.1 �0.215 �0.215 �0.038 1264.5 622.2 �11.9 �13.7 �68.00.6123 0.2705 1009.2 �0.205 �0.205 �0.033 1264.2 620.0 �9.5 �11.0 �67.20.6323 0.2504 1013.0 �0.195 �0.195 �0.028 1264.4 617.5 �8.3 �9.2 �66.70.6578 0.2337 1017.0 �0.184 �0.184 �0.025 1264.9 614.5 �8.8 �9.2 �66.70.6906 0.2138 1022.1 �0.169 �0.169 �0.023 1265.5 611.0 �9.5 �9.6 �66.70.7021 0.2067 1023.8 �0.164 �0.164 �0.022 1265.6 609.8 �9.7 �9.7 �66.70.7212 0.1898 1027.1 �0.153 �0.153 �0.018 1266.2 607.3 �9.3 �8.2 �66.40.7587 0.1687 1032.6 �0.136 �0.135 �0.017 1266.5 603.8 �9.9 �9.0 �66.40.7885 0.1483 1037.1 �0.121 �0.119 �0.014 1266.8 600.9 �9.7 �8.3 �66.30.8199 0.1298 1041.5 �0.105 �0.102 �0.013 1266.6 598.5 �9.5 �8.6 �66.2

o-Chlorotoluene (i) + tetrahydropyran (j) + cyclohexane (k) T/K = 298.150.0823 0.8445 889.62 0.030 0.026 �0.049 1269.3 697.7 �3.5 �3.5 �85.00.0907 0.8302 890.87 0.030 0.029 �0.054 1269.3 696.7 �3.9 �3.8 �84.70.1098 0.7956 893.42 0.034 0.032 �0.064 1269.1 695.0 �4.5 �4.5 �83.80.1278 0.7651 896.04 0.037 0.037 �0.073 1269.0 693.0 �5.1 �5.1 �82.90.1424 0.7406 898.17 0.040 0.039 �0.080 1268.9 691.5 �5.5 �5.5 �82.20.1601 0.7168 901.43 0.041 0.047 �0.086 1269.1 688.8 �6.2 �6.2 �81.50.1701 0.7002 902.87 0.044 0.048 �0.091 1269.1 687.7 �6.5 �6.4 �80.90.1813 0.6812 904.44 0.048 0.048 �0.096 1268.9 686.7 �6.7 �6.8 �80.30.2001 0.6601 908.30 0.050 0.056 �0.101 1269.4 683.2 �7.5 �7.5 �79.70.2154 0.6354 910.54 0.055 0.054 �0.107 1269.3 681.6 �7.8 �7.9 78.90.2310 0.6172 913.62 0.057 0.058 �0.111 1269.7 678.9 �8.4 �8.4 �78.30.2501 0.5932 917.18 0.060 0.059 �0.116 1270.0 676.0 �8.9 �9.0 �77.60.2704 0.5712 921.32 0.062 0.062 �0.119 1270.5 672.4 �9.6 �9.6 �76.90.3309 0.5022 933.19 0.058 0.055 �0.130 1271.9 662.4 �11.2 �11.2 �74.90.3556 0.4802 938.66 0.056 0.054 �0.130 1272.8 657.7 �11.8 �11.8 �74.40.3703 0.4673 941.92 0.054 0.052 �0.131 1273.4 654.8 �12.2 �12.2 �74.00.3872 0.4534 945.75 0.052 0.050 �0.130 1274.0 651.5 �12.5 �12.5 �73.70.4005 0.4409 948.59 0.049 0.047 �0.130 1274.5 649.0 �12.8 �12.8 �73.40.4203 0.4219 952.76 0.042 0.041 �0.131 1275.1 645.6 �13.1 �13.1 �72.90.4404 0.4065 957.39 0.038 0.037 �0.129 1276.0 641.5 �13.5 �13.5 �72.60.4627 0.3865 962.19 0.029 0.029 �0.129 1276.8 637.6 �13.7 �13.7 �72.10.4943 0.3642 969.58 0.022 0.022 �0.124 1278.3 631.2 �14.1 �14.1 �71.60.5232 0.3421 976.10 0.013 0.012 �0.120 1279.5 625.8 �14.2 �14.3 �71.10.6357 0.2684 1002.3 �0.016 �0.018 �0.093 1285.1 604.1 �13.9 �14.0 �69.30.6673 0.2471 1009.5 �0.025 �0.027 �0.085 1286.6 598.4 �13.5 �13.5 �68.70.6981 0.2290 1016.7 �0.033 �0.033 �0.075 1288.3 592.7 �13.0 �13.0 �68.00.7195 0.2198 1022.0 �0.039 �0.034 �0.065 1289.6 588.3 �12.6 �12.5 �67.60.7465 0.1990 1027.7 �0.044 �0.041 �0.059 1290.7 584.1 �11.9 �11.8 �67.0

T/K = 303.150.0823 0.8445 884.57 0.024 0.021 �0.051 1246.9 727.2 �4.2 �4.0 �87.60.0907 0.8302 885.81 0.025 0.023 �0.055 1246.9 726.1 �4.6 �4.4 �87.30.1098 0.7956 888.35 0.031 0.030 �0.066 1246.8 724.1 �5.3 �5.2 �86.50.1278 0.7651 890.96 0.035 0.035 �0.075 1246.8 722.1 �5.9 �5.9 �85.70.1424 0.7406 893.09 0.039 0.040 �0.082 1246.8 720.3 �6.4 �6.5 �85.10.1601 0.7168 896.36 0.039 0.040 �0.089 1247.1 717.3 �7.2 �7.1 �84.40.1701 0.7002 897.81 0.042 0.044 �0.093 1247.1 716.2 �7.5 �7.5 �83.90.1813 0.6812 899.38 0.046 0.048 �0.099 1247.1 715.0 �7.8 �7.9 �83.40.2001 0.6601 903.28 0.044 0.045 �0.103 1247.6 711.3 �8.6 �8.5 �82.70.2154 0.6354 905.52 0.048 0.051 �0.110 1247.6 709.5 �9.0 �9.1 �82.00.2310 0.6172 908.63 0.049 0.050 �0.114 1247.9 706.7 �9.5 �9.6 �81.50.2501 0.5932 912.20 0.050 0.051 �0.119 1248.3 703.5 �10.1 �10.2 �80.70.2704 0.5712 916.38 0.049 0.049 �0.122 1248.9 699.7 �10.8 �10.8 �80.00.3309 0.5022 928.23 0.049 0.049 �0.133 1250.7 688.8 �12.6 �12.7 �77.9

246 V.K. Sharma et al. / J. Chem. Thermodynamics 78 (2014) 241–253

0.3556 0.4802 933.71 0.045 0.044 �0.134 1251.6 683.7 �13.2 �13.3 �77.20.3703 0.4673 936.98 0.042 0.041 �0.134 1252.2 680.6 �13.6 �13.6 �76.90.3872 0.4534 940.83 0.039 0.037 �0.133 1253.0 677.0 �14.0 �14.0 �76.40.4005 0.4409 943.66 0.037 0.035 �0.134 1253.6 674.4 �14.3 �14.3 �76.10.4203 0.4219 947.79 0.035 0.034 �0.134 1254.4 670.6 �14.7 �14.7 �75.50.4404 0.4065 952.43 0.030 0.029 �0.132 1255.4 666.2 �15.1 �15.0 �75.00.4627 0.3865 957.18 0.027 0.027 �0.132 1256.4 661.9 �15.4 �15.4 �74.50.4943 0.3642 964.59 0.018 0.018 �0.127 1258.1 655.0 �15.8 �15.8 �73.80.5232 0.3421 971.09 0.012 0.012 �0.123 1259.5 649.2 �16.0 �16.0 �73.10.6357 0.2684 997.33 �0.019 �0.019 �0.095 1265.5 626.1 �15.4 �15.5 �70.80.6673 0.2471 1004.48 �0.026 �0.026 �0.087 1267.2 620.0 �14.9 �15.0 �70.10.6981 0.229 1011.70 �0.035 �0.035 �0.076 1269.0 613.9 �14.3 �14.3 �69.50.7195 0.2198 1017.12 �0.046 �0.048 �0.066 1270.3 609.2 �13.8 �13.6 �69.00.7465 0.199 1022.74 �0.047 �0.047 �0.060 1271.6 604.7 �13.1 �13.0 �68.4

T/K = 308.150.0823 0.8445 879.49 0.018 0.016 �0.052 1224.7 758.0 �4.6 �4.4 �90.30.0907 0.8302 880.73 0.020 0.017 �0.056 1224.9 756.8 �5.1 �4.8 �89.90.1098 0.7956 883.25 0.028 0.027 �0.067 1224.9 754.6 �5.9 �5.8 �89.10.1278 0.7651 885.87 0.033 0.034 �0.077 1225.0 752.2 �6.7 �6.7 �88.30.1424 0.7406 887.99 0.038 0.040 �0.084 1225.1 750.3 �7.3 �7.4 �87.60.1601 0.7168 891.28 0.036 0.032 �0.090 1225.4 747.1 �8.1 �7.8 �86.90.1701 0.7002 892.74 0.039 0.039 �0.095 1225.4 745.9 �8.4 �8.3 �86.40.1813 0.6812 894.30 0.044 0.048 �0.101 1225.4 744.6 �8.7 �9.1 �85.90.2001 0.6601 898.25 0.037 0.034 �0.105 1225.9 740.8 �9.5 �9.2 �85.20.2154 0.6354 900.48 0.044 0.047 �0.112 1226.0 738.9 �9.9 �10.2 �84.50.2310 0.6172 903.62 0.040 0.041 �0.116 1226.3 735.9 �10.4 �10.5 �83.90.2501 0.5932 907.20 0.040 0.042 �0.121 1226.8 732.4 �11.1 �11.2 �83.10.2704 0.5712 911.41 0.036 0.036 �0.125 1227.4 728.4 �11.7 �11.7 �82.40.3309 0.5022 923.24 0.040 0.043 �0.136 1229.5 716.5 �13.8 �14.1 �80.20.3556 0.4802 928.75 0.033 0.034 �0.136 1230.6 711.0 �14.5 �14.6 �79.50.3703 0.4673 932.02 0.030 0.030 �0.137 1231.3 707.7 �14.9 �14.9 �79.10.3872 0.4534 935.89 0.025 0.023 �0.136 1232.1 703.8 �15.3 �15.2 �78.70.4005 0.4409 938.70 0.025 0.024 �0.136 1232.8 700.9 �15.7 �15.6 �78.30.4203 0.4219 942.80 0.028 0.028 �0.137 1233.9 696.7 �16.3 �16.3 �77.70.4404 0.4065 947.44 0.022 0.021 �0.135 1234.9 692.1 �16.6 �16.5 �77.20.4627 0.3865 952.15 0.025 0.025 �0.134 1236.3 687.2 �17.2 �17.2 �76.60.4943 0.3642 959.58 0.014 0.014 �0.129 1238.0 680.0 �17.5 �17.5 �75.90.5232 0.3421 966.06 0.011 0.012 �0.125 1239.7 673.5 �17.8 �17.8 �75.20.6357 0.2684 992.35 �0.023 �0.022 �0.097 1246.2 648.9 �17.0 �17.1 �72.80.6673 0.2471 999.49 �0.029 �0.026 �0.089 1248.1 642.3 �16.5 �16.7 �72.10.6981 0.2290 1006.7 �0.040 �0.040 �0.078 1249.8 635.9 �15.7 �15.7 �71.40.7195 0.2198 1012.2 �0.055 �0.053 �0.068 1251.1 631.2 �14.9 �14.4 �71.00.7465 0.1990 1017.8 �0.051 �0.056 �0.061 1252.6 626.2 �14.2 �13.9 �70.3

Standard uncertainties u are u(xi) = ±1 � 10�4, u(q) = ±0.5 kg �m�3, u(u) = ±0.1 m � s�1, u(VE) = 0.1%, u(P) = ±100 Pa.

V.K. Sharma et al. / J. Chem. Thermodynamics 78 (2014) 241–253 247

mixtures may be due to high dipole moment of NMF (l = 3.86) orDMF (l = 3.24) [10] which leads to strong molecular interactions inmixtures containing NMF or DMF.

5. Graph theory

5.1. Excess molar volumes and excess isentropic compressibilities ofternary mixtures

The analysis of excess molar volumes, VE; excess molar enthal-pies, HEand IR spectral data of o-CT (i) + THP or NMF or DMF (j); or(THP (i) + cyclohexane (j)) mixtures has suggested that while pureo-CT or NMF or DMF exist as associated molecular entities; THP ischaracterized by (dipole-dipole) interactions and cyclohexaneexists as monomer [43,44,17].

The addition of NMF or DMF (k) to o-CT (i) + THP (j) results ino-CT (i) + THP (j) + NMF or DMF (k) ternary mixtures formation.The o-CT (i) + THP (j) + NMF or DMF (k) mixtures formation maybe assumed to be comprised of processes; (i) formation of unlike(a) in � jn (n = 2); (b) jn � kn(n = 2); and (c) in � kn (n = 2) contactsamong the constituent molecules; (ii) unlike contact formationleads to breakdown of (a) in; (b) jn; and (c) kn associated entitiesto give (i), (j) and (k) molecules; and (iii) interactions between

(i), (j) and (k) molecules lead to the formation of (a) i:j (b) j:k (c)i:k molecular complexes. If vij;vjkvik are molar volumes and molarcompressibilities interaction parameters of unlike in � jn, jn � kn

and in � kn contacts, then change in molar properties (DX = V orjS) due to processes (i) (a) to (c) were given by [51–57]

ðDXÞ1 ¼xixj

3ni=3nj

� �xi þ xj

3ni=3nj� �

" #½vij� þ

xjxk3nj=

3nk

� �xj þ xk

3nj=3nk� �

" #½vjk�

þxixk

3ni=3nk

� �xi þ xk

3ni=3nkð Þ

� �½vik�; ð12Þ

where (3ni) (i = i or j or k) denote the connectivity parameters ofthird degree of i or j or k molecules and defined [58] by

3n ¼X

m<n<o<p

ðdmmdm

ndmod

mp�0:5

; ð13Þ

where dvm, etc. reflect the valency [59a] of mth vertex in molecular

graph of a molecule and can be determined by using relation[59b]: dm

m = Zm � hm; where Zm represent the maximum valency ofconstituent atoms and hm is the number of hydrogen atomsattached to it.

Also, if viivjj;vkk;v12;v=12 and v==12 are the molar volumes and

compressibilities interaction parameters for breakdown of in, jn,

TABLE 4Measured densities, q, excess molar volumes VE, speeds of sound, u, isentropiccompressibilities, jS and excess isentropic compressibilities, jE

S data for the studied(i + j) mixtures as a function of mole fraction, xi, of component (i) at T/K = (298.15,303.15, 308.15) and 0.1 MPa.

xi q/kg �m�3VE/cm3 �mol�1 u/m � s�1 jS/TPa�1 jE

S/TPa�1

o-Chlorotoluene (i) + cyclohexane (j) T/K = 298.150.1098 808.15 0.200 1251.3 790.4 �2.00.1437 818.67 0.248 1251.0 780.5 �2.70.1987 835.72 0.309 1251.1 764.4 �3.80.2356 847.14 0.341 1251.5 753.7 �4.40.2874 863.12 0.376 1252.4 738.6 �5.40.3256 874.88 0.393 1253.4 727.6 �6.10.3876 893.92 0.407 1255.3 709.9 �6.90.4135 901.85 0.409 1256.2 702.6 �7.10.4834 923.20 0.401 1259.3 683.0 �7.80.5243 935.64 0.391 1261.4 671.8 �7.90.5763 951.42 0.368 1264.3 657.6 �7.90.6143 962.90 0.349 1266.5 647.4 �7.70.6654 978.29 0.316 1269.9 633.9 �7.40.7154 993.29 0.279 1273.4 620.8 �6.90.7654 1008.2 0.237 1277.2 608.0 �6.10.8165 1023.4 0.192 1281.3 595.1 �5.10.8324 1028.1 0.176 1282.6 591.2 �4.60.8965 1047.1 0.112 1288.4 575.3 �3.1

T/K = 303.150.1098 803.38 0.199 1227.6 825.9 �2.50.1437 813.90 0.245 1227.7 815.2 �3.30.1987 830.93 0.306 1228.2 797.8 �4.70.2356 842.33 0.337 1228.8 786.3 �5.50.2874 858.30 0.372 1230.0 770.1 �6.50.3256 870.06 0.389 1231.2 758.2 �7.20.3876 889.08 0.403 1233.6 739.1 �8.20.4135 897.01 0.405 1234.8 731.1 �8.70.4834 918.34 0.398 1238.4 710.1 �9.30.5243 930.78 0.386 1240.7 697.9 �9.50.5763 946.54 0.364 1244.0 682.7 �9.60.6143 958.02 0.345 1246.6 671.7 �9.40.6654 973.40 0.314 1250.3 657.2 �9.10.7154 988.40 0.277 1254.3 643.1 �8.50.7654 1003.3 0.236 1258.4 629.4 �7.60.8165 1018.5 0.190 1262.9 615.6 �6.50.8324 1023.2 0.175 1264.3 611.4 �6.00.8965 1042.2 0.112 1270.3 594.7 �4.0

T/K = 308.150.1098 798.58 0.198 1204.7 862.8 �3.60.1437 809.09 0.242 1205.0 851.2 �4.60.1987 826.11 0.303 1205.9 832.5 �6.10.2356 837.50 0.335 1206.7 820.1 �6.90.2874 853.47 0.368 1208.1 802.8 �8.00.3256 865.22 0.383 1209.5 790.1 �8.70.3876 884.22 0.398 1212.2 769.7 �9.70.4135 892.15 0.399 1213.4 761.3 �10.00.4834 913.47 0.392 1217.4 738.7 �10.70.5243 925.90 0.381 1220.0 725.6 �10.90.5763 941.65 0.361 1223.6 709.3 �11.00.6143 953.13 0.341 1226.5 697.4 �10.90.6654 968.50 0.311 1230.7 681.7 �10.60.7154 983.48 0.276 1235.0 666.7 �10.00.7654 998.42 0.235 1239.6 651.9 �9.10.8165 1013.6 0.189 1244.4 637.1 �7.90.8324 1018.3 0.174 1246.0 632.6 �7.40.8965 1037.3 0.111 1252.3 614.7 �5.2

Tetrahydropyran (i) + cyclohexane (j) T/K = 298.150.0987 782.47 0.126 1251.6 815.8 5.10.1432 786.46 0.170 1250.7 812.9 7.50.1876 790.51 0.209 1249.8 809.8 9.50.2378 795.20 0.244 1249.0 806.2 11.70.2791 799.14 0.265 1248.5 802.8 13.20.3165 802.76 0.283 1248.1 799.6 14.40.3782 808.86 0.301 1247.9 793.9 15.90.4237 813.45 0.309 1248.0 789.3 16.50.4521 816.36 0.311 1248.3 786.1 16.70.4982 821.15 0.310 1248.8 780.9 16.80.5318 824.70 0.305 1249.5 776.7 16.60.5643 828.18 0.300 1250.2 772.5 16.2

TABLE 4 (continued)

xi q/kg �m�3VE/cm3 �mol�1 u/m � s�1 jS/TPa�1 jE

S/TPa�1

0.5918 831.15 0.293 1251.0 768.8 15.70.6236 834.62 0.283 1252.0 764.4 15.00.6982 842.94 0.252 1254.8 753.4 12.70.7341 847.03 0.231 1256.4 748.0 11.50.7949 854.07 0.193 1259.3 738.3 8.90.8632 862.20 0.138 1262.9 727.3 5.8

T/K = 303.150.0987 777.69 0.130 1226.7 854.5 6.20.1432 781.65 0.175 1225.6 851.7 9.00.1876 785.69 0.214 1224.6 848.7 11.60.2378 790.36 0.248 1223.6 845.1 14.20.2791 794.28 0.272 1223.0 841.7 15.90.3165 797.88 0.289 1222.6 838.5 17.30.3782 803.96 0.307 1222.4 832.5 19.00.4237 808.53 0.315 1222.5 827.6 19.90.4521 811.43 0.317 1222.7 824.3 20.00.4982 816.20 0.316 1223.3 818.7 20.20.5318 819.74 0.312 1224.0 814.2 19.90.5643 823.20 0.305 1224.9 809.6 19.30.5918 826.17 0.297 1225.7 805.7 18.80.6236 829.63 0.287 1226.8 800.8 17.90.6982 837.92 0.255 1230.0 788.9 15.30.7341 841.99 0.235 1231.7 782.9 13.70.7949 849.02 0.195 1235.0 772.3 10.70.8632 857.11 0.140 1238.9 760.1 7.1

T/K = 308.150.0987 772.88 0.133 1202.3 895.1 7.50.1432 776.83 0.179 1201.0 892.5 10.80.1876 780.84 0.219 1199.8 889.6 13.80.2378 785.49 0.255 1198.7 886.1 16.90.2791 789.39 0.277 1197.8 882.9 19.20.3165 792.98 0.294 1197.3 879.6 21.00.3782 799.03 0.314 1197.0 873.5 23.10.4237 803.59 0.321 1197.1 868.4 23.90.4521 806.48 0.323 1197.4 864.9 24.20.4982 811.24 0.320 1198.1 858.8 24.30.5318 814.76 0.316 1198.9 854.0 23.90.5643 818.21 0.310 1199.9 848.9 23.20.5918 821.16 0.302 1200.8 844.6 22.50.6236 824.61 0.292 1202.1 839.3 21.50.6982 832.88 0.258 1205.6 826.0 18.20.7341 836.93 0.239 1207.7 819.2 16.10.7949 843.94 0.198 1211.4 807.5 12.40.8632 852.00 0.142 1215.8 794.0 8.1

Standard uncertainties u are u(xi) = ±1 � 10�4, u(q) = ±0.5 kg �m�3, u(u) = ±0.1 m � s�1,u(VE) = 0.1%, u(P) = ±100 Pa.

248 V.K. Sharma et al. / J. Chem. Thermodynamics 78 (2014) 241–253

kn associated entities and interactions among the constituent mol-ecules in mixed state, then change in thermodynamic properties,DX(X = V or jS), due to processes (ii) (a) to (c) and (iii) (a) to (c)were expressed [51–57] by

ðDXÞ2 ¼x2

i xjð3ni=3njÞ

xi þ xjð3ni=3njÞ

� �½vii� þ

x2j xkð3nj=

3nkÞxj þ xkð3nj=3nkÞ

" #½vjj�

þ x2kxið3nk=

3niÞxk þ xið3nk=3niÞ

� �½vkk�; ð14Þ

ðDXÞ3 ¼xix2

j ð3ni=3njÞ

xi þ xjð3ni=3njÞ

" #½v12� þ

xjx2kð3nj=

3nkÞxj þ xkð3nj=3nkÞ

� �½v=12�

þ xkx2i ð3nk=

3niÞxk þ xið3n3=3n1Þ

� �½v==12�: ð15Þ

The thermodynamics properties, XEijk (X = V or jS) due to pro-

cesses (i) to (iii) were then given by

TABLE 5Ternary adjustable parameters XðnÞijk (X = V or jS; n = 0 to 2) of equation (8) along withstandard deviations, rðXEÞðX ¼ V or jSÞ of VE

ijk and ðjESÞijk at T/K = (298.15, 303.15,

308.15).

Parameters T/K

298.15 303.15 308.15

o-Chlorotoluene (i) + tetrahydropyran (j) + N-methylformamide (k)

V ð0Þijk�22.467 �24.111 �25.028

V ð1Þijk325.099 350.600 339.033

V ð2Þijk�1304.036 �1410.432 �1281.547

rðVEijkÞ=cm3 �mol�1 0.001 0.001 0.001

ðjð0ÞS Þijk �319.7 �340.4 �439.8

ðjð1ÞS Þijk 544.8 1609.2 2695.3

ðjð2ÞS Þijk 1371.7 �5481.5 �8454.6

rðjESÞijk/T � Pa�1 0.1 0.1 0.1

o-Chlorotoluene (i) + tetrahydropyran (j) + N,N-dimethylformamide (k)

V ð0Þijk�4.038 �3.353 �2.428

V ð1Þijk�12.974 �6.474 1.409

V ð2Þijk4.781 �17.955 �43.683

rðVEijkÞ=cm3 �mol�1 0.001 0.001 0.001

ðjð0ÞS Þijk 778.0 827.0 874.5

ðjð1ÞS Þijk 4082.2 4094.0 4125.4

ðjð2ÞS Þijk �60647.8 �62861.5 �64531.1

rðjESÞijk/T � Pa�1 0.1 0.1 0.1

o-Chlorotoluene (i) + tetrahydropyran (j) + cyclohexane (k)

V ð0Þijk�3.065 �2.015 �0.885

V ð1Þijk�52.770 6.389 63.605

V ð2Þijk681.034 70.209 �523.432

rðVEijkÞ=cm3 �mol�1 0.001 0.001 0.001

ðjð0ÞS Þijk �48.4 �78.5 �142.7

ðjð1ÞS Þijk �1102.5 �2166.1 �4334.2

ðjð2ÞS Þijk 8985.3 18306.4 39572.8

rðjESÞijk/T � Pa�1 0.1 0.1 0.1

TABLE 6Binary adjustable parameters, Xn (X = V or jS; n = 0 to 2) of equation (9) along withtheir standard deviations, rðXEÞðX ¼ V or jSÞ of VE and jE

S at T/K = (298.15, 303.15,308.15).

Parameters T/K

298.15 303.15 308.15

Tetrahydropyran (i) + cyclohexane (j)V(0) 1.237 1.260 1.283V(1) �0.151 �0.164 �0.179V(2) 0.089 0.096 0.096

rðVEÞ=cm3 �mol�1 0.001 0.001 0.001

jð0ÞS67.1 80.5 97.0

jð1ÞS�7.3 �9.3 �12.9

jð2ÞS�23.1 �26.9 �37.3

rðjESÞ/T � Pa�1 0.1 0.1 0.1

o-Chlorotoluene (i) + cyclohexane (j)V(0) 1.590 1.573 1.554V(1) �0.539 �0.529 �0.520V(2) 0.067 0.081 0.096

rðVEÞ=cm3 �mol�1 0.001 0.001 0.001

jð0ÞS�31.3 �37.6 �43.1

jð1ÞS�8.4 �11.3 �11.6

jð2ÞS7.5 4.6 �5.3

rðjESÞ/T � Pa�1 0.1 0.1 0.1

FIGURE 1. Excess molar volumes, VEijk, for (o-chlorotoluene (i) + tetrahydropyran

(j) + N-methylformamide (k)) ternary mixture at T = 298.15 K and 0.1 MPa,( ), the experimental data in front of the plane; (———————), theexperimental data behind the plane.

FIGURE 2. Excess molar volumes, VEijk, for (o-chlorotoluene (i) + tetrahydropyran

(j) + N,N-dimethylformamide (k)) ternary mixture at T = 298.15 K and 0.1 MPa,( ), the experimental data in front of the plane; (———————), theexperimental data behind the plane.

V.K. Sharma et al. / J. Chem. Thermodynamics 78 (2014) 241–253 249

XEijk ¼

xixjð3ni=3njÞ

xi þ xjð3ni=3njÞ

� �½vij þ xivii þ xjv12�

þ xjxkð3nj=3nkÞ

xj þ xkð3nj=3nkÞ

� �½vjk þ xjvjj þ xkv=12�

þ xkxið3nk=3niÞ

xk þ xið3nk=3niÞ

� �½vik þ xkvkk þ xiv==12�: ð16Þ

For the present o-CT (i) + THP (j) + NMF or DMF (k) mixtures,we assumed that vij ffi v12 ¼ v�ij; vjk ffi v=12 ¼ v�jk; vik ffi v==12 ¼ v�ik;

vii ffi vjj ffi vkk ¼ v�; equation (16) was, therefore, reduced to

XEijk ¼

xixjð3ni=3njÞ

xi þ xjð3ni=3njÞ

� �½ð1þ xjÞv�ij þ xiv��

þ xjxkð3nj=3nkÞ

xj þ xkð3nj=3nkÞ

� �½ð1þ xkÞv�jk þ xjv��

þ xkxið3nk=3niÞ

xk þ xið3nk=3niÞ

� �½ð1þ xiÞv�ik þ xkv��: ð17Þ

FIGURE 3. Excess molar volumes, VEijk , for (o-chlorotoluene (i) + tetrahydropyran

(j) + cyclohexane (k)) ternary mixture at T = 298.15 K and 0.1 MPa, ( ), theexperimental data in front of the plane; (———————), the experimental databehind the plane.

FIGURE 4. Excess isentropic compressibilities, ðjESÞijk, for (o-chlorotoluene (i) + tet-

rahydropyran (j) + N-methylformamide (k)) ternary mixture at T = 298.15 K and0.1 MPa, ( ), the experimental data in front of the plane; (———————), theexperimental data behind the plane.

FIGURE 5. Excess isentropic compressibilities, ðjESÞijk , for (o-chlorotoluene (i) + tet-

rahydropyran (j) + N,N-dimethylformamide (k)) ternary mixture at T = 298.15 K and0.1 MPa, ( ), the experimental data in front of the plane; (———————), theexperimental data behind the plane.

FIGURE 6. Excess isentropic compressibilities, ðjESÞijk , for (o-chlorotoluene (i) + tet-

rahydropyran (j) + cyclohexane (k)) ternary mixture at T = 298.15 K and 0.1 MPa,( ), the experimental data in front of the plane; (———————), theexperimental data behind the plane.

250 V.K. Sharma et al. / J. Chem. Thermodynamics 78 (2014) 241–253

For (o-CT (i) + THP (j) + cyclohexane (k)) mixture, as cyclohex-ane (k) exists as monomer, the interaction energy, vkk would bezero. Consequently, thermodynamic properties XE

ijk (X = V or jS)for (o-CT (i) + THP (j) + cyclohexane (k)) mixture were, therefore,expressed by equation (18)

XEijk ¼

xixjð3ni=3njÞ

xi þ xjð3ni=3njÞ

� �½vij þ xivii þ xjv12�

þ xjxkð3nj=3nkÞ

xj þ xkð3nj=3nkÞ

� �½vjk þ xjvjj þ xkv=12�

þ xkxið3nk=3niÞ

xk þ xið3nk=3niÞ

� �½vik þ xiv==12�: ð18Þ

For the (o-CT (i) + THP (j) + cyclohexane (k)) mixture, itwas assumed that; vij ffi v12 ¼ v�ij; vjk ffi v=12 ¼ v�jk; vik ffi v==12 ¼ v�ik;

vii ffi vjj ¼ v�; equation (18) was, therefore, expressed by

XEijk ¼

xixjð3ni=3njÞ

xi þ xjð3ni=3njÞ

� �½ð1þ xjÞv�ij þ xiv��

þ xjxkð3nj=3nkÞ

xj þ xkð3nj=3nkÞ

� �½ð1þ xkÞv�jk þ xjv��

þ xkxið3nk=3niÞ

xk þ xið3nk=3niÞ

� �½ð1þ xiÞv�ik�: ð19Þ

Four unknown v�ij;v�jk;v�ik;v� parameters in equations (17) and(19) were evaluated by using VE

ijk and ðjESÞijk data at four arbitrary

compositions. The resulting parameters were then used to computeXE

ijk (X = V or jS) data at various compositions. The calculated XEijk

(X = V or jS) values for the studied mixtures are reported and com-pared with experimental values in table 3. The (3ni) (i = i or j or k)etc. parameters for various liquids along with v�ij etc. parametersand deviation between experimental values and values calculatedfrom Graph theory are recorded in table 7. A perusal of data in table3 reveal that XE

ijk (X = V or jS) values predicted from Graph theoryare in agreement with the corresponding experimental values.The comparison between theoretical and experimental values indi-cates that there is a rupture of associated entities o-CT, THP or NMF

FIGURE 7. Densities, q of (tetrahydropyran (i) + cyclohexane (j)) mixture atT = 298.15 K; experimental ( ); Brocos et al. ( ); Inglese et al. ( ); T = 308.15 Kand 0.1 MPa; experimental ( ); Brocos et al. ( ) Siwach et al. ( ).

FIGURE 8. Speeds of sound, u of (tetrahydropyran (i) + cyclohexane (j)) mixture atT = 308.15 K and 0.1 MPa; experimental ( ); Siwach et al., ( ).

FIGURE 9. Excess molar volumes, VE, for (o-chlorotoluene (i) + cyclohexane (j))mixture at T = 298.15 K experimental ( ), Mahl et al. ( ); and T = 308.15 Kand 0.1 MPa; experimental ( ), Mahl et al. ( ).

IGURE 10. Excess molar volumes, VE, for (tetrahydropyran (i) + cyclohexane (j))ixture at T = 298.15 K; experimental ( ); Brocos et al. ( ); Inglese et al.

); T = 308.15 K and 0.1 MPa; experimental ( ); Brocos et al. ( )iwach et al. ( ).

V.K. Sharma et al. / J. Chem. Thermodynamics 78 (2014) 241–253 251

Fm(S

FIGURE 11. Excess isentropic compressibilities, jES , for (tetrahydropyran (i) + cyclo-

hexane (j)) mixture at T = 308.15 K and 0.1 MPa; experimental ( ); Siwach et al.( ).

or DMF and formation of i:j; j:k; i:k complexes due to interactionsamong the constituent molecules. The cumulative effect of thesecontributions leads to VE

ijk and ðjESÞijk of the present mixtures.

6. Prigogine–Flory–Patterson (PFP) theory

6.1. Excess molar volumes

According to this theory [60], excess molar volumes, for(i + j + k) ternary mixture, are assumed to be comprised of three

contributions, namely, (i) an interactional contribution VEint

� �ijk

;

(ii) free volume contribution VEfv

� �ijk

; and (iii) internal pressure

contribution VEP�

� �ijk

; and are given by

VEijk ¼ VE

int

� �ijkþ VE

fv

� �ijkþ VE

P�

� �ijk; ð20Þ

VEint

� �ijk¼

Xk

i¼i

xiv�i

" # Xk

i¼i

ð~v1=3 � 1Þ~v2=3wihjv��ijh i½ð4=3Þ~v�1=3 � 1�~v

24

35; ð21Þ

252 V.K. Sharma et al. / J. Chem. Thermodynamics 78 (2014) 241–253

VEfv

� �ijk¼

Xk

i¼i

xiv�i

" # Xj or k or i

i¼i or j or k

ð~v i � ~v jÞ2fð14=9Þ~v�1=3 � 1gh i" #

�Xk

i¼i

wiwj

½ð4=3Þ~v�1=3 � 1�~v

" #; ð22Þ

VEP�

� �ijk¼

Xk

i¼i

xiv�i

" # Xj or k or i

i¼i or j or k

ð~v i � ~v jÞðP�i � P�j Þwiwj

ðP�i wj � P�j wiÞ

" #; ð23Þ

where xi, /iv�i ; ~v i, P�i , wi, ~T i and hi (i = i or j or k) represent the molefraction, hard-core volume fraction, characteristic volume, reducedvolume, characteristic pressure, molecular contact energy fraction,reduced temperature, molecular surface fraction of component (i)and parameters ~v , P�; are the reduced volume, characteristic pres-sure, reduced temperature for the (i + j + k) mixture and have thesame significance as described elsewhere [61,62].

TABLE 7Interaction energy parameters v�ij;v�jk ;v�ik;v� of equations (17) and (19) along withconnectivity parameters of third degree of a molecule, (3ni) = (3ni)m (i = i or j or k)utilized in Graph theory for the determination of VE

ijk and ðjESÞijk and deviations

between experimental values and values obtained from Graph theory at T/K =(298.15, 303.15, 308.15).

Parameters T/K

298.15 303.15 308.15

o-Chlorotoluene (i) + tetrahydropyran (j) + N-methylformamide (k)(3ni) = (3ni)m 1.331 1.331 1.331(3nj) = (3nj)m 1.101 1.101 1.101(3nk) = (3nk)m 1.090 1.090 1.090v�ij/cm3 �mol�1 7.833 8.508 8.582

v�jk/cm3 �mol�1 5.801 6.335 6.084

v�ik/cm3 �mol�1 3.803 4.121 4.155v�/cm3 �mol�1 �28.411 �30.784 �30.752

rðVEijkÞ=cm3 �mol�1 0.008 0.009 0.008

v�ij/T � Pa�1 �1.6 9.5 44.3

v�jk/T � Pa�1 60.4 66.8 85.1

v�ik/T � Pa�1 56.3 69.5 94.3v�/T � Pa�1 �171.4 �228.3 �355.3rðjE

SÞijk/T � Pa�1 1.0 0.6 0.7

o-Chlorotoluene (i) + tetrahydropyran (j) + N,N-dimethylformamide (k)(3ni) = (3ni)m 1.331 1.331 1.331(3nj) = (3nj)m 1.101 1.101 1.101(3nk) = (3nk)m 0.901 0.901 0.901v�ij/cm3 �mol�1 �1.062 �0.888 �0.642

v�jk/cm3 �mol�1 �0.341 �0.379 �0.443

v�ik/cm3 �mol�1 �0.905 �0.581 �0.118v�/cm3 �mol�1 1.311 0.853 0.196

rðVEijkÞ=cm3 �mol�1 0.004 0.003 0.001

v�ij/T � Pa�1 �123.6 �123.4 �127.5

v�jk/T � Pa�1 155.1 149.7 155.6

v�ik/T � Pa�1 60.3 80.4 81.4v�/T � Pa�1 �4.8 �23.4 �28.2rðjE

SÞijk/T � Pa�1 0.8 0.8 0.9

o-Chlorotoluene (i) + tetrahydropyran (j) + cyclohexane (k)(3ni) = (3ni)m 1.331 1.331 1.331(3nj) = (3nj)m 1.101 1.101 1.101(3nk) = (3nk)m 1.300 1.300 1.300v�ij/cm3 �mol�1 0.985 �0.356 �1.684

v�jk/cm3 �mol�1 �0.292 1.220 2.719

v�ik/cm3 �mol�1 �0.129 0.331 0.803v�/cm3 �mol�1 �1.624 �0.329 0.930

rðVEijkÞ=cm3 �mol�1 0.003 0.001 0.002

v�ij/T � Pa�1 �22.2 1.2 55.0

v�jk/T � Pa�1 56.4 27.8 �33.1

v�ik/T � Pa�1 �46.3 �58.5 �84.6v�/T � Pa�1 �35.6 �63.7 �119.6r ðjE

SÞijk/T � Pa�1 0.1 0.1 0.2

6.2. Excess isentropic compressibilities

According to PFP theory, isentropic compressibility, jS is given[35] by

jS ¼ �1V

@V@P

� �S; ð24Þ

where@V@P

� �S¼ @V

@P

� �Tþ TC�1

P@V@T

� �2

P; ð25Þ

and@V@P

� �T

¼ �~v7=3 þ 2~v2 � ~v5=3

4=3� ~v1=3

v�P�

1~T; ð26Þ

@V@T

� �P

¼~v4=3 � ~v

4=3� ~v1=3

v�T; ð27Þ

and excess isentropic compressibilties, jES is given by

jES ¼ jS � jid

S ; ð28Þ

where C�pi;~T are heat capacities of pure component and reduced

temperature for the (i + j + k) mixture respectively. The VEijk and

ðjESÞijk values could be evaluated by employing Flory’s parameters

of pure liquids along with interaction energy parameters, v��ij (i = ior j or k) etc. for (i + j), (j + k), (i + k) mixtures. The v��ij etc. parame-ters were determined by using excess molar enthalpies, HE values of(i + j) etc. mixtures [17,43,44,47,48,50] at xi = 0.5 using

HE ¼Xj

i¼i

xiP�i ðU

�1i � U�1

calÞ þ xiUihjv��ij U�1cal : ð29Þ

The parameters of pure components have been taken from liter-ature [16,35,43,44]. The calculated VE

ijk and ðjESÞijk are given in table

3. A perusal of data in table 3 suggest that PFP theory correctly pre-dicts the sign of VE

ijk of o-CT (i) + THP (j) + NMF or DMF (k); andðjE

SÞijk of o-CT (i) + THP (j) + DMF or cyclohexane (k) mixtures.However, quantitative agreement is poor. The v��ij etc. parametersalong with deviation between experimental values and values cal-culated from PFP theory are reported in table 8. The failure of the-ory to correctly predict the magnitude of VE

ijk and ðjESÞijk and sign of

TABLE 8Interaction energy parameters of appropriate equations of Prigogine–Flory–Patterson(PFP) theory and deviations between experimental values and values obtained fromPFP theory at T/K = (298.15, 303.15, 308.15).

Parameters T/K

298.15 303.15 308.15

o-Chlorotoluene (i) + tetrahydropyran (j) + N-methylformamide (k)v��ij /J � cm�3 �8.9 �8.9 �8.8

v��jk /J � cm�3 20.5 20.2 19.8

v��ik /J � cm�3 25.5 25.5 25.4

rðVEijkÞ=cm3 �mol�1 0.577 0.621 0.627

r ðjESÞijk/T � Pa�1 60.7 61.4 61.5

o-Chlorotoluene (i) + tetrahydropyran (j) + N,N-dimethylformamide (k)v��ij /J � cm�3 �8.9 �8.9 �8.8

v��jk /J � cm�3 29.5 29.0 28.4

v��ik /J � cm�3 26.1 26.1 26.0

rðVEijkÞ=cm3 �mol�1 0.188 0.169 0.153

r ðjESÞijk/T � Pa�1 57.1 58.2 59.2

o-Chlorotoluene (i) + tetrahydropyran (j) + cyclohexane (k)v��ij /J � cm�3 �8.9 �8.9 �8.8

v��jk /J � cm�3 26.5 26.0 25.5

v��ik /J � cm�3 21.5 21.2 20.8

rðVEijkÞ=cm3 �mol�1 0.138 0.134 0.130

r ðjESÞijk/T � Pa�1 66.0 66.7 67.9

V.K. Sharma et al. / J. Chem. Thermodynamics 78 (2014) 241–253 253

VEijk of o-CT (i) + THP (j) + cyclohexane (k); ðjE

SÞijk of o-CT (i) + THP(j) + NMF (k) mixture may be due to strong interactions amongthe studied mixtures.

7. Conclusion

Densities and speeds of sound data for the o-CT (i) + THP(j) + NMF or DMF or cyclohexane (k) and their sub-binary o-CT orTHP + cyclohexane mixtures are reported at temperatures(298.15, 303.15, 308.15) K and at 0.1 MPa. The VE

ijk and ðjESÞijk data

for the studied mixtures are calculated from the experimental val-ues. The VE

ijk of o-CT (i) + THP (j) + NMF or DMF (k) mixtures; andðjE

SÞijk of o-CT (i) + THP (j) + DMF or cyclohexane (k) mixtures arenegative over entire values of xi and xj. However, sign as well asmagnitude of VE

ijk values for o-CT (i) + THP (j) + cyclohexane (k)mixture; and ðjE

SÞijk values for o-CT (i) + THP (j) + NMF (k) mixtureare dictated by the relative proportion of components in the mixedstate. The thermodynamic properties have been analyzed in termsof (i) Graph; (ii) PFP theories. The results indicate that Graph the-ory correctly predicts the sign and magnitude of VE

ijk and ðjESÞijk val-

ues. The comparison between theoretical and experimental valuesindicates that there is a rupture of associated entities o-CT, THP orNMF or DMF and formation of i:j; j:k; i:k complexes due to inter-actions among the constituent molecules.

Acknowledgements

Rajni Dua is grateful to University Grants Commission (UGC),New Delhi for the award of Teacher fellowship. The authors arealso grateful to the Head, Department of Chemistry and authoritiesof M. D. University, Rohtak, for providing research facilities.

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JCT 14-217