J. Chem. Thermodynamics 43 (2011) 39–46

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J. Chem. Thermodynamics

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Excess molar volumes, excess molar enthalpies, and excess isentropiccompressibilities of tetrahydropyran with aromatic hydrocarbons

V.K. Sharma ⇑, Rajesh K. Siwach, DimpleDepartment of Chemistry, Maharshi Dayanand University, Rohtak 124001, Haryana, India

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

Article history:Received 2 January 2010Received in revised form 29 July 2010Accepted 30 July 2010Available online 11 August 2010

Keywords:Excess molar volumes, VE

Excess molar enthalpies, HE

Excess isentropic compressibilities, jES

Connectivity parameter of third degree, 3nInteraction parameter, v

0021-9614/$ - see front matter � 2010 Elsevier Ltd. Adoi:10.1016/j.jct.2010.07.016

⇑ Corresponding author. Tel.: +91 1262295012.E-mail address: v_sharmachem58@rediffmail.com

Excess molar volumes VE, excess molar enthalpies HE, and speeds of sound u, data of {tetrahydropyran(i) + benzene, or toluene, or o-, or p-, or m-xylene (j)} binary mixtures have been measured as a functionof composition at a temperature of 308.15 K. Speeds of sound data have been utilized to predict excessisentropic compressibilities, jE

S . VE, HE, and jES data for the investigated mixtures have been analyzed

in terms of the Graph theory which in turn deals with topology of the constituents of mixtures. An anal-ysis of VE data in terms of Graph theory suggests that these mixtures are characterized by interactionsbetween dipole of tetrahydropyran and p-electron cloud of aromatic ring of aromatic hydrocarbons toform 1:1 molecular complex. It has been observed that VE, HE, and jE

S values predicted by the Graph the-ory compare well with their corresponding experimental values.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Industry demands reliable and accessible reference data on thethermodynamic properties (excess molar volumes, excess molarenthalpies, and excess isentropic compressibilities) of a wide vari-ety of liquid mixtures. These properties not only provide reliabledata and empirical rules for science and technology, but also en-hance the understanding of the behavior of liquid mixtures. Cyclicethers are of technical importance as solvents. They are used asoxygenating agents in gasoline technology. The interactionsbetween cyclic ethers and linear or cyclic alkanes, or aromatichydrocarbons, or alkanols have been subject of many researchers[1–5]. In recent studies topology of the constituents of mixtureshave been utilized to (i) extract information about the state ofcomponents in pure and mixed state along with nature and extentof interactions operating among them and (ii) predict thermody-namic properties of binary and ternary mixtures [6–8]. In the pres-ent study, we report excess molar volumes VE, excess molarenthalpies HE, and speeds of sound data u, of {tetrahydropyran(i) + benzene, or toluene, or o-, or p-, or m-xylene (j)} binarymixtures. An attempt has also been made to predict thermody-namic properties excess molar volumes, VE, excess molar enthal-pies, HE, and excess isentropic compressibilities, jE

S , of thestudied binary mixtures.

ll rights reserved.

(V.K. Sharma).

2. Experimental

Tetrahydropyran (THP) (puriss P99%), benzene (puriss P99%),toluene (puriss P99%), and o-, p-, m-xylene (puriss P99%) werefrom Fluka and were purified by standard methods. The puritiesof the purified liquids were checked by measuring their densitiesusing pycknometer (recorded in table 1) at a temperature of298.15 ± 0.01 K and these agreed to with in ±0.05 kg �m�3 withtheir literature values [1,9]. Excess molar volumes, VE, for binary(i + j) mixtures were determined as a function of composition ina V-shaped dilatometer in the manner described elsewhere [10].The change in liquid level of dilatometer capillary was measuredwith a cathetometer that could read to ±0.001 cm. The uncertain-ties in the measured VE values are 0.5%.

Excess molar enthalpies, HE, for the studied mixtures weremeasured by 2-drop calorimeter (model, 4600) supplied by theCalorimetery Sciences Corporation (CSC), USA at a temperature of308.15 K in a manner described elsewhere [11]. The uncertaintiesin the measured HE values are 1%.

Speeds of sound, u, (at frequency 2 MHz) in binary mixtureswere measured using a variable path inteferometer (Model M 84,Mittal Enterprises, India) and a measuring cell. The measuring cellwas a specially designed cell in which water was circulatedthrough the cell to maintain the desired temperature. The speedsof sound values for the purified liquids at a temperature of(298.15 ± 0.01) K (recorded in table 1) compare well with their cor-responding experimental values [12–17]. The uncertainties in themeasured speeds of sound values are 1 m � s�1.

TABLE 1Comparison of densities q and speeds of sound u of pure liquids with their literaturevalues at a temperature of 298.15 K respectively.

Liquids u/(m � s�1) q/(kg �m�3)

Exp. Lit. Exp. Lit.

Tetrahydropyran 1272 1271.1 [12] 868.81a 868.82a [1]Benzene 1298 1298.9 [13] 873.64 873.60 [9]Toluene 1303 1304.0 [14] 862.22 862.19 [9]o-xylene 1346 1345.0 [15] 875.90 875.94 [9]p-xylene 1310 1309.6 [16] 856.65 856.61 [9]m-xylene 1283 1282.2 [17] 859.96 860.02 [9]

a Value at a temperature of 308.15 K.

40 V.K. Sharma et al. / J. Chem. Thermodynamics 43 (2011) 39–46

Samples for IR were prepared by mixing i and j components in1:1 (w/w) ratio and their IR spectra were recorded on a PerkinElmer- Spectrum RX-I, FTIR spectrometer.

3. Results

Excess molar volumes VE, excess molar enthalpies HE, and speeds of sound u,data of {tetrahydropyran (i) + benzene, or toluene, or o-, or p-, or m-xylene (j)}mixtures measured as a function of composition at a temperature of 308.15 K arerecorded in tables 2 to 4. The isentropic compressibilities, jS, for these mixtureswere determined from their speeds of sound data using relation:

TABLE 2Measured excess molar volumes, VE, data for the various (i + j) mixtures as a functionof mole fraction, xi, of component (i) at a temperature of 308.15 K.

xi VE/(cm3 �mol�1) xi VE/(cm3 �mol�1)

{Tetrahydropyran (i) + benzene(j)}0.0684 �0.049 0.5291 �0.1520.1029 �0.069 0.5990 �0.1420.1673 �0.101 0.6543 �0.1300.1835 �0.108 0.7452 �0.1050.2430 �0.129 0.7823 �0.0930.3143 �0.145 0.8754 �0.0570.4085 �0.156 0.9539 �0.023V(0) = �0.6176, V(1) = 0.1432, V(2) = �0.0284; r(VE) = 0.003 cm3 �mol�1

{Tetrahydropyran (i) + toluene(j)}0.0554 �0.031 0.4109 �0.1530.0673 �0.037 0.5273 �0.1590.0850 �0.046 0.6433 �0.1460.1534 �0.079 0.7215 �0.1270.1861 �0.092 0.8202 �0.0930.2311 �0.110 0.9297 �0.0400.2942 �0.129 0.9735 �0.016V(0) = �0.6362, V(1) = �0.0139, V(2) = 0.0431; r(VE) = 0.003 cm3 �mol�1

{Tetrahydropyran (i) + o-xylene(j)}0.0536 �0.012 0.4935 �0.0550.0643 �0.014 0.5200 �0.0540.0805 �0.017 0.5642 �0.0530.1127 �0.023 0.6421 �0.0480.1816 �0.034 0.7314 �0.0400.2975 �0.047 0.8832 �0.0190.3954 �0.053 0.9228 �0.013V(0) = �0.219, V(1) = 0.0281, V(2) = �0.0213; r(VE) = 0.003 cm3 �mol�1

{Tetrahydropyran (i) + p-xylene (j)}0.0639 �0.022 0.5127 �0.0570.1503 �0.043 0.5515 �0.0540.2321 �0.055 0.6027 �0.0490.2835 �0.059 0.6529 �0.0440.3331 �0.061 0.7211 �0.0360.3832 �0.061 0.7905 �0.0270.4421 �0.06 0.8673 �0.017V(0) = �0.2222, V(1) = 0.1345, V(2) = �0.023; r(VE) = 0.003 cm3 �mol�1

{Tetrahydropyran (i) + m-xylene (j)}0.0626 �0.006 0.5413 �0.0320.1258 �0.012 0.6033 �0.0320.1731 �0.017 0.6541 �0.0300.2459 �0.022 0.7113 �0.0270.3452 �0.028 0.7852 �0.0220.4411 �0.032 0.8934 �0.0120.4801 �0.032 0.9229 �0.009V(0) = �0.130, V(1) = �0.012, V(2) = 0.0165; r(VE) = 0.002 cm3 �mol�1

jS ¼ ðqiju2Þ�1

: ð1Þ

The densities, qij, of binary mixtures were evaluated from their excess molarvolumes data by employing equation (2)

VE ¼Xj

i¼i

xiMiðqijÞ�1 �

Xj

i¼i

xiMiðqiÞ�1; ð2Þ

where xi, Mi, and qi are the mole fraction, molar mass, and density of component (i)of (i + j) binary mixture. Excess isentropic compressibilities, jE

S , for various binarymixtures were determined using equation (3)

jES ¼ jS � jid

S ; ð3Þ

jidS values were obtained as suggested by Benson and Kiyohara [18]

jidS ¼

Xj

i¼i

/i jS;i þTv ia2

i

Cp;i

� �� T

Xj

i¼i

xiv i

! Pji¼i/iai

� �2

Pji¼ixiCp;i

� � ; ð4Þ

where /i is the volume fraction of component (i) in the mixed state; jS,i, vi, ai, and Cp,i

are isentropic compressibility, molar volume, thermal expansion coefficient, andmolar heat capacity, respectively, of the pure component (i). The values of ai andCp,i were taken from literature [19]. ai for THP was evaluated in the same manner

TABLE 3Measured excess molar enthalpies HE values for the various (i + j) mixtures as afunction of mole fraction, xi, of component (i) at a temperature of 308.15 K.

xi HE/(J �mol�1) xi HE/(J �mol�1)

{Tetrahydropyran (i) + benzene (j)}0.0484 �32.6 0.4982 �236.50.0757 �51.6 0.6013 �222.00.0978 �67.1 0.6875 �190.90.1432 �98.5 0.7073 �181.60.2425 �160.8 0.7832 �139.90.3110 �195.2 0.8501 �97.40.385 �221.6 0.923 �48.8H(0) = �945.8, H(1) = 31.3, H(2) = 320.5; r(HE) = 1.7 J �mol�1

{Tetrahydropyran (i) + toluene (j)}0.0445 �28.5 0.3970 �210.10.0662 �42.7 0.5319 �222.50.0837 �54.1 0.6305 �205.80.1138 �73.7 0.7413 �162.90.2154 �135.4 0.8325 �112.10.2806 �168.7 0.9352 �44.50.3031 �178.7 0.9727 �18.7H(0) = �893.0, H(1) = �25.3, H(2) = 239; r(HE) = 2.2 J �mol�1

{Tetrahydropyran (i) + o-xylene (j)}0.0587 �26.6 0.3872 �46.50.0691 �30.5 0.4425 �34.20.0838 �35.6 0.5752 2.40.1451 �51.6 0.6470 22.00.1809 �57.3 0.7443 42.10.2454 �61.3 0.8495 46.70.3023 �58.8 0.9437 26.7H(0) = �76.3, H(1) = 555.4, H(2) = 108.5; r(HE) = 0.6 J �mol�1

{Tetrahydropyran (i) + p-xylene (j)}0.0804 �28.6 0.6454 �126.40.1402 �53.3 0.6914 �113.30.2416 �94.4 0.7432 �95.50.3002 �114.7 0.7919 �76.70.3842 �136.0 0.8476 �54.00.4706 �146.1 0.9021 �32.20.5776 �140.2 0.9415 �17.7H(0) = �585.9, H(1) = 24.6, H(2) = 311.8; r(HE) = 1.3 J �mol�1

{Tetrahydropyran (i) + m-xylene (j)}0.0474 �18.3 0.4765 �9.20.086 �29.7 0.5624 13.00.1141 �36.1 0.6834 40.90.1754 �44.8 0.7603 51.20.2600 �46.2 0.8001 52.70.3488 �36.5 0.8744 46.70.4432 �17.4 0.9453 26.9H(0) = �13.0, H(1) = 516.8, H(2) = 91.1; r(HE) = 0.6 J �mol�1

TABLE 4Speeds of sound, u, isentropic compressibilities, jS, and excess isentropic compress-ibilities, jE

S , for the various (i + j) mixtures as a function of mole fraction, xi ofcomponent (i) at a temperature of 308.15 K.

xi u/(m � s�1) jS/(T � Pa�1) jES=ðT � Pa�1Þ

{Tetrahydropyran (i) + benzene (j)}0.0555 1256 733.8 0.60.1165 1253 737.0 1.30.1472 1251 738.5 1.60.2223 1248 742.0 2.20.2728 1246 744.3 2.50.3751 1241 748.8 3.00.4395 1239 751.4 3.20.4821 1237 753.1 3.30.5313 1238 754.9 3.30.6223 1233 758.1 3.10.6810 1231 760.0 2.90.7321 1230 761.5 2.60.8253 1228 764.1 1.90.9123 1226 766.3 1.1

jð0ÞS ¼ 13:1; jð1ÞS ¼ 0:6; jð2ÞS ¼ �0:7; rðjESÞ ¼ 0:1 T � Pa�1

{Tetrahydropyran (i) + toluene (j)}0.0925 1259 740.3 �1.00.1343 1258 740.9 �1.60.1789 1257 741.6 �2.20.2587 1256 743.1 �3.20.3742 1254 745.3 �4.50.4263 1253 746.5 �4.90.4815 1251 748.0 �5.20.5187 1250 749.1 �5.30.5795 1248 751.1 �5.20.6765 1243 754.7 �4.80.7122 1242 756.1 �4.50.7646 1239 758.5 �3.90.8487 1234 762.5 �2.70.9252 1229 766.4 �1.4

jð0ÞS ¼ �20:8; jð1ÞS ¼ �5:3; jð2ÞS ¼ 6:6; rðjESÞ ¼ 0:1 T � Pa�1

{Tetrahydropyran (i) + o-xylene (j)}0.0854 1319 663.1 �4.40.1494 1315 667.2 �6.30.2134 1309 672.4 �7.20.2834 1303 679.2 �7.40.3778 1293 689.8 �6.40.4756 1281 702.2 4.40.5132 1277 707.1 �3.60.5668 1270 714.4 �2.30.6124 1265 720.6 �1.30.7035 1254 733.1 0.60.7866 1245 744.2 1.60.8645 1237 754.3 1.90.9344 1230 762.8 1.30.9545 1228 765.2 1.0

jð0ÞS ¼ �15:6; jð1ÞS ¼ 46:1; jð2ÞS ¼ �3:6; rðjESÞ ¼ 0:1 T � Pa�1

{Tetrahydropyran (i) + p-xylene (j)}0.0784 1271 728.6 1.50.1521 1267 732.8 3.00.2123 1263 736.2 4.10.2876 1258 740.3 5.30.3342 1255 742.7 5.90.4091 1251 746.6 6.60.4953 1247 750.5 6.90.5186 1245 751.5 6.90.5684 1243 753.6 6.80.6175 1241 755.4 6.40.7077 1237 758.6 5.40.7909 1233 761.4 4.10.8666 1230 763.7 2.60.9354 1227 766.0 1.3

jð0ÞS ¼ 27:7; jð1ÞS ¼ �0:1; jð2ÞS ¼ �9:1; rðjESÞ ¼ 0:1 T � Pa�1

{Tetrahydropyran (i) + m-xylene (j)}0.0923 1277 719.5 1.40.1515 1273 723.2 2.30.2161 1269 727.3 3.30.2850 1264 731.8 4.3

TABLE 4 (continued)

xi u/(m � s�1) jS/(T � Pa�1) jES=ðT � Pa�1Þ

0.3278 1261 734.6 4.90.3611 1259 736.6 5.20.4081 1256 739.5 5.60.4621 1253 742.7 5.90.5179 1250 745.9 6.00.5568 1248 748.0 5.90.6179 1244 751.4 5.70.7078 1239 756.0 4.90.7889 1235 759.8 3.70.8646 1231 763.6 2.5

jð0ÞS ¼ 23:9; jð1ÞS ¼ 2:5; jð2ÞS ¼ �8:9; rðjESÞ ¼ 0:1 T � Pa�1

V.K. Sharma et al. / J. Chem. Thermodynamics 43 (2011) 39–46 41

as described elsewhere [20]. Such jES values for the investigated mixtures are re-

corded in table 4. VE, HE, and jES values for the investigated (i + j) mixtures are plotted

in figures 1 to 3.Excess molar volumes VE, excess molar enthalpies HE, and excess isentropic

compressibilities jES of various binary mixtures were fitted to equation (5)

XEðX ¼ V ; or H; or; jSÞ ¼ xixj ½Xð0Þ þ Xð1Þð2xi � 1Þ þ Xð2Þð2xi � 1Þ2�; ð5Þ

where X(n) (n = 0 to 2) are the parameters characteristic of (i + j) mixtures. Theseparameters were evaluated by fitting XE (X = V, or H, or jS) data to equation (5)by least squares methods and are recorded along with standard deviations, r(XE)(X = V, or H, or jS) defined by equation (6)

rðXEÞ ¼X

XEexptl � XE

calc: Eq: ð5Þ

� �2�ðm� nÞ

� �0:5

; ð6Þ

(where m and n are the number of data points and adjustable parameters in equation(6)) in tables 2 to 4.

4. Discussion

VE values for {THP (i) + toluene (j)} mixtures at a temperature of308.15 K have been reported in literature [1]. Our VE values atxi P 0.6 are about 0.005 cm3 �mol�1 higher than those reportedin literature. Further, our VE values for {THP (i) + benzene (j) or p-xylene (j)} mixtures are 0.007 and 0.004 cm3 �mol�1 higher thanthose reported in the literature [21,22] at a temperature of298.15 K. The general shape of the curves for all the mixtures arethe same. Our HE values for {THP (i) + benzene (j)} mixtures are(10 to 20) J �mol�1 higher than values reported in the literature[23] at a temperature of 298.15 K. Further, HE values for {THP(i) + p-xylene (j)} mixtures are (10 to 30) J �mol�1 higher than the

FIGURE 1. Excess molar volumes VE at a temperature of 308.15 K of (i) {tetrahy-dropyran (i) + benzene (j)} (�); (II) {tetrahydropyran (i) + toluene (j)} (j); (III){tetrahydropyran (i) + o-xylene (j)} (d); (IV) {tetrahydropyran (i) + p-xylene (j)}(s); and (V) {tetrahydropyran (i) + m-xylene (j)} (N).

FIGURE 2. Excess molar enthalpies, HE at a temperature of 308.15 K of (i){tetrahydropyran (i) + benzene (j) (�); (II) {tetrahydropyran (i) + toluene (j)} (j);(III) {tetrahydropyran (i) + o-xylene (j)} (d); (IV) {tetrahydropyran (i) + p-xylene (j)}(s); and (V) {tetrahydropyran (i) + m-xylene (j)} (N).

42 V.K. Sharma et al. / J. Chem. Thermodynamics 43 (2011) 39–46

values reported in the literature [22] at a temperature of 298.15 K.We are unaware of any VE, HE, and jE

S data of the remaining mix-tures with which to compare our results. While VE data for the var-ious (i + j) mixtures are negative over entire composition range.However, HE data are negative for {THP (i) + benzene, or toluene,or p-xylene (j)} mixtures are negative over whole mole fractionrange and change sign from negative to positive with increase inmole fraction of THP for {THP (i) + o-, or m-xylene (j)} mixtures.While VE data for an equimolar mixture vary in the order: m-xyle-ne > p-xylene � o-xylene > toluene � benzene; HE data for anequimolar mixture vary in the order: m-xylene > o-xylene >p-xylene > toluene > benzene. jE

S values of {THP (i) + benzene, orp-xylene, or m-xylene (j)} mixtures are positive and for {THP

FIGURE 3. Excess isentropic compressibilities of mixing, jES at a temperature of 308.15 K

(j); (III) {tetrahydropyran (i) + o-xylene (j)} (d); (IV) {tetrahydropyran (i) + p-xylene (j)

(i) + toluene (j)} are negative over entire range of composition.The sign of jE

S values for {THP (i) + o-xylene (j)} mixture changesfrom negative to positive with relative increase in proportion of(i) and for an equimolar mixture, jE

S values vary in the order: p-xy-lene > m-xylene > benzene > toluene > o-xylene.

At the simplest qualitative level the observed HE data for thevarious (i + j) mixtures can be explained if it is assumed that (1)THP exists as associated molecular entity (in) due to dipole–dipoleinteractions; (2) there is interaction between dipole of THP and p-electron cloud of aromatic ring of aromatic hydrocarbons to formp-complex [24]; (3) interactions between (in) and (j) then weakensi–i interactions which in turn leads to lack of association of (i) toform a single (i) molecule; (4) molecule of (i) then undergo inter-actions with molecule of (j) to form i:j molecular complex; (5)there is steric hindrance between THP and toluene/xylene mole-cules due to presence of bulky –CH3 groups. The negative valuesof HE for {THP (i) + benzene, or toluene, or p-xylene (j)} mixturessuggest that contribution due to factors (1), (2), and (4) far out-weigh the contribution due to factors (3) and (5) so that over allHE values are negative for these mixtures. The introduction of –CH3 group in benzene (as in toluene) will increase the p-electrondensity of aromatic ring which in turn will lead to stronger inter-actions in toluene as compared to benzene with THP. Thus HE for(THP + toluene) mixture should be higher negative than those of(THP + benzene) mixture. The experimental HE values do not sup-port this view point. This may be due to the reason that contribu-tion due to factor (3) (breaking of dipole–dipole interactions) to HE

be more in toluene as compared to benzene. The introduction oftwo –CH3 groups in benzene (as in xylenes) would further increasethe p-electron density of aromatic ring of xylenes. Thus HE valuesfor {THP (i) + o-, or p-, or m-xylene (j)} mixtures be more thanthose of {THP (i) + benzene or toluene (j)} mixtures. This is indeedtrue. The change of sign in HE values for {THP (i) + o- or m-xylene(j)} mixtures with increase in xi may be due to more contributionto HE due to factors (3) and (5).

of (i) {tetrahydropyran (i) + benzene (j)} (�); (II) {tetrahydropyran (i) + toluene (j)}} (s); (V) {tetrahydropyran (i) + m-xylene (j)} (N).

TABLE 5Comparison of VE, HE, and jE

S values calculated from equations (7) and (15) with their corresponding experimental values at temperature of 308.15 K along with their (3ni) and(3ni)m (i = i or j); aij and v0ij parameters for the various (i + j) mixtures as a function of xi, mole fraction of component (i), mole fraction xi.

Property 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

{Tetrahydropyran (i) + benzene (j)}VE (Exptl)/(cm3 �mol�1) �0.068 �0.114 �0.143 �0.155 �0.154 �0.142 �0.119 �0.087 �0.047VE (Graph)/(cm3 �mol�1) �0.075 �0.122 �0.149 �0.158 � �0.139 �0.115 �0.083 �0.044HE (Exptl)/(J �mol�1) �68.6 �135.6 �190.3 �225.4 �236.5 �222.4 �185.1 �129.6 �64.1HE (Graph)/(J �mol�1) �68.6 �135.6 �190.3 �225.4 � � �148.7 �117.6 �69.0jE

S (Exptl)/(T � Pa�1) 1.1 2.0 2.7 3.1 3.3 3.2 2.7 2.1 1.2

jES (Graph)/(T � Pa�1) 1.1 2.0 2.7 3.3 2.8 2.2 1.3

(3ni) = (3ni)m = 1.301; (3nj) = (3nj)m = 0.666; aij = 1.302 cm3 �mol�1

v0ij ¼ �205:9; v12 ¼ �387:6 J �mol�1

v0ij ¼ 6:2; v12 ¼ 0:6 T � Pa�1

{Tetrahydropyran (i) + toluene (j)}VE (Exptl)/(cm3 �mol�1) �0.054 �0.098 �0.131 �0.152 �0.159 �0.153 �0.133 �0.101 �0.059VE (Graph)/(cm3 �mol�1) �0.069 �0.117 �0.146 �0.160 �0.146 �0.123 �0.090 �0.049HE (Exptl)/(J �mol�1) �45.0 �88.7 �123.2 �143.4 �146.7 �133.0 �105.0 �67.8 �29.0HE (Graph)/(J �mol�1) �62.4 �107.2 �135.2 �140.0 �108.9 �76.7 �39.2jE

S (Exptl)/(T � Pa�1) �1.1 �2.5 �3.7 �4.7 �5.2 �5.2 �4.6 �3.4 �1.9

jES (Graph)/(T � Pa�1) �1.1 �2.8 �3.9 �5.2 � �4.8 �3.9 �2.3

(3ni) = (3ni)m = 1.302; (3nj) = (3nj)m = 0.840; aij = 3.501 cm3 �mol�1

v0ij ¼ �125:3; v12 ¼ �590:0 J �mol�1

v0ij ¼ �8:9; v12 ¼ �7:4 T � Pa�1

{Tetrahydropyran (i) + o-xylene (j)}VE (Exptl)/(cm3 �mol�1) �0.020 �0.036 �0.048 �0.054 �0.055 �0.051 �0.043 �0.031 �0.016VE (Graph)/(cm3 �mol�1) �0.019 �0.034 �0.045 �0.052 �0.053 �0.047 �0.036 �0.021HE (Exptl)/(J �mol�1) �40.6 �59.3 �59.0 �43.9 �19.1 9.4 34.3 47.4 39.4HE (Graph)/(J �mol�1) �50.5 �69.8 �65.9 �46.6 32.1 42.3 33.6jE

S (Exptl)/(T � Pa�1) �4.9 �7.1 �7.3 �6.0 �3.9 �1.6 0.5 1.7 1.7

jES (Graph)/(T � Pa�1) �4.9 �7.1 �7.2 �4.0 0.5 1.8 1.8

(3ni) = (3ni)m = 1.303; (3nj) = (3nj)m = 1.425; aij = 36.154 cm3 �mol�1

v0ij ¼ �31:9; v12 ¼ 31:3 J �mol�1

v0ij ¼ 31:1; v12 ¼ �87:1 T � Pa�1

{Tetrahydropyran (i) + p-xylene (j)}VE (Exptl)/(cm3 �mol�1) �0.031 �0.050 �0.059 �0.060 �0.056 �0.047 �0.036 �0.024 �0.012VE (Graph)/(cm3 �mol�1) �0.021 �0.036 �0.047 �0.054 �0.054 �0.047 �0.035 �0.020HE (Exptl)/(J �mol�1) �36.6 �78.2 �114.6 �138.8 �146.5 �136.4 �110.5 �73.4 �28.2HE (Graph)/(J �mol�1) �37.4 �64.6 �82.3 �91.2 �72.2 �53.0 �28.7jE

S (Exptl)/(T � Pa�1) 2.1 4.0 5.5 6.6 6.9 6.6 5.5 4.1 2.2

jES (Graph)/(T � Pa�1) 2.5 4.3 5.7 6.9 5.6 4.4 2.5

(3ni) = (3ni)m = 1.302; (3nj) = (3nj)m = 1.250; aij = 178.639 cm3 �mol�1

v0ij ¼ �147:2; v12 ¼ �280:2 J �mol�1

v0ij ¼ 13:8; v12 ¼ 6:4 T � Pa�1

{Tetrahydropyran (i) + m-xylene (j)}VE (Exptl)/(cm3 �mol�1) �0.011 �0.20 �0.026 �0.030 �0.032 �0.031 �0.028 �0.021 �0.012VE (Graph)/(cm3 �mol�1) �0.012 �0.021 �0.027 �0.031 �0.030 �0.026 �0.020 0.011HE (Exptl)/(J �mol�1) �33.1 �46.4 �43.1 �27.0 �3.2 22.6 43.8 52.8 41.3HE (Graph)/(J �mol�1) �37.8 �51.4 �46.3 �28.2 42.7 50.4 38.6jE

S (Exptl)/(T � Pa�1) 1.6 3.2 4.6 5.5 6.0 5.8 4.9 3.8 2.0

jES (Graph)/(T � Pa�1) 1.9 3.5 4.7 5.9 5.2 4.1 2.4

(3ni) = (3ni)m = 1.301; (3nj) = (3nj)m = 1.174; aij = 15.001 cm3 �mol�1

v0ij ¼ 246:1;v12 ¼ �762:6 J �mol�1

v0ij ¼ 10:2; v12 ¼ 7:1 T � Pa�1

V.K. Sharma et al. / J. Chem. Thermodynamics 43 (2011) 39–46 43

Lower values of VE for {THP (i) + benzene or toluene (j)} mix-tures than those for {THP (i) + o-, or p-, or m-xylene (j)} mixturessuggest that benzene or toluene give relatively more packed struc-ture in THP as compared to xylenes.

5. Conceptual aspects of the Graph theory and results

A binary mixture is formed by the replacement of like contactsi–i or j–j in pure state by unlike contacts in the mixed state. Theaddition of (i) to (j) thus reflect change in topology of pure liquidsand as excess molar volume VE is a packing effect (which in turn

reflects change in topology of (i) or (j)), So VE data of various(i + j) mixtures were analyzed in terms of Graph theory. Accordingto Graph theory [25], VE is given by

VE ¼ aij

Xxið3niÞm

h i�1�X

xið3niÞh i�1

� �; ð7Þ

where aij is a constant characteristic of (i + j) mixture; xi is the molefraction of component (i). (3ni) (i = i or j) and (3ni)m (i = i or j) are con-nectivity parameters of the third degree of (i) and (j) components of

SCHEME 1. Connectivity parameters of various molecular entities in pure state.

44 V.K. Sharma et al. / J. Chem. Thermodynamics 43 (2011) 39–46

(i + j) mixtures in pure and mixed state and are defined [26] byequation (8)

3n ¼X

m<n<o<p

dvmdv

ndvo dv

p

� ��0:5; ð8Þ

where dmm, etc. represent the degree of mth, etc. vertices of the graph

of a molecule and is related to maximum valency, Zm, and the num-ber of hydrogen atoms attached to the mth vertex hm, by the rela-tion [27] dm

m ¼ Zm � hm.

As the degree of association of THP, or benzene, or toluene, oro-, or p-, or m-xylene was not known with certainty, we presumed(3ni) (i = i or j) and (3ni)m (i = i or j) as adjustable parameters. Theseparameters were predicted by employing VE data to equation (7).Only those (3ni) (i = i or j) and (3ni)m (i = i or j) values were takenthat best reproduced the experimental VE data. Such (3ni) (i = i orj) and (3ni)m (i = i or j) along with VE values (at xi = 0.1,0.2, . . . , 0.9) for various (i + j) mixtures are recorded in table 5and VE values are also compared with their corresponding experi-

V.K. Sharma et al. / J. Chem. Thermodynamics 43 (2011) 39–46 45

mental values. A perusal of data in table 5 reveals that VE valuescompare well with their corresponding experimental VE valuesand so 3ni (i = i or j) and (3ni)m (i = i or j) values can be relied uponto extract information about the aggregation of (i) or (j) in pure andmixed state.

A number of structures were assumed for THP and their 3n0 val-ues were calculated from their structural considerations. Onlythose structure or combinations of structures of THP that yielded3n0 (predicted by equation (8)) value which compare well with 3nvalues (evaluated via equation (7)) were taken to representativestructure of THP. For this purpose we assumed that THP exists asmolecular entities I to II (scheme 1). 3n0 values for these molecularentities were then calculated to be 1.078 and 1.349. 3ni values of1.301, 1.302, 1.303, 1.301, and 1.302 for THP (table 5) suggest thatTHP exist as molecular entity II. These observations are consistentwith the observations inferred from qualitative analysis of VE dataof (THP + toluene) mixtures [1]. 3n0 values of 0.666, 0.840, 1.426,1.250, and 1.174 for benzene, toluene, o-, p-, and m-xylene (molec-ular entities III to VII) suggest that they exist as monomers.ð3n0iÞm values were next predicted to extract information about

the state of THP in benzene, or toluene, or o-, or p-, or m-xylene.It was assumed that studied (i + j) mixtures contain molecular en-tity VIII. In evaluating ð3n0iÞm value for molecular entity VIII, it wasassumed that molecular entity is characterized by interaction be-tween dipole of THP and p-electron cloud of aromatic ring of aro-matic hydrocarbons. dv, etc. values for various vertices are shown inmolecular entities I to VIII. dv(p) = 1 [27] (where p-electron cloudof aromatic hydrocarbon involved in interaction with THP dipole).ð3n0iÞm value for molecular entity VIII was then calculated to be1.358. ð3n0iÞm values of 1.301, 1.302, 1.303, 1.301, and 1.302 forTHP in {THP (i) + benzene, or toluene, or o-, or p-, or m-xylene}mixtures (table 5) suggest that studied mixtures are characterizedby the presence of molecular entity VIII. The presence of molecularentity VIII in these mixtures then suggests that addition of (i) to (j)should have influenced not only the ring vibrations of (j) but alsoinfluenced the C–O stretching of THP in the mixture. A comparisonof the IR spectral data of pure THP, benzene, and their equimolarmixture showed that characteristic absorptions at (1440, 1498,and 1580) cm�1 (ring vibrations) in pure benzene shifted to(1454, 1494, and 1603) cm�1 (ring vibrations) [28], respectively,in the mixture. The C–O stretching in THP also shifted from(1090 to 1096) cm�1 in the mixture. The IR spectrum thus clearlyreveals that addition of i to j influence not only ring vibration ofaromatic ring of aromatic hydrocarbons but also the C–O stretch-ing vibrations of THP. This lends support to the proposed molecularentity VIII in the various (i + j) mixtures.

To analyze the observed HE and jES data of the studied mixtures in

terms of Graph theory, it was assumed that {THP (i) + aromatichydrocarbons (j)} mixtures formation involve processes; (1) THP ex-ist as associated molecular entity; (2) formation of unlike contactsbetween THP (in) and aromatic hydrocarbons (j) then weakens i–iinteractions to form single molecule of (i); (3) there are specificinteractions between dipole of THP and p-electron cloud of aromatichydrocarbons to form i:j molecular complex. If vij, vii, and v12 aremolar interaction energies and molar compressibilities parametersof i–j, i–i contacts and specific interactions respectively, then changein molar thermodynamic properties, DX (X = H or jS) due to pro-cesses (1 to 3) would be given [29–31] by the relation

DX1 ðX ¼ H or jSÞ ¼ xivijSj; ð9Þ

where Sj, the surface fraction of j, involved in (i–j) contacts is de-fined [29] by

Sj ¼ xjv j

Xj

i¼i

xiv i

,

so that

DX1 ðX ¼ H or jSÞ ¼ xixjv jvij

Xxiv i

.; ð10Þ

DX2 ðX ¼ H or jSÞ ¼ x2i xjv jvii

Xxiv i

.; ð11Þ

DX3 ðX ¼ H or jSÞ ¼ xix2j v jv12

Xxiv i

.; ð12Þ

where vj is the molar volume of component (j). The overall changein thermodynamic property, XE (X = H or jS) due to processes (1 to3) then can be expressed as equation (13)

XE ¼X4

i¼1

DXi ðX ¼ H or jSÞ ¼ xixjv j

Xxiv i

.h i½vij þ xivij þ xjv12�:

ð13Þ

For the studied mixtures, if it is assumed that vii ffi vij ¼ v0ij thenequation (13) reduces to equation (14)

XE ¼ xixjv j

Xxiv i

.h ið1þ xiÞv0ij þ xjv12

h i: ð14Þ

Further mj=v i ¼ 3ni=3nj [32]; equation (14) can, therefore, be

expressed as:

XE ðX ¼ H or jsÞ ¼xixjð3ni=

3njÞxi þ xjð3ni=3njÞ

� �ð1þ xiÞv0ij þ xjv12

h i: ð15Þ

Equation (15) contains two unknown parameters (v0ij and v12) and

these parameters were determined by employing XE (X = H or jS)data at two compositions. Predicted parameters were then utilizedto determine XE (X = H or jS) data at various values of xi. Such HE

and jES values along with v0ij and v12 parameters are recorded in ta-

ble 5 and HE; jES values are also compared with their corresponding

experimental values.Examination of data in table 5 reveals that HE and jE

S valuescompare well with corresponding experimental values. This lendsadditional support to the basic assumptions made in qualitativeanalysis of thermodynamic data of the investigated mixtures andalso to the assumptions made in deriving equation (15).

Acknowledgement

The authors are thankful to the Head, Department of Chemistryand authorities of Maharshi Dayanand University, Rohtak, for pro-viding research facilities.

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JCT 09–429