topological investigations of molecular interactions of binary and ternary mixtures containing...

Tm

Na

b

c

a

ARRAA

KEEECmI

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dptmd2iatateIod(oT

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Thermochimica Acta 524 (2011) 92– 103

Contents lists available at ScienceDirect

Thermochimica Acta

journa l h o me page: www.elsev ier .com/ locate / tca

opological investigations of molecular interactions of binary and ternaryixtures containing tetrahydropyran, o-toluidine and N-methylformamide

eeti a, Sunil K. Jangraa, J.S. Yadavb, Dimplec, V.K. Sharmaa,∗

Maharshi Dayanand University, Rohtak, Haryana 124001, IndiaA.I.J.H.M. College, Rohtak 124001, Haryana, IndiaP.D.M. College of Engineering for women, Bahadurgarh, Haryana, India

r t i c l e i n f o

rticle history:eceived 10 April 2011eceived in revised form 28 June 2011ccepted 29 June 2011vailable online 6 July 2011

a b s t r a c t

The densities �, speed of sound u, data of o-toluidine (i) + tetrahydropyran (j) + N-methylformamide (k)and its sub-binary o-toluidine (i) + tetrahydropyran (j); tetrahydropyran (j) + N-methylformamide (k); o-toluidine (i) + N-methylformamide (k) mixtures have been measured over entire mole fraction at 298.15,303.15 and 308.15 K. The excess molar enthalpies, HE data of o-toluidine (i) + N-methylformamide (k);tetrahydropyran (j) + N-methylformamide (k) binary mixtures have also been measured as a function ofcomposition at 308.15 K. The densities and speeds of sound of binary and ternary mixtures have been

eywords:xcess molar volumes, VE

xcess molar enthalpies, HE

xcess isentropic compressibilities, �ES

onnectivity parameter of third degree of aolecule, 3�

nteraction parameter, �

utilized to determine their excess molar volumes, VE and excess isentropic compressibilities, �ES . The

topology of the constituents (Graph theory) has been employed to determine VE, HE and �ES data of binary

as well as ternary mixtures. It has been observed that the estimated excess properties compare well withtheir corresponding experimented values.

© 2011 Elsevier B.V. All rights reserved.

. Introduction

Amides are interesting compounds as they possessonor–accepter –CO–NH peptide bond. They also display theroperty of self-association [1] by hydrogen bond and are relatedo structural problems in molecular biology. N-methylformamide

ainly consists of chain like hydrogen bond structure [2] and hasielectric constant (ε = 182.4) and dipole moment (� = 3.86 D) at98.15 K. Further, tetrahydropyran is used as solvent in chemical

ndustries in polymerisation processes, pharmaceutical industriess a reaction intermediate [3]. Thus a systematic study of o-oluidine (i) or tetrahydropyran (j) + N-methylformamide (k) binarynd o-toluidine (i) + tetrahydropyran (j) + N-methylformamide (k)ernary mixtures can provide information about the structural andnergy consequence of the interactions between these mixtures.n continuing our study on mixtures containing tetrahydropyranr o-toluidine as one of the component [4–9], we present hereensities, speeds of sound data of o-toluidine (i) + tetrahydropyran
j) + N-methylformamide (k) ternary and its sub-binary mixturesver entire composition range at 293.15, 298.15 and 308.15 K.he excess molar enthalpies, HE data of o-toluidine (i) or tetrahy-
∗ Corresponding author. Tel.: +91 9729071881.E-mail address: v [email protected] (V.K. Sharma).

040-6031/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.tca.2011.06.020

dropyran (j) + N-methylformamide (k) binary mixtures have alsobeen reported as a function of composition at 308.15 K. In recentstudies, Graph theory has been successfully employed [4–9]to predict VE, HE and �E

S data of o-toluidine or tetrahydropy-ran + aromatic hydrocarbons or cyclo or n-alkane binary mixtures.It would be of interest to see how Graph theory describes thethermodynamic data of the investigated binary and ternarymixture.

2. Experimental

o-Toluidine (OT) (Fluka, 0.99 GC), tetrahydropyran (THP) (Fluka,0.98 GC), N-methylformamide (NMF) (Fluka, 0.98 GC) were purifiedby standard methods [10]. The purities of the purified liquids werechecked by measuring their densities [recorded in Table 1] usingAnton Paar DSA 5000 at 298.15 ± 0.01 K and these agreed to within±2 × 10−3 kg m−3 with their literature values [10–13].

Densities, � and speeds of sound, u of the pure liquids andtheir binary or ternary mixtures were measured using an AntonPaar vibrating-tube digital density and sound analyzer (model DSA5000) as explained in the literature [14,15]. The measurements are
based on measuring the period of oscillation of a vibrating U-shapedhollow tube filled with the sample. The calibration of the apparatuswas carried out with the double distilled, deionized water beforeeach series of measurements. The mole fraction of mixture was
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dx.doi.org/10.1016/j.tca.2011.06.020

Neeti et al. / Thermochimica A

Table 1Comparison of densities, � and speed of sound, u pure liquids with their literaturevalues at a temperature of 298.15 K.

Liquids �/kg m−3 u/m s−1

Exptl. Lit. Exptl. Lit.

o-toluidine 994.351 994.30 [10] 1602.57 1603.0 [4]Tetrahydropyran 879.136 879.16 [11] 1269.88 1270.0 [16]

oeofiwta

sCmtsm

pP

3

((2oaV

f

V

V

wom

cm

�

(

�

�mvicw

)

N-methylformamide 999.004 999.06 [12] 1431.86 1431.21[12]999.00 [13] 1431.5 [17]

btained with uncertainty of 1 × 10−4 from the measured appar-nt masses of the components. All the mixtures were weighedn an electric balance. The speeds of sound values for the puri-ed liquids at 298.15 ± 0.01 K (recorded in Table 1) compare wellith their experimental values [4,12,16,17]. The uncertainties in

he density and speeds of sound measurements are 2 × 10−3 kg m−3

nd 0.1 m s−1 respectively.Excess molar enthalpies, HE for the binary mixtures were mea-

ured by a 2-drop calorimeter (Model, 4600) supplied by thealorimeter Sciences Corporation (CSC), USA at 308.15 K in aanner described in the literature [4]. The uncertainty in the

emperature measurement (in 2-drop calorimeter measured byoftware provided by CSC; USA) is 0.01 K. The uncertainty in theeasured HE value is 1%.Samples for IR studies were prepared by mixing (i) and (j) com-

onents in 1:1 (w/w) ratio and their IR spectra were recorded onerkin Elmer-Spectrum RX-I, FTIR spectrometer.

. Results

The densities, �ijk, speeds of sound, uijk, data of ternary OTi) + THP (j) + NMF (k); and densities, �, speeds of sound, u of OTi) + THP (j); THP (j) + NMF (k); OT (i) + NMF (k)of binary mixtures at98.15, 303.15, 308.15 K; excess molar enthalpies, HE data of OT (i)r THP (j) + NMF (k) mixtures over entire composition at 308.15 Kre recorded in Tables 2–4 respectively. Excess molar volumesE, VE

ijkfor various binary and ternary mixtures were determined

rom their measured density data using

E =k∑

i=i or j

xiMi(�)−1 −k∑

i=i or j

xiMi(�i)−1 (1)

Eijk =

k∑i=i

xiMi(�ijk)−1 −k∑

i=i

xiMi(�i)−1 (2)

here xi, Mi and �i are the mole fraction, molar mass and densityf component (i) and �, �ijk are the densities of binary and ternaryixtures respectively.The isentropic compressibilities, �S, (�S)ijk and excess isentropic

ompressibilities �ES , (�E

S )ijk

for the investigated binary and ternaryixtures were calculated using equations

S = (� u2)−1

(3)

�S)ijk = (�ijku2ijk)

−1(4)

ES = �S − �id

S (5)

idS values for binary and ternary mixtures were obtained in theanner suggested by Benson and Kiyohara [18]. The Cp,i, �i and ˛

alues used in Benson and Kiyohara equation represent heat capac-ty, volume fraction and thermal expansion coefficient of the ithomponent respectively. The Cp,i values for the pure componentsere taken from the literature [10,19]. The ̨ value for various

cta 524 (2011) 92– 103 93

components were evaluated in the same manner as described else-where [20]. The resulting VE, VE

ijk, �S, (�S)ijk, �E

S , (�ES )

ijkvalues for

the various binary and ternary are recorded in Tables 2 and 5.The VE, HE and �E

S data for the binary mixtures (plotted inFigs. 1–3 respectively) were fitted to relation:

XE(X = V or H or �S) = xixj[X(0) + X(1)(2xi − 1) + X(2)(2xj − 1)2] (6)

where X(n) (X = V or H or �S) etc. are the parameters characteristicof binary mixtures and were determined by fitting XE(X = V or Hor �S) data to Eq. (6) using least- squares methods. Such param-eters along with standard deviations, (XE) (X = V or H or �S) arerecorded in Tables 2 and 3.

The VEijk

and (�ES )

ijkdata for ternary mixtures were fitted to

Redlich–Kister equation

XEijk

(X = V or �S) = xixj

[2∑

n=0

(X(n)ij

)(xi − xj)n

]+ xjxk

[2∑

n=0

(X(n)jk

)(xj − xk)n

]

+xixk

[2∑

n=0

(X(n)ik

)(xk − xj)n

]+ xixjxk

[2∑

n=0

(X(n)ijk

)(xj − xk)nxni

] (7

The X(n)ij

(n = 0–2) etc. are the adjustable parameters of (i + j),

(j + k), and (i + k) binary mixtures Further, X(n)ijk

(X = V or �S) (n = 0–2)etc. are adjustable parameters of the ternary mixtures and weredetermined by fitting the XE

ijkdata to Eq. (7) by least squares

method. Such parameters along with standard deviations, (XEijk

)(X = V or �S) expressed by the relation:

(XEijk) =

⎧⎪⎨⎪⎩

[∑XE

ijk− XE

ijk{calc. Eq. (7 ) }

](m − n)

2⎫⎪⎬⎪⎭

0.5

(8)

where m is the number of data points and n is the number ofadjustable parameters of Eq. (7) are recorded in Tables 2 and 3respectively. The various surfaces generated by VE

ijkand (�E)ijk val-

ues [calculated via Eq. (7)] for OT (i) + THP (j) + NMF (k) ternarymixtures are shown in Figs. 4–9 respectively. Figs. 4–9 are plottedby calculating VE

ijkand (�E

S )ijk

values from Eq. (7) keeping the molefraction of the one component constant and varying the other molefractions. In Fig. 4, keeping mole fraction of xj constant VE

ijkvalues

(corresponding to i–k axis) were calculated and are represented by( ). The VE

ijkvalues (corresponding to i–j axis) were obtained

keeping xk constant and varying the values of xi and xj. Such VEijk

values are shown as ( ).

4. Discussion

The VE values for THP + NMF binary mixture have been reportedin literature at 298.15, 303.15, 308.15 K, our VE values differ by0.003 cm3 mol−1 than those reported in literature [13], Further, ourVE values for OT (i) + THP (j) binary mixture are in excellent agree-ment with values reported in literature at 308.15 K. We are unawareof the VE data of the remaining binary and ternary mixtures,; HE

and �ES data of the investigated binary and �E

S data of the studiedternary mixtures with which to compare our results. The VE data ofbinary OT (i) + THP (j); THP (j) + NMF (k); OT (i) + NMF (k) and HE, �E

Svalues of OT (i) + NMF (k) binary mixtures are negative over entirerange of composition. However, HE and �E

S values of THP (j) + NMF(k) mixtures are positive over whole mole fraction. Further, VE and
�E
S data of the investigated ternary mixtures are negative over entirecomposition range.

The HE data of OT (i) or THP (j) + NMF (k) mixtures can beexplained qualitatively, if it is assumed that (i) OT (i) or THP (j)

94 Neeti et al. / Thermochimica Acta 524 (2011) 92– 103

Table 2Measured densities, �; excess molar volumes, VE; speeds of sound, u; isentropic compressibilities, �S and excess isentropic compressibilities, �E

Sdata for the various binary

mixtures as a function of mole fraction, xi , of component (i) at a temperature of 298.15, 303.15 and 308.15 K.

xi �/kg m3 VE/cm3 mol−1 u/m s−1 �S/TPa−1 �ES/TPa−1

o-toluidine (i) + tetrahydropyran (j)T = 298.15 Ka

0.0 879.136 – 1269.88 – –0.0732 890.691 −0.2594 1296.39 668.04 −14.360.1342 899.769 −0.4242 1318.61 639.20 −24.060.1768 905.846 −0.5156 1333.98 620.36 −29.530.2207 911.867 −0.5881 1349.85 601.86 −34.260.2721 918.660 −0.6510 1368.16 581.53 −38.460.3328 926.351 −0.6978 1389.27 559.30 −41.640.3562 929.219 −0.7078 1397.33 551.17 −42.430.3901 933.275 −0.7139 1408.97 539.74 −43.220.4288 937.818 −0.7148 1421.78 527.49 −43.330.4567 940.995 −0.7072 1430.96 518.99 −43.080.5014 945.986 −0.6882 1445.54 505.89 −42.150.5362 949.788 −0.6678 1456.56 496.27 −40.850.5982 956.336 −0.6141 1475.66 480.19 −37.470.6243 959.040 −0.5886 1483.59 473.74 −35.740.6644 963.103 −0.5426 1495.66 464.15 −32.740.7125 967.870 −0.4807 1510.15 453.05 −28.750.7703 973.454 −0.3977 1527.40 440.33 −23.330.8025 976.501 −0.3478 1537.04 433.47 −20.091.0 994.351 – 1602.57 – –303.15 Kb

0.0000 873.992 – 1246.83 – –0.0732 885.730 −0.2754 1274.12 695.47 −16.350.1342 894.897 −0.4454 1296.85 664.43 −27.240.1768 900.991 −0.5352 1312.52 644.27 −33.320.2207 907.057 −0.6087 1328.63 624.53 −38.560.2721 913.860 −0.6678 1347.13 602.98 −43.130.3328 921.578 −0.7113 1368.74 579.21 −46.860.3562 924.445 −0.7187 1376.92 570.56 −47.770.3901 928.536 −0.7249 1388.49 558.62 −48.510.4288 933.094 −0.7232 1401.63 545.52 −48.830.4567 936.325 −0.7182 1411.09 536.37 −48.760.5014 941.370 −0.6998 1425.65 522.65 −47.710.5362 945.194 −0.6776 1437.04 512.32 −46.550.5982 951.867 −0.6299 1456.47 495.24 −43.140.6243 954.607 −0.605 1464.71 488.28 −41.480.6644 958.737 −0.5611 1476.95 478.16 −38.360.7125 963.596 −0.5031 1491.34 466.61 −34.020.7703 969.292 −0.4248 1508.67 453.27 −28.260.8025 972.384 −0.3755 1518.08 446.24 −24.651.0 990.224 – 1577.82 – –308.15 Kc

0.0 868.831 – 1224.47 – –0.0732 880.749 −0.2915 1252.49 723.77 −18.260.1342 890.021 −0.4688 1275.85 690.24 −30.440.1768 896.174 −0.5617 1291.97 668.51 −37.260.2207 902.258 −0.6332 1308.47 647.36 −43.040.2721 909.112 −0.6930 1327.61 624.09 −48.310.3328 916.872 −0.7349 1349.47 598.91 −52.240.3562 919.758 −0.7418 1357.79 589.74 −53.220.3901 923.890 −0.7488 1369.76 576.89 −54.210.4288 928.469 −0.7451 1383.06 563.06 −54.490.4567 931.715 −0.7386 1392.32 553.65 −54.130.5014 936.823 −0.7219 1407.17 539.07 −53.060.5362 940.693 −0.7005 1418.24 528.51 −51.440.5982 947.455 −0.6549 1437.56 510.73 −47.520.6243 950.235 −0.6311 1445.68 503.53 −45.580.6644 954.427 −0.5891 1457.60 493.15 −41.920.7125 959.361 −0.5330 1471.77 481.21 −37.020.7703 965.131 −0.4553 1488.59 467.59 −30.410.8025 968.276 −0.4076 1497.88 460.31 −26.421.0 986.069 – 1558.38 – –o-toluidine (i) + N-methylformamide (k)T = 298.15 Kd

0.0 999.004 – 1431.86 – –0.0656 1000.18 −0.1063 1454.27 472.75 −8.510.1258 1000.98 −0.1914 1472.38 460.82 −14.660.1673 1001.39 −0.2439 1484.06 453.41 −18.090.2127 1001.71 −0.2935 1496.05 446.03 −21.110.2466 1001.88 −0.3268 1504.40 441.02 −22.870.2789 1001.99 −0.3556 1512.07 436.51 −24.280.3081 1002.03 −0.3772 1518.62 432.74 −25.250.3356 1002.04 −0.3957 1524.41 429.45 −25.90

Neeti et al. / Thermochimica Acta 524 (2011) 92– 103 95

Table 2 (Continued )


0.3898 1001.96 −0.4245 1535.19 423.48 −26.670.4383 1001.79 −0.4428 1543.96 418.74 −26.750.4802 1001.56 −0.4503 1551.07 415.01 −26.460.5269 1001.25 −0.4533 1558.20 411.35 −25.640.5599 1000.97 −0.4492 1562.89 409.01 −24.820.6006 1000.59 −0.4405 1568.18 406.40 −23.520.6519 1000.02 −0.4190 1574.36 403.44 −21.550.7244 999.105 −0.3726 1582.15 399.84 −18.190.7904 998.148 −0.3129 1588.23 397.17 −14.530.8485 997.204 −0.2451 1592.85 395.24 −10.881.0 994.351 – 1602.60 – –303.15 Ke

0.0 994.653 – 1417.66 – –0.0656 995.882 −0.1087 1438.44 485.31 −8.740.1258 996.704 −0.1951 1456.30 473.08 −15.270.1673 997.124 −0.2475 1467.84 465.47 −18.950.2127 997.464 −0.2984 1479.70 457.89 −22.240.2466 997.650 −0.3326 1488.16 452.61 −24.310.2789 997.753 −0.3603 1495.69 448.01 −25.850.3081 997.811 −0.3831 1502.34 444.03 −27.070.3356 997.839 −0.4026 1508.21 440.57 −27.930.3898 997.768 −0.4315 1518.88 434.43 −28.940.4383 997.624 −0.4505 1527.61 429.55 −29.240.4802 997.416 −0.4596 1534.6 425.73 −29.090.5269 997.104 −0.4618 1541.45 422.08 −28.320.5599 996.843 −0.4591 1545.93 419.75 −27.530.6006 996.484 −0.4512 1551.11 417.11 −26.320.6519 995.935 −0.4305 1556.65 414.37 −24.210.7244 995.043 −0.3855 1563.43 411.15 −20.570.7904 994.083 −0.3244 1568.28 409.01 −16.470.8485 993.140 −0.2555 1571.88 407.52 −12.461.0 990.224 – 1577.82 – –308.15 Kf

0.0 990.302 – 1402.55 – –0.0656 991.550 −0.1094 1423.32 497.83 −9.220.1258 992.418 −0.1984 1440.91 485.32 −15.960.1673 992.870 −0.2527 1452.23 477.57 −19.740.2127 993.254 −0.3064 1463.85 469.83 −23.130.2466 993.459 −0.3417 1471.94 464.59 −25.130.2789 993.588 −0.3711 1479.40 459.86 −26.770.3081 993.675 −0.3958 1485.71 455.92 −27.910.3356 993.709 −0.4157 1491.39 452.44 −28.760.3898 993.664 −0.4463 1501.86 446.17 −29.840.4383 993.525 −0.4655 1510.38 441.21 −30.150.4802 993.334 −0.4756 1517.25 437.31 −30.040.5269 993.020 −0.4774 1524.11 433.52 −29.360.5599 992.760 −0.4744 1528.45 431.17 −28.550.6006 992.392 −0.4654 1533.61 428.44 −27.390.6519 991.837 −0.4435 1539.19 425.57 −25.340.7244 990.907 −0.3938 1545.99 422.23 −21.740.7904 989.937 −0.3305 1550.91 419.97 −17.680.8485 988.977 −0.2586 1554.24 418.58 −13.511.0 986.069 – 1558.38 – –Tetrahydropyran (j) + N-methylformamide (k)T = 298.15 Kg

0.0 999.004 – 1431.860.0822 984.359 −0.0531 1411.82 509.67 4.210.1587 971.886 −0.0952 1394.05 529.45 7.330.2344 960.487 −0.1289 1377.93 548.34 9.730.2633 956.359 −0.1397 1372.11 555.41 10.490.3005 951.208 −0.1515 1364.96 564.27 11.260.3572 943.711 −0.1666 1354.53 577.54 12.180.3814 940.623 −0.1714 1350.33 583.05 12.420.4163 936.288 −0.1767 1344.43 590.90 12.670.4334 934.212 −0.1787 1341.60 594.72 12.760.4851 928.124 −0.1824 1333.40 606.01 12.780.5122 925.036 −0.1826 1329.29 611.79 12.670.5693 918.752 −0.1795 1321.01 623.73 12.170.6064 914.817 −0.1745 1315.89 631.29 11.650.6571 909.625 −0.1647 1309.14 641.45 10.770.6988 905.507 −0.1541 1303.83 649.63 9.860.7315 902.361 −0.1434 1299.83 655.91 9.020.7743 898.361 −0.1276 1294.70 664.06 7.850.8468 891.856 −0.0944 1286.41 677.56 5.561.0 879.136 – 1269.88 – –303.15 Kh

0.0 994.653 – 1417.66 – –




0.0822 979.949 −0.0577 1396.37 523.36 3.730.1587 967.407 −0.1024 1377.92 544.43 6.770.2344 955.945 −0.1385 1361.03 564.72 9.210.2633 951.788 −0.1496 1354.95 572.29 9.970.3005 946.607 −0.1623 1347.37 581.91 10.820.3572 939.057 −0.1779 1336.47 596.20 11.740.3814 935.944 −0.1825 1332.02 602.19 12.020.4163 931.584 −0.1884 1325.82 610.67 12.280.4334 929.494 −0.1904 1322.87 614.78 12.360.4851 923.354 −0.1934 1314.31 626.96 12.350.5122 920.247 −0.1938 1310.01 633.22 12.220.5693 913.910 −0.1897 1301.35 646.11 11.650.6064 909.949 −0.1845 1295.98 654.32 11.110.6571 904.722 −0.1744 1288.96 665.28 10.120.6988 900.569 −0.1627 1283.45 674.11 9.110.7315 897.401 −0.1515 1279.26 680.92 8.220.7743 893.366 −0.1344 1273.89 689.77 6.980.8468 886.811 −0.0993 1265.07 704.59 4.711.0 873.992 – 1246.83 – –308.15 Ki

0.0 990.302 – 1402.55 – –0.0822 975.601 −0.0664 1380.66 537.71 3.480.1587 963.009 −0.1157 1361.68 560.04 6.350.2344 951.454 −0.1524 1344.41 581.51 8.560.2633 947.263 −0.1637 1338.11 589.58 9.290.3005 942.041 −0.1766 1330.33 599.81 10.050.3572 934.409 −0.1906 1319.09 615.06 10.880.3814 931.277 −0.1956 1314.46 621.48 11.150.4163 926.867 −0.2001 1308.04 630.58 11.370.4334 924.763 −0.2023 1304.99 634.98 11.420.4851 918.566 −0.2041 1296.11 648.05 11.350.5122 915.428 −0.2037 1291.60 654.82 11.220.5693 909.049 −0.1995 1282.56 668.74 10.620.6064 905.053 −0.1935 1276.98 677.57 10.020.6571 899.790 −0.1829 1269.56 689.53 9.080.6988 895.605 −0.1704 1263.71 699.17 8.120.7315 892.421 −0.1595 1259.26 706.64 7.270.7743 888.365 −0.1423 1253.53 716.38 6.120.8468 881.763 −0.1058 1244.09 732.73 4.031.0 868.831 – 1224.47 – –

a V(0) = −2.7547; V(1) = 1.0670; V(2) = −0.2148; (VE) = 0.0006 cm3 mol−1 �(0)S

= −168.56; �(1)S

= 61.44; �(2)S

= 12.40; (�ES) = 0.03 TPa−1.

b V(0) = −2.7991; V(1) = 1.0246; V(2) = −0.5254; (VE) = 0.0007 cm3 mol−1 �(0)S

= −191.22; �(1)S

= 58.69; �(2)S

= 0.06; (�ES) = 0.04 TPa−1.

c V(0) = −2.8877; V(1) = 0.9953; V(2) = −0.7740; (VE) = 0.0007 cm3 mol−1 �(0)S

= −121.21; �(1)S

= 71.43; �(2)S

= 5.19; (�ES) = 0.05 TPa−1.

d V(0) = −1.8101; V(1) = −0.1140; V(2) = −0.0324; (VE) = 0.0004 cm3 mol−1 �(0)S

= −104.53; �(1)S

= 33.27; �(2)S

= −7.02; (�ES) = 0.02 TPa−1.

e V(0) = −1.8456; V(1) = −0.1521; V(2) = −0.0780; (VE) = 0.0004 cm3 mol−1 �(0)S

= −115.28; �(1)S

= 28.89; �(2)S

= −3.12; (�ES) = 0.02 TPa−1.

f V(0) = −1.9095; V(1) = −0.1432; V(2) = −0.0021; (VE) = 0.0004 cm3 mol−1 �(0)S

= −119.11; �(2)S

= 27.04; �(2)S

= −10.06; (�ES) = 0.03 TPa−1.

g V(0) = −0.7302; V(1) = -0.0115; V(2) = −0.0233; (VE) = 0.0001 cm3 mol−1 �(0)S

= 50.87; �(1)S

= −8.62; �(2)S

= −4.20; (�ES) = 0.01 TPa−1.

h V(0) = −0.7747; V(1) = 0.0021; V(2) = 0.0127; (VE) = 0.0002 cm3 mol−1 �(0)S

= 49.22; �(1)S

= −10.22; �(2)S

= −12.02; (�ES) = 0.01 TPa−1.

5; �(1S

oaTruott(aapsT

nos

i V(0) = −0.8168; V(1) = −0.356; V(2) = 0.0509; (VE) = 0.0002 cm3 mol−1 �(0)S

= 45.1

r NMF (k) are associated molecular entities, (ii) there is inter-ction between THP or OT with NMF; (iii) interactions betweenHP or OT with NMF leads to their depolymerisation to form theirespective monomers; and (iv) monomers of OT or THP or NMFndergo interactions to form 1:1 molecular complex. The HE dataf THP (j) + NMF (k) mixtures suggest that contribution due to fac-or (iii) far outweigh the contribution due to factors (ii) and (iv) sohat overall HE values for this are positive. However, HE data of OTi) + NMF (k) mixtures suggest that contribution due to factors (ii)nd (iv) is more significant as compared to factor (iii). Further, VE

nd �ES data of these mixtures suggest that OT gives relatively more

acked structure in NMF as compared to THP. This may be due totrong interactions between OT (i) and NMF (k) as compared toHP.

The VEijk

and (�ES )

ijkdata of OT (i) + THP (j) + NMF (k) mixture are

egative over entire composition range and suggest that additionf NMF (k) to OT (i) + THP (j) mixture gives relatively more packedtructure and strong interactions in mixed state as compared to

) = −11.63; �(2)S

= −12.59; (�ES) = 0.01 TPa−1.

pure state. Further decrease in speed of sound values with increasein temperature lends additional supports to this view point.

5. Graph theory

5.1. Excess molar volumes of binary mixtures

The VE reflects packing effect (which in turn depends on thetopology of (i)/(j)/(k)) and as topology of the components (i)/(j)/(k)changes in (i + j) or (j + k) mixtures, it was therefore worthwhile toanalyze VE data of (i + j) or (j + k) mixtures in terms of Graph theory.This theory deals with connectivity parameter of third degree, 3� ofa molecule (which depends upon its topology). According to Graph
theory (21)
VE = ˛

{[∑xi(

3�i)m

]−1−

[∑xi(

3�i)]−1

}(9)


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

xi HE/J mol−1 xi HE/J mol−1

o-toluidine (i) + N-methyl formamide (k)a

0.0486 −168.1 0.4811 −756.30.0972 −313.2 0.5306 −732.10.1358 −420.8 0.5822 −679.10.1888 −527.6 0.6225 −638.50.2267 −606.5 0.6788 −578.40.2786 −668.5 0.7121 −519.30.3432 −730.2 0.7826 −404.40.3972 −761.4 0.8127 −358.90.4209 −765.1 0.8455 −298.1Tetrahydropyran (j) + N-methyl formamide (k)b

0.0662 34.1 0.5562 326.60.1805 122.4 0.5923 324.50.2254 155.6 0.6242 312.60.2892 206.1 0.6675 304.20.3252 236.1 0.7153 275.50.3743 267.9 0.7576 252.10.4016 278.8 0.7901 223.20.4724 313.5 0.8152 201.70.5114 323.1 0.8676 153.7

a H(0) = −2978; H(1) = 915.4; H(2) = 174.7; (HE) = 6.5 J mol−1.b H(0) = 1270.6; H(1) = 418.9; H(2) = −465.8; (HE) = 2.5 J mol−1.

Fig. 1. Excess molar volumes, VE for tetrahydropyran (j) + N-methyl formamide (k)

at (I) 298.15 K Exptl. ( ), Graph ; (II) 303.15 K Exptl. ( ),Graph ;

(III) 308.15 K Exptl. ( ),Graph ; o-toluidine (i) + N-methyl formamide (k)(

3(

w(p

3

wa

Vr(u(g3

m

Fig. 2. Excess isentropic compressibilities, �ES

for tetrahydropyran (j) + N-methyl for-mamide (k) (I) 308.15 K Exptl. ( ) Graph ; (II) 303.15 K Exptl. (

),Graph ; (III) 308.15 K Exptl. ( ),Graph ; o-toluidine (i) + N-methylformamide (k) (IV) 298.15 K Exptl. ( ), Graph ; (V) 303.15 K Exptl.

( ) Graph ; (VI) 308.15 K Exptl. ( ), Graph ; o-toluidine(i) + tetrahydropyran (j) (VII) Exptl. (—); (VIII) Exptl. ( ); (IX) Exptl. ().

/

IV) 298.15 Exptl. ( )Graph ; (V) 303.15 Exptl. ( ),Graph ; (VI)

08.15 Exptl. ( ),Graph ; o-toluidine (i) + tetrahydropyran (j) (VII) Exptl. ); (VIII) Exptl. ( ); (IX) Exptl. ( ).

here ̨ is a constant characteristic of (i + j), (j + k) mixtures. The 3�i,3�i)m (i = i or j or k) are connectively parameters of third degree inure and mixed state defined by [21]

� =∑

m<n<o<p

(ım ı

n ıo ı

p)−0.5 (10)

here ım etc. have the same significance as described in the liter-

ture [22].The 3� etc. parameters were determined by fitting experiments

E data to Eq. (9) and only those values of 3� etc. parameters wereetained that best reproduced the experimental VE values. Such 3�ii = i or j or k), (3�i)m (i = i or j or k) parameter along with the VE val-es [calculated via Eq. (9)] at various mole fraction of component
i), xi are recorded in Table 4. Examination of data in Table 4 sug-ests that VE values compare well with experimental values. The� etc. parameters values were therefore utilized to extract infor-ation about the state of components (i)/(j)/(k) in their pure and
Fig. 3. Excess molar enthalpies, HE for tetrahydropyran (j) + N-methyl formamide(k) (I) 308.15 K Exptl. ( ) Graph ; (II); o-toluidine (i) + N-methyl formamide

(k) (IV) 308.15 K Exptl. ( ), Graph .

mixed state. For this purpose numbers of structures were assumedfor OT, THP, NMF (Scheme 1) and their 3�/values were calculatedfrom structural consideration [using Eq. (10)]. These 3�/ valueswere compared with 3� values [determined via Eq. (9)]. Any struc-ture or combination of structures that provided 3�/ value whichcompare with 3� value was taken to be representative structureof that component. Such an analysis revealed that OT (molecularentities I–II; 3�/ = 0.949, 1.405 3� = 1.202); THP (molecular entitiesIII–IV; 3� = 1.078, 1.349, 3� = 1.301), NMF (molecular entities V–VI;3�/ = 0.236, 0.947, 3� = 0.890) exits as associated molecular entities;II, IV and VI respectively.

The information about the state of OT (i) or THP (j) in (i + j) or
(j + k) mixtures was obtained by predicting (3�
i)m

(i = i or j) values.For this purpose it was assumed that studied mixtures may havemolecular entities VII and VIII respectively. While molecular entityVII is assumed to be characterized by interactions between oxy-


ird de

gVOtrst

Scheme 1. Connectivity parameters of th

en atom of THP with hydrogen atom of NMF; molecular entityIII is characterized by interactions between hydrogen atom ofT and oxygen atom of NMF. The (3�/

i)m

(i = i or j) values for
hese molecular entities were then calculated to be 1.142, 1.505espectively. The (3�i)m (i = i or j) value of 1.201, 1.301 (Table 4)uggests the presence of molecular entities VII, VIII in the inves-igated mixtures. The existence of molecular entities VII, VIII in
gree, 3�/ , for various molecular entities.

the mixtures suggest that addition of NMF (k) to OT(i) or THP(j) must change the C–O–C vibrations of THP; N–H vibrations ofOT; and C O vibrations of NMF. The IR spectral data were, there-
fore, analyzed for pure OT, THP, NMF and their equimolar OT (i)or THP (j) + NMF (k) binary mixtures. It was observed that char-acteristic (C–O–C) vibration at 1090 cm−1 in pure [23] THP (j)shifted to 1110 cm−1; (N–H stretching) at 3471, 3366 cm−1 (sym-


Table 4Comparison of calculated VE , HE (at T = 308.15 K) and �E

Svalues from appropriate equations with their corresponding experimental values at temperature of (298.15, 303.15

and 308.15) K along with their (3�i) = (3�j)m (i = i or j); ˛ij ik or jk and �/ij

parameters for the various binary mixtures as a function of xi , mole fraction of component (i).

Properties Mole fraction of component (i), xi

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

o-toluidine (i) + N-methylformamide (k)298.15 Ka

VE (Exptl.) −0.1565 −0.2805 −0.3716 −0.4293 −0.4525 −0.4402 −0.3908 −0.3025 −0.1730VE (Graph) −0.1850 −0.3181 −0.4042 −0.4478 − −0.4218 −0.3587 −0.2658 −0.1455�E

S(Exptl.) −12.21 −20.31 −24.98 −26.75 −26.13 −23.55 −19.39 −13.94 −7.42

�ES

(Graph) −11.59 −19.73 −24.69 – −26.25 – −19.07 −13.29 −6.73303.15 Kb


S(Exptl.) −12.64 −21.40 −26.74 −29.08 −28.82 −26.31 −21.89 −15.85 −8.48

�ES

(Graph) −12.26 −21.03 −26.56 – −28.89 – −21.69 −15.45 −8.04308.15 Kc

VE (Exptl.) −0.1614 −0.2965 −0.3889 −0.4514 −0.4774 −0.4651 −0.4130 −0.3192 −0.1821VE (Graph) −0.1951 −0.3356 −0.4265 −0.4724 −0.4774 −0.4450 −0.3784 −0.2804 −0.1535HE (Exptl.) −324.1 −554.5 −696.6 −757.2 −744.8 −669.4 −542.8 −378.7 −192.2HE (Graph) −326.8 −556.9 −697.7 – −744.4 – −543.6 −380.1 −193.3�E

S (Exptl) −13.25 −22.23 −27.62 −29.98 −29.77 −27.38 −23.08 −17.04 −9.35�E

S (Graph) −12.51 −21.53 −27.27 −29.98 −29.92 −27.38 −22.71 −16.29 −8.56Tetrahydropyran (j) + N-methylformamide (k)298.15 Kd


S(Exptl.) 4.96 8.72 11.27 12.58 12.72 11.75 9.82 7.07 3.72

�ES

(Graph) 5.11 8.87 11.33 – 12.67 – 9.87 7.19 3.84303.15 Ke

VE (Exptl.) −0.0689 −0.1231 −0.1623 −0.1859 −0.1937 −0.1858 −0.1621 −0.1231 −0.0687VE (Graph) −0.0820 −0.1397 −0.1759 −0.1932 – −0.1792 −0.1514 −0.1114 −0.0606�E

S(Exptl.) 4.47 8.16 10.79 12.19 12.30 11.21 9.07 6.20 3.00

�ES

(Graph) 5.03 8.69 11.05 − 12.21 − 9.33 6.71 3.53308.15 Kf

VE (Exptl.) −0.0791 −0.1370 −0.1762 −0.1982 −0.2042 −0.1948 −0.1702 −0.1302 −0.0739VE (Graph) −0.0865 −0.1473 −0.1854 −0.2037 − −0.1889 −0.1596 −0.1175 −0.0639HE (Exptl.) 57.0 136.3 216.1 280.4 317.7 320.6 286.4 216.7 117.7HE (Graph) 86.2 163.8 229.6 – 312.2 – 300.3 245.1 147.0�E

S(Exptl.) 4.18 7.61 10.03 11.27 11.28 10.16 8.08 5.38 2.50

�ES

(Graph) 4.75 8.15 10.30 – 11.18 – 8.34 5.91 3.05

a (3�i) = (3�i)m = 1.202; (3�k) = (3�k)m = 0.890; ˛ik = 20.8063 cm3 mol−1; �/ik

= 66.99 TPa−1; �* = 9.11 TPa−1.

b (3�i) = (3�i)m = 1.202; (3�k) = (3�k)m = 0.890; ˛ik = 21.2156 cm3 mol−1; �/ik

= −70.33 TPa−1; �* = 4.92 TPa−1.

c (3�i) = (3�i)m = 1.202; (3�k) = (3�k)m = 0.890; ˛ik = 21.9513 cm3 mol−1; �/ik

= −1886.4 Jmol−1; �* = 238.4 J mol−1; �/ik

= −71.60 TPa−1; �* = 3.28 TPa−1.

d (3�j) = (3�j)m = 1.301; (3�k) = (3�k)m = 0.890; ˛jk = 5.4848 cm3 mol−1; �/jk

= 29.01 TPa−1; �* = −0.78 TPa−1.

e (3�j) = (3�j)m = 1.301; (3�k) = (3�k)m = 0.890; ˛jk = 5.8182 cm3 mol−1; �/jk

= 28.71 TPa−1;

f (3�j) = (3�j)m = 1.301; (3�k) = (3�k)m = 0.890; ˛jk = 6.1336 cm3 mol−1; �/jk

= 448.42Jmol−

Fig. 4. Excess molar volumes, VEijk

, for o-toluidine (i) + tetrahydropyran (j) + N-methyl formamide (k) ternary mixture at 298.15 K, , the experimentaldata in front of the plane; - - - - - - - - -, the experimental data behind the plane.

�* = −1.94 TPa−1.

1; �* = 379.04 J mol−1; �/jk

= 27.23 TPa−1; �* = −3.17 TPa−1.

metric and asymmetric vibrations) in pure OT (i) shifted to 3449,3350 cm−1; and (C O) vibrations at 1670 cm−1 in pure NMF shiftedto 1655 cm−1 in mixed state. The IR spectral data of the mixturesthus reveals that addition of NMF (k) to OT(i) or THP (j) influencethe (C–O–C stretching), (N–H stretching), (C O) vibrations of THP,OT, NMF which in turn lends additional support to the presenceof molecular entities VII, VIII in OT(i) or THP (j) + NMF (k) mix-tures.

5.2. Excess molar enthalpies and excess isentropiccompressibilities of binary mixtures

The HE and �ES data of the investigated mixtures were next ana-

lyzed in terms of Graph theory. For this purpose it was assumed that(i + k) or (j + k) mixtures formation involve processes; (1) formationof unlike in–kn or jn–kn contacts; (2) unlike contact formation then
weakens in–kn or jn–kn interactions which leads to their depoly-merisation to form their respective monomers; and (3) monomersof i, j and k undergo specific interactions to form i:k or j:k molecularcomplex. If �ik, �jk, �ii, �jj, �kk and �12 are molar interactions and


Table 5Measured densities, �; excess molar volumes, VE; speeds of sound, u; isentropic compressibilities, �S and excess isentropic compressibilities, �E

Sdata compared with Graph

theory for the various (i + j + k) mixtures as a function of mole fraction, xi , of component (i) and xj , of component (j) at a temperature of 298.15, 303.15 and 308.15 K.

xi xj �ijk/kg m−3 u/m s−1 VE (Exptl.)/cm3 mol−1 VE (Graph)/cm3 mol−1 (�S)ijk/TPa−1 (�ES)ijk

(Exptl/TPa−1) (�ES)ijk

(Graph)/TPa−1

o-toluidine (i) + tetrahydropyran (j) + N-methylformamide (k)T = 298.15 Ka

0.1093 0.7213 910.408 1335.90 −0.3656 −0.4078 615.48 −18.81 −18.310.1254 0.7001 913.084 1342.65 −0.3755 −0.3925 607.52 −20.61 −19.700.1448 0.6782 915.874 1349.72 −0.3773 −0.3662 599.34 −22.16 −20.890.1659 0.6503 919.239 1358.08 −0.3746 −0.3580 589.83 −23.58 −22.760.1822 0.6212 922.649 1366.84 −0.3813 −0.3817 580.13 −25.38 −25.350.2043 0.6011 925.149 1373.05 −0.3626 −0.3533 573.34 −25.67 −26.080.2457 0.5501 931.399 1389.86 −0.3572 −0.3633 555.81 −28.13 −29.560.2665 0.5347 933.275 1394.20 −0.3306 −0.3394 551.24 −27.34 −29.650.2826 0.4452 945.635 1436.27 −0.5887 −0.5730 512.63 −44.96 −42.080.3018 0.4426 946.019 1437.95 −0.5564 −0.5348 511.22 −43.95 −40.970.3329 0.3982 952.375 1459.53 −0.6391 −0.5934 492.91 −49.62 −45.100.3652 0.4266 947.664 1439.91 −0.4155 −0.4159 508.95 −36.62 −36.660.3564 0.4023 951.651 1457.15 −0.5688 −0.5285 494.89 −46.25 −42.300.3703 0.4477 944.118 1423.21 −0.2694 −0.3099 522.92 −26.74 −31.350.4008 0.4124 949.112 1441.33 −0.3387 −0.3606 507.18 −31.87 −34.090.4216 0.3888 952.521 1454.20 −0.3914 −0.3973 496.45 −35.46 −35.980.4582 0.3851 952.035 1445.19 −0.2365 −0.2836 502.92 −24.65 −29.520.4787 0.3576 956.216 1463.08 −0.3329 −0.3501 488.55 −31.07 −32.730.5025 0.3343 959.569 1476.41 −0.3851 −0.3874 478.11 −34.16 −34.120.5236 0.3136 962.536 1486.28 −0.4315 −0.4176 470.30 −35.42 −36.690.5458 0.3089 962.661 1485.41 −0.3644 −0.3588 470.80 −31.76 −31.420.5765 0.2872 965.488 1495.46 −0.3788 −0.3607 463.13 −31.75 −30.480.5903 0.2671 968.484 1509.23 −0.4485 −0.4239 453.31 −35.87 −33.800.6266 0.2348 972.697 1525.56 −0.4869 −0.4686 441.74 −36.92 −35.360.6499 0.2137 975.337 1535.45 −0.5031 −0.4996 434.89 −36.94 −36.600.6676 0.2035 976.410 1538.71 −0.4871 −0.4875 432.57 −35.33 −35.290.6782 0.1913 977.915 1543.95 −0.4975 −0.5172 428.98 −35.25 −36.950.6912 0.1874 978.174 1544.26 −0.4733 −0.4850 428.69 −33.43 −34.450.7143 0.1667 980.501 1551.86 −0.4674 −0.5124 423.50 −31.91 −35.740.7328 0.1766 978.767 1543.81 −0.3924 −0.3539 428.68 −27.08 −24.34T = 303.15 Kb

0.1093 0.7213 906.256 1312.75 −0.4524 −0.4725 640.31 −19.65 −19.090.1254 0.7001 909.129 1319.75 −0.4801 −0.4873 631.53 −21.91 −21.280.1448 0.6782 912.177 1327.50 −0.5056 −0.4973 622.09 −24.35 −23.620.1659 0.6503 915.822 1336.49 −0.5279 −0.5183 611.30 −26.56 −26.170.1822 0.6212 919.451 1345.12 −0.5528 −0.5522 601.11 −28.36 −28.390.2043 0.6011 922.224 1352.72 −0.5591 −0.5551 592.58 −30.05 −30.340.2457 0.5501 928.896 1370.34 −0.5891 −0.5932 573.29 −33.40 −34.200.2665 0.5347 931.011 1376.54 −0.5836 −0.5899 566.85 −34.24 −35.370.2826 0.4452 942.558 1405.82 −0.7501 −0.7417 536.82 −41.65 −40.040.3018 0.4426 943.164 1409.2 −0.7392 −0.7249 533.91 −42.13 −40.580.3329 0.3982 949.282 1427.27 −0.7939 −0.7651 517.12 −45.51 −42.960.3652 0.4266 945.481 1419.35 −0.6642 −0.6636 525.01 −41.26 −41.220.3564 0.4023 948.879 1428.38 −0.7557 −0.7301 516.54 −44.84 −42.820.3703 0.4477 942.443 1410.37 −0.5729 −0.5991 533.43 −37.33 −39.510.4008 0.4352 947.211 1425.28 −0.6151 −0.6295 519.71 −39.86 −40.920.4216 0.3888 950.435 1435.66 −0.6466 −0.6493 510.48 −41.55 −41.750.4582 0.3851 950.446 1435.50 −0.5437 −0.5724 510.58 −37.11 −39.430.4787 0.3576 954.225 1448.27 −0.5958 −0.6072 499.63 −39.64 −40.480.5025 0.3343 957.317 1458.83 −0.6192 −0.6197 490.83 −40.69 −40.730.5236 0.3136 960.049 1468.37 −0.6397 −0.6309 483.11 −41.55 −40.900.5458 0.3089 960.322 1469.07 −0.5879 −0.5847 482.50 −38.94 −39.060.5765 0.2872 962.952 1478.52 −0.5803 −0.5696 475.05 −38.37 −37.740.5903 0.2671 965.637 1487.96 −0.6161 −0.6004 467.74 −39.64 −38.630.6266 0.2348 969.521 1501.54 −0.6176 −0.6054 457.48 −38.85 −38.030.6499 0.2137 971.959 1509.87 −0.6109 −0.6089 451.31 −37.84 −37.640.6676 0.2035 972.994 1513.43 −0.5898 −0.5893 448.71 −36.36 −36.390.6782 0.1913 974.390 1517.99 −0.5877 −0.6001 445.38 −35.81 −36.610.6912 0.1874 974.650 1519.32 −0.5632 −0.5708 444.48 −34.56 −35.010.7143 0.1667 976.858 1526.50 −0.5426 −0.5706 439.32 −32.66 −34.460.7328 0.1766 975.268 1522.03 −0.4834 −0.4566 442.62 −29.94 −28.69T = 308.15 Kc

0.1093 0.7213 901.282 1292.67 −0.4581 −0.4701 663.99 −22.32 −21.510.1254 0.7001 904.289 1300.01 −0.4978 −0.5024 654.33 −25.05 −24.330.1448 0.6782 907.498 1308.17 −0.5377 −0.5350 643.91 −28.04 −27.450.1659 0.6503 911.22 1317.71 −0.5653 −0.5760 632.03 −30.81 −30.580.1822 0.6212 915.031 1326.54 −0.6061 −0.6067 621.04 −32.83 −32.860.2043 0.6011 918.04 1334.84 −0.6339 −0.6312 611.34 −35.31 −35.520.2457 0.5501 924.964 1353.16 −0.6838 −0.6829 590.44 −39.27 −39.820.2665 0.5347 927.272 1359.85 −0.6969 −0.6958 583.19 −40.61 −41.510.2826 0.4452 937.836 1385.81 −0.7581 −0.7583 555.22 −44.28 −43.070.3018 0.4426 938.641 1389.64 −0.7654 −0.7621 551.69 −45.31 −44.280.3329 0.3982 944.496 1406.84 −0.7906 −0.7833 534.95 −47.78 −45.85



xi xj �ijk/kg m−3 u/m s−1 VE (Exptl.)/cm3 mol−1 VE (Graph)/cm3 mol−1 (�S)ijk/TPa−1 (�ES)ijk

(Exptl/TPa−1) (�ES)ijk

(Graph)/TPa−1

0.3652 0.4266 941.709 1402.34 −0.7611 −0.7604 539.98 −46.88 −46.830.3564 0.4023 944.443 1408.91 −0.7855 −0.7794 533.4 −48.12 −46.760.3703 0.4477 939.286 1395.59 −0.7338 −0.7386 546.62 −45.12 −46.610.4008 0.4352 943.945 1409.62 −0.7609 −0.7515 533.15 −46.69 −47.330.4216 0.3888 946.827 1419.14 −0.7555 −0.7573 524.42 −47.43 −47.610.4582 0.3851 947.484 1421.83 −0.7176 −0.7251 522.07 −45.33 −46.820.4787 0.3576 950.902 1433.05 −0.7299 −0.7321 512.09 −46.36 −46.830.5025 0.3343 953.78 1442.65 −0.7289 −0.7282 503.77 −46.47 −46.420.5236 0.3136 956.287 1451.12 −0.7244 −0.7230 496.6 −46.36 −45.930.5458 0.3089 956.818 1453.04 −0.6982 −0.6967 495.02 −44.62 −44.630.5765 0.2872 959.365 1461.74 −0.6796 −0.6739 487.84 −43.34 −43.120.5903 0.2671 961.735 1468.88 −0.6809 −0.6755 481.91 −42.83 −43.430.6266 0.2348 965.39 1482.23 −0.6551 −0.6510 471.48 −41.57 −41.060.6499 0.2137 967.712 1489.96 −0.6339 −0.6333 465.49 −39.97 −39.800.6676 0.2035 968.746 1493.53 −0.6112 −0.6119 462.77 −38.40 −38.430.6782 0.1913 970.095 1497.85 −0.6028 −0.6058 459.46 −37.59 −37.960.6912 0.1874 970.4 1499.26 −0.5821 −0.5845 458.45 −36.36 −36.640.7143 0.1667 972.552 1507.71 −0.5531 −0.5621 452.33 −35.01 −35.140.7328 0.1766 971.193 1502.78 −0.5182 −0.5044 455.93 −32.15 −31.60

a V(0) = −3.5554; V(1) = −8.4779; V(2) = 1768.07; ( (VE) = 0.0004 cm3 mol −1 �(0)S

= −715.54; �(1)S

= −3919.32; �(2)S

= 129694.72 (�ES) = 0.04 TPa−1 �* = −1.7656 cm3 mol−1;

�∗ij

= 2.8378 cm3 mol−1; �∗jk

= −1.9412 cm3 mol−1; �∗ik

= −3.7267 cm3 mol−1 �* = 119.17 TPa−1; �∗ij

= 48.75 TPa−1; �∗jk

= −134.41 TPa−1; �∗ik

= −298.01 TPa−1.b V(0) = −6.2034; V(1) = −7.5072; V(2) = 1037.6708; ( (VE) = 0.0006 cm3 mol −1 �(0)

S= −462.75; �(1)

S= −1227.90; �(2)

S= 56352.32 (�E

S) = 0.04 TPa−1 �* = 0.4688 cm3mol−1;

�∗ij

= 0.6967cm3mol−1; �∗jk

= −1.6874 cm3 mol−1; �∗ik

= −2.9540 cm3mol−1 �* = 62.89 TPa−1; �∗ij

= −48.60 TPa−1; �∗jk

= −50.68 TPa−1; �∗ik

= −184.81 TPa−1.c V(0) = −4.5961; V(1) = −1.1855; V(2) = 311.7890; ( (VE) = 0.0007cm3 mol −1 �(0)

S= −403.05; �(1)

S= −494.80; �(2)

S= 30483.79 (�E

S) = 0.05 TPa−1 �* = −0.1533 cm3 mol−1;

�∗ij

= −0.8511 cm3 mol−1; �∗jk

= −0.9630 cm3 mol−1; �∗ik

= −1.8801 cm3 mol−1 �* = 61.43 TPa−1; �∗ij

= −104.09 TPa−1; �∗jk

= −29.08 TPa−1; �∗ik

= −139.23 TPa−1.

Fig. 5. Excess molar volumes, VEijk

, for o-toluidine (i) + tetrahydropyran (j) + N-methyl formamide (k) ternary mixture at 303.15 K, , the experimentaldata in front of the plane; - - - - - - - - -, the experimental data behind the plane.

mkm{b

X

X

Fig. 6. Excess molar volumes, VE , for o-toluidine (i) + tetrahydropyran (j) + N-

Sxi = 0.4 and 0.6. These parameters were then utilized to determine

E E E E

olar compressibility interactions parameters for i–k, j–k, i–i, j–j,–k contacts and specific interactions respectively, then change inolar thermodynamic properties, XE(X = H or �S) due to processes

1, 2 and 3} for (i + k) and (j + k) mixtures would be given [24–27]y Eqs. (11) and (12) respectively

E =[

xixk

(3�i/

3�k

)xi + xk

(3�i/3�k

)]

[�ik + xi�ii + xi�kk + xk�12] (11)

E

[xjxk

(3�j/

3�k

) ][ ]
=
xj + xk

(3�j/3�k

) �jk + xj�jj + xj�kk + xk�12 (12)

ijk

methyl formamide (k) ternary mixture at 308.15 K, , the experimentaldata in front of the plane; - - - - - - - - -, the experimental data behind the plane.

For the studied mixtures, it is reasonable to assume that �ik∼=

�12 = �/ik

; �ii = �kk = �∗, �jk∼= �12 = �/

jk; �jj = �kk = �∗ then Eqs.

(11) and (12) can be expressed by

XE =[

xixk

(3�i/

3�k

)xi + xk

(3�i/3�k

)] [

(1 + xk) �/ik

+ 2xi�∗]

(13)

XE =[

xjxk

(3�j/

3�k

)xj + xk

(3�j/3�k

)] [

(1 + xk) �/jk

+ 2xj�∗]

(14)

Eqs. (13) and (14) contain two unknown parameters and weredetermined by employing HE and �E data of the studied mixtures at

H and �S values of mixtures at other values of xi. Such H and �S

values along with �/ik

, �/jk

and �∗ parameters are recorded in Table 4.


Fig. 7. Isentropic compressibilities, (�ES)ijk

for o-toluidine (i) + tetrahydropyran(j) + N-methyl formamide (k) ternary mixture at 298.15 K, , the exper-imental data in front of the plane; - - - - - - - - -, the experimental data behind theplane.


for o-toluidine (i) + tetrahydropyran(ip

EmTd

5o

ma


for o-toluidine (i) + tetrahydropyran

k i k i

j) + N-methyl formamide (k) ternary mixture at 303.15 K, , the exper-mental data in front of the plane; - - - - - - - - -, the experimental data behind thelane.

xamination of data in Table 4 reveals that HE and �ES values differ by

aximum of 1 and 6% respectively with their experimental values.his gives additional support to the various assumptions made ineriving Eqs. (13) and (14).

.3. Excess molar volumes and excess isentropic compressibilitiesf ternary mixtures

Topological analysis of VE, HE and �ES data of (i + k) or (j + k)

ixtures has revealed that OT (i) or THP (j) or NMF (k) exists asssociated molecular entities, in, jn, kn respectively. If a component

(j) + N-methyl formamide (k) ternary mixture at 308.15 K, , the exper-imental data in front of the plane; - - - - - - - - -, the experimental data behind theplane.

like NMF (k) is added to OT (i) + THP (j) mixture then ternary OT(i) + THP (j) + NMF (k) mixture formation may be assumed to involveprocesses; (1) establishment of unlike (a) in–jn, jn–kn, in–kn con-tacts; (2) unlike contact formation leads to depolymerisation of in,jn, kn to form their monomers; and (3) monomers of i, j and k thenundergo specific interactions to form (a) i:j (b) j:k and (c) i:k molec-ular complexes. If �ij, �jk, �ik; �/

ii, �/

jj, �/

kk; and �12, �/

12, �//12 are

the molar volumes and molar compressibilities interaction param-eters for in–jn, jn–kn, in–kn contacts; depolymerisation of in, jn, kn;and specific interactions between i:j; j:k and i:k components of theternary mixtures then change in thermodynamic properties, �X(X = V or �S) due to processes 1 (a)–(c), (2) (a)–(b) and (3) (a)–(c) isgiven by [24–27]

XEijk

(X = V or �S) =[

xixj

(3�i/

3�j

)xi + xj

(3�i/3�j

)][

�ij + xi�/ii

+ xj�12

]

+[

xjxk

(3�j/

3�k

)xj + xk

(3�j/3�k

)][

�jk + xj�/jj

+ xk�/12

]

+[

xkxi

(3�k/3�i

)xk + xi

(3�k/3�i

)][

�ik + xk�/kk

+ xi�//12

](15)

For the present (i + j + k) mixture, if it is assumed that; �ij∼= �12 =

�∗ij; �jk

∼= �/12 = �∗

jk; �ii = �jj = �kk = �∗ then Eq. (15) reduces to

XEijk

(X = V or �S) =[

xixj

(3�i/

3�j

)xi + xj

(3�i/3�j

)][

(1 + xj)x∗ij

+ xix∗]

−8pt +[

xjxk(3�j/3�k)

xj + xk(3�j/3�k)

][(1 + xk)�∗

jk+ xj�

∗]

−8pt +[

xkxi(3�k/3�i)x + x (3� /3� )

][(1 + xi) �∗

ik+ xk�∗]

(16)

Eq. (16) has four unknown �∗ij

etc. parameters and for the presentanalysis, we utilized the observed data at four arbitrary compo-sitions to evaluate them. These parameters were then used to

mica A

e

vapoiolE

A

af

R

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

Neeti et al. / Thermochi

valuate XEijk

(X = V or �S) data of the investigated mixtures at other

alues of xi and xj. Such XEijk

(X = V or �S) for the studied mixtureslong with �∗

ijetc. parameters are recorded in Table 5 and also com-

ared with their corresponding experimental values. Examinationf data in Table 5 reveals that VE

ijkand (�E

S )ijk

values of the stud-ed ternary mixtures [predicted by Eq. (16)] differ by maximumf eight percent with the corresponding experimental values. Thisends additional support the various assumptions made in derivingq. (16).

cknowledgements

The authors are thankful to the Head, Department of Chemistrynd authorities of M.D. University, Rohtak, for providing researchacilities.

eferences

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