Article pubs.acs.org/jced
Thermodynamic Properties of Ternary Liquid Mixtures Containing o‑Chlorotoluene: Excess Molar Volumes and Excess Isentropic Compressibilities V. K. Sharma,*,† Rajni Dua,† and D. Sharma‡ †
Department of Chemistry, Maharshi Dayanand University, Rohtak-124001, Haryana, India Department of Chemistry, Hindu College, Sonepat-131001, Haryana, India
‡
S Supporting Information *
ABSTRACT: Densities and speeds of sound of ternary o-chlorotoluene (1) + tetrahydropyran (2) + benzene or toluene or o-xylene (3) mixtures and their subbinaries o-chlorotoluene (1) + toluene or o-xylene (2) at (298.15, 303.15, and 308.15) K have been measured, and of tetrahydropyran (1) + benzene or toluene or o-xylene (2) mixtures at (298.15 and 303.15) K and 0.1 MPa. Excess molar volumes, VE123 and VE, and excess isentropic compressibilities, (κES )123 and κES , have been computed from experimental data. The VE123 for o-chlorotoluene (1) + tetrahydropyran (2) + o-xylene (3) and (κES )123 for o-chlorotoluene (1) + tetrahydropyran (2) + benzene or toluene or o-xylene (3) are negative over the entire mole fraction of 1 and 2. However, the sign and magnitude of VE123 for ochlorotoluene (1) + tetrahydropyran (2) + benzene or toluene (3) mixtures are dictated by the relative proportion of the constituents. The excess functions have been analyzed in terms of Graph theory, Prigogine−Flory−Patterson theory, and Sanchez and Lacombe’s theories.
1. INTRODUCTION Thermodynamic properties of liquid mixtures provide an important tool in the proper design and development of separation processes in chemical industries. These properties of liquid mixtures have significance in theoretical and applied areas of research.1−3 Thermodynamic studies of chemical and biological systems are of vital importance, particularly from the point of view of contemporary development of science and technology from the nano level to the global level, and are utilized for the welfare of human being. Analyses of the thermodynamic properties of liquid mixtures provide information about the state of liquid in pure and mixed states along with the nature of molecular interactions, which in turn are of primary importance in designing solvent extraction processes with greater efficacy.4 These properties have also been used as qualitative and quantitative guides to predict the extent of complex formation in mixtures5 and are also required in chemical industry for the design of industrial equipment, namely heat exchangers, reactors, separation units, etc., and also in many applications involved in engineering calculations, research on mass transfer, heat transfer, and development of molecular models for describing the behavior of mixtures. oChlorotoluene is used as a solvent for chemical processing as well as a solvent for the formulation of agricultural pesticides. oChlorotoluene breaks down to intermediates which are further used in the production of coloring agents, agrochemicals, and pharmaceuticals. Tetrahydropyran is of technical importance as a solvent. It is also used as an oxygenating agent in gasoline © 2014 American Chemical Society
technology. Aromatic hydrocarbons are important industrial solvents and precursors in the production of drugs, plastics, synthetic rubber, dyes, detergents, explosives, pharmaceuticals, artificial leather, linoleum oil, cloth varnishes, and lacquers. Consequently, thermodynamic properties of mixtures comprising of o-chlorotoluene, tetrahydropyran, benzene, toluene, and o-xylene components may be of vital interest for various industrial processes. In a continuation of our earlier related study on excess molar volumes, VE, excess isentropic compressibilities, κES , excess molar enthalpies, HE, and excess heat capacities, CEP, of o-chlorotoluene + cyclic ether mixtures,6 we present here densities and speed of sound data for ochlorotoluene (1) + tetrahydropyran (2) + benzene or toluene or o-xylene (3) mixtures at (298.15, 303.15, and 308.15) K. Our aim is to provide new experimental data on the densities and speeds of sound of the present mixtures and also to see how the various theories of liquid mixtures describe the excess molar volumes, VE123, and excess isentropic compressibilities, (κES )123, of (1 + 2 + 3) mixtures.
2. EXPERIMENTAL SECTION o-Chlorotoluene (o-CT; Fluka, mass fraction, 0.993; GC), tetrahydropyran (THP; Fluka, mass fraction, 0.995; GC), benzene (Fluka, mass fraction, 0.996; GC), toluene (Fluka, Received: May 27, 2014 Accepted: September 23, 2014 Published: October 7, 2014 3524
dx.doi.org/10.1021/je5004719 | J. Chem. Eng. Data 2014, 59, 3524−3538
Journal of Chemical & Engineering Data
Article
Table 1. Details of Chemical Source, CAS Registry Number, Molar Weight, Purification Method, Final Purity and Analysis Method
a
chemical name
source
CAS no.
molar weight
purification method
final purity (mass fraction)
analysis method
o-chlorotoluene tetrahydropyran benzene toluene o-xylene
Fluka Fluka Fluka Fluka Fluka
95-49-8 142-68-7 71-43-2 108-88-3 95-47-6
126.58 86.14 78.11 92.14 106.17
fractional distillation vacuum distillation fractional distillation fractional distillation fractional distillation
0.993 0.995 0.996 0.995 0.997
GCa GC GC GC GC
GC = gas chromatography.
Table 2. Comparison of Densities, ρ, and Speeds of Sound, u, of Pure Liquids with Their Literature Values at T = (298.15, 303.15, and 308.15) K and p = 0.1 MPa ρ/kg·m−3
u/m·s−1
component
T/K
exptl
lit.
exptl
lit.
o-chlorotoluene
298.15
1077.3
1298.7
1299.06c
303.15
1072.5
1077.38a 1077.40b 1072.60b
1280.7
308.15
1067.6
1068.2a
1262.7
1279.33c 1282.00d 1261.82d 1265.64a
tetrahydropyran
benzene
toluene
o-xylene
298.15
879.13
879.16e
1269.8
1269.3h 1270.00i
303.15 308.15
873.99 868.83
873.95f 868.85g
1246.8 1224.4
298.15
873.54
873.56j
1299.4
303.15 308.15
868.20 862.84
868.2k 862.8l
1276.07 1252.91
298.15
862.18
862.20p
1304.6
303.15
857.51
1283.2
308.15
852.82
857.464n 857.55p 852.86p
1304.00l 1304.69q 1283.80n
1261.8
1262.00r
298.15
875.91
1346.2
1346.00v
303.15 308.15
871.70 867.48
875.70s 876.2t 871.72u 867.1t
1326.2 1306.1
1326.36u
1299.2m 1299.73n 1276.37n 1252.9o
a
Ref 10. bRef 7. cRef 11. dRef 12. eRef 13. fRef 14. gRef 15. hRef 16. iRef 17. jRef 18. kRef 19. lRef 20. mRef 21. nRef 22. oRef 23. pRef 24. qRef 25. Ref 26. sRef 27. tRef 28. uRef 29. vRef 30. Standard uncertainties u are u(T) = 0.01 K, u(ρ) = 0.5 kg·m−3, and u(u) = 0.1 m·s−1.
r
VE values calculated from density results is 0.001·VE. Further, uncertainty in the temperature measurement is ±0.01 K.
mass fraction, 0.995; GC), and o-xylene (Fluka, mass fraction, 0.997; GC) were purified by standard methods.7−9 The source of chemicals, CAS Registry Number, molar weight, purification method, final purity, and analysis method for purity are collected in Table 1. The densities and speed of sound values of the purified liquids compared with the literature7,10−30 data are reported in Table 2. Densities and speed of sound values for the pure liquids and their mixtures were measured using a density and sound analyzer (Anton Paar DSA 5000). The apparatus was calibrated with doubly distilled, deionized, and degassed water. Various mole fractions of binary or ternary liquid mixtures were prepared by measuring masses of components using an electric balance (Mettler AX-205 Delta Range) with uncertainty of ±10−5 g. The uncertainty in mole fraction is 1·10−4.The uncertainties in the density and speed of sound measurements are 0.5 kg·m−3 and 0.1 m·s−1, respectively. The uncertainty in
3. RESULTS The experimental results for the densities and speeds of sound for the ternary and binary mixtures under study are given in Tables 3 and 4, respectively. The excess molar volumes, VE123 and VE, for ternary and binary mixtures were calculated using 3 E V123 =
3
∑ xiMi(ρm )−1 − ∑ xiMi(ρi )−1 i=1
i=1
2 E
V = 3525
2 −1
∑ xiMi(ρ) i=1
(1)
−
∑ xiMi(ρi )−1 i=1
(2)
dx.doi.org/10.1021/je5004719 | J. Chem. Eng. Data 2014, 59, 3524−3538
Journal of Chemical & Engineering Data
Article
Table 3. Measured Densities, ρm, Excess Molar Volumes, VE123, Speeds of Sound, um, Isentropic Compressibilities, (κS)123, and Excess Isentropic Compressibilities, (κES )123, Data for the Studied (1 + 2 + 3) Mixtures as a Function of Mole Fraction, x1 of Component (1) and x2 of Component (2), and Comparison of VE123 and (κES )123 Values with Graph Theory at T = (298.15, 303.15, and 308.15) K and p = 0.1 MPaa VE123/cm3· mol−1 x1
x2
ρm/kg·m
−3
0.1038 0.1171 0.1312 0.1495 0.1567 0.1746 0.2085 0.2978 0.3178 0.3516 0.3824 0.4003 0.4203 0.4578 0.4701 0.4927 0.5108 0.5308 0.5516 0.6001 0.6213 0.6498 0.7123 0.7302 0.7534 0.7834
0.8419 0.8215 0.8014 0.7587 0.7168 0.7004 0.6767 0.6014 0.5823 0.5467 0.4876 0.4366 0.3912 0.3425 0.3309 0.3012 0.2807 0.2617 0.2402 0.1975 0.1806 0.1603 0.1134 0.1002 0.0844 0.0689
904.22 907.36 910.67 914.98 916.75 920.84 928.45 947.86 952.10 959.22 965.85 969.79 973.99 981.53 983.96 988.35 991.81 995.61 999.49 1008.4 1012.3 1017.4 1028.5 1031.7 1035.8 1041.0
0.1038 0.1171 0.1312 0.1495 0.1567 0.1746 0.2085 0.2978 0.3178 0.3516 0.3824 0.4003 0.4203 0.4578 0.4701 0.4927 0.5108 0.5308 0.5516 0.6001 0.6213 0.6498 0.7123 0.7302 0.7534 0.7834
0.8419 0.8215 0.8014 0.7587 0.7168 0.7004 0.6767 0.6014 0.5823 0.5467 0.4876 0.4366 0.3912 0.3425 0.3309 0.3012 0.2807 0.2617 0.2402 0.1975 0.1806 0.1603 0.1134 0.1002 0.0844 0.0689
899.11 902.27 905.58 909.92 911.71 915.82 923.45 942.88 947.13 954.26 960.96 964.96 969.20 976.74 979.17 983.55 987.00 990.78 994.64 1003.5 1007.4 1012.5 1023.6 1026.7 1030.8 1036.1
exptl
Graph
(κES )123/TPa−1 um/m·s
−1
(κS)123/TPa
o-Chlorotoluene (1) + Tetrahydropyran (2) + Benzene (3) T = 298.15 K −0.119 −0.122 1276.9 −0.132 −0.135 1277.8 −0.143 −0.150 1278.7 −0.167 −0.168 1280.6 −0.189 −0.189 1282.6 −0.196 −0.204 1283.2 −0.200 −0.219 1283.8 −0.199 −0.219 1285.7 −0.198 −0.212 1286.2 −0.197 −0.197 1287.2 −0.214 −0.202 1289.8 −0.230 −0.224 1292.3 −0.231 −0.235 1294.2 −0.215 −0.215 1295.6 −0.209 −0.203 1295.8 −0.189 −0.187 1296.4 −0.172 −0.172 1296.6 −0.155 −0.152 1296.8 −0.132 −0.132 1296.8 −0.083 −0.083 1296.6 −0.064 −0.063 1296.5 −0.042 −0.037 1296.3 0.008 0.008 1295.8 0.020 0.017 1295.6 0.032 0.028 1295.5 0.035 0.038 1295.7 T = 303.15 K −0.124 −0.143 1254.2 −0.139 −0.159 1255.2 −0.152 −0.177 1256.1 −0.179 −0.189 1257.9 −0.204 −0.204 1259.6 −0.212 −0.228 1260.3 −0.218 −0.256 1261.2 −0.218 −0.255 1263.5 −0.217 −0.243 1264.1 −0.217 −0.217 1265.2 −0.241 −0.220 1268.0 −0.264 −0.253 1270.9 −0.269 −0.276 1273.2 −0.252 −0.252 1275.1 −0.245 −0.236 1275.4 −0.224 −0.220 1276.2 −0.204 −0.202 1276.7 −0.185 −0.177 1276.9 −0.159 −0.154 1277.1 −0.102 −0.096 1277.2 −0.080 −0.072 1277.1 −0.055 −0.041 1277.1 0.002 0.002 1276.8 0.016 0.008 1276.7 0.029 0.014 1276.7 0.033 0.023 1277.0
3526
−1
exptl
Graph
678.2 674.9 671.6 666.4 663.1 659.5 653.5 638.3 634.9 629.2 622.4 617.5 613.0 607.0 605.3 602.0 599.7 597.3 594.9 589.8 587.7 584.9 579.0 577.4 575.2 572.2
−9.6 −10.7 −11.7 −13.3 −14.6 −15.4 −16.5 −18.2 −18.5 −18.9 −20.1 −21.4 −22.1 −22.0 −21.8 −21.3 −20.8 −20.1 −19.2 −17.0 −15.9 −14.6 −11.1 −10.1 −8.9 −7.7
−9.7 −10.8 −12.0 −13.4 −14.6 −15.9 −17.6 −19.3 −19.2 −18.9 −19.8 −21.5 −22.6 −22.0 −21.5 −21.0 −20.3 −19.4 −18.5 −16.2 −15.1 −13.7 −11.1 −10.5 −9.7 −8.6
707.0 703.5 699.9 694.6 691.3 687.4 680.8 664.3 660.8 654.6 647.2 641.6 636.5 629.7 627.8 624.2 621.6 619.0 616.4 610.9 608.6 605.6 599.3 597.5 595.2 591.9
−10.1 −11.1 −12.2 −13.8 −14.8 −15.8 −17.0 −18.9 −19.2 −19.6 −21.1 −22.7 −23.7 −23.9 −23.8 −23.4 −22.8 −22.2 −21.2 −18.8 −17.6 −16.2 −12.4 −11.3 −10.0 −8.7
−10.5 −11.7 −13.0 −14.0 −14.8 −16.6 −19.0 −20.8 −20.4 −19.6 −20.5 −22.8 −24.5 −23.9 −23.2 −22.8 −22.1 −21.0 −20.1 −17.5 −16.3 −14.7 −12.4 −12.0 −11.5 −10.5
dx.doi.org/10.1021/je5004719 | J. Chem. Eng. Data 2014, 59, 3524−3538
Journal of Chemical & Engineering Data
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Table 3. continued VE123/cm3· mol−1 x1 0.1038 0.1171 0.1312 0.1495 0.1567 0.1746 0.2085 0.2978 0.3178 0.3516 0.3824 0.4003 0.4203 0.4578 0.4701 0.4927 0.5108 0.5308 0.5516 0.6001 0.6213 0.6498 0.7123 0.7302 0.7534 0.7834
x2 0.8419 0.8215 0.8014 0.7587 0.7168 0.7004 0.6767 0.6014 0.5823 0.5467 0.4876 0.4366 0.3912 0.3425 0.3309 0.3012 0.2807 0.2617 0.2402 0.1975 0.1806 0.1603 0.1134 0.1002 0.0844 0.0689
ρm/kg·m−3 893.98 897.14 900.47 904.82 906.62 910.75 918.39 937.86 942.11 949.25 956.01 960.06 964.33 971.89 974.31 978.69 982.13 985.91 989.75 998.61 1002.4 1007.6 1018.6 1021.7 1025.8 1031.1
0.1019 0.1201 0.1402 0.1587 0.2354 0.2484 0.2695 0.2874 0.3008 0.3203 0.3436 0.3603 0.3788 0.4076 0.4326 0.4664 0.4902 0.5167 0.5406 0.5641 0.5801 0.6004 0.6239 0.6553 0.6806 0.7107
0.8218 0.7879 0.7578 0.7314 0.6798 0.6674 0.6465 0.6206 0.6016 0.5713 0.5367 0.5112 0.4884 0.4518 0.4208 0.3772 0.3486 0.3156 0.2795 0.2528 0.2311 0.2005 0.1796 0.1501 0.1208 0.1089
902.53 906.55 911.03 915.13 932.52 935.35 939.87 943.56 946.30 950.24 954.92 958.24 961.97 967.70 972.62 979.11 983.61 988.47 992.49 996.62 999.20 1002.2 1006.4 1011.8 1015.8 1021.9
0.1019 0.1201 0.1402
0.8218 0.7879 0.7578
897.50 901.54 906.04
exptl −0.130 −0.145 −0.159 −0.189 −0.217 −0.226 −0.234 −0.234 −0.233 −0.234 −0.263 −0.293 −0.301 −0.284 −0.277 −0.254 −0.233 −0.212 −0.183 −0.121 −0.097 −0.069 −0.006 0.010 0.025 0.029
Graph T = 308.15 K −0.156 −0.173 −0.194 −0.204 −0.217 −0.247 −0.282 −0.281 −0.266 −0.234 −0.237 −0.279 −0.309 −0.284 −0.266 −0.250 −0.230 −0.201 −0.176 −0.112 −0.085 −0.050 −0.006 −0.001 0.003 0.012
(κES )123/TPa−1 um/m·s−1
(κS)123/TPa−1
exptl
Graph
1231.6 1232.5 1233.5 1235.2 1236.8 1237.7 1238.8 1241.5 1242.1 1243.4 1246.7 1250.1 1252.8 1255.0 1255.4 1256.4 1256.8 1257.1 1257.3 1257.3 1257.2 1257.2 1257.0 1256.9 1257.0 1257.6
737.5 733.7 729.9 724.3 721.0 716.8 709.5 691.8 688.0 681.4 673.0 666.6 660.7 653.3 651.2 647.3 644.6 641.8 639.2 633.5 631.1 627.9 621.4 619.5 616.9 613.2
−9.9 −11.1 −12.2 −13.7 −14.7 −15.8 −17.3 −19.3 −19.5 −20.0 −21.9 −24.2 −25.7 −26.1 −25.9 −25.5 −24.9 −24.1 −23.0 −20.1 −18.8 −17.1 −12.8 −11.6 −10.2 −8.9
−11.1 −12.4 −13.9 −14.5 −14.7 −17.2 −20.5 −22.3 −21.6 −20.0 −20.8 −24.1 −26.7 −26.1 −25.1 −24.8 −24.0 −22.6 −21.5 −18.3 −16.9 −15.0 −12.8 −12.7 −12.5 −11.6
678.0 673.4 668.8 664.8 651.2 649.0 645.3 641.9 639.4 635.7 631.4 628.3 625.1 620.2 616.0 610.7 607.2 603.5 600.8 598.3 596.9 595.7 593.5 590.7 589.0 584.7
−9.8 −11.2 −12.4 −13.4 −15.7 −15.9 −16.3 −16.8 −17.0 −17.5 −17.9 −18.2 −18.4 −18.7 −18.8 −18.7 −18.4 −17.7 −16.5 −15.3 −14.0 −11.8 −10.5 −8.4 −6.1 −6.2
−9.8 −11.1 −12.0 −12.8 −14.4 −14.9 −15.7 −16.5 −17.0 −17.7 −18.3 −18.5 −18.8 −19.1 −19.2 −18.8 −18.5 −17.7 −16.3 −15.3 −14.1 −12.1 −11.0 −9.0 −6.5 −6.2
706.3 701.4 696.3
−10.5 −12.0 −13.4
−10.5 −11.9 −13.0
o-Chlorotoluene (1) + Tetrahydropyran (2) + Toluene (3) T = 298.15 K −0.133 −0.133 1278.3 −0.157 −0.145 1279.8 −0.177 −0.144 1281.1 −0.194 −0.143 1282.1 −0.202 −0.155 1283.2 −0.203 −0.167 1283.5 −0.204 −0.188 1284.1 −0.212 −0.205 1284.9 −0.217 −0.217 1285.6 −0.228 −0.229 1286.6 −0.240 −0.241 1287.9 −0.250 −0.245 1288.8 −0.255 −0.256 1289.6 −0.264 −0.267 1290.8 −0.269 −0.274 1291.9 −0.271 −0.270 1293.3 −0.266 −0.267 1294.0 −0.252 −0.252 1294.7 −0.222 −0.207 1295.0 −0.191 −0.186 1295.1 −0.157 −0.153 1294.9 −0.096 −0.092 1294.2 −0.063 −0.074 1294.0 −0.014 −0.031 1293.5 0.041 0.042 1292.8 0.025 0.025 1293.7 T = 303.15 K −0.142 −0.142 1256.0 −0.168 −0.154 1257.6 −0.190 −0.152 1259.0 3527
dx.doi.org/10.1021/je5004719 | J. Chem. Eng. Data 2014, 59, 3524−3538
Journal of Chemical & Engineering Data
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Table 3. continued VE123/cm3· mol−1 x1
x2
ρm/kg·m−3
exptl
0.1587 0.2354 0.2484 0.2695 0.2874 0.3008 0.3203 0.3436 0.3603 0.3788 0.4076 0.4326 0.4664 0.4902 0.5167 0.5406 0.5641 0.5801 0.6004 0.6239 0.6553 0.6806 0.7107
0.7314 0.6798 0.6674 0.6465 0.6206 0.6016 0.5713 0.5367 0.5112 0.4884 0.4518 0.4208 0.3772 0.3486 0.3156 0.2795 0.2528 0.2311 0.2005 0.1796 0.1501 0.1208 0.1089
910.16 927.53 930.35 934.87 938.56 941.32 945.27 949.98 953.32 957.07 962.83 967.77 974.29 978.81 983.70 987.73 991.86 994.43 997.41 1001.6 1006.9 1010.9 1017.0
−0.207 −0.213 −0.214 −0.214 −0.222 −0.228 −0.240 −0.254 −0.266 −0.272 −0.282 −0.289 −0.294 −0.290 −0.277 −0.247 −0.214 −0.179 −0.113 −0.078 −0.024 0.037 0.021
0.1019 0.1201 0.1402 0.1587 0.2354 0.2484 0.2695 0.2874 0.3008 0.3203 0.3436 0.3603 0.3788 0.4076 0.4326 0.4664 0.4902 0.5167 0.5406 0.5641 0.5801 0.6004 0.6239 0.6553 0.6806 0.7107
0.8218 0.7879 0.7578 0.7314 0.6798 0.6674 0.6465 0.6206 0.6016 0.5713 0.5367 0.5112 0.4884 0.4518 0.4208 0.3772 0.3486 0.3156 0.2795 0.2528 0.2311 0.2005 0.1796 0.1501 0.1208 0.1089
892.44 896.50 901.02 905.15 922.50 925.32 929.84 933.54 936.30 940.27 945.00 948.37 952.12 957.91 962.87 969.43 973.98 978.88 982.92 987.05 989.62 992.58 996.71 1002.1 1006.0 1012.2
−0.151 −0.178 −0.201 −0.219 −0.224 −0.224 −0.224 −0.232 −0.238 −0.251 −0.266 −0.279 −0.286 −0.299 −0.307 −0.315 −0.312 −0.299 −0.269 −0.235 −0.197 −0.128 −0.090 −0.032 0.035 0.018
0.1188 0.1346 0.1518 0.1909 0.2034 0.2442
0.8103 0.7906 0.7731 0.7189 0.6987 0.6539
906.68 910.20 914.05 922.47 925.07 933.81
Graph T = 303.15 K −0.150 −0.160 −0.172 −0.195 −0.215 −0.228 −0.243 −0.256 −0.261 −0.274 −0.288 −0.297 −0.295 −0.292 −0.277 −0.229 −0.207 −0.172 −0.105 −0.086 −0.039 0.039 0.021 T = 308.15 K −0.151 −0.163 −0.161 −0.157 −0.164 −0.177 −0.202 −0.223 −0.238 −0.254 −0.270 −0.276 −0.290 −0.306 −0.317 −0.316 −0.314 −0.299 −0.248 −0.225 −0.188 −0.116 −0.096 −0.047 0.038 0.018
(κES )123/TPa−1 um/m·s−1
(κS)123/TPa−1
exptl
Graph
1260.1 1261.8 1262.2 1262.9 1263.8 1264.5 1265.7 1267.1 1268.1 1268.9 1270.3 1271.5 1273.0 1273.9 1274.7 1275.2 1275.4 1275.3 1274.7 1274.7 1274.4 1273.9 1274.9
691.9 677.1 674.7 670.7 667.0 664.3 660.4 655.7 652.3 648.9 643.6 639.2 633.4 629.6 625.6 622.6 619.8 618.3 617.0 614.5 611.5 609.5 605.0
−14.5 −17.1 −17.4 −17.9 −18.3 −18.6 −19.0 −19.5 −19.8 −20.0 −20.2 −20.3 −20.2 −19.9 −19.2 −17.9 −16.6 −15.3 −12.9 −11.5 −9.4 −7.0 −7.0
−13.8 −15.8 −16.4 −17.2 −18.0 −18.6 −19.3 −19.9 −20.1 −20.4 −20.7 −20.8 −20.4 −20.0 −19.2 −17.6 −16.5 −15.3 −13.2 −12.1 −10.0 −7.4 −7.0
1234.1 1236.0 1237.6 1239.1 1241.1 1241.5 1242.3 1243.4 1244.3 1245.8 1247.5 1248.8 1249.9 1251.7 1253.2 1255.2 1256.2 1257.1 1257.4 1257.3 1256.8 1255.5 1255.0 1254.9 1253.1 1254.5
735.8 730.2 724.6 719.6 703.8 701.1 696.9 692.8 689.8 685.3 680.0 676.1 672.3 666.3 661.3 654.8 650.6 646.5 643.5 640.9 639.7 639.2 637.0 633.7 633.1 627.8
−11.2 −13.0 −14.7 −16.1 −18.8 −19.2 −19.6 −20.2 −20.6 −21.3 −22.1 −22.6 −23.0 −23.6 −23.9 −24.0 −23.7 −22.9 −21.2 −19.4 −17.5 −14.1 −12.1 −9.9 −5.8 −6.1
−11.2 −12.4 −13.1 −13.6 −16.3 −17.2 −18.6 −19.8 −20.6 −21.5 −22.3 −22.6 −23.3 −24.0 −24.3 −24.1 −23.8 −22.9 −20.3 −19.0 −17.2 −13.7 −12.5 −9.1 −5.7 −6.1
674.4 670.5 666.4 656.5 653.2 643.7
−7.3 −8.4 −9.8 −12.5 −13.3 −16.2
−7.9 −9.4 −11.4 −13.3 −13.3 −16.0
o-Chlorotoluene (1) + Tetrahydropyran (2) + o-Xylene (3) T = 298.15 K −0.076 −0.070 1278.9 −0.081 −0.078 1280.1 −0.087 −0.088 1281.3 −0.095 −0.097 1285.0 −0.096 −0.096 1286.4 −0.106 −0.107 1289.8 3528
dx.doi.org/10.1021/je5004719 | J. Chem. Eng. Data 2014, 59, 3524−3538
Journal of Chemical & Engineering Data
Article
Table 3. continued VE123/cm3· mol−1 x1
x2
ρm/kg·m−3
0.3007 0.3206 0.3449 0.3659 0.3894 0.4128 0.4321 0.4568 0.4728 0.4938 0.5268 0.5479 0.5718 0.5937 0.6135 0.6323 0.6598 0.6838 0.7125 0.7315
0.6017 0.5816 0.5629 0.5463 0.5216 0.5076 0.4863 0.4615 0.4415 0.4182 0.3912 0.3738 0.3542 0.3328 0.3178 0.2978 0.2684 0.2489 0.2276 0.2093
945.89 950.03 955.22 959.65 964.38 969.38 973.15 978.01 980.98 984.94 991.45 995.57 1000.2 1004.3 1008.1 1011.5 1016.3 1020.8 1026.2 1029.6
0.1188 0.1346 0.1518 0.1909 0.2034 0.2442 0.3007 0.3206 0.3449 0.3659 0.3894 0.4128 0.4321 0.4568 0.4728 0.4938 0.5268 0.5479 0.5718 0.5937 0.6135 0.6323 0.6598 0.6838 0.7125 0.7315
0.8103 0.7906 0.7731 0.7189 0.6987 0.6539 0.6017 0.5816 0.5629 0.5463 0.5216 0.5076 0.4863 0.4615 0.4415 0.4182 0.3912 0.3738 0.3542 0.3328 0.3178 0.2978 0.2684 0.2489 0.2276 0.2093
901.67 905.20 909.07 917.53 920.14 928.91 941.00 945.15 950.33 954.76 959.50 964.48 968.27 973.13 976.11 980.09 986.60 990.72 995.35 999.42 1003.2 1006.6 1011.5 1016.0 1021.4 1024.8
0.1188 0.1346 0.1518 0.1909 0.2034 0.2442 0.3007 0.3206 0.3449 0.3659
0.8103 0.7906 0.7731 0.7189 0.6987 0.6539 0.6017 0.5816 0.5629 0.5463
896.63 900.18 904.05 912.56 915.19 923.98 936.09 940.26 945.43 949.86
exptl
Graph
(κES )123/TPa−1 um/m·s−1
o-Chlorotoluene (1) + Tetrahydropyran (2) + o-Xylene (3) T = 298.15 K −0.125 −0.125 1293.7 −0.130 −0.128 1295.1 −0.139 −0.138 1296.3 −0.147 −0.146 1297.2 −0.148 −0.145 1298.4 −0.158 −0.158 1298.9 −0.156 −0.154 1299.8 −0.154 −0.150 1300.5 −0.146 −0.141 1301.1 −0.139 −0.131 1301.6 −0.138 −0.133 1301.7 −0.136 −0.132 1301.6 −0.133 −0.132 1301.5 −0.125 −0.123 1301.4 −0.124 −0.124 1301.1 −0.114 −0.111 1300.9 −0.100 −0.090 1300.6 −0.095 −0.086 1300.2 −0.092 −0.084 1299.8 −0.085 −0.072 1299.5 T = 303.15 K −0.082 −0.077 1257.0 −0.088 −0.086 1258.2 −0.095 −0.097 1259.4 −0.106 −0.108 1263.2 −0.108 −0.108 1264.7 −0.120 −0.120 1268.1 −0.139 −0.139 1272.2 −0.144 −0.143 1273.6 −0.153 −0.152 1274.9 −0.160 −0.160 1275.9 −0.162 −0.159 1277.2 −0.171 −0.171 1277.8 −0.169 −0.167 1278.7 −0.167 −0.164 1279.6 −0.160 −0.155 1280.2 −0.154 −0.147 1280.6 −0.152 −0.147 1280.9 −0.150 −0.146 1281.0 −0.147 −0.145 1281.0 −0.139 −0.137 1281.0 −0.137 −0.137 1280.8 −0.127 −0.125 1280.7 −0.114 −0.105 1280.5 −0.109 −0.100 1280.3 −0.104 −0.097 1280.1 −0.097 −0.085 1280.0 T = 308.15 K −0.088 −0.084 1235.3 −0.095 −0.093 1236.7 −0.103 −0.105 1238.0 −0.116 −0.118 1242.1 −0.118 −0.118 1243.7 −0.132 −0.133 1247.4 −0.154 −0.154 1251.8 −0.159 −0.158 1253.3 −0.169 −0.168 1254.7 −0.176 −0.176 1255.8 3529
(κS)123/TPa−1
exptl
Graph
631.6 627.6 623.0 619.3 615.0 611.5 608.3 604.5 602.2 599.3 595.3 592.8 590.2 588.0 586.0 584.2 581.7 579.5 576.8 575.1
−19.8 −20.8 −21.9 −22.8 −23.3 −23.9 −24.0 −23.9 −23.5 −22.9 −22.3 −21.7 −20.9 −19.8 −19.1 −17.9 −16.0 −14.8 −13.6 −12.4
−19.8 −20.5 −21.9 −22.8 −22.9 −23.9 −23.6 −23.4 −22.7 −22.1 −21.7 −21.3 −20.6 −19.8 −19.1 −18.2 −16.8 −15.8 −14.5 −13.5
702.0 697.8 693.5 683.0 679.5 669.4 656.6 652.3 647.4 643.4 638.9 635.0 631.6 627.6 625.1 622.1 617.7 615.1 612.3 609.8 607.6 605.7 602.9 600.4 597.4 595.5
−8.2 −9.4 −10.8 −13.5 −14.3 −17.2 −20.9 −21.8 −23.1 −24.0 −24.5 −25.2 −25.2 −25.1 −24.5 −23.8 −23.2 −22.6 −21.8 −20.6 −19.9 −18.6 −16.6 −15.4 −14.2 −13.0
−8.7 −10.2 −12.3 −14.3 −14.3 −17.0 −20.9 −21.6 −23.0 −24.0 −24.1 −25.2 −24.9 −24.5 −23.7 −23.0 −22.6 −22.1 −21.5 −20.5 −19.9 −18.8 −17.1 −16.1 −14.8 −13.7
730.9 726.4 721.8 710.3 706.5 695.5 681.8 677.1 671.9 667.6
−8.9 −10.2 −11.7 −14.8 −15.6 −18.8 −22.8 −23.9 −25.2 −26.1
−9.5 −11.2 −13.5 −15.6 −15.6 −18.6 −22.8 −23.6 −25.1 −26.2
dx.doi.org/10.1021/je5004719 | J. Chem. Eng. Data 2014, 59, 3524−3538
Journal of Chemical & Engineering Data
Article
Table 3. continued VE123/cm3· mol−1 x1
x2
0.3894 0.4128 0.4321 0.4568 0.4728 0.4938 0.5268 0.5479 0.5718 0.5937 0.6135 0.6323 0.6598 0.6838 0.7125 0.7315
0.5216 0.5076 0.4863 0.4615 0.4415 0.4182 0.3912 0.3738 0.3542 0.3328 0.3178 0.2978 0.2684 0.2489 0.2276 0.2093
ρm/kg·m−3 954.62 959.60 963.39 968.26 971.26 975.24 981.75 985.87 990.50 994.58 998.40 1001.8 1006.7 1011.2 1016.6 1020.0
exptl
(κES )123/TPa−1
Graph T = 308.15 K −0.175 −0.188 −0.184 −0.181 −0.172 −0.164 −0.164 −0.163 −0.161 −0.152 −0.151 −0.139 −0.119 −0.113 −0.109 −0.097
−0.178 −0.188 −0.186 −0.184 −0.177 −0.171 −0.168 −0.166 −0.162 −0.154 −0.151 −0.142 −0.128 −0.122 −0.117 −0.109
um/m·s−1
(κS)123/TPa−1
exptl
Graph
1257.3 1258.0 1259.0 1259.9 1260.6 1261.2 1261.6 1261.7 1261.7 1261.7 1261.6 1261.6 1261.4 1261.3 1261.1 1261.1
662.7 658.5 654.9 650.6 647.9 644.6 640.0 637.2 634.2 631.6 629.3 627.2 624.3 621.6 618.5 616.5
−26.7 −27.5 −27.5 −27.3 −26.7 −26.0 −25.2 −24.5 −23.6 −22.4 −21.5 −20.1 −17.9 −16.6 −15.3 −13.9
−26.2 −27.5 −27.0 −26.6 −25.8 −25.0 −24.5 −24.0 −23.3 −22.2 −21.5 −20.3 −18.6 −17.4 −16.0 −14.8
Standard uncertainties u are u(T) = 0.01 K, u(x1) = 1·10−4, u(ρm) = 0.5 kg·m−3, u(um) = 0.1 m·s−1, u(VE123) = 0.001·VE123, and u((κES )123) = 0.002· (κES )123.
a
where xi, Mi, and ρi (i = 1, 2, or 3) are the mole fraction, molar mass, and density, respectively; ρm and ρ represent densities of ternary and binary mixtures. The isentropic compressibilities, (κS)123 and κS, and excess isentropic compressibilities, (κES )123 and κES , were determined using the relations 2 −1
(κS)123 = (ρm um )
2 E (n) (X = V or κS) = x1x 2[ ∑ (X12 )(x1 − x 2)n ] X123 n=0 2 (n) )(x 2 − x3)n ] + x 2x3[ ∑ (X 23 n=0 2 (n) )(x1 − x3)n ] + x1x3[ ∑ (X13
(3)
n=0 2
2 −1
κS = (ρu )
(4)
κSE = κS − κSid
(5)
(κSE)123 = (κS)123 − κSid
(6)
(n) )(x 2 − x3)n x1n] + x1x 2x3[ ∑ (X123 n=0
X E(X = V or κS) = x1x 2[X (0) + X (1)(2x1 − 1) + X (2)(2x1 − 1)2 ] (9)
where and etc. (X = V or κS) (n = 0 to 2) are parameters characteristic of (1 + 2 + 3) and (1 + 2), (2 + 3), (1 + 3) mixtures. The X(n) 12 etc. (X = V or κS) (n = 0 to 2) {except for o-CT (1) + toluene or o-xylene (2) at (298.15, 303.15, and 308.15) K; and THP (1) + benzene or toluene or o-xylene (2) at (298.15 and 303.15) K mixtures} were taken from the (n) literature.6,35,36 The X(n) 123 and X12 etc. (X = V or κS) (n = 0 to 2) parameters were determined by fitting the measured data to eqs 8 and 9 using least-squares optimization. The resulting parameters along with standard deviations, σ(XE) and σ(XE123) (X = V or κS), are expressed by X(n) 123
where um and u denote speeds of sound of ternary and binary mixtures, respectively. The κidS , the ideal compressibilities of the ternary and binary mixtures, were calculated using the relation suggested by Benson and Kiyohara,31 2 or 3
κSid
=
∑ i=1
(8)
2 or 3 2 or 3 ⎡ (∑i = 1 φα )2 Tviαi 2 ⎤ ⎥ − T ( ∑ xivi) 2or3 i i φi⎢κS, i + ⎢⎣ C P, i ⎥⎦ (∑i = 1 xiC P, i) i=1
(7)
where ϕi, κS,i, vi, αi, and CP,i (i = 1, 2, or 3) are the volume fraction, isentropic compressibility, molar volume, thermal expansion coefficient, and molar heat capacity of pure component (1). The α values were calculated using experimental density data in the manner described elsewhere.32 The CP,i values for o-CT, THP, benzene, toluene, and o-xylene were taken from the literature.6,33 The VE123, (κES )123, and VE, κES values for the studied mixtures are listed in Tables 3 and 4. The excess functions, XE123 or XE (X = V or κS), were fitted to the Redlich−Kister34 equation,
X(n) 12
E E E σ(X123 ) = {[∑ X123 − X123 ]2 /(m − n)}0.5 {calc eq 8}
(10)
σ(X E) = {[∑ X E − X E{calc eq 9}]2 /(m − n)}0.5
(11)
where m is the number of data points and n is the number of adjustable parameters in eqs 8 and 9 (recorded in Tables 5 and 6). The various surfaces generated37 for the ternary mixtures by VE123 and (κES )123 data at 298.15 K are shown in Figures 1, 2, and 3 and Figures 4, 5, and 6, respectively. In Figure 1, VE123 values corresponding to the 1−2 axis, obtained by keeping x3 constant and varying the values of x1 and x2, are represented as blue 3530
dx.doi.org/10.1021/je5004719 | J. Chem. Eng. Data 2014, 59, 3524−3538
Journal of Chemical & Engineering Data
Article
Table 4. Measured Densities, ρ, Excess Molar Volumes, VE, Speeds of Sound, u, Isentropic Compressibilities, κS, and Excess Isentropic Compressibilities, κES , Data for the Studied (1 + 2) Mixtures as a Function of Mole Fraction, x1 of Component (1), at T = (298.15, 303.15, and 308.15) K and p = 0.1 MPaa x1
0.0935 0.1346 0.1681 0.2393 0.2782 0.3342 0.3871 0.4375 0.4872 0.5312 0.5912 0.6218 0.6753 0.7231 0.7854 0.8351 0.8824 0.9231 0.0935 0.1346 0.1681 0.2393 0.2782 0.3342 0.3871 0.4375 0.4872 0.5312 0.5912 0.6218 0.6753 0.7231 0.7854 0.8351 0.8824 0.9231 0.0935 0.1346 0.1681 0.2393 0.2782 0.3342 0.3871 0.4375 0.4872 0.5312 0.5912 0.6218 0.6753 0.7231 0.7854 0.8351 0.8824 0.9231
ρ/kg·m−3
VE/cm3·mol−1
u/m·s−1
κS/TPa−1
o-Chlorotoluene (1) + Toluene (2) T = 298.15 K 884.20 −0.013 1302.0 667.1 893.74 −0.018 1301.2 660.9 901.47 −0.022 1300.5 655.8 917.70 −0.028 1299.5 645.3 926.47 −0.030 1299.0 639.6 938.97 −0.033 1298.5 631.6 950.65 −0.035 1298.1 624.2 961.66 −0.036 1297.9 617.3 972.41 −0.036 1297.7 610.7 981.84 −0.035 1297.6 604.9 994.55 −0.033 1297.4 597.3 1001.0 −0.032 1297.4 593.5 1012.1 −0.029 1297.4 587.0 1022.0 −0.026 1297.4 581.3 1034.7 −0.021 1297.6 574.0 1044.7 −0.016 1297.7 568.4 1054.2 −0.012 1297.9 563.1 1062.3 −0.008 1298.1 558.6 T = 303.15 K 879.51 −0.015 1281.3 692.6 889.04 −0.021 1280.6 685.8 896.76 −0.026 1280.2 680.4 912.99 −0.034 1279.4 669.2 921.75 −0.037 1279.0 663.1 934.25 −0.041 1278.7 654.6 945.92 −0.043 1278.5 646.8 956.92 −0.044 1278.3 639.5 967.66 −0.044 1278.3 632.4 977.07 −0.043 1278.3 626.3 989.78 −0.041 1278.4 618.2 996.20 −0.039 1278.5 614.1 1007.3 −0.035 1278.7 607.2 1017.2 −0.031 1278.9 601.1 1029.9 −0.024 1279.2 593.4 1039.9 −0.019 1279.5 587.4 1049.3 −0.013 1279.8 581.8 1057.4 −0.009 1280.1 577.1 T = 308.15 K 874.80 −0.018 1260.6 719.3 884.33 −0.025 1260.2 712.1 892.04 −0.030 1259.9 706.3 908.26 −0.040 1259.3 694.3 917.02 −0.044 1259.0 687.9 929.51 −0.049 1258.8 679.0 941.17 −0.052 1258.7 670.7 952.17 −0.053 1258.7 662.9 962.89 −0.053 1258.8 655.4 972.30 −0.052 1259.0 648.9 984.99 −0.049 1259.3 640.2 991.40 −0.047 1259.5 635.8 1002.5 −0.042 1260.0 628.3 1012.3 −0.036 1260.4 621.8 1025.0 −0.028 1261.0 613.5 1035.0 −0.021 1261.5 607.1 1044.5 −0.015 1262.0 601.2 1052.5 −0.009 1262.3 596.3
κES /TPa−1
x1
−2.1 −2.9 −3.6 −4.8 −5.4 −6.0 −6.5 −6.8 −6.9 −6.9 −6.6 −6.4 −5.9 −5.4 −4.4 −3.5 −2.6 −1.7
0.0872 0.1276 0.1754 0.2243 0.2765 0.3241 0.3762 0.4216 0.4932 0.5243 0.5721 0.6158 0.6761 0.7245 0.7865 0.8254 0.8795 0.9192
−2.6 −3.6 −4.3 −5.6 −6.2 −6.9 −7.3 −7.6 −7.7 −7.7 −7.4 −7.2 −6.7 −6.1 −5.1 −4.1 −3.1 −2.1
0.0872 0.1276 0.1754 0.2243 0.2765 0.3241 0.3762 0.4216 0.4932 0.5243 0.5721 0.6158 0.6761 0.7245 0.7865 0.8254 0.8795 0.9192
−3.2 −4.3 −5.1 −6.5 −7.1 −7.7 −8.1 −8.4 −8.4 −8.4 −8.2 −8.0 −7.5 −6.9 −5.9 −4.9 −3.8 −2.7
0.0872 0.1276 0.1754 0.2243 0.2765 0.3241 0.3762 0.4216 0.4932 0.5243 0.5721 0.6158 0.6761 0.7245 0.7865 0.8254 0.8795 0.9192
3531
ρ/kg·m−3
VE/cm3·mol−1
u/m·s−1
κS/TPa−1
o-Chlorotoluene (1) + o-Xylene (2) T = 298.15 K 893.06 −0.010 1341.6 622.1 901.04 −0.015 1339.4 618.6 910.51 −0.021 1337.0 614.5 920.22 −0.026 1334.4 610.3 930.61 −0.031 1331.8 605.9 940.11 −0.035 1329.4 601.9 950.54 −0.038 1326.8 597.6 959.64 −0.040 1324.6 593.9 974.04 −0.041 1321.2 588.2 980.31 −0.042 1319.7 585.7 989.96 −0.041 1317.5 582.0 998.81 −0.039 1315.5 578.6 1011.0 −0.036 1312.7 574.0 1020.9 −0.032 1310.6 570.3 1033.5 −0.027 1307.8 565.7 1041.5 −0.022 1306.1 562.8 1052.5 −0.016 1303.8 558.9 1060.7 −0.011 1302.1 556.0 T = 303.15 K 888.78 −0.010 1321.9 643.9 896.73 −0.014 1319.8 640.2 906.16 −0.020 1317.4 635.8 915.84 −0.025 1315.0 631.4 926.19 −0.030 1312.4 626.8 935.66 −0.034 1310.1 622.7 946.05 −0.037 1307.6 618.2 955.13 −0.039 1305.4 614.4 969.48 −0.041 1302.1 608.4 975.73 −0.041 1300.7 605.8 985.35 −0.040 1298.6 601.8 994.17 −0.039 1296.7 598.2 1006.4 −0.035 1294.1 593.3 1016.2 −0.032 1292.1 589.4 1028.8 −0.026 1289.6 584.5 1036.7 −0.022 1288.0 581.5 1047.7 −0.015 1285.8 577.3 1055.9 −0.010 1284.1 574.3 T = 308.15 K 884.50 −0.009 1302.1 666.8 892.42 −0.013 1300.2 662.8 901.82 −0.019 1298.0 658.2 911.46 −0.024 1295.6 653.6 921.78 −0.029 1293.1 648.8 931.22 −0.033 1290.8 644.5 941.57 −0.037 1288.4 639.8 950.62 −0.039 1286.3 635.8 964.92 −0.041 1283.1 629.5 971.15 −0.041 1281.8 626.7 980.74 −0.040 1279.8 622.6 989.52 −0.038 1278.0 618.8 1001.7 −0.035 1275.6 613.6 1011.4 −0.031 1273.7 609.4 1024.0 −0.025 1271.3 604.2 1031.9 −0.021 1269.8 601.0 1042.9 −0.014 1267.7 596.6 1051.0 −0.009 1266.1 593.5
κES /TPa−1
−0.9 −1.2 −1.5 −1.8 −2.1 −2.2 −2.4 −2.4 −2.5 −2.5 −2.4 −2.3 −2.1 −1.9 −1.6 −1.4 −1.0 −0.7 −1.1 −1.4 −1.8 −2.1 −2.3 −2.4 −2.5 −2.6 −2.6 −2.6 −2.5 −2.5 −2.3 −2.2 −1.9 −1.7 −1.3 −0.9 −1.3 −1.7 −2.1 −2.4 −2.6 −2.7 −2.8 −2.8 −2.8 −2.8 −2.7 −2.6 −2.5 −2.4 −2.1 −1.9 −1.5 −1.1
dx.doi.org/10.1021/je5004719 | J. Chem. Eng. Data 2014, 59, 3524−3538
Journal of Chemical & Engineering Data
Article
Table 4. continued T = 298.15 K
a
x1
ρ/kg·m−3
VE/cm3·mol−1
u/m·s−1
0.0789 0.1324 0.1784 0.2239 0.2876 0.3276 0.3769 0.4285 0.4794 0.5598 0.6024 0.6534 0.7006 0.7432 0.7943 0.8213 0.8763 0.9148
874.60 875.21 875.68 876.10 876.63 876.92 877.26 877.58 877.87 878.27 878.46 878.66 878.82 878.95 879.07 879.12 879.18 879.20
−0.059 −0.090 −0.110 −0.127 −0.143 −0.151 −0.157 −0.161 −0.162 −0.158 −0.153 −0.146 −0.136 −0.126 −0.110 −0.100 −0.076 −0.056
1298.9 1298.2 1297.5 1296.6 1295.2 1294.2 1292.9 1291.4 1289.8 1287.2 1285.8 1284.0 1282.3 1280.7 1278.8 1277.7 1275.4 1273.7
0.0834 0.1245 0.1765 0.2387 0.3017 0.3541 0.4098 0.4467 0.4915 0.5487 0.6008 0.6472 0.6954 0.7321 0.7832 0.8241 0.8937 0.9205
863.93 864.77 865.79 866.99 868.16 869.11 870.10 870.74 871.51 872.47 873.33 874.08 874.84 875.41 876.18 876.78 877.76 878.12
−0.056 −0.078 −0.101 −0.124 −0.141 −0.151 −0.157 −0.160 −0.161 −0.159 −0.154 −0.147 −0.137 −0.128 −0.112 −0.096 −0.064 −0.050
1303.2 1302.3 1301.2 1299.7 1298.1 1296.6 1295.0 1293.9 1292.5 1290.6 1288.8 1287.1 1285.2 1283.7 1281.5 1279.6 1276.1 1274.6
0.0908 0.1432 0.1897 0.2318 0.2953 0.331 0.3872 0.4287 0.4792 0.5187 0.5725 0.6182 0.6682 0.7187 0.7729 0.8367 0.8952 0.9274
876.43 876.68 876.87 877.04 877.26 877.39 877.57 877.70 877.86 877.99 878.16 878.31 878.47 878.62 878.78 878.94 879.05 879.10
−0.038 −0.052 −0.060 −0.065 −0.070 −0.072 −0.073 −0.073 −0.073 −0.072 −0.071 −0.070 −0.067 −0.064 −0.059 −0.050 −0.038 −0.028
1345.3 1343.1 1340.4 1337.4 1332.1 1328.8 1323.2 1319.0 1313.7 1309.6 1304.1 1299.5 1294.6 1290.0 1285.3 1280.2 1276.1 1274.0
T = 303.15 K κS/TPa−1
κES /TPa−1
x1
ρ/kg·m−3
Tetrahydropyran (1) + Benzene (2) −2.5 0.0789 869.25 −3.7 0.1324 869.87 −4.6 0.1784 870.35 −5.3 0.2239 870.78 −5.9 0.2876 871.32 −6.2 0.3276 871.63 −6.4 0.3769 871.97 −6.5 0.4285 872.30 −6.5 0.4794 872.59 −6.2 0.5598 872.99 −6.0 0.6024 873.17 −5.6 0.6534 873.37 −5.2 0.7006 873.53 −4.8 0.7432 873.65 −4.1 0.7943 873.77 −3.7 0.8213 873.83 −2.8 0.8763 873.92 −2.1 0.9148 873.96 Tetrahydropyran (1) + Toluene (2) 681.6 −1.9 0.0834 859.19 681.8 −2.7 0.1245 859.99 682.2 −3.5 0.1765 860.99 682.8 −4.4 0.2387 862.15 683.6 −5.1 0.3017 863.30 684.4 −5.6 0.3541 864.23 685.3 −6.0 0.4098 865.20 686.0 −6.2 0.4467 865.83 686.9 −6.4 0.4915 866.59 688.1 −6.5 0.5487 867.53 689.4 −6.5 0.6008 868.36 690.6 −6.4 0.6472 869.09 692.0 −6.1 0.6954 869.83 693.2 −5.8 0.7321 870.38 695.0 −5.2 0.7832 871.13 696.6 −4.6 0.8241 871.71 699.7 −3.2 0.8937 872.65 701.0 −2.6 0.9205 873.00 Tetrahydropyran (1) + o-Xylene (2) 630.4 −6.4 0.0908 872.06 632.3 −8.5 0.1432 872.25 634.7 −9.5 0.1897 872.40 637.5 −10.0 0.2318 872.53 642.4 −9.8 0.2953 872.71 645.5 −9.4 0.331 872.81 650.8 −8.4 0.3872 872.95 654.9 −7.4 0.4287 873.05 660.0 −6.1 0.4792 873.17 664.1 −5.0 0.5187 873.26 669.6 −3.6 0.5725 873.38 674.2 −2.4 0.6182 873.48 679.2 −1.2 0.6682 873.58 684.0 −0.2 0.7187 873.67 688.9 0.6 0.7729 873.77 694.2 1.1 0.8367 873.86 698.6 1.1 0.8952 873.93 700.9 0.9 0.9274 873.96 677.7 677.9 678.3 678.9 680.0 680.8 682.0 683.3 684.7 687.2 688.5 690.3 692.0 693.6 695.7 696.8 699.2 701.0
VE/cm3·mol−1
u/m·s−1
κS/TPa−1
κES /TPa−1
−0.057 −0.088 −0.109 −0.125 −0.143 −0.150 −0.156 −0.160 −0.159 −0.154 −0.148 −0.138 −0.127 −0.115 −0.099 −0.089 −0.066 −0.048
1274.0 1272.5 1271.2 1269.8 1267.9 1266.7 1265.2 1263.6 1262.0 1259.6 1258.3 1256.9 1255.5 1254.2 1252.8 1252.0 1250.4 1249.3
708.8 710.0 711.1 712.2 713.9 715.1 716.5 718.0 719.5 722.0 723.3 724.8 726.3 727.6 729.2 730.1 731.8 733.1
−0.8 −1.2 −1.4 −1.5 −1.7 −1.7 −1.7 −1.6 −1.6 −1.4 −1.4 −1.3 −1.2 −1.1 −0.9 −0.8 −0.6 −0.5
−0.051 −0.072 −0.095 −0.118 −0.135 −0.146 −0.154 −0.157 −0.159 −0.158 −0.153 −0.146 −0.136 −0.127 −0.111 −0.095 −0.063 −0.049
1281.1 1280.0 1278.7 1277.1 1275.3 1273.8 1272.2 1271.0 1269.5 1267.5 1265.6 1263.7 1261.8 1260.2 1257.9 1255.9 1252.5 1251.1
709.2 709.7 710.3 711.2 712.2 713.1 714.2 715.0 716.0 717.5 719.0 720.5 722.1 723.5 725.5 727.3 730.5 731.8
−1.4 −2.0 −2.8 −3.7 −4.5 −5.0 −5.5 −5.7 −5.9 −6.0 −5.9 −5.8 −5.4 −5.1 −4.5 −3.9 −2.6 −2.0
−0.027 −0.038 −0.046 −0.051 −0.057 −0.060 −0.062 −0.063 −0.063 −0.062 −0.061 −0.059 −0.056 −0.052 −0.046 −0.037 −0.027 −0.020
1323.7 1321.0 1317.9 1314.7 1309.2 1305.9 1300.4 1296.2 1291.0 1286.9 1281.4 1276.8 1272.0 1267.3 1262.5 1257.3 1253.1 1251.0
654.5 657.0 660.0 663.1 668.5 671.8 677.4 681.7 687.1 691.4 697.3 702.2 707.5 712.7 718.0 723.8 728.7 731.1
−5.4 −7.3 −8.2 −8.6 −8.6 −8.2 −7.3 −6.5 −5.3 −4.3 −2.9 −1.8 −0.7 0.2 1.0 1.5 1.4 1.2
Standard uncertainties u are u(T) = 0.01 K, u(x1) = 1·10−4, u(ρ) = 0.5 kg·m−3, u(u) = 0.1 m·s−1, u(VE) = 0.001·VE, and u(κES ) = 0.002·κES .
3532
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Figure 1. Excess molar volumes, VE123, for o-chlorotoluene (1) + tetrahydropyran (2) + benzene (3) ternary mixture at 298.15 K: solid lines, experimental data in front of the plane; dashed lines, experimental data behind the plane.
Figure 4. Excess isentropic compressibilities, (κSE)123, for ochlorotoluene (1) + tetrahydropyran (2) + benzene (3) ternary mixture at 298.15 K: solid lines, experimental data in front of the plane; dashed lines, experimental data behind the plane.
Figure 2. Excess molar volumes, VE123, for o-chlorotoluene (1) + tetrahydropyran (2) + toluene (3) ternary mixture at 298.15 K: solid lines, experimental data in front of the plane; dashed lines, experimental data behind the plane.
Figure 5. Excess isentropic compressibilities, (κSE)123, for ochlorotoluene (1) + tetrahydropyran (2) + toluene (3) ternary mixture at 298.15 K: solid lines, experimental data in front of the plane; dashed lines, experimental data behind the plane.
Figure 3. Excess molar volumes, VE123, for o-chlorotoluene (1) + tetrahydropyran (2) + o-xylene (3) ternary mixture at 298.15 K: solid lines, experimental data in front of the plane; dashed lines, experimental data behind the plane.
Figure 6. Excess isentropic compressibilities, (κSE)123, for ochlorotoluene (1) + tetrahydropyran (2) + o-xylene (3) ternary mixture at 298.15 K: solid lines, experimental data in front of the plane; dashed lines, experimental data behind the plane.
lines; VE123 values corresponding to the 2−3 axis, obtained by keeping x1 constant and varying the values of x2 and x3, are represented as red lines. 3533
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Table 6. Binary Adjustable Parameters, Xn (X = V or κS; n = 0 to 2), from Eq 9, Along with Standard Deviations, σ(XE) (X = V or κS), of VE and κES at T = (298.15, 303.15, and 308.15) K
Table 5. Ternary Adjustable Parameters, XE123 (X = V or κS; n = 0 to 2), from Eq 8, Along with Standard Deviations, σ(XE) (X = V or κS), of VE123 and (κES )123 at T = (298.15, 303.15, and 308.15) K T/K parameter
298.15
303.15
T/K 308.15
parameter
o-Chlorotoluene (1) + Tetrahydropyran (2) + Benzene (3) V(0) −2.153 −2.775 −3.306 V(1) −40.476 −50.886 −59.090 V(2) 273.391 327.905 374.328 σ(VE123)/cm3·mol−1 0.001 0.001 0.001 κ(0) −190.8 −253.8 −297.2 S κ(1) −874.3 −1138.0 −1969.2 S κ(2) 9730.7 13405.0 20080.5 S σ(κES )123/TPa−1 0.1 0.1 0.1 o-Chlorotoluene (1) + Tetrahydropyran (2) + Toluene (3) V(0) 1.363 0.893 0.589 V(1) −98.721 −106.432 −114.296 V(2) 511.640 568.136 623.900 σ(VE123)/cm3·mol−1 0.001 0.001 0.001 κ(0) 55.4 45.1 31.2 S κ(1) −2787.6 −2911.6 −4877.0 S κ(2) 15572.4 16167.3 26791.1 S σ(κES )123/TPa−1 0.1 0.1 0.1 o-Chlorotoluene (1) + Tetrahydropyran (2) + o-Xylene (3) V(0) 3.429 1.777 0.115 V(1) 25.217 33.518 47.221 V(2) −214.722 −231.457 −281.915 σ(VE123)/cm3·mol−1 0.001 0.001 0.001 κ(0) 426.7 302.5 217.9 S κ(1) −3944.3 −1813.3 −1167.2 S κ(2) −5607.4 −13762.8 −16983.8 S σ(κES )123/TPa−1 0.1 0.1 0.1
298.15
303.15
o-Chlorotoluene (1) + Toluene (2) V(0) −0.142 −0.177 V(1) 0.027 0.034 V(2) 0.012 0.038 σ(VE)/cm3·mol−1 0.001 0.001 κ(0) −27.6 −30.9 S κ(1) −0.1 0.5 S κ(2) 4.2 0.9 S σ(κES )/TPa−1 0.1 0.1 o-Chlorotoluene (1) +o-Xylene (2) V(0) −0.166 −0.164 V(1) −0.010 −0.010 V(2) 0.042 0.052 σ(VE)/cm3·mol−1 0.001 0.001 κ(0) −9.9 −10.4 S κ(1) 0.7 0.7 S κ(2) −0.3 −3.6 S σ(κES )/TPa−1 0.1 0.1 Tetrahydropyran (1) + Benzene (2) V(0) −0.645 −0.634 V(1) 0.055 0.106 V(2) −0.173 −0.091 σ(VE)/cm3·mol−1 0.001 0.001 κ(0) −25.7 −6.2 S κ(1) 4.5 3.0 S κ(2) −6.6 −3.5 S σ(κES )/TPa−1 0.1 0.1 Tetrahydropyran (1) + Toluene (2) V(0) −0.643 −0.634 V(1) 0.026 −0.001 V(2) −0.091 −0.053 σ(VE)/cm3·mol−1 0.001 0.001 κ(0) −25.6 −23.6 S κ(1) −6.0 −5.8 S κ(2) −6.1 1.3 S σ(κES )/TPa−1 0.1 0.1 Tetrahydropyran (1) + o-Xylene (2) V(0) −0.290 −0.250 V(1) 0.029 0.024 V(2) −0.215 −0.088 σ(VE)/cm3·mol−1 0.001 0.001 κ(0) −22.2 −19.2 S κ(1) 54.8 50.2 S κ(2) −15.1 −8.4 S σ(κES )/TPa−1 0.1 0.1
4. DISCUSSION The VE data of o-CT (1) + toluene or o-xylene (2) at (298.15 and 308.15) K, VE data of THP (1) + benzene or toluene (2), and κES values of THP (1) + benzene (2) mixtures at 298.15 K are reported in the literature. Our VE values for these mixtures are in agreement with literature values2,32,38−42 (shown in Figures 7, 8, and 9). Further, experimental VE and κES values for THP (1) + benzene or toluene or o-xylene (2) mixtures at 303.15 K are (0.005, 0.001, and 0.008) cm3·mol−1, (4.8, 0.7, and 1.0) TPa−1 lower than the VE and κES values at 308.15 K.36 The general shape of VE and κES curves of all the mixtures is the same. We are unaware of any VE, VE123 and κES , (κES )123 data of the remaining mixtures in the literature with which the measured results can be compared. The VE and κES data of o-CT (1) + toluene or o-xylene (2) mixtures are negative over the full range of composition and at 308.15 K for an equimolar composition follow the order oxylene > toluene. The VE of THP (1) + benzene or toluene or o-xylene (2), and κES values for THP (1) + toluene (2) mixtures, are negative over the entire composition range. However, the sign of κES for the THP (1) + o-xylene (2) mixture changes from negative to positive with increases in the composition of THP. The sign of κES for the THP (1) + benzene (2) mixture also changes from positive to negative with decreases in temperature.2,36 The (κES )123 of o-CT (1) + THP (2) + benzene or toluene or o-xylene (3) and VE123 values for o-CT (1) + THP (2) + oxylene (3) mixtures are negative over all values of x1 and x2.
308.15 −0.212 0.044 0.063 0.001 −33.8 0.6 −5.7 0.1 −0.163 −0.009 0.064 0.001 −11.1 1.1 −6.2 0.1
However, the VE123 values of o-CT (1) + THP (2) + benzene or toluene (3) mixtures change sign with increase in o-CT. The VE123 data for (1 + 2 + 3) mixtures suggest that benzene molecules pack the least in comparison to toluene or o-xylene molecules in the o-CT:THP molecular entity. This may be due to the presence of −CH3 group(s) in toluene or o-xylene mixtures, which leads to stronger interactions between toluene or o-xylene with the o-CT:THP molecular entity. The temperature coefficients, ∂(VE123)/∂T and ∂(κES )123/∂T, for the present ternary mixtures are negative. This may be due to an 3534
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Figure 9. Excess molar volumes, VE, for tetrahydropyran (1) + benzene or toluene (2) mixture at 298.15 K. For benzene: green stars, experimental; green dashed line, Giner et al.;2 and green solid line, Gonzalez et al.41 For toluene: red circles, experimental; red dashed line, Brocos et al.;32 purple dashed line, Gonzalez et al.;41 and red solid line, Francesconi et al.42
Figure 7. Excess molar volumes, VE, for o-chlorotoluene (1) + toluene (2) mixture at 298.15 K (red circles, experimental; red solid line, Mahl et al.;40 and red dashed line, Dahiya et al.39) and 308.15 K (green stars, experimental; green solid line, Mahl et al.;40 and green dashed line, Dahiya et al.38).
(1) and (2) molecules; and (iii) interactions between 1, 2, and 3 to form (a) 1:2, (b) 2:3, and (c) 1:3 molecular complexes. If χ12, χ23, χ13; χ11, χ22; and χ′12, χ′12′ , χ′12′′ are molar volumes and molar compressibility interaction parameters for the establishment of 1n−2n, 2n−3, and 1n−3 contacts; disruption of associated entities, 1n or 2n; and molecular interactions among the constituent molecules to form 1:2, 2:3, and 1:3 molecular complexes, then in thermodynamic properties, XE123 (X = V or κS) due to processes (i) (a)−(c), (ii) (a)−(b), and (iii) (a)−(c) are presented by43−48 ⎡ x x (3ξ /3ξ ) ⎤ E X123 = ⎢ 1 2 13 32 ⎥[χ12 + x1χ11 + x 2χ12′ ] ⎣ x1 + x 2( ξ1/ ξ 2) ⎦ ⎡ x x (3ξ /3ξ ) ⎤ + ⎢ 2 3 32 33 ⎥[χ23 + x 2χ22 + x3χ12′′ ] ⎣ x 2 + x3( ξ 2/ ξ 3) ⎦
Figure 8. Excess molar volumes, VE, for o-chlorotoluene (1) + o-xylene (2) mixture at 298.15 K (red circles, experimental; red solid line, Mahl et al.;40 and red dashed line, Dahiya et al.39) and 308.15 K (green stars, experimental; green solid line, Mahl et al.;40 and green dashed line, Dahiya et al.38).
⎡ x x (3ξ /3ξ ) ⎤ + ⎢ 3 1 33 13 ⎥[χ13 + x1χ12′′′ ] ⎣ x3 + x1( ξ 3/ ξ1) ⎦
(12)
where (3ξ1) (1 = 1, 2, or 3) denotes the connectivity parameters of third degree of 1 or 2 or 3 molecules and is defined by49
increase in the disruption of THP or o-CT associated entities with increases in temperature, which in turn leads to a more packed structure. 4.1. Graph Theory. Excess Molar Volumes and Excess Isentropic Compressibilities of Ternary Mixtures. The analyses of excess molar volumes, VE, excess molar enthalpies, HE, and IR spectral data of o-CT (1) + THP (2) or THP (1) + benzene or toluene or o-xylene (2) mixtures have suggested that, while o-CT exists as associated molecular entities, THP is characterized by dipole−dipole interactions and benzene, toluene, and o-xylene exist as monomers.6,36 Consequently, oCT (1) + tetrahydropyran (2) + benzene or toluene or o-xylene (3) ternary mixtures may involve the following processes: (i) establishment of (a) 1n(n=2)−2n(n=2), (b) 2n(n=2)−3, and (c) 1n(n=2)−3 contacts; (ii) unlike contact formation leading to rupture of (a) 1n or (b) 2n associated molecular entities to form
3
ξ=
(δm νδn νδo νδp ν)−0.5
∑ m
