Article pubs.acs.org/jced
Thermodynamic Properties of Ternary Mixtures Containing Ionic Liquids and Organic Solvents V. K. Sharma,* S. Bhagour, S. Solanki, and A. Rohilla Department of Chemistry, M. D. University, Rohtak, Haryana, India ABSTRACT: The densities, ρ, speed of sound, u, heat capacities, C p of pure 1-ethyl-3-methylimidazolium tetrafluoroborate, 1-methyl pyrrolidin-2-one, pyrrolidin-2-one, pyridine and ternary mixtures of 1-ethyl-3-methylimidazolium tetrafluoroborate (1) + 1methyl pyrrolidin-2-one or pyrrolidin-2-one (2) + pyridine (3) and their binary mixtures of 1-methyl pyrrolidin-2-one or pyrrolidin-2one (2) + pyridine (3) have been measured as a function of composition at (293.15, 298.15, 303.15, and 308.15) K and atmospheric pressure. The observed densities and speeds of sound data have been employed to determine excess molar volumes, VE and excess isentropic compressibilities, κES of the investigated mixtures. The observed thermodynamic properties of the binary as well as ternary mixtures have been calculated by utilizing the topology of the constituents of mixtures (graph theory). It has been observed that graph theory successfully describes well the VE and κES data of the studied binary and ternary ionic liquid mixtures.
1. INTRODUCTION The ionic liquids (ILs) stand for a class of liquids composed entirely of ions with very low melting points below 373.15 K. Because of their unique physical properties like low vapor pressure at normal temperature, thermal stablility, high conductivity, etc.,1−4 they have been considered as heat transfer solvents, lubricants for processing biomass, and the working fluid in batteries, capacitors, solar cells, and in biocatalysts.5−11 The design of industrial processes and new products based on ILs or their mixtures with organic solvents are only possible when their thermodynamics properties like excess molar volumes, VE, excess isentropic compressibilities, excess molar enthalpies, HE, and excess heat capacities, CEp are adequately known. However, these properties of the ionic liquids mixtures with organic molecular liquids are limited,12−20 which greatly restricts their applications and further development. Thus, there is a need of thermodynamic and physical properties data of ionic liquid mixtures. The diesel extractive desulfurization (EDS) process involves separation of sulfur compounds from fuel using a liquid extracting agent that is not miscible with diesel. According to the literature, oxidative desulfurization (ODS) seems to be a good alternative for diesel desulfurization.21−25 Imidazolium based ionic liquids are used for most of EDS, ODS, and ECODS studies.26,27 The 1-ethyl-3-methylimidazolium tetrafluoroborate is one of the investigated ionic liquids. In recent studies, we have studied VE, HE, and κES data of 1-ethyl-3-methylimidazolium tetrafluoroborate + 1-methylpyrrolidin-2-one or pyrrolidin-2-one binary mixtures to understand the molecular interactions among the constituents of mixtures and also tested graph theory28 (which deals with topology of a molecule) successfully to predict their © XXXX American Chemical Society
thermodynamic properties. Further, thermodynamics of ternary mixtures29−31 of ionic liquids has not received as much as attention as those of binary mixtures despite that all thermodynamic properties of ternary mixtures should, in principle, be determinable from the properties of their subbinary mixtures. In continuation of our work, we report here densities and speeds of sound data of 1-ethyl-3-methylimidazolium tetrafluoroborate + 1-methyl-pyrrolidin-2-one or pyrrolidin-2-one + pyridine ternary mixtures. It would be of great value to see how the topology of the constituent molecules of mixtures (graph theory) describes the VE and κES values of the investigated mixtures.
2. EXPERIMENTAL SECTION 1-Ethyl-3-methylimidazolium tetrafluoroborate [emim][BF4] (Fluka, 0.98 GC) was used without further purification. The content of water in ionic liquid was regularly checked using Karl Fischer titration32 and the content of water was less than 340 ppm. 1-Methyl pyrrolidin-2-one (NMP) [Fluka, 0.99 GC] was purified by fractional distillation under reduced pressure,33 pyrrolidin-2-one (2-Py) [Fluka, 0.99 GC] was purified by vacuum distillation over calcium oxide,34 and pyridine (Py) [Fluka, 0.99 GC] was refluxed over potassium hydroxide pellets for 5 h to 6 h and then distilled with careful exclusion of water.35 The purities of the liquids were checked by measuring their densities and speeds of sound values. The density and Received: December 21, 2012 Accepted: May 8, 2013
A
dx.doi.org/10.1021/je301353z | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
Table 1. Comparison of Densities, ρ, Speeds of Sound, u, Coefficients of Thermal Expansion, α, and Heat Capacities, Cp of the Pure Liquids with Their Literature Values at (293.15, 298.15, 303.15, and 308.15) Ka. ρ/(kg·m−3) liquids 1-ethyl-3-methyl imidazolium tetrafluoro borate
pyrrolidin-2-one
1-methyl pyrrolidin-2-one
pyridine
u/(m·s−1)
T/K
exptl.
lit.
exptl.
293.15 298.15 303.15 308.15 293.15 298.15 303.15 308.15 293.15 298.15 303.15 308.15 293.15 298.15 303.15 308.15
1283.89 1279.91 1276.26 1272.07 1111.28 1107.15 1103.02 1098.90 1033.23 1028.23 1023.46 1018.66 983.195 978.252 973.228 968.171
1284.3b 1279.6c 1280.07d 1276.5b 1275.7c 1271.9c 1272.48d
1631.05 1619.40 1607.63 1596.31 1650.13 1633.92 1617.14 1601.85 1565.52 1546.02 1527.24 1507.41 1442.04 1417.81 1397.97 1377.11
1107.01e 1107.20f 1102.0g 1103.37h 1098.63h 1033.23h 1032.87j 1028.23h 1023.47k 1023.40l m
983.19 978.249m 973.224m 968.166m
α(·103)/K−1
Cp/J·K−1·mol−1
lit.
exptl.
exptl.
lit.
303.41 305.12 306.81 308.58 168.36 169.55 171.18 172.37 165.44 166.22 166.92 167.21 130.49 131.74 132.71 133.82
303.2n 304.9n 306.6n 308.4n
1633.2I 1633.95h 1617.61h 1601.87h 1565.30h 1565.50j 1545.10h 1546.06I 1526.5h 1527.21j 1507.38h 1442.0m 1417.8m 1398.0m 1377.1m
0.615 0.596 0.614 0.648 0.743 0.746 0.748 0.749 0.951 0.950 0.934 0.942 1.012 1.029 1.036 1.043
169.37h
166.1g 167.0o 131.55p
a The standard uncertainty in temperature is ± 0.01 K. The standard uncertainty in density value is 0.5 kg·m−3. The standard uncertainty in speed of sound value is 0.1 m·s−1. The standard uncertainty in heat capacity is ± 0.3%. bReference 36. cReference 37. dReference 38. eReference 39. f Reference 40. gReference 41. hReference 42. IReference 43. jReference 44. kReference 45. lReference 46. mReference 47. nReference 51. oReference 52. pReference 53.
speed of sound values for the purified liquids at (293.15, 298.15, 303.15, and 308.15) K are reported in Table 1 and are also compared with literature values.36−47 Densities, ρ, and speeds of sound, u, values of the pure liquids and their binary as well as ternary mixtures were measured using a commercial density and sound analyzer apparatus (Anton Paar DSA 5000) in the manner as described elsewhere.48,49 The apparatus was calibrated with double distilled, deionized, and degassed water. The mole fraction of each mixture (made by mixing the two components in an airtight glass bottle) was obtained from the measured apparent masses of the components with uncertainty of 1.10−4 g. All the measurements were performed on an electric balance. 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 VE values calculated from density results is 0.1 %. Further, uncertainty in the temperature measurement is ± 0.01 K. The heat capacities of the pure studied liquids were measured by high sensitivity differential scanning calorimeter Micro DSC (model, 7 Evo) manufactured by Setaram Instrumentation, France, in the manner described elsewhere.50 The heat capacity of a liquid was measured in a standard batch cell (Hastalloy C276) composed of a cylinder of 6.4 mm of internal diameter and 19.5 mm height and had a capacity of containing 1 cm3 of a liquid. The calibration of equipment was done by Joule effect method which in turn is controlled by SETARAM software and checked by measuring the heat capacity of naphthalene (147.78 J·g−1). The reference experimental cell was filled with water (equivalent to the mass of liquid in a standard batch cell). For a scanning sequence the initial and final temperature were supplied along with heating rate of 0.4 K·min−1. The uncertainty in measuring heat capacity is ± 0.3%. The heat capacities of the pure liquids are recorded in Table 1 and also compared with literature values.41,42,51−53
Samples for IR studies were prepared by mixing components (2) and (3) in a 1:1 (w/w) ratio and their IR spectra were recorded on a Perkin-Elmer-Spectrum RX-I, FTIR spectrometer.
3. RESULTS The densities, ρ, speeds of sound, u, of binary mixtures NMP or 2-Py(2) + Py (3) and ρ123, u123, ternary mixtures [emim][BF4] (1) + NMP or 2-Py (2) + Py (3) at (293.15, 298.15, 303.15, and 308.15) K of the investigated mixtures are reported in Tables 2 and 3. The densities and speeds of sound data were utilized to determine excess molar volumes, VE, VE123, and isentropic compressibilities, κS, (κS)123 of binary and ternary mixtures using the following equations: 3
VE =
3
∑ xiMi(ρ)−1 − ∑ xiMi(ρi )−1 i=2
i=2
3 E V123 =
(1)
3
∑ xiMi(ρijk )−1 −
∑ xiMi(ρi )−1
i=1
i=1
(2)
(κS) = (ρu 2)−1
(3)
2 −1 (κS)123 = (ρ123 u123 )
(4)
also xi, Mi and ρi are the mole fraction, molar mass, and density of component i and ρ and ρ123 are the densities of binary and ternary mixtures, respectively. Excess isentropic compressibilities, κES and (κES )123 for the binary as well as ternary mixtures were determined using relation:
κSE = κS − κSid
(5)
κidS values for binary and ternary mixtures were obtained in the manner as suggested by Benson and Kiyohara54 using B
dx.doi.org/10.1021/je301353z | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
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Table 2. Measured Densities, ρ, Excess Molar Volumes, VE, Speeds of Sound, u, Isentropic Compressibilities, κS, and Excess Isentropic Compressibilities, κES , Data for the Studied Mixtures as a Function of Mole Fraction, x2, of Component (2) at (293.15, 298.15, 303.15, 308.15) Ka x2
0.1276 0.1779 0.2348 0.2664 0.3291 0.3707 0.4328 0.4749 0.5215 0.5647 0.6364 0.6778 0.7312 0.7701 0.8321 0.8711 0.9011 0.9312 0.1276 0.1779 0.2348 0.2664 0.3291 0.3707 0.4328 0.4749 0.5215 0.5647 0.6364 0.6778 0.7312 0.7701 0.8321 0.8711 0.9011 0.9312 0.1276 0.1779 0.2348 0.2664 0.3291 0.3707 0.4328 0.4749 0.5215 0.5647 0.6364 0.6778 0.7312 0.7701 0.8321 0.8711 0.9011 0.9312
ρ/kg·m−3
VE/cm3.mol−1
u/m·s−1
κS/TPa−1
1-Methyl Pyrrolidin-2-one (2) + Pyridine (3) T = 293.15 Kb 994.55 −0.3242 1467.79 466.71 998.64 −0.4309 1478.38 458.16 1003.00 −0.5349 1490.64 448.70 1005.29 −0.5853 1497.64 443.50 1009.56 −0.6671 1511.10 433.79 1012.20 −0.7101 1519.63 427.82 1015.86 −0.7553 1532.17 419.32 1018.16 −0.7748 1540.40 413.92 1020.50 −0.7814 1548.41 408.71 1022.48 −0.7736 1555.72 404.10 1025.43 −0.7385 1565.56 397.88 1026.91 −0.7018 1569.80 395.16 1028.58 −0.6356 1574.48 392.18 1029.65 −0.5761 1576.53 390.76 1031.09 −0.4602 1577.64 389.66 1031.80 −0.3712 1576.68 389.87 1032.27 −0.2968 1575.42 390.31 1032.65 −0.2143 1573.29 391.23 T = 298.15 Kc 989.82 −0.3464 1444.98 483.86 993.95 −0.4571 1455.90 474.65 998.35 −0.5662 1468.42 464.53 1000.65 −0.6179 1475.55 459.00 1004.94 −0.7033 1488.98 448.83 1007.56 −0.7454 1498.03 442.27 1011.21 −0.7910 1510.72 433.30 1013.51 −0.8103 1518.57 427.86 1015.82 −0.8148 1526.97 422.20 1017.80 −0.8082 1534.36 417.33 1020.74 −0.7718 1544.50 410.69 1022.19 −0.7322 1548.97 407.74 1023.87 −0.6670 1553.63 404.63 1024.90 −0.6039 1556.15 402.92 1026.29 −0.4824 1557.56 401.65 1026.99 −0.3919 1556.80 401.76 1027.41 −0.3122 1555.69 402.17 1027.76 −0.2265 1553.53 403.15 T = 303.15 Kd 985.09 −0.3719 1425.54 499.53 989.28 −0.4878 1436.75 489.68 993.72 −0.6005 1449.36 479.05 996.04 −0.6536 1456.17 473.48 1000.35 −0.7405 1469.79 462.74 1002.99 −0.7830 1478.87 455.87 1006.65 −0.8291 1491.60 446.50 1008.96 −0.8486 1499.51 440.79 1011.28 −0.8533 1508.29 434.67 1013.27 −0.8468 1515.26 429.83 1016.23 −0.8103 1525.63 422.78 1017.71 −0.7720 1530.76 419.33 1019.36 −0.7024 1535.63 416.01 1020.40 −0.6394 1537.76 414.43 1021.76 −0.5136 1539.31 413.05 1022.43 −0.4188 1538.89 413.00 1022.83 −0.3356 1537.40 413.64 1023.14 −0.2437 1535.38 414.61
κES /TPa−1
x2
ρ/kg·m−3
VE/cm3.mol−1
u/m·s−1
κS/TPa−1
κES /TPa−1
e
0.1276 0.1779 0.2348 0.2664 0.3291 0.3707 0.4328 0.4749 0.5215 0.5647 0.6364 0.6778 0.7312 0.7701 0.8321 0.8711 0.9011 0.9312
−10.38 −14.19 −18.29 −20.51 −24.31 −26.37 −29.01 −30.45 −31.27 −31.81 −31.27 −30.09 −28.04 −25.80 −21.05 −17.17 −13.90 −10.15 −11.70 −15.80 −20.13 −22.45 −26.25 −28.58 −31.24 −32.40 −33.32 −33.80 −33.16 −31.90 −29.58 −27.34 −22.31 −18.23 −14.77 −10.73
0.1333 0.1801 0.2312 0.2713 0.3312 0.3717 0.4312 0.4752 0.5316 0.5717 0.6219 0.6772 0.7314 0.7714 0.8312 0.8712 0.9013 0.9311
−12.60 −17.07 −21.62 −23.82 −27.86 −30.28 −33.02 −34.23 −35.37 −35.59 −34.98 −34.00 −31.62 −29.04 −23.80 −19.68 −15.83 −11.65
0.1333 0.1801 0.2312 0.2713 0.3312 0.3717 0.4312 0.4752 0.5316 0.5717 0.6219 0.6772 0.7314 0.7714 0.8312 0.8712 0.9013 0.9311
C
T = 308.15 K 980.30 −0.3954 1405.29 516.54 984.53 −0.5144 1416.42 506.28 988.98 −0.6282 1429.08 495.11 991.33 −0.6835 1436.21 489.04 995.65 −0.7708 1449.70 477.9 998.31 −0.8149 1458.76 470.72 1001.96 −0.8588 1471.49 460.93 1004.25 −0.8762 1479.41 454.97 1006.63 −0.8846 1487.90 448.73 1008.63 −0.8780 1495.42 443.35 1011.56 −0.8379 1505.86 435.95 1013.05 −0.7994 1510.48 432.65 1014.76 −0.7326 1515.39 429.13 1015.79 −0.6669 1518.07 427.18 1017.16 −0.5395 1519.65 425.72 1017.79 −0.4393 1519.08 425.78 1018.17 −0.3529 1517.60 426.45 1018.45 −0.2578 1515.59 427.46 Pyrrolidin-2-one (2) + Pyridine (3) T = 293.15 Kf 1001.83 −0.1805 1468.55 462.83 1008.31 −0.2322 1478.13 453.92 1015.32 −0.2811 1488.56 444.49 1020.76 −0.3127 1496.94 437.18 1028.79 −0.3479 1509.44 426.62 1034.17 −0.3656 1517.97 419.65 1041.94 −0.3789 1530.76 409.59 1047.59 −0.3792 1540.22 402.39 1054.74 −0.3705 1552.27 393.48 1059.77 −0.3586 1560.91 387.29 1065.97 −0.3342 1571.89 379.67 1072.71 −0.2997 1583.70 371.68 1079.26 −0.2590 1595.43 364.01 1084.05 −0.2245 1603.92 358.58 1091.16 −0.1676 1616.41 350.76 1095.91 −0.1283 1624.74 345.67 1099.48 −0.0976 1630.77 342.00 1103.03 −0.0677 1636.80 338.39 T = 298.15 Kg 997.07 −0.1895 1445.62 479.92 1003.57 −0.2420 1455.49 470.36 1010.62 −0.2913 1466.40 460.16 1016.10 −0.3229 1475.11 452.29 1024.17 −0.3584 1488.12 440.92 1029.56 −0.3755 1496.85 433.50 1037.41 −0.3911 1510.01 422.75 1043.13 −0.3938 1519.72 415.09 1050.35 −0.3866 1532.10 405.60 1055.45 −0.3767 1540.95 399.01 1061.74 −0.3559 1552.09 390.98 1068.57 −0.3233 1564.47 382.35 1075.19 −0.2840 1576.40 374.27 1080.04 −0.2510 1585.07 368.52 1087.20 −0.1931 1598.21 360.10 1091.96 −0.1509 1606.74 354.73 1095.53 −0.1179 1613.18 350.76 1099.05 −0.0835 1619.56 346.89
−13.73 −18.33 −23.09 −25.60 −29.68 −32.17 −34.97 −36.19 −37.18 −37.70 −37.02 −35.66 −33.16 −30.73 −25.21 −20.76 −16.71 −12.31
−5.13 −6.62 −7.94 −8.89 −9.95 −10.50 −11.12 −11.34 −11.30 −11.13 −10.78 −10.00 −9.07 −8.16 −6.49 −5.24 −4.13 −3.01 −5.92 −7.51 −9.02 −10.06 −11.24 −11.76 −12.38 −12.56 −12.45 −12.21 −11.70 −10.91 −9.77 −8.71 −6.95 −5.51 −4.36 −3.16
dx.doi.org/10.1021/je301353z | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
Table 2. continued ρ/kg·m−3
x2
VE/cm3.mol−1
u/m·s−1
κS/TPa−1
κES /TPa−1
ρ/kg·m−3
x2
VE/cm3.mol−1
h
0.1333 0.1801 0.2312 0.2713 0.3312 0.3717 0.4312 0.4752 0.5316 0.5717 0.6219 0.6772 0.7314 0.7714 0.8312 0.8712 0.9013 0.9311 a
992.29 998.88 1006.02 1011.55 1019.70 1025.16 1033.04 1038.77 1046.02 1051.12 1057.40 1064.23 1070.86 1075.69 1082.86 1087.64 1091.23 1094.78
T = 303.15 K −0.2041 1426.50 −0.2610 1436.72 −0.3145 1447.89 −0.3486 1456.59 −0.3865 1469.80 −0.4055 1478.85 −0.4198 1491.94 −0.4203 1501.85 −0.4113 1514.39 −0.3987 1523.21 −0.3729 1534.39 −0.3364 1546.67 −0.2929 1558.77 −0.2557 1567.58 −0.1933 1580.71 −0.1491 1589.35 −0.1152 1595.96 −0.0802 1602.39
u/m·s−1
κS/TPa−1
κES /TPa−1
511.94 501.11 489.60 480.75 468.03 459.74 447.82 439.39 428.83 421.50 412.68 403.27 394.43 388.06 378.80 372.87 368.44 364.21
−7.38 −9.32 −11.12 −12.35 −13.69 −14.28 −14.90 −14.97 −14.81 −14.52 −13.81 −12.71 −11.25 −10.02 −7.92 −6.25 −4.96 −3.53
i
495.24 485.00 474.16 465.95 453.95 446.03 434.89 426.80 416.85 410.04 401.69 392.79 384.33 378.31 369.59 363.98 359.78 355.74
−6.65 −8.51 −10.20 −11.23 −12.50 −13.17 −13.65 −13.86 −13.71 −13.34 −12.70 −11.69 −10.45 −9.30 −7.31 −5.76 −4.57 −3.27
0.1333 0.1801 0.2312 0.2713 0.3312 0.3717 0.4312 0.4752 0.5316 0.5717 0.6219 0.6772 0.7314 0.7714 0.8312 0.8712 0.9013 0.9311
T = 308.15 K −0.2101 1406.53 −0.2678 1416.90 −0.3200 1428.32 −0.3527 1437.43 −0.3922 1450.93 −0.4104 1460.01 −0.4247 1473.60 −0.4277 1483.49 −0.4222 1496.33 −0.4099 1505.57 −0.3881 1516.97 −0.3558 1529.51 −0.3142 1541.68 −0.2774 1550.73 −0.2165 1564.28 −0.1699 1573.18 −0.1331 1579.99 −0.0951 1586.56
987.38 994.01 1001.17 1006.71 1014.93 1020.41 1028.34 1034.15 1041.50 1046.65 1053.03 1059.98 1066.70 1071.59 1078.85 1083.64 1087.24 1090.78
The footnotes letters indicate the (2 + 3) mixtures at 293.15, 298.15, 303.15, and 308.15 K, respectively. The standard uncertainty in mole fraction value is 1.10−4. The standard uncertainty in temperature is ± 0.01 K. The standard uncertainty in density value is 0.5 kg·m−3. The standard uncertainty in speed of sound value is 0.1 m·s−1. The standard uncertainty in VE value is 0.1 %. Also included are various Vn and κnS (n = 0 to 2) parameters of eq 8 along with standard deviations, σ(VE) and σ(κES ). bV(0) = −3.1162; V(1) = −0.2652; V(2) = 0.0055; σ(VE) = 0.0008 cm3·mol−1; (1) (2) E −1 c (0) = −3.2580; V(1) = −0.2493; V(2) = −0.0769; σ(VE) = 0.0008 cm3·mol−1; κ(0) S = −123.87; κS = −40.53; κS = 1.24; σ(κS ) = 0.06 TPa . V (1) (2) E −1 d (0) = −132.15; κ = −38.96; κ = −3.03; σ(κ ) = 0.06 TPa . V = −3.4115; V(1) = −0.2563; V(2) = −0.2242; σ(VE) = 0.0008 cm3·mol−1; κ(0) S S S S (0) (1) (2) E −1 e (0) κS = −139.61; κS = −41.32; κS = −8.33; σ(κS ) = 0.07 TPa . V = −3.5294; V(1) = −0.2493; V(2) = −0.3675; σ(VE) = 0.0009 cm3·mol−1; (1) (2) E −1 f (0) = −1.5090; V(1) = 0.2842; V(2) = 0.2836; σ(VE) = 0.0004 cm3·mol−1; κ(0) κ(0) S = −147.51; κS = −41.32; κS = −11.42; σ(κS ) = 0.07 TPa . V S = (1) (2) E −1 g (0) −45.40; κS = −1.28; κS = −0.27; σ(κS ) = 0.03 TPa . V = −1.5676; V(1) = 0.1988; V(2) = 0.1312; σ(VE) = 0.0004 cm3·mol−1; κ(0) S = −50.18; (2) E (1) −1 h (0) = −1.6733; V(1) = 0.2949; V(2) = 0.2241; σ(VE) = 0.0004 cm3·mol−1; κ(0) κ(1) S = 1.21; κS = −0.02; σ(κS ) = 0.03 TPa . V S = −55.23; κS = 4.25; (2) E (1) (2) −1 i (0) (1) (2) E 3 −1 (0) κS = −1.05; σ(κS ) = 0.03 TPa . V = −1.7068; V = 0.2050; V = 0.0671; σ(V ) = 0.0005 cm ·mol ; κS = −59.92; κS = 5.30; κS = 0.24; σ(κES ) = 0.03 TPa−1. 3 3 ⎡ (∑ j = 2 ϕα )2 Tvjαj2 ⎤ j j ⎢ ⎥ = ∑ ϕj κS, j + − T (∑ xjvj) 3 ⎢ Cp, j ⎥⎦ (∑ j = 2 xjCp, j) j=2 ⎣ j=2
The VE123 and (κES )123 values of the ternary mixtures were fitted to Redlich−Kister eq 9
3
κSid
E (X = V or κS) X123
(6)
2 (n) )(x1 − x 2)n ] = x1x 2[ ∑ (X12
3 3 ⎡ (∑i = 1 ϕα )2 Tviαi2 ⎤ i i ⎢ ⎥ T ( x v ) ϕ κ + − ∑ i S,i ∑ ii 3 ⎢ Cp, i ⎥⎦ (∑i = 1 xiCp, i) i=1 ⎣ i=1 3
κSid =
n=0 2 (n) )(x 2 − x3)n ] + x 2x3[ ∑ (X 23
(7)
n=0 2
where ϕi, κS,i, vi, αi, and Cp,i (i = 1 or 2 or 3) are the volume fraction, isentropic compressibility, molar volume, thermal expansion coefficient, and molar heat capacity of pure component i. The α values for [emim][BF4], NMP, 2-Py, and Py were calculated using experimental density data in the manner described elsewhere55 and are listed in Table 1. The VE, κES and VE123, (κES )123 values for the studied mixtures are recorded in Tables 2 and 3. The VE and κES data for the binary mixtures were expressed by eq 8
(n) )(x1 − x3)n ] + x1x3[ ∑ (X13 n=0 2 (n) )(x 2 − x3)n x1n] + x1x 2x3[ ∑ (X123 n=0
where (n = 0 to 2) etc. are the adjustable parameters of the constituent binaries. The Xn parameters for [emim][BF4] + NMP or 2-Py or Py mixtures were taken from literature.15,34 The X(n) 123 (X = V or κS) (n = 0 to 2) and so forth, are parameters characteristic of (1 + 2 + 3) mixture and were determined by fitting the measured data to eq 9 by least-squares optimization. The resulting parameters along with standard deviations σ (XE123) (X = V or κS) expressed by the relation,
X E(X = V or κS) = x 2x3[X (0) + X (1)(2x 2 − 1) + X (2)(2x 2 − 1)2 ]
(9)
X(n) 12
(8)
where X(n)(X = V or κS) (n = 0 to 2), and so forth, are the parameters characteristic of binary mixtures. These parameters were determined by fitting XE(X = V or κS) data to eq 8 using least-squares method and are recorded along with standard deviations, σ(XE) (X = V or κS) in Table 2.
E E E σ(X123 ) = {[∑ X123 − X123{calc.Eq.(9)} ]2 /(m − n)}0.5
(10)
where m is the number of data points and n is the number of adjustable parameters of eq 9 and are recorded in Table 3. The D
dx.doi.org/10.1021/je301353z | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
Table 3. Measured Densities, ρ123, Excess Molar Volumes, VE, Speeds of Sound, u123, Isentropic Compressibilities, κS, and Excess Isentropic Compressibilities, κES Data Compared with Graph Theory for the Various (1 + 2 + 3) Mixtures as a Function of Mole Fraction, x1, of Component (1) and x2, of Component (2) at (293.15, 298.15, 303.15, and 308.15) Ka ρ123 x1
x2
0.1799 0.1941 0.2044 0.2223 0.2602 0.3018 0.3271 0.3476 0.3645 0.3893 0.3947 0.4029 0.4121 0.4330 0.4454 0.4676 0.4844 0.5024 0.5247 0.5405 0.5531 0.5768 0.5862 0.6003 0.6221 0.6462 0.6651 0.6788 0.6918 0.7231
0.7366 0.7092 0.6892 0.6252 0.5285 0.4912 0.4723 0.4674 0.4481 0.4215 0.4159 0.4076 0.3985 0.3784 0.3669 0.3469 0.3323 0.3169 0.2985 0.2856 0.2755 0.2567 0.2493 0.2383 0.2214 0.2021 0.1883 0.1778 0.1679 0.1443
0.1799 0.1941 0.2044 0.2223 0.2602 0.3018 0.3271 0.3476 0.3645 0.3893 0.3947 0.4029 0.4121 0.4330 0.4454 0.4676 0.4844 0.5024 0.5247 0.5405 0.5531 0.5768 0.5862 0.6003
0.7366 0.7092 0.6892 0.6252 0.5285 0.4912 0.4723 0.4674 0.4481 0.4215 0.4159 0.4076 0.3985 0.3784 0.3669 0.3469 0.3323 0.3169 0.2985 0.2856 0.2755 0.2567 0.2493 0.2383
−3
kg·m
u123 −1
m·s
VE123 (exptl) cm ·mol 3
VE123 (graph)
−1
−1
cm ·mol 3
(κS)123 TPa
−1
(κES )123 (exptl) TPa
−1
1-Ethyl-3-methylimidazolium Tetrafluoroborate (1) + 1-Methyl pyrrolidin-2-one (2) + Pyridine (3) T = 293.15 Kb 1100.18 1579.56 −0.3810 −0.3656 364.3 −20.09 1103.06 1578.10 −0.2446 −0.2446 364.03 −20.16 1105.18 1577.06 −0.1510 −0.1598 363.81 −20.24 1110.58 1580.83 −0.2327 −0.2353 360.31 −26.25 1126.73 1591.98 −0.7734 −0.7762 350.19 −38.04 1138.55 1591.15 −0.6873 −0.6814 346.92 −36.66 1145.13 1589.74 −0.5949 −0.5909 345.53 −34.86 1148.10 1583.65 −0.2814 −0.2919 347.30 −29.53 1154.01 1586.22 −0.4018 −0.4081 344.40 −30.93 1162.61 1590.19 −0.5836 −0.5861 340.15 −32.82 1164.48 1591.08 −0.6245 −0.6245 339.22 −33.21 1167.28 1592.43 −0.6847 −0.6835 337.84 −33.77 1170.39 1593.92 −0.7509 −0.7495 336.31 −34.35 1177.35 1597.34 −0.9002 −0.8942 332.89 −35.56 1181.38 1599.33 −0.9842 −0.9771 330.93 −36.17 1188.39 1602.81 −1.1235 −1.1163 327.55 −37.07 1193.54 1605.24 −1.2231 −1.2140 325.15 −37.55 1198.89 1607.81 −1.3198 −1.3074 322.67 −37.95 1205.18 1610.62 −1.4182 −1.4112 319.86 −38.11 1209.48 1612.47 −1.4790 −1.4722 317.99 −38.09 1212.78 1613.81 −1.5189 −1.5148 316.6 −37.96 1218.71 1616.04 −1.5765 −1.5765 314.19 −37.49 1220.97 1616.81 −1.5927 −1.5941 313.31 −37.22 1224.23 1617.84 −1.6088 −1.6136 312.08 −36.72 1229.01 1619.10 −1.6152 −1.6256 310.38 −35.73 1233.97 1620.13 −1.6002 −1.6002 308.74 −34.46 1237.52 1620.44 −1.5597 −1.5816 307.74 −33.05 1239.98 1620.55 −1.5229 −1.5483 307.09 −32.00 1242.20 1620.52 −1.4795 −1.5087 306.55 −30.92 1247.16 1620.10 −1.3456 −1.3821 305.49 −28.06 T = 298.15 Kc 1095.57 1560.23 −0.4044 −0.3901 374.96 −20.82 1098.35 1558.73 −0.2548 −0.2548 374.73 −20.84 1100.38 1557.72 −0.1517 −0.1598 374.52 −20.91 1105.68 1562.25 −0.2222 −0.2249 370.57 −27.60 1122.01 1575.27 −0.7802 −0.7863 359.16 −40.85 1133.81 1574.74 −0.6871 −0.6909 355.66 −39.38 1140.38 1573.36 −0.5897 −0.5811 354.24 −37.40 1143.22 1566.76 −0.2592 −0.2687 356.34 −31.48 1149.21 1569.75 −0.3865 −0.3923 353.13 −33.09 1157.94 1574.32 −0.5795 −0.5820 348.44 −35.26 1159.84 1575.33 −0.6230 −0.6230 347.42 −35.71 1162.68 1576.87 −0.6871 −0.6861 345.9 −36.35 1165.84 1578.60 −0.7578 −0.7567 344.21 −37.03 1172.91 1582.51 −0.9173 −0.9117 340.44 −38.44 1177.01 1584.77 −1.0072 −1.0005 338.29 −39.15 1184.16 1588.70 −1.1599 −1.1501 334.58 −40.21 1189.37 1591.49 −1.2639 −1.2552 331.95 −40.79 1194.80 1594.41 −1.3682 −1.3559 329.23 −41.28 1201.20 1597.59 −1.4749 −1.4682 326.18 −41.51 1205.56 1599.70 −1.5411 −1.5344 324.14 −41.53 1208.90 1601.24 −1.5848 −1.5807 322.62 −41.42 1214.92 1603.77 −1.6485 −1.6485 320.01 −40.95 1217.20 1604.65 −1.6667 −1.6680 319.07 −40.67 1220.49 1605.81 −1.6852 −1.6901 317.75 −40.14 E
(κES )123 (graph) TPa−1
−19.56 −20.16 −20.59 −26.91 −38.62 −37.13 −35.28 −30.01 −31.22 −32.88 −33.21 −33.70 −34.23 −35.31 −35.87 −36.71 −37.21 −37.59 −37.87 −37.90 −37.84 −37.49 −37.26 −36.83 −35.93 −34.46 −33.30 −32.21 −31.08 −27.94 −20.18 −20.84 −21.31 −28.41 −41.36 −39.89 −37.93 −32.04 −33.42 −35.33 −35.71 −36.28 −36.89 −38.15 −38.80 −39.80 −40.40 −40.87 −41.24 −41.32 −41.28 −40.95 −40.72 −40.27
dx.doi.org/10.1021/je301353z | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
Table 3. continued x1
x2
ρ123
u123
VE123 (exptl)
kg·m−3
m·s−1
cm3·mol−1
VE123 (graph)
(κS)123
(κES )123 (exptl)
(κES )123 (graph)
cm3·mol−1
TPa−1
TPa−1
TPa−1
−1.7051 −1.6807 −1.6631 −1.6293 −1.5889 −1.4586
315.92 314.18 313.13 312.45 311.9 310.86
−39.09 −37.72 −36.19 −35.05 −33.87 −30.72
−39.32 −37.72 −36.46 −35.27 −34.02 −30.55
−0.3888 −0.2344 −0.1257 −0.1987 −0.7811 −0.6821 −0.5610 −0.1977 −0.3301 −0.5345 −0.5788 −0.6471 −0.7236 −0.8920 −0.9888 −1.1523 −1.2678 −1.3789 −1.5036 −1.5779 −1.6304 −1.7088 −1.7322 −1.7597 −1.7821 −1.7645 −1.7517 −1.7208 −1.6829 −1.5570
384.57 384.15 383.82 379.54 367.65 363.81 362.17 364.16 360.82 355.92 354.84 353.26 351.50 347.57 345.32 341.45 338.69 335.85 332.64 330.5 328.91 326.15 325.14 323.74 321.79 319.91 318.77 318.02 317.40 316.21
−22.44 −22.62 −22.80 −29.93 −43.72 −42.29 −40.31 −34.28 −35.93 −38.15 −38.62 −39.27 −39.95 −41.38 −42.09 −43.16 −43.74 −44.22 −44.43 −44.43 −44.30 −43.79 −43.50 −42.94 −41.84 −40.42 −38.83 −37.65 −36.43 −33.18
−21.80 −22.62 −23.21 −30.53 −44.21 −42.79 −40.84 −34.85 −36.28 −38.23 −38.62 −39.20 −39.82 −41.09 −41.76 −42.75 −43.35 −43.81 −44.16 −44.21 −44.16 −43.79 −43.54 −43.07 −42.07 −40.42 −39.10 −37.88 −36.59 −33.03
−0.3542 −0.1767 −0.0516 −0.0981 −0.6924 −0.5701 −0.4616 −0.0825 −0.2259 −0.4484 −0.4968 −0.5715 −0.6552 −0.8402 −0.9468 −1.1276 −1.2558 −1.3799 −1.5199 −1.6042
395.13 394.53 394.05 389.17 376.24 371.95 370.12 372.14 368.55 363.33 362.19 360.51 358.64 354.48 352.10 348.02 345.12 342.14 338.78 336.54
−24.07 −24.41 −24.71 −32.57 −47.44 −46.10 −44.09 −37.78 −39.55 −41.91 −42.41 −43.09 −43.81 −45.30 −46.04 −47.13 −47.71 −48.17 −48.34 −48.30
−23.35 −24.41 −25.17 −26.57 −29.90 −33.99 −36.48 −38.42 −39.94 −42.00 −42.41 −43.02 −43.67 −44.98 −45.66 −46.68 −47.27 −47.72 −48.03 −48.05
c
0.6221 0.6462 0.6651 0.6788 0.6918 0.7231
0.2214 0.2021 0.1883 0.1778 0.1679 0.1443
1225.32 1230.32 1233.88 1236.34 1238.56 1243.50
1607.26 1608.44 1608.80 1608.94 1608.92 1608.41
0.1799 0.1941 0.2044 0.2223 0.2602 0.3018 0.3271 0.3476 0.3645 0.3893 0.3947 0.4029 0.4121 0.4330 0.4454 0.4676 0.4844 0.5024 0.5247 0.5405 0.5531 0.5768 0.5862 0.6003 0.6221 0.6462 0.6651 0.6788 0.6918 0.7231
0.7366 0.7092 0.6892 0.6252 0.5285 0.4912 0.4723 0.4674 0.4481 0.4215 0.4159 0.4076 0.3985 0.3784 0.3669 0.3469 0.3323 0.3169 0.2985 0.2856 0.2755 0.2567 0.2493 0.2383 0.2214 0.2021 0.1883 0.1778 0.1679 0.1443
1090.92 1093.54 1095.47 1100.85 1117.37 1129.14 1135.67 1138.11 1144.19 1153.07 1155.00 1157.90 1161.12 1168.34 1172.52 1179.83 1185.15 1190.71 1197.24 1201.70 1205.12 1211.26 1213.59 1216.95 1221.87 1226.95 1230.56 1233.05 1235.30 1240.28
1543.89 1542.87 1542.18 1547.05 1560.21 1560.24 1559.25 1553.31 1556.35 1560.98 1562.03 1563.58 1565.31 1569.27 1571.54 1575.53 1578.38 1581.34 1584.60 1586.77 1588.36 1591.01 1591.95 1593.19 1594.78 1596.15 1596.66 1596.92 1597.01 1596.81
0.1799 0.1941 0.2044 0.2223 0.2602 0.3018 0.3271 0.3476 0.3645 0.3893 0.3947 0.4029 0.4121 0.4330 0.4454 0.4676 0.4844 0.5024 0.5247 0.5405
0.7366 0.7092 0.6892 0.6252 0.5285 0.4912 0.4723 0.4674 0.4481 0.4215 0.4159 0.4076 0.3985 0.3784 0.3669 0.3469 0.3323 0.3169 0.2985 0.2856
1085.80 1088.21 1090.00 1095.05 1111.81 1123.44 1129.88 1132.33 1138.51 1147.56 1149.53 1152.49 1155.78 1163.16 1167.44 1174.92 1180.38 1186.06 1192.75 1197.32
1526.70 1526.18 1525.85 1531.84 1546.15 1546.96 1546.37 1540.50 1543.76 1548.67 1549.79 1551.41 1553.23 1557.35 1559.72 1563.84 1566.77 1569.79 1573.13 1575.34
T = 298.15 K −1.6943 −1.6807 −1.6397 −1.6018 −1.5569 −1.4175 T = 303.15 Kd −0.4015 −0.2344 −0.1189 −0.1973 −0.7750 −0.6721 −0.5672 −0.1906 −0.3258 −0.5321 −0.5788 −0.6477 −0.7238 −0.8963 −0.9940 −1.1607 −1.2749 −1.3902 −1.5093 −1.5841 −1.6341 −1.7088 −1.7310 −1.7550 −1.7714 −1.7645 −1.7264 −1.6902 −1.6462 −1.5066 T = 308.15 Ke −0.3660 −0.1767 −0.0455 −0.0925 −0.6986 −0.5774 −0.4598 −0.0772 −0.2227 −0.4461 −0.4968 −0.5718 −0.6549 −0.8438 −0.9512 −1.1352 −1.2620 −1.3907 −1.5250 −1.6101 F
dx.doi.org/10.1021/je301353z | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
Table 3. continued x1
x2
ρ123
u123
VE123 (exptl)
kg·m−3
m·s−1
cm3·mol−1
VE123 (graph)
(κS)123
(κES )123 (exptl)
(κES )123 (graph)
cm3·mol−1
TPa−1
TPa−1
TPa−1
−48.12 −47.51 −47.17 −46.54 −45.31 −43.73 −41.99 −40.70 −39.37 −35.85
−47.97 −47.51 −47.22 −46.68 −45.55 −43.73 −42.27 −40.92 −39.51 −35.60
319.27 319.81 320.81 317.13 322.43 322.34 321.85 321.26 320.17 319.06 318.18 316.67 315.85 315.85 313.90 313.07 311.54 310.69 309.68 308.00 306.82 306.01 304.64 304.31 303.29 301.51 298.34 297.45 296.5 296.27
−16.58 −18.55 −19.75 −21.32 −23.07 −24.58 −25.9 −26.69 −27.64 −28.26 −28.65 −29.11 −29.28 −29.38 −29.54 −29.58 −29.61 −29.63 −29.60 −29.55 −29.51 −29.51 −29.54 −29.58 −29.66 −30.14 −32.50 −33.60 −30.31 −27.64
−16.07 −18.55 −20.08 −21.88 −23.64 −25.05 −26.26 −26.96 −27.81 −28.35 −28.71 −29.11 −29.27 −29.36 −29.50 −29.53 −29.55 −29.57 −29.54 −29.50 −29.47 −29.49 −29.54 −29.59 −29.71 −30.25 −32.50 −33.42 −31.44 −29.38
326.64 327.08 328.09 324.04 329.63 329.45 328.87 328.2 326.98 325.78 324.81 323.2 322.31 321.7 320.21
−17.46 −19.71 −21.07 −22.85 −24.83 −26.53 −28.01 −28.89 −29.95 −30.64 −31.07 −31.57 −31.76 −31.87 −32.04
−16.84 −19.71 −21.50 −23.59 −25.61 −27.19 −28.52 −29.28 −30.20 −30.78 −31.15 −31.57 −31.73 −31.83 −31.96
e
0.5531 0.5768 0.5862 0.6003 0.6221 0.6462 0.6651 0.6788 0.6918 0.7231
0.2755 0.2567 0.2493 0.2383 0.2214 0.2021 0.1883 0.1778 0.1679 0.1443
0.1797 0.1952 0.2041 0.2181 0.2381 0.2598 0.2831 0.3001 0.3255 0.3471 0.3637 0.3897 0.4036 0.4131 0.4355 0.4487 0.4731 0.4865 0.5025 0.5285 0.5465 0.5587 0.5789 0.5835 0.5979 0.6206 0.6489 0.6531 0.6911 0.7144
0.7437 0.7087 0.6838 0.6798 0.6106 0.5748 0.5407 0.5184 0.4879 0.4642 0.4468 0.4212 0.4081 0.3993 0.3793 0.3679 0.3472 0.3358 0.3226 0.3013 0.2867 0.2767 0.2602 0.2563 0.2444 0.2245 0.1946 0.1881 0.1678 0.1572
0.1797 0.1952 0.2041 0.2181 0.2381 0.2598 0.2831 0.3001 0.3255 0.3471 0.3637 0.3897 0.4036 0.4131 0.4355
0.7437 0.7087 0.6838 0.6798 0.6106 0.5748 0.5407 0.5184 0.4879 0.4642 0.4468 0.4212 0.4081 0.3993 0.3793
T = 308.15 K 1200.81 1576.94 −1.6678 −1.6643 1207.09 1579.61 −1.7557 −1.7557 1209.47 1580.55 −1.7826 −1.7838 1212.90 1581.81 −1.8131 −1.8179 1217.92 1583.40 −1.8381 −1.8492 1223.09 1584.74 −1.8392 −1.8392 1226.74 1585.23 −1.8044 −1.8321 1229.26 1585.47 −1.7701 −1.8042 1231.53 1585.54 −1.7272 −1.7687 1236.53 1585.31 −1.5870 −1.6467 1-Ethyl-3-methylimidazolium tetrafluoroborate (1) + Pyrrolidin-2-one T = 293.15 Kf 1159.56 1643.51 −0.3359 −0.3042 1161.36 1640.86 −0.3482 −0.3482 1162.05 1637.81 −0.3733 −0.3754 1167.13 1643.70 −0.4192 −0.4186 1167.14 1630.12 −0.4806 −0.4803 1171.38 1627.40 −0.5451 −0.5472 1176.28 1625.24 −0.6174 −0.6181 1179.98 1624.17 −0.6677 −0.6684 1185.60 1623.09 −0.7402 −0.7407 1190.39 1622.61 −0.7973 −0.7988 1194.06 1622.38 −0.8411 −0.8414 1199.72 1622.39 −0.9033 −0.9033 1202.69 1622.49 −0.9342 −0.9340 1204.70 1622.47 −0.9550 −0.9540 1209.35 1623.05 −0.9983 −0.9976 1212.02 1623.39 −1.0207 −1.0210 1216.84 1624.16 −1.0586 −1.0594 1219.42 1624.64 −1.0793 −1.0780 1222.41 1625.31 −1.0985 −1.0974 1227.10 1626.61 −1.1242 −1.1227 1230.21 1627.67 −1.1363 −1.1354 1232.26 1628.47 −1.1430 −1.1418 1235.51 1629.99 −1.1481 −1.1481 1236.23 1630.39 −1.1493 −1.1489 1238.42 1631.68 −1.1478 −1.1491 1241.67 1634.35 −1.1418 −1.1437 1245.06 1640.77 −1.1255 −1.1255 1245.37 1643.03 −1.1218 −1.1213 1250.58 1642.23 −1.0165 −1.0765 1253.75 1640.78 −0.9456 −1.0409 T = 298.15 Kg 1156.09 1627.31 −0.3935 −0.3719 1157.92 1624.92 −0.4111 −0.4111 1158.58 1621.97 −0.4351 −0.4337 1163.62 1628.53 −0.4773 −0.4697 1163.50 1614.75 −0.5332 −0.5232 1167.65 1612.32 −0.5914 −0.5827 1172.43 1610.45 −0.6557 −0.6468 1176.06 1609.59 −0.7003 −0.6928 1181.58 1608.81 −0.7646 −0.7593 1186.29 1608.58 −0.8152 −0.8128 1189.90 1608.52 −0.8539 −0.8520 1195.48 1608.78 −0.909 −0.9090 1198.41 1609.02 −0.9365 −0.9372 1200.40 1609.22 −0.955 −0.9556 1205.00 1609.86 −0.9938 −0.9956 G
334.88 332.02 330.97 329.51 327.49 325.56 324.39 323.62 323.00 321.79 (2) + Pyridine (3)
dx.doi.org/10.1021/je301353z | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
Table 3. continued x1
x2
ρ123
u123
VE123 (exptl)
kg·m−3
m·s−1
cm3·mol−1
VE123 (graph)
(κS)123
(κES )123 (exptl)
(κES )123 (graph)
cm3·mol−1
TPa−1
TPa−1
TPa−1
−1.0169 −1.0521 −1.0694 −1.0873 −1.1114 −1.1242 −1.1313 −1.1399 −1.1416 −1.1449 −1.1485 −1.1575 −1.1628 −1.1161 −1.0730
319.33 317.69 316.79 315.68 313.88 312.61 311.72 310.21 309.85 308.72 306.72 303.02 301.93 301.09 301.01
−32.08 −32.11 −32.13 −32.11 −32.06 −32.03 −32.05 −32.11 −32.17 −32.29 −32.9 −35.73 −37.04 −33.33 −30.31
−32.00 −32.01 −32.04 −32.01 −31.98 −31.97 −32.01 −32.11 −32.18 −32.35 −33.04 −35.73 −36.81 −34.63 −32.32
−0.3775 −0.4145 −0.4357 −0.4719 −0.5282 −0.5921 −0.6615 −0.7116 −0.7841 −0.8428 −0.8857 −0.9483 −0.9793 −0.9995 −1.0435 −1.0669 −1.1054 −1.1240 −1.1433 −1.1683 −1.1809 −1.1873 −1.1937 −1.1945 −1.1951 −1.1909 −1.1780 −1.1759 −1.1294 −1.0906
334.29 334.76 335.82 331.52 337.33 337.07 336.35 335.58 334.17 332.81 331.7 329.87 328.86 328.16 326.48 325.48 323.62 322.58 321.35 319.3 317.87 316.88 315.2 314.8 313.55 311.35 307.34 306.18 305.25 305.14
−18.28 −20.63 −22.05 −23.95 −26.08 −27.92 −29.56 −30.54 −31.76 −32.56 −33.09 −33.72 −33.98 −34.14 −34.42 −34.52 −34.66 −34.75 −34.79 −34.86 −34.9 −34.97 −35.11 −35.18 −35.36 −36.07 −39.13 −40.52 −36.63 −33.45
−17.68 −20.63 −22.46 −24.62 −26.74 −28.45 −29.95 −30.83 −31.92 −32.65 −33.13 −33.72 −33.97 −34.12 −34.38 −34.48 −34.61 −34.70 −34.74 −34.81 −34.86 −34.94 −35.11 −35.20 −35.41 −36.20 −39.13 −40.30 −37.99 −35.53
−0.3983 −0.4305 −0.4480 −0.4808 −0.5359 −0.6010 −0.6729 −0.7254 −0.8021 −0.8646 −0.9104
341.51 342.03 343.14 338.57 344.73 344.42 343.64 342.8 341.28 339.8 338.61
−19.4 −21.87 −23.39 −25.41 −27.68 −29.66 −31.42 −32.48 −33.8 −34.68 −35.26
−18.77 −21.87 −23.79 −26.06 −28.31 −30.15 −31.77 −32.73 −33.94 −34.75 −35.30
g
0.4487 0.4731 0.4865 0.5025 0.5285 0.5465 0.5587 0.5789 0.5835 0.5979 0.6206 0.6489 0.6531 0.6911 0.7144
0.3679 0.3472 0.3358 0.3226 0.3013 0.2867 0.2767 0.2602 0.2563 0.2444 0.2245 0.1946 0.1881 0.1678 0.1572
1207.66 1212.45 1215.01 1218.00 1222.70 1225.83 1227.89 1231.18 1231.91 1234.15 1237.49 1241.15 1241.56 1246.79 1249.94
1610.30 1611.27 1611.86 1612.69 1614.20 1615.42 1616.36 1618.11 1618.58 1620.06 1623.15 1630.62 1633.29 1632.13 1630.29
0.1797 0.1952 0.2041 0.2181 0.2381 0.2598 0.2831 0.3001 0.3255 0.3471 0.3637 0.3897 0.4036 0.4131 0.4355 0.4487 0.4731 0.4865 0.5025 0.5285 0.5465 0.5587 0.5789 0.5835 0.5979 0.6206 0.6489 0.6531 0.6911 0.7144
0.7437 0.7087 0.6838 0.6798 0.6106 0.5748 0.5407 0.5184 0.4879 0.4642 0.4468 0.4212 0.4081 0.3993 0.3793 0.3679 0.3472 0.3358 0.3226 0.3013 0.2867 0.2767 0.2602 0.2563 0.2444 0.2245 0.1946 0.1881 0.1678 0.1572
1152.11 1153.85 1154.49 1159.58 1159.45 1163.63 1168.47 1172.14 1177.73 1182.5 1186.15 1191.80 1194.77 1196.78 1201.43 1204.11 1208.94 1211.52 1214.53 1219.25 1222.38 1224.44 1227.73 1228.45 1230.67 1233.95 1237.39 1237.7 1243.01 1246.23
1611.34 1609 1606.02 1612.85 1598.99 1596.73 1595.12 1594.44 1594.01 1594.05 1594.25 1594.88 1595.34 1595.7 1596.71 1597.37 1598.76 1599.6 1600.69 1602.7 1604.24 1605.41 1607.53 1608.06 1609.83 1613.35 1621.57 1624.43 1623.44 1621.63
0.1797 0.1952 0.2041 0.2181 0.2381 0.2598 0.2831 0.3001 0.3255 0.3471 0.3637
0.7437 0.7087 0.6838 0.6798 0.6106 0.5748 0.5407 0.5184 0.4879 0.4642 0.4468
1148.07 1149.75 1150.37 1155.46 1155.27 1159.44 1164.28 1167.95 1173.55 1178.34 1182.01
1597.04 1594.66 1591.65 1598.81 1584.61 1582.45 1580.96 1580.39 1580.13 1580.34 1580.67
T = 298.15 K −1.0140 −1.0485 −1.0676 −1.0858 −1.1109 −1.1239 −1.1317 −1.1399 −1.1421 −1.1443 −1.1474 −1.1575 −1.1638 −1.0587 −0.9840 T = 303.15 Kh −0.4032 −0.4145 −0.4383 −0.482 −0.5408 −0.6026 −0.672 −0.7204 −0.7903 −0.8455 −0.8879 −0.9483 −0.9785 −0.9987 −1.0412 −1.0633 −1.1009 −1.1216 −1.141 −1.1673 −1.1801 −1.1874 −1.1937 −1.1952 −1.1948 −1.1908 −1.1780 −1.1751 −1.0737 −1.0046 T = 308.15 Ki −0.4216 −0.4305 −0.4540 −0.4979 −0.5569 −0.6193 −0.6903 −0.7400 −0.8123 −0.8697 −0.914 H
dx.doi.org/10.1021/je301353z | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
Table 3. continued x1
x2
ρ123
u123
VE123 (exptl)
kg·m−3
m·s−1
cm3·mol−1
VE123 (graph)
(κS)123
(κES )123 (exptl)
(κES )123 (graph)
cm3·mol−1
TPa−1
TPa−1
TPa−1
336.62 335.53 334.78 332.97 331.89 329.88 328.76 327.42 325.22 323.67 322.6 320.79 320.37 319.03 316.68 312.45 311.24 308.78 307.90
−35.97 −36.27 −36.45 −36.77 −36.9 −37.08 −37.2 −37.27 −37.38 −37.45 −37.54 −37.71 −37.79 −37.99 −38.76 −41.99 −43.44 −40.78 −38.17
−35.97 −36.26 −36.44 −36.75 −36.88 −37.06 −37.17 −37.24 −37.34 −37.42 −37.52 −37.71 −37.80 −38.04 −38.89 −41.99 −43.22 −40.78 −38.17
i
0.3897 0.4036 0.4131 0.4355 0.4487 0.4731 0.4865 0.5025 0.5285 0.5465 0.5587 0.5789 0.5835 0.5979 0.6206 0.6489 0.6531 0.6911 0.7144
0.4212 0.4081 0.3993 0.3793 0.3679 0.3472 0.3358 0.3226 0.3013 0.2867 0.2767 0.2602 0.2563 0.2444 0.2245 0.1946 0.1881 0.1678 0.1572
1187.68 1190.67 1192.69 1197.37 1200.06 1204.92 1207.52 1210.55 1215.29 1218.44 1220.51 1223.81 1224.54 1226.76 1230.04 1233.44 1233.72 1239.06 1242.31
1581.53 1582.12 1582.55 1583.75 1584.54 1586.15 1587.13 1588.39 1590.65 1592.38 1593.67 1595.99 1596.58 1598.48 1602.25 1610.84 1613.78 1616.69 1616.88
T = 308.15 K −0.9775 −0.9775 −1.0094 −1.0108 −1.0309 −1.0326 −1.0761 −1.0800 −1.0998 −1.1054 −1.1403 −1.1471 −1.1627 −1.1672 −1.1839 −1.1882 −1.213 −1.2155 −1.2275 −1.2293 −1.2358 −1.2363 −1.2434 −1.2434 −1.2452 −1.2443 −1.2453 −1.2450 −1.2414 −1.2403 −1.2246 −1.2246 −1.2195 −1.2216 −1.1196 −1.1748 −1.0518 −1.1360
a
The footnotes letters indicate the (1 + 2 + 3) mixtures at (293.15, 298.15, 303.15, and 308.15) K, respectively. The standard uncertainty in mole fraction value is 1.10−4. The standard uncertainty in temperature is ± 0.01 K. The standard uncertainty in density value is 0.5 kg·m−3. The standard uncertainty in speed of sound value is 0.1 m·s−1. The standard uncertainty in VE value is 0.1 %. Also included are various X(n) 123 (X = V or κS) (n = 0 to 2) parameters of eq 9 along with standard deviations, σ(VE123) and σ (κES )123 and various (3ξi), (3ξi)m (i = 1 or 2 or 3); χ*12 etc. and χ* parameters: b (0) (1) (2) E V = −3.3910; V(1) = −252.1199 V(2) = 8439.2679; σ(VE) = 0.0016 cm3·mol−1; κ(0) S = −284.24; κS = −4476.79; κS = 106638.44; σ(κS ) = 0.07 TPa−1. (3ξi) = (3ξi)m = 1.504, (3ξj) = (3ξj)m = 1.397, (3ξk) = (3ξk)m = 0.901. χ*12 = −7.4323; χ*23 = 17.3566; χ*13 = 3.0276; χ* = −23.5230 cm3.mol−1; * = −90.86; χ23 * = 81.65; χ13 * = 49.62; χ* = −294.18 TPa−1. cV(0) = −2.0386; V(1) = −258.6249 V(2) = 8981.8426; σ(VE) = 0.0017 cm3·mol−1. κ(0) χ12 S = (2) E −1 3 3 3 3 3 3 = −5007.45; κ −336.49; κ(1) S S = 119020.18; σ(κS ) = 0.08 TPa . ( ξi) = ( ξi)m = 1.504, ( ξj) = ( ξj)m = 1.397, ( ξk) = ( ξk)m = 0.901. χ* 12 = −8.1575; * = 19.0259; χ13 * = 2.9002; χ* = −24.5383 cm3.mol−1. χ12 * = −93.56; χ23 * = 88.42; χ13 * = 62.91; χ* = −343.17 TPa−1. dV(0) = −1.1349; V(1) = χ23 (1) E −1 3 3 = −358.56; κ = −5103.30; κ(2) −267.2340; V(2) = 9573.68; σ(VE) = 0.0018 cm3·mol−1. κ(0) S S S = 120027.21; σ(κS ) = 0.08 TPa . ( ξi) = ( ξi)m = * = −8.9153; χ23 * = 21.1536; χ13 * = 2.0413; χ* = −24.9309 cm3.mol−1. χ12 * = −95.75; χ23 * = 84.37; 1.504, (3ξj) = (3ξj)m = 1.397, (3ξk) = (3ξk)m = 0.901. χ12 (1) χ*13 = 50.40; χ* = −339.23 TPa−1. eV(0) = −1.0003; V(1) = −276.1261; V(2) = 10343.0731; σ(VE) = 0.0018 cm3·mol−1. κ(0) S = −393.85; κS = E −1 3 3 3 3 3 3 * = −9.6703; χ23 * = 23.5938; −5619.63; κ(2) S = 125632.12; σ(κS ) = 0.09 TPa . ( ξi) = ( ξi)m = 1.504, ( ξj) = ( ξj)m = 1.397, ( ξk) = ( ξk)m = 0.901. χ12 χ*13 = 1.4434; χ* = −25.9595 cm3.mol−1. χ*12 = −95.57; χ*23 = 74.52; χ*13 = 59.99; χ* = −370.73 TPa−1. fV(0) = −7.0438; V(1) = −118.6822; V(2) = (1) (2) E −1 3 3 3 3 2847.3394; σ(VE) = 0.0011 cm3·mol−1. κ(0) S = −607.44; κS = 12251.59; κS = −64022.36; σ(κS ) = 0.06 TPa . ( ξi) = ( ξi)m = 1.502, ( ξj) = ( ξj)m = 1.368, (3ξk) = (3ξk)m = 0.901. χ*12 = −0.3168; χ*23 = 0.6779; χ*13 = −1.9718; χ* = −6.4517 cm3.mol−1. χ*12 = −26.98; χ*23 = −7.15; χ*13 = −287.18; χ* = (1) (2) 216.98 TPa−1. gV(0) = −9.7043; V(1) = 20.2038; V(2) = 1751.5904; σ(VE) = 0.0012 cm3·mol−1. κ(0) S = −727.51; κS = 14969.92; κS = −79842.78; σ(κES ) = 0.07 TPa−1. (3ξi) = (3ξi)m = 1.502, (3ξj) = (3ξj)m = 1.368, (3ξk) = (3ξk)m = 0.901. χ*12 = −0.7257; χ*23 = 1.2462; χ*13 = −4.3486; χ* = −3.0547 * = −36.46; χ23 * = −8.80; χ13 * = −180.96; χ* = 73.06 TPa−1. hV(0) = −5.6646; V(1) = −124.1258; V(2) = 2832.1566; σ(VE) = 0.0012 cm3.mol−1. χ12 (1) E −1 3 3 3 3 3 3 = −773.26; κ = 15784.56; κ(2) cm3·mol−1. κ(0) S S S = −81724.24; σ(κS ) = 0.08 TPa . ( ξi) = ( ξi)m = 1.502, ( ξj) = ( ξj)m = 1.368, ( ξk) = ( ξk)m = * = −0.7638; χ23 * = 1.2132; χ13 * = −2.8766; χ* = −5.3541 cm3.mol−1. χ12 * = −25.35; χ23 * = −5.87; χ13 * = −352.48; χ* = 257.37 TPa−1. iV(0) = 0.901. χ12 (1) (2) E −1 −4.9559; V(1) = −165.5809; V(2) = 3206.2688; σ(VE) = 0.0013 cm3·mol−1. κ(0) S = −803.04; κS = 16256.97; κS = −83570.91; σ(κS ) = 0.09 TPa . * = −0.9192; χ23 * = 1.5294; χ13 * = −2.8984; χ* = −5.7803 cm3.mol−1. (3ξi) = (3ξi)m = 1.502, (3ξj) = (3ξj)m = 1.368, (3ξk) = (3ξk)m = 0.901. χ12 χ*12 = −38.64; χ*23 = −0.04; χ*13 = −246.20; χ* = 111.77 TPa−1.
(i) interactions between π-electron cloud spilling over nitrogen, carbon and oxygen atom of 2-Py or NMP with π-electron cloud of aromatic ring of Py and (ii) molecular packing among the constituents of the mixtures. The more negative values of VE and κES for NMP + Py than those of 2-Py + Py mixture may be due to the presence of electron releasing −CH3 group on the nitrogen atom of the NMP. Because of this, electrons spilling over the nitrogen, carbon, and oxygen atoms of NMP will be more easily available for interaction with a π-electron cloud of aromatic ring of Py. The ∂VE/∂T for the study is negative. This may be due to strong interactions operating among the constituents of mixtures. The VE123 and (κES )123 data for [emim][BF4] + NMP or 2-Py + Py mixtures are negative over the entire composition range. ILs are complex solvents and are capable of interacting simultaneously with other organic molecules via ionic hydrogen bonding,57 and dipole interactions. The negative VE123 and
E various surfaces generated by V123 and (κSE)123 values56 {evaluated by employing eq 9} for the investigated mixtures are shown in Figures 1 and 2, 3, and 4, respectively.
4. DISCUSSION We are unaware of any densities, speeds of sound, excess molar volumes, and excess molar compressibilities data of the studied binary and ternary mixtures that are available in literature with which our results can be compared. The VE and κES values for NMP or 2-Py + Py mixtures are negative over whole range of composition and for an equimolar mixture follow the order: 2-Py > NMP. The sign and magnitude of VE and κES values are due to the commutative effect of several contributions like (i) interactions between the constituents molecules of the mixtures; (ii) packing effect; (iii) dissociation of associated molecular entities. The negative VE and κES values of the studied mixtures suggest I
dx.doi.org/10.1021/je301353z | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
and δvm etc. have the same significance as described elsewhere.60 These parameters were calculated by fitting measured VE data to eq 11. Only those values of (3ξi) or (3ξi)m (i = 2 or 3) were taken that described well the experimental data. Such (3ξi) or (3ξi)m (i = 2 or 3) parameters along with calculated VE data are reported in Table 4, where they are compared with experimental values. Examination of data in Table 4 suggests that VE values calculated from graph theory compare well with experimental VE data. The (3ξi) or (3ξi)m (i = 2 or 3) values were, therefore, utilized to extract information about the state of 2/3 components in pure and mixed state. Structures were assumed for NMP or 2-Py or Py. Any structure or combination of structures that provided 3ξ′ value {calculated via structural consideration (eq 12)} which compare well with 3ξ value (determined via eq 11) was taken to be structure of that component. It was assumed that NMP or 2-Py or Py exist as molecular entities I−II, III−V, and VI−VIII, respectively. The 3ξ′ values for these molecular entities were then calculated to be 0.837, 1.405, 0.903, 1.377, 1.271, 0.516, 0.706, and 1.033 respectively (Scheme 1). The 3ξ values of 1.201, 1.368, 1.198, and 1.112 for NMP, 2-Py and Py suggest that while NMP exist as the mixture of monomer and dimer (3ξ′ = 1.121); 2-Py in pure state mainly exist as a mixture of cyclic and open dimer (3ξ′ = 1.324); and Py mixture of molecular entities VII and VIII (3ξ′ = 0.871). Our observations about the association of NMP or 2-Py or Py are consistent with observations inferred from (i) NMR and X-ray studies of NMP61−63 suggesting that the NMP molecule is associated through a bond between the N-methyl group and keto oxygen atoms of neighboring molecule; (ii) ab initio calculations on the different associated structures of NMP, 2Py, and Py.64−67 To extract information about the state of NMP or 2-Py in Py, we assumed that (2 + 3) mixtures may have molecular entities IX to X. In evaluating (3ξ2′ )m values for these molecular entities, it was assumed that molecular interactions are operating between π-electron cloud spilling over nitrogen and oxygen atom of NMP or 2-Py and π-electron cloud of aromatic ring of Py. The various δv values for various vertices are shown in molecular entities and the δv (π) has been assigned to a value of 1.68 The (3ξ′2)m values for molecular entities IX and X were calculated to be 1.486 and 1.111 respectively. The (3ξ2)m values of 1.201 and 1.368 for NMP and 2-Py in (2 + 3) (Table 4) mixtures suggest the presence of molecular entities IX and X in the studied mixtures. The presence of molecular entities IX and X suggest that addition of Py to NMP or 2-Py must influence the CO vibrations and C−N stretching of 2-Py or NMP along with ring vibrations of aromatic ring of Py. For this purpose, we analyzed the IR spectral data of pure NMP, 2- Py, Py, and an equimolar mixture of NMP + Py. It was observed that investigated liquids in the pure state showed characteristic vibrations of NMP at 1679 cm−1 (CO), 1443 cm−1 (C−N); Py showed ring vibrations at (1581, 1490, 1438) cm−1.69 The IR data of NMP + Py mixtures showed characteristic vibrations at 1672 cm−1 (CO); 1459 cm−1 (C−N); (1588, 1498, 1454) cm−1 (ring vibrations) which in turn suggest that the addition of Py to NMP or 2-Py does influence CO, C−N, stretching of NMP along with ring vibrations of the aromatic ring of Py. The IR spectral data of this mixture thus provided support to the existence of molecular entities IX and X. 5.2. Excess Isentropic Compresibilties Binary Mixtures. Topology of the constituent molecules was then utilized to analyze the κES values of the investigated binary mixtures. It was assumed that the (2 + 3) mixtures formation may involve
Figure 1. Excess molar volumes, VE123, evaluated by employing eq 9 for 1-ethyl-3-methylimidazolium tetrafluoroborate (1) + 1-methyl pyrrolidin-2-one (2) + pyridine (3) ternary mixture at 298.15 K: solid line, the experimental data in front of the plane; dashed line, the experimental data behind the plane.
(κES )123 values for the studied mixtures suggest that a more efficient packing and/or attractive intermolecular interactions occurred when NMP or 2-Py is mixed with [emim][BF4]. The more negative values of VE123 and (κES)123 for [emim][BF4] + NMP + Py than those of [emim][BF4] + 2-Py + Py mixtures may be due to the presence of bulky −CH3 groups on the nitrogen atom of NMP which in turn increase the π-electron density spilling over nitrogen, carbon, and oxygen atoms of NMP in comparison to 2-Py and thus leads to more molecular interactions. Consequently, ionic interactions will be stronger between NMP and the [emim][BF4]:Py molecular entity as compared to 2-Py and the [emim][BF4]:Py molecular entity. Thus, the contribution to VE123 due to an attractive effect is more pronounced than those of packing effect in the investigated mixtures.
5. GRAPH THEORY To extract information about the state of components of the mixtures in pure and mixed state it was worthwhile to analyze the observed VE data of the binary mixtures in terms of graph theory. 5.1. Excess Molar Volumes of Binary Mixtures. In (2 + 3) binary mixtures interactions are operating among the constituents of mixtures. The question of interest involves the specific point on NMP or Py where interactions exist with Py. The addition of Py to NMP or 2-Py leads to influence molecular interactions in the mixed state which in turn reflects in the topology of constituents molecules. Since VE reflects packing effect, it was therefore, worthwhile to analyze the measured VE data in terms of Graph theory (which deals with the topology of the constituents of mixtures) to extract information about the state of components in pure and mixed state along with nature and extent of interactions existing in mixtures. According to Graph theory, VE for binary mixtures is given by58 3
3
V E = a 23{[∑ xi(3ξi)m ]−1 − i=2
∑ xi(3ξi)−1} i=2
(11)
where xi is the mole fraction of component i (i = 2 or 3). The (3ξi), (3ξi)m (i = 2 or 3) are connectivity parameter of the third degree of the constituents molecules in pure as well as mixed state.59 These parameters are defined by 3
ξ=
∑ m
