Density, Speed of Sound, Viscosity, Excess Properties, and Prigogine

Article pubs.acs.org/jced

Density, Speed of Sound, Viscosity, Excess Properties, and Prigogine−Flory−Patterson (PFP) Theory of Binary Mixtures of Amine and Alcohols Gyan Prakash Dubey*,† and Krishan Kumar‡ †

Department of Chemistry, Kurukshetra University, Kurukshetra-136119, India Department of Chemistry, Deenbandhu Chhotu Ram University of Science & Technology, Murthal, Sonepat-131039, India

‡

S Supporting Information *

ABSTRACT: Various thermodynamic parameters of the binary mixtures of [diisopropylamine (DIIPA) + 2-methyl-1-propanol, + 2-propanol, and + 1-butanol] have been measured over the entire composition range and at a temperature range of (293.15 to 313.15) K. Here, the Redlich− Kister type polynomial equation is used to derive the coefficients and standard deviations. The negative value obtained for excess molar volume (VEm) and excess molar isentropic compressibility (KES,m) shows the presence of strong molecular interactions. The calculated apparent molar volume, Vφ,1, and apparent molar compressibility, Kφ,1, predicts volume contraction of the solution with the addition of alcohol in DIIPA. The obtained excess molar volume (VEm) has then been correlated by using the Prigogine−Flory−Patterson (PFP) theory.

1. INTRODUCTION The partial molar volume at infinite dilution in water (standard partial molar volume) is a property that is necessary in a process to get the solute standard chemical potential in wide ranges of temperature and pressure. Partial molar properties of dilute solutions provide information about solute−solute and solute−solvent molecular interactions. The partial molar volumes depend upon molecular size, shape, interactions, and structural effects among the different components. It is of interest and it is important to study the partial molar volumes of alkylamines in different solvents to extract information on specific interactions, conformational effects, and packing efficiencies. Excess thermodynamic functions and deviations of nonthermodynamic ones of binary liquid mixtures are essential for understanding the interactions between molecules in these types of mixtures, particularly when polar components are involved. These functions have also been used as a qualitative and quantitative guide to predict the extent of complex formation in these kinds of mixtures.1−3 This article represents the systematic studies on thermodynamic properties for binary mixtures of amine and alcohols. Herein, we report the measurements of densities, ρ, viscosities, η, and speeds of sound, u of (DIIPA + 2-methyl-1-propanol, + 2-propanol, and +1-butanol) over the entire composition range at (293.15 to 313.15) K and at atmospheric pressure. Furthermore, using the experimental results, excess molar volumes, VEm, molar isentropic compressibilities, KS,m, excess molar isentropic compressibilities, KES,m, deviations of the speeds of sound, uD, from their ideal values in an ideal mixture, uid, viscosity deviations, Δη, and excess Gibbs free energies of activation for viscous flow have been calculated in order to gain a better understanding of the intermolecular interactions between the component molecules. © XXXX American Chemical Society

2. EXPERIMENTAL SECTION 2.1. Materials. All of the chemicals used were obtained from SD Fine Chemicals, India, and are of HPLC, Spectroscopic, and analytical grade. In all cases, chemicals with purity greater than 0.995 by mass were used for the experimental investigations (Table 1a). The experimental densities, viscosities, and speeds of sound of the pure components at temperatures (298.15 to 308.15) K are summarized in Table 1b. For comparison, existing values found in the literature4−22 are also included. Also given in Table 1b are our measured or literature values of those quantities which were required in the estimation of KS,m, KES,m, and uD (Table 1b). 2.2. Apparatus and Procedure. The weighing was done on an A&D Company Limited, electronic balance (Japan, Model GR-202) with a precision of ±0.01 mg. The uncertainty in the mole fraction was found to be ur(x1) = 1 × 10−4. Densities and speeds of sound in pure liquids of diisopropylamine and alcohols and their binary liquid mixtures at different temperatures were measured simultaneously and automatically, using an Anton Paar DSA 5000 (oscillating U-tube density and speed of sound analyzer) instrument23 with a working frequency for the speed of sound of 3 MHz. The precision in density and speed of sound measurements are 1 × 10−3 kg·m−3 and 1 × 10−2 m·s−1, respectively. The repeatability in density, speed of sound, and viscosity measurements is found to be 5 × 10−4 kg·m−3, 2 m·s−1, and 4 × 10−2 mPa·s, respectively, and the standard uncertainty in density and speed of sound measurements is found to be u(ρ) = 0.25 kg·m−3and u(u) = 5.0 m·s−1. The kinematic viscosity (v = η/ρ) was measured Received: March 8, 2015 Accepted: April 27, 2016

A

DOI: 10.1021/acs.jced.5b00216 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1a. Sample Information Table S. no.

sample

CAS no.

1. 2. 3. 4.

diisopropylamine 2-methyl-1-propanol 2-propanol 1-butanol

108-18-9 78-83-1 67-63-0 71-36-3

initial mass fraction purity

make SD. SD. SD. SD.

Fine Fine Fine Fine

Chemicals, Chemicals, Chemicals, Chemicals,

India India India India

0. 0. 0. 0.

purification method

990 990 995 997

final mass fraction purity

distillation distillation distillation distillation

0. 0. 0. 0.

990 990 995 997

analysis method none none none none

Table 1b. Experimental and Literature Values of Densities, ρ*, Viscosities, η, Speeds of Sound, u*, Isobaric Expansivity, αP*, Isobaric Molar Heat Capacity, CP,m * , and Molar Isentropic Compressibility, KS,m * of Pure Liquid Components at (298.15 to 313.15) K and p = 0.1 MPaa ρ* × 10−3/(kg·m−3)

u*/(m·s−1)

η/(mPa·s)

components

exptl.

lit.

exptl.

lit.

exptl.

DIIPA 2-methyl-1-propanol 2-propanol 1-butanol

0.711509 0.798104 0.781051 0.805953

0.714811 0.79825 0.78118 0.8059079

0.382 3.307 2.063 2.565

3.333 2.0618 2.5739


0.706633 0.794197 0.776777 0.802104

0.7099811 0.794612 0.7768615 0.802217

0.364 2.781 1.785 2.268

2.7437 1.78916 2.27618


0.701737 0.790245 0.772422 0.798228

0.7051811 0.790620 0.772613 0.7980419

0.347 2.231 1.579 1.962

2.26120 1.5738 1.98122

6

lit.

αP*/(kK−1)

CP,m * (J K−1 mol−1)

KS,m * (mm3 mol−1 MPa−1)

1.374 0.986 1.105 0.959

266.0011 181.004 155.788 314.544

167.66 82.33 75.75 74.08

1.384 0.991 1.111 0.964

268.011 214.9814 159.908 178.8819

177.21 85.54 79.01 76.87

1.393 0.996 1.118 0.969

270.011 220.1514 164.0121 180.6018

187.45 88.91 82.49 79.79

T/K = 298.15 1091.89 1096.011 1188.8 1189.07 1140.4 1139.38 1241.1 1240.610 T/K = 303.15 1069.37 1071.011 1172.09 1172.013 1122.73 1122.013 1224.24 1223.013 T/K = 308.15 1047.01 1046.011 1155.38 1154.013 1105.02 1104.508 1207.42 1208.013

a The standard uncertainties are u(ρ) = 0.25 kg·m−3, u(u) = 5.0 m·s−1, u(x1) = 1 × 10−4, u(T) = 0.01 K, and u(P) = 1 kPa. The relative standard uncertainties are ur(η) = 1.5%.

Table 2. Densities, ρ, Speeds of Sound, u, Excess Molar Volumes, VEm, Molar Compressibilities, KS,m, Excess Molar Isentropic Compressibilities, KES,m, and Deviations in Speeds of Sound, uD, for the Binary Mixtures (DIIPA + 2-Methyl-1-propanol) at Different Temperatures and p = 0.1 MPaa x1

ρ × 10−3 (kg m−3)

u (m s−1)

VEm × 106 (m3 mol−1)

0.0000 0.0559 0.1015 0.1519 0.2069 0.2516 0.3055 0.3944 0.4988 0.6017 0.7131 0.8018 0.8650 0.9062 0.9423 1.0000

0.801977 0.799358 0.797256 0.794750 0.791388 0.788402 0.784440 0.777053 0.767362 0.757207 0.745695 0.736752 0.730130 0.726063 0.722406 0.716367

1205.72 1212.93 1217.62 1221.52 1223.41 1223.13 1221.28 1214.09 1201.00 1184.93 1165.08 1149.23 1137.28 1130.18 1123.43 1114.58

0.0000 −0.5339 −0.9629 −1.4034 −1.7897 −2.0562 −2.3098 −2.5556 −2.5927 −2.4076 −1.9603 −1.5119 −1.0754 −0.8029 −0.5253 0.0000

0.0000 0.0559 0.1015 0.1519 0.2069 0.2516 0.3055 0.3944 0.4988

0.798104 0.795373 0.79317 0.79054 0.787053 0.783975 0.779915 0.772406 0.762627

1188.84 1195.37 1199.48 1202.71 1203.99 1203.15 1200.8 1192.93 1179.39

0.0000 −0.5372 −0.9671 −1.4060 −1.7901 −2.0549 −2.3066 −2.5511 −2.5896

KS,m (mm3 mol−1 MPa−1)

KES,m (mm3 mol−1 MPa−1)

uD (ms−1)

0.00 −3.62 −6.40 −9.25 −11.89 −13.66 −15.47 −17.40 −18.22

0.00 18.41 31.27 43.32 53.32 58.97 63.81 66.49 63.61

T/K = 293.15

T/K = 298.15 82.33 83.67 84.92 86.54 88.78 90.97 93.94 99.88 108.31 B



Article

Table 2. continued x1

ρ × 10−3 (kg m−3)

u (m s−1)

VEm × 106 (m3 mol−1)

0.6017 0.7131 0.8018 0.8650 0.9062 0.9423 1.0000

0.75243 0.740894 0.731939 0.72531 0.721237 0.717572 0.711509

1163.01 1142.98 1126.97 1114.75 1107.67 1100.75 1091.89

−2.4085 −1.9649 −1.5189 −1.0825 −0.8099 −0.5309 0.0000

0.0000 0.0559 0.1015 0.1519 0.2069 0.2516 0.3055 0.3944 0.4988 0.6017 0.7131 0.8018 0.8650 0.9062 0.9423 1.0000

0.794197 0.791352 0.789048 0.786295 0.782684 0.779523 0.775364 0.76774 0.757875 0.747635 0.736075 0.727108 0.720468 0.716388 0.712714 0.706633

1172.09 1177.92 1181.48 1184.01 1184.62 1183.39 1180.48 1171.97 1157.92 1141.25 1120.97 1104.78 1092.43 1085.28 1078.23 1069.37

0.0000 −0.5402 −0.9709 −1.4083 −1.7901 −2.0541 −2.3036 −2.5476 −2.5877 −2.4103 −1.9702 −1.5265 −1.0893 −0.8162 −0.5356 0.0000

0.0000 0.0559 0.1015 0.1519 0.2069 0.2516 0.3055 0.3944 0.4988 0.6017 0.7131 0.8018 0.8650 0.9062 0.9423 1.0000

0.790245 0.78729 0.784881 0.782015 0.778285 0.775033 0.770785 0.763053 0.753106 0.742816 0.731236 0.722253 0.715609 0.711516 0.707832 0.701737

1155.38 1160.5 1163.4 1165.36 1165.32 1163.61 1160.22 1151.10 1136.58 1119.61 1099.09 1082.74 1070.31 1063.05 1055.93 1047.01

0.0000 −0.5436 −0.9745 −1.4114 −1.7912 −2.0533 −2.3017 −2.5458 −2.5878 −2.4129 −1.9767 −1.5342 −1.0973 −0.8225 −0.5399 0.0000

0.0000 0.0559 0.1015 0.1519 0.2069 0.2516 0.3055 0.3944 0.4988 0.6017 0.7131 0.8018 0.8650 0.9062 0.9423 1.0000

0.786237 0.783172 0.780666 0.777684 0.773834 0.770500 0.766167 0.758327 0.748298 0.737966 0.726358 0.717362 0.710709 0.706606 0.702918 0.696811

1138.71 1143.044 1145.41 1146.73 1146.01 1143.92 1140.03 1130.34 1115.20 1097.99 1077.18 1060.73 1048.21 1040.82 1033.64 1023.80

0.0000 −0.5468 −0.9788 −1.4146 −1.7922 −2.0533 −2.3009 −2.5449 −2.5883 −2.4168 −1.9828 −1.5417 −1.1039 −0.8277 −0.5441 0.0000



uD (ms−1)

118.06 130.28 140.83 149.20 154.57 159.69 167.66

−17.59 −15.24 −12.55 −9.78 −8.06 −6.14 0.00

56.26 44.66 34.54 26.14 21.40 16.43 10.54

85.54 87.05 88.45 90.26 92.74 95.11 98.35 104.74 113.78 124.19 137.22 148.50 157.45 163.20 168.71 177.21

0.00 −3.81 −6.75 −9.73 −12.49 −14.37 −16.26 −18.32 −19.21 −18.60 −16.16 −13.32 −10.38 −8.55 −6.48 0.00

0.00 18.46 31.29 43.15 52.97 58.58 63.24 65.81 62.93 55.70 44.23 34.18 25.80 21.09 16.07 0.00

88.91 90.61 92.19 94.20 96.92 99.51 103.02 109.91 119.59 130.71 144.64 156.70 166.26 172.44 178.34 187.45

0.00 −4.02 −7.10 −10.24 −13.14 −15.12 −17.11 −19.31 −20.30 −19.70 −17.16 −14.16 −11.05 −9.09 −6.87 0.00

0.00 18.50 31.20 43.00 52.66 58.13 62.68 65.16 62.32 55.19 43.83 33.86 25.55 20.82 15.80 0.00

T/K = 298.15

T/K = 303.15

T/K = 308.15

T/K = 313.15

a The standard uncertainties are u(ρ) = 0.25 kg·m−3, u(u) = 5.0 m·s−1, u(x1) = 1 × 10−4, u(t) = 0.01 K, and u(P) = 1 kPa. The relative standard uncertainties are ur(η) = 1.5%.

C



Article

Table 3. Densities, ρ, Speeds of Sound, u, Excess Molar Volumes, VEm, Molar Isentropic Compressibilities, KS,m, Excess Molar Isentropic Compressibilities, KES,m, and Deviations in Speeds of Sound, uD, for the Binary Mixtures (DIIPA + 2-propanol) at Different Temperatures and p = 0.1 MPaa x1

ρ × 10−3 (kg m−3)

u (m s−1)

VEm × 106 (m3 mol−1)

0.0000 0.0499 0.1033 0.1405 0.2062 0.2498 0.3030 0.4121 0.4955 0.5984 0.6982 0.7902 0.8632 0.9067 0.9459 1.0000

0.785253 0.784394 0.781722 0.779524 0.775598 0.772861 0.769103 0.761148 0.754667 0.746657 0.739031 0.731947 0.726469 0.723300 0.720432 0.716367

1157.86 1168.16 1173.34 1176.06 1178.33 1178.63 1177.10 1170.94 1164.52 1155.02 1146.01 1135.18 1127.49 1122.81 1118.54 1114.58

0.0000 −0.4917 −0.8722 −1.0884 −1.4347 −1.6271 −1.7853 −1.9752 −1.9661 −1.8234 −1.5799 −1.1977 −0.8426 −0.6177 −0.3791 0.0000

0.0000 0.0499 0.1033 0.1405 0.2062 0.2498 0.3030 0.4121 0.4955 0.5984 0.6982 0.7902 0.8632 0.9067 0.9459 1.0000

0.781051 0.780036 0.777229 0.774943 0.770881 0.768073 0.764243 0.756200 0.749703 0.741695 0.734796 0.727028 0.721574 0.718413 0.715555 0.711509

1140.36 1149.72 1154.12 1156.38 1157.81 1157.68 1155.65 1148.91 1142.27 1132.58 1122.58 1112.58 1104.65 1100.01 1095.67 1091.89

0.0000 −0.4880 −0.8649 −1.0779 −1.4192 −1.6092 −1.7644 −1.9523 −1.9456 −1.8069 −1.5205 −1.1905 −0.8390 −0.6093 −0.3773 0.0000

0.0000 0.0499 0.1033 0.1405 0.2062 0.2498 0.3030 0.4121 0.4955 0.5984 0.6982 0.7902 0.8632 0.9067 0.9459 1.0000

0.776777 0.775608 0.772674 0.770304 0.766113 0.763241 0.759341 0.751219 0.744704 0.736697 0.728964 0.722068 0.716643 0.713499 0.710656 0.706633

1122.73 1131.34 1134.94 1136.65 1137.32 1136.86 1134.36 1127.02 1120.13 1110.28 1100.67 1090.01 1082.04 1077.37 1073.01 1069.37

0.0000 −0.4844 −0.8579 −1.0678 −1.4040 −1.5919 −1.7441 −1.9302 −1.9251 −1.7896 −1.5314 −1.1802 −0.8327 −0.6053 −0.3751 0.0000

0.0000 0.0499 0.1033 0.1405 0.2062 0.2498 0.3030 0.4121

0.772422 0.771111 0.768054 0.765604 0.761291 0.758348 0.754392 0.746196

1105.02 1112.91 1115.71 1116.91 1116.89 1115.97 1113.15 1105.32

0.0000 −0.4816 −0.8516 −1.0583 −1.3895 −1.5741 −1.7242 −1.9082



uD (m s−1)

75.75 77.27 79.96 82.02 86.08 88.99 93.01 102.05 109.71 120.01 129.80 141.48 150.42 155.89 161.01 167.66

0.00 −3.07 −5.28 −6.64 −8.63 −9.72 −10.60 −11.58 −11.58 −10.74 −10.12 −6.89 −4.66 −3.19 −1.68 0.00

0.00 15.65 25.00 30.36 36.66 39.41 40.56 39.40 36.34 30.43 23.48 16.05 9.88 6.21 2.70 0.00

79.01 80.71 83.67 85.92 90.32 93.45 97.78 107.47 115.63 126.58 137.92 149.43 158.94 164.76 170.20 177.21

0.00 −3.20 −5.49 −6.89 −8.94 −10.09 −10.99 −12.02 −12.04 −11.19 −9.66 −7.18 −4.84 −3.29 −1.70 0.00

0.00 14.52 23.68 28.87 35.02 37.79 38.86 37.80 34.93 29.24 22.94 15.40 9.42 5.84 2.42 0.00

82.49 84.38 87.62 90.08 94.84 98.24 102.88 113.24

0.00 −3.34 −5.71 −7.15 −9.29 −10.47 −11.42 −12.51

0.00 14.34 23.20 28.20 34.14 36.73 37.79 36.78

T/K = 293.15

T/K = 298.15

T/K = 303.15

T/K = 308.15

D



Article


ρ × 10−3 (kg m−3)

u (m s−1)

VEm × 106 (m3 mol−1)

0.4955 0.5984 0.6982 0.7902 0.8632 0.9067 0.9459 1.0000

0.739666 0.731662 0.723946 0.717078 0.711684 0.708558 0.705732 0.701737

1098.16 1088.13 1078.61 1067.76 1059.73 1055.00 1050.63 1047.01

−1.9044 −1.7717 −1.5164 −1.1691 −0.8256 −0.6004 −0.3721 0.0000

0.0000 0.0499 0.1033 0.1405 0.2062 0.2498 0.3030 0.4121 0.4955 0.5984 0.6982 0.7902 0.8632 0.9067 0.9459 1.0000

0.767987 0.766527 0.763350 0.760823 0.756393 0.753392 0.749377 0.741117 0.734566 0.726573 0.718712 0.712050 0.706682 0.703577 0.700770 0.696811

1087.10 1094.32 1096.35 1097.03 1096.36 1095.03 1091.97 1083.66 1076.24 1066.00 1055.85 1045.59 1037.58 1032.75 1028.40 1023.80

0.0000 −0.4494 −0.8172 −1.0218 −1.3498 −1.5334 −1.6822 −1.8677 −1.8661 −1.7396 −1.4705 −1.1512 −0.8125 −0.5912 −0.3661 0.0000



uD (m s−1)

−12.55 −11.69 −10.16 −7.53 −5.08 −3.43 −1.76 0.00

33.99 28.57 22.86 15.07 9.19 5.65 2.30 0.00

T/K = 308.15 121.95 133.61 145.62 157.90 168.02 174.23 180.02 187.45 T/K = 313.15

The standard uncertainties are u(ρ) = 0.25 kg·m−3, u(u) = 5.0 m·s−1, u (x1) = 1 × 10−4, u(T) = 0.01 K, and u(P) = 1 kPa. The relative standard uncertainties are ur(η) = 1.5%. a

Table 4. Densities, ρ, Speeds of Sound, u, Excess Molar Volumes, VEm, Molar Isentropic Compressibilities, KS,m, Excess Molar Isentropic Compressibilities, KES,m, and Deviations in Speeds of Sound, uD for the Binary Mixtures (DIIPA + 1-Butanol) at Different Temperatures, and p = 0.1 MPaa x1

ρ × 10−3 (kg m−3)

u (m s−1)

0.0000 0.0499 0.1095 0.1542 0.2062 0.2500 0.2969 0.4059 0.5062 0.6009 0.7043 0.8059 0.8543 0.8987 0.9489 1.0000

0.809778 0.807061 0.803951 0.801212 0.797717 0.794484 0.790843 0.780740 0.770572 0.760453 0.749151 0.738230 0.732777 0.727824 0.722518 0.716367

1258.13 1260.57 1262.58 1262.75 1261.40 1258.75 1254.66 1239.60 1221.55 1201.87 1179.24 1157.16 1145.87 1135.71 1124.95 1114.58

0.0000 0.0499 0.1095 0.1542 0.2062 0.2500 0.2969 0.4059 0.5062 0.6009

0.805953 0.803124 0.799884 0.797042 0.793435 0.79011 0.786387 0.776134 0.765887 0.755726

1241.13 1242.98 1244.35 1243.97 1242.11 1238.93 1234.39 1218.54 1200.03 1180.12

VEm × 106 (m3 mol−1)


DIIPA + 1-Butanol, T/K = 293.15 0.0000 −0.4993 −1.0943 −1.4789 −1.8718 −2.1507 −2.4086 −2.7049 −2.7301 −2.5513 −2.1633 −1.6495 −1.3010 −0.9542 −0.5762 0.0000 T/K = 298.15 0.0000 74.08 −0.5018 75.74 −1.0992 77.81 −1.4838 79.64 −1.8763 82.06 −2.1540 84.42 −2.4117 87.19 −2.7075 95.15 −2.7357 103.97 −2.5608 113.64 E


uD (m s−1)

0.00 −3.01 −6.52 −8.86 −11.31 −13.06 −14.67 −16.91 −17.48 −16.67

0.00 17.51 35.41 46.11 55.94 61.72 65.99 67.97 63.23 54.48



Article


ρ × 10−3 (kg m−3)

u (m s−1)

VEm × 106 (m3 mol−1)

0.7043 0.8059 0.8543 0.8987 0.9489 1.0000

0.744384 0.733434 0.727978 0.723009 0.717683 0.711509

1157.09 1134.96 1123.51 1113.2 1102.23 1091.89

−2.1576 −1.6612 −1.3134 −0.9642 −0.5829 0.0000

0.0000 0.0499 0.1095 0.1542 0.2062 0.2500 0.2969 0.4059 0.5062 0.6009 0.7043 0.8059 0.8543 0.8987 0.9489 1.0000

0.802104 0.799161 0.795791 0.792847 0.789120 0.785710 0.781907 0.771512 0.761183 0.750975 0.739605 0.728625 0.723154 0.718174 0.712825 0.706633

1224.24 1225.56 1226.18 1225.29 1222.72 1219.19 1214.23 1197.59 1178.62 1158.41 1135.19 1112.86 1101.31 1090.82 1079.67 1069.37

0.0000 −0.5040 −1.1040 −1.4886 −1.8796 −2.1570 −2.4148 −2.7111 −2.7417 −2.5699 −2.1872 −1.6745 −1.3250 −0.9741 −0.5889 0.0000

0.0000 0.0499 0.1095 0.1542 0.2062 0.2500 0.2969 0.4059 0.5062 0.6009 0.7043 0.8059 0.8543 0.8987 0.9489 1.0000

0.798228 0.795163 0.791669 0.788621 0.784784 0.781288 0.777412 0.766871 0.756466 0.746209 0.734804 0.723796 0.718312 0.713314 0.707945 0.701737

1207.42 1208.20 1208.15 1206.71 1203.56 1199.57 1194.23 1176.83 1157.44 1136.86 1113.44 1090.82 1079.23 1068.64 1057.40 1047.01

0.0000 −0.5054 −1.1086 −1.4930 −1.8838 −2.1606 −2.4194 −2.7156 −2.7496 −2.5806 −2.2003 −1.6883 −1.3374 −0.9835 −0.5948 0.0000

0.0000 0.0499 0.1095 0.1542 0.2062 0.2500 0.2969 0.4059 0.5062 0.6009 0.7043 0.8059 0.8543 0.8987 0.9489 1.0000

0.794312 0.791130 0.787512 0.784355 0.780410 0.776830 0.772878 0.762199 0.751715 0.741411 0.729969 0.718929 0.713431 0.708419 0.703033 0.696811

1190.42 1190.97 1190.24 1188.22 1184.97 1180.04 1174.27 1156.08 1136.18 1115.30 1091.64 1068.69 1057.10 1046.52 1035.22 1023.80

0.0000 −0.5073 −1.1139 −1.4974 −2.0058 −2.1647 −2.4239 −2.7210 −2.7579 −2.5920 −2.2137 −1.7014 −1.3487 −0.9924 −0.6004 0.0000



uD (m s−1)

125.61 138.45 145.37 151.98 159.50 167.66

−14.38 −11.04 −8.65 −6.20 −3.38 0.00

41.99 28.85 21.27 14.31 6.92 0.00

76.87 78.68 80.96 82.96 85.61 88.15 91.15 99.70 109.12 119.44 132.20 145.91 153.32 160.42 168.51 177.21

0.00 −3.20 −6.90 −9.38 −11.95 −13.81 −15.52 −17.90 −18.55 −17.73 −15.35 −11.82 −9.28 −6.63 −3.58 0.00

0.00 17.77 35.70 46.39 56.00 61.80 65.99 67.83 63.09 54.38 42.01 28.91 21.34 14.28 6.80 0.00

79.80 81.77 84.26 86.46 89.34 92.09 95.32 104.50 114.56 125.60 139.21 153.90 161.82 169.43 178.11 187.45

0.00 −3.40 −7.32 −9.94 −12.66 −14.62 −16.44 −19.00 −19.73 −18.89 −16.41 −12.65 −9.95 −7.12 −3.84 0.00

0.00 18.03 36.09 46.72 56.25 61.94 66.09 67.81 63.09 54.34 42.06 28.90 21.38 14.31 6.81 0.00

T/K = 298.15

T/K = 303.15

T/K = 308.15

T/K = 313.15

The standard uncertainties are u(ρ) = 0.25 kg·m−3, u(u) = 5.0 m·s−1, u(x1) = 1 × 10−4, u(T) = 0.01 K, and u(P) = 1 kPa. The relative standard uncertainties are ur(η) = 1.5%. a

F



Article

Table 5. Viscosities, η, Viscosity Deviations, Δη, Excess Gibbs Free Energies of Activation for Viscous Flow, ΔG*E for the Binary Mixtures at Different Temperatures and p = 0.1 MPaa

using an Ubbelohde suspended-level viscometer.23 The relative standard uncertainty in the viscosity measurements has been found to be ur(η) = 1.5%. The densimeter and the viscometer were calibrated at working temperatures with dry air, toluene, cyclohexane, and distilled water.

x1

3. RESULTS AND DISCUSSION The experimental values of density were used to calculate the excess molar volume VEm of the mixtures using the following equation:

0.0000 0.0559 0.1015 0.1519 0.2069 0.2516 0.3055 0.3944 0.4988 0.6017 0.7131 0.8018 0.8650 0.9062 0.9423 1.0000

2

VmE =

∑ xiMi(ρ−1 − ρi−1)

(1)

i=1

where ρ is the density of the mixture, and xi, Mi, and ρi are the mole fraction, molar mass, and density of pure component i, respectively. The isentropic compressibility, κS, and molar isentropic compressibility,24 Ks,m, were calculated using the equations given in Supporting Information. κS = −V m−1(δVm/δP)S = (ρu 2)−1 = Vm(Mu 2)−1

(2)

where Vm is the molar volume and M the molar mass of the mixture. The deviations of the speed of sound from their values in an ideal mixture were calculated from the following equation:25

u D = u − uid

0.0000 0.0559 0.1015 0.1519 0.2069 0.2516 0.3055 0.3944 0.4988 0.6017 0.7131 0.8018 0.865 0.9062 0.9423 1.0000

(3)

The variation of ρ, VEm, u, uD, KS,m, and KES,m at all temperatures of interest for the studied binaries are given in Tables 2 to 4. The deviations of the viscosities from the linear dependence were calculated from the following relationship: 2

Δη = η −

∑ xiηi

(4)

i=1

where η and ηi are viscosities of the mixture and the pure component i, respectively. On the basis of the theory of reaction rates, the excess Gibbs energy of activation of viscous flow ΔG*E was calculated24 using the following equation: 2

ΔG*E = RT[ln(ηV ) −

∑ xi ln(ηiVi )]

0.0000 0.0559 0.1015 0.1519 0.2069 0.2516 0.3055 0.3944 0.4988 0.6017 0.7131 0.8018 0.865 0.9062 0.9423 1.0000

(5)

i=1

where R is the universal constant of gas, T is the absolute temperature, V and Vi are the molar volumes of the binary mixtures and pure components, respectively. The variation of Δη and ΔG*E at all temperatures of interest for the studied binaries are given in Table 5. The excess molar volumes and deviations in speed of sound, isentropic compressibility, viscosity, and excess Gibbs energy of activation of viscous flow were fitted to a Redlich−Kister equation:25 p

Y (x) = x1x 2 ∑ Ai (x1 − x 2)i

(6)

i=1

where p is the number of estimated parameters Ai. The standard deviation was calculated using the following equation:

0.0000 0.0499 0.1033 0.1405 0.2062 0.2498

n 2

1/2

σ = [∑ {Y (x)exptl − Y (x)cal } /(n − p)] i=1

(7)

where Y(x)exp tl and Y(x)cal are the values of the experimental and calculated properties (VEm, Δu, Δη, Δκs, and ΔG*E), respectively, G

η (mPas)

Δη (mPas)

ΔG*E (J mol−1)

DIIPA + 2-Methyl-1-propanol, T/K = 298.15 3.307 0.000 0.000 2.916 −0.227 −17.756 2.616 −0.394 −44.050 2.295 −0.567 −99.663 1.995 −0.706 −153.014 1.765 −0.806 −217.854 1.507 −0.907 −321.415 1.194 −0.959 −421.450 0.926 −0.922 −488.927 0.730 −0.816 −524.212 0.586 −0.635 −472.694 0.504 −0.457 −368.323 0.455 −0.322 −284.601 0.433 −0.224 −192.144 0.409 −0.142 −138.358 0.382 0.000 0.000 T/K = 303.15 2.781 0.000 0.000 2.467 −0.178 −15.231 2.232 −0.303 −35.306 1.980 −0.434 −79.941 1.738 −0.542 −126.54 1.549 −0.623 −187.951 1.346 −0.696 −265.551 1.067 −0.761 −394.292 0.837 −0.738 −467.457 0.674 −0.652 −484.045 0.553 −0.504 −411.295 0.485 −0.358 −286.789 0.441 −0.249 −203.541 0.419 −0.171 −122.835 0.396 −0.107 −81.8744 0.364 0.000 0.000 T/K = 308.15 2.231 0.000 0.000 2.005 −0.121 −7.780 1.833 −0.207 −21.204 1.662 −0.283 −32.751 1.459 −0.382 −103.104 1.319 −0.437 −148.044 1.155 −0.499 −230.553 0.931 −0.557 −359.785 0.743 −0.548 −437.548 0.607 −0.490 −473.668 0.509 −0.377 −375.213 0.448 −0.271 −280.879 0.409 −0.192 −216.849 0.395 −0.128 −111.819 0.379 −0.077 −47.5147 0.347 0.000 0.000 DIIPA + 2-Propanol, T/K = 298.15 2.063 0.000 0.000 1.789 −0.189 −133.383 1.565 −0.324 −228.603 1.437 −0.389 −276.221 1.245 −0.471 −345.127 1.123 −0.519 −410.868 DOI: 10.1021/acs.jced.5b00216 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

Table 5. continued x1 0.3030 0.4121 0.4955 0.5984 0.6982 0.7902 0.8632 0.9067 0.9459 1.0000 0.0000 0.0499 0.1033 0.1405 0.2062 0.2498 0.3030 0.4121 0.4955 0.5984 0.6982 0.7902 0.8632 0.9067 0.9459 1.0000 0.0000 0.0499 0.1033 0.1405 0.2062 0.2498 0.3030 0.4121 0.4955 0.5984 0.6982 0.7902 0.8632 0.9067 0.9459 1.0000 0.0000 0.0499 0.1095 0.1542 0.2062 0.2500 0.2969 0.4059 0.5062 0.6009 0.7043 0.8059 0.8543 0.8987 0.9489

η (mPas)

Table 5. continued Δη (mPas)

DIIPA + 2-Propanol, T/K = 298.15 1.003 −0.550 0.809 −0.560 0.698 −0.531 0.592 −0.465 0.520 −0.378 0.468 −0.267 0.434 −0.178 0.412 −0.127 0.397 −0.075 0.382 0.000 T/K = 303.15 1.785 0.000 1.565 −0.149 1.393 −0.245 1.280 −0.305 1.108 −0.384 1.012 −0.418 0.904 −0.451 0.735 −0.464 0.639 −0.441 0.551 −0.384 0.498 −0.308 0.447 −0.215 0.419 −0.139 0.401 −0.095 0.388 −0.052 0.364 0.000 T/K = 308.15 1.579 0.000 1.397 −0.120 1.253 −0.198 1.153 −0.252 1.004 −0.321 0.922 −0.349 0.825 −0.380 0.677 −0.393 0.593 −0.376 0.513 −0.328 0.466 −0.262 0.421 −0.184 0.398 −0.117 0.382 −0.079 0.3694 −0.044 0.347 0.000 DIIPA + 1-Butanol, T/K = 298.15 2.564 0.0000 2.316 −0.139 2.056 −0.269 1.880 −0.347 1.699 −0.415 1.552 −0.466 1.414 −0.502 1.129 −0.549 0.916 −0.543 0.755 −0.497 0.620 −0.407 0.516 −0.289 0.477 −0.223 0.444 −0.159 0.408 −0.085

ΔG*E (J mol−1)

x1

−461.307 −528.559 −543.573 −527.084 −458.554 −330.663 −227.182 −180.253 −113.067 0.000

1.0000 0.0000 0.0499 0.1095 0.1542 0.2062 0.2500 0.2969 0.4059 0.5062 0.6009 0.7043 0.8059 0.8543 0.8987 0.9489 1.0000

0.000 −120.638 −185.814 −241.262 −327.416 −374.627 −439.908 −512.682 −528.613 −494.404 −400.168 −276.549 −159.68 −107.539 −40.309 0.000

0.0000 0.0499 0.1095 0.1542 0.2062 0.2500 0.2969 0.4059 0.5062 0.6009 0.7043 0.8059 0.8543 0.8987 0.9489 1.0000

0.000 −107.713 −165.395 −222.334 −310.277 −352.786 −422.200 −493.681 −511.467 −482.587 −382.200 −271.644 −146.582 −88.861 −34.968 0.000

η (mPas)

Δη (mPas)

DIIPA + 1-Butanol, T/K = 298.15 0.382 0.000 T/K = 303.15 2.268 0.000 2.061 −0.112 1.834 −0.225 1.688 −0.286 1.529 −0.345 1.405 −0.387 1.285 −0.417 1.037 −0.458 0.849 −0.454 0.707 −0.417 0.583 −0.344 0.489 −0.244 0.451 −0.190 0.420 −0.136 0.391 −0.069 0.364 0.000 T/K = 308.15 1.962 0.000 1.793 −0.088 1.609 −0.175 1.483 −0.229 1.353 −0.275 1.251 −0.307 1.149 −0.333 0.940 −0.366 0.777 −0.367 0.656 −0.336 0.548 −0.276 0.467 −0.193 0.432 −0.149 0.402 −0.108 0.374 −0.055 0.347 0.000

ΔG*E (J mol−1) 0.000 0.000 −11.629 −32.173 −35.817 −45.419 −57.970 −66.211 −101.695 −139.830 −165.589 −173.447 −146.827 −129.320 −103.500 −52.342 0.000 0.000 −9.382 −22.654 −34.846 −38.560 −45.559 −54.541 −83.533 −123.328 −137.214 −134.090 −97.024 −79.722 −66.273 −35.710 0.000

a The standard uncertainties are u(ρ) = 0.25 kg·m−3, u(u) = 5.0 m·s−1, u(x1) = 1 × 10−4, u(T) = 0.01 K, and u(P) = 1 kPa. The relative standard uncertainties are ur(η) = 1.5%.

and n is the number of experimental data points. The calculated values of the coefficients, Ai along with the standard deviations (σ) are given in Table 6. The values of VEm are plotted as a function of x1 in Figures 1 to 3 which show that mixtures (DIIPA + 2-methyl-1-propanol, + 2-propanol, and +1-butanol) exhibit negative VEm values for the whole range of composition and at all of the studied temperatures. In Figure 3, VEm values of 1-butanol have been compared with those in the literature,25 and the observed trend justifies our results. This may imply that volume contraction takes place upon mixing DIIPA with alcohols due to the crossassociation between these dissimilar molecules. The negative trend in the values of VEm is observed in all of the three binary mixtures with minima at x1 ≈ 0.5. There is no significant change observed in the values of VEm with temperature. Further, it is also observed from Figures 1 to 3 that as we move from 1-butanol to 2-methyl-1-propanol to 2-propanol the negative values of VEm decrease. This shows that there are strong forces of attraction in 1-butanol among the three alcohols. The large negative value of VEm for the mixture with 1-butanol indicates that the most efficient packing of molecules occurs in this

0.000 −17.519 −33.045 −44.650 −51.949 −68.824 −79.171 −120.287 −162.164 −192.413 −191.201 −168.047 −135.049 −107.080 −77.689 H



Article

Table 6. Coefficients, Ai of the Redlich−Kister Equation (eq 6) along with Standard Deviations, σ, for the Binary Mixtures at Different Temperatures excess property

A0

VEm × 106 (m3 mol−1)

−10.3786

VEm × 106 (m3 mol−1) uD (m s−1) E (TPa−1) KS,m Δη (mPa s) ΔG*E (J mol−1)

−10.365 281.9200 −73.218 −3.708 −1997.982


−10.356 278.597 −77.222 −2.964 −1872.354


−10.354 275.489 −81.574 −2.207 −1748.121

VEm × 106 (m3 mol−1)

−10.356

VEm × 106 (m3 mol−1)

−7.893


−8.022 144.766 −46.465 −2.130 −2211.939


−7.837 139.175 −48.273 −1.764 −2125.161


−7.627 136.663 −50.237 −1.501 −2055.816

VEm × 106 (m3 mol−1)

−7.452

VEm × 106 (m3 mol−1)

−10.945

VEm × 106 (m3 mol−1) Δη (m s−1) uD (m s−1) E (TPa−1) KS,m ΔG*E (J mol−1)

−10.954 254.045 −69.553 −2.1804 −645.346


−10.988 253.422 −74.025 −1.821 −542.926

VEm × 106 (m3 mol−1) uD (m s−1)

−11.018 253.311

A1

A2

DIIPA + 2-Methyl-1-propanol, T/K = 293.15 1.8150 0.6016 T/K = 298.15 1.763 0.491 −119.068 −8.3464 3.743 4.663 1.488 0.1225 −1052.381 910.663 T/K = 303.15 1.708 0.395 −116.596 −2.504 3.003 4.325 1.049 0.529 −1056.230 1464.023 T/K = 308.15 1.653 0.306 −114.319 2.365 2.189 4.116 0.635 0.644 −1172.996 1541.203 T/K = 313.15 1.600 0.231 DIIPA + 2-Propanol, T/K = 293.15 1.000 −0.652 T/K = 298.15 −0.303 −0.624 −93.945 45.979 3.554 −8.574 0.981 −0.155 −33.485 722.737 T/K = 303.15 0.251 −0.678 −87.228 41.330 4.138 −7.409 0.822 −0.015 58.352 1056.465 T/K = 308.15 0.947 −0.737 −84.181 38.785 5.026 −5.641 0.677 −0.000 17.450 1024.424 T/K = 313.15 1.095 −0.602 DIIPA + 1-Butanol, T/K = 293.15 1.722 0.021 T/K = 298.15 1.732 −0.071 −141.490 42.585 2.270 −2.177 0.5249 0.0249 −691.599 46.845 T/K = 303.15 1.604 −0.154 −140.171 46.728 0.712 −2.424 0.403 −0.025 −666.043 −223.247 T/K = 308.15 1.545 −0.226 −139.902 48.426

I

A3

A4

σ

−1.6732

-

0.0128

−1.625 190.185 −27.984 −0.711 −238.720

223.210 −29.513 0.315 -

0.0130 2.3771 0.2865 0.0068 12.0136

−1.571 179.387 −28.641 −3.888 480.034

211.909 −30.620 −0.773 -

0.0132 2.2039 0.2961 0.0042 10.4514

−1.517 170.238 −29.660 −0.332 536.144

202.380 −32.185 −0.232 -

0.0131 2.0558 0.3081 0.0067 18.7666

−1.449

-

0.0132

0.622

-

0.0305

2.852 −50.294 14.612 0.431 465.592

10.872 −0.664 −1220.428

0.1187 0.5819 0.2663 0.0045 10.6982

1.854 −51.292 14.621 0.259 767.379

9.183 −0.360 −492.224

0.0744 0.4594 0.2171 0.0048 9.5619

0.625 −52.118 13.747 0.170 765.265

5.958 −0.186 −187.872

0.0242 0.5853 0.1587 0.0042 10.1703

0.082

-

0.0139

−2.402

-

0.0196

−2.491 21.260 7.826 0.186 230.436

−48.739 7.826 −0.271 −441.748

0.0207 0.2584 0.1079 0.0014 6.7025

−2.336 15.726 −5.186 0.162 270.260

−50.085 8.574 −0.143 -

0.0199 0.2828 0.0967 0.0016 3.7000

−2.308 11.590

−47.223

0.0202 0.2762



Article

Table 6. continued excess property

A0

A1

E (TPa−1) KS,m Δη (mPa s) ΔG*E (J mol−1)

−78.710 −1.465 −472.350

−0.174 0.313 −505.566

VEm × 106 (m3 mol−1)

−11.060

1.607

A2 T/K = 308.15 −2.875 0.050 188.559 T/K = 313.15 −0.484

A3 −4.921 0.141 387.101 −2.267

A4

σ

8.909 −0.152 −278.616

0.1012 0.0018 5.9152 0.0406

Figure 3. Excess molar volumes VEm against mole fractions x1 for DIIPA (1) + 1-butanol (2) at ■, 293.15 K; ●, 298.15 K; ▲, 303.15 K; ▼, 308.15 K; and ◆, 313.15 K. The smoothing of the curves has been drawn from eq 6, the dotted curve from PFP theory, and the dashed curve from ref 25 at 298.15 K.

Figure 1. Excess molar volumes VEm against mole fractions x1 for DIIPA (1) + 2-methyl-1-propanol (2) at ■, 293.15 K; ●, 298.15 K; ▲, 303.15 K; ▼, 308.15 K; and ◆, 313.15 K. The smoothing of the curves has been drawn from eq 6 and the dotted curve from PFP theory at 298.15 K.

Figure 4. Excess molar compressibility KES,m against mole fractions x1 for DIIPA (1) + ■, 2-methyl-1-propanol (2); + ●, 2-propanol (2); and + ▲, 1-butanol (2) at 298.15 K. The smoothing of the curves has been drawn from eq 6.

Figure 2. Excess molar volumes VEm against mole fractions x1 for DIIPA (1) + 2-propanol (2) at ■, 293.15 K; ●, 298.15 K; ▲, 303.15 K; ▼, 308.15 K; and ◆, 313.15 K. The smoothing of the curves has been drawn from eq 6 and the dotted curve from PFP theory at 298.15 K.

The negative VEm values show the presence of strong intermolecular forces of attraction. The present results can be interpreted qualitatively by taking into account the fact that several expansion and contraction processes proceed simultaneously when amine−alkanol mixtures are formed. The following effects can be considered:24,25 (i) expansion due to depolymerization of alcohol and amine by one another, (ii) contraction due

mixtures. Since 1-butanol is a linear chain compound while 2-methyl-1-propanol and 2-propanol are branched, this results in the decrease in value of VEm. This suggests that molecular size is probably a primary factor affecting the excess molar volume of mixing for the systems investigated.7,13 The maximum negative value is obtained for the (DIIPA + 1-butanol) mixture. J



Article

to the free volume difference of unlike molecules, and (iii) contraction due to hydrogen bond formation12,13 between amine and alcohol through NH2···OH and OH···NH2. This interaction can be considered as the reaction between alkanol as a Lewis acid and amine as a Lewis base. For the mixtures of (DIIPA + 2-methyl-1-propanol, + 2-propanol, and +1-butanol) the values of KES,m and uD are plotted in Figures 4 and 5, respectively. The excess molar

Figure 6. Viscosity deviations Δη against mole fractions x1 for DIIPA (1) + ■, 2-methyl-1-propanol (2); + ●, 2-propanol (2); and + ▲, 1-butanol (2) at 298.15 K. The smoothing of the curves has been drawn from eq 6.

viscosity deviations of the mixture under study cannot explain the graded behavior of the complex formation between the amine and alcohol. This shows that strength of the intermolecular hydrogen bonding is not the only factor affecting the viscosity deviation of liquid mixtures. The molecular sizes and shape of the components are equally important factors. The ΔG*E parameter can also be considered as a reliable criterion to detect or exclude the presence of interactions between unlike molecules.28,29 According to Reed and Taylor and Meyer et al., positive ΔG*E values indicate specific interactions, while negative values indicate the dominance of dispersion forces.30 From ΔG*E values shown in Figure 7, it is seen that these values are negative for the studied mixtures.

Figure 5. Deviations of speeds of sound uD from their ideal values against mole fractions x1 for DIIPA (1) ■, 2-methyl-1-propanol (2); + ●, 2-propanol (2); and + ▲, 1-butanol (2) at 298.15 K. The smoothing of the curves has been drawn from eq 6.

isentropic compressibility KES,m shows a negative trend for all the systems over the entire composition range. The behavior of VEm with x1 is well reflected in the behavior of KES,m for the binary mixtures investigated. The KES,m values can be interpreted in terms of (i) interstitial accommodation of alcohol molecules in the aggregates of amine, (ii) decrease in free volume in the mixture as compared to those in pure components due to the rupture of amine aggregates with the addition of alcohol. The negative KES,m values for the studied binary mixtures show that first factor predominates in these mixtures and that the mixture is less compressible than the corresponding ideal mixture. In these binary mixtures, contraction in free volume makes the mixture less compressible than ideal mixtures. Negative KES,m means that the mixture is less compressible than the ideal mixture. It is evident from Figure 5 that the trend in uD values are similar to KES,m but with the opposite sign. The variation of the viscosity deviations, Δη with the mole fraction, x1, for the binary mixtures is presented in Figure 6. The Δη values are negative for all three binary mixtures over the whole composition range. The negative values of Δη show a decrease with increase in temperature. The viscosity of a mixture strongly depends upon the entropy of the mixture,26 which is related to the structure of the liquid and consequently to the molecular interaction between the components of the mixture. Vogel and Weiss27 affirm that mixtures with strong interaction between different molecules present positive viscosity deviations, whereas for mixtures without specific interactions, the viscosity deviations are negative. So, the viscosity deviations are functions of the molecular interaction as well as the size and shape of the molecules. The negative value observed for

Figure 7. Excess Gibbs free energy of activation for viscous flow ΔG*E for DIIPA (1) + ■, 2-methyl-1-propanol (2); + ●, 2-propanol (2); and + ▲, 1-butanol (2) at 298.15 K. The smoothing of the curves has been drawn from eq 6.

The apparent molar volume, Vφ,1 and apparent molar compressibility, Kφ,1 of DIIPA (1) in cosolvent alcohols (2) defined30,31 K



Article

Table 7. Values of Partial Molar Volumes and Partial Molar Isentropic Compressibilties at Infinite Dilution at (298.15 to 308.15) Ka T (K)

V*1 × 106 (m3 mol−1)

V̅φ0,1 × 106 (m3 mol−1)

V*2 × 106 (m3 mol−1)

V̅φ0,2 × 106 (m3 mol−1)

0

binary mixture

K̅ φ ,1 (mm3 mol−1 MPa−1)

K̅ φ ,2 (mm3 mol−1 MPa−1)

DIIPA + 2-methyl-1-propanol

298.15 303.15 308.15 298.15 303.15 308.15 298.15 303.15 308.15

142.220 143.202 144.201 142.220 143.202 144.201 142.220 143.202 144.201

132.208 133.103 134.016 131.024 132.580 134.263 126.970 132.791 133.719

92.872 93.329 93.796 76.942 77.365 77.802 91.968 92.409 92.858

83.136 83.506 83.884 70.845 67.246 71.011 85.165 80.534 80.850

−57.060 −60.157 −63.428 −45.568 −47.537 −49.948 −56.809 −56.047 −48.835

−114.076 −120.601 −128.222 −18.424 −19.839 −22.897 −59.237 −64.658 −69.792

DIIPA + 2-propanol

DIIPA + 1-butanol

a

0

The standard uncertainties are u(ρ) = 0.25 kg·m−3, u(u) = 5.0 m·s−1, u(x1) = 1 × 10−4, u(T) = 0.01 K, and u(P) = 1 kPa.

volume of the solute molecules is affected and that the molecules are in a force field different from that present in the pure liquid state. The observed negative ΔK values indicate that the partial molar isentropic compressibility of alcohol decreases when dissolved in DIIPA. Hall and Sile32 analyzed these deviations in terms of structural and geometrical compressibility. Similarly lower Vφ̅ 0, i values of DIIPA in alcohol rather than the corresponding molar volume, i.e., negative ΔV, indicate that volume contraction is taking place with the addition of alcohol in DIIPA. This provides support to the conclusions drawn earlier from other experimental data. Partial molar volumes and partial molar isentropic compressibilities at infinite dilution for all components are listed in Table 7. 3.1. Theoretical Analysis. The PFP theory has been applied to predict and correlate VEm. The relevant equations are given elsewhere.33−41 Table 8 contains characteristic parameters for the pure components at several temperatures used in PFP theory calculations. Table 9 reports the interaction parameter, χ12, calculated and the experimental values of VEm at x1 ≈ 0.5. It is also clear from Table 9 that the contribution due to the interactional term is dominant and acts as a deciding factor for the sign and magnitude of the VEm due to its greater values compared to the other two contributions for all investigated systems at all temperatures. Figures 1 to 3 show the comparison between the excess molar volumes determined experimentally and calculated using PFP theory. It is evident from Figures 1 and 3 that the PFP theory predicts the experimental data quite satisfactorily, while a small deviation in magnitude is observed in Figure 2.

Table 8. Characteristic and Reduced Parameters for the Pure Components at 298.15 K Used in PFP Theory components DIIPA 2-methyl-1propanol 2-propanol 1-butanol

ν̃

T̃

V* × 106 (m3 mol−1)

P* × 106 (J m−3)

T* (K)

1.3196 1.2448

0.0669 0.0565

107.77 74.61

480 440

4455 5272

1.2676 1.2392

0.0599 0.0556

60.69 74.21

452 464

4972 5354

in terms of mole fraction concentration unit are calculated from the following relationship: Vφ ,1 = V1* + (VmE /x1)

(8)

Kφ ,1 = Kφ*,1 + (KSE, m/x1)

(9)

where Kφ,1 * is the molar isentropic compressibility, which is the same as KS,m * (1). Simple graphical or analytical extrapolation of Vφ,1 and Kφ,1 to x1 = 0 (x2 = 1) and of Vφ,2 and Kφ,2 to x2 = 0 (x1 = 1) gives values of V0φ,1 or V0φ,2 and K0φ,1 or K0φ,2 at infinite dilutions. These are also the desired partial molar volumes and partial molar compressibilities at infinite dilution represented by Vφ̅ 0,1 or Vφ̅ 0,2 and K̅ φ0,1 or K̅ φ0,2 . The limiting values of apparent molar volume and apparent molar isentropic compressibilities were calculated by a linear extrapolation, and it is denoted as V0φ,i, i.e., infinite dilution molar volume and K0φ,i, i.e., infinite dilution molar isentropic compressibility. At infinite dilution, V φ0 , i = Vφ̅ 0, i and Kφ0 , i = K̅ φ0, i , where Vφ̅ 0, i is partial molar volume and K̅ φ0, i is partial molar isentropic compressibility at infinite dilution. A comparison of Vφ̅ 0,1 values with the corresponding molar isentropic compressibility K*s,1 (where K*s,1 can be considered as the partial molar compressibility of the solute when dissolved in itself, i.e., pure liquid) shows negative deviations, ΔK, in all three binary mixtures. This can be analyzed in terms that the molecular

4. CONCLUSIONS In this article, an attempt has been made to measure the density and speed of sound at (293.15 to 313.15) K over the entire composition range of (DIIPA+ 2-methyl-1-propanol, + 2-propanol, and +1-butanol). Viscosity measurement has also been done at (298.15 to 313.15) K. From the experimentally measured data, excess molar volume, excess molar isentropic

Table 9. PFP Interaction Parameter, χ12, and Calculated Values of the Three Contributions from the PFP Theory with Experimental Excess Molar Volumes at Equimolar Composition VEm × 106 (m3 mol−1) −3

calculated contributions

binary mixtures

χ12 × 10 (J m )

exptl.

PFP

VEm(int.)

DIIPA + 2-methyl-1-propanol DIIPA + 2-propanol DIIPA + 1-butanol

−106.90 −89.95 −112.96

−2.5913 −2.0056 −2.7387

−2.5901 −2.5897 −2.7449

−2.5523 −2.5518 −2.4741

6

L

VEm(fv)

VEm(P*)

−0.1795 −0.1798 −0.2105

0.1417 0.1419 0.0616



Article

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compressibility, deviation in speed of sound, deviation in viscosity, and excess Gibb’s energy of activation have been calculated and correlated by a Redlich−Kister type polynomial equation to derive the coefficients and standard deviations. Negative values of VEm and KES,m for the studied systems show the presence of strong intermolecular interactions. The apparent molar volume, Vφ,1, and apparent molar compressibility, Kφ,1, have also been calculated; the negative ΔV indicates that volume contraction is taking place with the addition of alcohol in DIIPA. The PFP theory has also been applied to predict and correlate VEm, which gives satisfactory results.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.5b00216. Calculations of the isentropic compressibility, κS, excess molar isentropic compressibility KES,m, and deviations of the speed of sound, uD (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Tel. +91-9416221007. E-mail:gyan.dubey@rediffmail.com. Funding

We gratefully acknowledge financial support for the work by Government of India through University Grants Commission, New Delhi (letter no. F. 14-2 (SC)/2008 (SA III) dated 31-032009). Notes

The authors declare no competing financial interest.

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REFERENCES

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Density, Speed of Sound, Viscosity, Excess Properties, and Prigogine

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