Thermodynamic and Spectroscopic Study of the Ternary System

Article pubs.acs.org/jced

Thermodynamic and Spectroscopic Study of the Ternary System Dimethyladipate + Tetrahydrofuran +1-Butanol at T = (288.15 to 323.15) K

Andjela B. Knežević-Stevanović,‡ Slobodan P. Šerbanović,† Ivona R. Radović,† Bojan D. Djordjević,† and Mirjana Lj. Kijevčanin*,† †

Faculty of Technology and Metallurgy, University of Belgrade, Karnegijeva 4, 11120 Belgrade, Serbia Metro Vancouver, 4330 Kingsway, Burnaby, BC V5H 4G8, Canada

‡

ABSTRACT: Experimental densities ρ, refractive indices nD, and viscosity η data of the ternary dimethyladipate + tetrahydrofuran + 1-butanol and the binary tetrahydrofuran + 1-butanol systems have been determined, while viscosities have been measured for the binary dimethyladipate + 1-butanol system. The properties ρ, nD, and η are experimentally determined at eight temperatures over the temperature range T = (288.15 to 323.15) K and at atmospheric pressure, using instruments from Anton Paar: digital vibrating tube densimeter DMA 5000, refractometer RXA 156, and SVM 3000/G2 digital Stabinger viscometer. Excess molar volumes VE, deviations of refractive indices ΔnD, and deviations of viscosities Δη were calculated from the measured data. The Redlich−Kister equation is used to correlate excess molar volumes, deviations of refractive indices, and viscosities for binary mixtures, while the Nagata− Tamura equation is applied for a ternary mixture. FT-IR studies of the binary constituents of the investigated ternary mixture have also been carried out at T = 298.15 K.

1. INTRODUCTION Volumetric and transport properties of binary and multicomponent mixtures are essential for a process design as well as for understanding a structure and packing changes in mixtures. This work is a continuation of our ongoing research of the thermophysical properties of multicomponent mixtures containing organic solvents, such as esters, ketones, and alcohols.1−6 The systems of dimethyladipate or dimethylphthalate and 1-butanol or 2-butanol with 2-butanone were investigated in our previous paper.5 Because of low cost and toxicity, dimethyladipate as a diester has a diverse industrial application. It is used as an additive to diesel fuel; when blended with polyalphaolefin diesters it improves additive solubility (in gear oils, engine oils, compressor oils, biodegradable hydraulic fuels, etc.).7 Also, dimethyladipate is a main constituent in dibasic ester blends, which are used as paint strippers. These ester blends can also be applied as green solvents and replace conventional high volatile and toxic organic solvents in many industries.8 Tetrahydrofuran is also widely used in industry, primarily as an industrial solvent for polyvinylchloride and varnishes. Alcohols are widely used as intermediates for the production of other chemicals and as solvents. In addition, some alcohols are used as alternative energy sources. As a continuation of our previous study related to determination of thermophysical properties of mixtures containing dimethyladipate, here densities, refractive indices, and viscosities of the ternary dimethyladipate + tetrahydrofuran +1-butanol and binary tetrahydrofuran +1-butanol systems are determined at eight temperatures from (288.15 to 323.15) K and © 2013 American Chemical Society

at atmospheric pressure. In addition, viscosities of the dimethyladipate +1-butanol are also given here, while densities and refractive indices of the same system were reported in our previous paper.5 In our recent work the same properties for the binary system dimethyladipate + tetrahydrofuran were reported.4 From the measured ρ, nD, and η data the excess molar volumes V E, the deviations of refractive indices ΔnD and viscosity deviations Δη were calculated. To correlate VE, ΔnD and Δη data of the binaries the Redlich− Kister9 equation was used, while the Nagata and Tamura10 equation was used to correlate ternary data. Literature densities11 and viscosities12 data are available for the binary system tetrahydrofuran +1-butanol at 298.15 K and 313.15 K. To the best of our knowledge, the nD experimental data are not available for the investigated binary system. In addition, no experimental ρ, nD, or η data have been reported in the literature for the investigated ternary system. Table 1. Sample Description chemical name

source

initial mass fraction purity

purification method

dimethyladipate tetrahydrofuran 1-butanol

Merck Merck Merck

≥ 0.99 min 0.995 ≥ 0.995

none none none

Received: April 7, 2013 Accepted: September 7, 2013 Published: September 26, 2013 2932

dx.doi.org/10.1021/je4003916 | J. Chem. Eng. Data 2013, 58, 2932−2951

Journal of Chemical & Engineering Data

Article

Table 2. Densities ρ, Refractive Indices nD, and Viscosities η of the Pure Components at Temperature T and Atmospheric Pressurea 10−3·ρ/kg·m−3 T/K

this work

lit

dimethyladipate

293.15 298.15

1.06193

1.06190b

293.15 298.15 298.15

0.88786 0.88240 0.80576

tetrahydrofuran 1-butanol

η/mPa·s

nD

component

this work

0.886684e 0.882502f 0.80575b

lit

1.4264

1.4215b 1.4283d

1.4043 1.3973

1.40496g 1.39741g 1.3973e

this work

lit

3.289 2.910

3.36c 2.98c

0.502 0.480 2.581

0.481f 0.460g 2.571e,g

Standard uncertainties σ for each variables are σ(T) = 0.01 K; the combined expanded uncertainty is σc(ρ) = ± 1·10−2 kg·m−3; σc(η) = ± 3·10−3 mPa·s and σc(nD) = 1·10−4, with a 0.95 level of confidence (k ≈ 2). bInce.13 cComuñas et al.7 dLide.14 eSelected Values of Properties of Chemical Compounds.15 fTRC Thermodynamic Tables -Non-Hydrocarbons.16 gRiddick et al.17 a

Table 3. Experimental Values of Densities ρ, Refractive Indices nD, Viscosities η, and Values of Calculated Excess Molar Volumes VE, Deviations in Refractive Indices ΔnD, and Viscosity Deviations Δη of the Tetrahydrofuran (1) + 1-Butanol (2) System at T = (288.15 to 323.15) K and Atmospheric Pressurea 10−3·ρ x1

kg·m

−3

0.0000 0.1001 0.2003 0.3000 0.4003 0.5000 0.6001 0.7003 0.8006 0.9002 1.0000

0.81337 0.82070 0.82811 0.83561 0.84328 0.85103 0.85898 0.86719 0.87564 0.88434 0.89329

0.0000 0.1001 0.2003 0.3000 0.4003 0.5000 0.6001 0.7003 0.8006 0.9002 1.0000

0.80957 0.81675 0.82399 0.83134 0.83884 0.84643 0.85421 0.86227 0.87054 0.87908 0.88786

0.0000 0.1001 0.2003 0.3000 0.4003 0.5000 0.6001 0.7003 0.8006 0.9002 1.0000

0.80576 0.81277 0.81986 0.82704 0.83438 0.84180 0.84943 0.85731 0.86541 0.87378 0.88240

0.0000 0.1001 0.2003 0.3000

0.80192 0.80876 0.81569 0.82271

106·VE −1

m ·mol 3

−0.017 −0.024 −0.026 −0.022 −0.012 0.000 0.006 0.011 0.006

−0.016 −0.021 −0.022 −0.016 −0.005 0.006 0.011 0.015 0.008

−0.013 −0.016 −0.016 −0.009 0.001 0.013 0.017 0.020 0.011

−0.010 −0.011 −0.010

nD T = 288.15 1.4014 1.4020 1.4028 1.4036 1.4043 1.4051 1.4059 1.4068 1.4077 1.4087 1.4096 T = 293.15 1.3993 1.3999 1.4006 1.4013 1.4021 1.4028 1.4035 1.4044 1.4052 1.4061 1.4070 T = 298.15 1.3973 1.3978 1.3985 1.3991 1.3998 1.4004 1.4011 1.4019 1.4027 1.4035 1.4043 T = 303.15 1.3952 1.3957 1.3963 1.3969 2933

η

Δη

ΔnD

mPa·s

mPa·s

−0.00016 −0.00023 −0.00028 −0.00032 −0.00037 −0.00038 −0.00032 −0.00025 −0.00009 0

3.375 2.377 1.788 1.416 1.150 0.962 0.836 0.723 0.642 0.578 0.522

−0.712 −1.015 −1.103 −1.083 −0.987 −0.827 −0.654 −0.449 −0.229

−0.00016 −0.00023 −0.00029 −0.00033 −0.00037 −0.00039 −0.00032 −0.00027 −0.0001

2.945 2.111 1.612 1.292 1.061 0.895 0.785 0.683 0.610 0.555 0.502

−0.589 −0.843 −0.920 −0.906 −0.829 −0.694 −0.551 −0.379 −0.191

−0.00018 −0.00026 −0.00032 −0.00035 −0.0004 −0.00041 −0.00036 −0.00026 −0.00012

2.581 1.882 1.460 1.184 0.979 0.834 0.736 0.645 0.579 0.528 0.480

−0.489 −0.700 −0.767 −0.761 −0.697 −0.584 −0.465 −0.320 −0.162

K

K

K

K −0.00016 −0.00025 −0.00029

2.272 1.687 1.331 1.087

−0.404 −0.578 −0.641



Article

Table 3. continued 10−3·ρ x1

kg·m

−3

0.4003 0.5000 0.6001 0.7003 0.8006 0.9002 1.0000

0.82989 0.83715 0.84461 0.85232 0.86026 0.86846 0.87691

0.0000 0.1001 0.2003 0.3000 0.4003 0.5000 0.6001 0.7003 0.8006 0.9002 1.0000

0.79805 0.80473 0.81149 0.81836 0.82536 0.83246 0.83975 0.84730 0.85506 0.86309 0.87138

0.0000 0.1001 0.2003 0.3000 0.4003 0.5000 0.6001 0.7003 0.8006 0.9002 1.0000

0.79415 0.80066 0.80726 0.81396 0.82081 0.82774 0.83486 0.84224 0.84983 0.85770 0.86581

0.0000 0.1001 0.2003 0.3000 0.4003 0.5000 0.6001 0.7003 0.8006 0.9002 1.0000

0.79023 0.79655 0.80299 0.80953 0.81621 0.82298 0.82993 0.83714 0.84456 0.85225 0.86020

0.0000 0.1001 0.2003 0.3000 0.4003 0.5000 0.6001 0.7003 0.8006 0.9002 1.0000

0.78624 0.79240 0.79867 0.80505 0.81157 0.81817 0.82496 0.83200 0.83925 0.84677 0.85455

106·VE −1

m ·mol 3

−0.003 0.008 0.019 0.023 0.025 0.014

−0.008 −0.007 −0.004 0.004 0.015 0.026 0.029 0.029 0.017

−0.005 −0.003 0.001 0.010 0.022 0.032 0.035 0.034 0.019

0.001 0.005 0.009 0.018 0.030 0.041 0.042 0.040 0.023

0.003 0.008 0.015 0.024 0.036 0.047 0.047 0.044 0.025

η

Δη

nD

ΔnD

mPa·s

mPa·s

T = 303.15 K 1.3974 1.3980 1.3987 1.3994 1.4001 1.4009 1.4016

−0.00035 −0.00039 −0.00041 −0.00035 −0.00028 −0.00013

0.908 0.779 0.692 0.610 0.550 0.502 0.459

−0.638 −0.587 −0.493 −0.393 −0.271 −0.138

T = 308.15 K 1.3932 1.3936 1.3941 1.3946 1.3951 1.3957 1.3962 1.3969 1.3975 1.3983 1.3990 T = 313.15 K 1.3911 1.3914 1.3919 1.3923 1.3928 1.3933 1.3938 1.3943 1.3949 1.3956 1.3963 T = 318.15 K 1.3890 1.3893 1.3897 1.3901 1.3905 1.3909 1.3913 1.3918 1.3923 1.3929 1.3936 T = 323.15 K 1.3869 1.3871 1.3874 1.3878 1.3881 1.3885 1.3888 1.3893 1.3897 1.3903 1.3909

−0.00018 −0.00026 −0.00031 −0.00036 −0.00041 −0.00042 −0.00036 −0.00031 −0.00013

2.008 1.517 1.215 1.000 0.843 0.728 0.652 0.576 0.521 0.478 0.440

−0.334 −0.479 −0.537 −0.538 −0.496 −0.415 −0.334 −0.231 −0.118

−0.00019 −0.00027 −0.00031 −0.00037 −0.00041 −0.00044 −0.00039 −0.00031 −0.00016

1.782 1.368 1.111 0.922 0.782 0.681 0.608 0.543 0.494 0.454 0.418

−0.278 −0.398 −0.451 −0.454 −0.419 −0.356 −0.284 −0.197 −0.101

−0.00019 −0.00028 −0.00032 −0.00037 −0.00041 −0.00044 −0.00040 −0.00034 −0.00019

1.587 1.238 1.019 0.852 0.727 0.637 0.571 0.513 0.466 0.428 0.396

−0.230 −0.329 −0.378 −0.383 −0.355 −0.301 −0.240 −0.167 −0.086

−0.00019 −0.00027 −0.00031 −0.00037 −0.00041 −0.00046 −0.00042 −0.00036 −0.00021

1.419 1.139 0.949 0.795 0.683 0.599 0.546 0.487 0.444 0.410 0.384

−0.172 −0.254 −0.301 −0.305 −0.281 −0.226 −0.177 −0.113 −0.077

Standard uncertainties σ for each variables are σ(T) = 0.01 K ; σ(p) = 5 % ; σ(x1) = 0.0001, and the combined expanded uncertainties σc are σc(ρ) = ± 1·10−2 kg·m−3; σc(η) = ± 3·10−3 mPa·s and σc(nD) = 1·10−4, with 0.95 level of confidence (k ≈ 2).

a

2934



Article

Table 4. Viscosities η and Viscosity Deviations Δη of the Dimethyladipate (1) + 1-Butanol (2) System at T = (288.15 to 323.15) K and Atmospheric Pressurea

a

η

Δη

x1

mPa·s

mPa·s

0.0000 0.0999 0.2004 0.2999 0.4003 0.4999

3.375 2.635 2.426 2.384 2.422 2.519

0 0.0999 0.2004 0.2999 0.4003 0.4999

2.945 2.322 2.147 2.114 2.149 2.237

0 0.0999 0.2004 0.2999 0.4003 0.4999

2.581 2.057 1.911 1.886 1.920 2.003

0 0.0999 0.2004 0.2999 0.4003 0.4999

2.272 1.837 1.716 1.699 1.732 1.805

x1

T = 288.15 K 0.6007 −0.777 0.6996 −1.024 0.7994 −1.103 0.8991 −1.104 1.0000 −1.044 T = 293.15 K 0.6007 −0.657 0.6996 −0.867 0.7994 −0.934 0.8991 −0.934 1 −0.881 T = 298.15 K 0.6007 −0.557 0.6996 −0.736 0.7994 −0.793 0.8991 −0.792 1 −0.742 T = 303.15 K 0.6007 −0.468 0.6996 −0.623 0.7994 −0.672 0.8991 −0.673 1 −0.633

η

Δη

η

Δη

mPa·s

mPa·s

x1

mPa·s

mPa·s

2.660 2.884 3.080 3.379 3.751

−0.941 −0.754 −0.596 −0.334

0 0.0999 0.2004 0.2999 0.4003 0.4999

2.008 1.646 1.546 1.536 1.569 1.636

2.361 2.556 2.723 2.977 3.289

−0.791 −0.630 −0.497 −0.278

0 0.0999 0.2004 0.2999 0.4003 0.4999

1.782 1.481 1.400 1.396 1.428 1.491

2.110 2.287 2.425 2.649 2.910

−0.669 −0.524 −0.420 −0.228

0 0.0999 0.2004 0.2999 0.4003 0.4999

1.587 1.338 1.272 1.273 1.306 1.365

1.902 2.060 2.183 2.374 2.604

−0.570 −0.444 −0.355 −0.196

0 0.0999 0.2004 0.2999 0.4003 0.4999

1.419 1.229 1.176 1.179 1.214 1.268

x1

T = 308.15 K 0.6007 −0.396 0.6996 −0.529 0.7994 −0.572 0.8991 −0.574 1 −0.539 T = 313.15 K 0.6007 −0.335 0.6996 −0.450 0.7994 −0.488 0.8991 −0.490 1 −0.461 T = 318.15 K 0.6007 −0.284 0.6996 −0.384 0.7994 −0.418 0.8991 −0.420 1 −0.396 T = 323.15 K 0.6007 −0.227 0.6996 −0.317 0.7994 −0.351 0.8991 −0.354 1 −0.337

η

Δη

mPa·s

mPa·s

1.724 1.868 1.975 2.144 2.343

−0.485 −0.374 −0.300 −0.165

1.572 1.704 1.797 1.947 2.121

−0.414 −0.315 −0.256 −0.140

1.440 1.562 1.645 1.778 1.933

−0.356 −0.268 −0.219 −0.120

1.339 1.456 1.528 1.648 1.790

−0.303 −0.223 −0.187 −0.104

Standard uncertainties σ for each variables are σ(T) = 0.01 K ; σ(p) = 5 % ; σ(x1) = 0.0001, and the combined expanded uncertainties σc is σc(η) = ± 3·10−3 mPa·s, with 0.95 level of confidence (k ≈ 2).

Table 5. Experimental Values of Densities ρ, Refractive Indices nD, Viscosities η, and Values of Calculated Excess Molar Volumes VE, Deviations in Refractive Indices ΔnD, and Viscosity Deviations Δη of the Dimethyladipate (1) + Tetrahydrofurane (2) + 1-Butanol (3) System at T = (288.15 to 323.15) K and Atmospheric Pressurea 10−3·ρ x1 0.0900 0.0800 0.0701 0.0600 0.0501 0.0400 0.0300 0.0200 0.0101 0.1799 0.1601 0.1400 0.1199 0.1000 0.0800 0.0596 0.0400 0.0200 0.3601 0.3195 0.2800

x2 0.0999 0.2000 0.3001 0.3999 0.4998 0.5999 0.7003 0.8001 0.8999 0.1002 0.2000 0.2999 0.4001 0.5001 0.5999 0.7020 0.7999 0.8998 0.1000 0.2006 0.2999

−3

kg·m

0.85794 0.86150 0.86501 0.86862 0.87241 0.87624 0.88022 0.88440 0.88876 0.89075 0.89105 0.89156 0.89187 0.89215 0.89247 0.89267 0.89284 0.89293 0.94604 0.94170 0.93741

106·VE −1

m ·mol 3

nD

T = 288.15 K 0.075 1.4061 0.043 1.4065 0.036 1.4069 0.022 1.4072 0.013 1.4076 0.009 1.4080 0.012 1.4082 0.007 1.4088 0.005 1.4093 0.130 1.4098 0.114 1.4098 0.064 1.4099 0.042 1.4099 0.031 1.4099 0.011 1.4099 0.008 1.4099 0.007 1.4099 0.014 1.4098 0.156 1.4162 0.138 1.4156 0.105 1.4152 2935

η

Δη

ΔnD

mPa·s

mPa·s

0.00127 0.00115 0.00098 0.00083 0.00066 0.00056 0.00018 0.00025 0.00020 0.00233 0.00214 0.00202 0.00178 0.00151 0.00126 0.00096 0.00075 0.00040 0.00354 0.00327 0.00323

2.095 1.705 1.403 1.174 0.999 0.858 0.748 0.656 0.583 2.020 1.692 1.433 1.219 1.043 0.899 0.777 0.680 0.593 2.101 1.802 1.566

−1.029 −1.129 −1.142 −1.082 −0.969 −0.820 −0.640 −0.443 −0.228 −1.137 −1.172 −1.139 −1.059 −0.943 −0.795 −0.618 −0.428 −0.222 −1.124 −1.121 −1.059



Article


x2

−3

kg·m

0.2400 0.1999 0.1600 0.1200 0.0801 0.0400 0.5401 0.4801 0.4192 0.3590 0.3000 0.2400 0.1789 0.1201 0.0601 0.7201 0.6376 0.5598 0.4801 0.4000 0.3202 0.2400 0.1600 0.0818 0.8101 0.7199 0.6300 0.5400 0.4498 0.3600 0.2701 0.1800 0.0898

0.4000 0.5000 0.5998 0.6999 0.8000 0.8999 0.0998 0.1999 0.2993 0.4017 0.4999 0.5999 0.7020 0.8000 0.9002 0.0999 0.2027 0.3000 0.4000 0.5000 0.6000 0.6999 0.7999 0.8978 0.0999 0.2001 0.2998 0.4001 0.5000 0.5998 0.7000 0.8001 0.9003

0.93254 0.92755 0.92190 0.91581 0.90909 0.90154 0.99058 0.98357 0.97574 0.96751 0.95844 0.94829 0.93681 0.92425 0.90983 1.02716 1.01809 1.00862 0.99787 0.98573 0.97219 0.95641 0.93839 0.91819 1.04306 1.03363 1.02315 1.01142 0.99810 0.98299 0.96562 0.94537 0.92151

0.0900 0.0800 0.0701 0.0600 0.0501 0.0400 0.0300 0.0200 0.0101 0.1799 0.1601 0.1400 0.1199 0.1000 0.0800 0.0596 0.0400 0.0200 0.3601 0.3195 0.2800 0.2400 0.1999 0.1600

0.0999 0.2000 0.3001 0.3999 0.4998 0.5999 0.7003 0.8001 0.8999 0.1002 0.2000 0.2999 0.4001 0.5001 0.5999 0.7020 0.7999 0.8998 0.1000 0.2006 0.2999 0.4000 0.5000 0.5998

0.85378 0.85721 0.86060 0.86407 0.86773 0.87142 0.87525 0.87928 0.88349 0.88642 0.88661 0.88703 0.88723 0.88739 0.88759 0.88766 0.88771 0.88766 0.94146 0.93706 0.93270 0.92776 0.92268 0.91694

106·VE −1

m ·mol 3

nD

T = 288.15 K 0.090 1.4146 0.043 1.4141 0.027 1.4134 0.006 1.4127 −0.004 1.4118 −0.003 1.4108 0.124 1.4213 0.107 1.4207 0.077 1.4197 0.055 1.4189 0.035 1.4178 0.013 1.4165 −0.009 1.4152 −0.012 1.4137 −0.011 1.4119 0.071 1.4257 0.049 1.4247 0.029 1.4237 0.011 1.4224 −0.006 1.4210 −0.031 1.4194 −0.025 1.4175 −0.014 1.4154 −0.015 1.4129 0.045 1.4276 0.026 1.4266 0.005 1.4254 −0.014 1.4240 −0.030 1.4225 −0.038 1.4207 −0.040 1.4187 −0.036 1.4163 −0.019 1.4132 T = 293.15 K 0.083 1.4040 0.052 1.4043 0.043 1.4046 0.029 1.4049 0.019 1.4053 0.014 1.4056 0.016 1.4057 0.010 1.4063 0.007 1.4067 0.142 1.4076 0.125 1.4076 0.073 1.4077 0.049 1.4077 0.037 1.4076 0.016 1.4075 0.012 1.4074 0.009 1.4074 0.015 1.4072 0.171 1.4141 0.151 1.4134 0.115 1.4130 0.097 1.4124 0.048 1.4118 0.030 1.4111

2936

η

Δη

ΔnD

mPa·s

mPa·s

0.00296 0.00279 0.00241 0.00201 0.00149 0.00088 0.00333 0.00367 0.00367 0.00371 0.00352 0.00321 0.00282 0.00222 0.00134 0.00258 0.00307 0.00353 0.00377 0.00385 0.00372 0.00340 0.00274 0.00176 0.00185 0.00257 0.00318 0.00364 0.00389 0.00385 0.00367 0.00303 0.00180

1.343 1.157 0.989 0.849 0.726 0.617 2.329 2.040 1.775 1.522 1.309 1.104 0.932 0.777 0.642 2.719 2.352 2.043 1.749 1.479 1.245 1.027 0.829 0.669 2.964 2.573 2.211 1.879 1.581 1.308 1.070 0.864 0.691

−0.981 −0.867 −0.735 −0.575 −0.397 −0.205 −0.965 −0.945 −0.903 −0.842 −0.753 −0.650 −0.507 −0.361 −0.187 −0.642 −0.684 −0.687 −0.665 −0.620 −0.538 −0.441 −0.324 −0.175 −0.431 −0.502 −0.546 −0.557 −0.537 −0.492 −0.410 −0.296 −0.149

0.00126 0.00115 0.00097 0.00082 0.00065 0.00056 0.00019 0.00025 0.00019 0.00230 0.00212 0.00202 0.00179 0.00152 0.00128 0.00098 0.00075 0.00041 0.00350 0.00325 0.00325 0.00299 0.00281 0.00248

1.871 1.544 1.281 1.083 0.929 0.804 0.705 0.623 0.557 1.808 1.531 1.310 1.123 0.969 0.841 0.733 0.644 0.566 1.881 1.629 1.429 1.234 1.071 0.923

−0.861 −0.940 −0.955 −0.906 −0.812 −0.689 −0.539 −0.374 −0.193 −0.954 −0.981 −0.951 −0.886 −0.789 −0.666 −0.518 −0.360 −0.188 −0.943 −0.936 −0.879 −0.817 −0.722 −0.612



Article


x2

−3

kg·m

0.1200 0.0801 0.0400 0.5401 0.4801 0.4192 0.3590 0.3000 0.2400 0.1789 0.1201 0.0601 0.7201 0.6376 0.5598 0.4801 0.4000 0.3202 0.2400 0.1600 0.0818 0.8101 0.7199 0.6300 0.5400 0.4498 0.3600 0.2701 0.1800 0.0898

0.6999 0.8000 0.8999 0.0998 0.1999 0.2993 0.4017 0.4999 0.5999 0.7020 0.8000 0.9002 0.0999 0.2027 0.3000 0.4000 0.5000 0.6000 0.6999 0.7999 0.8978 0.0999 0.2001 0.2998 0.4001 0.5000 0.5998 0.7000 0.8001 0.9003

0.91075 0.90392 0.89625 0.98584 0.97879 0.97092 0.96262 0.95350 0.94327 0.93171 0.91906 0.90453 1.02233 1.01322 1.00372 0.99291 0.98072 0.96713 0.95128 0.93317 0.91288 1.03819 1.02872 1.01821 1.00645 0.99307 0.97790 0.96047 0.94014 0.91619

0.0900 0.0800 0.0701 0.0600 0.0501 0.0400 0.0300 0.0200 0.0101 0.1799 0.1601 0.1400 0.1199 0.1000 0.0800 0.0596 0.0400 0.0200 0.3601 0.3195 0.2800 0.2400 0.1999 0.1600 0.1200 0.0801 0.0400

0.0999 0.2000 0.3001 0.3999 0.4998 0.5999 0.7003 0.8001 0.8999 0.1002 0.2000 0.2999 0.4001 0.5001 0.5999 0.7020 0.7999 0.8998 0.1000 0.2006 0.2999 0.4000 0.5000 0.5998 0.6999 0.8000 0.8999

0.84959 0.85290 0.85617 0.85950 0.86303 0.86657 0.87026 0.87413 0.87819 0.88206 0.88216 0.88248 0.88257 0.88262 0.88270 0.88264 0.88254 0.88235 0.93687 0.93240 0.92797 0.92296 0.91780 0.91197 0.90567 0.89873 0.89093

106·VE −1

m ·mol 3

nD

T = 293.15 K 0.007 1.4102 −0.003 1.4093 −0.003 1.4083 0.137 1.4191 0.116 1.4185 0.084 1.4175 0.058 1.4166 0.036 1.4155 0.013 1.4142 −0.011 1.4128 −0.014 1.4112 −0.013 1.4094 0.078 1.4236 0.052 1.4225 0.030 1.4215 0.010 1.4202 −0.009 1.4188 −0.036 1.4171 −0.030 1.4152 −0.019 1.4129 −0.018 1.4104 0.049 1.4255 0.026 1.4244 0.003 1.4232 −0.018 1.4218 −0.036 1.4202 −0.045 1.4184 −0.047 1.4163 −0.042 1.4138 −0.023 1.4107 T = 298.15 K 0.093 1.4018 0.061 1.4021 0.051 1.4024 0.037 1.4027 0.026 1.4029 0.020 1.4032 0.021 1.4033 0.014 1.4038 0.009 1.4041 0.156 1.4055 0.137 1.4054 0.083 1.4055 0.058 1.4054 0.043 1.4052 0.021 1.4051 0.016 1.4049 0.012 1.4048 0.017 1.4046 0.187 1.4119 0.164 1.4112 0.125 1.4108 0.105 1.4101 0.052 1.4095 0.033 1.4087 0.008 1.4078 −0.003 1.4068 −0.003 1.4057 2937

η

Δη

ΔnD

mPa·s

mPa·s

0.00204 0.00154 0.00089 0.00330 0.00368 0.00371 0.00376 0.00358 0.00329 0.00291 0.00229 0.00139 0.00259 0.00310 0.00358 0.00386 0.00396 0.00382 0.00348 0.00282 0.00181 0.00185 0.00263 0.00325 0.00372 0.00400 0.00398 0.00379 0.00312 0.00187

0.798 0.687 0.589 2.082 1.838 1.614 1.393 1.207 1.025 0.874 0.734 0.611 2.422 2.110 1.847 1.597 1.359 1.153 0.958 0.782 0.635 2.630 2.300 1.993 1.708 1.449 1.208 0.998 0.814 0.657

−0.479 −0.331 −0.171 −0.805 −0.784 −0.744 −0.695 −0.620 −0.537 −0.418 −0.298 −0.155 −0.527 −0.559 −0.558 −0.536 −0.502 −0.436 −0.359 −0.264 −0.145 −0.350 −0.404 −0.437 −0.445 −0.430 −0.395 −0.330 −0.239 −0.119

0.00120 0.00111 0.00096 0.00081 0.00064 0.00054 0.00019 0.00025 0.00017 0.00223 0.00207 0.00199 0.00177 0.00151 0.00126 0.00097 0.00074 0.00038 0.00344 0.00325 0.00325 0.00299 0.00287 0.00251 0.00208 0.00156 0.00090

1.678 1.405 1.174 1.001 0.865 0.754 0.667 0.590 0.531 1.628 1.391 1.200 1.038 0.901 0.787 0.691 0.610 0.539 1.696 1.479 1.311 1.138 0.995 0.862 0.751 0.650 0.561

−0.723 −0.782 −0.800 −0.760 −0.682 −0.580 −0.453 −0.316 −0.163 −0.802 −0.823 −0.797 −0.742 −0.662 −0.560 −0.435 −0.303 −0.158 −0.793 −0.786 −0.732 −0.682 −0.602 −0.511 −0.399 −0.276 −0.143



Article


x2

−3

kg·m

0.5401 0.4801 0.4192 0.3590 0.3000 0.2400 0.1789 0.1201 0.0601 0.7201 0.6376 0.5598 0.4801 0.4000 0.3202 0.2400 0.1600 0.0818 0.8101 0.7199 0.6300 0.5400 0.4498 0.3600 0.2701 0.1800 0.0898

0.0998 0.1999 0.2993 0.4017 0.4999 0.5999 0.7020 0.8000 0.9002 0.0999 0.2027 0.3000 0.4000 0.5000 0.6000 0.6999 0.7999 0.8978 0.0999 0.2001 0.2998 0.4001 0.5000 0.5998 0.7000 0.8001 0.9003

0.98110 0.97400 0.96607 0.95772 0.94853 0.93824 0.92659 0.91384 0.89919 1.01749 1.00834 0.99880 0.98795 0.97570 0.96205 0.94613 0.92793 0.90754 1.03332 1.02382 1.01327 1.00146 0.98804 0.97281 0.95530 0.93490 0.91084

0.0900 0.0800 0.0701 0.0600 0.0501 0.0400 0.0300 0.0200 0.0101 0.1799 0.1601 0.1400 0.1199 0.1000 0.0800 0.0596 0.0400 0.0200 0.3601 0.3195 0.2800 0.2400 0.1999 0.1600 0.1200 0.0801 0.0400 0.5401 0.4801 0.4192

0.0999 0.2000 0.3001 0.3999 0.4998 0.5999 0.7003 0.8001 0.8999 0.1002 0.2000 0.2999 0.4001 0.5001 0.5999 0.7020 0.7999 0.8998 0.1000 0.2006 0.2999 0.4000 0.5000 0.5998 0.6999 0.8000 0.8999 0.0998 0.1999 0.2993

0.84538 0.84856 0.85170 0.85491 0.85829 0.86170 0.86524 0.86896 0.87285 0.87769 0.87769 0.87790 0.87788 0.87782 0.87778 0.87758 0.87735 0.87701 0.93226 0.92772 0.92323 0.91814 0.91290 0.90697 0.90057 0.89351 0.88558 0.97635 0.96920 0.96122

106·VE −1

m ·mol 3

nD

T = 298.15 K 0.151 1.4170 0.126 1.4163 0.090 1.4153 0.062 1.4144 0.037 1.4132 0.012 1.4118 −0.013 1.4104 −0.016 1.4087 −0.015 1.4068 0.085 1.4215 0.056 1.4204 0.031 1.4193 0.008 1.4180 −0.013 1.4165 −0.041 1.4147 −0.035 1.4128 −0.024 1.4105 −0.022 1.4078 0.051 1.4234 0.025 1.4223 0.000 1.4210 −0.023 1.4196 −0.042 1.4180 −0.052 1.4161 −0.055 1.4140 −0.048 1.4114 −0.027 1.4081 T = 303.15 K 0.102 1.3997 0.070 1.3999 0.060 1.4002 0.044 1.4004 0.033 1.4005 0.026 1.4008 0.026 1.4008 0.017 1.4012 0.011 1.4015 0.170 1.4033 0.150 1.4032 0.093 1.4032 0.066 1.4031 0.050 1.4029 0.026 1.4027 0.019 1.4025 0.014 1.4023 0.018 1.4020 0.204 1.4098 0.178 1.4090 0.135 1.4086 0.112 1.4078 0.057 1.4072 0.035 1.4063 0.009 1.4053 −0.003 1.4043 −0.003 1.4031 0.163 1.4148 0.136 1.4142 0.097 1.4131

2938

η

Δη

ΔnD

mPa·s

mPa·s

0.00327 0.00368 0.00372 0.00382 0.00364 0.00335 0.00298 0.00232 0.00140 0.00258 0.00313 0.00363 0.00394 0.00405 0.00392 0.00360 0.00290 0.00185 0.00187 0.00266 0.00331 0.00381 0.00411 0.00409 0.00391 0.00321 0.00191

1.874 1.666 1.476 1.280 1.116 0.955 0.822 0.693 0.581 2.172 1.906 1.681 1.466 1.253 1.071 0.897 0.737 0.603 2.355 2.071 1.807 1.565 1.333 1.120 0.933 0.767 0.624

−0.675 −0.653 −0.614 −0.575 −0.513 −0.445 −0.343 −0.246 −0.128 −0.436 −0.459 −0.454 −0.432 −0.409 −0.355 −0.293 −0.216 −0.119 −0.283 −0.327 −0.351 −0.353 −0.345 −0.320 −0.266 −0.192 −0.095

0.00120 0.00110 0.00096 0.00081 0.00064 0.00055 0.00021 0.00025 0.00017 0.00222 0.00206 0.00200 0.00179 0.00154 0.00130 0.00101 0.00077 0.00041 0.00343 0.00324 0.00326 0.00303 0.00291 0.00257 0.00213 0.00161 0.00092 0.00325 0.00369 0.00376

1.516 1.283 1.080 0.928 0.807 0.708 0.630 0.560 0.506 1.475 1.268 1.106 0.962 0.841 0.740 0.652 0.579 0.514 1.540 1.352 1.209 1.053 0.926 0.808 0.707 0.616 0.534 1.700 1.522 1.356

−0.605 −0.653 −0.671 −0.639 −0.575 −0.490 −0.383 −0.268 −0.138 −0.675 −0.695 −0.669 −0.624 −0.558 −0.472 −0.368 −0.256 −0.134 −0.671 −0.662 −0.612 −0.573 −0.506 −0.430 −0.336 −0.232 −0.120 −0.570 −0.547 −0.512



Article


x2

−3

kg·m

0.3590 0.3000 0.2400 0.1789 0.1201 0.0601 0.7201 0.6376 0.5598 0.4801 0.4000 0.3202 0.2400 0.1600 0.0818 0.8101 0.7199 0.6300 0.5400 0.4498 0.3600 0.2701 0.1800 0.0898

0.4017 0.4999 0.5999 0.7020 0.8000 0.9002 0.0999 0.2027 0.3000 0.4000 0.5000 0.6000 0.6999 0.7999 0.8978 0.0999 0.2001 0.2998 0.4001 0.5000 0.5998 0.7000 0.8001 0.9003

0.95280 0.94356 0.93318 0.92144 0.90860 0.89383 1.01264 1.00346 0.99388 0.98298 0.97067 0.95696 0.94096 0.92267 0.90218 1.02844 1.01891 1.00832 0.99646 0.98299 0.96770 0.95012 0.92963 0.90547

0.0900 0.0800 0.0701 0.0600 0.0501 0.0400 0.0300 0.0200 0.0101 0.1799 0.1601 0.1400 0.1199 0.1000 0.0800 0.0596 0.0400 0.0200 0.3601 0.3195 0.2800 0.2400 0.1999 0.1600 0.1200 0.0801 0.0400 0.5401 0.4801 0.4192 0.3590 0.3000 0.2400

0.0999 0.2000 0.3001 0.3999 0.4998 0.5999 0.7003 0.8001 0.8999 0.1002 0.2000 0.2999 0.4001 0.5001 0.5999 0.7020 0.7999 0.8998 0.1000 0.2006 0.2999 0.4000 0.5000 0.5998 0.6999 0.8000 0.8999 0.0998 0.1999 0.2993 0.4017 0.4999 0.5999

0.84114 0.84420 0.84721 0.85028 0.85353 0.85679 0.86018 0.86375 0.86749 0.87328 0.87318 0.87330 0.87317 0.87299 0.87282 0.87249 0.87213 0.87163 0.92763 0.92303 0.91847 0.91329 0.90797 0.90194 0.89544 0.88826 0.88020 0.97157 0.96438 0.95635 0.94787 0.93856 0.92810

106·VE −1

m ·mol 3

nD

T = 303.15 K 0.066 1.4121 0.038 1.4109 0.011 1.4095 −0.015 1.4080 −0.019 1.4062 −0.016 1.4042 0.092 1.4194 0.059 1.4182 0.031 1.4171 0.006 1.4158 −0.018 1.4142 −0.047 1.4124 −0.042 1.4104 −0.029 1.4080 −0.025 1.4053 0.054 1.4213 0.025 1.4202 −0.003 1.4189 −0.029 1.4174 −0.050 1.4157 −0.060 1.4137 −0.063 1.4116 −0.055 1.4089 −0.031 1.4056 T = 308.15 K 0.112 1.3975 0.079 1.3977 0.068 1.3979 0.052 1.3980 0.040 1.3982 0.032 1.3984 0.031 1.3983 0.021 1.3986 0.013 1.3988 0.185 1.4012 0.162 1.4010 0.103 1.4010 0.074 1.4008 0.057 1.4005 0.031 1.4003 0.023 1.4000 0.017 1.3997 0.020 1.3994 0.221 1.4076 0.191 1.4068 0.145 1.4063 0.119 1.4055 0.061 1.4048 0.038 1.4039 0.009 1.4029 −0.004 1.4018 −0.004 1.4005 0.178 1.4127 0.146 1.4120 0.103 1.4109 0.069 1.4098 0.039 1.4086 0.009 1.4071

2939

η

Δη

ΔnD

mPa·s

mPa·s

0.00386 0.00372 0.00345 0.00306 0.00240 0.00143 0.00259 0.00317 0.00370 0.00401 0.00415 0.00403 0.00370 0.00300 0.00191 0.00189 0.00271 0.00339 0.00390 0.00421 0.00420 0.00401 0.00332 0.00197

1.187 1.036 0.893 0.772 0.656 0.552 1.965 1.735 1.537 1.355 1.162 0.998 0.841 0.696 0.573 2.124 1.881 1.650 1.449 1.235 1.043 0.875 0.724 0.593

−0.476 −0.429 −0.372 −0.287 −0.206 −0.108 −0.365 −0.382 −0.377 −0.351 −0.337 −0.292 −0.242 −0.180 −0.099 −0.236 −0.267 −0.287 −0.277 −0.280 −0.262 −0.218 −0.157 −0.077

0.00116 0.00107 0.00094 0.00080 0.00064 0.00055 0.00023 0.00023 0.00015 0.00219 0.00204 0.00198 0.00178 0.00153 0.00130 0.00100 0.00077 0.00039 0.00339 0.00321 0.00326 0.00304 0.00293 0.00261 0.00216 0.00163 0.00091 0.00324 0.00368 0.00379 0.00390 0.00377 0.00351

1.373 1.178 0.996 0.861 0.754 0.665 0.595 0.530 0.481 1.341 1.164 1.020 0.894 0.786 0.694 0.615 0.548 0.488 1.403 1.241 1.118 0.978 0.863 0.757 0.666 0.583 0.508 1.550 1.395 1.251 1.103 0.965 0.836

−0.508 −0.543 −0.565 −0.540 −0.487 −0.416 −0.325 −0.229 −0.119 −0.570 −0.584 −0.564 −0.527 −0.471 −0.400 −0.312 −0.218 −0.116 −0.569 −0.560 −0.514 −0.483 −0.428 −0.364 −0.284 −0.197 −0.102 −0.483 −0.460 −0.428 −0.395 −0.360 −0.312



Article


x2

−3

kg·m

0.1789 0.1201 0.0601 0.7201 0.6376 0.5598 0.4801 0.4000 0.3202 0.2400 0.1600 0.0818 0.8101 0.7199 0.6300 0.5400 0.4498 0.3600 0.2701 0.1800 0.0898

0.7020 0.8000 0.9002 0.0999 0.2027 0.3000 0.4000 0.5000 0.6000 0.6999 0.7999 0.8978 0.0999 0.2001 0.2998 0.4001 0.5000 0.5998 0.7000 0.8001 0.9003

0.91628 0.90333 0.88845 1.00779 0.99856 0.98894 0.97799 0.96563 0.95184 0.93577 0.91738 0.89678 1.02356 1.01399 1.00336 0.99145 0.97792 0.96257 0.94492 0.92433 0.90007

0.0900 0.0800 0.0701 0.0600 0.0501 0.0400 0.0300 0.0200 0.0101 0.1799 0.1601 0.1400 0.1199 0.1000 0.0800 0.0596 0.0400 0.0200 0.3601 0.3195 0.2800 0.2400 0.1999 0.1600 0.1200 0.0801 0.0400 0.5401 0.4801 0.4192 0.3590 0.3000 0.2400 0.1789 0.1201 0.0601

0.0999 0.2000 0.3001 0.3999 0.4998 0.5999 0.7003 0.8001 0.8999 0.1002 0.2000 0.2999 0.4001 0.5001 0.5999 0.7020 0.7999 0.8998 0.1000 0.2006 0.2999 0.4000 0.5000 0.5998 0.6999 0.8000 0.8999 0.0998 0.1999 0.2993 0.4017 0.4999 0.5999 0.7020 0.8000 0.9002

0.83686 0.83980 0.84268 0.84562 0.84873 0.85185 0.85509 0.85851 0.86208 0.86885 0.86865 0.86867 0.86843 0.86813 0.86784 0.86738 0.86687 0.86623 0.92298 0.91831 0.91368 0.90843 0.90301 0.89689 0.89028 0.88298 0.87478 0.96679 0.95954 0.95146 0.94292 0.93354 0.92300 0.91108 0.89803 0.88302

106·VE −1

m ·mol 3

nD

T = 308.15 K −0.019 1.4055 −0.022 1.4037 −0.019 1.4016 0.099 1.4173 0.062 1.4161 0.031 1.4149 0.003 1.4135 −0.022 1.4119 −0.053 1.4101 −0.048 1.4080 −0.035 1.4055 −0.029 1.4027 0.056 1.4192 0.024 1.4180 −0.007 1.4167 −0.035 1.4152 −0.057 1.4135 −0.069 1.4114 −0.072 1.4092 −0.063 1.4064 −0.036 1.4030 T = 313.15 K 0.123 1.3954 0.089 1.3955 0.077 1.3956 0.060 1.3957 0.046 1.3958 0.038 1.3959 0.035 1.3958 0.024 1.3960 0.015 1.3962 0.199 1.3990 0.175 1.3988 0.113 1.3987 0.082 1.3984 0.063 1.3981 0.035 1.3978 0.026 1.3975 0.019 1.3972 0.021 1.3967 0.238 1.4054 0.205 1.4046 0.155 1.4040 0.126 1.4032 0.065 1.4025 0.039 1.4015 0.010 1.4004 −0.004 1.3992 −0.005 1.3978 0.191 1.4105 0.156 1.4098 0.109 1.4086 0.071 1.4075 0.039 1.4062 0.007 1.4047 −0.022 1.4031 −0.026 1.4012 −0.021 1.3990 2940

η

Δη

ΔnD

mPa·s

mPa·s

0.00311 0.00245 0.00146 0.00260 0.00319 0.00375 0.00408 0.00422 0.00411 0.00378 0.00305 0.00195 0.00191 0.00277 0.00346 0.00398 0.00431 0.00431 0.00412 0.00338 0.00203

0.728 0.621 0.523 1.786 1.586 1.413 1.255 1.079 0.934 0.789 0.656 0.543 1.927 1.716 1.514 1.349 1.157 0.972 0.821 0.684 0.565

−0.239 −0.173 −0.093 −0.306 −0.318 −0.312 −0.286 −0.279 −0.240 −0.201 −0.151 −0.085 −0.196 −0.219 −0.235 −0.212 −0.218 −0.216 −0.179 −0.130 −0.061

0.00113 0.00106 0.00094 0.00080 0.00063 0.00054 0.00024 0.00022 0.00013 0.00215 0.00202 0.00197 0.00179 0.00155 0.00131 0.00100 0.00076 0.00038 0.00334 0.00318 0.00325 0.00305 0.00295 0.00263 0.00218 0.00165 0.00092 0.00322 0.00367 0.00380 0.00392 0.00382 0.00354 0.00316 0.00249 0.00148

1.248 1.084 0.919 0.801 0.705 0.624 0.559 0.501 0.455 1.225 1.070 0.943 0.831 0.735 0.652 0.580 0.519 0.462 1.285 1.142 1.037 0.909 0.805 0.710 0.628 0.552 0.482 1.419 1.283 1.159 1.028 0.900 0.783 0.685 0.587 0.495

−0.428 −0.453 −0.477 −0.456 −0.412 −0.353 −0.278 −0.197 −0.103 −0.482 −0.494 −0.477 −0.446 −0.399 −0.339 −0.265 −0.186 −0.100 −0.483 −0.475 −0.431 −0.409 −0.363 −0.308 −0.240 −0.166 −0.087 −0.410 −0.389 −0.358 −0.328 −0.302 −0.262 −0.201 −0.145 −0.080



Article


x2

−3

kg·m

0.7201 0.6376 0.5598 0.4801 0.4000 0.3202 0.2400 0.1600 0.0818 0.8101 0.7199 0.6300 0.5400 0.4498 0.3600 0.2701 0.1800 0.0898

0.0999 0.2027 0.3000 0.4000 0.5000 0.6000 0.6999 0.7999 0.8978 0.0999 0.2001 0.2998 0.4001 0.5000 0.5998 0.7000 0.8001 0.9003

1.00292 0.99365 0.98399 0.97299 0.96057 0.94671 0.93055 0.91207 0.89136 1.01866 1.00906 0.99839 0.98643 0.97285 0.95743 0.93970 0.91902 0.89464

0.0900 0.0800 0.0701 0.0600 0.0501 0.0400 0.0300 0.0200 0.0101 0.1799 0.1601 0.1400 0.1199 0.1000 0.0800 0.0596 0.0400 0.0200 0.3601 0.3195 0.2800 0.2400 0.1999 0.1600 0.1200 0.0801 0.0400 0.5401 0.4801 0.4192 0.3590 0.3000 0.2400 0.1789 0.1201 0.0601 0.7201 0.6376 0.5598

0.0999 0.2000 0.3001 0.3999 0.4998 0.5999 0.7003 0.8001 0.8999 0.1002 0.2000 0.2999 0.4001 0.5001 0.5999 0.7020 0.7999 0.8998 0.1000 0.2006 0.2999 0.4000 0.5000 0.5998 0.6999 0.8000 0.8999 0.0998 0.1999 0.2993 0.4017 0.4999 0.5999 0.7020 0.8000 0.9002 0.0999 0.2027 0.3000

0.83255 0.83536 0.83812 0.84093 0.84390 0.84687 0.84996 0.85322 0.85664 0.86438 0.86409 0.86400 0.86365 0.86324 0.86282 0.86222 0.86158 0.86078 0.91830 0.91357 0.90886 0.90353 0.89803 0.89181 0.88509 0.87766 0.86932 0.96198 0.95469 0.94655 0.93794 0.92849 0.91788 0.90586 0.89270 0.87756 0.99804 0.98873 0.97902

106·VE −1

m ·mol 3

nD

T = 313.15 K 0.105 1.4151 0.065 1.4139 0.030 1.4127 −0.001 1.4113 −0.029 1.4096 −0.061 1.4077 −0.056 1.4055 −0.042 1.4030 −0.034 1.4001 0.058 1.4171 0.022 1.4159 −0.012 1.4145 −0.042 1.4129 −0.066 1.4112 −0.079 1.4091 −0.082 1.4068 −0.071 1.4039 −0.042 1.4004 T = 318.15 K 0.136 1.3932 0.101 1.3933 0.087 1.3933 0.070 1.3934 0.055 1.3934 0.045 1.3934 0.041 1.3934 0.028 1.3934 0.018 1.3935 0.217 1.3968 0.190 1.3966 0.125 1.3964 0.091 1.3961 0.070 1.3957 0.041 1.3954 0.030 1.3950 0.021 1.3946 0.023 1.3941 0.257 1.4033 0.220 1.4024 0.166 1.4018 0.134 1.4009 0.069 1.4001 0.042 1.3990 0.010 1.3979 −0.005 1.3966 −0.005 1.3952 0.207 1.4084 0.166 1.4076 0.116 1.4064 0.074 1.4052 0.039 1.4039 0.005 1.4023 −0.026 1.4006 −0.030 1.3987 −0.024 1.3964 0.112 1.4131 0.068 1.4117 0.029 1.4105

2941

η

Δη

ΔnD

mPa·s

mPa·s

0.00259 0.00323 0.00379 0.00415 0.00430 0.00421 0.00385 0.00311 0.00199 0.00193 0.00281 0.00353 0.00406 0.00441 0.00440 0.00419 0.00347 0.00206

1.653 1.456 1.304 1.167 1.005 0.874 0.743 0.619 0.513 1.758 1.573 1.395 1.230 1.070 0.917 0.772 0.646 0.535

−0.237 −0.266 −0.259 −0.233 −0.231 −0.199 −0.166 −0.126 −0.073 −0.163 −0.181 −0.193 −0.189 −0.183 −0.169 −0.147 −0.107 −0.050

0.00113 0.00103 0.00091 0.00077 0.00061 0.00051 0.00029 0.00019 0.00010 0.00213 0.00197 0.00195 0.00175 0.00152 0.00129 0.00100 0.00076 0.00037 0.00329 0.00314 0.00321 0.00302 0.00294 0.00261 0.00218 0.00164 0.00092 0.00317 0.00364 0.00378 0.00389 0.00381 0.00354 0.00317 0.00251 0.00151 0.00257 0.00320 0.00379

1.139 1.001 0.851 0.745 0.660 0.586 0.528 0.472 0.429 1.121 0.986 0.875 0.775 0.687 0.613 0.547 0.489 0.436 1.181 1.055 0.964 0.848 0.753 0.666 0.592 0.523 0.455 1.306 1.185 1.076 0.961 0.841 0.735 0.646 0.554 0.468 1.519 1.343 1.208

−0.361 −0.376 −0.403 −0.386 −0.349 −0.301 −0.235 −0.169 −0.089 −0.409 −0.418 −0.403 −0.377 −0.339 −0.287 −0.225 −0.159 −0.086 −0.411 −0.403 −0.363 −0.346 −0.307 −0.262 −0.202 −0.138 −0.074 −0.349 −0.330 −0.300 −0.272 −0.255 −0.220 −0.167 −0.121 −0.068 −0.198 −0.223 −0.216



Article


x2

kg·m

−3

0.4801 0.4000 0.3202 0.2400 0.1600 0.0818 0.8101 0.7199 0.6300 0.5400 0.4498 0.3600 0.2701 0.1800 0.0898

0.4000 0.5000 0.6000 0.6999 0.7999 0.8978 0.0999 0.2001 0.2998 0.4001 0.5000 0.5998 0.7000 0.8001 0.9003

0.96797 0.95548 0.94156 0.92531 0.90673 0.88590 1.01376 1.00412 0.99340 0.98139 0.96775 0.95226 0.93445 0.91367 0.88918

0.0900 0.0800 0.0701 0.0600 0.0501 0.0400 0.0300 0.0200 0.0101 0.1799 0.1601 0.1400 0.1199 0.1000 0.0800 0.0596 0.0400 0.0200 0.3601 0.3195 0.2800 0.2400 0.1999 0.1600 0.1200 0.0801 0.0400 0.5401 0.4801 0.4192 0.3590 0.3000 0.2400 0.1789 0.1201 0.0601 0.7201 0.6376 0.5598 0.4801 0.4000 0.3202 0.2400

0.0999 0.2000 0.3001 0.3999 0.4998 0.5999 0.7003 0.8001 0.8999 0.1002 0.2000 0.2999 0.4001 0.5001 0.5999 0.7020 0.7999 0.8998 0.1000 0.2006 0.2999 0.4000 0.5000 0.5998 0.6999 0.8000 0.8999 0.0998 0.1999 0.2993 0.4017 0.4999 0.5999 0.7020 0.8000 0.9002 0.0999 0.2027 0.3000 0.4000 0.5000 0.6000 0.6999

0.82820 0.83089 0.83352 0.83619 0.83903 0.84185 0.84479 0.84789 0.85115 0.85988 0.85949 0.85930 0.85884 0.85830 0.85776 0.85703 0.85624 0.85529 0.91360 0.90778 0.90402 0.89860 0.89301 0.88669 0.87986 0.87231 0.86383 0.95687 0.94981 0.94162 0.93295 0.92342 0.91272 0.90060 0.88733 0.87206 0.99315 0.98317 0.97404 0.96293 0.95038 0.93638 0.92004

106·VE −1

m ·mol 3

nD

T = 318.15 K −0.005 1.4090 −0.034 1.4073 −0.069 1.4053 −0.064 1.4031 −0.049 1.4004 −0.039 1.3975 0.060 1.4150 0.021 1.4137 −0.017 1.4123 −0.049 1.4107 −0.076 1.4089 −0.090 1.4067 −0.092 1.4043 −0.080 1.4014 −0.047 1.3978 T = 323.15 K 0.146 1.3911 0.110 1.3911 0.095 1.3911 0.077 1.3910 0.061 1.3910 0.050 1.3909 0.046 1.3909 0.031 1.3909 0.019 1.3908 0.232 1.3947 0.202 1.3943 0.135 1.3941 0.099 1.3937 0.076 1.3933 0.045 1.3929 0.032 1.3924 0.023 1.3920 0.023 1.3914 0.274 1.4011 0.364 1.4002 0.175 1.3995 0.140 1.3986 0.072 1.3977 0.042 1.3966 0.009 1.3954 −0.007 1.3940 −0.006 1.3925 0.261 1.4063 0.175 1.4054 0.121 1.4041 0.075 1.4029 0.037 1.4015 0.001 1.3999 −0.031 1.3981 −0.035 1.3961 −0.028 1.3937 0.119 1.4110 0.159 1.4096 0.028 1.4083 −0.010 1.4068 −0.042 1.4050 −0.078 1.4030 −0.074 1.4006 2942

η

Δη

ΔnD

mPa·s

mPa·s

0.00417 0.00433 0.00425 0.00389 0.00311 0.00199 0.00191 0.00280 0.00354 0.00411 0.00445 0.00446 0.00424 0.00348 0.00210

1.088 0.938 0.819 0.698 0.584 0.485 1.612 1.449 1.289 1.144 1.001 0.849 0.726 0.611 0.507

−0.189 −0.192 −0.164 −0.138 −0.106 −0.061 −0.137 −0.149 −0.159 −0.154 −0.146 −0.148 −0.121 −0.085 −0.039

0.00115 0.00104 0.00092 0.00078 0.00062 0.00050 0.00032 0.00019 0.00007 0.00212 0.00197 0.00193 0.00175 0.00152 0.00128 0.00098 0.00071 0.00034 0.00328 0.00312 0.00323 0.00305 0.00293 0.00263 0.00218 0.00162 0.00088 0.00319 0.00364 0.00380 0.00395 0.00385 0.00358 0.00320 0.00249 0.00145 0.00260 0.00324 0.00383 0.00423 0.00438 0.00432 0.00393

1.056 0.934 0.796 0.702 0.622 0.553 0.501 0.427 0.367 1.043 0.921 0.834 0.731 0.650 0.580 0.519 0.463 0.389 1.101 0.988 0.902 0.825 0.711 0.628 0.561 0.490 0.414 1.222 1.108 1.008 0.903 0.793 0.697 0.613 0.524 0.434 1.409 1.258 1.129 1.018 0.881 0.773 0.660

−0.293 −0.307 −0.339 −0.326 −0.298 −0.259 −0.209 −0.171 −0.124 −0.339 −0.350 −0.327 −0.318 −0.288 −0.248 −0.196 −0.143 −0.106 −0.348 −0.341 −0.311 −0.269 −0.264 −0.230 −0.178 −0.131 −0.088 −0.294 −0.282 −0.257 −0.233 −0.220 −0.190 −0.146 −0.112 −0.076 −0.174 −0.188 −0.188 −0.165 −0.169 −0.144 −0.124



Article

Table 5. continued 10−3·ρ x1 0.1600 0.0818 0.8101 0.7199 0.6300 0.5400 0.4498 0.3600 0.2701 0.1800 0.0898

106·VE

−3

x2

kg·m

0.7999 0.8978 0.0999 0.2001 0.2998 0.4001 0.5000 0.5998 0.7000 0.8001 0.9003

−1

m ·mol 3

nD

T = 323.15 K −0.057 1.3979 −0.016 1.3948 0.062 1.4129 0.019 1.4116 −0.022 1.4101 −0.058 1.4085 −0.087 1.4066 0.008 1.4044 −0.104 1.4019 −0.042 1.3989 −0.039 1.3952

0.90136 0.88012 1.00885 0.99916 0.98840 0.97634 0.96264 0.94617 0.92918 0.90785 0.88353

η

Δη

ΔnD

mPa·s

mPa·s

0.00312 0.00195 0.00195 0.00283 0.00359 0.00417 0.00453 0.00457 0.00428 0.00351 0.00205

0.553 0.451 1.501 1.353 1.209 1.076 0.945 0.804 0.688 0.579 0.465

−0.098 −0.069 −0.115 −0.126 −0.134 −0.129 −0.123 −0.128 −0.107 −0.079 −0.017

Standard uncertainties σ for each variables are σ(T) = 0.01 K ; σ(p) = 5 % ; σ(x1) = 0.0001, and the combined expanded uncertainties σc are σc(ρ) = ± 1·10−2 kg·m−3; σc(η) = ± 3·10−3 mPa·s and σc(nD) = 1·10−4, with 0.95 level of confidence (k ≈ 2).

a

Table 6. Parameters Ap of eq 4 and the Corresponding rmsd σ for the Tetrahydrofuran (1) + 1-Butanol (2) and Dimethyl adipate (1) + 1-Butanol (2) Binary Mixtures at Temperature T and Atmospheric Pressure

106·VE/m3·mol−1

ΔnD

Δη/mPa·s

Δη/mPa·s

T/K

A0

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

−0.047 −0.022 0.0045 0.032 0.059 0.085 0.119 0.144 −0.00147 −0.00149 −0.00159 −0.00157 −0.00162 −0.00165 −0.00166 −0.00167 −3.931 −3.299 −2.774 −2.338 −1.973 −1.676 −1.418 −1.198

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

−4.186 −3.531 −2.982 −2.540 −2.164 −1.848 −1.586 −1.346

A1

A2

Tetrahydrofuran + 1-Butanol 0.215 0.038 0.217 0.030 0.217 0.040 0.217 0.042 0.219 0.052 0.222 0.054 0.224 0.057 0.223 0.061 −0.00076 0.00011 −0.00051 0.00009 −0.00049 −0.00011 −0.00060 −0.00009 −0.00068 −0.00021 −0.00083 −0.00046 −0.00077 −0.00071 −0.00086 −0.00083 2.494 −1.425 2.049 −1.160 1.685 −0.865 1.387 −0.666 1.149 −0.523 0.931 −0.351 0.772 −0.226 0.638 −0.154 Dimethyladipate +1-Butanol 1.616 −1.249 1.427 −1.009 1.252 −0.899 1.071 −0.664 0.938 −0.517 0.821 −0.401 0.714 −0.298 0.622 −0.180

A3

A4

σ·103

−0.089 −0.085 −0.085 −0.085 −0.084 −0.086 −0.113 −0.109 0.00172 0.00140 0.00135 0.00125 0.00151 0.00168 0.00128 0.00113 1.283 1.055 0.848 0.659 0.490 0.408 0.298 0.014

−0.096 −0.085 −0.088 −0.083 −0.093 −0.092 −0.052 −0.049

−0.949 −0.727 −0.710 −0.602 −0.492 −0.484 −0.468 −0.264

0.7 0.8 0.9 0.8 0.9 0.8 0.9 1.0 0.01 0.01 0.00 0.01 0.01 0.01 0.01 0.01 3.9 3.8 3.8 3.3 3.7 2.7 2.8 3.6

2.140 1.760 1.484 1.191 0.956 0.759 0.603 0.318

−2.944 −2.522 −2.014 −1.811 −1.562 −1.360 −1.194 −0.974

10.9 9.5 10.3 8.4 7.8 7.5 7.0 7.1

2. EXPERIMENTAL SECTION

To try to comprehend specific behavior and molecular interactions between the compounds, a spectroscopic study was performed. The FT-IR spectra of pure compounds and the binary constituents of the investigated ternary mixture (dimethyladipate + tetrahydrofuran, dimethyladipate +1-butanol, and tetrahydrofuran +1-butanol) were analyzed at 298.15 K.

2.1. Chemicals. Dimethyl adipate (Merck, ω ≥ 0.99), tetrahydrofuran (Merck, ω >0.995) and 1-butanol (Merck, ω ≥ 0.995) were used without further purification (the sample description is given in Table 1). Chemicals were kept in dark 2943



Article

Figure 1. Experimental values of (a) VE, (b) ΔnD, and (c) Δη for the binary system tetrahydrofuran (1) + 1-butanol (2) at temperatures: -■-, 288.15 K; □, 293.15 K; -●-, 298.15 K; -○-, 303.15 K; -▲-, 308.15 K; -△-, 313.15 K; -⧫-, 318.15 K; -◊-, 323.15 K. The lines present the results calculated by eq 4.

components agree with literature values within 6×10−4 for tetrahydrofuran and 1-butanol and within 0.005 for dimethyladipate. The agreement with literature values for viscosity measurements was within 0.02 mPa·s for tetrahydrofuran and 1-butanol, up to 0.07 mPa·s for dimethyladipate. 2.2. Measurements. The densities ρ of the ternary and binary mixtures and corresponding pure substances were measured

bottles under inert nitrogen atmosphere and ultrasonically degassed just before sample preparation. Table 2 lists the measured densities, refractive indices, and viscosities of pure components along with the corresponding literature values.7,13−17 The agreement between experimental and literature data for density was within 0.1 kg·m−3 except for tetrahydrofuran at 293.15 K. The experimental refractive indices of pure 2944


6

E

3

10 ·V /m ·mol B0 B1 B2 B3 B4 B5 B6 B7 B8 106·σ /m3·mol−1 ΔnD B0 B1 B2 B3 B4 B5 B6 B7 B8 103σ Δη/mPa·s B0 B1 B2 B3 B4 B5 B6 B7 B8 σ/mPa·s

−1

−1.2112·10−4 −9.2904·10−3 −2.2137·10−3 3.1106·10−2 6.8498·10−3 7.3558·10−3 −2.3556·10−2 −5.3988·10−3 −1.6824·10−2 0.0055 −9.9700·10−7 1.1135·10−5 −3.8542·10−5 −3.2475·10−5 6.4281·10−5 3.3090·10−6 2.7841·10−5 −3.5320·10−5 1.3576·10−5 0.046 7.4188·10−3 2.1276·10−2 1.4154·10−2 −2.6972·10−2 −5.3956·10−3 −2.8803·10−2 1.3310·10−2 −1.4333·10−3 2.1338·10−2 0.0055

−1.4470·10−6 8.1970·10−6 −4.0802·10−5 −2.6139·10−5 6.5297·10−5 1.3850·10−5 2.4057·10−5 −3.6373·10−5 −1.1050·10−6 0.045

8.9464·10−3 2.5542·10−2 1.7226·10−2 −3.2419·10−2 −6.8168·10−3 −3.4369·10−2 1.5966·10−2 −1.7466·10−3 2.5326·10−2 0.0062

293.15 K

−1.2813·10−4 −9.3051·10−3 −2.2650·10−3 3.0905·10−2 6.8980·10−3 7.4166·10−3 −2.3289·10−2 −5.4172·10−3 −1.6660·10−2 0.0055

288.15 K

2945

6.0614·10−3 1.7661·10−2 1.0881·10−2 −2.2019·10−2 −2.1983·10−3 −2.4135·10−2 1.0586·10−2 −2.8833·10−3 1.7686·10−2 0.0053

2.7000·10−8 1.9908·10−5 −3.6107·10−5 −4.7030·10−5 6.5045·10−5 −1.7578·10−5 3.2839·10−5 −3.6470·10−5 4.2961·10−5 0.045

−1.6709·10−4 −9.6525·10−3 −2.3023·10−3 3.1755·10−2 6.8398·10−3 7.8944·10−3 −2.3872·10−2 −5.3390·10−3 −1.7448·10−2 0.0056

298.15 K

4.7726·10−3 1.3735·10−2 8.1484·10−3 −1.6854·10−2 −6.0663·10−4 −1.8739·10−2 8.2091·10−3 −3.0875·10−3 1.2938·10−2 0.0051

−2.3980·10−6 5.2750·10−6 −4.6114·10−5 −1.8205·10−5 8.4637·10−5 1.1656·10−5 1.5247·10−5 −5.4293·10−5 6.6060·10−6 0.047

−2.0163·10−4 −9.8511·10−3 −2.3245·10−3 3.1854·10−2 6.7127·10−3 8.1795·10−3 −2.3753·10−2 −5.2122·10−3 −1.7668·10−2 0.0057

303.15 K

3.9423·10−3 1.1318·10−2 6.4944·10−3 −1.3214·10−2 6.7101·10−4 −1.5581·10−2 6.3513·10−3 −3.6471·10−3 9.2576·10−3 0.0056

−1.3060·10−6 4.6170·10−6 −3.6035·10−5 −1.6838·10−5 6.0930·10−5 8.0450·10−6 1.4376·10−5 −3.7082·10−5 1.4033·10−5 0.044

−2.1981·10−4 −9.9321·10−3 −2.3454·10−3 3.2259·10−2 6.6643·10−3 8.3332·10−3 −2.4147·10−2 −5.1274·10−3 −1.8072·10−2 0.0058

308.15 K

3.2706·10−3 1.1778·10−2 4.4761·10−3 −1.7517·10−2 3.4851·10−3 −1.8646·10−2 8.6651·10−3 −4.9303·10−3 2.0969·10−2 0.0058

6.8800·10−7 1.2614·10−5 −2.8325·10−5 −2.6523·10−5 4.8889·10−5 −2.6760·10−6 1.6599·10−5 −3.0111·10−5 2.0503·10−5 0.041

−2.2656·10−4 −9.9585·10−3 −2.3494·10−3 3.2030·10−2 6.6482·10−3 8.3717·10−3 −2.3895·10−2 −5.1175·10−3 −1.7823·10−2 0.0059

313.15 K

2.3981·10−3 9.0011·10−3 1.6943·10−3 −1.3100·10−2 7.6407·10−3 −1.4363·10−2 5.6662·10−3 −7.7129·10−3 1.7512·10−2 0.0064

2.2880·10−6 1.1916·10−5 −1.6782·10−5 −1.9967·10−5 2.8115·10−5 −5.7800·10−7 1.1327·10−5 −1.7743·10−5 2.1980·10−6 0.039

−2.8999·10−4 −1.0251·10−2 −2.4358·10−3 3.2544·10−2 6.5424·10−3 8.7281·10−3 −2.4172·10−2 −4.9386·10−3 −1.8169·10−2 0.0059

318.15 K

1.7410·10−3 3.8111·10−3 5.3513·10−3 −4.4344·10−3 −1.2746·10−2 −7.8570·10−3 1.1861·10−3 1.4520·10−2 1.4469·10−2 0.0078

3.7060·10−6 2.0650·10−5 −4.2060·10−6 −4.8541·10−5 −6.4750·10−6 −1.6802·10−5 3.2613·10−5 1.2490·10−5 3.9702·10−5 0.037

−3.4737·10−4 −1.0493·10−2 −2.6054·10−3 3.3095·10−2 6.7034·10−3 9.1408·10−3 −2.4606·10−2 −5.0193·10−3 −1.8723·10−2 0.0060

323.15 K

Table 7. Parameters Bp of eq 6 and Corresponding rmsd σ for Dimethyladipate (1) + Tetrahydrofuran (2) + 1-Butanol (3) at temperature T and Atmospheric Pressure

Journal of Chemical & Engineering Data Article



Article

by Anton Paar DMA 5000 digital vibrating U-tube densimeter, while for the viscosity and refractive index measurements the Stabinger viscometer (model SVM 3000/G2) and Anton Paar RXA 156 refractometer were used. A detailed explanation of the characteristics of the apparatus and measurement methods used can be found in our previous work.1−3 The mixtures were prepared gravimetrically using a Mettler AG 204 balance with a precision of 1·10−7 kg, and the procedure described previously was used.18,19 The uncertainty of the mole fraction calculation was less than ± 1·10−4. All molar quantities were based on the IUPAC relative atomic mass table. The experimental uncertainties in the density and refractive index are about ± 1·10−2 kg·m−3, ± 1·10−4, while the relative uncertainty in dynamic viscosity measurements was estimated to be 1.5 %. The average uncertainties in calculated properties are estimated to be: ± 2·10−9 m3·mol−1 for excess molar volumes, ± 2·10−4 for refractive index deviations, and ± 3·10−3 mPa·s for viscosity deviations. A NICOLET 6700 FT-IR spectrometer was utilized to record the FT-IR spectra of pure components and binary mixtures. For each spectrum 32 scans were made with a selected resolution of 2 cm−1. All the spectroscopic measurements were carried out at T = 298.15 K.

3. RESULTS AND DISCUSSION Excess molar volumes VE were calculated from the equation ⎡⎛ ⎞ ⎛ ⎞⎤ 1 1 ⎟ − ⎜⎜ ⎟⎟⎥ ⎢⎣⎝ ρ ⎠ ⎝ ρi ⎠⎥⎦

N

VE =

Figure 2. Experimental Δη values for the binary system dimethyladipate (1) + 1-butanol (2) at temperatures: -■-, 288.15 K; -□-, 293.15 K; -●-, 298.15 K; -○-, 303.15 K; -▲-, 308.15 K; -△-, 313.15 K; -⧫-, 318.15 K; -◊-, 323.15 K. The lines present the results calculated by eq 4

∑ xiM i⎢⎜ i=1

(1)

Refractive index deviations ΔnD were obtained from the expression

corresponding root-mean-square deviations (rmsd) defined by the equation

N

ΔnD = nD −

∑ xinDi i=1

(2)

2 ⎞1/2 ⎛ m (Y expt , i − Ycalc, i) ⎜ ⎟ σ = ⎜∑ ⎟ m ⎝ i=1 ⎠

while for the viscosity deviation Δη calculations the following equation was used: N

Δη = η −

∑ xiηi i=1

are given in Table 6. In eq 5, m is the number of experimental data points. The ternary VE, ΔnD, and Δη data were correlated by Nagata and Tamura10 equation:

(3)

In equations 1−3, N denotes a number of components; xi is a mole fraction of the component i in the mixture; Mi is its molecular weight; ρ, nD, and η are the measured densities, refractive indices, and viscosities of a mixture, while ρi, nDi and ηi are the measured densities, refractive indices, and viscosities of a pure component i, respectively. Experimental data are reported in Table 3 for the binary system tetrahydrofuran (1) + 1-butanol (2), in Table 4 for the dimethyladipate (1) + 1-butanol (2) system and in Table 5 for the investigated ternary system. Data for the binary mixture were correlated with the Redlich−Kister (RK) equation:9

Y123 = Y12 + Y13 + Y23 + x1x 2x3RT (B0 − B1x1 − B2 x 2 − B3x12 − B4 x 22 − B5x1x 2 − B6 x13 − B7 x 23 − B8x12x 2) (6)

·VE123/m3·mol−1,

where Y123 denotes 10 ΔnD,123, or Δη123/mPa·s. x1, x2, and x3 are the component mole fractions of the ternary system; Yij represent the excess molar volumes (VE12, VE13, and VE23), deviations of refractive indices (ΔnD,12, ΔnD,13 and ΔnD,23) or deviations of viscosities (Δη12, Δη13 and Δη23) calculated using eq 4, with ternary compositions xi and xj. The adjustable parameters Bp (p = 0 to 8) are obtained from experimental VE, ΔnD, and Δη of the ternary system. Table 7 lists the parameters Bp of eq 6 and the corresponding σ, calculated from eq 5. Determinations of the experimental VE, ΔnD, and Δη data of the ternary system were made following the lines of constant ratio of the first and the third compound (z = x1/x3). In Figure 1 panels a, b, and c the experimental VE, ΔnD, and Δη data, respectively, are plotted for the binary system tetrahydrofuran (1) + 1-butanol (2) for all investigated temperatures while the experimental values are listed in Table 3. 6

k

Y = xixj

∑ A p(2xi − 1)p p=0

(5)

(4)

where Y denotes 106·VEij /m3·mol−1, ΔnD or Δη/mPa·s; Ap are the adjustable parameters of the related property, and the number of adjustable parameters (k + 1) has been determined using the F-test. The parameters obtained by fitting eq 4 to experimental data of VE, ΔnD, and Δη at each temperature separately, and the 2946



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Figure 3. (a) VE, (b) ΔnD, and (c) Δη at 303.15 K for the ternary system dimethyladipate (1) + tetrahydrofuran (2) + 1-butanol (3), along the curves of constant ratio z = x1/x3 as a function of the tetrahydrofuran composition: -■-, z1 = 0.111; -●-, z2 = 0.250; -▲-, z3 = 0.667; -⧫-, z4 = 1.500; -□-, z5 = 4.000; -○-, z6 = 9.000. Symbols represent the experimental points. Solid curves were calculated by eq 6.

Valén et al.11 reported the VE values for the tetrahydrofuran +1-butanol system at 298.15 K and 313.15 K. The VE−x1 curves of Valén et al. follow the same trend as in this work. Discrepancies between our and literature experimental results11 are the largest in the tetrahydrofuran-rich region at 313.15 K. At the maximum of VE−x1 curve (at x1 = 0.72), VE values of Valén et al.11 are 0.016 cm3 mol−1 higher than ours. At 298.15 K absolute deviations between our and literature data are the largest in the alcohol-rich region, and equal 0.005 cm3 mol−1 at x1 = 0.20. Mariano et al.12 measured the viscosities for tetrahydrofuran +1-butanol system at 298.15 K and 313.15 K. The agreement between viscosity measurements of this work and that of

Mariano et al.12 is very good with relative absolute deviations less than 2% at both investigated temperatures. The binary system tetrahydrofuran + 1-butanol is characterized by sigmoid VE curves vs mole fraction (Figure 1a) at temperatures below 318.15 K (negative VE values for mixtures richer in 1-butanol and positive for mixtures with higher tetrahydrofuran concentration), while for the temperatures 318.15 K and 323.15 K excess molar volumes are positive, and the VE−x1 curves are skewed toward mixtures richer in tetrahydrofuran (curve maxima around x1 = 0.7). The ΔnD−x1 curves are markedly asymmetrical over the entire composition range (Figure 1b). The minimums are skewed toward higher mole fractions of tetrahydrofuran (curve minimums around x1 = 0.6) and 2947



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Figure 4. Curves of constant (a) 106·VE/m3·mol−1, (b) ΔnD and (c) Δη/mPa·s for the ternary system dimethyladipate (1) + tetrahydrofuran (2) + 1butanol (3) at 303.15 K; the lines present results calculated by eq 6.

approaches dimethyladipate + tetrahydrofuran binary mixture. Despite the fact that deviations in refractive indices for the binary tetrahydrofuran +1-butanol system have small negative values, ΔnD values of the ternary system are positive in the entire concentration area; on the contrary, experimental viscosity deviations of the ternary system are negative over the entire composition range for all investigated temperatures (Figures 3 to 5). FT-IR spectra corresponding to the minimum/maximum excess volume of the binary mixtures are presented in Figure 6. Excess molar volumes for the binary system dimethyladipate + tetrahydrofuran are negative over the entire composition range at all investigated temperatures with the minimum of the curves located at around 0.4 mol fraction of dimethyladipate.4 On the contrary, nearly symmetric positive VE trend is obtained for the system dimethyladipate +1-butanol in the whole temperature range.5 Negative excess molar volume values are usually a result of specific interactions among unlike molecules or the geometric fitting of molecules of one component between molecules of the other, while positive values are attributed to rupture or stretch of the hydrogen bonding of self-associated molecules. The compounds analyzed here have good hydrogen-bond abilities and polar nature. 1-Butanol and tetrahydrofuran have similar dipole moments, 1.8 D and 1.7 D, respectively,20 whereas that of dimethyladipate is somewhat higher at 2.2 D.8 1-Butanol acts both as a good proton donor and a proton acceptor (it possesses

this trend is slightly more pronounced with temperature increase. Viscosity deviations for this binary mixture are negative for all investigated temperatures. The curves Δη vs mole fractions are asymmetrical and reach clearly defined minimums for mole fraction of tetrahydrofuran around x1 = 0.3 (Figure 1c). Figure 2 depicts experimental Δη data for the binary system dimethyladipate (1) + 1-butanol (2) for all investigated temperatures. Experimental Δη values are provided in Table 4. Experimental VE and ΔnD are given in our previous paper.5 Viscosity deviations for this binary mixture are negative for all investigated temperatures. The curves Δη vs mole fractions are very similar to those of the previous system with minimums around x1 = 0.3. As temperature increases the absolute viscosity deviations decrease. Table 5 lists experimental VE, ΔnD, and Δη data for the ternary system demethyladipate (1) + tetrahydrofuran (2) + 1-butanol (3) for all investigated temperatures. Figure 3 depicts experimental VE, ΔnD, and Δη data versus mole fraction of tetrahydrofuran following the lines of constant ratio z (= x1/x3). Figure 4 represents the curves of constant VE, ΔnD, and Δη data and in Figure 5, three-dimensional representations of analyzed properties for the ternary system are provided. From Figure 4 it is evident that the values of VE ternary data are positive in the greater part of the concentration area and become negative as the amount of 1-butanol decreases and the ternary mixture 2948



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Figure 5. Three-dimensional surface for the (a) 106·VE/m3·mol−1, (b) ΔnD, and (c) Δη/mPa·s for the ternary system dimethyladipate (1) + tetrahydrofuran (2) + 1-butanol (3) at 303.15 K, generated by eq 6.

hydrogen-bond acidity and basicity),21 while both tetrahydrofuran and dimethyladipate molecules are hydrogen-bond acceptors. In Figure 6a, the infrared spectra (IR) of dimethyladipate + tetrahydrofuran mixture with the composition corresponding to the minimum excess molar volume are compared with those of the pure components. Since both tetrahydrofuran and dimethyladipate molecules act as hydrogen-bond acceptors there is no possibility of the formation of hydrogen-bonded associates. Because of distinguished polarities of tetrahydrofuran and dimethyladipate, molecular association between components through dipolar forces might be expected. However, inspection of the spectra shown in Figure 6a reveals that stretching frequencies of CO (at 1739 cm−1) and C−O (at 1173.1, 1201, and 1251.9 cm−1) groups in dimethyladipate and that of C−O−C (at 1069.1 cm−1) in tetrahydrofuran remain unchanged in the solution. This result seems to indicate that there is no dipole−dipole interaction between dimethyladipate and tetrahydrofuran molecules. However, the negative VE values might be contributed to the interstitial accommodation of molecules of one component into the network of molecules of the other component. The interstitial accommodation of the smaller molecules of tetrahydrofuran (Vm = 81.09 cm3 mol−1 at 298.15 K) into the larger molecules of dimethyladipate (Vm = 164.34 cm3 mol−1 at 298.15 K) could be a possible explanation for negative VE values. The FT-IR spectra of pure compounds as well as the spectra of a solution of dimethyladipate and 1-butanol at x1 = 0.4 are shown in Figure 6b. As in the case of the previous system, the IR absorption for the stretch of the CO group in the pure component and in the solution remains unchanged at 1739 cm−1. Consequently, it can be assumed there is no interaction between the CO group of dimethyladipate and the 1-butanol molecule. Additionally, any interactions affecting the electronic density of

the OH group would influence the contraction or elongation of the bond and shift the characteristic wavenumber. The OH stretching band observed at 3340 cm−1 in pure 1-butanol is due to self-associated molecules. In the mixture, the band corresponding to the OH group has been shifted to a higher wavenumber (3451 cm−1), indicating the presence of interactions that shorten the OH bond and displacements toward the blue. Additional heteromolecular interactions that extend the bond cause absorption at lower frequencies. A significant blue shift in the band position of the O−H stretch band (Figure 6b) confirms the assumption5 of a predominance of the expansion effect associated with the rupture of monomolecular interactions in the 1-butanol and dimethyladipate molecules and the absence of new heteromolecular interactions that would result in volume contraction. Finally, FT-IR spectra for the system tetrahydrofuran + 1butanol (Figure 6c) are recorded for two solutions, at x1 = 0.3 corresponding to the minimum of VE−x1 curve and at x1 = 0.8 corresponding to the maximal positive VE values. As previously explained, both compounds act as good proton acceptors, while 1-butanol acts as proton donor as well. As it was explained before, the OH stretching band at 3340 cm−1 is due to intramolecular hydrogen-bonded OH (Figure 6c, green line). From Figure 6c it is obvious that there is no change of OH band peak in the alcohol-richer region (at x1 = 0.3, red line) so it can be assumed that the intramolecular alcohol complexes still exist resulting in volume contraction. On the contrary, as the amount of tetrahydrofuran in the solution raises, excess molar volume becomes positive. In the mixture-rich in tetrahydrofuran (at x1 = 0.8), significant blue shift in the band position of the O−H stretch band is observable (Figure 6c, yellow line). The positive values of VE are result of the dominant disruptive effect of tetrahydrofuran molecules on the self-associatied of 1-butanol structure. An 2949



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Figure 6. Infrared spectra of (a) pure dimethyladipate (blue), pure tetrahydrofuran (cyan), and the mixture dimethyladipate + tetrahydrofuran with xDMA = 0.4 (red); (b) pure dimethyladipate (blue), pure 1-butanol (green) and the mixture dimethyladipate +1-butanol with xDMA = 0.4 (red); (c) pure tetrahydrofuran (cyan), pure 1-butanol (green) and the mixture tetrahydrofuran +1-butanol with xTHF = 0.3 (red) and tetrahydrofuran +1-butanol with xTHF = 0.8 (yellow). 2950



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(5) Knežević-Stevanović, A. B.; Šerbanović, S. P.; Djordjević, B. D.; Grozdanić, D. K.; Smiljanić, J. D.; Kijevčanin, M. Lj. Experimental determination and modeling of densities and refractive indices of the binary mixtures of dimethylphthalate (or dimethyladipate) + 1-butanol, or + 2-butanol, or + 2-butanone at T = (288.15−323.15) K. Thermochim. Acta 2012, 533, 28−38. (6) Radović, I. R.; Šerbanović, S. P.; Djordjević, B. D.; Kijevčanin, M. Lj. Experimental determination of densities and refractive indices of the ternary mixture 2-methyl-2-propanol + cyclohexylamine + n-heptane at T = (303.15 to 323.15) K. J. Chem. Eng. Data 2011, 56, 344−349. (7) Comuñas, M. J. P.; Bazile, J.-P.; Lugo, L.; Baylaucq, A.; Fernández, J.; Boned, C. Influence of the molecular structure on the volumetric properties and viscosities of dialkyl adipates (dimethyl, diethyl and diisobutyl adipates). J. Chem. Eng. Data 2010, 55, 3697−3703. (8) Lee, M.-J.; Lai, C.-H.; Wang, T.-B.; Lin, H.-M. Vapor−liquid equilibrium of mixtures containing adipic acid, glutaric acid, dimethyl adipate, dimethyl glutarate, methanol, and water. J. Chem. Eng. Data 2007, 52, 1291−1296. (9) Redlich, O.; Kister, A. Thermodynamics of nonelectrolytic solutions. algebraic representation of thermodynamic properties and the classification of solutions. Ind. Eng. Chem. 1948, 40, 345−348. (10) Nagata, I.; Tamura, K. Excess molar enthalpies of {methanol or ethanol + (2-butanone + benzene)} at 298.15 K. J. Chem. Thermodyn. 1990, 22, 279−283. (11) Valén, A.; López, M. C.; Urieta, J. S.; Royo, F. M.; Lafuente, C. Thermodynamic study of mixtures containing oxygenated compounds. J. Mol. Liq. 2002, 95, 157−165. (12) Mariano, A.; Camacho, A.; Postigo, M.; Valen, A.; Artigas, H.; Royo, F. M.; Urieta, J. S. Viscosities and excess energy of activation for viscous flow for binary mixtures of tetrahydrofuran with 1-butanol, 2butanol and 1-chlorobutane at 283.15, 298.15 and 313.15 K. Braz. J. Chem. Eng. 2000, 17, 459−470. (13) Ince, E. Liquid−liquid equilibria of the ternary system water + acetic acid + dimethyl adipate. Fluid Phase Equilib. 2005, 230, 58−63. (14) Lide, D.R. Handbook of Chemistry and Physics, 83rd ed.; CRC Press Inc.: Boca Raton, FL, 2002; section 3. (15) Selected Values of Properties of Chemical Compounds; Data Project, loose-leaf data sheets, extant, TRC; Texas A&M University: College Station, TX, 1980. (16) TRC Thermodynamic TablesNon-Hydrocarbons; Thermodynamics Research Center, Texas A&M University System: College Station, TX, 1985. (17) Riddick, J. A.; Bunger, W. B.; Sakano, T. K. Organic Solvents. Physical Properties and Methods of Purification, 4th ed.; John Wiley & Sons: New York, 1986. (18) Radojković, N.; Tasić, A.; Djordjević, B.; Grozdanić, D. Mixing cell for indirect measurements of excess volume. J. Chem. Thermodyn. 1976, 8, 1111−1114. (19) Tasić, A. Ž .; Grozdanić, D. K.; Djordjević, B. D.; Šerbanović, S. P.; Radojković, N. Refractive indices and densities of the system acetone + benzene + cyclohexane at 298.15 K. Changes of refractivity and of volume on mixing. J. Chem. Eng. Data 1995, 40, 586−588. (20) Poling, B. E.; Prausnitz, J. M.; O’Connell, J. P. The Properties of Gases and Liquids, 5th ed.; McGraw-Hill: Singapore, 2007. (21) Abraham, M. H. Physicochemical and biological processes. Chem. Soc. Rev. 1993, 22, 73−83.

absence of a band shift at lower wavenumber confirms that there is no existence of hydrogen bonding between tetrahydrofuran and 1-butanol molecules.

4. CONCLUSION In this article, density ρ, refractive index nD, and viscosity η measurements of the ternary dimethyladipate + tetrahydrofuran + 1-butanol and binary tetrahydrofuran + 1-butanol systems at T = (288.15 to 323.15) K and atmospheric pressure have been experimentally determined. Also, viscosities of the dimethyladipate + 1-butanol at the same conditions are measured. From the measured properties the excess molar volume VE, deviations in refractive indices ΔnD, and viscosity deviations Δη were calculated. In addition, FT-IR studies of the binary constituents of the investigated ternary mixture have been carried out at T = 298.15 K. The values of VE data for the analyzed ternary system are mainly positive except for the ternary mixtures with the reduced amount of 1-butanol. Deviations in refractive indices are positive, while experimental viscosity deviations are negative in the entire ternary concentration area for all investigated temperatures. Because of distinguish hydrogen-bond abilities and polar nature of the compounds it was assumed that molecular association between unlike compounds is a probable reason for nonideal behavior of the investigated mixtures. However, FT-IR absorption spectra do not confirm the existence of heteroassociates due to hydrogen bonding or dipole−dipole interactions.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +381 11 3370523. Fax: +381 11 3370387. E-mail: [email protected]. Funding

The authors gratefully acknowledge the financial support received from the Research Fund of the Ministry of Education and Science, Serbia and the Faculty of Technology and Metallurgy, University of Belgrade (project No 172063). Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Spasojević, V. D.; Šerbanović, S. P.; Djordjević, B. D.; Kijevčanin, M.Lj. Densities, Viscosities, and refractive indices of aqueous alkanolamine solutions as potential carbon dioxide removal reagents. J. Chem. Eng. Data 2013, 58, 84−92. (2) Kijevčanin, M.Lj.; Ž ivković, E. M.; Djordjević, B. D.; Radović, I. R.; Jovanović, J.; Šerbanovic, S. P. Experimental determination and modeling of excess molar volumes, viscosities and refractive indices of the binary systems (pyridine + 1-propanol, + 1,2-propanediol, + 1,3propanediol, and + glycerol). New UNIFAC-VISCO parameters determination. J. Chem. Thermodyn. 2013, 56, 49−56. (3) Bajić, D. M.; Ivaniš, G. R.; Višak, Z. P.; Ž ivković, E. M.; Šerbanović, S. P.; Kijevčanin, M.Lj. Densities, viscosities, and refractive indices of the binary systems (PEG200 + 1,2-propanediol, + 1,3-propanediol) and (PEG400 + 1,2-propanediol, +1,3-propanediol) at (288.15 to 333.15) K and atmospheric pressure: Measurements and modeling. J. Chem. Thermodyn. 2013, 57, 510−529. (4) Knežević-Stevanović, A. B.; Smiljanić, J. D.; Šerbanović, S. P.; Radović, I. R.; Kijevčanin, M.Lj. Densities, refractive indices an viscosities of the binary mixtures of dimethylphthalate or dimethyladipate with tetrahydrofurane. J. Serb. Chem. Soc. (submitted for publication). 2951


Thermodynamic and Spectroscopic Study of the Ternary System

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