Densities and Viscosities for Binary Liquid Mixtures ... - ACS Publications

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Densities and Viscosities for Binary Liquid Mixtures of n‑Undecane + 1‑Propanol, + 1‑Butanol, + 1‑Pentanol, and + 1-Hexanol from 283.15 to 363.15 K at 0.1 MPa Gustavo A. Iglesias-Silva,* Adriana Guzmán-López, and Guadalupe Pérez-Durán Departamento de Ingeniería Química, Instituto Tecnológico de Celaya Celaya, Guanajuato CP 38010, México

Mariana Ramos-Estrada Facultad de Ingeniería Química, Universidad Michoacana de San Nicolás de Hidalgo, Morelia, Mich. CP 58030, México ABSTRACT: This paper presents densities and viscosities of binary mixtures of n-undecane with 1-propanol, 1-butanol, 1-pentanol, and 1-hexanol from 283.15 to 363.15 K at 0.1 MPa over the entire composition range. Densities come from a vibrating tube densimeter, while viscosities are from a pellet microviscometer. A three-body McAllister equation correlates the kinematic viscosities together with an equation based upon a quadratic mixing rule for the Gibbs energy of activation. The excess molar volumes and viscosity deviations calculated from the experimental data have positive and negative deviations from ideality over the temperature range, respectively.

Table 1. Sample Information

1. INTRODUCTION Densities and viscosities of mixtures are essential in industrial applications that involve mass, and heat transfer. Alcohols and their mixtures are used as solvents or in the manufacture of perfumes and brake fluids. This work is a continuation of our work of n-alkanes + 1-alcohols.1 Thermodynamic properties of n-alkanes + n-alcohols have been measured to explain the way in which the alcohol structure is modified with the addition of n-alkane. This modification has been suggested to be due to a partial destruction of the structure formed by the hydrogen bonding of the pure 1-alcohol during the mixing process. Densities and viscosities of binary mixtures of n-undecane + 1-alcohols are scarce. Densities of n-undecane with ethanol have been measured by Peleteiro et al.2 To the best of our knowledge, densities with n-undecane + 1-propanol, + 1 butanol, 1-pentanol, and 1-hexanol does not exist in the literature. Viscosities for the binary mixtures of this work also have not been measured previously. This work reports the densities and viscosities for binary mixtures of n-undecane with 1-propanol, 1-butanol, 1-pentanol, and 1-hexanol at 0.1 MPa from 283.15 and 363.15 K over the entire composition range. A Redlich−Kister3 type equation correlates excess molar volume and viscosity deviations. The McAllister4 and Nava-Rios et al.5 equations are used to represent the kinematic viscosities.

a

source

CAS No.

n-undecane 1-propanol 1-butanol 1-pentanol 1-hexanol

SAFC Sigma-Aldrich Sigma-Aldrich Sigma-Aldrich Sigma-Aldrich

1120-21-4 71-23-8 71-36-3 71-41-0 111-27-3

initial purity purification analysis mass fraction method methoda 0.99 0.997 0.998 0.99 0.99

none none none none none

GC GC GC GC GC

Gas chromatography provided by the supplier.

fraction %). The samples have been prepared using an analytical balance (Ohaus model AS120S) with an accuracy 0.1 mg. Substances are used as received and kept in airtight containers. Table 1 shows the specifications of the samples. Apparatuses and Procedures. A vibrating tube densimeter (Anton Paar, DMA 5000) was used to measure the density with a stated reproducibility by the manufacturer of 1 × 10−6 g·cm−3 for the density and 0.001 K for the temperature. The densimeter is excited by a harmonic electromagnetic force and then senses the change of the oscillating frequency. An oscilloscope measures the resonance frequency of the tube. Densities are related to the harmonic oscillation period considering Hook’s law. The densimeter is calibrated by the manufacturer using two reference fluids: ultrapure

2. EXPERIMENTAL SECTION Samples. The samples were supplied by SAFC for n-undecane (≥99 in mass fraction %), Sigma-Aldrich for 1-propanol anhydrous (99.7 in mass fraction %), 1-butanol (99.8 in mass fraction %), 1-pentanol (≥99 in mass fraction %), and 1-hexanol (≥99 in mass © 2016 American Chemical Society

chemical name

Special Issue: In Honor of Kenneth R. Hall Received: February 11, 2016 Accepted: June 17, 2016 Published: July 6, 2016 2682

DOI: 10.1021/acs.jced.6b00121 J. Chem. Eng. Data 2016, 61, 2682−2699

Journal of Chemical & Engineering Data

Article

Table 2. Comparison between the Experimental Pure Component Liquid Density and Viscosity and Literature Values at Pressure p = 0.1 MPaa ρ/g·cm−3 component n-undecane

1-propanol

T/K 283.15 288.15 293.15

0.74778 0.74406 0.74035

298.15

0.73664

303.15

0.73293

308.15

0.72923

313.15

0.72553

318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 283.15 288.15 293.15 298.15

0.72182 0.71811 0.71439 0.71068 0.70695 0.70322 0.69947 0.69572 0.69196 0.68818 0.81148 0.80754 0.80358 0.79959

303.15

0.79558

308.15 313.15 318.15 323.15 328.15

1-butanol

a

this work

ρ/g·cm−3

η/mPa·s

literature 0.744297 0.74059,7 0.740248 0.7369,7 0.73658 0.7332,7 0.732828 0.72951,7 0.72919 0.7255,9 0.725410

this work 1.371 1.249 1.145

1.17427

1.062

1.08227

0.982

0.990527

0.910

0.927327

0.847

0.687512 0.811413 0.8075514 0.803515 0.799514 0.79616

1.714

0.703211

14

0.79153 0.78744 0.78330 0.77911 0.77486

0.79147 0.787515 0.7831214 0.778516 0.7746414

1.536 1.372 1.229 1.113 1.002

333.15 338.15 343.15 348.15 353.15 358.15 363.15 283.15 288.15 293.15 298.15 303.15

0.77054 0.76615 0.76167 0.75709 0.75244 0.74765 0.74277 0.81707 0.81332 0.80955 0.80576 0.80194

14

0.905 0.819 0.752 0.685 0.625 0.574 0.528 4.046 3.514 3.006 2.590 2.280

308.15 313.15 318.15 323.15

0.79809 0.79420 0.79027 0.78630

0.77022 0.7658914 0.76116 0.7568914 0.75215 0.742516 0.817317 0.8132418 0.8094318 0.8056218 0.80179,18 0.80219 0.797920 0.794020 0.790120 0.786220

component

1-pentanol

0.790 0.740 0.692 0.651 0.615 0.580 0.549 0.522 0.497 0.475 2.834 2.489 2.195 1.929

0.710610

literature

2.015 1.786 1.589 1.427

0.855528

0.747228 0.661128

2.18729 1.945,29 1.95430 1.705,29 1.73430 1.54530 1.38430 1.24130 1.11630 1.011,19 1.00930

1-hexanol

0.68219

2.9831 2.58332 2.2894,31 2.27133 2.01532 1.79533 1.58932 1.42134

T/K

this work

η/mPa·s

literature 19

0.7829 0.778717

this work

328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 283.15 288.15 293.15 298.15

0.78227 0.77818 0.77403 0.76980 0.76549 0.76112 0.75664 0.75208 0.82190 0.81830 0.81468 0.81103 0.80737 0.80367 0.79994 0.79617 0.79236 0.78850 0.78459 0.78062 0.77658 0.77249 0.76833 0.76408 0.75977 0.82594 0.82242 0.81888 0.81532

303.15

0.81174

0.8226724 0.818825 0.81554,24 0.815225 0.811825

308.15 313.15

0.80813 0.80450

0.8083424 0.803725

3.361 2.912

318.15 323.15

0.80083 0.79712

2.538 2.228

328.15

0.79337

333.15

0.78957

338.15

0.78572

343.15

0.78183

348.15

0.77786

353.15 358.15 363.15

0.77386 0.76978 0.76564

0.8010324 0.79734,23 0.796625 0.79409,23 0.7935624 0.78967,23 0.789225 0.78602,23 0.7853424 0.78178,23 0.781125 0.77768,23 0.778224 0.7738923 0.7702224 0.7654723

0.770317 0.76719 0.761617 0.752717 0.8174421 0.81463522 0.8109722 0.8072822 0.8035622 0.799822

23

0.78892 0.783415 0.7805923 23

0.77192 0.76815 0.7636423 0.7593623

1.278 1.147 1.032 0.934 0.842 0.762 0.693 0.633 5.431 4.655 4.011 3.474 3.023 2.642 2.320 2.045 1.810 1.608 1.434 1.283 1.152 1.038 0.939 0.852 0.776 7.487 6.307 5.348 4.555

literature 1.26932 1.13734 1.02733 0.92034 0.75934 0.6334

4.045731 3.498831 3.036731 2.646931 2.3334 1.82234 1.58635 1.44034 1.14634 0.93134

1.970

0.76734 7.45936 6.29324 5.33536 4.5406,37 4.5938 3.763,36 3.864437 3.41524 2.937,36 2.912837 2.59624 2.243,37 2.17236 2.00724

1.744

1.749737

1.553

1.583,24 1.57337 1.411,36 1.393537 1.268,24 1.245737 1.124237 1.03124

3.903

1.390 1.255 1.125 1.018 0.925

Standard uncertainties: ur(ρ) = 0.001, ur(η) = 0.005, u(T) = 0.01 K for density, u(T) = 0.05 K for viscosity, and u(p) = 10 kPa.

estimated by the manufacturer of less than 0.1%. The temperature standard uncertainty is 0.05 K, and the reproducibility of the measured time is 0.001 s. The operating principle of the microviscosimeter consists of rolling a ball of knowing density down a capillary tube completely filled with the sample. The time that takes to roll the ball certain distance is recorded, and it is

water and dry air. The standard uncertainty in the measurements given by the manufacturer of the density and temperature are 5 × 10−6 g·cm−3 and 0.01 K, respectively. However, the estimated relative standard uncertainty is equal to 0.001. A rolling ball microviscosimeter (Anton Paar model AMVn) is used to obtain the viscosity of the mixtures with a repeatability 2683


g·cm

0.81148 0.79454 0.78293 0.77429 0.76769 0.76246 0.75808 0.75468 0.75172 0.74945 0.74778

0.79558 0.77873 0.76715 0.75859 0.75204 0.74690 0.74264 0.73934 0.73655 0.73441 0.73293

0.77911 0.76228 0.75073 0.74226 0.73582 0.73081 0.72672 0.72359 0.72101 0.71909 0.71811

0.76167 0.74480 0.73333 0.72501 0.71877

0.0000 0.1003 0.2009 0.3004 0.3997 0.4998 0.6005 0.6974 0.8000 0.8963 1.0000

0.0000 0.1003 0.2009 0.3004 0.3997 0.4998 0.6005 0.6974 0.8000 0.8963 1.0000

0.0000 0.1003 0.2009 0.3004 0.3997 0.4998 0.6005 0.6974 0.8000 0.8963 1.0000

0.0000 0.1003 0.2009 0.3004 0.3997

−3

x1

ρ

VE

−1

mPa·s

η

T = 283.15 K 0.0000 2.834 0.1865 2.378 0.2719 2.098 0.3386 1.867 0.3676 1.722 0.3699 1.585 0.3782 1.482 0.3540 1.412 0.3001 1.371 0.2162 1.356 0.0000 1.371 T = 303.15 K 0.0000 1.714 0.2134 1.487 0.3260 1.332 0.4106 1.223 0.4586 1.129 0.4705 1.061 0.4778 1.012 0.4509 0.978 0.3740 0.961 0.2673 0.957 0.0000 0.982 T = 323.15 K 0.0000 1.113 0.2683 0.976 0.4299 0.889 0.5520 0.828 0.6296 0.786 0.6601 0.754 0.6733 0.732 0.6409 0.717 0.5426 0.712 0.4005 0.715 0.0000 0.740 T = 343.15 K 0.0000 0.752 0.3632 0.672 0.6022 0.626 0.7839 0.596 0.9046 0.576

cm ·mol

3

2684

0.0000 −0.0628 −0.0917 −0.1044 −0.1077

0.0000 −0.0996 −0.1491 −0.1727 −0.1784 −0.1724 −0.1573 −0.1354 −0.1029 −0.0637 0.0000

0.0000 −0.1539 −0.2353 −0.2709 −0.2927 −0.2869 −0.2622 −0.2249 −0.1672 −0.1005 0.0000

0.0000 −0.3091 −0.4416 −0.5272 −0.5270 −0.5179 −0.4734 −0.4012 −0.2924 −0.1666 0.0000

mPa·s

Δη −3

0.75709 0.74024 0.72880 0.72053 0.71434

0.77486 0.75802 0.74649 0.73804 0.73164 0.72668 0.72264 0.71957 0.71705 0.71521 0.71439

0.79153 0.77469 0.76312 0.75457 0.74805 0.74293 0.73871 0.73545 0.73270 0.73061 0.72923

0.80754 0.79063 0.77903 0.77041 0.76382 0.75860 0.75426 0.75086 0.74796 0.74571 0.74406

g·cm

ρ VE −1

mPa·s

η

T = 288.15 K 0.0000 2.489 0.1915 2.104 0.2822 1.861 0.3509 1.690 0.3847 1.539 0.3891 1.426 0.3952 1.338 0.3720 1.280 0.3098 1.246 0.2231 1.235 0.0000 1.249 T = 308.15 K 0.0000 1.536 0.2242 1.333 0.3466 1.196 0.4388 1.106 0.4928 1.025 0.5089 0.968 0.5170 0.929 0.4886 0.901 0.4064 0.886 0.2926 0.885 0.0000 0.910 T = 328.15 K 0.0000 1.002 0.2878 0.885 0.4658 0.811 0.6012 0.760 0.6882 0.723 0.7243 0.698 0.7400 0.681 0.7062 0.669 0.6020 0.665 0.4477 0.669 0.0000 0.692 T = 348.15 K 0.0000 0.685 0.3922 0.617 0.6556 0.578 0.8561 0.553 0.9924 0.537

cm ·mol 3

0.0000 −0.0543 −0.0797 −0.0905 −0.0935

0.0000 −0.0860 −0.1290 −0.1493 −0.1547 −0.1489 −0.1349 −0.1168 −0.0885 −0.0548 0.0000

0.0000 −0.1404 −0.2146 −0.2417 −0.2606 −0.2552 −0.2314 −0.1987 −0.1488 −0.0898 0.0000

0.0000 −0.2609 −0.3792 −0.4260 −0.4538 −0.4438 −0.4060 −0.3443 −0.2507 −0.1431 0.0000

mPa·s

Δη −3

0.75244 0.73557 0.72418 0.71597 0.70986

0.77054 0.75370 0.74218 0.73376 0.72741 0.72250 0.71852 0.71551 0.71306 0.71130 0.71068

0.78744 0.77060 0.75904 0.75052 0.74402 0.73893 0.73475 0.73152 0.72883 0.72679 0.72553

0.80358 0.78669 0.77510 0.76650 0.75992 0.75473 0.75041 0.74704 0.74417 0.74196 0.74035

g·cm

ρ VE −1

mPa·s

η

T = 293.15 K 0.0000 2.195 0.1975 1.865 0.2939 1.656 0.3674 1.515 0.4053 1.382 0.4115 1.286 0.4177 1.214 0.3930 1.165 0.3261 1.138 0.2330 1.130 0.0000 1.145 T = 313.15 K 0.0000 1.372 0.2371 1.198 0.3706 1.080 0.4715 1.004 0.5327 0.935 0.5532 0.888 0.5626 0.855 0.5329 0.833 0.4460 0.821 0.3231 0.822 0.0000 0.847 T = 333.15 K 0.0000 0.905 0.3094 0.805 0.5058 0.741 0.6556 0.698 0.7530 0.668 0.7954 0.648 0.8132 0.634 0.7786 0.625 0.6679 0.623 0.4993 0.628 0.0000 0.651 T = 353.15 K 0.0000 0.625 0.4271 0.568 0.7171 0.535 0.9374 0.515 1.0867 0.502

cm ·mol 3

0.0000 −0.0471 −0.0696 −0.0794 −0.0818

0.0000 −0.0742 −0.1123 −0.1302 −0.1351 −0.1299 −0.1182 −0.1026 −0.0788 −0.0494 0.0000

0.0000 −0.1215 −0.1867 −0.2101 −0.2270 −0.2219 −0.2016 −0.1732 −0.1305 −0.0798 0.0000

0.0000 −0.2243 −0.3272 −0.3637 −0.3928 −0.3837 −0.3499 −0.2969 −0.2164 −0.1235 0.0000

mPa·s

Δη −3

0.74765 0.73081 0.71945 0.71132 0.70529

0.76615 0.74930 0.73780 0.72943 0.72312 0.71827 0.71436 0.71141 0.70904 0.70737 0.70695

0.783304 0.766466 0.754911 0.746411 0.739944 0.734891 0.730749 0.727572 0.724934 0.722953 0.721818

0.79959 0.78272 0.77114 0.76256 0.75600 0.75083 0.74654 0.74320 0.74037 0.73820 0.73664

g·cm

ρ VE

η mPa·s

T = 298.15 K 0.0000 1.929 0.2048 1.655 0.3082 1.481 0.3870 1.357 0.4296 1.246 0.4383 1.166 0.4451 1.106 0.4190 1.065 0.3470 1.044 0.2475 1.038 0.0000 1.062 T = 318.15 K 0.0000 1.229 0.2517 1.079 0.3986 0.979 0.5094 0.913 0.5783 0.856 0.6034 0.816 0.6150 0.789 0.5838 0.772 0.4907 0.763 0.3593 0.765 0.0000 0.790 T = 338.15 K 0.000 0.819 0.334 0.734 0.551 0.680 0.716 0.645 0.825 0.619 0.875 0.604 0.895 0.593 0.859 0.586 0.742 0.586 0.557 0.592 0.000 0.615 T = 358.15 K 0.0000 0.574 0.4623 0.525 0.7836 0.497 1.0258 0.481 1.1907 0.471

cm ·mol−1 3

Table 3. Experimental Densities, Excess Volumes, Viscosities, and Viscosity Deviations for n-Undecane (1) + 1-Propanol (2) at Pressure p = 0.1 MPaa Δη

0.0000 −0.0414 −0.0609 −0.0697 −0.0719

0.0000 −0.0644 −0.0977 −0.1132 −0.1179 −0.1134 −0.1038 −0.0902 −0.0699 −0.0443 0.0000

0.0000 −0.1056 −0.1621 −0.1840 −0.1977 −0.1932 −0.1765 −0.1514 −0.1147 −0.0704 0.0000

0.0000 −0.1868 −0.2738 −0.3109 −0.3360 −0.3296 −0.3019 −0.2590 −0.1916 −0.1142 0.0000

mPa·s

Journal of Chemical & Engineering Data Article


a

−1

ρ

−3

−3

0.70964 0.70588 0.70309 0.70090 0.69945 0.69947

2685

VE −1

mPa·s

η

T = 348.15 K 1.0567 0.527 1.0829 0.522 1.0437 0.519 0.9081 0.521 0.6860 0.528 0.0000 0.549

cm ·mol 3

−1

0.0000 0.5045 0.8555 1.1204 1.3012 1.3953 1.4306 1.3840 1.2138 0.9036 0.0000

cm ·mol 3

−0.0899 −0.0813 −0.0716 −0.0555 −0.0353 0.0000 VE

mPa·s

Δη −3

VE −1

mPa·s

η

mPa·s

η

mPa·s

Δη

−0.0790 −0.0714 −0.0638 −0.0505 −0.0323 0.0000

0.5280 0.4864 0.4635 0.4506 0.4430 0.4401 0.4396 0.4398 0.4438 0.4531 0.4750

T = 353.15 K 1.1613 0.495 1.1900 0.492 1.1493 0.490 1.0048 0.492 0.7546 0.501 0.0000 0.522

cm ·mol 3

T = 363.15 K

0.70523 0.70157 0.69886 0.69677 0.69546 0.69572

g·cm

ρ −3

0.70075 0.69719 0.69458 0.69262 0.69144 0.69196

g·cm

ρ VE

η mPa·s

0.0000 −0.0364 −0.0540 −0.0615 −0.0639 −0.0614 −0.0566 −0.0512 −0.0418 −0.0273 0.0000

mPa·s

T = 358.15 K 1.2752 0.466 1.3061 0.465 1.2639 0.463 1.1047 0.467 0.8295 0.476 0.0000 0.497 Δη

cm ·mol−1 3

Δη mPa·s −0.0692 −0.0631 −0.0567 −0.0453 −0.0292 0.0000

Standard uncertainties: ur(ρ) = 0.001, ur(η) = 0.005, u(x1) = 0.0002, u(VE) = 0.006 cm3·mol−1, u(Δη) = 0.01 mPa·s, u(T) = 0.01 K for density, u(T) = 0.05 K for viscosity, u(p) = 10 kPa.

0.74277 0.72593 0.71464 0.70659 0.70067 0.69622 0.69277 0.69027 0.68842 0.68741 0.68818

−0.1033 −0.0939 −0.0815 −0.0630 −0.0401 0.0000

T = 343.15 K 0.9628 0.563 0.9860 0.555 0.9483 0.551 0.8210 0.552 0.6181 0.558 0.0000 0.580

ρ g·cm

0.0000 0.1003 0.2009 0.3004 0.3997 0.4998 0.6005 0.6974 0.8000 0.8963 1.0000

mPa·s

Δη

mPa·s

η

g·cm

0.71398 0.71014 0.70727 0.70499 0.70343 0.70322

0.4998 0.6005 0.6974 0.8000 0.8963 1.0000

VE

cm ·mol

3

x1

g·cm

−3

x1

ρ

Table 3. continued



g·cm

0.81707 0.80180 0.79028 0.78112 0.77360 0.76702 0.76198 0.75732 0.75351 0.75022 0.74778

0.80194 0.78657 0.77495 0.76575 0.75822 0.75170 0.74669 0.74214 0.73842 0.73523 0.73293

0.78630 0.77078 0.75907 0.74984 0.74234 0.73591 0.73100 0.72658 0.72299 0.71999 0.71811

0.76980 0.75412 0.74234 0.73315 0.72575

0.0000 0.1007 0.2004 0.2990 0.3981 0.5006 0.5964 0.6982 0.7979 0.9000 1.0000

0.0000 0.1007 0.2004 0.2990 0.3981 0.5006 0.5964 0.6982 0.7979 0.9000 1.0000

0.0000 0.1007 0.2004 0.2990 0.3981 0.5006 0.5964 0.6982 0.7979 0.9000 1.0000

0.0000 0.1007 0.2004 0.2990 0.3981

−3

x1

ρ

VE

−1

mPa·s

η

T = 283.15 K 0.0000 4.046 0.1363 3.124 0.2070 2.611 0.2590 2.240 0.2912 1.939 0.3303 1.722 0.3246 1.582 0.3209 1.471 0.2763 1.416 0.1965 1.385 0.0000 1.371 T = 303.15 K 0.0000 2.280 0.1602 1.871 0.2565 1.595 0.3285 1.392 0.3759 1.248 0.4200 1.139 0.4163 1.071 0.4001 1.016 0.3423 0.991 0.2387 0.975 0.0000 0.982 T = 323.15 K 0.0000 1.427 0.2092 1.192 0.3502 1.042 0.4580 0.934 0.5317 0.858 0.5880 0.804 0.5890 0.771 0.5659 0.749 0.4944 0.733 0.3566 0.727 0.0000 0.740 T = 343.15 K 0.0000 0.934 0.2902 0.802 0.5004 0.720 0.6597 0.663 0.7705 0.626

cm ·mol

3

2686

0.0000 −0.0958 −0.1427 −0.1648 −0.1670

0.0000 −0.1664 −0.2478 −0.2879 −0.2952 −0.2786 −0.2465 −0.1983 −0.1455 −0.0818 0.0000

0.0000 −0.2775 −0.4241 −0.4991 −0.5151 −0.4911 −0.4340 −0.3570 −0.2528 −0.1365 0.0000

0.0000 −0.6530 −0.8984 −1.0055 −1.0421 −0.9843 −0.8685 −0.7071 −0.4952 −0.2533 0.0000

mPa·s

Δη −3

0.76549 0.74978 0.73801 0.72884 0.72147

0.78227 0.76671 0.75497 0.74575 0.73826 0.73186 0.72699 0.72261 0.71907 0.71613 0.71439

0.79809 0.78269 0.77105 0.76184 0.75431 0.74780 0.74282 0.73830 0.73460 0.73145 0.72923

0.81332 0.79803 0.78648 0.77731 0.76979 0.76323 0.75818 0.75356 0.74976 0.74649 0.74406

g·cm

ρ VE −1

mPa·s

η

T = 288.15 K 0.0000 3.514 0.1400 2.731 0.2165 2.294 0.2720 1.978 0.3061 1.723 0.3457 1.541 0.3411 1.425 0.3330 1.329 0.2868 1.287 0.2012 1.260 0.0000 1.249 T = 308.15 K 0.0000 2.015 0.1698 1.663 0.2755 1.426 0.3550 1.253 0.4081 1.130 0.4542 1.038 0.4513 0.979 0.4325 0.936 0.3717 0.915 0.2609 0.902 0.0000 0.910 T = 328.15 K 0.0000 1.278 0.2264 1.074 0.3825 0.945 0.5009 0.853 0.5835 0.790 0.6443 0.744 0.6471 0.716 0.6231 0.693 0.5477 0.685 0.3988 0.680 0.0000 0.692 T = 348.15 K 0.0000 0.842 0.3163 0.732 0.5455 0.662 0.7202 0.614 0.8445 0.583

cm ·mol 3

0.0000 −0.0805 −0.1217 −0.1406 −0.1428

0.0000 −0.1453 −0.2158 −0.2500 −0.2544 −0.2408 −0.2123 −0.1758 −0.1254 −0.0700 0.0000

0.0000 −0.2406 −0.3673 −0.4316 −0.4447 −0.4234 −0.3766 −0.3077 −0.2181 −0.1188 0.0000

0.0000 −0.5552 −0.7663 −0.8594 −0.8897 −0.8389 −0.7387 −0.6037 −0.4196 −0.2154 0.0000

mPa·s

Δη −3

0.76112 0.74537 0.73360 0.72446 0.71714

0.77818 0.76258 0.75083 0.74161 0.73414 0.72778 0.72294 0.71861 0.71512 0.71224 0.71068

0.79420 0.77877 0.76710 0.75788 0.75036 0.74387 0.73891 0.73442 0.73076 0.72765 0.72553

0.80955 0.79424 0.78267 0.77349 0.76596 0.75941 0.75438 0.74977 0.74600 0.74275 0.74035

g·cm

ρ VE −1

mPa·s

η

T = 293.15 K 0.0000 3.006 0.1453 2.398 0.2270 2.025 0.2877 1.755 0.3255 1.540 0.3661 1.387 0.3616 1.290 0.3507 1.212 0.3010 1.176 0.2087 1.152 0.0000 1.145 T = 313.15 K 0.0000 1.786 0.1814 1.483 0.2974 1.279 0.3851 1.131 0.4447 1.028 0.4938 0.950 0.4915 0.901 0.4719 0.864 0.4066 0.847 0.2879 0.837 0.0000 0.847 T = 333.15 K 0.0000 1.147 0.2456 0.974 0.4175 0.860 0.5483 0.782 0.6401 0.729 0.7065 0.690 0.7112 0.667 0.6869 0.647 0.6069 0.641 0.4460 0.638 0.0000 0.651 T = 353.15 K 0.0000 0.762 0.3443 0.671 0.5964 0.611 0.7884 0.570 0.9240 0.544

cm ·mol 3

0.0000 −0.0668 −0.1033 −0.1201 −0.1221

0.0000 −0.1227 −0.1872 −0.2168 −0.2201 −0.2091 −0.1840 −0.1538 −0.1103 −0.0626 0.0000

0.0000 −0.2084 −0.3183 −0.3738 −0.3843 −0.3655 −0.3247 −0.2659 −0.1892 −0.1042 0.0000

0.0000 −0.4203 −0.6079 −0.6944 −0.7247 −0.6872 −0.6061 −0.4941 −0.3451 −0.1783 0.0000

mPa·s

Δη −3

0.75664 0.74087 0.72910 0.72001 0.71273

0.77403 0.75839 0.74661 0.73742 0.72997 0.72365 0.71886 0.71457 0.71113 0.70834 0.70695

0.79027 0.77480 0.76311 0.75388 0.74637 0.73991 0.73497 0.73051 0.72689 0.72383 0.72182

0.80576 0.79042 0.77883 0.76963 0.76211 0.75557 0.75055 0.74597 0.74222 0.73900 0.73664

g·cm

ρ VE

η mPa·s

T = 298.15 K 0.0000 2.590 0.1519 2.115 0.2405 1.795 0.3065 1.564 0.3484 1.383 0.3909 1.254 0.3866 1.173 0.3730 1.108 0.3194 1.077 0.2211 1.058 0.0000 1.062 T = 318.15 K 0.0000 1.589 0.1943 1.326 0.3222 1.152 0.4194 1.026 0.4857 0.938 0.5385 0.882 0.5375 0.832 0.5160 0.801 0.4475 0.787 0.3203 0.779 0.0000 0.790 T = 338.15 K 0.0000 1.032 0.2668 0.882 0.4576 0.785 0.6012 0.719 0.7027 0.675 0.7748 0.641 0.7826 0.622 0.7579 0.606 0.6736 0.602 0.4972 0.601 0.0000 0.615 T = 358.15 K 0.0000 0.693 0.3738 0.617 0.6522 0.565 0.8618 0.531 1.0115 0.510

cm ·mol−1 3

Table 4. Experimental Densities, Excess Volumes, Viscosities, and Viscosity Deviations for n-Undecane (1) + 1-Butanol (2) at Pressure p = 0.1 MPaa Δη

0.0000 −0.0564 −0.0885 −0.1034 −0.1052

0.0000 −0.1075 −0.1625 −0.1880 −0.1910 −0.1814 −0.1605 −0.1345 −0.0965 −0.0554 0.0000

0.0000 −0.1820 −0.2771 −0.3243 −0.3329 −0.3069 −0.2806 −0.2307 −0.1647 −0.0915 0.0000

0.0000 −0.3216 −0.4888 −0.5691 −0.5987 −0.5716 −0.5059 −0.4156 −0.2940 −0.1569 0.0000

mPa·s



a

−1

ρ

−3

−3

0.71524 0.71054 0.70638 0.70307 0.70047 0.69947

2687

VE −1

mPa·s

η

T = 348.15 K 0.9310 0.560 0.9472 0.546 0.9198 0.535 0.8266 0.534 0.6128 0.536 0.0000 0.549

cm ·mol 3

−1

0.0000 0.4087 0.7100 0.9395 1.1032 1.2174 1.2468 1.2194 1.1002 0.8097 0.0000

cm ·mol 3

−0.1352 −0.1216 −0.1024 −0.0740 −0.0423 0.0000 VE

mPa·s

Δη −3

VE −1

mPa·s

η

η

0.633 0.569 0.525 0.497 0.479 0.465 0.458 0.452 0.455 0.460 0.475

mPa·s

T = 353.15 K 1.0180 0.525 1.0387 0.514 1.0126 0.506 0.9097 0.505 0.6757 0.508 0.0000 0.522

cm ·mol 3

T = 363.15 K

0.71097 0.70632 0.70222 0.69899 0.69651 0.69572

g·cm

ρ

−0.1172 −0.1046 −0.0889 −0.0654 −0.0379 0.0000

mPa·s

Δη −3

0.70663 0.70204 0.69802 0.69488 0.69252 0.69196

g·cm

ρ VE

η mPa·s

0.0000 −0.0479 −0.0759 −0.0891 −0.0911 −0.0889 −0.0808 −0.0701 −0.0519 −0.0312 0.0000

mPa·s

T = 358.15 K 1.1136 0.493 1.1402 0.485 1.1143 0.477 1.0013 0.479 0.7435 0.483 0.0000 0.497 Δη

cm ·mol−1 3

Δη mPa·s −0.1017 −0.0916 −0.0787 −0.0576 −0.0337 0.0000


0.75208 0.73628 0.72455 0.71549 0.70828 0.70224 0.69772 0.69378 0.69073 0.68852 0.68818

−0.1587 −0.1411 −0.1181 −0.0854 −0.0487 0.0000

T = 343.15 K 0.8489 0.598 0.8607 0.582 0.8364 0.569 0.7461 0.566 0.5544 0.567 0.0000 0.580

ρ g·cm

0.0000 0.1007 0.2004 0.2990 0.3981 0.5006 0.5964 0.6982 0.7979 0.9000 1.0000

mPa·s

Δη

mPa·s

η

g·cm

0.71948 0.71472 0.71049 0.70712 0.70441 0.70322

0.5006 0.5964 0.6982 0.7979 0.9000 1.0000

VE

cm ·mol

3

x1

g·cm

−3

x1

ρ

Table 4. continued



g·cm

0.82190 0.80813 0.79668 0.78676 0.77865 0.77141 0.76549 0.76002 0.75527 0.75187 0.74778

0.80737 0.79340 0.78178 0.77175 0.76360 0.75632 0.75042 0.74500 0.74028 0.73692 0.73293

0.79236 0.77815 0.76637 0.75627 0.74809 0.74084 0.73498 0.72962 0.72497 0.72169 0.71811

0.77658 0.76215 0.75025 0.74012 0.73198

0.0000 0.0999 0.2000 0.3026 0.4001 0.5022 0.5976 0.6984 0.8010 0.8822 1.0000

0.0000 0.0999 0.2000 0.3026 0.4001 0.5022 0.5976 0.6984 0.8010 0.8822 1.0000

0.0000 0.0999 0.2000 0.3026 0.4001 0.5022 0.5976 0.6984 0.8010 0.8822 1.0000

0.0000 0.0999 0.2000 0.3026 0.4001

−3

x1

ρ

VE

−1

mPa·s

η

T = 283.15 K 0.0000 5.431 0.0863 4.269 0.1505 3.406 0.2068 2.731 0.2584 2.210 0.2790 1.884 0.2906 1.694 0.2816 1.551 0.2213 1.452 0.1741 1.413 0.0000 1.371 T = 303.15 K 0.0000 3.023 0.1072 2.428 0.1941 1.995 0.2684 1.656 0.3288 1.428 0.3563 1.283 0.3645 1.202 0.3436 1.095 0.2737 1.026 0.2139 0.999 0.0000 0.982 T = 323.15 K 0.0000 1.810 0.1507 1.468 0.2751 1.266 0.3791 1.087 0.4586 0.974 0.4982 0.896 0.5094 0.836 0.4860 0.796 0.4085 0.764 0.3294 0.748 0.0000 0.740 T = 343.15 K 0.0000 1.152 0.2183 0.979 0.3989 0.857 0.5461 0.760 0.6556 0.708

cm ·mol

3

2688

0.0000 −0.1159 −0.1804 −0.2184 −0.2148

0.0000 −0.2347 −0.3301 −0.3991 −0.4073 −0.3765 −0.3345 −0.2668 −0.1891 −0.1177 0.0000

0.0000 −0.3906 −0.6193 −0.7487 −0.7783 −0.7142 −0.6014 −0.4627 −0.3616 −0.2232 0.0000

0.0000 −0.7558 −1.2122 −1.4714 −1.5959 −1.5079 −1.3110 −1.0444 −0.7265 −0.4357 0.0000

mPa·s

Δη −3

0.77249 0.75801 0.74609 0.73595 0.72783

0.78850 0.77423 0.76242 0.75230 0.74413 0.73688 0.73104 0.72570 0.72107 0.71784 0.71439

0.80367 0.78965 0.77798 0.76793 0.75977 0.75250 0.74660 0.74120 0.73649 0.73314 0.72923

0.81830 0.80449 0.79298 0.78304 0.77492 0.76766 0.76174 0.75630 0.75155 0.74815 0.74406

g·cm

ρ VE −1

mPa·s

η

T = 288.15 K 0.0000 4.655 0.0895 3.679 0.1587 2.958 0.2187 2.390 0.2704 1.945 0.2936 1.689 0.3045 1.535 0.2899 1.419 0.2274 1.335 0.1784 1.287 0.0000 1.249 T = 308.15 K 0.0000 2.642 0.1160 2.136 0.2108 1.768 0.2915 1.481 0.3558 1.290 0.3852 1.153 0.3934 1.062 0.3711 0.998 0.2990 0.951 0.2352 0.922 0.0000 0.910 T = 328.15 K 0.0000 1.608 0.1650 1.336 0.3016 1.142 0.4159 0.989 0.5013 0.895 0.5455 0.828 0.5585 0.776 0.5356 0.742 0.4575 0.714 0.3711 0.702 0.0000 0.692 T = 348.15 K 0.0000 1.038 0.2387 0.889 0.4361 0.784 0.5993 0.701 0.7183 0.659

cm ·mol 3

0.0000 −0.1008 −0.1565 −0.1891 −0.1833

0.0000 −0.1807 −0.2823 −0.3418 −0.3464 −0.3197 −0.2843 −0.2257 −0.1598 −0.0980 0.0000

0.0000 −0.3329 −0.5275 −0.6376 −0.6598 −0.6192 −0.5447 −0.4341 −0.3041 −0.1926 0.0000

0.0000 −0.6358 −1.0160 −1.2347 −1.3480 −1.2556 −1.0849 −0.8578 −0.5921 −0.3635 0.0000

mPa·s

Δη −3

0.76833 0.75380 0.74187 0.73174 0.72364

0.78459 0.77026 0.75842 0.74829 0.74012 0.73289 0.72707 0.72176 0.71715 0.71396 0.71068

0.79994 0.78586 0.77415 0.76408 0.75591 0.74864 0.74276 0.73736 0.73267 0.72934 0.72553

0.81468 0.80081 0.78927 0.77930 0.77117 0.76391 0.75799 0.75255 0.74781 0.74441 0.74035

g·cm

ρ VE −1

mPa·s

η

T = 293.15 K 0.0000 4.011 0.0941 3.187 0.1682 2.580 0.2321 2.103 0.2865 1.743 0.3105 1.529 0.3202 1.404 0.3032 1.308 0.2387 1.236 0.1863 1.176 0.0000 1.145 T = 313.15 K 0.0000 2.320 0.1259 1.887 0.2296 1.572 0.3174 1.330 0.3857 1.170 0.4185 1.058 0.4276 0.976 0.4045 0.924 0.3306 0.881 0.2619 0.859 0.0000 0.847 T = 333.15 K 0.0000 1.434 0.1813 1.200 0.3312 1.035 0.4557 0.903 0.5487 0.825 0.5978 0.767 0.6139 0.723 0.5911 0.694 0.5108 0.670 0.4174 0.659 0.0000 0.651 T = 353.15 K 0.0000 0.939 0.2619 0.810 0.4777 0.720 0.6537 0.649 0.7837 0.615

cm ·mol 3

0.0000 −0.0874 −0.1355 −0.1639 −0.1568

0.0000 −0.1560 −0.2427 −0.2944 −0.2962 −0.2735 −0.2437 −0.1933 −0.1375 −0.0850 0.0000

0.0000 −0.2855 −0.4527 −0.5442 −0.5610 −0.5223 −0.4633 −0.3674 −0.2587 −0.1613 0.0000

0.0000 −0.5376 −0.8578 −1.0403 −1.1210 −1.0426 −0.8943 −0.7011 −0.4787 −0.3062 0.0000

mPa·s

Δη −3

0.76408 0.74951 0.73758 0.72746 0.71938

0.78062 0.76624 0.75437 0.74423 0.73607 0.72886 0.72306 0.71777 0.71320 0.71006 0.70695

0.79617 0.78203 0.77028 0.76019 0.75202 0.74475 0.73888 0.73351 0.72883 0.72553 0.72182

0.81103 0.79712 0.78554 0.77554 0.76740 0.76013 0.75422 0.74878 0.74405 0.74067 0.73664

g·cm

ρ VE

η mPa·s

T = 298.15 K 0.0000 3.474 0.1001 2.777 0.1801 2.260 0.2490 1.862 0.3059 1.571 0.3316 1.395 0.3404 1.295 0.3214 1.214 0.2536 1.153 0.1979 1.080 0.0000 1.062 T = 318.15 K 0.0000 2.045 0.1378 1.675 0.2510 1.409 0.3467 1.200 0.4209 1.065 0.4564 0.972 0.4658 0.902 0.4428 0.856 0.3671 0.819 0.2934 0.801 0.0000 0.790 T = 338.15 K 0.0000 1.283 0.1988 1.082 0.3636 0.940 0.4997 0.827 0.6000 0.763 0.6552 0.714 0.6742 0.675 0.6531 0.652 0.5711 0.630 0.4687 0.621 0.0000 0.615 T = 358.15 K 0.0000 0.852 0.2859 0.744 0.5216 0.663 0.7142 0.602 0.8550 0.577

cm ·mol−1 3

Table 5. Experimental Densities, Excess Volumes, Viscosities, and Viscosity Deviations for n-Undecane (1) + 1-Pentanol (2) at Pressure p = 0.1 MPaa Δη

0.0000 −0.0730 −0.1177 −0.1424 −0.1334

0.0000 −0.1342 −0.2096 −0.2535 −0.2528 −0.2333 −0.2083 −0.1645 −0.1176 −0.0724 0.0000

0.0000 −0.2444 −0.3844 −0.4650 −0.4775 −0.4426 −0.3931 −0.3128 −0.2207 −0.1376 0.0000

0.0000 −0.4556 −0.7312 −0.8824 −0.9380 −0.8681 −0.7379 −0.5757 −0.3890 −0.2663 0.0000

mPa·s



a

−1

ρ

−3

−3

0.72065 0.71491 0.70970 0.70521 0.70219 0.69947

2689

VE −1

mPa·s

η

T = 348.15 K 0.7881 0.624 0.8145 0.595 0.7956 0.578 0.7108 0.561 0.5847 0.556 0.0000 0.549

cm ·mol 3

−1

0.0000 0.3116 0.5683 0.7777 0.9333 1.0314 1.0748 1.0595 0.9625 0.7865 0.0000

cm ·mol 3

−0.1692 −0.1509 −0.1193 −0.0853 −0.0508 0.0000 VE

mPa·s

Δη −3

VE −1

mPa·s

η

η

0.776 0.680 0.614 0.560 0.542 0.519 0.500 0.490 0.480 0.480 0.475

mPa·s

T = 353.15 K 0.8624 0.585 0.8947 0.560 0.8774 0.545 0.7874 0.531 0.6482 0.528 0.0000 0.522

cm ·mol 3

T = 363.15 K

0.71649 0.71078 0.70561 0.70117 0.69822 0.69572

g·cm

ρ

−0.1441 −0.1300 −0.1031 −0.0740 −0.0433 0.0000

mPa·s

Δη −3

0.71226 0.70659 0.70147 0.69710 0.69422 0.69196

g·cm

ρ VE

η mPa·s

0.0000 −0.0658 −0.1022 −0.1245 −0.1140 −0.1061 −0.0962 −0.0757 −0.0552 −0.0309 0.0000

mPa·s

T = 358.15 K 0.9450 0.551 0.9826 0.528 0.9667 0.517 0.8718 0.504 0.7182 0.502 0.0000 0.497 Δη

cm ·mol−1 3

Δη mPa·s −0.1232 −0.1117 −0.0874 −0.0632 −0.0364 0.0000


0.75977 0.74517 0.73323 0.72313 0.71508 0.70800 0.70237 0.69730 0.69299 0.69022 0.68818

−0.1985 −0.1772 −0.1395 −0.1001 −0.0610 0.0000

T = 343.15 K 0.7196 0.666 0.7425 0.633 0.7220 0.613 0.6373 0.594 0.5257 0.587 0.0000 0.580

ρ g·cm

0.0000 0.0999 0.2000 0.3026 0.4001 0.5022 0.5976 0.6984 0.8010 0.8822 1.0000

mPa·s

Δη

mPa·s

η

g·cm

0.72477 0.71900 0.71375 0.70922 0.70613 0.70322

0.5022 0.5976 0.6984 0.8010 0.8822 1.0000

VE

cm ·mol

3

x1

g·cm

−3

x1

ρ

Table 5. continued



g·cm

0.82594 0.81286 0.80210 0.79219 0.78350 0.77587 0.76889 0.76282 0.75718 0.75228 0.74778

0.81174 0.79847 0.78752 0.77745 0.76867 0.76101 0.75398 0.74789 0.74227 0.73738 0.73293

0.79712 0.78363 0.77251 0.76231 0.75347 0.74577 0.73874 0.73265 0.72706 0.72224 0.71811

0.78183 0.76813 0.75686 0.74658 0.73770

0.0000 0.1011 0.1989 0.2998 0.4001 0.4994 0.6004 0.6989 0.8001 0.8991 1.0000

0.0000 0.1011 0.1989 0.2998 0.4001 0.4994 0.6004 0.6989 0.8001 0.8991 1.0000

0.0000 0.1011 0.1989 0.2998 0.4001 0.4994 0.6004 0.6989 0.8001 0.8991 1.0000

0.0000 0.1011 0.1989 0.2998 0.4001

−3

x1

ρ

VE

−1

mPa·s

η

T = 283.15 K 0.0000 7.487 0.0967 5.655 0.1316 4.274 0.1775 3.340 0.2074 2.615 0.2174 2.198 0.2217 1.950 0.2033 1.720 0.1702 1.564 0.0981 1.455 0.0000 1.371 T = 303.15 K 0.0000 3.903 0.1105 3.016 0.1613 2.374 0.2263 1.952 0.2649 1.687 0.2729 1.470 0.2787 1.305 0.2551 1.176 0.2095 1.090 0.1261 1.031 0.0000 0.982 T = 323.15 K 0.0000 2.228 0.1425 1.799 0.2233 1.528 0.3137 1.301 0.3687 1.136 0.3858 1.011 0.3977 0.931 0.3776 0.853 0.3251 0.801 0.2218 0.773 0.0000 0.740 T = 343.15 K 0.0000 1.390 0.1953 1.189 0.3199 1.025 0.4485 0.901 0.5322 0.811

cm ·mol

3

2690

0.000 −0.118 −0.203 −0.246 −0.255

0.000 −0.279 −0.404 −0.481 −0.497 −0.474 −0.404 −0.335 −0.237 −0.117 0.000

0.000 −0.592 −0.948 −1.075 −1.047 −0.974 −0.844 −0.685 −0.476 −0.245 0.000

0.000 −1.213 −1.997 −2.313 −2.425 −2.235 −1.865 −1.492 −1.029 −0.532 0.000

mPa·s

Δη −3

0.77786 0.76412 0.75283 0.74254 0.73366

0.79337 0.77982 0.76866 0.75844 0.74958 0.74189 0.73486 0.72877 0.72320 0.71841 0.71439

0.80813 0.79481 0.78382 0.77371 0.76491 0.75724 0.75021 0.74412 0.73850 0.73362 0.72923

0.82242 0.80929 0.79849 0.78853 0.77981 0.77218 0.76518 0.75910 0.75347 0.74857 0.74406

g·cm

ρ VE −1

mPa·s

η

T = 288.15 K 0.0000 6.307 0.0983 4.784 0.1351 3.651 0.1868 2.880 0.2190 2.322 0.2261 2.019 0.2319 1.752 0.2122 1.554 0.1735 1.419 0.1006 1.329 0.0000 1.249 T = 308.15 K 0.0000 3.361 0.1165 2.620 0.1738 2.090 0.2439 1.746 0.2859 1.517 0.2951 1.334 0.3016 1.193 0.2780 1.080 0.2310 1.002 0.1436 0.954 0.0000 0.910 T = 328.15 K 0.0000 1.970 0.1543 1.612 0.2442 1.374 0.3429 1.180 0.4037 1.039 0.4244 0.930 0.4398 0.862 0.4204 0.793 0.3677 0.747 0.2582 0.724 0.0000 0.692 T = 348.15 K 0.0000 1.255 0.2116 1.054 0.3494 0.934 0.4892 0.828 0.5828 0.750

cm ·mol 3

0.0000 −0.1298 −0.1808 −0.2152 −0.2226

0.0000 −0.2284 −0.3421 −0.4071 −0.4192 −0.4012 −0.3400 −0.2833 −0.1998 −0.0966 0.0000

0.0000 −0.4934 −0.7837 −0.8805 −0.8637 −0.8031 −0.6962 −0.5680 −0.3979 −0.2036 0.0000

0.0000 −1.0115 −1.6503 −1.9102 −1.9611 −1.7623 −1.5182 −1.2189 −0.8416 −0.4304 0.0000

mPa·s

Δη −3

0.77386 0.76007 0.74876 0.73845 0.72957

0.78957 0.77597 0.76478 0.75453 0.74566 0.73797 0.73093 0.72487 0.71931 0.71455 0.71068

0.80450 0.79112 0.78008 0.76994 0.76113 0.75345 0.74641 0.74032 0.73471 0.72984 0.72553

0.81888 0.80571 0.79485 0.78485 0.77612 0.76847 0.76146 0.75538 0.74975 0.74485 0.74035

g·cm

ρ VE −1

mPa·s

η

T = 293.15 K 0.0000 5.348 0.1015 4.073 0.1419 3.136 0.1980 2.505 0.2315 2.118 0.2384 1.808 0.2444 1.580 0.2232 1.410 0.1823 1.293 0.1053 1.218 0.0000 1.145 T = 313.15 K 0.0000 2.912 0.1242 2.290 0.1885 1.857 0.2647 1.574 0.3102 1.372 0.3215 1.226 0.3295 1.106 0.3065 0.996 0.2573 0.927 0.1654 0.886 0.0000 0.847 T = 333.15 K 0.0000 1.744 0.1668 1.466 0.2674 1.240 0.3750 1.073 0.4441 0.955 0.4679 0.859 0.4888 0.801 0.4691 0.738 0.4150 0.699 0.2997 0.681 0.0000 0.651 T = 353.15 K 0.0000 1.125 0.2286 0.981 0.3808 0.855 0.5357 0.765 0.6382 0.696

cm ·mol 3

0.0000 −0.0832 −0.1496 −0.1789 −0.1875

0.0000 −0.1676 −0.2875 −0.3433 −0.3524 −0.3396 −0.2867 −0.2423 −0.1709 −0.0812 0.0000

0.0000 −0.4131 −0.6444 −0.7187 −0.7139 −0.6545 −0.5661 −0.4729 −0.3326 −0.1699 0.0000

0.0000 −0.8494 −1.3763 −1.5822 −1.5479 −1.4414 −1.2444 −1.0006 −0.6921 −0.3508 0.0000

mPa·s

Δη −3

0.76978 0.75596 0.74462 0.73431 0.72543

0.78572 0.77208 0.76084 0.75057 0.74170 0.73401 0.72699 0.72093 0.71539 0.71068 0.70695

0.80083 0.78739 0.77631 0.76614 0.75731 0.74963 0.74259 0.73650 0.73090 0.72605 0.72182

0.81532 0.80210 0.79120 0.78116 0.77240 0.76475 0.75773 0.75165 0.74602 0.74112 0.73664

g·cm

ρ VE

η mPa·s

T = 298.15 K 0.0000 4.555 0.1057 3.494 0.1507 2.719 0.2106 2.198 0.2467 1.886 0.2535 1.626 0.2596 1.432 0.2368 1.284 0.1939 1.182 0.1133 1.116 0.0000 1.062 T = 318.15 K 0.0000 2.538 0.1328 2.020 0.2049 1.664 0.2876 1.437 0.3382 1.245 0.3516 1.100 0.3612 1.008 0.3388 0.921 0.2884 0.861 0.1916 0.822 0.0000 0.790 T = 338.15 K 0.0000 1.553 0.1804 1.318 0.2926 1.124 0.4111 0.982 0.4855 0.878 0.5160 0.796 0.5399 0.744 0.5236 0.691 0.4688 0.656 0.3428 0.641 0.0000 0.615 T = 358.15 K 0.0000 1.018 0.2468 0.895 0.4152 0.787 0.5825 0.707 0.6975 0.649

cm ·mol−1 3

Table 6. Experimental Densities, Excess Volumes, Viscosities, and Viscosity Deviations for n-Undecane (1) + 1-Hexanol (2) at Pressure p = 0.1 MPaa Δη

0.0000 −0.0706 −0.1275 −0.1545 −0.1609

0.0000 −0.1402 −0.2429 −0.2894 −0.2993 −0.2888 −0.2455 −0.2065 −0.1464 −0.0689 0.0000

0.0000 −0.3409 −0.5262 −0.5764 −0.5933 −0.5647 −0.4804 −0.3954 −0.2790 −0.1444 0.0000

0.0000 −0.7081 −1.1413 −1.3100 −1.2721 −1.1848 −1.0262 −0.8306 −0.5787 −0.2987 0.0000

mPa·s



a

−1

−3

0.72598 0.71897 0.71294 0.70747 0.70287 0.69947 ρ

2691

VE −1

mPa·s

η

T = 348.15 K 0.6261 0.687 0.6617 0.652 0.6532 0.607 0.5932 0.580 0.4431 0.571 0.0000 0.549

cm ·mol 3

−1

0.0000 0.2686 0.4536 0.6350 0.7637 0.8340 0.8913 0.8887 0.8184 0.6147 0.0000

cm ·mol 3

−0.2154 −0.1793 −0.1549 −0.1108 −0.0498 0.0000 VE

mPa·s

Δη −3

VE −1

η

0.925 0.820 0.726 0.657 0.605 0.562 0.540 0.512 0.490 0.487 0.475

mPa·s

Δη

−0.1818 −0.1522 −0.1319 −0.0965 −0.0428 0.0000 mPa·s

mPa·s

η

T = 353.15 K 0.6898 0.642 0.7334 0.611 0.7238 0.572 0.6617 0.546 0.5001 0.540 0.0000 0.522

cm ·mol 3

T = 363.15 K

0.72190 0.71490 0.70890 0.70347 0.69894 0.69572

g·cm

ρ −3

0.71776 0.71079 0.70482 0.69943 0.69499 0.69196

g·cm

ρ VE

η mPa·s

0.0000 −0.0594 −0.1095 −0.1331 −0.1392 −0.1380 −0.1144 −0.0984 −0.0746 −0.0328 0.0000

mPa·s

T = 358.15 K 0.7602 0.600 0.8074 0.573 0.8022 0.540 0.7373 0.516 0.5554 0.512 0.0000 0.497 Δη

cm ·mol−1 3

Δη

−0.1573 −0.1319 −0.1138 −0.0850 −0.0372 0.0000

mPa·s

Standard uncertainties: ur(ρ) = 0.001, ur(η) = 0.005, u(x1) = 0.0002, u(VE) = 0.006 cm3·mol−1, u(Δη) = 0.01 mPa·s, u(T) = 0.01 K for density, u(T) = 0.05 K for viscosity, and u(p) = 10 kPa.

0.76564 0.75178 0.74043 0.73012 0.72124 0.71359 0.70664 0.70070 0.69537 0.69102 0.68818

−0.247 −0.209 −0.177 −0.126 −0.058 0.000

T = 343.15 K 0.5697 0.739 0.5980 0.695 0.5852 0.647 0.5278 0.616 0.3915 0.604 0.0000 0.580

−3

g·cm

ρ

0.0000 0.1011 0.1989 0.2998 0.4001 0.4994 0.6004 0.6989 0.8001 0.8991 1.0000

mPa·s

Δη

mPa·s

η

g·cm

0.73001 0.72300 0.71695 0.71144 0.70679 0.70322

0.4994 0.6004 0.6989 0.8001 0.8991 1.0000

VE

cm ·mol

3

x1

g·cm

−3

x1

ρ

Table 6. continued




Article

directly related to the kinematic viscosity. The relative standard uncertainty of the viscosity measurements is 0.005. Mixtures are prepared gravimetrically using an analytical balance (Ohaus model AS120S) with an accuracy of 0.1 mg. We have a standard uncertainty in the mole fraction of less than 0.0002. The calibration was performed by the manufacturer, and we have checked periodically the calibration by comparing the density of water with the densities from the reference standard equation of state of water developed by Pruss and Wagner.6 The agreement with the values from the equation of state is less than 0.00001 g·cm−3; therefore, we consider the calibration correct.

3. RESULTS AND DISCUSSION A comparison of the densities and viscosities of n-undecane to the literature data are in Table 2. Our experimental densities agree with the literature density values7−25 within an absolute average percentage deviation of 0.03, 0.03, 0.05, 0.05, and 0.04% for n-undecane, 1-propanol, 1-butanol, 1-pentanol, and 1-hexanol. Densities for the binary mixtures of n-undecane + 1-propanol, + 1-butanol, + 1-pentanol, and + 1-hexanol have been measured from 283.15 to 363.15 K over the whole composition range and atmospheric pressure. These densities are reported in Tables 3−6, respectively. We also present in the same tables the excess molar volume calculated from the densities using ⎛1 ⎛1 1⎞ 1⎞ V E = x1M1⎜⎜ − ⎟⎟ + x 2M 2⎜⎜ − ⎟⎟ ρ1 ⎠ ρ2 ⎠ ⎝ρ ⎝ρ

Figure 2. Viscosity deviations for n-undecane (1) + 1-propanol (2): ●, 283.15 K; ○, 293.15 K; ■, 298.15 K; □, 303.15 K; ▲, 313.15 K; △, 323.15 K; ▼, 333.15 K; ▽, 343.15 K; ◆, 353.15 K; ◇, 363.15 K.

(1)

where Mi is the molar mass and ρi is the density of components i, respectively; ρ is the density of the mixture; xi is the molar fraction; and i indicates species 1 or 2. Using a propagation error formula,26 the standard uncertainty in the excess molar volume is 0.006 cm3·mol−1. Figure 1 shows the excess molar volume for the mixtures at 298.15 and 363.15 K. The numerical value of excess

Figure 3. Viscosity deviations for n-undecane (1) + 1-hexanol (2): ●, 283.15 K; ○, 293.15 K; ■, 298.15 K; □, 303.15 K; ▲, 313.15 K; △, 323.15 K; ▼, 333.15 K; ▽, 343.15 K; ◆, 353.15 K; ◇, 363.15 K.

molar volume of the mixtures follow the order of 1-propanol > 1-butanol > 1-pentanol > 1-hexanol. The excess molar volume increases with temperature, and they are positive at all temperatures, compositions, and mixtures of this work. Our viscosity measurements for the pure substances agree with the literature values27−38 within an average absolute percentage deviation of 1.51, 0.733, 0.531, 0.703, and 1.073% for n-undecane, 1-propanol, 1-butanol, 1-pentanol, and 1-hexanol, respectively. This comparison of the viscosities of the pure components is shown in Table 2. Unfortunately, viscosities have not been measured for the binary mixtures considered in this work. Also, viscosity deviations are calculated from the experimental viscosity measurements using 2

Δη = η −

∑ xiηi i=1

(2)

where ηi is the dynamic viscosity; η is the dynamic viscosity of the mixture; and subscript i again denotes pure species. Viscosity deviations values are shown in Tables 3−6. In this work, the value of Δη is negative for all the mixtures. The excess molar volume is positive, and the positive deviations are negative due to breaking of the associative bonds of the molecules. Also, physical contribution from the dispersion interactions between two different molecules is weaker than those between two similar ones. This result is an expansion of the mixture therefore the excess molar volume is positive. The value of Δη is negative in the whole composition and temperature intervals. This is an indication of dispersion interactions.39 Figures 2 and 3

Figure 1. Excess molar volumes of n-undecane (1) mixtures at 298.15 K (a) and 363.15 K (b): ●, + 1-propanol (2); ■, + 1-butanol (2); ▲, + 1-pentanol (2); ▼, + 1-hexanol (2). 2692



Article

Table 7. Parameters for the Redlich−Kister Equation To Calculate Excess Molar Volumes σ

a2 system

T/K

a0

a1

n-undecane (1) + 1-propanol (2)

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

1.4941 1.5679 1.6578 1.7645 1.8916 2.0418 2.2156 2.4142 2.6362 2.9334 3.2183 3.5354 3.8880 4.2671 4.6815 5.1361 5.6164 1.2693 1.3336 1.4165 1.5153 1.6586 1.7971 1.9565 2.1362 2.3360 2.5620 2.8114 3.0854 3.3843 3.7135 4.0638 4.4492 4.8588 1.1218 1.1773 1.2434 1.3257 1.4222 1.5356 1.6658 1.8135 1.9770 2.1617 2.3672 2.5920 2.8412 3.1124 3.4054 3.7282 4.0719 0.8733 0.9171 0.9693 1.0312 1.1168 1.2066 1.3135 1.4353

0.1331 0.1444 0.1693 0.1593 0.1953 0.2369 0.2885 0.3415 0.4006 0.4631 0.5377 0.6191 0.7198 0.8087 0.9318 1.0425 1.1822 0.3717 0.3333 0.3452 0.3595 0.3735 0.3919 0.4241 0.4580 0.4999 0.5512 0.6128 0.6857 0.7666 0.8801 0.9881 1.1161 1.2689 0.4155 0.4078 0.4146 0.3688 0.3762 0.3892 0.4212 0.4520 0.4970 0.5508 0.6198 0.7004 0.8110 0.9044 1.0451 1.1941 1.3481 0.2159 0.2068 0.2045 0.2033 0.2051 0.2185 0.2473 0.2787

1-butanol (2)

1-pentanol (2)

1-hexanol (2)

2693

−3

cm·mol

0.9671 0.9449 0.9391 0.9521 0.9899 1.0463 1.1263 1.2246 1.3467 0.6772 0.7460 0.8256 0.9086 0.9921 1.1718 1.3074 1.5046 0.7616 0.7438 0.7252 0.7298 0.2466 0.2473 0.2610 0.2806 0.3310 0.3837 0.4416 0.5559 0.6795 0.7571 0.9219 1.0985 1.2569 0.2340 0.2027 0.1986 0.2071 0.2375 0.2940 0.3771 0.4812 0.6067 0.7585 0.9223 1.1134 1.3168 1.5278 1.7514 1.9846 2.2072 0.2518 0.2108 0.2020 0.2089 0.0630 0.0962 0.1404 0.1789

a3

a4

0.1453 0.1983 0.2752 0.3716 0.5001 0.6568 0.8454 1.0343 1.2444 1.4054 1.6670 1.8277 2.0505 2.1730

1.5330 1.7057 1.9067 2.1177 2.3539 2.4478 2.5914 2.6687

0.1262 0.1356 0.1732 0.2465 0.3515 0.4632 0.6150 0.7781 0.9610 1.1593 1.3616 1.5900 1.7702 1.9665 2.1656 2.2876

0.9588 1.0506 1.1597 1.3036 1.4289 1.5995 1.7943 1.9288 2.0897 2.3163 2.4252 2.5209 2.6500

0.1874 0.2546 0.3471 0.4495 0.5845 0.7246 0.8989 1.0651 1.2534 1.4193 1.6507 1.7920 1.9793 2.1483 −0.2340 −0.2099 −0.1864 −0.1431 −0.0644 0.0360 0.1359 0.2729

0.3184 0.3627 0.4256 0.5343

cm·mol−3 0.0072 0.0073 0.0073 0.0078 0.0080 0.0086 0.0094 0.0105 0.0116 0.0077 0.0082 0.0083 0.0092 0.0097 0.0092 0.0101 0.0093 0.0074 0.0072 0.0070 0.0072 0.0040 0.0039 0.0040 0.0042 0.0042 0.0045 0.0050 0.0054 0.0062 0.0056 0.0065 0.0074 0.0064 0.0062 0.0061 0.0062 0.0064 0.0066 0.0070 0.0074 0.0082 0.0089 0.0096 0.0107 0.0115 0.0130 0.0132 0.0143 0.0154 0.0154 0.0054 0.0059 0.0060 0.0062 0.0062 0.0061 0.0060 0.0060



Article

Table 7. continued σ

a2 system

−3

T/K

a0

a1

323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15

1.5727 1.7293 1.9096 2.0996 2.3145 2.5442 2.8035 3.0788 3.3801

0.3311 0.3856 0.4514 0.5341 0.6427 0.7728 0.8904 1.0480 1.2287

a4

cm·mol−3

0.6060 0.7733 0.9980 1.0881 1.2804 1.3829 1.6290 1.7394 1.8133

0.0060 0.0060 0.0064 0.0063 0.0062 0.0067 0.0074 0.0064 0.0070

a3

cm·mol

0.2598 0.3216 0.3589 0.4910 0.5800 0.7374 0.8080 0.9472 1.1265

0.4060 0.5800 0.7748 0.9617 1.1452 1.3171 1.5489 1.7062 1.8265

Table 8. Parameters for the Redlich−Kister Equation To Calculate Viscosity Deviations σ

a1 system

T/K

a0

mPa·s

a2

mPa·s

n-undecane (1) + 1-propanol (2)

283.15

−2.0623

0.8026

−0.7632

0.0114

1-butanol (2)

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15

−1.7573 −1.5162 −1.3029 −1.1372 −1.0072 −0.8762 −0.7648 −0.6861 −0.5924 −0.5175 −0.4522 −0.4100 −0.3560 −0.3125 −0.2746 −0.2443 −3.8911 −3.3193 −2.7258 −2.2719 −1.9561 −1.6892 −1.4580 −1.2485 −1.1069 −0.9580 −0.8317 −0.7221 −0.6318 −0.5416 −0.4667 −0.4059 −0.3544

0.6381 0.5446 0.4076 0.3352 0.3192 0.2710 0.2313 0.2379 0.2089 0.1733 0.1433 0.1487 0.1248 0.1002 0.0829 0.0650 2.1374 1.8323 1.3819 1.0173 0.9003 0.7801 0.6752 0.5872 0.5464 0.4738 0.3972 0.3402 0.2978 0.2451 0.1948 0.1557 0.1190

−0.6214 −0.5263 −0.4579 −0.3512 −0.3579 −0.3193 −0.2815 −0.3012 −0.2589 −0.2336 −0.2089 −0.2190 −0.1955 −0.1814 −0.1657 −0.1566 −1.4530 −1.2234 −0.7718 −0.5111 −0.4746 −0.4210 −0.3835 −0.3955 −0.3640 −0.3290 −0.2859 −0.2603 −0.2421 −0.2055 −0.1719 −0.1443 −0.1287

0.0113 0.0103 0.0072 0.0041 0.0041 0.0034 0.0026 0.0015 0.0012 0.0008 0.0007 0.0012 0.0009 0.0007 0.0006 0.0005 0.0302 0.0251 0.0143 0.0066 0.0040 0.0035 0.0027 0.0032 0.0027 0.0026 0.0015 0.0016 0.0016 0.0012 0.0007 0.0008 0.0007

system 1-pentanol (2)

1-hexanol (2)

i

i=0

a0

mPa·s

a2

mPa·s

−6.0071 −5.0116 −4.1520 −3.4506 −2.8565 −2.4829 −2.1056 −1.7888 −1.5129 −1.2956 −1.1089 −0.9469 −0.8060 −0.6885 −0.5903 −0.5063 −0.4352 −8.8965 −7.1603 −5.7989 −4.7697 −3.9174 −3.2262 −2.6378 −2.2201 −1.8706 −1.5844 −1.3494 −1.1490 −0.9804 −0.8417 −0.7212 −0.6231 −0.5420

2.6071 2.2808 2.0090 1.7732 1.4362 1.1810 1.0264 0.8768 0.7958 0.6626 0.5707 0.4978 0.4367 0.3877 0.3360 0.2933 0.2600 5.0118 4.1907 3.4776 2.8571 2.3784 1.9430 1.5844 1.2334 0.9388 0.7881 0.6131 0.5056 0.4169 0.4142 0.2880 0.2386 0.1980

−0.2195 −0.1647 −0.2305 −0.3296 −0.6091 −0.3927 −0.3670 −0.3307 −0.4344 −0.2704 −0.2513 −0.2300 −0.2108 −0.1958 −0.1838 −0.1535 −0.1540 −1.3028 −1.5459 −1.6433 −1.5271 −1.3378 −1.1628 −1.0566 −0.7395 −0.4269 −0.3182 −0.1477 −0.1063 −0.0724 −0.2147 −0.0515 −0.0394 −0.0210

0.0157 0.0175 0.0149 0.0153 0.0183 0.0033 0.0025 0.0029 0.0077 0.0026 0.0025 0.0024 0.0024 0.0025 0.0028 0.0032 0.0032 0.0262 0.0205 0.0192 0.0168 0.0139 0.0112 0.0093 0.0099 0.0081 0.0058 0.0058 0.0050 0.0045 0.0064 0.0047 0.0043 0.0040

⎡ ∑N (Y E,exp − Y E,calc)2 ⎤1/2 i i ⎥ σ = ⎢ i=1 ⎢⎣ ⎥⎦ N−n

n

Y = x1x 2 ∑ ai(x1 − x 2)

T/K 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15

where YE are either VE or Δη, n is the number of estimated parameters, and the ai’s are the adjusting coefficients of the Redlich− Kister polynomial. These coefficients are obtained by optimizing eq 3 using a least-squares technique. Parameter values are shown in Tables 7 and 8 together with the standard deviation calculated by

show the values of the viscosity deviations for the mixtures undecane + 1-propanol and + 1-hexanol, respectively. The absolute value of Δη decreases as the temperature increases for all the systems, as shown in Figures 2 and 3. The composition dependency of derived quantities is expressed using a Redlich− Kister equation E

σ

a1

(3) 2694

(4)



Article

where σ is the standard deviation; N is the number of experimental data; and n is the number of parameters. The superscripts, exp and calc, indicate experimental and calculated values, respectively. Nava-Rios et al.5 developed an equation to correlate the kinematic viscosity of binary mixtures. The equation is based upon assuming a quadratic mixing rule for the Gibbs energy of activation. Then ln νm = −ln(M mix ) + x1 ln ν1 + x1 ln(M1) + x 2 ln ν2 ⎡ * + x 2 ln(M 2) + x1x 2⎢ln(δν12) + x13 ln δg12 ⎢⎣ ⎛ M 3 ⎞⎤ ⎛ M3 ⎞ * + x1 ln⎜ 112 ⎟ + x 2 ln⎜ 122 ⎟⎥ + x 23 ln δg21 2 2 ⎝ M1M 2 ⎠⎥⎦ ⎝ M1 M 2 ⎠

Figure 4. Percentage deviations of experimental kinematic viscosities ́ et al.5 of n-undecane (1) + 1 alcohol (2) mixtures from Nava-Rios model: ●, + 1-propanol (2); ■, + 1-butanol (2); ▲,+ 1-pentanol (2); ▼, + 1 hexanol (2).

(5)

Table 9. Correlated McAllister Equation Parameters AAPD system

T/K

v12

v21

%

undecane (1) + 1-propanol (2)

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15

1.7777 1.616 1.4824 1.3494 1.2431 1.1591 1.0794 1.0083 0.9537 0.8998 0.8461 0.7981 0.7615 0.7231 0.6856 0.6535 0.6223 1.8664 1.7063 1.5426 1.3911 1.2956 1.2055 1.1259 1.0593 1.0002 0.9407 0.8829 0.8339 0.7901 0.7487 0.7086 0.6723 0.6378 1.6958 1.6019 1.5372 1.4783 1.3682 1.2393 1.1712

2.3100 2.0993 1.8921 1.7282 1.5780 1.4235 1.3036 1.1970 1.0856 1.0045 0.9355 0.8742 0.8064 0.7592 0.7181 0.6801 0.6471 2.3586 2.0943 1.9290 1.7826 1.5946 1.4423 1.3116 1.1981 1.0862 1.0023 0.9334 0.8684 0.8096 0.7634 0.7242 0.6877 0.6562 3.0800 2.6646 2.3205 2.0359 1.8385 1.6609 1.4928

0.425 0.417 0.390 0.370 0.252 0.341 0.339 0.320 0.389 0.360 0.366 0.363 0.449 0.445 0.456 0.451 0.467 0.541 0.490 0.305 0.184 0.119 0.101 0.125 0.269 0.264 0.293 0.323 0.349 0.379 0.373 0.353 0.333 0.337 1.274 1.341 1.200 1.154 0.686 0.427 0.346

1-butanol (2)

1-pentanol (2)

2695

bias −2

mm·s

−0.107 −0.098 −0.090 −0.102 −0.071 −0.091 −0.092 −0.089 −0.117 −0.107 −0.108 −0.108 −0.136 −0.131 −0.135 −0.134 −0.139 −0.109 −0.096 −0.024 0.002 −0.011 −0.019 −0.032 −0.067 −0.083 −0.083 −0.083 −0.092 −0.102 −0.094 −0.088 −0.078 −0.081 0.347 0.324 0.259 0.164 0.021 0.079 0.063

σ mm·s

max −2

0.015 0.014 0.012 0.010 0.006 0.007 0.006 0.005 0.006 0.005 0.005 0.005 0.005 0.005 0.005 0.004 0.004 0.029 0.024 0.012 0.005 0.003 0.002 0.003 0.005 0.005 0.005 0.004 0.004 0.005 0.004 0.004 0.003 0.003 0.045 0.045 0.038 0.032 0.019 0.010 0.008

% 1.100 1.135 1.099 1.023 0.629 0.778 0.846 0.830 1.064 0.972 1.021 1.008 1.114 1.031 1.038 1.002 1.055 1.809 1.697 0.890 0.406 0.224 0.323 0.491 1.043 1.006 0.818 0.912 0.953 0.909 0.814 0.828 0.718 0.788 2.908 3.420 3.037 2.745 2.206 0.919 0.796



Article

Table 9. continued AAPD system

1-hexanol (2)

T/K

v12

v21

%

318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15

1.1032 1.0568 0.9918 0.9389 0.8943 0.8547 0.8187 0.7807 0.7479 0.7177 1.9378 1.8624 1.7682 1.6378 1.5392 1.4338 1.3501 1.2296 1.1286 1.0617 0.9839 0.9269 0.8753 0.8494 0.7856 0.7458 0.7100

1.3570 1.2159 1.1316 1.0427 0.9634 0.8944 0.8322 0.7802 0.7349 0.6915 3.4919 2.9775 2.5802 2.2705 2.0126 1.8130 1.6503 1.5343 1.4486 1.3312 1.2495 1.1571 1.0764 0.9696 0.9355 0.8767 0.8241

0.295 0.328 0.236 0.244 0.245 0.265 0.275 0.306 0.376 0.404 1.512 0.935 0.532 0.586 0.589 0.596 0.705 0.499 0.392 0.353 0.497 0.456 0.460 0.570 0.527 0.499 0.505

σ

bias −2

mm·s

mm·s

0.044 −0.056 0.020 0.000 −0.011 −0.021 −0.029 −0.040 −0.030 −0.052 0.455 0.268 0.112 0.005 −0.031 −0.071 −0.135 −0.086 0.005 0.037 0.115 0.115 0.114 −0.024 0.095 0.089 0.090

max −2

%

0.007 0.008 0.005 0.004 0.004 0.004 0.004 0.004 0.005 0.005 0.066 0.044 0.029 0.024 0.019 0.016 0.016 0.011 0.008 0.006 0.009 0.008 0.007 0.008 0.007 0.006 0.006

0.736 0.960 0.689 0.737 0.774 0.846 0.909 0.973 1.157 1.199 3.301 2.487 1.370 1.367 0.949 1.107 1.633 1.014 0.762 1.006 1.357 1.367 1.443 1.014 1.333 1.281 1.164

Table 10. Correlated Nava-Rios et al.5 Equation Parameters AAPD system

T/K

v12

δg12

δg21

%

undecane (1) + 1-propanol (2)

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

0.5593 0.5744 0.5817 0.5912 0.5893 0.6004 0.6144 0.6274 0.6418 0.6626 0.6821 0.7026 0.7208 0.7471 0.7727 0.7977 0.8215 0.3726 0.3772 0.3831 0.3899 0.4008 0.4130 0.4288 0.4591 0.4656 0.4876 0.5055

0.7115 0.7100 0.7332 0.7006 0.7473 0.7433 0.7474 0.7582 0.7538 0.7810 0.7732 0.7700 0.7626 0.7637 0.7442 0.7403 0.7195 0.8731 0.9274 1.0454 1.0479 1.0723 1.0797 1.0702 0.9969 1.0387 1.0254 1.0089

0.8810 0.9103 0.9178 0.9480 1.0154 0.9387 0.9319 0.9307 0.8318 0.8364 0.8396 0.8461 0.7663 0.7764 0.7838 0.7927 0.8001 0.6661 0.6667 0.8294 0.9734 0.9207 0.8901 0.8550 0.7722 0.7303 0.7085 0.7180

0.316 0.330 0.322 0.247 0.141 0.152 0.153 0.131 0.057 0.065 0.076 0.073 0.082 0.071 0.061 0.057 0.057 0.608 0.562 0.349 0.176 0.125 0.100 0.108 0.218 0.180 0.131 0.147

1-butanol (2)

2696

σ

bias −2

mm·s

0.007 0.006 0.003 −0.004 −0.005 −0.005 −0.007 −0.006 −0.006 −0.005 −0.005 −0.005 −0.006 −0.004 −0.003 −0.003 −0.002 0.020 0.016 0.006 −0.005 −0.007 −0.009 −0.011 −0.005 −0.019 −0.009 −0.008

max −2

mm·s

0.010 0.010 0.009 0.007 0.004 0.004 0.003 0.002 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.022 0.018 0.010 0.005 0.003 0.002 0.002 0.004 0.003 0.002 0.002

% 0.597 0.850 1.020 0.764 0.520 0.624 0.587 0.454 0.178 0.177 0.219 0.217 0.168 0.136 0.209 0.184 0.181 1.177 1.066 0.741 0.404 0.244 0.291 0.367 0.681 0.552 0.299 0.382



Article

Table 10. continued AAPD system

1-pentanol (2)

1-hexanol (2)

T/K

v12

δg12

δg21

%

338.15 343.15 348.15 353.15 358.15 363.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15

0.5282 0.5510 0.5783 0.6031 0.6254 0.6509 0.2319 0.2393 0.2602 0.2838 0.3367 0.3290 0.3487 0.3698 0.4153 0.4171 0.4415 0.4681 0.4988 0.5298 0.5605 0.5857 0.6206 0.2018 0.2387 0.2826 0.3072 0.3364 0.3689 0.4163 0.4259 0.4299 0.4445 0.4418 0.4611 0.4818 0.5411 0.5252 0.5446 0.5586

0.9855 0.9652 0.9577 0.9419 0.9344 0.8962 1.4920 1.7762 1.9173 1.9353 1.2828 1.3462 1.3538 1.3339 1.1455 1.3338 1.2920 1.2776 1.2631 1.2524 1.2066 1.2273 1.1704 2.2905 1.9367 1.5304 1.3243 1.2766 1.1667 1.0306 1.0387 1.1433 1.2259 1.3663 1.3531 1.3399 1.1007 1.2684 1.2449 1.2487

0.7029 0.6825 0.7012 0.7353 0.7684 0.7930 2.0965 1.9669 1.6849 1.4101 1.0473 1.1372 1.0430 0.9827 0.7460 0.8702 0.8251 0.7849 0.7464 0.7087 0.6837 0.6908 0.6514 1.8927 1.3522 0.9799 0.8421 0.7448 0.6807 0.6040 0.6860 0.8508 0.8835 1.0703 1.0725 1.0772 0.7602 1.0492 1.0485 1.0682

0.135 0.095 0.094 0.108 0.122 0.129 0.478 0.607 0.684 0.796 0.704 0.269 0.272 0.309 0.302 0.305 0.306 0.299 0.284 0.277 0.295 0.357 0.380 0.772 0.760 0.626 0.661 0.572 0.497 0.500 0.351 0.381 0.339 0.456 0.410 0.414 0.523 0.472 0.458 0.458

where x1 and x2 are the mole fraction compositions of species 1 and 2; M1 and M2 are the molecular weight of species 1 and 2; and * , and δg21 * are temperature-dependent characteristic paramδv12, δg12 eters available from experimental measurements. These parameters are related to an activation energy difference; therefore, they are expressed with a delta. In eq 5, Mijk = (Mi + Mj + Mk)/3. Figure 4 shows the correlation capability of eq 5. Another common equation for the correlation of the kinematic viscosity is the McAllister equation.4 He assumes that three-body interactions exist for binary mixtures and that all occur in a plane. In the equation the rate of each individual interaction is proportional to the energy of activation, and then the logarithm of the kinematic viscosity is ln ν =

x13

ln ν1 +

3x12x 2

ln ν12 +

− ln[x1M1 + x 2M 2 /M1]+

3x1x 22 3x12x 2

ln ν21 +

x 23

σ

bias −2

mm·s

−0.008 −0.005 −0.002 −0.002 0.000 0.000 −0.015 −0.040 −0.060 −0.089 −0.043 −0.024 −0.017 −0.016 −0.018 −0.010 −0.010 −0.007 −0.004 0.002 0.007 0.011 0.013 −0.067 −0.042 −0.003 −0.009 0.001 0.010 0.013 0.011 0.010 0.014 0.017 0.019 0.021 0.019 0.024 0.024 0.024

max −2

mm·s

0.002 0.001 0.001 0.001 0.001 0.001 0.022 0.023 0.019 0.021 0.018 0.006 0.005 0.006 0.008 0.005 0.005 0.005 0.004 0.004 0.004 0.005 0.005 0.032 0.030 0.027 0.025 0.020 0.015 0.012 0.009 0.008 0.006 0.008 0.007 0.006 0.007 0.006 0.006 0.006

% 0.349 0.229 0.204 0.246 0.242 0.238 1.154 1.710 1.740 2.970 2.479 0.852 0.621 0.584 1.062 0.742 0.826 0.891 0.985 1.066 1.137 1.315 1.361 2.359 1.785 1.237 1.429 1.090 0.918 0.941 0.770 0.737 0.862 1.303 1.077 1.131 1.211 1.341 1.226 1.247

where x1 and x2 are the mole fraction composition of species 1 and 2; M1 and M2 are the molecular weight of species 1 and 2; and v12 and v21 are temperature-dependent parameters that can be found from experimental kinematic viscosity measurements. Tables 9 and 10 show the parameters for eqs 6 and 5 together with the average absolute percentage deviation (AAPD) defined as N

AAPD =

100∑i = 1 |(νiexp − νieqn)/νiexp| (7)

N

the bias calculated as bias =

ln ν2

ln[(2 + M 2 /M1)/3]

100 N

npts

∑ (νiexp − νieqn)/νiexp i=1

(8)

and the maximum absolute percentage deviation

+ 3x1x 22 ln[(1 + 2M 2 /M1)/3] + x 23 ln(M 2 /M1)

max = max[100|(νiexp − νieqn)/νiexp|]

(6) 2697

(9)



Article

eqn where vexp are the experimental and calculated from the i and vi equation kinematic viscosities; N is the number of data points. In these models all of the parameters are statistically valid within 95% confidence limits. Equations 5 and 6 correlate the kinematic viscosity within an average absolute percentage deviation of 0.142, 0.199, 0.407, and 0.509% and 0.388, 0.302, 0.553, and 0.6% for the n-undecane + 1-propanol, + 1-butanol, + 1-pentanol, and + 1-hexanol mixtures, respectively, as shown in Tables 9 and 10. Equation 5 correlates better the kinematic viscosity data than the McAllister equation.

Viscosities of Multicomponent Mixtures. Fluid Phase Equilib. 2012, 329, 8−21. (6) Wagner, W.; Pruss, A. The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use. J. Phys. Chem. Ref. Data 2002, 31, 387−535. (7) García, M.; Rey, C.; Pérez-Villar, V.; Rodríguez, J. R. Excess Volumes of (n-Heptane + n-Undecane) between 288.15 to 308.15 K. J. Chem. Thermodyn. 1986, 18, 551−554. (8) Camin, D. L.; Rossini, F. D. Physical Properties of Fourteen API Research Hydrocarbons, C 9 to C 15. J. Phys. Chem. 1955, 59, 1173− 1179. (9) Wu, J.; Asfour, A. A. Composition Dependence of Densities and Excess Molar Volumes of Mixing of C8-C15 n-Alkane Binary Liquid Systems at 308.15 and 315.15 K. Fluid Phase Equilib. 1991, 61, 275− 284. (10) Dixon, J. A. Binary Solutions of Saturated Hydrocarbons. J. Chem. Eng. Data 1959, 4, 289−294. (11) Schmidt, A. W.; Schoeller, V.; Eberlein, K. Ü ber Physikalische Daten von 1-Olefinen und n-Paraffinen. Ber. Dtsch. Chem. Ges. B 1941, 74, 1313−1324. (12) Dornte, R. W.; Smyth, C. P. The Dielectric Polarization of Liquids. X. The Polarization and Refraction of the Normal Paraffins. J. Am. Chem. Soc. 1930, 52, 3546−3552. (13) Westmeier, S. Exzessenthalpie, Freie Exzessenthalpie, Exzessvolumen und Viskosität von ausgewählten binären flüssigen Mischungen Teil III. Das Wasser -n-Propanol und Wasser - Isopropanol Systeme. Chem. Technol. (Leipzig) 1976, 28, 480−483. (14) Kretschmer, C. B. The Thermal Expansion of Water and 1Propanol. J. Phys. Chem. 1951, 55, 1351−1355. (15) Costello, J. M.; Bowden, S. T. The Temperature Variation of Orthobaric Density Difference in Liquid-Vapor Systems III. Alcohols. Recl. Trav. Chim. Pays-Bas 1958, 77, 36−48. (16) Zhuravlev, V. I.; Durov, V. A.; Usacheva, T. M.; Shakhparonov, M. I. Dielectric-Properties of 1, 3-Propanediol and Its Binary-Solutions with Normal-Propanol. 1. Dielectric Radiospectra. Zh. Fiz. Khim. 1985, 59, 1677−1682. (17) Smyth, C. P.; Stoops, W. N. The Dielectric Polarization of Liquids VI. Ethyl iodide, Ethanol Normal-Butanol and NormalOctanol. J. Am. Chem. Soc. 1929, 51, 3312−3329. (18) Troncoso, J.; Tovar, C. A.; Cerdeirina, C. A.; Carballo, E.; Romani, L. Temperature Dependence of Densities and Speed of Sound of Nitromethane + Butanol Isomers in the Range (288.15− 308.15) K. J. Chem. Eng. Data 2001, 46, 312−316. (19) Ling, T.; Van Winkle, M. Properties of Binary Mixtures as a Function of Composition. Chem. Eng. Data Ser. 1958, 3, 88−95. (20) Rahman, M. S.; Saleh, M. A.; Chowdhury, F. I.; Ahmed, M. S.; Rocky, M. M. H.; Akhtar, S. Density and Viscosity for the Solutions of 1-Butanol with Nitromethane and Acetonitrile at 303.15 to 323.15 K. J. Mol. Liq. 2014, 190, 208−214. (21) Khimenko, M. T.; Aleksandrov, V. V.; Gritsenko, N. N. Polarizabilities and Molecular Radii of Some Pure Liquids. Zh. Fiz. Khim. 1973, 47, 2914−2915. (22) Radovic, I. R.; Kijevcanin, M. L.; Djordjevic, E. M.; Djordjevic, B. D.; Serbanovic, S. P. Influence of Chain Length and Degree of Branching of Alcohol + Chlorobenzene Mixtures on Determination and Modeling of VE by CEOS and CEOS/GE Mixing Rules. Fluid Phase Equilib. 2008, 263, 205−213. (23) Garg, S. K.; Banipal, T. S.; Ahluwalia, J. C. Densities, Molar Volumes, Cubic Expansion Coefficients, and Isothermal Compressibilities of 1-Alkanols from 323.15 to 373.15 K and at pressures up to 10 MPa. J. Chem. Eng. Data 1993, 38, 227−230. (24) Hovorka, F.; Lankelma, H. P.; Stanford, S. C. Thermodynamic Properties of the Hexyl Alcohols II. Hexanols-1, −2 and −3 and 2Methyl-Pentanol-1 and −4. J. Am. Chem. Soc. 1938, 60, 820−827. (25) Fukuchi, K.; Ogiwara, K.; Tashima, Y.; Yonezawa, S.; Arai, Y. Measurement and Correlation of Densities for Liquids and Their Mixtures. Ube Kogyo Koto Senmon Gakko Kenkyu Hokoku 1983, 29, 93−111.

4. CONCLUSIONS In this work we have measured densities and viscosities for n-undecane + 1-alcohols mixtures from 283.15 to 363.15 K at atmospheric pressure. Our experimental results agree with the literature values within an average absolute percentage deviation of 0.05 and 1.6% for the density and viscosity, respectively. Excess molar volumes and viscosities deviations have been correlated a Redlich−Kister equation. We have tested the correlative capability of two common equations. The model developed by Navas-Rios et al.5 correlates the viscosity within an average absolute percentage error of 0.31%, while the McAllister model4 correlates within 0.46%.

■

AUTHOR INFORMATION

Corresponding Author

*Tel.: 011 52 461 611 7575; fax: 011 52 461 611 7744. E-mail address: [email protected]. Funding

The authors want to thank Consejo Nacional de Ciencia y Tecnologiá (CONACyT) for providing financial support for this work through project CB-2012-177920. Notes

The authors declare no competing financial interest.

■

DEDICATION I (G.A.I.-S.) am fortunate to have met in my life with Ken. This event became one of the highlights of my life. As a graduate student, he taught me the first steps in my scientific and academic career. After our first meeting at Texas A&M, I felt his passion for thermodynamics, and immediately I wanted to be part of it. Our interaction has become me a better person, engineer, and scientist. He has always been available to give an advice either professional or personal. From Ken I have learnt to enjoy doing research, and it is better when it is done together with a friend.

■

REFERENCES

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