Article pubs.acs.org/jced
Volumetric and Transport Properties of Binary Mixtures of n‑Octane + Ethanol, + 1‑Propanol, + 1‑Butanol, and + 1‑Pentanol from (293.15 to 323.15) K at Atmospheric Pressure A. Estrada-Baltazar,* G. A. Iglesias-Silva, and C. Caballero-Cerón Departamento de Ingeniería Química, Instituto Tecnológico de Celaya, CP 38010, Celaya, Guanajuato, México ABSTRACT: We present densities and dynamic viscosities of binary mixtures of n-octane with ethanol, 1-propanol, 1-butanol, and 1-pentanol. Measurements are performed at atmospheric pressure from (293.15 to 323.15) K using a vibrating-tube densimeter and three Cannon−Fenske viscosimeters. We have calculated the excess molar volumes and the viscosity deviations from the experimental measurements. Results have been correlated to Redlich−Kister type equations.
1. INTRODUCTION Complete knowledge of different thermodynamic and transport properties of liquid systems are of great importance in industrial applications. These properties are necessary in numerous engineering calculations from scaling processes and dimensions of equipment for their simulation and optimization. Mixtures of n-alkanes + n-alcohols are important in the chemical industry. Numerous investigations have been done in which the authors try to explain the way in which the alcohol structure is modified with the addition of n-alkanes.1−8 This modification has been related to the partial destruction of the structure formed by the hydrogen bonding of the pure 1-alcohol during the mixing process with an n-alkane bringing a high degree of nonrandomness to the mixture.9 Excess molar properties (volume, enthalpy, Gibbs energy, speed of sound) and viscosity deviations provide information about the intermolecular interaction. Previously, several researchers have measured the thermodynamic properties of n-alkane + 1-alcohol binary mixtures. Treszczanowicz et al.10 and Handa and Benson11 show excellent revisions about the excess molar volume of these mixtures. With the experimental information, several liquid theories, correlations, or models have been developed in the past, for example, group contribution methods,12−16 association models17−22 among others. Liquid viscosities of these mixtures have been measured before.23−36 However, experimental measurements of this transport property are scarce in comparison with other measured properties. In particular, different thermodynamic properties for the binary mixtures of n-octane with ethanol, 1-propanol, 1-butanol, and 1-pentanol have been reported in the literature at various temperatures. Densities for n-octane + ethanol have been measured at 298.15 K by Segade et al.37 and Orge et al.23 Later, Orge et al.38 measured the densities at a wider temperature interval © 2013 American Chemical Society
Table 1. Sample Information
a
chemical name
source
n-octane ethanol 1-propanol 1-butanol 1-pentanol
Sigma Aldrich J. T. Baker Sigma Aldrich Sigma Aldrich Sigma Aldrich
initial purity purification analysis CAS No. molar fraction method method 111-65-9 64-17-5 71-23-8 71-36-3 71-41-0
0.998 0.999 0.998 0.998 0.999
none none none none none
GCa GCa GCa GCa GCa
Gas chromatography.
from (303.15 to 318.15) K. Feitosa et al.24 measured them from (273.15 to 298.15) K with increments of 2.5 K. Density measurements for n-octane + 1-propanol at 298.15 K have been reported by Kaur et al.,39 Iglesias et al.,40 Orge et al.,23 and Mato et al.41 Gupta et al.42 measured the excess molar volume of this mixture at 303.15 K. Measurements from (293.15 to 308.15) K were performed by Jiménez et al.25,43 Densities for the system n-octane + 1-butanol have been measured by Nath44 at 293.15 K, by Gupta et al.42 at 303 K, by Nath and Pandey45 at (288.15 and 298.15) K, by De Cominges et al.46 from (288.15 to 308.15) K, and by Dubey et al.26 from (298.15 to 308.15) K. Also, different authors have measured the density of this mixture at 298.15 K.27,28,39,40,47−49 For the mixture of n-octane + 1-pentanol, several authors39,40,45,50,51 have measured the liquid density at 298.15 K. Gupta et al.42 report the excess molar volume for the same mixture at 303.15 K. Experimental measurements of viscosities of n-octane + ethanol have been reported by Orge et al.23 at 298.15 K. However, Feitosa et al.24 reported viscosity measurements at Received: May 17, 2013 Accepted: November 6, 2013 Published: November 22, 2013 3351
dx.doi.org/10.1021/je4004806 | J. Chem. Eng. Data 2013, 58, 3351−3363
Journal of Chemical & Engineering Data
Article
Table 2. Comparison of Densities and Viscosities of Pure Components of This Work with Literature Values.a 10−3 ρ/kg·m−3 compound n-octane
ethanol
1-propanol
T/K
exp.
293.15
0.70254
298.15
0.69849
303.15
0.69444
308.15
0.69037
313.15
10−3 ρ/kg·m−3
η/mPa·s
lit.
exp. 52
lit.
compound
25
exp.
η/mPa·s
lit.
exp.
lit.
0.8098 0.80966054 0.8096555 0.806053 0.80584554 0.8058455 0.802153 0.80200454 0.8020055 0.798253 0.79813354 0.7981255 0.794353 0.79422254
2.968
3.010053 2.93754 2.980055 2.606253 2.56954 2.606255 2.314753 2.26054 2.289455 2.065553 1.99854 2.018355 1.847653 1.78454 1.76856 1.659753 1.62558 1.495253 4.045755
53
0.545
0.537 0.543959
0.513
0.49925 0.517759
0.80570
0.485
0.47625 0.479559
0.80186
0.459
0.45325 0.435859
0.79799
0.68629
0.70235 0.7025525 0.702559 0.6983452 0.6985225 0.698559 0.6943052 0.6944225 0.694559 0.6902452 0.6904225 0.686359 0.6861752
0.433
0.79410
318.15
0.68219
0.6820652
0.412
0.79018
0.790453
1.596
323.15 293.15
0.67808 0.79091
0.392 1.204
0.78621 0.81459
0.786453 0.8144155 0.81463557
1.414 4.042
298.15
0.78660
0.81093
0.78228
308.15
0.77794
313.15
0.77356
0.8107955 0.810956 0.81096857 0.8071055 0.807756 0.80727857 0.8033855 0.804756 0.80355857 0.800956 0.79981757
3.518
303.15
318.15 323.15
0.76915 0.76469
0.6779452 0.789053 0.78938654 0.7895255 0.785553 0.78509654 0.7852755 0.780353 0.78077954 0.7809555 0.776053 0.77643154 0.7766055 0.772053 0.77204454 0.767453 0.763053
293.15
0.80384
2.210
298.15
0.79985
303.15
0.79581
308.15
0.79174
313.15
0.78764
0.8037125 0.803653 0.80351654 0.7995225 0.799653 0.79950654 0.7957025 0.795653 0.79547654 0.7917225 0.791553 0.79140654 0.787453 0.78729654
318.15
0.78355
0.783353
1.242
323.15
0.77932
0.779153
1.115
1.093
0.997
0.910
0.835 0.762 0.698
1.962
1.746
1.556
1.386
53
1-butanol
1.1617 1.20554 1.198855 1.056953 1.09354 1.085955 0.964553 0.99454 0.9885555 0.882753 0.90754 0.9037155 0.810053 0.83454 0.745153 0.686853
1-pentanol
0.80953
0.80724
0.80353
0.79979 0.79603 0.79223 0.80953
2.602
2.292
2.025
1.796
3.060
2.659
2.334 2.042 1.805
3.498855 3.47156 3.50458 3.036755 3.01756 2.646955 2.63956 2.65758 2.31656 2.04658
2.12525 2.410453 2.19754 1.89825 2.117853 1.94754 1.72725 1.874253 1.72654 1.53125 1.670953 1.54254 1.523753 1.37954 1.34256 1.383353 1.29558 1.256053
Standard uncertainty in the density measurement = 3·10−2 kg·m−3, standard uncertainty in the viscosity measurement = 0.004 mPa·s, and standard uncertainty in the temperature measurement = 0.01 K.
a
temperatures from (273.15 to 298.15) K with increments of 2.5 K. Viscosities for n-octane + 1-propanol have been measured at 298.15 K by Orge et al.23 Also, Jiménez et al.25
measured the viscosities of this mixture from (293.15 to 308.15) K. Viscosity measurements for n-octane + 1-butanol have been carried out at 298.15 by several researchers.26−28 3352
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Table 3. Experimental Densities and Excess Molar Volumes for n-Octane (1) + Ethanol (2)a 10−3 ρ/kg·m−3 x1
T/K = 293.15
T/K = 298.15
T/K = 303.15
1.0000 0.9031 0.7931 0.6991 0.6008 0.4663 0.4008 0.2998 0.2015 0.1008 0.0000
0.70254 0.70473 0.70831 0.71203 0.71677 0.72497 0.72983 0.73883 0.75057 0.76688 0.79091
0.69849 0.70059 0.70412 0.70781 0.71252 0.72068 0.72555 0.73453 0.74627 0.76256 0.78660
0.69444 0.69643 0.69990 0.70355 0.70823 0.71637 0.72122 0.73020 0.74194 0.75823 0.78228
1.0000 0.9031 0.7931 0.6991 0.6008 0.4663 0.4008 0.2998 0.2015 0.1008 0.0000
0.0000 0.2345 0.3564 0.4267 0.4659 0.4817 0.4839 0.4809 0.4030 0.2665 0.0000
0.0000 0.2545 0.3834 0.4566 0.4971 0.5111 0.5094 0.5022 0.4176 0.2754 0.0000
T/K = 308.15
0.69037 0.69224 0.69565 0.69927 0.70391 0.71202 0.71686 0.72583 0.73757 0.75387 0.77794 106 VE/m3·mol−1 0.0000 0.0000 0.2793 0.3070 0.4164 0.4533 0.4924 0.5330 0.5329 0.5734 0.5436 0.5803 0.5394 0.5729 0.5264 0.5536 0.4348 0.4542 0.2847 0.2952 0.0000 0.0000
T/K = 313.15
T/K = 318.15
T/K = 323.15
0.68629 0.68803 0.69137 0.69494 0.69956 0.70763 0.71246 0.72142 0.73315 0.74947 0.77356
0.68219 0.68378 0.68705 0.69058 0.69515 0.70319 0.70800 0.71696 0.72869 0.74503 0.76915
0.67808 0.67951 0.68270 0.68617 0.69070 0.69869 0.70350 0.71245 0.72418 0.74054 0.76469
0.0000 0.3413 0.4945 0.5783 0.6181 0.6211 0.6104 0.5838 0.4843 0.3067 0.0000
0.0000 0.3773 0.5410 0.6289 0.6690 0.6672 0.6526 0.6182 0.5092 0.3199 0.0000
0.0000 0.4160 0.5930 0.6853 0.7259 0.7194 0.7004 0.6569 0.5371 0.3348 0.0000
a Standard uncertainty in the density measurement = 3·10−2 kg·m−3, standard uncertainty in the temperature measurement = 0.01 K, and standard uncertainty in mole fraction = 0.002.
with an uncertainty of ± 0.01 K according to the ITS-90. Standard deviation of the repeatability provided by the manufacturer for the density and temperature is ± 1.0·10−3 kg·m−3 and ± 0.001 K, respectively. The densimeter is calibrated periodically using ultrapure water and dry air. The standard uncertainties of the density measurements and the temperature are better than ± 3·10−2 kg·m−3 and 0.01 K (ITS-90), respectively. 2.3. Viscosity Measurement. We have used three viscosimeter Cannon-Fenske, size 25, 50, and 75 with viscosity intervals of (0.5 to 2), (0.8 to 4), and (1.6 to 8) mPa·s, respectively. Measurements are done according to the norm ASTM D445. The viscosimeter is inside a constant temperature bath where the temperature is controlled with a precision of ± 0.01 K between (253.15 and 373.15) K using a Polyscience. A Cole-Parmer digital thermometer was used to measure the temperature. The uncertainty of the thermometer is ± 0.01 K. The descending time of the substance was measured with a digital chronometer with a precision of ± 0.2 s. Each measurement is an average of 5 runs with a maximum deviation in the viscosity of ± 0.1 % and the standard uncertainties of each measurement is 0.004 mPa·s. The kinematic viscosity was obtained by multiplying the calibration constant of the viscosimeter with the flowing time of the sample through the viscosimeter.
To the best of our knowledge, we have not found in the literature any reported viscosity measurements for n-octane + 1-pentanol. In this work, we report the density and viscosity of binary mixtures of n-octane with ethanol, 1-propanol, 1-butanol, and 1-pentanol at temperatures from (293.15 to 323.15) K in the overall composition range. Also from the experimental measurements, we have calculated excess molar volumes and viscosity deviations, and they have been correlated to Redlich− Kister equations.
2. EXPERIMENTAL SECTION 2.1. Samples. All chemicals used were from J. T. Baker and Sigma Aldrich. The purities of these liquid compounds were tested by gas chromatography, and they did not require any additional purification of the compounds since the impurity content is less than 0.002 % and the water content was less than this percentage. This percentage is within the uncertainty in the detection of the gas chromatography. A summary of the purity of the samples are shown in Table 1. The density and viscosity of the pure components were compared to literature values showing good agreement as depicted in Table 2. Preparation of the mixtures was done gravimetrically using an analytical balance Ohaus (Voyager AS120S) with a precision of ± 0.1·10−6 kg. Samples were maintained at 273.15 K to avoid evaporation loses during the preparation of the mixtures. The uncertainty in the mole fraction is estimated to be ± 0.002. 2.2. Density Measurement. A vibrating-tube densimeter from Anton Paar (DMA 5000) was used to measure the density of the four binary mixtures and their pure substances. A description of the apparatus was given previously by BernalGarciá et al.60 The cell contains a platinum resistor thermometer
3. RESULTS AND DISCUSSION Experimental densities of n-octane with ethanol, 1-propanol, 1-butanol, and 1-pentanol were measured at atmospheric pressure and from (293.15 to 323.15) K in the overall composition range, and they are shown in Tables 3 to 6, respectively. From the experimental densities, we have calculated the excess molar volume using 3353
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Table 4. Experimental Densities, Viscosities, and Derived Quantities for n-Octane (1) + 1-Propanol (2)a 10−3 ρ
T K
x1
293.15
1.0000 0.9000 0.7994 0.6991 0.6020 0.4993 0.3997 0.3000 0.1999 0.0997 0.0000 1.0000 0.9000 0.7994 0.6991 0.6020 0.4993 0.3997 0.3000 0.1999 0.0997 0.0000 1.0000 0.9000 0.7994 0.6991 0.6020 0.4993 0.3997 0.3000 0.1999 0.0997 0.0000 1.0000 0.9000 0.7994 0.6991 0.6020 0.4993 0.3997 0.3000 0.1999 0.0997 0.0000
298.15
303.15
308.15
kg·m
−3
0.70254 0.70648 0.71155 0.71748 0.72419 0.73243 0.74180 0.75287 0.76637 0.78297 0.80384 0.69849 0.70235 0.70739 0.71330 0.71999 0.72824 0.73762 0.74872 0.76225 0.77890 0.79985 0.69444 0.69819 0.70320 0.70909 0.71577 0.72401 0.73340 0.74453 0.75810 0.77480 0.79581 0.69037 0.69402 0.69898 0.70485 0.71151 0.71975 0.72915 0.74030 0.75391 0.77067 0.79174
η
ν 2 −1
Δη
106 VE
T
−1
mPa·s
mm ·s
mPa·s
m ·mol
0.545 0.556 0.587 0.632 0.703 0.798 0.934 1.092 1.356 1.692 2.210 0.513 0.523 0.550 0.589 0.650 0.734 0.854 0.991 1.216 1.508 1.962 0.485 0.491 0.515 0.550 0.603 0.675 0.777 0.899 1.097 1.352 1.746 0.459 0.463 0.484 0.514 0.560 0.623 0.712 0.817 0.992 1.211 1.556
0.776 0.787 0.825 0.881 0.970 1.089 1.259 1.450 1.769 2.161 2.749 0.735 0.744 0.777 0.826 0.903 1.007 1.158 1.324 1.595 1.936 2.453 0.698 0.704 0.733 0.775 0.843 0.933 1.059 1.208 1.448 1.745 2.194 0.664 0.667 0.692 0.729 0.787 0.866 0.977 1.103 1.316 1.572 1.966
0.00 −0.16 −0.29 −0.41 −0.51 −0.58 −0.61 −0.62 −0.52 −0.35 0.00 0.00 −0.14 −0.25 −0.36 −0.44 −0.51 −0.53 −0.54 −0.46 −0.31 0.00 0.00 −0.12 −0.22 −0.32 −0.38 −0.44 −0.47 −0.47 −0.40 −0.27 0.00 0.00 −0.11 −0.20 −0.28 −0.34 −0.39 −0.41 −0.41 −0.35 −0.24 0.00
0.0000 0.2165 0.3007 0.3412 0.3477 0.3361 0.3144 0.2817 0.2189 0.1287 0.0000 0.0000 0.2356 0.3262 0.3692 0.3764 0.3628 0.3374 0.3000 0.2314 0.1357 0.0000 0.0000 0.2596 0.3567 0.4024 0.4094 0.3941 0.3638 0.3199 0.2447 0.1419 0.0000 0.0000 0.2872 0.3910 0.4404 0.4475 0.4292 0.3941 0.3429 0.2602 0.1493 0.0000
3
K 313.15
318.15
323.15
10−3 ρ kg·m
−3
0.68629 0.68981 0.69473 0.70057 0.70721 0.71544 0.72485 0.73604 0.74969 0.76650 0.78764 0.68219 0.68558 0.69045 0.69625 0.70287 0.71109 0.72051 0.73172 0.74541 0.76228 0.78355 0.67808 0.68132 0.68613 0.69190 0.69849 0.70670 0.71612 0.72735 0.74108 0.75802 0.77932
η
ν 2 −1
Δη
106 VE
mPa·s
mm ·s
mPa·s
m3·mol−1
0.433 0.436 0.455 0.481 0.520 0.576 0.653 0.745 0.898 1.090 1.386 0.412 0.412 0.427 0.451 0.485 0.534 0.605 0.680 0.817 0.984 1.242 0.392 0.389 0.403 0.423 0.452 0.496 0.554 0.623 0.742 0.890 1.115
0.631 0.633 0.655 0.686 0.736 0.806 0.901 1.012 1.198 1.422 1.759 0.604 0.601 0.619 0.647 0.690 0.751 0.839 0.929 1.096 1.291 1.585 0.578 0.570 0.587 0.611 0.648 0.702 0.774 0.857 1.002 1.174 1.430
0.00 −0.09 −0.17 −0.24 −0.29 −0.33 −0.35 −0.36 −0.30 −0.20 0.00 0.00 −0.08 −0.15 −0.21 −0.26 −0.29 −0.31 −0.31 −0.26 −0.18 0.00 0.00 −0.08 −0.13 −0.19 −0.23 −0.26 −0.27 −0.28 −0.23 −0.15 0.00
0.0000 0.3175 0.4293 0.4821 0.4893 0.4681 0.4277 0.3691 0.2777 0.1579 0.0000 0.0000 0.3515 0.4729 0.5299 0.5379 0.5145 0.4685 0.4025 0.3016 0.1719 0.0000 0.0000 0.3892 0.5199 0.5804 0.5882 0.5613 0.5088 0.4333 0.3211 0.1791 0.0000
Standard uncertainty in the density measurement = 3·10−2 kg·m−3, standard uncertainty in the viscosity measurement = 0.004 mPa·s, standard uncertainty in the temperature measurement = 0.01 K, and standard uncertainty in mole fraction = 0.002.
a
⎛1 ⎛1 1⎞ 1⎞ V E = x1M1⎜⎜ − ⎟⎟ + x 2M 2⎜⎜ − ⎟⎟ ρ1 ⎠ ρ2 ⎠ ⎝ρ ⎝ρ
groups have measured the density and excess molar volume of mixtures of n-octane with ethanol, 1-propanol, 1-butanol, and 1-pentanol. However, most of these measurements have been done at 298.15 K27,28,39−41,45,47,48,50,51,63 and at a maximum temperature of 318.15 K for the mixture of n-octane + ethanol.38 Excess molar volumes have been measured by several authors.25,39,42,43,45,47,48,51 In the case of the viscosity, experimental measurements are scarce, and most of the reported values in the literature are at 298.15 K for the mixtures of n-octane with the 1-alcohols.23,25−28 Jiménez et al.25 have been measured the viscosity of these mixtures at different temperatures than 298.15 K.
(1)
where M1, M2, ρ1, and ρ2 are the molar masses and the density of the pure components 1 and 2, respectively, and ρ is the density of the mixture. Excess molar volumes are also depicted in Tables 3 to 6. Using a propagation error formula61,62 the calculated experimental uncertainty in the excess molar volume is 0.0008·10−6 m3·mol−1. Unfortunately, we cannot draw uncertainty errors in the figures because they are within the size of the symbols. As mentioned before, several research 3354
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Table 5. Experimental Densities, Viscosities, and Derived Quantities for n-Octane (1) + 1-Butanol (2)a 10−3 ρ
T K
x1
293.15
1.0000 0.8991 0.7999 0.7002 0.6004 0.4995 0.4064 0.3022 0.1999 0.0967 0.0000 1.0000 0.8991 0.7999 0.7002 0.6004 0.4995 0.4064 0.3022 0.1999 0.0967 0.0000 1.0000 0.8991 0.7999 0.7002 0.6004 0.4995 0.4064 0.3022 0.1999 0.0967 0.0000 1.0000 0.8991 0.7999 0.7002 0.6004 0.4995 0.4064 0.3022 0.1999 0.0967 0.0000
298.15
303.15
308.15
kg·m
−3
0.70254 0.70811 0.71461 0.72195 0.73023 0.73967 0.74945 0.76186 0.77592 0.79200 0.80953 0.69849 0.70400 0.71050 0.71780 0.72612 0.73556 0.74537 0.75783 0.77193 0.78810 0.80570 0.69444 0.69987 0.70635 0.71365 0.72197 0.73143 0.74127 0.75377 0.76792 0.78417 0.80186 0.69037 0.69572 0.70218 0.70947 0.71779 0.72727 0.73713 0.74968 0.76390 0.78022 0.79799
η
ν 2 −1
Δη
106 VE
T
−1
mPa·s
mm ·s
mPa·s
m ·mol
0.545 0.571 0.603 0.672 0.766 0.903 1.078 1.363 1.722 2.243 2.968 0.513 0.537 0.565 0.626 0.709 0.826 0.974 1.223 1.537 1.983 2.602 0.485 0.503 0.529 0.584 0.655 0.758 0.885 1.102 1.375 1.762 2.292 0.459 0.473 0.497 0.546 0.609 0.698 0.809 0.996 1.232 1.577 2.025
0.776 0.807 0.843 0.931 1.049 1.221 1.438 1.788 2.219 2.832 3.666 0.735 0.762 0.795 0.872 0.976 1.123 1.307 1.614 1.991 2.516 3.229 0.698 0.718 0.749 0.818 0.908 1.037 1.194 1.462 1.791 2.247 2.859 0.664 0.681 0.708 0.769 0.849 0.959 1.097 1.329 1.613 2.021 2.537
0.00 −0.22 −0.43 −0.60 −0.75 −0.86 −0.91 −0.87 −0.76 −0.49 0.00 0.00 −0.19 −0.37 −0.51 −0.64 −0.73 −0.78 −0.75 −0.65 −0.42 0.00 0.00 −0.17 −0.32 −0.44 −0.55 −0.63 −0.67 −0.64 −0.56 −0.36 0.00 0.00 −0.14 −0.28 −0.38 −0.48 −0.55 −0.58 −0.56 −0.48 −0.30 0.00
0.0000 0.1757 0.2377 0.2700 0.2715 0.2520 0.2213 0.1726 0.0990 0.0544 0.0000 0.0000 0.1904 0.2568 0.2977 0.2940 0.2746 0.2394 0.1854 0.1104 0.0587 0.0000 0.0000 0.2116 0.2813 0.3246 0.3218 0.3003 0.2617 0.2020 0.1213 0.0634 0.0000 0.0000 0.2352 0.3114 0.3551 0.3523 0.3289 0.2869 0.2212 0.1334 0.0689 0.0000
3
K 313.15
318.15
323.15
10−3 ρ kg·m
η
−3
0.68629 0.69154 0.69797 0.70527 0.71359 0.72307 0.73296 0.74556 0.75983 0.77624 0.79410 0.68219 0.68733 0.69372 0.70103 0.70935 0.71884 0.72875 0.74139 0.75573 0.77222 0.79018 0.67808 0.68310 0.68948 0.69675 0.70507 0.71457 0.72450 0.73718 0.75158 0.76816 0.78621
ν 2 −1
Δη
106 VE
mPa·s
mm ·s
mPa·s
m3·mol−1
0.433 0.447 0.467 0.511 0.566 0.644 0.740 0.904 1.110 1.400 1.796 0.412 0.420 0.440 0.479 0.527 0.595 0.679 0.821 1.000 1.258 1.590 0.392 0.397 0.415 0.450 0.493 0.552 0.625 0.751 0.907 1.134 1.414
0.631 0.646 0.669 0.725 0.794 0.890 1.010 1.213 1.461 1.804 2.262 0.604 0.612 0.634 0.684 0.744 0.828 0.931 1.108 1.324 1.630 2.012 0.578 0.582 0.601 0.646 0.699 0.773 0.862 1.019 1.207 1.476 1.799
0.00 −0.12 −0.24 −0.33 −0.41 −0.47 −0.50 −0.48 −0.41 −0.26 0.00 0.00 −0.11 −0.21 −0.29 −0.36 −0.41 −0.43 −0.41 −0.35 −0.22 0.00 0.00 −0.10 −0.18 −0.25 −0.31 −0.35 −0.37 −0.35 −0.30 −0.18 0.00
0.0000 0.2615 0.3456 0.3891 0.3860 0.3605 0.3147 0.2431 0.1477 0.0753 0.0000 0.0000 0.2903 0.3851 0.4262 0.4232 0.3957 0.3461 0.2672 0.1639 0.0828 0.0000 0.0000 0.3223 0.4199 0.4677 0.4648 0.4347 0.3809 0.2947 0.1823 0.0915 0.0000
Standard uncertainty in the density measurement = 3·10−2 kg·m−3, standard uncertainty in the viscosity measurement = 0.004 mPa·s, standard uncertainty in the temperature measurement = 0.01 K, and standard uncertainty in mole fraction = 0.002.
a
of the excess molar volume and the viscosity deviation using a Redlich−Kister64 equation
With the new experimental viscosity measurements, the viscosity deviation has been calculated using
n
2
Δη = η −
∑ xiηi i=1
Y E = x1(1 − x1) ∑ Ai (1 − 2x1)i (2)
i=0
(3)
where YE is either VE or Δη, n is the number of adjusting parameters, and Ai are the adjusting parameters which can be obtained from the experimental measurements by least-squares optimization method of eq 3 using a SAS65 software. For all of the mixtures, we need three parameters to represent the composition dependence of the excess molar volume or the
where xi and ηi are the molar fraction and the dynamic viscosity of the pure component i, respectively, and η is the dynamic viscosity of the mixture. Calculated values of the viscosity deviation are shown in Tables 3 to 6. The calculated experimental uncertainty61 of the viscosity deviation is 0.04 mPa·s. For each binary mixture, we have represented the composition dependence 3355
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Table 6. Experimental Densities, Viscosities, and Derived Quantities for n-Octane (1) + 1-Pentanol (2)a 10−3 ρ
T K
x1
293.15
1.0000 0.8998 0.7983 0.6976 0.5967 0.4984 0.4000 0.3001 0.2010 0.1004 0.0000 1.0000 0.8998 0.7983 0.6976 0.5967 0.4984 0.4000 0.3001 0.2010 0.1004 0.0000 1.0000 0.8998 0.7983 0.6976 0.5967 0.4984 0.4000 0.3001 0.2010 0.1004 0.0000 1.0000 0.8998 0.7983 0.6976 0.5967 0.4984 0.4000 0.3001 0.2010 0.1004 0.0000
298.15
303.15
308.15
−3
η
ν 2 −1
Δη
106 VE
T
−1
mPa·s
mm ·s
mPa·s
m ·mol
0.70254 0.70968 0.71779 0.72670 0.73639 0.74671 0.75791 0.77030 0.78365 0.79843 0.81459 0.69849 0.70559 0.71372 0.72264 0.73234 0.74270 0.75394 0.76639 0.77981 0.79468 0.81093 0.69444 0.70148 0.70962 0.71855 0.72827 0.73867 0.74995 0.76245 0.77594 0.79089 0.80724
0.545 0.588 0.652 0.737 0.863 1.046 1.311 1.695 2.237 2.938 4.042 0.513 0.550 0.605 0.685 0.796 0.953 1.180 1.509 1.972 2.568 3.518 0.485 0.516 0.567 0.638 0.736 0.873 1.068 1.349 1.747 2.254 3.060
0.776 0.829 0.909 1.014 1.172 1.401 1.730 2.200 2.854 3.679 4.962 0.735 0.780 0.848 0.948 1.087 1.284 1.566 1.969 2.529 3.232 4.338 0.698 0.736 0.799 0.888 1.010 1.182 1.425 1.770 2.252 2.850 3.790
0.00 −0.31 −0.60 −0.87 −1.09 −1.25 −1.33 −1.30 −1.10 −0.75 0.00 0.00 −0.26 −0.51 −0.74 −0.93 −1.07 −1.14 −1.11 −0.94 −0.65 0.00 0.00 −0.23 −0.44 −0.63 −0.79 −0.90 −0.96 −0.94 −0.80 −0.55 0.00
0.0000 0.1323 0.1860 0.1878 0.1750 0.1408 0.1044 0.0639 0.0324 0.0101 0.0000 0.0000 0.1451 0.2010 0.2038 0.1942 0.1567 0.1182 0.0736 0.0385 0.0126 0.0000 0.0000 0.1627 0.2207 0.2243 0.2143 0.1755 0.1341 0.0857 0.0457 0.0156 0.0000
0.69037 0.69735 0.70549 0.71444 0.72418 0.73460 0.74593 0.75849 0.77205 0.78709 0.80353
0.459 0.486 0.532 0.596 0.682 0.802 0.971 1.219 1.564 1.984 2.659
0.664 0.697 0.753 0.834 0.941 1.091 1.302 1.608 2.026 2.521 3.309
0.00 −0.19 −0.37 −0.53 −0.66 −0.76 −0.81 −0.78 −0.65 −0.45 0.00
0.0000 0.1828 0.2442 0.2474 0.2375 0.1971 0.1525 0.0998 0.0550 0.0195 0.0000
kg·m
3
K 313.15
318.15
323.15
10−3 ρ kg·m
−3
0.68629 0.69320 0.70134 0.71030 0.72007 0.73052 0.74188 0.75450 0.76813 0.78326 0.79979 0.68219 0.68902 0.69716 0.70614 0.71592 0.72640 0.73781 0.75047 0.76417 0.77940 0.79603 0.67808 0.68481 0.69295 0.70194 0.71174 0.72224 0.73369 0.74641 0.76018 0.77550 0.79223 0.68629 0.69320
η
ν 2 −1
Δη
106 VE
mPa·s
mm ·s
mPa·s
m3·mol−1
0.433 0.457 0.499 0.557 0.636 0.738 0.882 1.110 1.393 1.755 2.334 0.412 0.431 0.470 0.521 0.589 0.681 0.807 1.010 1.249 1.557 2.042 0.392 0.406 0.442 0.488 0.549 0.630 0.740 0.911 1.117 1.389 1.805 0.433 0.457
0.631 0.659 0.712 0.784 0.884 1.010 1.188 1.472 1.813 2.240 2.919 0.604 0.626 0.674 0.738 0.823 0.938 1.093 1.346 1.634 1.998 2.565 0.578 0.594 0.638 0.696 0.772 0.873 1.008 1.221 1.469 1.791 2.279 0.631 0.659
0.00 −0.17 −0.32 −0.45 −0.56 −0.65 −0.69 −0.65 −0.56 −0.39 0.00 0.00 −0.15 −0.27 −0.38 −0.48 −0.55 −0.58 −0.54 −0.47 −0.32 0.00 0.00 −0.13 −0.24 −0.33 −0.41 −0.47 −0.50 −0.47 −0.40 −0.28 0.00 0.00 −0.17
0.0000 0.2050 0.2696 0.2731 0.2625 0.2202 0.1724 0.1154 0.0654 0.0238 0.0000 0.0000 0.2295 0.2978 0.3017 0.2902 0.2455 0.1939 0.1327 0.0771 0.0290 0.0000 0.0000 0.2575 0.3295 0.3336 0.3207 0.2739 0.2184 0.1520 0.0900 0.0347 0.0000 0.0000 0.2050
Standard uncertainty in the density measurement = 3·10−2 kg·m−3, standard uncertainty in the viscosity measurement = 0.004 mPa·s, standard uncertainty in the temperature measurement = 0.01 K, and standard uncertainty in mole fraction = 0.002.
a
calculated value from the experimental measurement and, and YEcal is the value obtained from eq 3. Figures 1 to 4 show excess molar volume deviations between calculated values from eq 3 and values reported by other authors at 298.15 K for n-octane + ethanol, + 1-propanol, + 1-butanol, and + 1-pentanol, respectively. For the system n-octane + ethanol, the maximum difference is 0.047·10−6 m3·mol−1 with values from Orge et al.23 at a n-octane mole fraction of 0.2622. They estimated an uncertainty for the excess molar volume at this mole fraction is 0.01·10−6 m3·mol−1. Also, values from Orge et al.38 present also a maximum difference average of (0.051, 0.050,
viscosity deviation. The degree of the polynomial was optimized through the application of the F test and t test for each parameter.66 Parameters are shown in Table 7, and the standard deviation of the curve fitting is shown. The standard deviation is calculated using ⎡ ∑N (Y E − Y E )2 ⎤1/2 exp , i cal, i ⎥ σ = ⎢ i=1 ⎢⎣ ⎥⎦ N−p
(4)
where σ is the standard deviation, N is the number of experimental data points and p is the order of the polynomial, YEexp is the 3356
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Table 7. Redlich−Kister Parameters at Different Temperatures for the Excess Molar Volume and Viscosity Deviation with Standard Deviation of the Fit YE
T/K
A0
106 VE/m3·mol−1
293.15 298.15 303.15 308.15 313.15 318.15 323.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15
1.32711 1.43818 1.55985 1.69682 1.84889 2.02977 2.21418 −2.31233 −2.00583 −1.75491 −1.53208 −1.33174 −1.16934 −1.03101
293.15 298.15 303.15 308.15 313.15 318.15 323.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15
1.00261 1.08957 1.18957 1.30115 1.42467 1.56166 1.71514 −3.40156 −2.91798 −2.51720 −2.17352 −1.87849 −1.62282 −1.40483
Δη/mPa·s
106 VE/m3·mol−1
Δη/mPa·s
A1
A2
A3
n-Octane (1) + 1-Propanol (2) −0.26625 0.80129 −0.42151 −0.32148 0.86567 −0.49145 −0.38484 0.92266 −0.58168 −0.45401 0.98586 −0.67796 −0.52604 1.06148 −0.79075 −0.59551 1.16792 −0.89439 −0.68116 1.24943 −1.07938 −1.10342 −0.70965 −0.33803 −0.94909 −0.67848 −0.38228 −0.84477 −0.57562 −0.26578 −0.73207 −0.51337 −0.23913 −0.63588 −0.42055 −0.16388 −0.54502 −0.38587 −0.13059 −0.48658 −0.33989 −0.06281 n-Octane (1) + 1-Butanol (2) −0.52754 0.29166 −0.48192 −0.59571 0.32129 −0.46438 −0.64068 0.36740 −0.55863 −0.69306 0.43125 −0.66949 −0.74895 0.51284 −0.79573 −0.81017 0.60793 −0.93732 −0.86420 0.68284 −1.07621 −1.53274 −0.86811 −0.66390 −1.32480 −0.70780 −0.49373 −1.15223 −0.59045 −0.33000 −1.01601 −0.47521 −0.15430 −0.85944 −0.44540 −0.21825 −0.75634 −0.35041 −0.03590 −0.64781 −0.27569 0.04696
σ
A0
0.007 0.005 0.006 0.007 0.008 0.009 0.010 0.006 0.005 0.004 0.005 0.004 0.004 0.003
0.56278 0.62692 0.69942 0.78255 0.87206 0.97047 1.08022 −4.97770 −4.23542 −3.58686 −3.01728 −2.56708 −2.17028 −1.86426
0.007 0.007 0.008 0.008 0.009 0.009 0.011 0.006 0.006 0.005 0.003 0.004 0.003 0.003
1.92409 2.04020 2.17269 2.32217 2.48574 2.67284 2.88432
A1
A2
A3
n-Octane (1) + 1-Pentanol (2) −0.71754 0.32692 −0.20364 −0.75154 0.34086 −0.25810 −0.78553 0.38739 −0.35640 −0.82222 0.44838 −0.46975 −0.86177 0.52162 −0.59446 −0.90863 0.60712 −0.72098 −0.95767 0.70507 −0.87701 −2.42449 −1.12479 −0.89071 −2.06980 −1.03290 −0.77257 −1.74445 −0.88085 −0.61819 −1.40057 −0.65517 −0.48897 −1.16938 −0.59087 −0.46569 −0.92857 −0.45719 −0.37787 −0.81892 −0.43180 −0.26051 n-Octane (1) + Ethanol (2) 0.31315 1.30798 −0.17627 0.26832 1.35910 −0.23050 0.21502 1.43537 −0.31708 0.15158 1.52030 −0.40506 0.10628 1.66702 −0.54376 0.03385 1.78140 −0.67553 −0.04724 1.89856 −0.81023
σ 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.014 0.013 0.011 0.012 0.012 0.010 0.007 0.007 0.007 0.008 0.008 0.009 0.010 0.010
Figure 2. Excess molar volume deviations of calculated values with respect to literature values for n-octane (1) + 1-propanol (2) at 298.15 K: ●, Jiménez et al.;25 ○, Jiménez et al.43 (accuracy 0.001·10−6 m3·mol−1); ▼, Orge et al.23 (accuracy 0.01·10−6 m3·mol−1); △, Mato et al.;41 ■, Kaur et al.;39 □, Iglesias et al.40 (accuracy 0.001·10−6 m3·mol−1).
Figure 1. Excess molar volume deviations of calculated values with respect to literature values for n-octane (1) + ethanol (2) at 298.15 K: ●, Orge et al.23 (accuracy 0.01·10−6 m3·mol−1); ○, Segade et al. 37 3357
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Figure 3. Excess molar volume deviations of calculated values with respect to literature values for n-octane (1) + 1-butanol (2) at 298.15 K: ●, Dubey et al.;26 ▼, Chaudhari and Katti48 (accuracy 0.002·10−6 m3· mol−1); △, Kaur et al.;39 ■, Iglesias et al.40 (accuracy 0.001·10−6 m3· mol−1); □, Franjo et al.;28 ◆, Nath and Pandey27 (accuracy 0.002·10−6 m3·mol−1); ◇, Nath and Pandey45 (accuracy 0.002·10−6 m3·mol−1); ▲, Yun et al.47 (accuracy 0.001·10−6 m3·mol−1).
Figure 5. Excess molar volume for (a) n-octane (1) + ethanol (2) and (b) n-octane (1) + 1-propanol (2) as a function of the mole fraction at ●, 293.15 K; ○, 298.15 K; ▼, 303.15 K; △, 308.15 K; ■, 313.15 K; □, 318.15 K and ◆, 323.15 K. The solid line corresponds to eq 3.
reported densities for this mixture at (293.15 and 298.15) K. However, our values excess molar volumes disagree with their values by ± 1·10−6 m3·mol−1. Excess molar volume deviations for the system n-octane + 1-propanol at 298.15 K are shown in Figure 2. The highest disagreement (0.032·10−6 m3·mol−1) occurs with excess molar volumes from Jiménez et al.43 at a n-octane mole fraction of 0.9837. At this mole fraction the estimated uncertainty of the excess molar volume is 0.001·10−6 m3·mol−1. At different temperatures, excess molar volumes have been reported by Jiménez et al.25 [T = (293.15, 298.15, 303.15, and 308.15) K], Jiménez et al.43 [T = (298.15 and 308.15) K], and Gupta et al.42 (T = 303.15 K). Our calculated values agree with the values of these authors within an absolute difference average of (0.044, 0.055, and 0.126)·10−6 m3·mol−1. Uncertainties reported for Jiménez et al.43 and Gupta et al.42 are 0.001·10−6 m3·mol −1 and 0.003·10−6 m3·mol −1, respectively. Jiménez et al.25 reported no accuracy. In Figure 3, we show a comparison between our calculated excess molar volumes and values from Dubey et al.,26 Chaudhari and Katti,48 Kaur et al.,39 Iglesias et al.,40 Franjo et al.,28 Nath
Figure 4. Excess molar volume deviations of calculated values with respect to literature values for n-octane (1) + 1-pentanol (2) at 298.15 K: ●, Verdes et al.;50 ○, Jiménez et al.;51 ▼, Kaur et al.;39 △, Iglesias et al.40 (accuracy 0.001·10−6 m3·mol −1); ■, Yun et al. 47 (accuracy 0.001·10−6 m3·mol−1).
0.030, and 0.049)·10−6 m3·mol−1 at (303.15, 308.15, 313.15, and 318.15) K, respectively. The average reported uncertainty by the authors is 0.009·10 −6 m 3·mol −1. Feitosa et al.24 3358
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Figure 7. Excess molar volume as a function of the mole fraction at 298.15 K: ●, ethanol (this work); ○, 1-propanol (this work); ▼, 1-butanol (this work); △, 1-pentanol (this work); ■, 1-hexanol (Treszczanowicz and Benson4); □, 1-heptanol (Legido et al.74); ◆, 1-octanol (Franjo et al.28). The solid line corresponds to eq 3.
Viscosity deviations at 298.15 K are reported for the mixture n-octane + 1-propanol by Orge et al.23 and Jiménez et al.25 Our calculated values agree within a maximum deviation of (0.035 and 0.044) mPa·s from viscosity deviations by Orge et al.23 (the reported uncertainty by the authors corresponds to 0.001 mPa·s) and Jiménez et al.,25 respectively. At different temperatures, viscosity deviations have been reported by Jiménez et al.25 [T = (293.15, 303.15, and 308.15) K]. Our calculated values agree within a maximum deviation of (0.041, 0.038, and 0.017) mPa·s. For the binary mixture, n-octane + 1-butanol, the only reported viscosity deviations are from Dubey et al.,26 Nath and Pandey,27 and Franjo et al.28 at 298.15 K. Our agreement with these values is within a maximum deviation of (0.021, 0.132, and 0.025) mPa·s, respectively. However, they did not report the uncertainty for the viscosity deviation. Unfortunately, we were unable to find viscosity measurements in the literature for the system n-octane + 1-pentanol. Several authors67−69 have found that the sign and magnitude of the excess property depend upon the interaction forces among different molecules in a mixture. Treszczanowicz and Benson2−4 suggested that the excess molar volume for the systems 1-alcohol + n-alkane is the result of the contribution of various effects: chemical, physical, and structural5 interactions. The physical interactions consist of dispersion forces which include nonpolar molecular interactions, weak dipole−dipole interactions, and interactions of van der Waals type. They contribute positively to the excess molar volume and negatively to the viscosity deviations. Chemical interactions that include forces due to charge transfer, hydrogen bonding, and interactions that form complexes contribute negatively to the excess molar volume and positively to the viscosity deviations. However, the
Figure 6. Excess molar volume for (a) n-octane (1) + 1-butanol (2) and (b) n-octane (1) + 1-pentanol (2) as a function of the mole fraction at ●, 293.15 K; ○, 298.15 K; ▼, 303.15 K; △, 308.15 K; ■, 313.15 K; □, 318.15 K, and ◆, 323.15 K. The solid line corresponds to eq 3.
and Pandey,27 Nath and Pandey,45 and Yun et al.47 for the mixture n-octane +1-butanol. The maximum difference is 0.114·10−6 m3· mol−1 at a mole fraction n-octane of 0.9180 which it corresponds to a value with a reported uncertainty of 0.002·10−6 m3·mol−1 by Nath and Pandey.27 At 293.15 K, our values agree within an maximum absolute deviation of 0.017·10−6 m3·mol−1 from values of Nath44 and De Cominges et al.46 The authors reported an uncertainty of 0.002·10−6 m3·mol−1 and 0.02·10−6 m3·mol−1, respectively. At the maximum reported temperature (308.15 K), the maximum deviation is 0.056·10−6 m3·mol−1, again with values reported by De Cominges et al.46 Differences of our calculated excess molar volumes and literature values at 298.15 K are shown in Figure 4. The maximum difference is of 0.036·10−6 m3·mol−1 at a n-octane mole fraction of 0.4823 with reported values by Yun et al.47 They reported an uncertainty of 0.001·10−6 m3·mol−1. Gupta et al.42 are the only authors that report the excess molar volumes at temperatures different than 298.15 K at 303.15 K; our values agree within a maximum difference of 0.193·10−6 m3·mol−1. They reported an uncertainty of 0.003·10−6 m3·mol−1. 3359
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Figure 9. Viscosity deviation as a function of the mole fraction at 298.15 K: ●, ethanol (Orge et al.23); ○, 1-propanol (this work); ▼, 1-butanol (this work); △, 1-pentanol (this work); ■, 1-hexanol (Dubey and Sharma75); □, 1-octanol (Franjo et al.28). The solid line corresponds to eq 3.
a destruction of the hydrogen bonding in the alcohols. In Figures 5 and 6, we show that for all of the mixtures the excess molar volume is positive in the entire composition range and in all cases there is an increment of the excess molar volume as the temperature increases. This is due to a decrease in the volume contraction because the kinetic energy of the molecules increases, provoking a reduction of the interactions between these molecules. The total effect is an increment of the excess molar volume. For the n-octane + 1-butanol mixture, Dubey et al.26 suggest that the increment of the molar excess volume with temperature is due to a separation of the alcohol molecules at high temperatures. In Figures 5 and 6, we can observe the degree of positive deviation of the excess molar volume follows the order ethanol > 1-propanol > 1-butanol > 1-pentanol. The excess molar volume, for all of the mixtures measured in this work, have a parabolic composition dependence without any unusual behavior. From a macroscopic point of view, the positive excess molar volumes indicates an expansion in the volume during mixing, considering the physical interactions important in these mixtures. Figure 7 shows the effect of the length of the alkyl chain of the alcohol in an n-octane mixture at a temperature of 298.15 K. The excess molar volume decreases as the length of alkyl chain increases, and it changes from a positive curve for an ethanol mixture to a sigmoid curve with positive and negative values for 1-octanol mixtures. This behavior was also observed by Franjo et al.28 Values of the viscosity deviations support the absence of specific interactions between different molecules. In Figure 8 we show that the viscosity deviation is negative for all compositions and temperatures. This is an indication of hydrogen bond breakage of the n-mers. The alkanes are strongly associated in
Figure 8. Viscosity deviation for (a) n-octane (1) + 1-propanol (2), (b) n-octane (1) + 1-butanol (2), and (c) n-octane (1) + 1-pentanol (2) as a function of the mole fraction at ●, 293.15 K; ○, 298.15 K; ▼, 303.15 K; △, 308.15 K; ■, 313.15 K; □, 318.15 K, and ◆, 323.15 K. The solid line corresponds to eq 3.
destruction of hydrogen bonding contributes positively to the excess molar volume. Structural interactions arise due to changes in the interstitial accommodation of the molecules. These changes are due because of changes in the form and size of the molecules and changes in the free volume. A fundamental role of these interactions is represented by the sign and magnitude of the value of the excess or deviation properties, which allow us to assess the intermolecular rearrangement experienced by components in the liquid mixture.70−73 Alcohols tend to associate their molecules through hydrogen bonding, but if we add a nonpolar solvent as n-octane, then we expect a higher molar volume since there is a perturbation and 3360
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the pure state. The absolute value of Δη decreases in all systems when the temperature increases. Dubey et al.26 mention that the negative value of Δη for systems with a short-chain alcohol (1-butanol) and various solvents (n-hexane, n-octane and n-decane) is due to the inclusion of the small molecule (1-butanol) to the structure of the big molecules. Their findings also apply to our systems since they are formed with small 1-alcohol molecules (1-propanol, 1-butanol, and 1-pentanol) and a big solvent molecule (n-octane). In this work, the viscosity deviation is negative for all binary systems and decreases when the number of carbon atoms in the 1-alcohol chain increases (see Figure 9). This behavior was also reported by Franjo et al.28
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4. CONCLUSIONS Densities and viscosities of binary mixtures of n-octane with 1-propanol, 1-butanol, and 1-pentanol and the density of the binary mixture of n-octane + ethanol have been measured in the entire composition range from (293.15 to 323.15) K at atmospheric pressure. Our density and viscosity values compare well with reported values in the literature at 298.15 K within 0.049 % and 1.674 %, respectively. Our calculated excess molar volumes agree with reported values within (0.018, 0.018, 0.024, and 0.030)·10−6 m3·mol−1 for n-octane + ethanol, + 1-propanol, + 1-butanol, and + 1-pentanol, respectively. For the viscosity deviations, our values agree within an absolute difference of 0.017 mPa·s for n-octane + butanol and n-octane + 1-pentanol. The excess molar volume is positive, and the viscosity deviation is negative for all the mixtures at any composition and any temperature considered in this work.
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AUTHOR INFORMATION
Corresponding Author
*E-mail addres:
[email protected]. Tel.: 011 52 461 611 7575. Fax: 011 52 461 611 7744. Funding
The authors thank Consejo Nacional de Ciencia and Tecnologiá (CONACyT) México for financial support during this work (SEP-2004-C01-47817). Notes
The authors declare no competing financial interest.
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REFERENCES
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