Density, dynamic viscosity, and derived properties of binary mixtures of methanol or ethanol with water, ethyl acetate, and methyl acetate at T = (293.15, 298.15, and 303.15) K

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J. Chem. Thermodynamics 39 (2007) 1578–1588 www.elsevier.com/locate/jct

Density, dynamic viscosity, and derived properties of binary mixtures of methanol or ethanol with water, ethyl acetate, and methyl acetate at T = (293.15, 298.15, and 303.15) K ´ ngeles Domı´nguez Begon˜a Gonza´lez, Noelia Calvar, Elena Go´mez, A

*

Chemical Engineering Department, University of Vigo, 36200 Vigo, Spain Received 16 February 2007; received in revised form 3 May 2007; accepted 5 May 2007 Available online 18 May 2007

Abstract Densities and dynamic viscosities for methanol or ethanol with water, ethyl acetate, and methyl acetate at several temperatures T = (293.15, 298.15, and 303.15) K have been measured over the whole composition range and 0.1 MPa, along with the properties of the pure components. Excess molar volumes, viscosity deviations, and excess free energy of activation for the binary systems at the above-mentioned temperatures, were calculated and fitted to the Redlich–Kister equation to determine the fitting parameters and the root-mean-square deviations. UNIQUAC equation was used to correlate the experimental viscosity data. The UNIFACVISCO method and ASOG-VISCO method, based on contribution groups, were used to predict the dynamic viscosities of the binary mixtures. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Viscosity; Density; Excess molar volume; Viscosity deviations; Excess free energy of activation; Water; Ethanol; Methanol; Ethyl acetate; Methyl acetate; UNIQUAC; UNIFAC-VISCO; ASOG-VISCO

1. Introduction In the chemical industry, information about the viscosity and the density of liquid mixtures and their dependence with composition and temperature is very important in different applications for surface facilities, pipeline systems, and mass transfer operations. As an extension of our work concerning dynamic viscosity of binary systems [1–3], in this paper we show experimental dynamic viscosity and density of {x1 water + (1  x1) ethanol}, {x1 water + (1  x1) methanol}, {x1 ethanol + (1  x1) ethyl acetate}, {x1 ethanol + (1  x1) methyl acetate}, {x1 methanol + (1  x1) ethyl acetate}, and {x1 methanol + (1  x1) methyl acetate} at T = (293.15, 298.15, and 303.15) K. Experimental data were used to calculate excess molar volumes, viscosity deviations, and excess free energy of activation *

Corresponding author. Tel.: +34 986812422; fax: +34 986812380. ´ . Domı´nguez). E-mail address: [email protected] (A

0021-9614/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2007.05.004

over the entire mole fraction range. Although these systems have been studied previously, most have been determined only at one temperature (T = 298.15 K) [4–6]. For the systems {x1 ethanol + (1  x1) ethyl acetate}, and {x1 methanol + (1  x1) ethyl acetate} [7], the techniques used to measure densities and viscosities were the pycnometer for measuring the density and digital stopwatch for measuring the flow time of the liquids, giving big differences in the excess properties. We have used reagents purer than the ones used by Arce et al. [4] and Nikam et al. [7]. In this work, the influence of temperature on these systems has been studied, using apparatus with major precision. In addition, viscosity data were correlated using the UNIQUAC [8] equation. The UNIFAC-VISCO [9,10] and ASOG-VISCO [11] methods have been applied to predict the viscosity of these systems and the results were compared with the experimental data. Both methods are based on the Eyring theory [12] and on group contributions methods.

B. Gonza´lez et al. / J. Chem. Thermodynamics 39 (2007) 1578–1588

and atmospheric pressure are reported in tables 2 to 7. The excess molar volumes and viscosity deviations were calculated by the following equations:

2. Experimental 2.1. Chemicals The pure components were supplied by Fluka and by Merck. The components were degassed ultrasonically, and dried over molecular sieves Type 4 Æ 108 m, that were supplied by Aldrich, and kept in inert argon with a maximum content in water of 2 Æ 106 by mass fraction. The maximum water content of the liquids was determined using a Metrohm 737 KF coulometer. Their mass fraction purities were >0.998 for ethanol, methanol, and ethyl acetate, >0.990 for methyl acetate. The water was triplydistilled. 2.2. Apparatus and procedure Samples were prepared by mass using a Mettler AX-205 Delta Range balance with a precision of ±105 g, covering the whole composition range of the mixture. Kinematic viscosities were determined using an automatic viscosimeter Lauda PVS1 with two Ubbelhode capillary microviscosimeters of 0.40 mm and 0.53 mm diameter (the uncertainty in experimental measurement is ±0.006 mPa Æ s). In order to verify the calibration, the viscosity of the pure liquids was compared with bibliographic data (table 1). The densities and the speed of sound of the pure liquids and mixtures were measured using an Anton Paar DSA5000 digital vibrating tube densimeter. Uncertainty in density measurement is ±2 Æ 106 g Æ cm3.

VE ¼

N X

xi M i ðq1  q1 i Þ;

Dynamic viscosity, density, excess molar volume, viscosity deviations, and excess free energy of activation for the binary systems {x1 water + (1  x1) ethanol}, {x1 water + (1  x1) methanol}, {x1 ethanol + (1  x1) ethyl acetate}, {x1 ethanol + (1  x1) methyl acetate}, {x1 methanol + (1  x1) ethyl acetate}, and {x1 methanol + (1  x1) methyl acetate} at T = (293.15, 298.15, and 303.15) K

TABLE 1 Comparison of density, q, and viscosity, g, with the literature data for pure components at T = 298.15 K q/(g Æ cm3) Experimental Methanol Ethanol Methyl acetate Ethyl acetate Water a b c d e

0.78720 0.78546 0.92698 0.89443 0.99705

Wei et al. [13] Riddick et al. [14]. Nikam et al. [15]. Lorenzi et al. [16] Kapadi et al. [17].

103g/(Pa Æ s) Literature a

0.7872 0.7854c 0.9268d 0.8945b 0.9971e

Experimental

Literature

0.545 1.082 0.367 0.426 0.890

0.545b 1.082c 0.367b 0.426b 0.890e

ð1Þ

i¼1

Dg ¼ g 

N X

ð2Þ

x i gi ;

i

where q and qi are the density of the mixture and the density of the pure components, respectively, xi represents the mole fraction of the component i, g and gi are the dynamic

TABLE 2 Density q, speed of sound u, dynamic viscosity g, excess molar volumes VE, viscosity deviations Dg, and excess Gibbs free energy of activation DG*E for {x1 water + (1  x1) methanol} Dg/ (mPa Æ s)

DG*E/ (J Æ mol1)

T = 293.15 K 0.000 0.173 0.334 0.603 0.809 0.938 0.990 0.957 0.838 0.620 0.304 0.135 0.000

0.000 0.050 0.109 0.233 0.376 0.535 0.687 0.837 0.916 0.870 0.561 0.291 0.000

0.0 229.5 461.7 855.2 1202.8 1499.9 1715.0 1880.4 1907.1 1754.0 1199.1 676.8 0.0

0.545 0.607 0.677 0.821 0.987 1.150 1.309 1.463 1.554 1.542 1.317 1.121 0.890

T = 298.15 K 0.000 0.178 0.341 0.612 0.819 0.946 0.996 0.962 0.841 0.625 0.311 0.141 0.000

0.000 0.045 0.098 0.208 0.339 0.468 0.591 0.711 0.768 0.721 0.462 0.248 0.000

0.0 226.4 453.7 842.2 1199.2 1471.9 1676.3 1830.2 1847.3 1689.2 1145.6 661.5 0.0

0.508 0.563 0.627 0.751 0.889 1.032 1.164 1.289 1.342 1.342 1.147 0.996 0.797

T = 303.15 K 0.000 0.182 0.347 0.622 0.828 0.955 0.990 0.968 0.846 0.630 0.318 0.147 0.000

0.000 0.041 0.090 0.186 0.295 0.409 0.511 0.608 0.632 0.603 0.379 0.213 0.000

0.0 222.8 455.5 829.6 1164.3 1442.8 1639.4 1781.7 1758.5 1626.7 1084.9 647.8 0.0

x1

q/ (g Æ cm3)

g/ (mPa Æ s)

0.0000 0.0490 0.0993 0.1973 0.2983 0.3985 0.5003 0.5994 0.6997 0.7986 0.8999 0.9512 1.0000

0.79190 0.80006 0.80862 0.82611 0.84503 0.86467 0.88557 0.90658 0.92845 0.94980 0.97159 0.98386 0.99820

0.585 0.655 0.735 0.900 1.086 1.287 1.481 1.673 1.793 1.789 1.522 1.274 1.003

0.0000 0.0490 0.0993 0.1973 0.2983 0.3985 0.5003 0.5994 0.6997 0.7986 0.8999 0.9512 1.0000

0.78720 0.79547 0.80411 0.82173 0.84079 0.86059 0.88169 0.90296 0.92521 0.94717 0.96984 0.98253 0.99705

0.0000 0.0490 0.0993 0.1973 0.2983 0.3985 0.5003 0.5994 0.6997 0.7986 0.8999 0.9512 1.0000

0.78248 0.79084 0.79956 0.81731 0.83650 0.85645 0.87732 0.89926 0.92189 0.94442 0.96790 0.98097 0.99565

3. Results and discussion

Component

1579

VE/ (cm3 Æ mol1)

B. Gonza´lez et al. / J. Chem. Thermodynamics 39 (2007) 1578–1588

1580

TABLE 3 Density q, speed of sound u, dynamic viscosity g, excess molar volumes VE, viscosity deviations Dg, and excess Gibbs free energy of activation DG*E for {x1 water + (1  x1) ethanol}

TABLE 4 Density q, speed of sound u, dynamic viscosity g, excess molar volumes VE, viscosity deviations Dg, and excess Gibbs free energy of activation DG*E for {x1 ethanol + (1  x1) ethylacetate}

Dg/ (mPa Æ s)

DG*E/ (J Æ mol1)

x1

q/ (g Æ cm3)

g/ (mPa Æ s)

T = 293.15 K 0.000 0.204 0.373 0.649 0.856 0.998 1.076 1.100 1.054 0.898 0.521 0.235 0.000

0.000 0.099 0.202 0.398 0.602 0.861 1.129 1.402 1.647 1.660 1.202 0.618 0.000

0.0 247.1 484.7 903.2 1289.6 1700.8 2061.2 2371.2 2598.4 2572.4 2045.1 1248.8 0.0

0.0000 0.0491 0.0990 0.1958 0.2961 0.3947 0.4948 0.5995 0.7004 0.8004 0.9003 0.9505 1.0000

0.90052 0.89691 0.89314 0.88548 0.87707 0.86809 0.85816 0.84681 0.83471 0.82145 0.80645 0.79836 0.78975

0.452 0.450 0.452 0.463 0.476 0.497 0.542 0.581 0.660 0.758 0.919 1.048 1.187

1.082 1.153 1.232 1.380 1.531 1.659 2.115 2.275 2.300 1.860 1.388 0.890

T = 298.15 K 0.000 0.203 0.371 0.643 0.846 0.986 1.083 1.035 0.880 0.516 0.239 0.000

0.000 0.081 0.169 0.336 0.506 0.654 1.148 1.327 1.372 0.951 0.488 0.000

0.0 231.5 465.1 876.8 1253.6 1557.3 2292.2 2494.8 2506.5 1930.1 1165.2 0.0

0.0000 0.0491 0.0990 0.1958 0.2961 0.3947 0.4948 0.5995 0.7004 0.8004 0.9003 0.9505 1.0000

0.89443 0.89086 0.88711 0.87955 0.87122 0.86238 0.85262 0.84147 0.82957 0.81655 0.80182 0.79391 0.78546

0.987 1.046 1.111 1.237 1.357 1.515 1.821 1.941 1.937 1.580 1.207 0.797

T = 303.15 K 0.000 0.201 0.367 0.635 0.836 0.973 1.067 1.017 0.863 0.512 0.243 0.000

0.000 0.069 0.143 0.287 0.426 0.604 0.948 1.087 1.102 0.764 0.400 0.000

0.0 224.4 449.5 858.4 1218.7 1608.2 2217.5 2405.5 2389.1 1827.1 1109.0 0.0

0.0000 0.0491 0.0990 0.1958 0.2961 0.3947 0.4948 0.5995 0.7004 0.8004 0.9003 0.9505 1.0000

0.88830 0.88476 0.88103 0.87357 0.86534 0.85663 0.84703 0.83607 0.82439 0.81161 0.79715 0.78942 0.78115

x1

q/ (g Æ cm3)

g/ (mPa Æ s)

0.0000 0.0501 0.0986 0.1961 0.2961 0.3991 0.4971 0.5989 0.6991 0.8001 0.8996 0.9499 1.0000

0.78975 0.79599 0.80209 0.81488 0.82905 0.84525 0.86282 0.88407 0.90869 0.93733 0.96571 0.97928 0.99820

1.187 1.277 1.371 1.549 1.735 1.975 2.225 2.479 2.705 2.700 2.223 1.630 1.002

0.0000 0.0501 0.0986 0.1961 0.2961 0.3991 0.5989 0.6991 0.8001 0.8996 0.9499 1.0000

0.78546 0.79168 0.79777 0.81054 0.82470 0.84094 0.87989 0.90465 0.93365 0.96324 0.97772 0.99705

0.0000 0.0501 0.0986 0.1961 0.2961 0.3991 0.5989 0.6991 0.8001 0.8996 0.9499 1.0000

0.78115 0.78735 0.79341 0.80614 0.82029 0.83655 0.87563 0.90055 0.92990 0.96061 0.97593 0.99565

VE/ (cm3 Æ mol1)

viscosity of the mixture and the pure component, respectively. The excess Gibbs free energies of activation of viscous flow were obtained from the following equation: " # N X E DG ¼ RT lnðgV Þ  xi lnðgi V i Þ ; ð3Þ i¼1

where R is the universal constant of gases, T is the absolute temperature, Vi is the molar volume of component i, V is the molar volume of the mixture, xi represents the mole fraction of the component i and g, gi are the dynamic viscosity of the mixture and the pure component, respectively. The binary deviations at several temperatures were fitted to a Redlich–Kister [18] type equation:

DQ12 ¼ x1 x2

M X

103Dg/ (Pa Æ s)

DG*E/ (J Æ mol1)

T = 293.15 K 0.000 0.033 0.061 0.102 0.122 0.135 0.138 0.129 0.111 0.078 0.051 0.022 0.000

0.000 0.038 0.073 0.133 0.194 0.245 0.274 0.312 0.307 0.282 0.195 0.103 0.000

0.0 112.3 205.9 353.1 504.2 618.8 636.8 714.1 648.8 562.9 353.2 168.0 0.0

0.426 0.425 0.429 0.435 0.448 0.467 0.502 0.543 0.614 0.701 0.843 0.958 1.082

T = 298.15 K 0.000 0.036 0.068 0.112 0.138 0.152 0.154 0.143 0.123 0.088 0.058 0.025 0.000

0.000 0.033 0.062 0.119 0.172 0.218 0.249 0.276 0.271 0.250 0.174 0.092 0.000

0.0 104.9 183.5 350.2 491.0 603.4 649.1 696.7 633.4 552.5 351.5 167.8 0.0

0.403 0.402 0.406 0.412 0.426 0.439 0.467 0.508 0.575 0.650 0.777 0.869 0.987

T = 303.15 K 0.000 0.039 0.076 0.124 0.153 0.169 0.171 0.159 0.136 0.098 0.065 0.028 0.000

0.000 0.030 0.055 0.105 0.150 0.195 0.225 0.245 0.237 0.220 0.152 0.089 0.000

0.0 102.3 176.2 334.6 458.4 592.3 655.9 680.4 604.4 538.2 339.9 189.0 0.0

VE/ (cm3 Æ mol1)

p

Bp ðx1  x2 Þ ;

ð4Þ

p¼0

where DQ12 is the excess property, x1 and x2 are the mole fraction of components 1 and 2, respectively, Bp is the fitting parameter and M is the degree of the polynomic expansion. The fitting parameters are given in table 8 together with the root-mean-square deviations r ( , )1=2 ndat X r¼ ðzexp  zcalc Þ2 ndat ; ð5Þ i

B. Gonza´lez et al. / J. Chem. Thermodynamics 39 (2007) 1578–1588 TABLE 5 Density q, speed of sound u, dynamic viscosity g, excess molar volumes VE, viscosity deviations Dg, and excess Gibbs free energy of activation DG*E for {x1 ethanol + (1x1) methylacetate} VE/ (cm3 Æ mol1)

x1

q/ (g Æ cm3)

g/ (mPa Æ s)

0.0000 0.0493 0.0987 0.1998 0.3006 0.3973 0.4863 0.6031 0.6972 0.7986 0.9009 0.9510 1.0000

0.93356 0.92783 0.92200 0.90985 0.89716 0.88452 0.87235 0.85548 0.84115 0.82484 0.80747 0.79876 0.78975

0.386 0.383 0.389 0.398 0.419 0.444 0.477 0.540 0.615 0.735 0.903 1.032 1.187

T = 293.15 K 0.000 0.037 0.071 0.116 0.152 0.168 0.175 0.172 0.155 0.125 0.075 0.031 0.000

0.367 0.363 0.365 0.377 0.395 0.418 0.449 0.505 0.572 0.684 0.838 0.945 1.082

T = 298.15 K 0.000 0.041 0.077 0.127 0.168 0.185 0.191 0.188 0.168 0.135 0.081 0.034 0.000

0.0000 0.0493 0.0987 0.1998 0.3006 0.3973 0.4863 0.6031 0.6972 0.7986 0.9009 0.9510 1.0000

0.0000 0.0493 0.0987 0.1998 0.3006 0.3973 0.4863 0.6031 0.6972 0.7986 0.9009 0.9510 1.0000

0.92698 0.92131 0.91554 0.90354 0.89100 0.87856 0.86659 0.84999 0.83591 0.81989 0.80285 0.79430 0.78546

0.92034 0.91473 0.90902 0.89715 0.88479 0.87254 0.86077 0.84445 0.83062 0.81490 0.79818 0.78981 0.78115

0.348 0.345 0.347 0.359 0.374 0.394 0.422 0.473 0.537 0.640 0.768 0.868 0.987

T = 303.15 K 0.000 0.045 0.084 0.140 0.185 0.204 0.209 0.205 0.183 0.147 0.087 0.037 0.000

TABLE 6 Density q, speed of sound u, dynamic viscosity g, excess molar volumes VE, viscosity deviations Dg, and excess Gibbs free energy of activation DG*E for {x1 methanol + (1  x1) ethylacetate}

103Dg/ (Pa Æ s)

DG*E/ (J Æ mol1)

x1

q/ (g Æ cm3)

g/ (mPa Æ s)

0.000 0.042 0.076 0.148 0.208 0.260 0.299 0.329 0.329 0.291 0.205 0.116 0.000

0.0 147.8 239.6 451.2 594.6 713.5 780.3 798.1 742.2 592.0 380.7 199.5 0.0

0.0000 0.0474 0.0970 0.1956 0.2999 0.3963 0.4962 0.5963 0.6998 0.7992 0.9005 1.0000

0.90052 0.89851 0.89618 0.89118 0.88493 0.87826 0.87014 0.86045 0.84826 0.83388 0.81552 0.79190

0.452 0.447 0.443 0.442 0.442 0.447 0.453 0.463 0.481 0.504 0.536 0.585

0.0000 0.0474 0.0970 0.1956 0.2999 0.3963 0.4962 0.5963 0.6998 0.7992 0.9005 1.0000

0.89443 0.89243 0.89012 0.88516 0.87899 0.87238 0.86436 0.85482 0.84281 0.82862 0.81050 0.78720

0.0000 0.0474 0.0970 0.1956 0.2999 0.3963 0.4962 0.5963 0.6998 0.7992 0.9005 1.0000

0.88830 0.88630 0.88401 0.87909 0.87298 0.86646 0.85855 0.84915 0.83730 0.82331 0.80545 0.78248

0.000 0.039 0.073 0.133 0.187 0.233 0.266 0.293 0.294 0.254 0.173 0.102 0.000

0.000 0.035 0.064 0.117 0.166 0.208 0.237 0.260 0.257 0.218 0.156 0.088 0.000

0.0 152.9 265.8 446.8 593.7 707.8 766.9 788.9 735.8 571.2 352.8 196.6 0.0

0.0 144.7 253.8 423.5 577.2 695.0 753.6 773.3 704.4 535.8 356.3 187.1 0.0

where zexp, zcalc, and ndat, are the values of the experimental and calculated property and the number of experimental data points, respectively. Figure 1 shows the fitted curve of excess molar volume values of systems {x1 water + (1  x1) ethanol}, {x1 water + (1  x1) methanol}, {x1 ethanol + (1  x1) ethyl acetate}, {x1 ethanol + (1  x1) methyl acetate}, {x1 methanol + (1  x1) ethyl acetate}, and {x1 methanol + (1  x1) methyl acetate} at T = (293.15, 298.15, and 303.15) K. In figure 1, the literature values of Arce et al. [4], Rodriguez et al. [5] and Nikam et al. [7] are also shown.

1581

103Dg/ (Pa Æ s)

DG*E/ (J Æ mol1)

T = 293.15 K 0.000 0.019 0.029 0.056 0.069 0.079 0.084 0.083 0.072 0.058 0.040 0.000

0.000 0.011 0.022 0.036 0.050 0.058 0.065 0.068 0.064 0.054 0.036 0.000

0.0 24.1 44.7 57.2 73.3 70.6 79.7 84.9 73.0 61.1 45.1 0.0

0.426 0.422 0.418 0.417 0.419 0.421 0.427 0.435 0.451 0.472 0.501 0.545

T = 298.15 K 0.000 0.017 0.026 0.051 0.062 0.072 0.076 0.077 0.068 0.055 0.038 0.000

0.000 0.010 0.020 0.032 0.043 0.052 0.058 0.062 0.058 0.049 0.032 0.000

0.0 18.8 42.6 46.9 48.8 61.4 65.8 76.3 66.3 54.4 40.2 0.0

0.403 0.400 0.396 0.396 0.398 0.398 0.403 0.410 0.425 0.443 0.469 0.508

T = 303.15 K 0.000 0.015 0.022 0.044 0.054 0.064 0.069 0.071 0.063 0.050 0.036 0.000

0.000 0.008 0.018 0.028 0.036 0.047 0.052 0.056 0.051 0.044 0.029 0.000

0.0 12.3 36.0 34.1 27.6 50.0 53.6 63.9 50.4 44.8 33.4 0.0

VE/ (cm3 Æ mol1)

The excess molar volume is negative over the entire composition range for the water (1) with methanol (2) and ethanol (2) and methanol (1) with methyl acetate (2) and ethyl acetate (2) mixtures. The negative excess molar volume can be attributed to the strong interactions between unlike molecules through hydrogen bonding. For the systems ethanol with esters, the excess molar volume is positive over the entire compositions range, where the excess molar volume increases when the ester chain length decreases. The deviations of the excess molar volume increase with the increase in the temperature for all studied systems, except for the binary system with water where the excess molar volume presents little variations with the temperature. For viscosity deviations (figure 2), the sign is negative for all systems except for the systems alcohol with water.

B. Gonza´lez et al. / J. Chem. Thermodynamics 39 (2007) 1578–1588

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TABLE 7 Density q, speed of sound u, dynamic viscosity g, excess molar volumes VE, viscosity deviations Dg, and excess Gibbs free energy of activation DG*E for {x1 methanol + (1x1) methylacetate} Dg/ (mPa Æ s)

DG*E/ (J Æ mol1)

T = 293.15 K 0.000 0.015 0.031 0.054 0.071 0.076 0.078 0.074 0.062 0.040 0.024 0.006 0.000

0.000 0.017 0.027 0.047 0.062 0.072 0.082 0.087 0.084 0.073 0.044 0.024 0.000

0.0 77.5 108.6 173.5 220.2 234.6 263.5 279.5 258.8 224.1 123.9 64.0 0.0

0.367 0.359 0.361 0.366 0.364 0.370 0.382 0.392 0.416 0.443 0.486 0.516 0.545

T = 298.15 K 0.000 0.014 0.027 0.049 0.066 0.070 0.072 0.071 0.058 0.037 0.022 0.006 0.000

0.000 0.016 0.023 0.036 0.055 0.068 0.074 0.080 0.076 0.067 0.041 0.020 0.000

0.0 80.4 96.1 124.8 203.3 248.4 255.7 276.2 252.4 219.0 127.5 54.5 0.0

0.348 0.341 0.342 0.348 0.347 0.351 0.360 0.371 0.393 0.417 0.455 0.483 0.508

T = 303.15 K 0.000 0.012 0.022 0.043 0.058 0.063 0.065 0.064 0.052 0.033 0.019 0.004 0.000

0.000 0.015 0.022 0.032 0.048 0.061 0.068 0.071 0.067 0.059 0.037 0.017 0.000

0.0 75.2 95.5 111.0 180.0 233.3 253.1 259.4 234.9 205.9 122.5 46.8 0.0

x1

q/ (g Æ cm3)

g/ (mPa Æ s)

0.0000 0.0471 0.0982 0.1983 0.2912 0.4015 0.5006 0.5878 0.7017 0.8015 0.9008 0.9504 1.0000

0.93356 0.93026 0.92648 0.91839 0.90997 0.89852 0.88679 0.87507 0.85733 0.83891 0.81751 0.80516 0.79190

0.386 0.378 0.378 0.379 0.382 0.394 0.404 0.416 0.442 0.472 0.521 0.551 0.585

0.0000 0.0471 0.0982 0.1983 0.2912 0.4015 0.5006 0.5878 0.7017 0.8015 0.9008 0.9504 1.0000

0.92698 0.92371 0.91995 0.91196 0.90365 0.89235 0.88078 0.86925 0.85173 0.83357 0.81245 0.80029 0.78720

0.0000 0.0471 0.0982 0.1983 0.2912 0.4015 0.5006 0.5878 0.7017 0.8015 0.9008 0.9504 1.0000

0.92034 0.91710 0.91337 0.90546 0.89726 0.88612 0.87471 0.86335 0.84609 0.82819 0.80737 0.79538 0.78248

VE/ (cm3 Æ mol1)

For the systems alcohol with ester, the negative deviation of viscosity increases when the length of chain of alcohol increases, and decreases when the length of chain of ester increases. Nevertheless, for the binary systems water (1) with methanol (2) and ethanol (2) the positive deviation decreases when the length of chain of alcohol increases. In this figure, the literature values of Canosa et al. [6] and Nikam et al. [7] are also shown. In figures 1 and 2, we can observe that there is a large difference between the excess properties of Nikam et al. [7] and the ones presented in this work. This difference can be explained because the use of automatic apparatus

reduces certain parameters such as errors in reading, measure time errors, etc. We can also observe that the literature data from Canosa et al. [6] present more agreement, although there are small differences. The apparatus used by Canosa et al. [6] yields results with less precision, one reason that can help explain these little differences. 4. Correlation and prediction The UNIQUAC equation is used for calculating the excess molar free energy of activation for flow, DG*E, which is related to the viscosity by: X lnðmMÞ ¼ xi lnðmi M i Þ þ DGE =R  T ; ð6Þ i

where m and mi are the kinematic viscosity of the mixture and kinematic viscosity of the pure component, and M and Mi are the molar mass of the mixture and the pure component, respectively. The correlation has been performed with experimental data using the UNIQUAC equation for calculating of the excess molar free energy, minimizing the following objective function: AAD ¼

N jgi;exp  gi;calc j 1 X ; N i¼1 gi;exp

ð7Þ

where N is the number of experimental data points and gi,exp and gi,calc are the experimental and calculated dynamic viscosity, respectively. The fitting parameters (s12, s21) and the average absolute deviation of dynamic viscosity (AAD) are reported in table 9. Figure 3 shows the viscosity data correlated by the UNIQUAC equation for the binary systems {x1 water + (1  x1) ethanol}, {x1 water + (1  x1) methanol}, {x1 ethanol + (1  x1) ethyl acetate}, {x1 ethanol + (1  x1) methyl acetate}, {x1 methanol + (1  x1) ethyl acetate}, and {x1 methanol + (1  x1) methyl acetate} at T = (293.15, 298.15, and 303.15) K. It can be seen that this equation fits fairly well the experimental data at several temperatures for all studied systems except for those containing water, which can be due to hydrogen bonds. UNIFAC-VISCO and ASOG-VISCO methods have been applied to show the difference between predicted and experimental dynamic viscosities. Table 10 shows the average absolute deviation of dynamic viscosity (AAD) resulting from the prediction using UNIFACVISCO and ASOG-VISCO methods for the binary mixtures {x1 ethanol + (1  x1) ethyl acetate}, {x1 ethanol + (1  x1) methyl acetate}, {x1 methanol + (1  x1) ethyl acetate}, and {x1 methanol + (1  x1) methyl acetate} at T = (293.15, 298.15, and 303.15) K. For those systems containing water, the prediction can only be calculated using the ASOG-VISCO method, due to the UNIFAC-VISCO method not having in its matrix the water as a functional group.

B. Gonza´lez et al. / J. Chem. Thermodynamics 39 (2007) 1578–1588

1583

TABLE 8 Fitting parameters and root-mean-square deviation,r, for binary mixtures at T = (273.15, 298.15, 303.15) K

VE/(cm3 Æ mol1) Dg/(mPa Æ s) DG*E/(J Æ mol1)

B0 = 3.9878 B0 = 2.7551 B0 = 6883.2

Water (1) + methanol (2) T = 293.15 K B1 = 0.2863 B2 = 0.5820 B1 = 3.2700 B2 = 2.4345 B1 = 3881.7 B2 = 3479.8

VE/(cm3 Æ mol1) Dg/(mPa Æ s) DG*E/(J Æ mol1)

B0 = 4.0108 B0 = 2.3766 B0 = 6733.4

B1 = 0.2359 B1 = 2.5959 B1 = 3543.7

VE/(cm3 Æ mol1) Dg/(mPa Æ s) DG*E/(J Æ mol1)

B0 = 4.0201 B0 = 2.0545 B0 = 6593.2

B1 = 0.1952 B1 = 2.0614 B1 = 3334.9

VE/(cm3 Æ mol1) Dg/(mPa Æ s) DG*E/(J Æ mol1)

B0 = 4.2860 B0 = 4.4918 B0 = 8233.8

Water (1) + ethanol (2) T = 293.15 K B1 = 1.3098 B2 = 2.2686 B1 = 6.0209 B2 = 6.2443 B1 = 6578.5 B2 = 6203.8

VE/(cm3 Æ mol1) Dg/(mPa Æ s) DG*E/(J Æ mol1)

B0 = 4.2125 B0 = 3.4834 B0 = 7724.0

B1 = 1.2230 B1 = 5.0507 B1 = 6707.1

VE/(cm3 Æ mol1) Dg/(mPa Æ s) DG*E/(J Æ mol1)

B0 = 4.1598 B0 = 3.0437 B0 = 7724.8

B1 = 1.1523 B1 = 3.8533 B1 = 6110.6

VE/(cm3 Æ mol1) Dg/(mPa Æ s) DG*E/(J Æ mol1)

B0 = 0.5590 B0 = 1.1238 B0 = 2764.8

Ethanol (1) + ethyl acetate (2) T = 293.15 K B1 = 0.0940 B1 = 0.6515 B2 = 0.5227 B1 = 942.6 B2 = 116.8

VE/(cm3 Æ mol1) Dg/(mPa Æ s) DG*E/(J Æ mol1)

B0 = 0.6239 B0 = 1.0051 B0 = 2687.6

B1 = 0.1073 B1 = 0.5600 B1 = 871.9

B3 = 0.8016 B3 = 0.2227 B3 = 1891.1

B4 = 1.5062 B4 = 207.1

r = 0.007 r = 0.007 r = 5.21

T = 298.15 K B2 = 0.5066 B2 = 1.8771 B2 = 3276.7

B3 = 0.7216 B3 = 0.0883 B3 = 2035.1

B4 = 1.5062 B4 = 175.5

r = 0.006 r = 0.004 r = 4.81

T = 303.15 K B2 = 0.3895 B2 = 1.2594 B2 = 2434.0

B3 = 0.6523 B3 = 0.0008 B3 = 1803.4

B4 = 0.5456 B4 = 1195.4

r = 0.007 r = 0.006 r = 11.05

B3 = 0.6225 B3 = 1.0193 B3 = 6278.0

B4 = 2.0215 B4 = 2.2780 B4 = 4011.0

r = 0.013 r = 0.023 r = 15.44

T = 298.15 K B2 = 2.2282 B2 = 6.5341 B2 = 7512.1

B3 = 0.4975 B3 = 0.3265 B3 = 5079.3

B4 = 1.8625 B4 = 3.8369 B4 = 1634.9

r = 0.011 r = 0.018 r = 18.58

T = 303.15 K B2 = 2.0609 B2 = 4.3019 B2 = 5751.4

B3 = 0.3835 B3 = 0.5727 B3 = 5212.4

B4 = 1.5632 B4 = 2.0780 B4 = 2859.8

r = 0.010 r = 0.014 r = 8.97

B4 = 493.8

r = 0.003 r = 0.004 r = 10.19

B4 = 212.0

r = 0.003 r = 0.003 r = 9.92

B4 = 1222.5

r = 0.004 r = 0.003 r = 9.63

B4 = 836.2

r = 0.002 r = 0.003 r = 6.99

B4 = 1018.6

r = 0.003 r = 0.003 r = 4.97

B4 = 1689.2

r = 0.003 r = 0.004 r = 8.14

B3 = 0.2530 B3 = 19.4

T = 298.15 K B2 = 0.4393 B2 = 264.6

B3 = 0.2720 B3 = 254.5

T = 303.15 K VE/(cm3 Æ mol1) Dg/(mPa Æ s) DG*E/(J Æ mol1)

B0 = 0.6941 B0 = 0.8931 B0 = 2645.8

B1 = 0.1142 B1 = 0.4756 B1 = 831.7

VE/(cm3 Æ mol1) Dg/(mPa Æ s) DG*E/(J Æ mol1)

B0 = 0.7038 B0 = 1.2025 B0 = 3152.9

Ethanol (1) + methyl acetate (2) T = 293.15 K B1 = 0.0244 B2 = 0.1342 B1 = 0.6630 B2 = 0.5283 B1 = 826.8 B2 = 16.4

VE/(cm3 Æ mol1) Dg/(mPa Æ s) DG*E/(J Æ mol1)

B0 = 0.7714 B0 = 1.0749 B0 = 3122.0

B1 = 0.0152 B1 = 0.5925 B1 = 854.2

T = 298.15 K B2 = 0.1357 B2 = 0.4390 B2 = 124.4

B3 = 0.1584 B3 = 441.2

VE/(cm3 Æ mol1) Dg/(mPa Æ s) DG*E/(J Æ mol1)

B0 = 0.8453 B0 = 0.9541 B0 = 3077.3

B1 = 0.0068 B1 = 0.4958 B1 = 743.9

T = 303.15 K B2 = 0.1447 B2 = 0.3559 B2 = 685.4

B3 = 0.1750 B3 = 216.5

B0 = 0.3314 B0 = 0.2592

Methanol (1) + ethyl acetate (2) T = 293.15 K B1 = 0.0241 B2 = 0.0812 B1 = 0.0897 B2 = 0.0862

VE/(cm3 Æ mol1) Dg/(mPa Æ s)

B2 = 0.3775 B2 = 368.5

B3 = 0.2969 B3 = 411.7

B3 = 0.2979 B3 = 21.4

r = 0.002 r = 0.001 (continued on next page)

B. Gonza´lez et al. / J. Chem. Thermodynamics 39 (2007) 1578–1588

1584 TABLE 8 (continued) DG*E/(J Æ mol1)

B0 = 322.4

B1 = 46.8

VE/(cm3 Æ mol1) Dg/(mPa Æ s) DG*E/(J Æ mol1)

B0 = 0.3044 B0 = 0.2323 B0 = 276.2

B1 = 0.0374 B1 = 0.0879 B1 = 128.6

T = 298.15 K B2 = 0.0791 B2 = 0.0761 B2 = 27.9

VE/(cm3 Æ mol1) Dg/(mPa Æ s) DG*E/(J Æ mol1)

B0 = 0.2740 B0 = 0.2074 B0 = 226.46

B1 = 0.0519 B1 = 0.0822 B1 = 144.66

T = 303.15 K B2 = 0.0697 B2 = 0.0596 B2 = 193.77

VE/(cm3 Æ mol1) Dg/(mPa Æ s) DG*E/(J Æ mol1)

B0 = 0.3150 B0 = 0.3269 B0 = 1049.3

Methanol (1) + methyl acetate (2) T = 293.15 K B1 = 0.0502 B2 = 0.0364 B1 = 0.1272 B2 = 0.1325 B1 = 384.1 B2 = 665.6

VE/(cm3 Æ mol1) Dg/(mPa Æ s) DG*E/(J Æ mol1)

B0 = 0.2943 B0 = 0.3005 B0 = 1051.7

B1 = 0.0370 B1 = 0.1284 B1 = 384.2

T = 298.15 K B2 = 0.0505 B2 = 0.0877 B2 = 385.9

B1 = 0.0225 B1 = 0.1153 B1 = 422.0

T = 303.15 K B2 = 0.0625 B2 = 0.0688 B2 = 48.6

B0 = 0.2659 B0 = 0.2697 B0 = 1010.5

0.0

0.0

-0.3

-0.3

3 -1 E V /(cm .mol )

3 -1 E V /(cm .mol )

VE/(cm3 Æ mol1) Dg/(mPa Æ s) DG*E/(J Æ mol1)

B2 = 63.3

-0.6

-0.9

B3 = 75.8

0.0

B4 = 413.2

r = 0.002 r = 0.001 r = 3.06

B4 = 598.54

r = 0.002 r = 0.001 r = 4.61

B4 = 255.2

r = 0.002 r = 0.001 r = 5.97

B4 = 20.5

r = 0.002 r = 0.002 r = 8.84

B4 = 458.4

r = 0.002 r = 0.002 r = 8.57

B3 = 0.0411 B3 = 533.3 B3 = 0.0458 B3 = 457.5 B3 = 0.0475 B3 = 537.5

-0.6

-0.9

0.5

1.0

0.0

x1 0.4

d

0.3

3 -1 E V /(cm .mol )

3 -1 E V /(cm .mol )

B3 = 197.38

r = 2.81

-1.2

-1.2

c

B3 = 200.5

B4 = 294.0

0.2

0.1

0.0

0.5

x1

1.0

0.3

0.2

0.1

0.0

0.0

0.5

x1

1.0

0.0

0.5

1.0

x1

FIGURE 1. Excess molar volume, VE, from the Redlich–Kister equation (——) plotted against mole fraction at T = 293.15 K (s), T = 298.15 K (h) and T = 313.15 K (n), for the binary mixtures: (a) {x1 water + (1  x1) ethanol} and Arce et al. ( , 298.15 K), (b) {x1 water + (1  x1) methanol}, (c) {x1 ethanol + (1  x1) ethyl acetate} and Nikam et al. ( , 298.15 K), (d) {x1 ethanol + (1  x1) methyl acetate} and Rodriguez et al. ( , 298.15 K), (e) {x1 methanol + (1  x1) ethyl acetate} and Nikam et al. (s, 298.15 K), and (f) {x1 methanol + (1  x1) methyl acetate} and Rodriguez et al. ( , 298.15 K).

B. Gonza´lez et al. / J. Chem. Thermodynamics 39 (2007) 1578–1588 0.00

3 -1 E V /(cm .mol )

0.00

3 -1 E V /(cm .mol )

1585

-0.05

-0.10

-0.05

-0.10

-0.15 0.0

0.5

x1

1.0

0.0

0.5

0.0

0.5

x1

1.0

Fig. 1 (continued)

a

d

2.0

Δη/(Pa.s)

-0.2

−3

1.0

10

10

−3

Δη/(Pa.s)

1.5

0.0

0.5

-0.4

0.0 0.0

0.5

1.0

e Δη/(Pa.s)

1.0

-0.08 0.0

0.5

x1

1.0

0.0

0.5

1.0

x1

0.0

Δη/(Pa.s)

f

0.00

-0.05

−3

-0.2

10

10

−3

Δη/(Pa.s)

-0.04

10

10

0.0

c

0.00

−3

0.5

−3

Δη/(Pa.s)

b

1.0

x1

x1

-0.10

-0.4 0.0

0.5

x1

1.0

0.0

0.5

1.0

x1

FIGURE 2. Viscosities deviations, Dg, from the Redlich–Kister equation (——) plotted against mole fraction at T = 293.15 K (s), T = 298.15 K (h) and T = 313.15 K (n), for the binary mixtures: (a) {x1 water + (1  x1) ethanol} and Arce et al. ( , 298.15 K), (b) {x1 water + (1  x1) methanol}, (c) {x1 ethanol + (1  x1) ethyl acetate} and Nikam et al. ( , 298.15 K), (d) {x1ethanol + (1  x1) methyl acetate} and Canosa et al. ( , 298.15 K), (e) {x1 methanol + (1  x1) ethyl acetate} and Nikam et al. ( , 298.15 K), and (f) {x1 methanol + (1  x1) methyl acetate} and Canosa et al. ( , 298.15 K).

B. Gonza´lez et al. / J. Chem. Thermodynamics 39 (2007) 1578–1588

1586

TABLE 9 UNIQUAC parameters and the average absolute deviation (AAD) Binary system

UNIQUAC equation

Water (1) + methanol (2) Water (1) + ethanol (2) Ethanol (1) + ethyl acetate (2) Ethanol (1) + methyl acetate (2) Methanol (1) + ethyl acetate (2) Methanol (1) + methyl acetate (2)

a

a12/ (J Æ mol1)

a21/ (J Æ mol1)

AAD

7400.0 5686.7 438.55 236.78 95.79 60.23

101.8 292.7 498.97 434.72 172.37 130.55

1.102 2.493 0.163 0.170 0.138 0.204

Figure 4 shows graphically the experimental dynamic viscosities and the predicted values by applying the UNIFAC-VISCO and ASOG-VISCO methods for the systems studied {ethanol (1) and methanol (1) with esters (2)} at T = (293.15, 298.15, and 303.15) K. In this figure, we can observe that the ASOG-VISCO method gives the worst prediction for the behaviour of these systems. The UNIFAC-VISCO method provides a very good prediction for the systems containing ethanol, but for the other systems studied this method do not obtain a good representation of the trend of the experimental data.

d

3.0

1.4

η/(Pa.s)

2.0

10

10

0.7

3

1.5

3

η/(Pa.s)

2.5

1.0 0.5

0.0

0.0 0.0

0.5

0.0

1.0

b

e

2.0

0.7

η/(Pa.s)

0.5

3

1.0

10

10

3

η/(Pa.s)

1.0

0.6

1.5

0.4

0.5

0.3

0.0 0.0

0.5

1.0

0.0

x1

c

0.5

x1

x1

0.5

1.0

x1

f

1.4

0.7

η/(Pa.s)

0.5

10

10

3

0.7

3

η/(Pa.s)

0.6

0.4

0.0

0.3 0.0

0.5

x1

1.0

0.0

0.5

1.0

x1

FIGURE 3. Dynamic viscosity, g, from the UNIQUAC equation plotted against mole fraction. Experimental points at T = 293.15 K (s), T = 298.15 K (h) and T = 313.15 K (n), for the binary mixtures: (a) {x1 water + (1  x1) ethanol}, (b) {x1 water + (1  x1) methanol}, (c) {x1 ethanol + (1  x1) ethyl acetate}, (d) {x1ethanol + (1  x1) methyl acetate}, (e) {x1 methanol + (1  x1) ethyl acetate}, and (f) {x1 methanol + (1  x1) methyl acetate}.

B. Gonza´lez et al. / J. Chem. Thermodynamics 39 (2007) 1578–1588 TABLE 10 Average absolute deviation (AAD) of dynamic viscosity resulting by the prediction using UNIFAC-VISCO and ASOG-VISCO methods for the binary mixtures ethanol (1) and methanol (1) with ethyl acetate (2) and methyl acetate (2) and water (1) with ethanol (2) and methanol (2) at several temperatures Systems

T/K

AAD UNIFACVISCO

AAD ASOGVISCO

Ethanol (1) + ethyl acetate (2)

293.15 298.15 303.15

2.75 2.70 2.68

25.85 24.64 23.40

Ethanol (1) + methyl acetate (2)

293.15 298.15 303.15

2.52 2.21 2.28

29.71 28.72 27.25

Methanol (1) + ethyl acetate (2)

293.15 298.15 303.15

6.72 5.94 5.10

15.97 13.91 13.72

Methanol (1) + methyl acetate (2)

293.15 298.15 303.15

6.83 6.07 5.60

17.59 16.70 16.05

Water (1) + ethanol (2)

293.15 298.15 303.15

16.04 14.02 13.17

Water (1) + methanol (2)

293.15 298.15 303.15

6.57 6.07 5.43

In this work, the dynamic viscosities and densities been determined for water (1) with ethanol (2) and methanol (2), ethanol (1) with ethyl acetate (2) and methyl acetate (2) and methanol (1) with ethyl acetate (2) and methyl acetate (2) at several temperatures T = (273.15, 298.15, and 303.15) K over the whole composition range. Excess molar volume, viscosity deviations, and excess Gibbs free energy of activation were calculated and fitted to the Redlich–Kister equation to test the quality of the experimental values. The correlation of the experimental viscosity data has been determined using the UNIQUAC equation. Very good results had been obtained with this equation for all studied systems except for those containing water. The prediction of viscosity using UNIFAC-VISCO and ASOG-VISCO methods were compared. We can observe that with the ASOG-VISCO method the deviations obtained are greater. The UNIFAC-VISCO method predicts better the behaviour of these systems than does the ASOG-VISCO method.

c

1.40

0.70

0.00 0.0

5. Conclusions

103η /(Pa.s)

103η /(Pa.s)

a

0.75

0.50

0.25 0.5

0.0

1.0

d

103η /(Pa.s)

103η /(Pa.s)

1.40

0.70

0.00 0.0

0.5

1.0

0.5

1.0

x1

x1

b

1587

0.65

0.45

0.25 0.5

x1

1.0

0.0

x1

FIGURE 4. Predicted values of dynamic viscosities, g, from the UNIFAC-VISCO (——) and ASOG-VISCO (– – –) methods plotted against mole fraction at T = 293.15 K (s), T = 298.15 K (h) and T = 313.15 K (n), for the binary mixtures: (a) {x1 ethanol + (1  x1) ethyl acetate}, (b) {x1ethanol + (1  x1) methyl acetate}, (c) {x1 methanol + (1  x1) ethyl acetate}, and (d) {x1 methanol + (1  x1) methyl acetate}.

1588

B. Gonza´lez et al. / J. Chem. Thermodynamics 39 (2007) 1578–1588

References [1] B. Gonzalez, A. Dominguez, J. Tojo, R. Cores, J. Chem. Eng. Data 49 (2004) 1225–1230. [2] B. Gonzalez, A. Dominguez, J. Tojo, J. Chem. Thermodyn. 39 (2007) 322–334. [3] B. Gonzalez, A. Dominguez, J. Tojo, R. Cores, J. Chem. Eng. Data 51 (2006) 1076–1087. [4] A. Arce, A. Blanco, A. Soto, I. Vidal, J. Chem. Eng. Data 38 (1993) 336–340. [5] A. Rodriguez, J. Canosa, B. Orge, M. Iglesias, J. Tojo, J. Chem. Eng. Data 41 (1996) 1446–1449. [6] J. Canosa, A. Rodriguez, J. Tojo, J. Chem. Eng. Data 43 (1998) 417– 421. [7] P.S. Nikam, T.R. Mahale, M. Hassan, Chem. Eng. Data 41 (1996) 1055–1058. [8] D.S. Abrams, J.M. Prausnitz, AIChE J. 21 (1975) 116–128. [9] J.L. Chevalier, P.J. Petrino, Y.H. Gaston-Bonhomme, J. Chem. Eng. Sci. 43 (1988) 1303–1309.

[10] Y. Gaston-Bonhomme, P. Petrino, J.L. Chevalier, J. Chem. Eng. Sci. 49 (1994) 1799–1806. [11] K. Tochigi, K. Yoshino, V.K. Rattan, in: The Sixteenth European Conference on Thermophysical Properties, 1–4 September, London, 2002. [12] H. Eyring, J. Chem. Phys. 4 (1936) 283–291. [13] I.-C. Wei, R.L. Rowley, J. Chem. Eng. Data 29 (1984) 332– 335. [14] J.A. Riddick, W.B. Bunger, T.K. Sakano, Organic Solvents, Willey, New York, 1986. [15] P. Nikam, M. Jadhav, M.J. Hassan, Chem. Eng. Data 40 (1995) 931– 934. [16] L. De Lorenzi, M. Fermeglia, G. Torriano, J. Chem. Eng. Data 40 (1995) 1172–1177. [17] U.R. Kapadi, D.G. Hundiwale, N.B. Patil, P.R. Patil, M.K. Lande, J. Ind. Chem. Soc. 77 (2000) 319–321. [18] O. Redlich, A.T. Kister, Ind. Eng. Chem. 40 (1948) 345–348.

JCT 07-73