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Viscosities, densities and speeds of sound of the binary systems: 2-propanol with octane, or decane, or dodecane at T=(293.15, 298.15, and 303.15) K
J. Chem. Thermodynamics 35 (2003) 939–953 www.elsevier.com/locate/jct
Viscosities, densities and speeds of sound of the binary systems: 2-propanol with octane, or decane, or dodecane at T ¼ (293.15, 298.15, and 303.15) K B. Gonz alez, A. Dominguez, J. Tojo
*
Chemical Engineering Department, Vigo University, 36200 Vigo, Spain Received 13 November 2002; accepted 4 February 2003
Abstract Viscosities, densities and speed of sound have been measured over the whole composition range for (2-propanol with octane, or decane, or dodecane) at T ¼ (293.15, 298.15, and 303.15) K and atmospheric pressure along with the properties of the pure components. Excess molar volumes, isentropic compressibility, deviations in isentropic compressibility and viscosity deviations for the binary systems at the above-mentioned temperatures were calculated and fitted to Redlich–Kister equation to determine the fitting parameters and the root-meansquare deviations. Prediction of the dynamic viscosities of this binary mixture from UNIFAC-VISCO and ASOG-VISCO methods has been determined. Ó 2003 Elsevier Science Ltd. All rights reserved. Keywords: Viscosity; Density; Speed of sound; 2-Propanol; Octane; Decane; Dodecane
1. Introduction In the chemical industry, the information on the viscosity of liquid mixtures is necessary in different applications for surface facilities, pipeline systems, mass-transfer operations, etc. As an extension of our work concerning dynamic viscosity of
*
Corresponding author. Tel.: +34-986-812287; fax: +34-986-812382. E-mail address: [email protected] (J. Tojo).
0021-9614/03/$ - see front matter Ó 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0021-9614(03)00047-8
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B. Gonzalez et al. / J. Chem. Thermodynamics 35 (2003) 939–953
binary and ternary systems [1–6], in this paper, we show experimental dynamic viscosity, density and speed of sound data of the binary systems 2-propanol with octane, or decane, or dodecane at T ¼ (293.15, 298.15, and 303.15) K. The results were used to calculate excess molar volumes, isentropic compressibility, deviations in isoentropic compressibility and viscosity over the entire mole fraction range for the mixtures. The UNIFAC-VISCO [7] and ASOG-VISCO [8] methods have been applied to compare the difference between predicted and experimental dynamic viscosities. 2. Experimental The pure components were supplied for Fluka, except for the 2-propanol which was supplied by Merck. The components were degassed ultrasonically, and dried , that were supplied by Aldrich, and kept in inert arover molecular sieves Type 4 A gon with a maximum content in water of 2 106 by mass fraction. Their mass fraction purities were >0.999 for 2-propanol, >0.995 for octane, >0.99 for decane and >0.99 for dodecane. The solvent purities were compared with recently published density and dynamic viscosity values at T ¼ 298:15 K in table 1. 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 0:4 103 and 0:53 103 m diameter. Gravity fall is the principle of measurement on which this viscosimeter is based. The capillary is maintained in a D20KP LAUDA thermostat with a resolution of 0.01 °C. The capillaries are calibrated and credited by the company which supplies us. The accuracy of the capillaries is 0.5%. In order to verify the calibration of the same ones the pure liquids, in table 1, were compared with data recently published. The uncertainty for the viscosimeter is better than 1%. The equipment has a control unit PVS1 (Processor Viscosity System) that is a PC-controlled instrument for the precise measurement of liquid viscosity using standardized glass capillaries with a accuracy of 0.01 s. TABLE 1 Comparison of density q and viscosity g with literature values for pure components at T ¼ 298:15 K Components
q=ðg cm3 Þ
103 g=ðPa sÞ
Exptl.
Lit.
Exptl.
Lit.
2-Propanol
0.7809
0.7809 [12] 0.7813 [9]
2.045
2.048 [9]
Octane
0.6985
0:6986 [11] 0.6985 [13]
0.506
0.506 [11]
Decane
0.7262
0.7262 [11] 0.7262 [10]
0.843
0.843 [11]
Dodecane
0.7453
0.7454 [11] 0.7455 [14]
1.348
1.345 [11] 1.359 [14]
B. Gonzalez et al. / J. Chem. Thermodynamics 35 (2003) 939–953
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The kinematic viscosity is determined from the following relationship: m ¼ kðt yÞ;
ð1Þ
where y is the Hagenbach correction, t is the flow time and k is the Ubbelhode capillary microviscosimeter constant which is supply for the company. The dynamic viscosity is determined from: g ¼ m q;
ð2Þ
where g is the dynamic viscosity, m is the kinematic viscosity and q is the density. The uncertainty for the dynamic viscosity is 2 106 . The densities and the speed of sound of the pure liquids and mixtures were measured using an Anton Paar DSA5000 digital vibrating tube densimeter. The accuracy and the precision for the density are 106 g cm3 and 2 106 g cm3 ; and for the speed of sound are 0:1 m s1 and 102 m s1 , respectively.
3. Results and discussion Dynamic viscosity, density, speed of sound, excess molar volume, isentropic compressibility (determined by means of the Laplace equation, kS ¼ q1 u2 ), deviation in isentropic compressibility and viscosity deviation of {x1 2-propanol + (1 x1 ) octane}, {x1 2-propanol + (1 x1 ) decane} and {x1 2-propanol + (1 x1 ) dodecane} at T ¼ (293.15, 298.15, and 303.15) K and atmospheric pressure are reported in tables 2–4. The excess molar volumes, the deviations in isentropic compressibility and the viscosity deviations are calculated by the equations: VE ¼
N X
xi Mi ðq1 q1 i Þ;
ð3Þ
i¼1 N X
DjS ¼ jS
ð4Þ
xi jS;i ;
i¼1
Dg ¼ g
N X
ð5Þ
x i gi ;
i
where q and qi are the density of the mixture and the density of the pure components, respectively; jS is the isentropic compressibility of the mixture; jS;i is the isentropic compressibility of the pure components; g and gi are the dynamic viscosity of the mixture and the pure component, respectively, and xi represents the mole fraction of the pure component. The binary deviations were fitted to a Redlich–Kister [15] type equation: DQij ¼ xi xj
M X p¼0
p
Bp ðxi xj Þ ;
ð6Þ
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TABLE 2 Dynamic viscosities g, densities q, speeds of sound u, isentropic compressibilities jS , excess molar volumes V E , deviations in isentropic compressibilities DjS , and viscosities deviations Dg of {x1 2-propanol + (1 x1 ) octane} at T ¼ (293.15, 298.15, and 303.15) K x1
q
u
103 g
ðg cm3 Þ
ðm s1 Þ
ðPa sÞ
0 0.0518 0.0896 0.2120 0.2820 0.4103 0.6027 0.6988 0.7988 0.9007 0.9496 1
0.7026 0.7038 0.7049 0.7095 0.7126 0.7195 0.7334 0.7424 0.7536 0.7675 0.7758 0.7851
1193 1188 1184 1175 1171 1164 1157 1155 1153 1153 1154 1156
0 0.0518 0.0896 0.2120 0.2820 0.4103 0.6027 0.6988 0.7988 0.9007 0.9496 1
0.6985 0.6997 0.7008 0.7053 0.7084 0.7152 0.7290 0.7380 0.7492 0.7632 0.7712 0.7809
0 0.0518 0.0896 0.2120 0.2820 0.4103 0.6027 0.6988 0.7988 0.9007 0.9496 1
0.6945 0.6955 0.6966 0.7010 0.7041 0.7108 0.7246 0.7336 0.7448 0.7589 0.7669 0.7766
VE
jS 1
ðcm3 mol Þ
103 Dg
DjS 1
1
ðTPa Þ
ðTPa Þ
ðPa sÞ
T ¼ 293:15 K 0.538 0.000 0.539 0.195 0.542 0.285 0.562 0.480 0.580 0.544 0.644 0.603 0.830 0.537 0.985 0.451 1.225 0.342 1.624 0.214 1.961 0.129 2.382 0.000
999 1007 1011 1020 1023 1025 1018 1010 998 980 968 953
0 10 16 31 37 45 47 44 36 23 13 0
0.000 )0.095 )0.161 )0.367 )0.478 )0.651 )0.819 )0.842 )0.786 )0.575 )0.328 0.000
1173 1167 1164 1155 1150 1144 1137 1135 1134 1134 1136 1139
T ¼ 298:15 K 0.507 0.000 0.507 0.216 0.510 0.311 0.526 0.518 0.542 0.587 0.596 0.653 0.752 0.584 0.883 0.489 1.088 0.370 1.429 0.228 1.690 0.137 2.045 0.000
1041 1050 1054 1063 1067 1069 1061 1052 1038 1018 1005 987
0 12 18 34 41 50 53 49 40 25 15 0
0.000 )0.079 )0.134 )0.307 )0.398 )0.542 )0.682 )0.699 )0.647 )0.463 )0.277 0.000
1152 1146 1143 1134 1130 1123 1117 1115 1114 1116 1118 1121
T ¼ 303:15 K 0.477 0.000 0.476 0.239 0.479 0.341 0.494 0.560 0.507 0.635 0.552 0.707 0.685 0.634 0.795 0.532 0.967 0.401 1.250 0.244 1.482 0.146 1.763 0.000
1085 1095 1099 1110 1113 1116 1107 1097 1081 1058 1043 1024
0 13 20 38 46 56 59 55 45 28 16 0
0.000 )0.068 )0.114 )0.256 )0.333 )0.453 )0.567 )0.581 )0.538 )0.386 )0.217 0.000
where DQij is the excess property, x is the mole fraction, Bp is the fitting parameter and M is the degree of the polynomic expansion, which was optimized using the F-test [16]. The fitting parameters are given in tables 5–7 together with the root-
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TABLE 3 Dynamic viscosities g, densities q, speeds of sound u, isentropic compressibilities jS , excess molar volumes V E , deviations in isentropic compressibilities DjS , and viscosities deviations Dg of {x1 2-propanol + (1 x1 ) decane} at T ¼ (293.15, 298.15, and 303.15) K x1
q
u
103 g
VE
ðg cm3 Þ
ðm s1 Þ
ðPa sÞ
0 0.0412 0.0998 0.1610 0.2938 0.3954 0.4988 0.5943 0.7019 0.8012 0.9017 0.9510 1
0.7299 0.7301 0.7310 0.7324 0.7351 0.7382 0.7421 0.7467 0.7531 0.7607 0.7710 0.7774 0.7851
1255 1249 1244 1237 1226 1218 1209 1201 1190 1180 1168 1162 1156
0.910 0.896 0.893 0.904 0.916 0.957 1.006 1.095 1.241 1.436 1.759 2.014 2.382
T ¼ 293:15 K 0.000 0.186 0.314 0.451 0.581 0.608 0.606 0.568 0.499 0.401 0.242 0.137 0.000
0 0.0412 0.0998 0.1610 0.2938 0.3954 0.4988 0.5943 0.7019 0.8012 0.9017 0.9510 1
0.7262 0.7263 0.7271 0.7285 0.7311 0.7341 0.7380 0.7425 0.7489 0.7565 0.7667 0.7732 0.7809
1235 1229 1224 1217 1206 1198 1189 1181 1171 1161 1150 1144 1139
0.843 0.831 0.827 0.847 0.845 0.878 0.916 0.986 1.110 1.273 1.538 1.742 2.045
0 0.0412 0.0998 0.1610 0.2938 0.3954 0.4988 0.5943 0.7019 0.8012 0.9017 0.9510 1
0.7224 0.7224 0.7232 0.7245 0.7271 0.7300 0.7338 0.7383 0.7446 0.7522 0.7625 0.7689 0.7766
1215 1210 1204 1197 1186 1178 1169 1161 1151 1142 1131 1126 1121
0.785 0.773 0.768 0.785 0.777 0.809 0.836 0.893 0.994 1.127 1.348 1.515 1.763
jS 1
ðcm3 mol Þ
103 Dg
DjS 1
ðTPa Þ
1
ðTPa Þ
ðPa sÞ
870 878 884 892 904 913 922 929 937 944 951 953 953
0 4 6 7 10 10 10 10 9 8 6 4 0
0.000 )0.075 )0.164 )0.272 )0.426 )0.535 )0.638 )0.690 )0.702 )0.654 )0.478 )0.296 0.000
T ¼ 298:15 K 0.000 0.204 0.342 0.487 0.605 0.655 0.655 0.615 0.538 0.431 0.258 0.145 0.000
903 911 918 927 940 949 958 966 974 981 987 988 987
0 4 7 9 12 13 13 13 12 10 8 5 0
0.000 )0.062 )0.136 )0.214 )0.351 )0.440 )0.527 )0.571 )0.577 )0.533 )0.389 )0.244 0.000
T ¼ 303:15 K 0.000 0.223 0.373 0.526 0.652 0.708 0.709 0.666 0.582 0.464 0.276 0.154 0.000
938 946 954 964 977 987 997 1005 1014 1020 1025 1026 1024
0 5 8 10 14 16 16 16 15 13 10 6 0
0.000 )0.053 )0.114 )0.177 )0.295 )0.363 )0.437 )0.473 )0.478 )0.442 )0.319 )0.201 0.000
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TABLE 4 Dynamic viscosities g, densities q, speeds of sound u, isentropic compressibilities jS , excess molar volumes V E , deviations in isentropic compressibilities DjS , and viscosities deviations Dg of {x1 2-propanol + (1 x1 Þ dodecane} at T ¼ (293.15, 298.15, and 303.15) K x1
q
u
103 g
VE
ðg cm3 Þ
ðm s1 Þ
ðPa sÞ
0 0.0422 0.0957 0.2215 0.3267 0.3943 0.4959 0.5981 0.6957 0.8012 0.9005 0.9502 1
0.7489 0.7489 0.7492 0.7502 0.7516 0.7528 0.7549 0.7578 0.7615 0.7668 0.7739 0.7788 0.7851
1298 1293 1288 1275 1265 1258 1247 1234 1220 1202 1182 1170 1156
1.476 1.446 1.424 1.397 1.396 1.407 1.421 1.480 1.566 1.714 1.920 2.101 2.382
T ¼ 293:15 K 0.000 0.170 0.279 0.480 0.562 0.594 0.604 0.571 0.509 0.404 0.260 0.151 0.000
0 0.0422 0.0957 0.2215 0.3267 0.3943 0.4959 0.5981 0.6957 0.8012 0.9005 0.9502 1
0.7453 0.7452 0.7455 0.7464 0.7478 0.7489 0.7510 0.7538 0.7574 0.7627 0.7698 0.7746 0.7809
1279 1274 1268 1256 1246 1238 1227 1215 1201 1184 1164 1152 1139
1.349 1.325 1.306 1.276 1.270 1.280 1.280 1.324 1.392 1.503 1.674 1.815 2.045
0 0.0422 0.0957 0.2215 0.3267 0.3943 0.4959 0.5981 0.6957 0.8012 0.9005 0.9502 1
0.7417 0.7415 0.7417 0.7426 0.7439 0.7449 0.7469 0.7497 0.7533 0.7585 0.7655 0.7704 0.7766
1260 1255 1249 1237 1226 1219 1207 1195 1182 1164 1145 1134 1121
1.238 1.219 1.191 1.177 1.164 1.167 1.160 1.192 1.243 1.330 1.467 1.580 1.763
jS 1
ðcm3 mol Þ
103 Dg
DjS 1
ðTPa Þ
1
ðTPa Þ
ðPa sÞ
792 799 805 819 831 840 853 866 882 902 925 939 953
0 )1 )3 )9 )14 )16 )19 )22 )22 )19 )12 )6 0
0.000 )0.068 )0.139 )0.280 )0.376 )0.426 )0.504 )0.538 )0.540 )0.488 )0.372 )0.236 0.000
T ¼ 298:15 K 0.000 0.188 0.306 0.517 0.605 0.641 0.654 0.618 0.550 0.434 0.276 0.159 0.000
820 827 834 849 862 871 885 899 915 936 960 973 987
0 0 )2 )8 )13 )15 )19 )21 )21 )18 )11 )6 0
0.000 )0.053 )0.109 )0.227 )0.306 )0.343 )0.414 )0.441 )0.441 )0.404 )0.302 )0.195 0.000
T ¼ 303:15 K 0.000 0.208 0.336 0.559 0.653 0.692 0.707 0.669 0.594 0.467 0.296 0.169 0.000
849 857 864 881 894 904 918 934 951 972 996 1010 1024
0 0 )2 )7 )13 )14 )18 )20 )20 )17 )10 )6 0
0.000 )0.041 )0.097 )0.178 )0.246 )0.278 )0.339 )0.360 )0.361 )0.329 )0.244 )0.157 0.000
TABLE 5 Fitting parameters and root-mean-square deviation (r) for {x1 2-propanol + (1 x1 ) octane} at T ¼ (273.15, 298.15, and 303.15) K B0 ¼ 2:3851 B0 ¼ 186:29 B0 ¼ 2:9374
B1 ¼ 0:6342 B1 ¼ 29:18 B1 ¼ 1:8055
T ¼ 293:15 K B2 ¼ 0:2122 B2 ¼ 58:89 B2 ¼ 1:8050
B3 ¼ 0:0468 B3 ¼ 11:89 B3 ¼ 1:3522
B4 ¼ 1:6519
r ¼ 0:002 r ¼ 0:39 r ¼ 0:007
V E =ðcm3 mol1 Þ DjS =ðTPa1 Þ 103 Dg=ðPa sÞ
B0 ¼ 2:5881 B0 ¼ 209:09 B0 ¼ 2:4492
B1 ¼ 0:6446 B1 ¼ 35:61 B1 ¼ 1:4893
T ¼ 298:15 K B2 ¼ 0:2956 B2 ¼ 62:47 B2 ¼ 1:4348
B3 ¼ 0:1875 B3 ¼ 6:29 B3 ¼ 1:0561
B4 ¼ 1:8774
r ¼ 0:002 r ¼ 0:46 r ¼ 0:005
V E =ðcm3 mol1 Þ DjS =ðTPa1 Þ 103 Dg=ðPa sÞ
B0 ¼ 2:8060 B0 ¼ 233:54 B0 ¼ 2:0470
B1 ¼ 0:6514 B1 ¼ 42:58 B1 ¼ 1:2543
T ¼ 303:15 K B2 ¼ 0:3535 B2 ¼ 68:05 B2 ¼ 1:1537
B3 ¼ 0:3480 B3 ¼ 1:53 B3 ¼ 0:7710
B4 ¼ 2:1009
r ¼ 0:003 r ¼ 0:52 r ¼ 0:005
TABLE 6 Fitting parameters and root-mean-square deviation (r) for {x1 2-propanol + (1 x1 Þ decane} at T ¼ (273.15, 298.15, and 303.15) K B0 ¼ 2:4313 B0 ¼ 39:65 B0 ¼ 2:5481
B1 ¼ 0:3087 B1 ¼ 5:80 B1 ¼ 1:4276
T ¼ 293:15 K B2 ¼ 0:3996 B2 ¼ 36:93 B2 ¼ 0:6632
B3 ¼ 0:3531 B3 ¼ 15:53 B3 ¼ 1:2358
B4 ¼ 1:2119
V E =ðcm3 mol1 Þ DjS =ðTPa1 Þ 103 Dg=ðPa sÞ
B0 ¼ 2:6273 B0 ¼ 51:01 B0 ¼ 2:1116
B1 ¼ 0:3084 B1 ¼ 1:14 B1 ¼ 1:1951
T ¼ 298:15 K B2 ¼ 0:3765 B2 ¼ 42:34 B2 ¼ 0:3351
B3 ¼ 0:4882 B3 ¼ 13:84 B3 ¼ 0:9675
B4 ¼ 1:3833
V E =ðcm3 mol1 Þ DjS =ðTPa1 Þ 103 Dg=ðPa sÞ
B0 ¼ 2:8443 B0 ¼ 63:35 B0 ¼ 1:7482
B1 ¼ 0:3022 B1 ¼ 5:18 B1 ¼ 0:9894
T ¼ 303:15 K B2 ¼ 0:3410 B2 ¼ 47:36 B2 ¼ 0:3304
B3 ¼ 0:6363 B3 ¼ 11:46 B3 ¼ 0:7679
B4 ¼ 1:5760
B4 ¼ 1:5333
B4 ¼ 1:4840
B4 ¼ 1:1443
r ¼ 0:008 r ¼ 0:49 r ¼ 0:003 r ¼ 0:008 r ¼ 0:52 r ¼ 0:004 r ¼ 0:009 r ¼ 0:54 r ¼ 0:004
945
V E =ðcm3 mol1 Þ DjS =ðTPa1 Þ 103 Dg=ðPa sÞ
B. Gonzalez et al. / J. Chem. Thermodynamics 35 (2003) 939–953
V E =ðcm3 mol1 Þ DjS =ðTPa1 Þ 103 Dg=ðPa sÞ
946
V E =ðcm3 mol1 Þ DjS =ðTPa1 Þ 103 Dg=ðPa sÞ
B0 ¼ 2:4178 B0 ¼ 80:09 B0 ¼ 2:0153
B1 ¼ 0:2296 B1 ¼ 59:73 B1 ¼ 0:9441
T ¼ 293:15 K B2 ¼ 0:2746 B2 ¼ 4:10 B2 ¼ 0:3413
V E =ðcm3 mol1 Þ DjS =ðTPa1 Þ 103 Dg=ðPa sÞ
B0 ¼ 2:6164 B0 ¼ 77:0 B0 ¼ 1:6445
B1 ¼ 0:2128 B1 ¼ 58:58 B1 ¼ 0:7952
T ¼ 298:15 K B2 ¼ 0:2254 B2 ¼ 1:80 B2 ¼ 0:3053
V E =ðcm3 mol1 Þ DjS =ðTPa1 Þ 103 Dg=ðPa sÞ
B0 ¼ 2:8298 B0 ¼ 73:41 B0 ¼ 1:3436
B1 ¼ 0:1979 B1 ¼ 56:05 B1 ¼ 0:7054
T ¼ 303:15 K B2 ¼ 0:2088 B2 ¼ 4:65 B2 ¼ 0:1462
B3 ¼ 0:0797
B4 ¼ 1:2819
B3 ¼ 0:9678
B4 ¼ 1:5546
B3 ¼ 0:2330
B4 ¼ 1:4841
B3 ¼ 0:8005
B4 ¼ 1:1984
B3 ¼ 0:3943
B4 ¼ 1:6829
B3 ¼ 0:5204
B4 ¼ 1:1372
r ¼ 0:006 r ¼ 0:32 r ¼ 0:005 r ¼ 0:006 r ¼ 0:40 r ¼ 0:005 r ¼ 0:007 r ¼ 0:45 r ¼ 0:004
B. Gonzalez et al. / J. Chem. Thermodynamics 35 (2003) 939–953
TABLE 7 Fitting parameters and root-mean-square deviation (r) for {x1 2-propanol + (1 x1 Þ dodecane} at T ¼ (273.15, 298.15, and 303.15) K
B. Gonzalez et al. / J. Chem. Thermodynamics 35 (2003) 939–953
947
mean-square deviations. These are calculated from the values of the property and the number of experimental data are represented by zexp and ndat , respectively ( , ) ndat X 2 r¼ ðzexp zpred Þ ndat : ð7Þ i
Figures 1–3 show the fitted curves, as well as excess and deviations values for binary mixtures at T ¼ (293.15, 298.15, and 303.15) K. Excess molar volumes are positive sign over the entire composition range. For the deviations in isentropic compressibility, the behaviour is similar to that for excess molar volumes with positive values observed over the entire composition range, except for (2-propanol + dodecane) where the deviation is negative over the composition range. For viscosity deviations, the sign is negative for all binary mixtures. Figures 4–6 show the variation with the length of carbon chain in the alkane and with the temperature of the excess as well as deviations for a certain composition. Figure 4 shows that the excess molar volumes are similar in magnitude for these three binary systems, and that magnitude increases slightly with the temperature whereas for the deviations in the isentropic compressibility decrease significantly as the length of the carbon chain in the alkane increases and this magnitude increases
FIGURE 1. Excess molar volume, V E , from the Redlich–Kister equation plotted against mole fraction at T ¼ 293:15 K (s), T ¼ 298:15 K () and T ¼ 313:15 K (M) for: (a) {x1 2-propanol + (1 x1 ) octane}, (b) {x1 2-propanol + (1 x1 ) decane}, (c) {x1 2-propanol + (1 x1 ) dodecane}.
948
B. Gonzalez et al. / J. Chem. Thermodynamics 35 (2003) 939–953
FIGURE 2. Deviations in isentropic compressibility, DjS , from the Redlich–Kister equation plotted against mole fraction at T ¼ 293:15 K (s), T ¼ 298:15 K () and T ¼ 313:15 K (M) for: (a) {x1 2-propanol + (1 x1 ) octane}, (b) {x1 2-propanol + (1 x1 ) decane}, (c) {x1 2-propanol + (1 x1 ) dodecane}.
with the temperature in the same way that the excess molar volume this is shown in figure 5. Figure 6 shows how the viscosity deviation and the dynamic viscosity increases as the length of the carbon chain in the alkane increases and how the viscosity deviation increases when the temperature increases whereas the dynamic viscosity decreases when the temperature increases. Prediction using the UNIFAC-VISCO and ASOG-VISCO methods has been determined. The UNIFAC-VISCO group contribution model combines the EyringÕs theory [17] with the UNIFAC group contribution method [18] adapted to viscosities. For liquid mixtures, Eyring [17] proposed the following equation for the kinematic viscosities: o. nX m ¼ h NA M 1 exp xi D Gi ðD GE =AÞ RT ; ð8Þ where D Gi is the free energy of activation for the pure component, D GE is the excess molar free energy of activation for flow, h is PlanckÕs constant, NA is AvogadroÕs number, M is molar mass and A is a empirical factor, Eyring sets equal to 2.45. Chevalier et al. [7] allow a similar equation for the viscosity of liquid mixture: m ¼ h NA M 1 expðD G=RT Þ;
where D G is the activated free energy at flow state.
ð9Þ
B. Gonzalez et al. / J. Chem. Thermodynamics 35 (2003) 939–953
949
FIGURE 3. Viscosity deviations, Dg, from the Redlich–Kister equation plotted against mole fraction at T ¼ 293:15 K (s), T ¼ 298:15 K () and T ¼ 313:15 K (M) for: (a) {x1 2-propanol + (1 x1 ) octane}, (b) {x1 2-propanol + (1 x1 ) decane}, (c) {x1 2-propanol + (1 x1 ) dodecane}.
FIGURE 4. Excess molar volume, V E , for a composition of x1 ¼ 0:4 plotted against the length of carbon chain in the alkane for (2-propanol with alkanes) at T ¼ 293:15 K (s), T ¼ 298:15 K () and T ¼ 313:15 K (M).
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FIGURE 5. Deviations in isentropic compressibility, DjS , for a composition of x1 ¼ 0:6 plotted against the length of carbon chain in the alkane for (2-propanol with alkanes) at T ¼ 293:15 K (s), T ¼ 298:15 K () and T ¼ 313:15 K (M).
FIGURE 6. Viscosities deviations, Dg, and dynamic viscosity, g, for a composition of x1 ¼ 0:7 plotted against the length of carbon chain in the alkane for (2-propanol with alkanes) at T ¼ 293:15 K (s), T ¼ 298:15 K () and T ¼ 313:15 K (M).
By definition for an non-ideal mixture, D G is obtained by D G ¼ D Gid þ D GE :
ð10Þ
E
Then D G is related to the viscosity by X lnðmMÞ ¼ xi lnðmi Mi Þ þ ðD GE =RT Þ:
ð11Þ
i
The excess molar free energy of activation for flow, D GE , is assumed to be the sum of two contributions: a combinatorial part, essentially due to differences in sizes and shape of the molecules in the mixture, and a residual part, essentially due to the energy interaction between structural groups contained in the molecules engaged in the mixture,
B. Gonzalez et al. / J. Chem. Thermodynamics 35 (2003) 939–953
D GE ¼ D GEC þ D GER :
951
ð12Þ
The expression of combinatorial term is X zX xi lnð/i =xi Þ þ qi xi lnðhi =/i Þ; D GEC =RT ¼ 2 i i
ð13Þ
where z is the coordination number which we set equal to 10; hi and /i are the molecular surface area fraction and molecular volume fraction, respectively; qi is the van der Waals surface area. The expression of residual term is given by X D GER =RT ¼ xi ln cR ð14Þ i : i
The minus sign is used to justify the difference existing between the thermodynamic equilibria excess mixing and the excess molar free energy of activation for flow, as has been shown by Meyer et al. [19]: it is assumed to be the sum of the individual contributions of each solute group k in the solution minus the sum of the individual contributions in the pure component environment: X ðiÞ ðiÞ ln cR nk ðln Ck ln Ck Þ; ð15Þ i ¼ k
" ln Ck
X
¼ Qk 1 ln
! hm wmk
m
X m
# hm wkm P ; n hn wnm
ð16Þ
where the group surface area fraction, hm , and the group fraction, Xk , are given by: , X hm ¼ Q m XM Qn X n ; ð17Þ n
Xm ¼
X
, nðjÞ m xj
j
XX j
nðjÞ n xj ;
ð18Þ
n
and the parameter wnm is given by wnm ¼ expðanm =T Þ;
ð19Þ
where anm is the group interaction parameters. The ASOG-VISCO group contribution model combines the EyringÕs theory [17] with the ASOG group contribution method [20]. Tochigi et al. [8] assumed the following equation between D GE and excess Gibbs free energy DGE at equilibrium state D GE =DGE ¼ k;
ð20Þ
where k is adjustable parameter and its meaning is the same as ð1=AÞ in EyringÕs paper [17]. The kinematic viscosity can be evaluated by the know values of excess Gibbs free energy with the given k
952
B. Gonzalez et al. / J. Chem. Thermodynamics 35 (2003) 939–953
lnðmMÞ ¼
X
xi lnðmi Mi Þ þ ðk DGE =RT Þ:
ð21Þ
i
As the value of k, 1 is used from the preliminary study and idea of Meyer et al. [19]. The excess Gibbs free energy, DGE , is evaluated using the ASOG group contribution method [20] given by the following equations: X X DGE ¼ xi ln ci ¼ xi ðln cFH þ ln cG ð22Þ i i Þ: i
i
The combinatorial term is given by ln cFH ¼ ln P i
mFH mFH i i P þ 1 ; FH FH j mj x j j mj xj
ð23Þ
FIGURE 7. Predicted values of dynamic viscosities, g, from the UNIFAC-VISCO and ASOG-VISCO methods plotted against mole fraction at T ¼ 293:15 K (s, experimental data; –––, UNIFAC-VISCO method; — —, ASOG-VISCO method); T ¼ 298:15 K (, experimental data; — —, UNIFACVISCO method; , ASOG-VISCO method) and T ¼ 303:15 K (M, experimental data; – – – UNIFACVISCO method; — —, ASOG-VISCO method) for: (a) {x1 2-propanol + (1 x1 ) octane}, (b) {x1 2-propanol + (1 x1 ) decane}, (c) {x1 2-propanol + (1 x1 ) dodecane}.
B. Gonzalez et al. / J. Chem. Thermodynamics 35 (2003) 939–953
and the residual term: X ðiÞ mk;i ðln Ck ln Ck Þ; ln cG i ¼
953
ð24Þ
k
ln Ck ¼ ln
X
Xl ak;l þ 1
X
l
Xl ¼
X
l
, xi mi;j
X
xi
i
ak;l ¼ expðmk;l þ nk;l T 1 Þ:
X
Xl al;k ; m XM al;m
P
ð25Þ
! mk;i ;
ð26Þ
k
ð27Þ
Here mk;l and nk;l are ASOG-VISCO group pair parameters. Figure 7 shows graphically the experimental dynamic viscosities and the predicted values by applying the UNIFAC-VISCO method and ASOG-VISCO method for {x1 2-propanol + ð1 x1 ) octane}, {x1 2-propanol + (1 x1 ) decane}, {x1 2-propanol + (1 x1 ) dodecane} at T ¼ (293.15, 298.15, and 303.15) K. The prediction made by ASOG-VISCO method is more exact than the prediction made by the UNIFAC-VISCO method. The UNIFAC-VISCO method is completely wrong in its predictions indicating that it would be advisable to calculate new parameters for the interaction between secondary alcohols and alkanes. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]
J Canosa, A. Rodriguez, J. Tojo, J. Chem. Eng. Data 43 (1998) 417–421. J. Canosa, A. Rodriguez, J. Tojo, J. Chem. Eng. Data 43 (1998) 961–966. J. Canosa, A. Rodriguez, J. Tojo, J. Chem. Thermodyn. 30 (1998) 1307–1318. J. Canosa, A. Rodriguez, J. Tojo, J. Chem. Thermodyn. 32 (2000) 551–565. J. Canosa, A. Rodriguez, J. Tojo, J. Chem. Eng. Data 45 (2000) 471–477. A. Rodriguez, J. Canosa, J. Tojo, J. Chem. Eng. Data 48 (2003) 146–151. Y. Gaston-Bonhome, P. Petrino, J.L. Chevalier, Chem. Eng. Sci. 49 (1994) 1799–1806. K. Tochigi, K. Yoshino, V.K. Rattan, in: The Sixteenth European Conference on Thermophysical Properties, September 1–4, London, 2002. S.N. Paudharinath, T.R. Mahale, M. Hasan, J. Chem. Eng. Data 41 (1996) 1055–1058. J.A. Riddick, W.B. Bunger, T.K. Sakano, Organic Solvents, Wiley, New York, 1986. J.L. Chevalier, P.J. Petrino, Y.H. Gaston-bonhomme, J. Chem. Eng. Data 35 (1990) 206–212. T.M. Aminabhavi, G. Bindu, J. Chem. Eng. Data 40 (1995) 462–467. B.M. Coursey, E.L. Heric, J. Chem. Eng. Data 14 (1969) 426–428. J.H. Dymond, K. Young, J. Int. J. Thermophys. 1 (4) (1980) 331–344. O. Redlich, A.T. Kister, Ind. Eng. Chem. 40 (1948) 345–348. P. Bevington, Data Reduction and Error Analysis for the Physical Sciences, McGraw-Hill, New York, 1969. H. Eyring, J. Chem. Phys. 4 (1936) 283–291. J.L. Chevalier, P.J. Petrino, Y.H. Gaston-bonhomme, Chem. Eng. Sci. 43 (1988) 1303–1309. R. Meyer, M. Metzger, J.A. Peneloux, J. Chem. Phys. 68 (1971) 406–408. K. Tochigi, D. Tiegs, J. Gmehling, K. Kojima, J. Chem. Eng. Jpn. 23 (1990) 456–466.
WE-382
Viscosities, densities and speeds of sound of the binary systems: 2-propanol with octane, or decane, or dodecane at T ¼ (293.15, 298.15, and 303.15) K B. Gonz alez, A. Dominguez, J. Tojo
*
Chemical Engineering Department, Vigo University, 36200 Vigo, Spain Received 13 November 2002; accepted 4 February 2003
Abstract Viscosities, densities and speed of sound have been measured over the whole composition range for (2-propanol with octane, or decane, or dodecane) at T ¼ (293.15, 298.15, and 303.15) K and atmospheric pressure along with the properties of the pure components. Excess molar volumes, isentropic compressibility, deviations in isentropic compressibility and viscosity deviations for the binary systems at the above-mentioned temperatures were calculated and fitted to Redlich–Kister equation to determine the fitting parameters and the root-meansquare deviations. Prediction of the dynamic viscosities of this binary mixture from UNIFAC-VISCO and ASOG-VISCO methods has been determined. Ó 2003 Elsevier Science Ltd. All rights reserved. Keywords: Viscosity; Density; Speed of sound; 2-Propanol; Octane; Decane; Dodecane
1. Introduction In the chemical industry, the information on the viscosity of liquid mixtures is necessary in different applications for surface facilities, pipeline systems, mass-transfer operations, etc. As an extension of our work concerning dynamic viscosity of
*
Corresponding author. Tel.: +34-986-812287; fax: +34-986-812382. E-mail address: [email protected] (J. Tojo).
0021-9614/03/$ - see front matter Ó 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0021-9614(03)00047-8
940
B. Gonzalez et al. / J. Chem. Thermodynamics 35 (2003) 939–953
binary and ternary systems [1–6], in this paper, we show experimental dynamic viscosity, density and speed of sound data of the binary systems 2-propanol with octane, or decane, or dodecane at T ¼ (293.15, 298.15, and 303.15) K. The results were used to calculate excess molar volumes, isentropic compressibility, deviations in isoentropic compressibility and viscosity over the entire mole fraction range for the mixtures. The UNIFAC-VISCO [7] and ASOG-VISCO [8] methods have been applied to compare the difference between predicted and experimental dynamic viscosities. 2. Experimental The pure components were supplied for Fluka, except for the 2-propanol which was supplied by Merck. The components were degassed ultrasonically, and dried , that were supplied by Aldrich, and kept in inert arover molecular sieves Type 4 A gon with a maximum content in water of 2 106 by mass fraction. Their mass fraction purities were >0.999 for 2-propanol, >0.995 for octane, >0.99 for decane and >0.99 for dodecane. The solvent purities were compared with recently published density and dynamic viscosity values at T ¼ 298:15 K in table 1. 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 0:4 103 and 0:53 103 m diameter. Gravity fall is the principle of measurement on which this viscosimeter is based. The capillary is maintained in a D20KP LAUDA thermostat with a resolution of 0.01 °C. The capillaries are calibrated and credited by the company which supplies us. The accuracy of the capillaries is 0.5%. In order to verify the calibration of the same ones the pure liquids, in table 1, were compared with data recently published. The uncertainty for the viscosimeter is better than 1%. The equipment has a control unit PVS1 (Processor Viscosity System) that is a PC-controlled instrument for the precise measurement of liquid viscosity using standardized glass capillaries with a accuracy of 0.01 s. TABLE 1 Comparison of density q and viscosity g with literature values for pure components at T ¼ 298:15 K Components
q=ðg cm3 Þ
103 g=ðPa sÞ
Exptl.
Lit.
Exptl.
Lit.
2-Propanol
0.7809
0.7809 [12] 0.7813 [9]
2.045
2.048 [9]
Octane
0.6985
0:6986 [11] 0.6985 [13]
0.506
0.506 [11]
Decane
0.7262
0.7262 [11] 0.7262 [10]
0.843
0.843 [11]
Dodecane
0.7453
0.7454 [11] 0.7455 [14]
1.348
1.345 [11] 1.359 [14]
B. Gonzalez et al. / J. Chem. Thermodynamics 35 (2003) 939–953
941
The kinematic viscosity is determined from the following relationship: m ¼ kðt yÞ;
ð1Þ
where y is the Hagenbach correction, t is the flow time and k is the Ubbelhode capillary microviscosimeter constant which is supply for the company. The dynamic viscosity is determined from: g ¼ m q;
ð2Þ
where g is the dynamic viscosity, m is the kinematic viscosity and q is the density. The uncertainty for the dynamic viscosity is 2 106 . The densities and the speed of sound of the pure liquids and mixtures were measured using an Anton Paar DSA5000 digital vibrating tube densimeter. The accuracy and the precision for the density are 106 g cm3 and 2 106 g cm3 ; and for the speed of sound are 0:1 m s1 and 102 m s1 , respectively.
3. Results and discussion Dynamic viscosity, density, speed of sound, excess molar volume, isentropic compressibility (determined by means of the Laplace equation, kS ¼ q1 u2 ), deviation in isentropic compressibility and viscosity deviation of {x1 2-propanol + (1 x1 ) octane}, {x1 2-propanol + (1 x1 ) decane} and {x1 2-propanol + (1 x1 ) dodecane} at T ¼ (293.15, 298.15, and 303.15) K and atmospheric pressure are reported in tables 2–4. The excess molar volumes, the deviations in isentropic compressibility and the viscosity deviations are calculated by the equations: VE ¼
N X
xi Mi ðq1 q1 i Þ;
ð3Þ
i¼1 N X
DjS ¼ jS
ð4Þ
xi jS;i ;
i¼1
Dg ¼ g
N X
ð5Þ
x i gi ;
i
where q and qi are the density of the mixture and the density of the pure components, respectively; jS is the isentropic compressibility of the mixture; jS;i is the isentropic compressibility of the pure components; g and gi are the dynamic viscosity of the mixture and the pure component, respectively, and xi represents the mole fraction of the pure component. The binary deviations were fitted to a Redlich–Kister [15] type equation: DQij ¼ xi xj
M X p¼0
p
Bp ðxi xj Þ ;
ð6Þ
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B. Gonzalez et al. / J. Chem. Thermodynamics 35 (2003) 939–953
TABLE 2 Dynamic viscosities g, densities q, speeds of sound u, isentropic compressibilities jS , excess molar volumes V E , deviations in isentropic compressibilities DjS , and viscosities deviations Dg of {x1 2-propanol + (1 x1 ) octane} at T ¼ (293.15, 298.15, and 303.15) K x1
q
u
103 g
ðg cm3 Þ
ðm s1 Þ
ðPa sÞ
0 0.0518 0.0896 0.2120 0.2820 0.4103 0.6027 0.6988 0.7988 0.9007 0.9496 1
0.7026 0.7038 0.7049 0.7095 0.7126 0.7195 0.7334 0.7424 0.7536 0.7675 0.7758 0.7851
1193 1188 1184 1175 1171 1164 1157 1155 1153 1153 1154 1156
0 0.0518 0.0896 0.2120 0.2820 0.4103 0.6027 0.6988 0.7988 0.9007 0.9496 1
0.6985 0.6997 0.7008 0.7053 0.7084 0.7152 0.7290 0.7380 0.7492 0.7632 0.7712 0.7809
0 0.0518 0.0896 0.2120 0.2820 0.4103 0.6027 0.6988 0.7988 0.9007 0.9496 1
0.6945 0.6955 0.6966 0.7010 0.7041 0.7108 0.7246 0.7336 0.7448 0.7589 0.7669 0.7766
VE
jS 1
ðcm3 mol Þ
103 Dg
DjS 1
1
ðTPa Þ
ðTPa Þ
ðPa sÞ
T ¼ 293:15 K 0.538 0.000 0.539 0.195 0.542 0.285 0.562 0.480 0.580 0.544 0.644 0.603 0.830 0.537 0.985 0.451 1.225 0.342 1.624 0.214 1.961 0.129 2.382 0.000
999 1007 1011 1020 1023 1025 1018 1010 998 980 968 953
0 10 16 31 37 45 47 44 36 23 13 0
0.000 )0.095 )0.161 )0.367 )0.478 )0.651 )0.819 )0.842 )0.786 )0.575 )0.328 0.000
1173 1167 1164 1155 1150 1144 1137 1135 1134 1134 1136 1139
T ¼ 298:15 K 0.507 0.000 0.507 0.216 0.510 0.311 0.526 0.518 0.542 0.587 0.596 0.653 0.752 0.584 0.883 0.489 1.088 0.370 1.429 0.228 1.690 0.137 2.045 0.000
1041 1050 1054 1063 1067 1069 1061 1052 1038 1018 1005 987
0 12 18 34 41 50 53 49 40 25 15 0
0.000 )0.079 )0.134 )0.307 )0.398 )0.542 )0.682 )0.699 )0.647 )0.463 )0.277 0.000
1152 1146 1143 1134 1130 1123 1117 1115 1114 1116 1118 1121
T ¼ 303:15 K 0.477 0.000 0.476 0.239 0.479 0.341 0.494 0.560 0.507 0.635 0.552 0.707 0.685 0.634 0.795 0.532 0.967 0.401 1.250 0.244 1.482 0.146 1.763 0.000
1085 1095 1099 1110 1113 1116 1107 1097 1081 1058 1043 1024
0 13 20 38 46 56 59 55 45 28 16 0
0.000 )0.068 )0.114 )0.256 )0.333 )0.453 )0.567 )0.581 )0.538 )0.386 )0.217 0.000
where DQij is the excess property, x is the mole fraction, Bp is the fitting parameter and M is the degree of the polynomic expansion, which was optimized using the F-test [16]. The fitting parameters are given in tables 5–7 together with the root-
B. Gonzalez et al. / J. Chem. Thermodynamics 35 (2003) 939–953
943
TABLE 3 Dynamic viscosities g, densities q, speeds of sound u, isentropic compressibilities jS , excess molar volumes V E , deviations in isentropic compressibilities DjS , and viscosities deviations Dg of {x1 2-propanol + (1 x1 ) decane} at T ¼ (293.15, 298.15, and 303.15) K x1
q
u
103 g
VE
ðg cm3 Þ
ðm s1 Þ
ðPa sÞ
0 0.0412 0.0998 0.1610 0.2938 0.3954 0.4988 0.5943 0.7019 0.8012 0.9017 0.9510 1
0.7299 0.7301 0.7310 0.7324 0.7351 0.7382 0.7421 0.7467 0.7531 0.7607 0.7710 0.7774 0.7851
1255 1249 1244 1237 1226 1218 1209 1201 1190 1180 1168 1162 1156
0.910 0.896 0.893 0.904 0.916 0.957 1.006 1.095 1.241 1.436 1.759 2.014 2.382
T ¼ 293:15 K 0.000 0.186 0.314 0.451 0.581 0.608 0.606 0.568 0.499 0.401 0.242 0.137 0.000
0 0.0412 0.0998 0.1610 0.2938 0.3954 0.4988 0.5943 0.7019 0.8012 0.9017 0.9510 1
0.7262 0.7263 0.7271 0.7285 0.7311 0.7341 0.7380 0.7425 0.7489 0.7565 0.7667 0.7732 0.7809
1235 1229 1224 1217 1206 1198 1189 1181 1171 1161 1150 1144 1139
0.843 0.831 0.827 0.847 0.845 0.878 0.916 0.986 1.110 1.273 1.538 1.742 2.045
0 0.0412 0.0998 0.1610 0.2938 0.3954 0.4988 0.5943 0.7019 0.8012 0.9017 0.9510 1
0.7224 0.7224 0.7232 0.7245 0.7271 0.7300 0.7338 0.7383 0.7446 0.7522 0.7625 0.7689 0.7766
1215 1210 1204 1197 1186 1178 1169 1161 1151 1142 1131 1126 1121
0.785 0.773 0.768 0.785 0.777 0.809 0.836 0.893 0.994 1.127 1.348 1.515 1.763
jS 1
ðcm3 mol Þ
103 Dg
DjS 1
ðTPa Þ
1
ðTPa Þ
ðPa sÞ
870 878 884 892 904 913 922 929 937 944 951 953 953
0 4 6 7 10 10 10 10 9 8 6 4 0
0.000 )0.075 )0.164 )0.272 )0.426 )0.535 )0.638 )0.690 )0.702 )0.654 )0.478 )0.296 0.000
T ¼ 298:15 K 0.000 0.204 0.342 0.487 0.605 0.655 0.655 0.615 0.538 0.431 0.258 0.145 0.000
903 911 918 927 940 949 958 966 974 981 987 988 987
0 4 7 9 12 13 13 13 12 10 8 5 0
0.000 )0.062 )0.136 )0.214 )0.351 )0.440 )0.527 )0.571 )0.577 )0.533 )0.389 )0.244 0.000
T ¼ 303:15 K 0.000 0.223 0.373 0.526 0.652 0.708 0.709 0.666 0.582 0.464 0.276 0.154 0.000
938 946 954 964 977 987 997 1005 1014 1020 1025 1026 1024
0 5 8 10 14 16 16 16 15 13 10 6 0
0.000 )0.053 )0.114 )0.177 )0.295 )0.363 )0.437 )0.473 )0.478 )0.442 )0.319 )0.201 0.000
944
B. Gonzalez et al. / J. Chem. Thermodynamics 35 (2003) 939–953
TABLE 4 Dynamic viscosities g, densities q, speeds of sound u, isentropic compressibilities jS , excess molar volumes V E , deviations in isentropic compressibilities DjS , and viscosities deviations Dg of {x1 2-propanol + (1 x1 Þ dodecane} at T ¼ (293.15, 298.15, and 303.15) K x1
q
u
103 g
VE
ðg cm3 Þ
ðm s1 Þ
ðPa sÞ
0 0.0422 0.0957 0.2215 0.3267 0.3943 0.4959 0.5981 0.6957 0.8012 0.9005 0.9502 1
0.7489 0.7489 0.7492 0.7502 0.7516 0.7528 0.7549 0.7578 0.7615 0.7668 0.7739 0.7788 0.7851
1298 1293 1288 1275 1265 1258 1247 1234 1220 1202 1182 1170 1156
1.476 1.446 1.424 1.397 1.396 1.407 1.421 1.480 1.566 1.714 1.920 2.101 2.382
T ¼ 293:15 K 0.000 0.170 0.279 0.480 0.562 0.594 0.604 0.571 0.509 0.404 0.260 0.151 0.000
0 0.0422 0.0957 0.2215 0.3267 0.3943 0.4959 0.5981 0.6957 0.8012 0.9005 0.9502 1
0.7453 0.7452 0.7455 0.7464 0.7478 0.7489 0.7510 0.7538 0.7574 0.7627 0.7698 0.7746 0.7809
1279 1274 1268 1256 1246 1238 1227 1215 1201 1184 1164 1152 1139
1.349 1.325 1.306 1.276 1.270 1.280 1.280 1.324 1.392 1.503 1.674 1.815 2.045
0 0.0422 0.0957 0.2215 0.3267 0.3943 0.4959 0.5981 0.6957 0.8012 0.9005 0.9502 1
0.7417 0.7415 0.7417 0.7426 0.7439 0.7449 0.7469 0.7497 0.7533 0.7585 0.7655 0.7704 0.7766
1260 1255 1249 1237 1226 1219 1207 1195 1182 1164 1145 1134 1121
1.238 1.219 1.191 1.177 1.164 1.167 1.160 1.192 1.243 1.330 1.467 1.580 1.763
jS 1
ðcm3 mol Þ
103 Dg
DjS 1
ðTPa Þ
1
ðTPa Þ
ðPa sÞ
792 799 805 819 831 840 853 866 882 902 925 939 953
0 )1 )3 )9 )14 )16 )19 )22 )22 )19 )12 )6 0
0.000 )0.068 )0.139 )0.280 )0.376 )0.426 )0.504 )0.538 )0.540 )0.488 )0.372 )0.236 0.000
T ¼ 298:15 K 0.000 0.188 0.306 0.517 0.605 0.641 0.654 0.618 0.550 0.434 0.276 0.159 0.000
820 827 834 849 862 871 885 899 915 936 960 973 987
0 0 )2 )8 )13 )15 )19 )21 )21 )18 )11 )6 0
0.000 )0.053 )0.109 )0.227 )0.306 )0.343 )0.414 )0.441 )0.441 )0.404 )0.302 )0.195 0.000
T ¼ 303:15 K 0.000 0.208 0.336 0.559 0.653 0.692 0.707 0.669 0.594 0.467 0.296 0.169 0.000
849 857 864 881 894 904 918 934 951 972 996 1010 1024
0 0 )2 )7 )13 )14 )18 )20 )20 )17 )10 )6 0
0.000 )0.041 )0.097 )0.178 )0.246 )0.278 )0.339 )0.360 )0.361 )0.329 )0.244 )0.157 0.000
TABLE 5 Fitting parameters and root-mean-square deviation (r) for {x1 2-propanol + (1 x1 ) octane} at T ¼ (273.15, 298.15, and 303.15) K B0 ¼ 2:3851 B0 ¼ 186:29 B0 ¼ 2:9374
B1 ¼ 0:6342 B1 ¼ 29:18 B1 ¼ 1:8055
T ¼ 293:15 K B2 ¼ 0:2122 B2 ¼ 58:89 B2 ¼ 1:8050
B3 ¼ 0:0468 B3 ¼ 11:89 B3 ¼ 1:3522
B4 ¼ 1:6519
r ¼ 0:002 r ¼ 0:39 r ¼ 0:007
V E =ðcm3 mol1 Þ DjS =ðTPa1 Þ 103 Dg=ðPa sÞ
B0 ¼ 2:5881 B0 ¼ 209:09 B0 ¼ 2:4492
B1 ¼ 0:6446 B1 ¼ 35:61 B1 ¼ 1:4893
T ¼ 298:15 K B2 ¼ 0:2956 B2 ¼ 62:47 B2 ¼ 1:4348
B3 ¼ 0:1875 B3 ¼ 6:29 B3 ¼ 1:0561
B4 ¼ 1:8774
r ¼ 0:002 r ¼ 0:46 r ¼ 0:005
V E =ðcm3 mol1 Þ DjS =ðTPa1 Þ 103 Dg=ðPa sÞ
B0 ¼ 2:8060 B0 ¼ 233:54 B0 ¼ 2:0470
B1 ¼ 0:6514 B1 ¼ 42:58 B1 ¼ 1:2543
T ¼ 303:15 K B2 ¼ 0:3535 B2 ¼ 68:05 B2 ¼ 1:1537
B3 ¼ 0:3480 B3 ¼ 1:53 B3 ¼ 0:7710
B4 ¼ 2:1009
r ¼ 0:003 r ¼ 0:52 r ¼ 0:005
TABLE 6 Fitting parameters and root-mean-square deviation (r) for {x1 2-propanol + (1 x1 Þ decane} at T ¼ (273.15, 298.15, and 303.15) K B0 ¼ 2:4313 B0 ¼ 39:65 B0 ¼ 2:5481
B1 ¼ 0:3087 B1 ¼ 5:80 B1 ¼ 1:4276
T ¼ 293:15 K B2 ¼ 0:3996 B2 ¼ 36:93 B2 ¼ 0:6632
B3 ¼ 0:3531 B3 ¼ 15:53 B3 ¼ 1:2358
B4 ¼ 1:2119
V E =ðcm3 mol1 Þ DjS =ðTPa1 Þ 103 Dg=ðPa sÞ
B0 ¼ 2:6273 B0 ¼ 51:01 B0 ¼ 2:1116
B1 ¼ 0:3084 B1 ¼ 1:14 B1 ¼ 1:1951
T ¼ 298:15 K B2 ¼ 0:3765 B2 ¼ 42:34 B2 ¼ 0:3351
B3 ¼ 0:4882 B3 ¼ 13:84 B3 ¼ 0:9675
B4 ¼ 1:3833
V E =ðcm3 mol1 Þ DjS =ðTPa1 Þ 103 Dg=ðPa sÞ
B0 ¼ 2:8443 B0 ¼ 63:35 B0 ¼ 1:7482
B1 ¼ 0:3022 B1 ¼ 5:18 B1 ¼ 0:9894
T ¼ 303:15 K B2 ¼ 0:3410 B2 ¼ 47:36 B2 ¼ 0:3304
B3 ¼ 0:6363 B3 ¼ 11:46 B3 ¼ 0:7679
B4 ¼ 1:5760
B4 ¼ 1:5333
B4 ¼ 1:4840
B4 ¼ 1:1443
r ¼ 0:008 r ¼ 0:49 r ¼ 0:003 r ¼ 0:008 r ¼ 0:52 r ¼ 0:004 r ¼ 0:009 r ¼ 0:54 r ¼ 0:004
945
V E =ðcm3 mol1 Þ DjS =ðTPa1 Þ 103 Dg=ðPa sÞ
B. Gonzalez et al. / J. Chem. Thermodynamics 35 (2003) 939–953
V E =ðcm3 mol1 Þ DjS =ðTPa1 Þ 103 Dg=ðPa sÞ
946
V E =ðcm3 mol1 Þ DjS =ðTPa1 Þ 103 Dg=ðPa sÞ
B0 ¼ 2:4178 B0 ¼ 80:09 B0 ¼ 2:0153
B1 ¼ 0:2296 B1 ¼ 59:73 B1 ¼ 0:9441
T ¼ 293:15 K B2 ¼ 0:2746 B2 ¼ 4:10 B2 ¼ 0:3413
V E =ðcm3 mol1 Þ DjS =ðTPa1 Þ 103 Dg=ðPa sÞ
B0 ¼ 2:6164 B0 ¼ 77:0 B0 ¼ 1:6445
B1 ¼ 0:2128 B1 ¼ 58:58 B1 ¼ 0:7952
T ¼ 298:15 K B2 ¼ 0:2254 B2 ¼ 1:80 B2 ¼ 0:3053
V E =ðcm3 mol1 Þ DjS =ðTPa1 Þ 103 Dg=ðPa sÞ
B0 ¼ 2:8298 B0 ¼ 73:41 B0 ¼ 1:3436
B1 ¼ 0:1979 B1 ¼ 56:05 B1 ¼ 0:7054
T ¼ 303:15 K B2 ¼ 0:2088 B2 ¼ 4:65 B2 ¼ 0:1462
B3 ¼ 0:0797
B4 ¼ 1:2819
B3 ¼ 0:9678
B4 ¼ 1:5546
B3 ¼ 0:2330
B4 ¼ 1:4841
B3 ¼ 0:8005
B4 ¼ 1:1984
B3 ¼ 0:3943
B4 ¼ 1:6829
B3 ¼ 0:5204
B4 ¼ 1:1372
r ¼ 0:006 r ¼ 0:32 r ¼ 0:005 r ¼ 0:006 r ¼ 0:40 r ¼ 0:005 r ¼ 0:007 r ¼ 0:45 r ¼ 0:004
B. Gonzalez et al. / J. Chem. Thermodynamics 35 (2003) 939–953
TABLE 7 Fitting parameters and root-mean-square deviation (r) for {x1 2-propanol + (1 x1 Þ dodecane} at T ¼ (273.15, 298.15, and 303.15) K
B. Gonzalez et al. / J. Chem. Thermodynamics 35 (2003) 939–953
947
mean-square deviations. These are calculated from the values of the property and the number of experimental data are represented by zexp and ndat , respectively ( , ) ndat X 2 r¼ ðzexp zpred Þ ndat : ð7Þ i
Figures 1–3 show the fitted curves, as well as excess and deviations values for binary mixtures at T ¼ (293.15, 298.15, and 303.15) K. Excess molar volumes are positive sign over the entire composition range. For the deviations in isentropic compressibility, the behaviour is similar to that for excess molar volumes with positive values observed over the entire composition range, except for (2-propanol + dodecane) where the deviation is negative over the composition range. For viscosity deviations, the sign is negative for all binary mixtures. Figures 4–6 show the variation with the length of carbon chain in the alkane and with the temperature of the excess as well as deviations for a certain composition. Figure 4 shows that the excess molar volumes are similar in magnitude for these three binary systems, and that magnitude increases slightly with the temperature whereas for the deviations in the isentropic compressibility decrease significantly as the length of the carbon chain in the alkane increases and this magnitude increases
FIGURE 1. Excess molar volume, V E , from the Redlich–Kister equation plotted against mole fraction at T ¼ 293:15 K (s), T ¼ 298:15 K () and T ¼ 313:15 K (M) for: (a) {x1 2-propanol + (1 x1 ) octane}, (b) {x1 2-propanol + (1 x1 ) decane}, (c) {x1 2-propanol + (1 x1 ) dodecane}.
948
B. Gonzalez et al. / J. Chem. Thermodynamics 35 (2003) 939–953
FIGURE 2. Deviations in isentropic compressibility, DjS , from the Redlich–Kister equation plotted against mole fraction at T ¼ 293:15 K (s), T ¼ 298:15 K () and T ¼ 313:15 K (M) for: (a) {x1 2-propanol + (1 x1 ) octane}, (b) {x1 2-propanol + (1 x1 ) decane}, (c) {x1 2-propanol + (1 x1 ) dodecane}.
with the temperature in the same way that the excess molar volume this is shown in figure 5. Figure 6 shows how the viscosity deviation and the dynamic viscosity increases as the length of the carbon chain in the alkane increases and how the viscosity deviation increases when the temperature increases whereas the dynamic viscosity decreases when the temperature increases. Prediction using the UNIFAC-VISCO and ASOG-VISCO methods has been determined. The UNIFAC-VISCO group contribution model combines the EyringÕs theory [17] with the UNIFAC group contribution method [18] adapted to viscosities. For liquid mixtures, Eyring [17] proposed the following equation for the kinematic viscosities: o. nX m ¼ h NA M 1 exp xi D Gi ðD GE =AÞ RT ; ð8Þ where D Gi is the free energy of activation for the pure component, D GE is the excess molar free energy of activation for flow, h is PlanckÕs constant, NA is AvogadroÕs number, M is molar mass and A is a empirical factor, Eyring sets equal to 2.45. Chevalier et al. [7] allow a similar equation for the viscosity of liquid mixture: m ¼ h NA M 1 expðD G=RT Þ;
where D G is the activated free energy at flow state.
ð9Þ
B. Gonzalez et al. / J. Chem. Thermodynamics 35 (2003) 939–953
949
FIGURE 3. Viscosity deviations, Dg, from the Redlich–Kister equation plotted against mole fraction at T ¼ 293:15 K (s), T ¼ 298:15 K () and T ¼ 313:15 K (M) for: (a) {x1 2-propanol + (1 x1 ) octane}, (b) {x1 2-propanol + (1 x1 ) decane}, (c) {x1 2-propanol + (1 x1 ) dodecane}.
FIGURE 4. Excess molar volume, V E , for a composition of x1 ¼ 0:4 plotted against the length of carbon chain in the alkane for (2-propanol with alkanes) at T ¼ 293:15 K (s), T ¼ 298:15 K () and T ¼ 313:15 K (M).
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B. Gonzalez et al. / J. Chem. Thermodynamics 35 (2003) 939–953
FIGURE 5. Deviations in isentropic compressibility, DjS , for a composition of x1 ¼ 0:6 plotted against the length of carbon chain in the alkane for (2-propanol with alkanes) at T ¼ 293:15 K (s), T ¼ 298:15 K () and T ¼ 313:15 K (M).
FIGURE 6. Viscosities deviations, Dg, and dynamic viscosity, g, for a composition of x1 ¼ 0:7 plotted against the length of carbon chain in the alkane for (2-propanol with alkanes) at T ¼ 293:15 K (s), T ¼ 298:15 K () and T ¼ 313:15 K (M).
By definition for an non-ideal mixture, D G is obtained by D G ¼ D Gid þ D GE :
ð10Þ
E
Then D G is related to the viscosity by X lnðmMÞ ¼ xi lnðmi Mi Þ þ ðD GE =RT Þ:
ð11Þ
i
The excess molar free energy of activation for flow, D GE , is assumed to be the sum of two contributions: a combinatorial part, essentially due to differences in sizes and shape of the molecules in the mixture, and a residual part, essentially due to the energy interaction between structural groups contained in the molecules engaged in the mixture,
B. Gonzalez et al. / J. Chem. Thermodynamics 35 (2003) 939–953
D GE ¼ D GEC þ D GER :
951
ð12Þ
The expression of combinatorial term is X zX xi lnð/i =xi Þ þ qi xi lnðhi =/i Þ; D GEC =RT ¼ 2 i i
ð13Þ
where z is the coordination number which we set equal to 10; hi and /i are the molecular surface area fraction and molecular volume fraction, respectively; qi is the van der Waals surface area. The expression of residual term is given by X D GER =RT ¼ xi ln cR ð14Þ i : i
The minus sign is used to justify the difference existing between the thermodynamic equilibria excess mixing and the excess molar free energy of activation for flow, as has been shown by Meyer et al. [19]: it is assumed to be the sum of the individual contributions of each solute group k in the solution minus the sum of the individual contributions in the pure component environment: X ðiÞ ðiÞ ln cR nk ðln Ck ln Ck Þ; ð15Þ i ¼ k
" ln Ck
X
¼ Qk 1 ln
! hm wmk
m
X m
# hm wkm P ; n hn wnm
ð16Þ
where the group surface area fraction, hm , and the group fraction, Xk , are given by: , X hm ¼ Q m XM Qn X n ; ð17Þ n
Xm ¼
X
, nðjÞ m xj
j
XX j
nðjÞ n xj ;
ð18Þ
n
and the parameter wnm is given by wnm ¼ expðanm =T Þ;
ð19Þ
where anm is the group interaction parameters. The ASOG-VISCO group contribution model combines the EyringÕs theory [17] with the ASOG group contribution method [20]. Tochigi et al. [8] assumed the following equation between D GE and excess Gibbs free energy DGE at equilibrium state D GE =DGE ¼ k;
ð20Þ
where k is adjustable parameter and its meaning is the same as ð1=AÞ in EyringÕs paper [17]. The kinematic viscosity can be evaluated by the know values of excess Gibbs free energy with the given k
952
B. Gonzalez et al. / J. Chem. Thermodynamics 35 (2003) 939–953
lnðmMÞ ¼
X
xi lnðmi Mi Þ þ ðk DGE =RT Þ:
ð21Þ
i
As the value of k, 1 is used from the preliminary study and idea of Meyer et al. [19]. The excess Gibbs free energy, DGE , is evaluated using the ASOG group contribution method [20] given by the following equations: X X DGE ¼ xi ln ci ¼ xi ðln cFH þ ln cG ð22Þ i i Þ: i
i
The combinatorial term is given by ln cFH ¼ ln P i
mFH mFH i i P þ 1 ; FH FH j mj x j j mj xj
ð23Þ
FIGURE 7. Predicted values of dynamic viscosities, g, from the UNIFAC-VISCO and ASOG-VISCO methods plotted against mole fraction at T ¼ 293:15 K (s, experimental data; –––, UNIFAC-VISCO method; — —, ASOG-VISCO method); T ¼ 298:15 K (, experimental data; — —, UNIFACVISCO method; , ASOG-VISCO method) and T ¼ 303:15 K (M, experimental data; – – – UNIFACVISCO method; — —, ASOG-VISCO method) for: (a) {x1 2-propanol + (1 x1 ) octane}, (b) {x1 2-propanol + (1 x1 ) decane}, (c) {x1 2-propanol + (1 x1 ) dodecane}.
B. Gonzalez et al. / J. Chem. Thermodynamics 35 (2003) 939–953
and the residual term: X ðiÞ mk;i ðln Ck ln Ck Þ; ln cG i ¼
953
ð24Þ
k
ln Ck ¼ ln
X
Xl ak;l þ 1
X
l
Xl ¼
X
l
, xi mi;j
X
xi
i
ak;l ¼ expðmk;l þ nk;l T 1 Þ:
X
Xl al;k ; m XM al;m
P
ð25Þ
! mk;i ;
ð26Þ
k
ð27Þ
Here mk;l and nk;l are ASOG-VISCO group pair parameters. Figure 7 shows graphically the experimental dynamic viscosities and the predicted values by applying the UNIFAC-VISCO method and ASOG-VISCO method for {x1 2-propanol + ð1 x1 ) octane}, {x1 2-propanol + (1 x1 ) decane}, {x1 2-propanol + (1 x1 ) dodecane} at T ¼ (293.15, 298.15, and 303.15) K. The prediction made by ASOG-VISCO method is more exact than the prediction made by the UNIFAC-VISCO method. The UNIFAC-VISCO method is completely wrong in its predictions indicating that it would be advisable to calculate new parameters for the interaction between secondary alcohols and alkanes. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]
J Canosa, A. Rodriguez, J. Tojo, J. Chem. Eng. Data 43 (1998) 417–421. J. Canosa, A. Rodriguez, J. Tojo, J. Chem. Eng. Data 43 (1998) 961–966. J. Canosa, A. Rodriguez, J. Tojo, J. Chem. Thermodyn. 30 (1998) 1307–1318. J. Canosa, A. Rodriguez, J. Tojo, J. Chem. Thermodyn. 32 (2000) 551–565. J. Canosa, A. Rodriguez, J. Tojo, J. Chem. Eng. Data 45 (2000) 471–477. A. Rodriguez, J. Canosa, J. Tojo, J. Chem. Eng. Data 48 (2003) 146–151. Y. Gaston-Bonhome, P. Petrino, J.L. Chevalier, Chem. Eng. Sci. 49 (1994) 1799–1806. K. Tochigi, K. Yoshino, V.K. Rattan, in: The Sixteenth European Conference on Thermophysical Properties, September 1–4, London, 2002. S.N. Paudharinath, T.R. Mahale, M. Hasan, J. Chem. Eng. Data 41 (1996) 1055–1058. J.A. Riddick, W.B. Bunger, T.K. Sakano, Organic Solvents, Wiley, New York, 1986. J.L. Chevalier, P.J. Petrino, Y.H. Gaston-bonhomme, J. Chem. Eng. Data 35 (1990) 206–212. T.M. Aminabhavi, G. Bindu, J. Chem. Eng. Data 40 (1995) 462–467. B.M. Coursey, E.L. Heric, J. Chem. Eng. Data 14 (1969) 426–428. J.H. Dymond, K. Young, J. Int. J. Thermophys. 1 (4) (1980) 331–344. O. Redlich, A.T. Kister, Ind. Eng. Chem. 40 (1948) 345–348. P. Bevington, Data Reduction and Error Analysis for the Physical Sciences, McGraw-Hill, New York, 1969. H. Eyring, J. Chem. Phys. 4 (1936) 283–291. J.L. Chevalier, P.J. Petrino, Y.H. Gaston-bonhomme, Chem. Eng. Sci. 43 (1988) 1303–1309. R. Meyer, M. Metzger, J.A. Peneloux, J. Chem. Phys. 68 (1971) 406–408. K. Tochigi, D. Tiegs, J. Gmehling, K. Kojima, J. Chem. Eng. Jpn. 23 (1990) 456–466.
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