Molar Volumes, Molar Refractions, and Isentropic Compressibilities of

Excess molar volumes (VE) and deviations in molar refractions (ΔR) and the isentropic compressibility (Δκs) were determined for the systems ethanol...
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J. Chem. Eng. Data 1997, 42, 721-726

721

Molar Volumes, Molar Refractions, and Isentropic Compressibilities of (Ethanol + Methanol + 2-Methoxy-2-methylpropane) and (Ethanol + Methanol + 2-Methoxy-2-methylbutane) at 298.15 K Alberto Arce,* Eva Rodil, and Ana Soto Department of Chemical Engineering, University of Santiago de Compostela, E-15706 Santiago, Spain

Excess molar volumes (VE) and deviations in molar refractions (∆R) and the isentropic compressibility (∆κs) were determined for the systems ethanol + methanol + 2-methoxy-2-methylpropane and ethanol + methanol + 2-methoxy-2-methylbutane at 298.15 K and atmospheric pressure. For both systems, these results were satisfactorily correlated by the Redlich-Kister polynomial. Several empirical equations allowing prediction of the results for the ternary systems from the VE, ∆R, and ∆κs of their constituent binary subsystems were also examined. The Kohler equation gives the best predictions of VE, while the equations of Radojkovic et al. and of Jacob and Fitzner give the best predictions of ∆R and ∆κs.

Introduction Determination of the effects of mixing on thermodynamic properties is of importance in chemical engineering. Moreover, since these effects arise through molecular interactions, knowledge of them is central to the study of the thermodynamics of solutions. The systems ethanol + methanol + 2-methoxy-2-methylpropane (MTBE) and ethanol + methanol + 2-methoxy2-methylbutane (TAME) are of interest because the ethers are efficient and economic alternatives to the gasoline additive tetraethyl lead, which is now considered a harmful pollutant. In this work, we determined the excess molar volumes of the above two systems and also the deviations of their molar refractions and isentropic compressibilities from the mole fraction or volume fraction average, respectively, of these properties of the pure components. These parameters were estimated from the densities and refractive indices of the systems at 298.15 K and atmospheric pressure and from the speed of sound. To our knowledge, data for the above mixtures are not available in the literature. Determination of the thermodynamic properties of mixtures becomes more tedious as the number of components increases. In this work we evaluated several empirical equations allowing prediction of the properties of ternary systems from the corresponding properties of their constituent binary subsystems (Scatchard et al., 1952; Tsao and Smith, 1953; Kohler, 1960; Toop, 1965; Colinet, 1967; Jacob and Fitzner, 1977; Radojkovic et al., 1977; Rastogi et al., 1977).

Table 1. Densities G and Refractive Indices nD of the Pure Components, and Speeds of Sound u through Them, at 298.15 K and Atmospheric Pressure nD

F/g‚cm-3 component ethanol methanol MTBE TAME

exptl

lit.

exptl

lit.

exptl

lit.

0.7851 0.7866 0.7356 0.7658

0.784 93a 0.786 37a 0.735 28c 0.765 77e

1.3592 1.3264 1.3666 1.3858

1.359 41a 1.326 52a 1.366 30c 1.385 80e

1143 1102 1037 1115

1145d 1102b g 1115b

a Riddick et al., 1986. b Arce et al., 1996. c Daubert and Danner, 1989. d Amanabhavi, 1993. e Linek, 1987. g Not found.

measured to within (0.0001 g. The densities and speeds of sound of the mixtures were measured to within (0.0001 g‚cm-3 and (1 m‚s-1, respectively, in an Anton Paar DSA48 Densimeter and Sound Analyzer calibrated with air and water. Refractive indices were measured to within (0.0001 in an ATAGO RX-1000 refractometer. A Hetotherm thermostat was used to maintain the temperature at (298.15 ( 0.02) K. Table 1 lists the densities, speeds of sound, and refractive indices measured for the pure components, together with published values for these parameters (Aminabhavi et al., 1993; Arce et al., 1996; Daubert and Danner, 1989; Linek, 1987; Riddick et al., 1986). Results Table 2 lists the densities, speeds of sound, and refractive indices measured for the binary and ternary systems. Included in Table 2 are the corresponding excess molar volumes (VE), which were calculated using the expression

Experimental Section Materials. Methanol and ethanol were supplied by Merck and had nominal purities >99.7 and >99.8 mass %, respectively; 2-methoxy-2-methylpropane (MTBE) was supplied by Aldrich with nominal purity >99.8 mass %, and 2-methoxy-2-methylbutane (TAME) was supplied by Fluka with nominal purity >98.9 mass %. Water contents of the ethanol, methanol, MTBE, and TAME (determined with a Metrohm 737 KF coulometer) were 0.08, 0.03, 0.03, and 0.02 mass %, respectively. Apparatus and Procedure. The mixtures were prepared by mass using a Mettler AE 240 balance that * E-mail: [email protected].

S0021-9568(97)00027-7 CCC: $14.00

u/m‚s-1

VE ) V -

∑x V i

i

(1)

i

where V is the molar volume of the mixture and Vi and xi are the molar volume and mole fraction respectively, of component i; the molar refractions (R), which were calculated using the Lorentz-Lorenz equation

n2D - 1 V R) 2 nD + 2

(2)

and the deviations of these values from a mole fraction average of the molar refraction of the pure components © 1997 American Chemical Society

722 Journal of Chemical and Engineering Data, Vol. 42, No. 4, 1997 Table 2. Densities G, Speeds of Sound u, Isentropic Compressibilities Ks, Refractive Indices nD, Excess Molar Volumes VE, and Deviations ∆Ks and ∆R for Mixtures of Ethanol (1) + Methanol (2) + MTBE (3) and Ethanol (1) + Methanol (2) + TAME (3) at 298.15 K and Atmospheric Pressure x1

x2

0.0523 0.1248 0.1631 0.2146 0.2621 0.3114 0.3500 0.4096 0.4567 0.4974 0.5357 0.6073 0.6508 0.6990 0.7371 0.7938 0.8346 0.8854 0.9435 0.0709 0.1130 0.1571 0.2085 0.2599 0.2903 0.3627 0.4095 0.4570 0.5033 0.5674 0.6088 0.6582 0.7018 0.7449 0.7934 0.8758 0.8901 0.9436 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.9056 0.7715 0.6485 0.5454 0.4528 0.3761 0.2897 0.2177 0.1428 0.0832 0.8037 0.6525 0.5730 0.4991 0.4118 0.3230 0.2772

0.9477 0.8752 0.8369 0.7854 0.7379 0.6886 0.6500 0.5904 0.5433 0.5026 0.4643 0.3927 0.3492 0.3010 0.2629 0.2062 0.1654 0.1146 0.0565 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0782 0.1265 0.1769 0.2224 0.2673 0.3116 0.3536 0.4067 0.4282 0.5172 0.5639 0.6060 0.6619 0.7090 0.7519 0.8388 0.8458 0.8905 0.9401 0.0000 0.1480 0.2839 0.3978 0.5000 0.5847 0.6800 0.7596 0.8423 0.9082 0.0000 0.1882 0.2870 0.3789 0.4876 0.5981 0.6551

F/ u/ κs/ g‚cm-3 m‚s-1 TPa-1 0.7865 0.7863 0.7862 0.7861 0.7860 0.7859 0.7859 0.7858 0.7857 0.7856 0.7856 0.7855 0.7854 0.7854 0.7853 0.7853 0.7852 0.7852 0.7851 0.7384 0.7399 0.7416 0.7437 0.7458 0.7471 0.7501 0.7522 0.7543 0.7564 0.7595 0.7615 0.7641 0.7664 0.7689 0.7717 0.7769 0.7778 0.7813 0.7384 0.7401 0.7418 0.7435 0.7452 0.7468 0.7485 0.7506 0.7515 0.7554 0.7575 0.7596 0.7625 0.7652 0.7677 0.7736 0.7741 0.7774 0.7814 0.7788 0.7796 0.7805 0.7812 0.7820 0.7826 0.7834 0.7841 0.7849 0.7856 0.7723 0.7743 0.7755 0.7767 0.7781 0.7797 0.7806

1106 1109 1111 1114 1116 1118 1120 1123 1125 1126 1128 1131 1132 1134 1135 1137 1139 1140 1142 1044 1048 1053 1058 1062 1065 1072 1076 1081 1085 1092 1097 1102 1107 1112 1118 1129 1130 1137 1043 1047 1051 1054 1057 1060 1063 1066 1067 1073 1076 1078 1082 1085 1089 1095 1095 1098 1100 1132 1129 1127 1124 1121 1119 1116 1113 1110 1107 1119 1119 1118 1117 1116 1114 1113

1040 1033 1030 1025 1021 1017 1014 1010 1006 1003 1001 996 993 990 988 985 982 980 977 1242 1229 1217 1202 1188 1180 1160 1148 1135 1122 1104 1092 1077 1064 1051 1036 1011 1006 991 1244 1233 1221 1211 1201 1192 1183 1172 1168 1150 1141 1132 1120 1109 1099 1078 1076 1067 1058 1002 1005 1009 1013 1017 1021 1026 1030 1035 1039 1033 1032 1031 1032 1033 1034 1035

nD 1.3288 1.3321 1.3337 1.3358 1.3376 1.3394 1.3408 1.3428 1.3444 1.3457 1.3469 1.3490 1.3503 1.3517 1.3527 1.3543 1.3553 1.3566 1.3580 1.3667 1.3667 1.3668 1.3668 1.3668 1.3667 1.3666 1.3665 1.3662 1.3660 1.3656 1.3653 1.3648 1.3644 1.3639 1.3633 1.3620 1.3618 1.3607 1.3660 1.3655 1.3650 1.3644 1.3638 1.3630 1.3623 1.3612 1.3607 1.3583 1.3568 1.3553 1.3530 1.3508 1.3485 1.3428 1.3423 1.3385 1.3336 1.3615 1.3580 1.3545 1.3512 1.3479 1.3450 1.3414 1.3382 1.3345 1.3314 1.3633 1.3588 1.3564 1.3539 1.3505 1.3464 1.3441

VE/cm3‚ ∆κs/ ∆R/cm3‚ mol-1 TPa-1 mol-1 0.001 0.003 0.003 0.004 0.005 0.005 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.005 0.005 0.004 0.003 0.003 0.001 -0.110 -0.176 -0.243 -0.313 -0.373 -0.404 -0.459 -0.481 -0.493 -0.496 -0.486 -0.472 -0.448 -0.420 -0.386 -0.340 -0.239 -0.217 -0.125 -0.171 -0.266 -0.355 -0.424 -0.483 -0.530 -0.565 -0.596 -0.604 -0.616 -0.607 -0.591 -0.558 -0.520 -0.476 -0.359 -0.348 -0.267 -0.160 -0.193 -0.169 -0.146 -0.125 -0.106 -0.089 -0.070 -0.053 -0.035 -0.021 -0.329 -0.296 -0.275 -0.253 -0.222 -0.186 -0.166

x1

x2

Ethanol + Methanol + MTBE 0 0.004 0.1907 0.7627 0 0.007 0.1324 0.8352 0 0.008 0.0683 0.9150 0 0.009 0.6978 0.0000 0 0.008 0.5644 0.1912 0 0.008 0.4935 0.2928 0 0.007 0.4228 0.3941 0 0.006 0.3585 0.4862 0 0.005 0.2696 0.6136 0 0.004 0.1917 0.7253 0 0.004 0.1239 0.8224 0 0.003 0.1074 0.8462 0 0.003 0.0613 0.9122 0 0.003 0.5955 0.0000 0 0.003 0.5116 0.1410 0 0.003 0.4789 0.1958 0 0.003 0.4139 0.3050 0 0.002 0.3507 0.4110 0 0.002 0.2971 0.5011 -11 -0.004 0.2470 0.5852 -17 -0.006 0.1674 0.7189 -22 -0.008 0.1271 0.7866 -28 -0.011 0.0734 0.8767 -32 -0.013 0.4965 0.0000 -35 -0.015 0.4207 0.1527 -40 -0.018 0.3742 0.2463 -42 -0.019 0.3274 0.3406 -44 -0.021 0.2994 0.3969 -45 -0.022 0.2482 0.5001 -46 -0.022 0.2023 0.5926 -46 -0.023 0.1482 0.7014 -45 -0.022 0.0902 0.8183 -44 -0.021 0.0546 0.8900 -42 -0.020 0.3966 0.0000 -38 -0.018 0.3347 0.1560 -28 -0.012 0.3044 0.2324 -26 -0.011 0.2766 0.3027 -15 -0.006 0.2415 0.3910 -13 -0.006 0.1932 0.5128 -20 -0.010 0.1607 0.5947 -27 -0.013 0.1178 0.7029 -33 -0.015 0.0826 0.7918 -38 -0.017 0.0449 0.8867 -42 -0.019 0.3100 0.0000 -46 -0.020 0.2733 0.1185 -50 -0.021 0.2412 0.2218 -51 -0.022 0.2130 0.3131 -55 -0.022 0.1819 0.4131 -56 -0.022 0.1480 0.5226 -56 -0.021 0.1213 0.6088 -56 -0.020 0.0930 0.7001 -55 -0.018 0.0649 0.7907 -53 -0.016 0.0328 0.8942 -46 -0.012 0.2139 0.0000 -45 -0.011 0.1838 0.1407 -36 -0.009 0.1650 0.2285 -22 -0.005 0.1450 0.3222 -23 -0.010 0.1260 0.4111 -21 -0.009 0.1048 0.5102 -19 -0.007 0.0844 0.6052 -17 -0.006 0.0653 0.6945 -15 -0.005 0.0424 0.8019 -14 -0.005 0.0233 0.8911 -11 -0.004 0.1049 0.0000 -9 -0.003 0.0909 0.1334 -6 -0.002 0.0804 0.2339 -4 -0.001 0.0711 0.3218 -37 -0.017 0.0615 0.4136 -35 -0.031 0.0526 0.4984 -34 -0.029 0.0414 0.6055 -32 -0.027 0.0315 0.6995 -28 -0.029 0.0212 0.7984 -24 -0.035 0.0104 0.9009 -22 -0.040

F/ u/ κ s/ g‚cm-3 m‚s-1 TPa-1 0.7823 0.7835 0.7850 0.7662 0.7692 0.7709 0.7727 0.7745 0.7770 0.7794 0.7818 0.7824 0.7841 0.7609 0.7635 0.7645 0.7668 0.7692 0.7713 0.7735 0.7772 0.7793 0.7822 0.7561 0.7594 0.7616 0.7639 0.7654 0.7682 0.7710 0.7746 0.7789 0.7818 0.7516 0.7553 0.7573 0.7593 0.7619 0.7658 0.7687 0.7728 0.7765 0.7808 0.7479 0.7510 0.7538 0.7566 0.7598 0.7637 0.7670 0.7708 0.7750 0.7803 0.7440 0.7478 0.7504 0.7535 0.7566 0.7604 0.7644 0.7685 0.7741 0.7793 0.7396 0.7438 0.7472 0.7503 0.7538 0.7573 0.7620 0.7666 0.7721 0.7788

1110 1109 1107 1107 1108 1109 1109 1109 1109 1108 1106 1106 1105 1095 1098 1099 1101 1102 1104 1104 1105 1105 1105 1085 1089 1092 1094 1096 1098 1100 1101 1102 1103 1075 1080 1083 1085 1088 1093 1095 1099 1101 1102 1069 1073 1077 1081 1085 1090 1093 1097 1100 1102 1058 1065 1069 1074 1078 1083 1087 1091 1096 1100 1048 1055 1061 1066 1072 1077 1083 1088 1093 1099

1037 1039 1040 1066 1059 1055 1052 1050 1047 1046 1045 1045 1044 1095 1087 1083 1076 1070 1065 1060 1054 1051 1047 1124 1111 1102 1093 1088 1080 1072 1064 1057 1052 1152 1135 1127 1119 1108 1094 1084 1072 1063 1055 1171 1157 1144 1132 1118 1103 1091 1079 1067 1056 1201 1180 1166 1151 1137 1122 1107 1093 1075 1061 1232 1207 1188 1172 1155 1139 1119 1102 1084 1063

nD 1.3393 1.3358 1.3321 1.3644 1.3605 1.3578 1.3549 1.3521 1.3475 1.3426 1.3376 1.3363 1.3327 1.3654 1.3627 1.3615 1.3589 1.3559 1.3530 1.3499 1.3440 1.3406 1.3353 1.3659 1.3632 1.3614 1.3592 1.3577 1.3544 1.3508 1.3459 1.3396 1.3354 1.3665 1.3638 1.3624 1.3608 1.3586 1.3549 1.3518 1.3469 1.3419 1.3357 1.3667 1.3650 1.3633 1.3614 1.3589 1.3555 1.3523 1.3483 1.3433 1.3362 1.3668 1.3650 1.3636 1.3618 1.3597 1.3569 1.3535 1.3496 1.3436 1.3372 1.3666 1.3654 1.3640 1.3624 1.3603 1.3580 1.3542 1.3500 1.3443 1.3366

VE/cm3‚ ∆κs/ ∆R/cm3‚ mol-1 TPa-1 mol-1

-0.122 -0.088 -0.048 -0.423 -0.409 -0.389 -0.360 -0.326 -0.266 -0.203 -0.139 -0.122 -0.072 -0.477 -0.475 -0.470 -0.453 -0.425 -0.392 -0.352 -0.269 -0.216 -0.135 -0.496 -0.527 -0.526 -0.513 -0.499 -0.461 -0.414 -0.339 -0.233 -0.152 -0.476 -0.533 -0.549 -0.557 -0.553 -0.522 -0.482 -0.403 -0.312 -0.188 -0.421 -0.505 -0.555 -0.580 -0.585 -0.560 -0.515 -0.443 -0.344 -0.195 -0.320 -0.447 -0.507 -0.552 -0.573 -0.569 -0.535 -0.472 -0.354 -0.218 -0.163 -0.387 -0.508 -0.579 -0.618 -0.623 -0.585 -0.509 -0.387 -0.214

-16 -11 -6 -44 -44 -43 -40 -38 -32 -24 -17 -15 -8 -46 -48 -48 -48 -46 -44 -41 -32 -27 -17 -45 -49 -51 -52 -52 -50 -47 -40 -27 -18 -42 -48 -50 -52 -54 -54 -53 -48 -40 -26 -36 -42 -47 -50 -53 -55 -54 -50 -43 -27 -28 -39 -45 -50 -53 -55 -55 -52 -43 -30 -16 -30 -40 -47 -53 -56 -57 -54 -46 -31

-0.045 -0.043 -0.031 -0.021 -0.024 -0.035 -0.040 -0.040 -0.039 -0.042 -0.045 -0.044 -0.036 -0.023 -0.024 -0.025 -0.025 -0.025 -0.025 -0.025 -0.023 -0.021 -0.015 -0.022 -0.033 -0.033 -0.035 -0.037 -0.045 -0.055 -0.064 -0.063 -0.050 -0.019 -0.031 -0.033 -0.034 -0.035 -0.038 -0.041 -0.043 -0.040 -0.030 -0.015 -0.021 -0.026 -0.031 -0.035 -0.038 -0.038 -0.035 -0.029 -0.018 -0.011 -0.015 -0.019 -0.024 -0.027 -0.030 -0.031 -0.030 -0.024 -0.016 -0.005 -0.010 -0.017 -0.024 -0.031 -0.037 -0.041 -0.041 -0.035 -0.022

Journal of Chemical and Engineering Data, Vol. 42, No. 4, 1997 723 Table 2. (Continued) x1

x2

0.9522 0.9009 0.8530 0.7985 0.7480 0.6978 0.6463 0.5990 0.5494 0.5022 0.4565 0.4066 0.3546 0.3092 0.2565 0.2047 0.1559 0.1059 0.0583 0.8988 0.7801 0.7042 0.6216 0.5411 0.4479 0.3446 0.2669 0.1904 0.1073 0.7970 0.6981 0.6224 0.5513 0.4883 0.3794 0.3187 0.2369 0.1707 0.0981 0.6984 0.6093 0.5432 0.4825 0.4268 0.3413 0.2828 0.2147 0.1436 0.0781 0.6030 0.5284 0.4789 0.4112 0.3636 0.2983

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1320 0.2165 0.3085 0.3980 0.5017 0.6166 0.7030 0.7882 0.8807 0.0000 0.1241 0.2191 0.3083 0.3873 0.5239 0.6001 0.7028 0.7858 0.8769 0.0000 0.1276 0.2222 0.3092 0.3888 0.5113 0.5950 0.6926 0.7944 0.8882 0.0000 0.1237 0.2058 0.3180 0.3971 0.5053

F/ u/ κs/ g‚cm-3 m‚s-1 TPa-1 0.7840 0.7828 0.7818 0.7806 0.7795 0.7785 0.7774 0.7765 0.7755 0.7746 0.7738 0.7729 0.7720 0.7712 0.7703 0.7694 0.7685 0.7677 0.7668 0.7829 0.7833 0.7835 0.7838 0.7841 0.7845 0.7849 0.7853 0.7856 0.7860 0.7807 0.7813 0.7818 0.7823 0.7827 0.7835 0.7839 0.7846 0.7851 0.7857 0.7784 0.7793 0.7800 0.7806 0.7812 0.7822 0.7828 0.7837 0.7846 0.7855 0.7766 0.7776 0.7783 0.7793 0.7800 0.7810

1143 1142 1142 1141 1139 1138 1136 1135 1133 1132 1131 1130 1128 1127 1125 1123 1122 1120 1118 1142 1139 1136 1133 1130 1126 1122 1118 1114 1109 1141 1138 1135 1133 1130 1126 1123 1119 1115 1110 1138 1136 1134 1132 1130 1127 1124 1120 1115 1110 1136 1134 1133 1131 1129 1126

977 979 981 984 988 992 996 1000 1004 1007 1010 1014 1018 1021 1025 1030 1034 1039 1044 979 985 989 993 998 1005 1013 1019 1026 1035 985 989 992 996 1000 1007 1012 1019 1025 1033 992 994 997 999 1002 1007 1011 1017 1025 1033 998 1000 1002 1004 1006 1009

nD 1.3622 1.3651 1.3675 1.3699 1.3718 1.3736 1.3751 1.3765 1.3777 1.3788 1.3798 1.3807 1.3816 1.3824 1.3831 1.3838 1.3844 1.3849 1.3854 1.3653 1.3620 1.3596 1.3569 1.3540 1.3504 1.3459 1.3422 1.3382 1.3334 1.3701 1.3670 1.3644 1.3617 1.3590 1.3538 1.3505 1.3456 1.3410 1.3354 1.3735 1.3704 1.3678 1.3652 1.3624 1.3576 1.3539 1.3488 1.3427 1.3360 1.3766 1.3737 1.3714 1.3680 1.3652 1.3608

VE/cm3‚ ∆κs/ ∆R/cm3‚ mol-1 TPa-1 mol-1

-0.070 -0.136 -0.190 -0.241 -0.280 -0.311 -0.335 -0.351 -0.361 -0.365 -0.364 -0.357 -0.343 -0.326 -0.299 -0.263 -0.220 -0.165 -0.100 -0.139 -0.126 -0.117 -0.107 -0.095 -0.082 -0.065 -0.052 -0.038 -0.022 -0.243 -0.230 -0.216 -0.201 -0.186 -0.155 -0.135 -0.105 -0.078 -0.047 -0.311 -0.303 -0.292 -0.276 -0.259 -0.224 -0.195 -0.157 -0.111 -0.063 -0.350 -0.349 -0.343 -0.325 -0.306 -0.272

x1

x2

Ethanol + Methanol + TAME -5 -0.004 0.2482 0.5884 -11 -0.007 0.1867 0.6904 -15 -0.010 0.1237 0.7949 -18 -0.013 0.0682 0.8868 -19 -0.015 0.4995 0.0000 -20 -0.017 0.4316 0.1358 -20 -0.019 0.3865 0.2262 -21 -0.020 0.3351 0.3291 -20 -0.020 0.2923 0.4148 -20 -0.020 0.2432 0.5130 -20 -0.020 0.2048 0.5900 -19 -0.020 0.1518 0.6961 -18 -0.019 0.1075 0.7848 -17 -0.017 0.0596 0.8807 -15 -0.016 0.4016 0.0000 -13 -0.013 0.3460 0.1385 -11 -0.011 0.3082 0.2326 -8 -0.008 0.2749 0.3154 -5 -0.004 0.2346 0.4158 -12 -0.007 0.1863 0.5360 -10 -0.008 0.1236 0.6923 -10 -0.009 0.1125 0.7198 -9 -0.009 0.0816 0.7969 -8 -0.008 0.0427 0.8938 -7 -0.008 0.3101 0.0000 -5 -0.007 0.2718 0.1236 -4 -0.006 0.2385 0.2308 -3 -0.004 0.2102 0.3223 -2 -0.003 0.1821 0.4128 -18 -0.013 0.1507 0.5139 -17 -0.010 0.1202 0.6125 -16 -0.007 0.0934 0.6987 -15 -0.005 0.0649 0.7906 -14 -0.004 0.0158 0.9492 -12 -0.002 0.1951 0.0000 -11 -0.001 0.1664 0.1473 -9 -0.000 0.1479 0.2419 -7 0.000 0.1310 0.3286 -4 0.000 0.1136 0.4177 -20 -0.017 0.0931 0.5230 -20 -0.013 0.0727 0.6275 -19 -0.011 0.0580 0.7027 -19 -0.009 0.0345 0.8231 -18 -0.007 0.0189 0.9030 -16 -0.005 0.1107 0.0000 -15 -0.004 0.0943 0.1482 -13 -0.002 0.0847 0.2352 -10 -0.001 0.0744 0.3282 -6 -0.001 0.0639 0.4226 -21 -0.020 0.0548 0.5052 -21 -0.019 0.0412 0.6279 -20 -0.018 0.0342 0.6915 -20 -0.017 0.0226 0.7961 -20 -0.016 0.0114 0.8967 -19 -0.014

F/ u/ κ s/ g‚cm-3 m‚s-1 TPa-1 0.7818 0.7829 0.7840 0.7851 0.7746 0.7759 0.7768 0.7779 0.7788 0.7799 0.7808 0.7821 0.7833 0.7847 0.7729 0.7744 0.7755 0.7765 0.7777 0.7792 0.7814 0.7818 0.7829 0.7846 0.7713 0.7728 0.7742 0.7754 0.7767 0.7781 0.7795 0.7809 0.7824 0.7855 0.7693 0.7714 0.7727 0.7740 0.7754 0.7771 0.7788 0.7802 0.7825 0.7842 0.7679 0.7702 0.7715 0.7730 0.7746 0.7760 0.7782 0.7794 0.7815 0.7838

1124 1120 1116 1111 1132 1132 1131 1130 1128 1126 1124 1120 1116 1110 1130 1129 1129 1128 1127 1125 1120 1119 1116 1110 1127 1128 1128 1127 1126 1125 1123 1120 1116 1107 1124 1125 1125 1125 1125 1124 1122 1119 1114 1110 1121 1123 1124 1124 1124 1123 1121 1120 1116 1111

1013 1018 1025 1033 1007 1006 1007 1007 1009 1011 1014 1019 1025 1034 1014 1012 1012 1012 1012 1014 1020 1021 1026 1035 1020 1018 1016 1015 1015 1016 1018 1021 1026 1039 1029 1024 1022 1020 1019 1019 1021 1023 1029 1035 1036 1030 1027 1024 1022 1021 1022 1024 1028 1034

VE/cm3‚ ∆κs/ ∆R/cm3‚ mol-1 TPa-1 mol-1

nD 1.3570 1.3514 1.3446 1.3374 1.3791 1.3760 1.3736 1.3704 1.3674 1.3633 1.3596 1.3535 1.3474 1.3393 1.3811 1.3781 1.3757 1.3732 1.3697 1.3646 1.3560 1.3541 1.3483 1.3393 1.3826 1.3802 1.3776 1.3750 1.3719 1.3678 1.3629 1.3576 1.3506 1.3338 1.3842 1.3814 1.3792 1.3768 1.3739 1.3696 1.3642 1.3594 1.3495 1.3407 1.3850 1.3825 1.3806 1.3781 1.3751 1.3719 1.3658 1.3618 1.3534 1.3425

-0.240 -0.193 -0.137 -0.079 -0.365 -0.381 -0.380 -0.368 -0.349 -0.317 -0.285 -0.229 -0.173 -0.102 -0.356 -0.393 -0.402 -0.400 -0.383 -0.345 -0.263 -0.245 -0.189 -0.106 -0.327 -0.390 -0.421 -0.431 -0.424 -0.398 -0.354 -0.300 -0.227 -0.063 -0.255 -0.370 -0.417 -0.440 -0.444 -0.425 -0.379 -0.330 -0.222 -0.131 -0.171 -0.330 -0.394 -0.437 -0.455 -0.450 -0.405 -0.365 -0.272 -0.153

-18 -15 -12 -8 -20 -22 -22 -23 -23 -22 -20 -17 -14 -8 -19 -21 -22 -23 -24 -23 -19 -18 -15 -8 -17 -20 -22 -24 -24 -24 -23 -20 -16 -6 -13 -18 -21 -23 -24 -24 -23 -21 -16 -11 -8 -15 -18 -21 -23 -24 -23 -22 -18 -12

-0.012 -0.010 -0.007 -0.004 -0.020 -0.020 -0.019 -0.018 -0.016 -0.014 -0.013 -0.010 -0.007 -0.004 -0.020 -0.020 -0.019 -0.019 -0.017 -0.015 -0.011 -0.010 -0.008 -0.004 -0.018 -0.018 -0.018 -0.017 -0.016 -0.014 -0.012 -0.010 -0.008 -0.002 -0.013 -0.015 -0.015 -0.015 -0.015 -0.013 -0.012 -0.010 -0.007 -0.004 -0.008 -0.011 -0.012 -0.012 -0.012 -0.012 -0.010 -0.009 -0.007 -0.004

Table 3. Polynomial Coefficients (An) and Standard Deviations (σ) Obtained for the Fits of Eq 7 to the VE, ∆Ks, ∆R Composition Data for the Binary Systems (for ∆Ks, System Compositions Were in Volume Fraction, Oi) property

A0

A1

A2

A3

A4

σ

Ethanol + Methanol VE/cm3‚mol-1 ∆κs/TPa-1 ∆R/cm3‚mol-1

0.0249 -0.0607 -0.0171

-0.0304

VE/cm3‚mol-1 ∆κs/TPa-1 ∆R/cm3‚mol-1

-2.4651 -214.7 -0.0885

72.0

VE/cm3‚mol-1 ∆κs/TPa-1 ∆R/cm3‚mol-1

-1.9854 -179.4 -0.0864

0.0379 46.5 -0.0377

VE/cm3‚mol-1 ∆κs/TPa-1 ∆R/cm3‚mol-1

-1.4593 -79.72 -0.0816

-0.0471 -33.84

VE/cm3‚mol-1 ∆κs/TPa-1 ∆R/cm3‚mol-1

-1.8559 -84.6 -0.0857

-0.1787 -52.6

0.001 0.2 0.001

0.0496 Methanol + MTBE -0.1678 -86.4

-0.3632 130.0

0.001 0.4 0.001

-0.5576 53.9

0.001 0.2 0.001

Ethanol + MTBE -56.4 TAME + Ethanol -0.2821 -42.51 TAME + Methanol -0.3252

0.001 0.2 0.001

-0.1467

-0.2319 -62.4

-128.4

0.001 0.2 0.001

724 Journal of Chemical and Engineering Data, Vol. 42, No. 4, 1997

Figure 1. Excess molar volume isolines for ethanol (1) + methanol (2) + MTBE (3) at 298.15 K and atmospheric pressure (system compositions in mole fraction).

(∆R), which were obtained from

∆R ) R -

∑x R i

Figure 2. Isolines for the deviation in isentropic compressibility of ethanol (1) + methanol (2) + MTBE (3) mixtures at 298.15 K and atmospheric pressure (system compositions in volume fraction).

(3)

i

i

where Ri is the molar refraction of pure component i. The speeds of sound through the mixtures (u) and the corresponding densities (F) were used to calculate isentropic compressibilities (κs, Table 2) using the equation

κs ) u-2F-1

(4)

and the deviations in isentropic compressibility (∆κs, Table 2) were obtained using the expression

∆κs ) κs -

∑φ κ

(5)

i si

i

where κs and κsi are the isentropic compressibilities of the mixture and component i, respectively, and φi is the volume fraction of component i in the mixture as given by

∑φ V

φi ) xiVi/

j

(6)

j

j

where j refers to all components of the mixture. For the ethanol + methanol + 2-methoxy-2-methylpropane system, Figure 1 shows excess volume isolines (system compositions in mole fractions, xi), and Figure 2 shows isolines for the deviation in isentropic compressibility (system compositions in volume fraction, φi). These data are shown for the ethanol + methanol + 2-methoxy2-methylbutane system in Figures 3 and 4. Correlation VE,

∆R, and ∆κs data were correlated with the The composition data by means of the Redlich-Kister polynomial (1948), which for binary mixtures is

∆M ) xixj

∑A (x - x )

n

n

i

j

(7)

n

where ∆M is VE or ∆R and xi is the mole fraction of component i in the mixture, or ∆M is ∆κs and xi is the volume fraction of component i in the mixture, An is the polynomial coefficient, and n is the number of the polyno-

Figure 3. Excess molar volume isolines for ethanol (1) + methanol (2) + TAME (3) at 298.15 K and atmospheric pressure (system compositions in mole fraction).

mial coefficient. For ternary systems the corresponding equation is

∆M123 ) ∆M12 + ∆M32 + ∆M31 + x1x2x3(A + B(x1 x2) + C(x3 - x2) + D(x3 - x1) + E(x1 - x2)2 + F(x3 x2)2 + G(x3 - x1)2 + ... (8) where ∆M123 is VE, ∆κs, or ∆R, xi is the mole fraction or volume fraction of component i, according to the parameter being correlated (as previously indicated), and ∆Mij is the value of the Redlich-Kister coefficient for the same property, as obtained by fitting the Redlich-Kister polynomial to the data for the binary system (i,j). Equations 6 and 7 were fitted to the appropriate parameter-composition data for the binary and ternary systems by least-squares regression, applying Fisher’s F-test to establish the number of coefficients. These coefficients and their mean standard deviations are listed in Table 3 for the binary systems (data for the TAME + methanol system

Journal of Chemical and Engineering Data, Vol. 42, No. 4, 1997 725 Table 4. Polynomial Coefficients and Standard Deviations (σ) Obtained for the Fits of Eq 8 to the VE, ∆Ks, and ∆R Composition Data for the Ternary Systems Ethanol (1) + Methanol (2) + MTBE (3) and Ethanol (1) + Methanol (2) + TAME (3) (for ∆Ks, System Compositions Were in Volume Fraction, Oi) property

A

B

C

VE/cm3‚mol-1 ∆κs/TPa-1 ∆R/cm3‚mol-1

-0.5696 89.37 0.1192

0.7923 -2.28 0.6700

VE/cm3‚mol-1 ∆κs/TPa-1 ∆R/cm3‚mol-1

-0.0747 59.49 0.0188

0.0925 57.66 0.0004

D

E

Ethanol + Methanol + MTBE -1.3317 -0.5394 -18.24 -20.51 -86.51 -0.8571 -0.1871 -2.5023

F

G

σ

506.35 -3.1130

78.04 1.2472

0.006 0.8 0.009

Ethanol + Methanol + TAME 0.8920 0.7995 90.09 32.43 -0.2316 -0.2312

0.003 0.6 0.009

Table 5. Standard Deviations in the Excess Molar Volumes and Deviations in Molar Refraction and Isentropic Compressibility Predicted for Ternary Mixtures at 298.15 K and Atmospheric Pressure Radojkovic et al. (eq 9)

Rastogi et al. (eq 10)

E /cm3‚mol-1 ∆V123 ∆R123/cm3‚mol-1 ∆κs123/TPa-1

0.061 0.023 3

0.148 0.024 13

E ∆V123 /cm3‚mol-1 ∆R123/cm3‚mol-1 ∆κs123/TPa-1

0.009 0.004 1

0.102 0.047 5

Jacob and Fitzner (eq 11)

Colinet (eq 12)

Toop (eq 13)

Kohler (eq 14)

Tsao and Smith (eq 15)

Scatchard et al. (eq 16)

Ethanol + Methanol + MTBE 0.049 0.246 0.029 0.023 0.009 0.021 2 19 8

0.017 0.022 5

0.078 0.020 13

0.203 0.021 24

Ethanol + Methanol + TAME 0.031 0.177 0.033 0.004 0.09 0.004 1 9 4

0.01 0.012 3

0.070 0.015 6

0.170 0.008 11

in which ∆Mij or ∆Mijk is the excess molar volume or the deviation in the molar refraction or in the isentropic compressibility and xi is the mole fraction or volume fraction of pure component i, as indicated above. The equation of Rastogi et al. (1977)

∆M123 ) 0.5[(x1 + x2)∆M′12(x′1,x′2) + (x′1 + x′3)∆M′13(x′1,x′3) + (x2 + x3)∆M′23(x′2,x′3)] (10) in which ∆M′ij(x′i,x′j) is the excess volume or the deviation in the molar refraction or isentropic compressibility of the binary mixture and x′i ) 1 - x′j ) xi/(xi + xj). The equation of Jacob and Fitzner (1977)

[

∆M123 ) 4

Prediction

∆M123 ) ∆M12(x1,x2) + ∆M23(x2,x3) + ∆M13(x1,x3)

(9)

]

The equation of Colinet (1967)

[( )

x2 ∆M′′12(x1,1-x1) + 1 - x1 x1 x3 ∆M′′12(1-x2,x2) + ∆M′′13(x1,1-x1) + 1 - x2 1 - x1 x1 x3 ∆M′′12(1-x3,x3) + ∆M′′23(x2,1-x2) + 0.5 1 - x3 1 - x2 x2 ∆M′′23(1-x3,x3) (12) 1 - x3

∆M123 ) 0.5

Although it would be desirable to be able to estimate the thermodynamic properties of multicomponent systems from the properties of their pure components, in practice such estimates are often inaccurate due to the effects of mixing. An attractive alternative that limits experimental work to binary mixtures is to evaluate the property changes of mixing of the multicomponent system from the properties of its constituent binary subsystems. To assess the viability of this approach for the ternary systems studied here, their VE, ∆R, and ∆κs were predicted from these properties of their constituent binary subsystems by means of empirical equations available in the literature. The equations used were as follows. The equation of Radojkovic et al. (1977)

]

[

Figure 4. Isolines for the deviation in isentropic compressibility of ethanol (1) + methanol (2) + TAME (3) mixtures at 298.15 K and atmospheric pressure (system compositions in volume fractions).

were taken from Arce et al., (1996)) and in Table 4 for the ternary system.

x1x2 ∆M′12(x′1,x′2) + (2x1 + x3)(2x2 + x3) x1x3 ∆M′13(x′1,x′3) + (2x1 + x2)(2x3 + x2) x2x3 4 ∆M′23(x′2,x′3) (11) (2x2 + x1)(2x3 + x1)

( ) [( )

( ) ( ) ( )

]

]

The equation of Toop (1965)

∆M123 )

( )

( )

x2 x3 ∆M′12(x′1,x′2) + ∆M′13(x′1,x′3) + 1 - x1 1 - x1 (1 - x1)2∆M′23(x′2,x′3) (13)

726 Journal of Chemical and Engineering Data, Vol. 42, No. 4, 1997 The equation of Kohler (1960)

∆M123 ) (x1 + x2)2∆M′12(x′1,x′2) + (x1 + x3)2(x′1,x′3)∆M′13 + (x2 + x3)2(x′2,x′3)∆M′23 (14) The equation of Tsao and Smith (1953)

∆M123 )

( )

( )

x2 x3 ∆M′12(x′1,x′2) + ∆M′13(x′1,x′3) + 1 - x1 1 - x1 (1 - x1)∆M′23(x′2,x′3) (15)

rather poor. The best predictions of ∆R were obtained with the equations of Toop (1965), Radojkovic et al. (1977), and Jacob and Fitzner (1977). The latter two equations also afforded the best predictions of ∆κs, while Kohler’s (1960) equation afforded somewhat poorer predictions, and the remaining equations were unsuitable for prediction of the ∆κs values for the systems studied. The equations of Scatchard et al. (1952), Colinet (1967), and Rastogi et al. (1977) were particularly unsuitable for the prediction of the VE, ∆R, or ∆κs data for the ternary systems studied. Literature Cited

The equation of Scatchard et al. (1952)

( )

( )

x2 x3 ∆M′12(x′1,x′2) + ∆M′13(x′1,x′3) + ∆M123 ) 1 - x1 1 - x1 ∆M′′23(x′2,x′3) (16) For each ternary system, Table 5 lists the standard deviations in the values of VE, ∆R, and ∆κs predicted by each equation. Conclusions For both the ethanol + methanol + MTBE system and the ethanol + methanol + TAME system, the excess molar volumes at 298.15 K and atmospheric pressure were negative, except for binary ethanol + methanol mixtures, which had small, positive VE. The system containing MTBE showed the largest deviation from ideality, with minimum VE around -0.62 cm3‚mol-1 for mixtures with MTBE and methanol in around 0.5 mole fraction. For the system containing TAME, minimum VE were around -0.46 cm3‚mol-1 and also occurred for mixtures with ether and methanol in around 0.5 mole fraction. The deviations in the molar refractions of the two systems studied were also negative except for the binary ethanol and methanol mixtures. Although the largest deviation in ∆R occurred for the system containing MTBE, these deviations were generally very small for both systems. As occurred for VE and ∆R, the deviations in the isentropic compressibility were negative except for methanol + ethanol mixtures, for which the components’ κs were additive. ∆κs was again largest for the system containing MTBE, for which the minimun deviation was around -57 TPa-1, as against -24 Tpa-1 for the system containing TAME. The thermodynamic properties were very satisfactorily correlated by the Redlich-Kister polynomial. Most of the predictive equations examined, but especially Kohler’s (1960) equation, allowed adequate prediction of VE for the ternary systems from the data for their constituent binary subsystems. However, the predictions of ∆R and ∆κs were

Aminabhavi, T. M.; Aralaguppi M. Y.; Harogoppad, Sh. B.; Balundgi, R. H. Densities, viscosities, refractive indices, and speeds of sound for methyl acetoacetate + aliphatic alcohols (C1-C8). J. Chem. Eng. Data 1993, 38, 31-39. Arce, A.; Mendoza, J.; Martı´nez-Ageitos, J.; Soto, A. Densities, refractive indices, speeds of sound, and isentropic compressibilities of water + methanol + 2-methoxy-2-methylbutane at 298.15 K. J. Chem. Eng. Data 1996, 41, 724-727. Colinet, C. Ph.D. Thesis, University of Grenoble, France, 1967. Daubert, T. E.; Danner, R. P. Physical and Thermodynamic Properties of Pure Chemicals: Data Compilation. Library of Congress Cataloging-in-Publication Data: New York, 1989. Jacob, K. T.; Fitzner, K. The estimation of the thermodynamic properties of ternary alloys from binary data using the shortest distance composition path. Thermochim. Acta 1977, 18, 197-206. Kohler, F. Estimation of the thermodynamic data for ternary system from the corresponding binary systems. Monatsh. Chem. 1960, 91, 738-740. Linek, J. Excess volumes and refractive indices in the benzene-tertamyl methyl ether and cyclohexane-tert-amyl methyl ether systems at 298.15 K. Collect. Czech. Chem. Commun. 1987, 52, 2839-2843. Radojkovic, N.; Tasic, A.; Grozdanic, D.; Djordjevic, B.; Malic, M. Mixing cell indirect measurements of excess volume. J. Chem. Thermodyn. 1977, 9, 349-352. Rastogi, R. P.; Nath, J.; Das, S. S. Thermodyamic properties of ternary mixtures. 2. The excess volumes of mixing of ternary mixtures of cyclohexane, aromatics, and halomethanes. J. Chem. Eng. Data 1977, 22, 249-252. Redlich, O. J.; Kister, A. T. Algebraic representation of thermodynamic properties and the classification of solutions. Ind. Eng. Chem. 1948, 40(2), 345-348. Riddick, J. A.; Bunger, W. B.; Sakano, T. Organic Solvents, 4th. ed.; John Wiley: New York, 1986. Scatchard, G.; Ticknor, L. B.; Goates, J. R.; McCartney, E. R. Heats of mixing in some nonelectrolyte solutions. J. Am Chem. Soc. 1952, 74, 3721-4. Toop, G. W. Predicting ternary activities using binary data. Trans. TMS-AIME 1965, 223, 850-855. Tsao, C. C.; Smith, J. M. Heat of mixing of liquids. Applied thermodynamics. Chem. Eng. Prog., Symp. Ser. 1953, 49, 107-117.

Received for review January 27, 1997. Accepted April 2, 1997.X This work was partly financed by the DGICYT (Spain) under Project PB94-0658 and Xunta de Galicia (Spain) under Project XUGA 20902B94.

JE9700277 X

Abstract published in Advance ACS Abstracts, May 15, 1997.