Physical properties of binary mixtures of (t-butyl methyl ether + alcohols) fromT = 288.15K...

Article No. jcht.1999.0506Available online at http://www.idealibrary.com on

J. Chem. Thermodynamics1999, 31, 1009–1023

Physical properties of binary mixtures of (t-butylmethyl ether + alcohols) fromT = 288.15 K toT = 298.15 K

A. Rodrıguez, J. Canosa, and J. Tojoa

Departamento de Ingenierıa Quımica, Universidade de Vigo, 36200 Vigo,Espana

Physical properties such as density, refractive index, and speed of sound of the binarymixtures {x(CH3)3COCH3 + (1− x)CH3OH}, {x(CH3)3COCH3 + (1− x)C2H5OH},{x(CH3)3COCH3 + (1− x)C3H7OH}, and{x(CH3)3COCH3 + (1− x)C4H9OH} fromT = 288.15 K to T = 298.15 K and atmospheric pressure have been measured over theentire composition rangex of the mixtures. Excess molar volumes, changes of refractiveindex on mixing, and deviation in isentropic compressibility for the above systems werecalculated and fitted with the Redlich–Kister equation to estimate the fitting parameters andthe root-mean-square deviations between calculated and experimental data. Excess molarvolumes were fitted as a function of the mole fraction, with temperature and their root-mean-square deviations shown. Values of partial excess molar volumes at infinite dilutionare also calculated.c© 1999 Academic Press

KEYWORDS: density; refractive index; speed of sound; CH3OH; C2H5OH; C3H7OH;C4H9OH; (CH3)3COCH3; correlation

1. Introduction

A study of the thermodynamics of the liquid binary mixtures of (t-butyl methyl ether+alcohols) (from C1 to C4),{x(CH3)3COCH3 + (1− x)CH3OH}, {x(CH3)3COCH3 +(1− x)C2H5OH}, {x(CH3)3COCH3 + (1− x)C3H7OH}, and {x(CH3)3COCH3 +(1− x)C4H9OH} from T = 288.15 K to T = 298.15 K and atmospheric pressure hasbeen reported. A survey of the literature shows previously reported densities, refractiveindices, and speed of sound measurements on some binary mixtures of (t-butyl methylether+ alcohols) atT = 298.15 K are available in the literature.(1, 2) A knowledge ofthese properties is relevant to the design of ether production plants. In this work, thedensities, refractive indices, and speeds of sound of homogeneous binary mixtures, at theaforementioned temperatures and atmospheric pressure, have been measured. The resultswere used to calculate excess molar volumes, changes of refractive index on mixing,

aTo whom correspondence should be addressed (E-mail: [email protected]).

0021–9614/99/081009 + 15 $30.00/0 c© 1999 Academic Press

1010 A. Rodr´ıguezet al.

TABLE 1. Comparison of experimental densitiesρ, refractive indicesnD, andspeeds of soundu for pure liquids atT = 298.15 K

ρ/(g · cm−3) nD u/(m · s−1)

Component expt lit expt lit expt lit

(CH3)3COCH3 0.7353 0.7353a 1.36597 1.36630c 1035 1037d

0.73528c

CH3OH 0.7866 0.78664a 1.32645 1.32652a 1102 1102d

0.78637b 1.32652b

C2H5OH 0.7850 0.78509a 1.35922 1.35941a 1143 1143d

0.78493b 1.35941b

C3H7OH 0.7995 0.79975a 1.38292 1.38370a 1206 1204e

0.79975b 1.38370b

C4H9OH 0.8056 0.8060a 1.39713 1.3973a 1240 1240e

0.8060b 1.3973b

aReference 8.bReference 9.cReference 10.dReference 2.eReference 11.

and deviation in isentropic compressibility over the entire mole fraction range for thebinary mixtures at several temperatures. These magnitudes were correlated using theRedlich–Kister(3) equation. Excess molar volumes were fitted as a function of the molefraction and temperature by Roman´ı et al.,(4) and their root-mean-square deviations areshown. Values of partial excess molar volumes at infinite dilution fromT = 298.15 K toT = 288.15 K were calculated.

2. Experimental

Chemicals were supplied by Merck and their mass fraction purities were>0.998. Theywere recently acquired and kept in an inert argon (N-55, with a maximum content in waterof 2 · 10−6 by volume) atmosphere, degassed in an ultrasound bath, and stored over freshlyactivated molecular sieves Type 0.4 nm, or 0.3 nm, for several days before using. Themaximum water contents are 1.5 · 10−4, 1.6 · 10−4, 8.7 · 10−5, 1.6 · 10−4, and 1.1 · 10−5

by volume fraction for CH3OH, C2H5OH, C3H7OH, C4H9OH, and (CH3)3COCH3,respectively. This water content was determined using a Metrohm 737 KF coulometer.Gas chromatographic analysis of the solvents yielded purities which fulfilled purchaserspecifications. The solvent purities were assessed by comparison with recommended andrecent published values. The results are listed in table 1.

The mixtures were prepared by weighing amounts of the pure liquids by syringing intostoppered bottles to prevent evaporation and reducing possible errors in mole fractioncalculations. A Mettler AT-261 Delta Range balance was used with a precision of±10−5 g,covering the entire composition rangex of the mixtures. The densities and the speedsof sound of the pure liquids and mixtures were measured with an Anton Paar DSA-48 densimeter and sound analyser with a precision of±10−4 g · cm−3 and±1 m · s−1.The refractive indicies were measured by the automatic refractometer ABBEMATHP Dr

Physical properties of (t-butyl methyl ether+ alcohols) 1011

Kernchen with a precision of±10−5. Before each series of measurements, these instrumentswere calibrated with Millipore quality water and ambient air, respectively, in accordancewith the instructions. The accuracy in the calculation of excess molar volumes, changes ofrefractive index on mixing, and deviation in isentropic compressibility were estimated asbetter than 10−2 cm3 ·mol−1, 5 · 10−5, and 2 m· s−1, respectively.

3. Results and discussion

The experimental density, refractive index, and speed of sound values were measured atT = 288.15 K, T = 293.15 K, andT = 298.15 K and atmospheric pressure, as shownin table 2. The excess molar volumes, changes of refractive index on mixing, isentropiccompressibilities (determined by means of the Laplace equationκS = ρ−1 · u−2) anddeviations in isentropic compressibility1κSof the binary mixtures are reported in table 2 forthe aforementioned temperatures. A survey of the literature(3, 4) shows previously reporteddensity, refractive index, and speed of sound measurements on binary mixtures of (t-butylmethyl ether+ alcohols) atT = 298.15 K but data for the above binary mixtures arenot available in the literature at the remaining temperatures. The differences between theexperimental values in the literature and our results, in terms of root-mean-square deviations,concerning the binary systems discussed are shown in table 3.

Excess molar volumes and changes of refractive indices on mixing of binary mixtureswere derived, respectively, from equations (1) and (2):

VEm =

N∑i=1

xi Mi (ρ−1− ρo−1

i ), (1)

1mixnD = nD −N∑

i=1

xi noD,i . (2)

In these equations,ρ is the density of the mixture,nD is the refractive index of the mixture,andρo

i andnoD,i are the density and refractive index of the pure components. The deviation

in isentropic compressibility values were calculated as:

1κS = κS−N∑

i=1

xi · κS,i , (3)

where κS is the isentropic compressibility of the mixture andκS,i is the isentropiccompressibility of the pure component. Excess isentropic compressibilities are calculatedby applying the equation:

κES = κS− κ id

S , (4)

whereκ idS was calculated by using the following relation:

κ idS =

∑i

φi {κS,i +T ·Vi ·(αi )2/Cp,i }−T ·

(∑i

xi ·Vi

)·(∑

i

φi ·αi

)2/(∑i

xi ·Cp,i

).

(5)


TABLE 2. Densitiesρ, refractive indiciesnD, speeds of soundu, excess molar volumesVEm, changes

of refractive index on mixing1nD, isentropic compressibilitiesκS, and deviations in isentropiccompressibility1κS for binary mixtures fromT = 298.15 K to T = 288.15 K, wherex is the mole

fraction of the components in the binary mixture

x1 ρ/(g · cm−3) VEm/(cm3 ·mol−1) nD 1mixnD u/(m · s−1) κS/(TPa−1) 1κS/(TPa−1)

T = 298.15 Kx(CH3)3COCH3 + (1− x)CH3OH

0 0.7866 0 1.32645 0 1102 1047 00.0535 0.7818 −0.145 1.33276 0.0042 1099 1058 −0.20.1088 0.7772 −0.264 1.33818 0.0074 1096 1070 −0.40.2032 0.7704 −0.427 1.34553 0.0110 1090 1092 0.00.2979 0.7646 −0.546 1.35094 0.0127 1084 1113 0.30.4019 0.7590 −0.618 1.35540 0.0131 1077 1136 −0.00.5043 0.7542 −0.648 1.35865 0.0123 1070 1157 −1.30.6031 0.7500 −0.628 1.36092 0.0106 1064 1177 −3.10.6961 0.7463 −0.561 1.36269 0.0087 1058 1196 −4.90.7856 0.7430 −0.463 1.36402 0.0065 1053 1215 −6.20.8888 0.7393 −0.287 1.36525 0.0037 1045 1238 −5.60.9494 0.7371 −0.139 1.36580 0.0018 1040 1254 −3.4

1 0.7353 0 1.36597 0 1035 1269 0

x(CH3)3COCH3 + (1− x)C2H5OH0 0.7850 0 1.35922 0 1143 976 0

0.0523 0.7814 −0.114 1.36042 0.0008 1136 991 0.20.0936 0.7786 −0.187 1.36128 0.0014 1131 1004 0.50.2029 0.7717 −0.341 1.36303 0.0024 1118 1037 2.20.2968 0.7663 −0.432 1.36419 0.0030 1106 1066 3.50.3955 0.7611 −0.493 1.36502 0.0031 1095 1096 4.00.5038 0.7558 −0.513 1.36567 0.0030 1083 1127 3.70.6010 0.7514 −0.497 1.36608 0.0028 1074 1154 2.40.6978 0.7472 −0.435 1.36633 0.0024 1065 1180 0.20.8077 0.7428 −0.336 1.36650 0.0018 1055 1210 −2.60.9037 0.7390 −0.191 1.36635 0.0010 1046 1237 −3.50.9453 0.7374 −0.115 1.36625 0.0006 1042 1250 −2.8

1 0.7353 0 1.36597 0 1035 1269 0

x(CH3)3COCH3 + (1− x)C3H7OH0 0.7995 0 1.38292 0 1206 860 0

0.0619 0.7950 −0.158 1.38209 0.0002 1195 881 −4.70.1050 0.7920 −0.264 1.38146 0.0003 1187 895 −7.90.2074 0.7848 −0.452 1.37989 0.0005 1168 933 −11.90.3099 0.7777 −0.571 1.37831 0.0006 1150 973 −13.90.4149 0.7707 −0.641 1.37657 0.0007 1131 1015 −15.30.5144 0.7643 −0.659 1.37490 0.0007 1114 1054 −16.20.6012 0.7589 −0.638 1.37340 0.0007 1100 1089 −16.80.7064 0.7526 −0.571 1.37156 0.0006 1084 1132 −17.1


TABLE 2—continued


0.7958 0.7473 −0.460 1.36993 0.0005 1070 1169 −16.10.8922 0.7416 −0.276 1.36814 0.0003 1055 1212 −12.30.9515 0.7381 −0.130 1.36699 0.0002 1045 1241 −7.3

1 0.7353 0 1.36597 0 1035 1269 0

x(CH3)3COCH3 + (1− x)C4H9OH0 0.8056 0 1.39713 0 1240 808 0

0.0496 0.8023 −0.137 1.39580 0.0002 1230 824 −6.80.1148 0.7979 −0.294 1.39392 0.0004 1217 846 −14.50.2124 0.7912 −0.480 1.39110 0.0006 1197 882 −23.30.3032 0.7848 −0.593 1.38840 0.0007 1177 919 −28.40.3974 0.7783 −0.687 1.38554 0.0008 1158 958 −32.80.5097 0.7705 −0.736 1.38208 0.0008 1135 1007 −35.70.5984 0.7643 −0.725 1.37930 0.0008 1118 1047 −36.50.7024 0.7570 −0.656 1.37598 0.0007 1098 1096 −35.20.8109 0.7492 −0.494 1.37244 0.0006 1076 1152 −29.20.8903 0.7435 −0.334 1.36979 0.0004 1060 1196 −21.60.9402 0.7398 −0.196 1.36808 0.0002 1050 1227 −14.4

1 0.7353 0 1.36597 0 1035 1269 0

T = 293.15 Kx(CH3)3COCH3 + (1− x)CH3OH

0 0.7917 0 1.32859 0 1120 1006 00.0489 0.7872 −0.126 1.33440 0.0038 1117 1017 1.30.1067 0.7825 −0.258 1.34024 0.0073 1114 1029 1.50.2043 0.7754 −0.421 1.34798 0.0111 1109 1048 1.50.2936 0.7698 −0.522 1.35321 0.0128 1005 1065 0.60.3963 0.7643 −0.599 1.35775 0.0132 1098 1084 0.30.5028 0.7593 −0.631 1.36120 0.0123 1093 1103 −1.90.6052 0.7551 −0.628 1.36374 0.0107 1086 1122 −2.90.7147 0.7508 −0.550 1.36584 0.0084 1080 1142 −4.00.8015 0.7477 −0.459 1.36723 0.0063 1074 1159 −4.80.8858 0.7446 −0.302 1.36823 0.0039 1068 1176 −3.70.9274 0.7431 −0.209 1.36860 0.0026 1065 1186 −2.5

1 0.7404 0 1.36896 0 1060 1202 0

x(CH3)3COCH3 + (1− x)C2H5OH0 0.7893 0 1.36126 0 1160 976 0

0.0476 0.7860 −0.095 1.36249 0.0009 1155 991 0.10.1057 0.7822 −0.199 1.36373 0.0017 1148 1004 1.30.2075 0.7759 −0.331 1.36546 0.0026 1136 1037 2.80.3034 0.7705 −0.419 1.36663 0.0030 1126 1066 3.50.4028 0.7654 −0.478 1.36756 0.0032 1115 1096 4.00.5084 0.7604 −0.501 1.36834 0.0032 1004 1127 3.9


TABLE 2—continued


0.6006 0.7563 −0.486 1.36882 0.0029 1096 1154 2.90.7009 0.7521 −0.435 1.36916 0.0025 1087 1180 1.20.8015 0.7481 −0.344 1.36938 0.0019 1078 1210 0.40.9070 0.7440 −0.192 1.36927 0.0010 1068 1237 −0.30.9436 0.7426 −0.126 1.36915 0.0006 1065 1250 −0.5

1 0.7404 0 1.36896 0 1060 1269 0

x(CH3)3COCH3 + (1− x)C3H7OH0 0.8035 0 1.38510 0 1223 833 0

0.0530 0.7997 −0.131 1.38442 0.0002 1214 849 −3.70.0987 0.7966 −0.245 1.38381 0.0003 1206 863 −6.20.2092 0.7890 −0.447 1.38223 0.0005 1187 900 −10.10.3136 0.7819 −0.563 1.38073 0.0007 1168 937 −11.40.4073 0.7758 −0.630 1.37930 0.0008 1152 971 −12.30.4984 0.7701 −0.661 1.37786 0.0008 1137 1004 −12.60.5942 0.7642 −0.642 1.37631 0.0008 1122 1039 −13.00.7434 0.7553 −0.521 1.37378 0.0007 1099 1096 −12.00.7965 0.7522 −0.450 1.37282 0.0006 1091 1116 −11.30.9114 0.7456 −0.242 1.37071 0.0003 1074 1163 −6.50.9561 0.7430 −0.131 1.36985 0.0002 1066 1183 −2.7

1 0.7404 0 1.36896 0 1060 1202 0

x(CH3)3COCH3 + (1− x)C4H9OH0 0.8094 0 1.39929 0 1257 782 0

0.0565 0.8057 −0.148 1.39770 0.0001 1246 799 −6.80.1100 0.8022 −0.277 1.39615 0.0002 1236 816 −12.60.2161 0.7951 −0.479 1.39313 0.0004 1215 852 −20.60.3098 0.7888 −0.612 1.39038 0.0005 1196 886 −26.00.4029 0.7823 −0.675 1.38761 0.0005 1177 923 −28.70.5092 0.7750 −0.711 1.38443 0.0006 1156 966 −30.30.6015 0.7687 −0.704 1.38163 0.0006 1138 1004 −30.60.7007 0.7618 −0.631 1.37858 0.0005 1119 1048 −28.80.8151 0.7539 −0.491 1.37498 0.0004 1098 1101 −23.70.9011 0.7477 −0.300 1.37223 0.0003 1081 1145 −15.80.9478 0.7443 −0.173 1.37067 0.0001 1071 1172 −8.8

1 0.7404 0 1.36896 0 1060 1202 0

T = 288.15 Kx(CH3)3COCH3 + (1− x)CH3OH

0 0.7965 0 1.33091 0 1137 971 00.0582 0.7910 −0.131 1.33782 0.0045 1135 981 0.60.1030 0.7873 −0.222 1.34235 0.0072 1133 989 0.80.2006 0.7801 −0.370 1.35029 0.0111 1129 1006 0.40.2990 0.7742 −0.489 1.35622 0.0130 1124 1022 −0.5


TABLE 2—continued


0.4030 0.7689 −0.575 1.36081 0.0134 1119 1038 −1.90.5052 0.7642 −0.604 1.36413 0.0125 1114 1055 −2.90.6011 0.7603 −0.600 1.36649 0.0110 1108 1070 −4.20.7128 0.7560 −0.529 1.36870 0.0085 1102 1088 −5.60.7923 0.7531 −0.439 1.36996 0.0065 1098 1102 −6.10.8569 0.7508 −0.338 1.37079 0.0047 1094 1114 −5.50.8731 0.7502 −0.304 1.37095 0.0042 1092 1117 −5.00.9313 0.7481 −0.174 1.37152 0.0024 1088 1129 −3.1

1 0.7457 0 1.37194 0 1083 1144 0

x(CH3)3COCH3 + (1− x)C2H5OH0 0.7935 0 1.36332 0 1178 909 0

0.0604 0.7895 −0.120 1.36499 0.0011 1171 923 0.30.1099 0.7863 −0.198 1.36614 0.0019 1166 935 0.60.2137 0.7802 −0.339 1.36799 0.0028 1155 960 1.50.2936 0.7758 −0.411 1.36906 0.0032 1147 980 2.30.3931 0.7707 −0.465 1.37007 0.0034 1137 1004 2.70.5033 0.7655 −0.484 1.37091 0.0032 1127 1029 1.80.5929 0.7616 −0.473 1.37145 0.0030 1118 1050 1.60.6950 0.7574 −0.425 1.37188 0.0026 1110 1072 −0.20.7972 0.7534 −0.336 1.37213 0.0019 1101 1095 −0.80.9060 0.7492 −0.178 1.37217 0.0010 1091 1121 −1.10.9499 0.7476 −0.107 1.37209 0.0006 1088 1130 −1.6

1 0.7457 0 1.37194 0 1083 1144 0

x(CH3)3COCH3 + (1− x)C3H7OH0 0.8074 0 1.38719 0 1241 805 0

0.0586 0.8033 −0.139 1.38648 0.0002 1231 825 −2.80.1016 0.8004 −0.236 1.38599 0.0003 1223 835 −4.20.2019 0.7936 −0.408 1.38460 0.0005 1206 866 −7.20.3081 0.7866 −0.532 1.38312 0.0006 1189 900 −9.20.3990 0.7808 −0.596 1.38175 0.0006 1174 930 −10.30.4996 0.7745 −0.614 1.38015 0.0006 1158 963 −10.90.5946 0.7688 −0.597 1.37860 0.0005 1143 995 −11.10.7055 0.7624 −0.533 1.37682 0.0004 1127 1033 −10.90.7970 0.7571 −0.415 1.37523 0.0002 1113 1066 −9.10.9104 0.7507 −0.213 1.37340 0.0010 1096 1108 −5.40.9607 0.7479 −0.101 1.37254 0 1089 1127 −3.2

1 0.7457 0 1.37194 0 1083 1144 0

x(CH3)3COCH3 + (1− x)C4H9OH0 0.8132 0 1.40128 0 1273 758 0

0.0529 0.8098 −0.132 1.39988 0.0001 1264 773 −5.70.1065 0.8063 −0.249 1.39845 0.0003 1254 789 −10.6


TABLE 2—continued


0.2103 0.7995 −0.439 1.39560 0.0005 1234 822 −17.80.3062 0.7931 −0.561 1.39283 0.0005 1215 854 −22.30.4023 0.7867 −0.643 1.39005 0.0006 1196 888 −25.10.5108 0.7794 −0.677 1.38693 0.0006 1176 928 −26.90.6455 0.7703 −0.637 1.38283 0.0005 1151 980 −26.70.7027 0.7664 −0.589 1.38116 0.0005 1140 1004 −25.20.8058 0.7593 −0.450 1.37798 0.0003 1121 1048 −21.30.9016 0.7526 −0.255 1.37498 0.0001 1103 1092 −14.10.9532 0.7490 −0.131 1.37337 0.0001 1093 1118 −7.3

1 0.7457 0 1.37194 0 1083 1144 0

0–0.8

–0.6

–0.4

–0.2

0

0.5x1

1

VE

/(cm

3 ·mol

–1)

m

a

0–0.8

–0.6

–0.4

–0.2

0

0.5x1

1

VE

/(cm

3 ·mol

–1)

m

b

FIGURE 1. Curves of excess molar volumesVEm/(cm3 ·mol−1) at: - - -, T = 298.15 K; —, T =

293.15 K; – –,T = 288.15 K for: a,◦, {x(CH3)3COCH3+(1− x)CH3OH}; ✩, {x(CH3)3COCH3+(1− x)C4H9OH}; and b, ¤, {x(CH3)3COCH3 + (1− x)C2H5OH}; 4, {x(CH3)3COCH3 +(1− x)C3H7OH}.

φi is defined by the relation:

φi = xi · Vi

/(∑i

xi · Vi

). (6)


00

0.005

0.010

0.015

0.5x1

1

1m

ixn

D

a

00

0.001

0.003

0.004

0.5x1

1

1m

ixn

D

b

FIGURE 2. Curves of changes of refractive index on mixing1mixnD at: - - -, T = 298.15 K;—, T = 293.15 K; and – –,T = 288.15 K for: a, ◦ {x(CH3)3COCH3 + (1− x)CH3OH};✩, {x(CH3)3COCH3 + (1− x)C4H9OH}; and b,¤, {x(CH3)3COCH3 + (1− x)C2H5OH}; 4,{x(CH3)3COCH3+ (1− x)C3H7OH}.

TABLE 3. Root-mean-square deviationsσ of the excess molar volumesVEm, changes of refractive

index on mixing1nD and deviations in isentropic compressibility1κS from available source atT = 298.15 K

SYSTEMS Referenceσ {VEm/(cm3 ·mol−1)} σ(1mixnD) σ {1κS/(TPa−1)}

{x(CH3)3COCH3 + (1− x)CH3OH} 1 0.006 n. a. n. a.{x(CH3)3COCH3 + (1− x)C2H5OH} 1 0.006 n. a. n. a.{x(CH3)3COCH3 + (1− x)C3H7OH} 1 0.008 n. a. n. a.{x(CH3)3COCH3 + (1− x)CH3OH} 2 0.031 0.0001 1.4{x(CH3)3COCH3 + (1− x)C2H5OH} 2 0.024 0.0001 0.8

The values ofVi , andαi were calculated from the densities, andCp,i was calculated fromthe literature compilations(5). This magnitude will be compared graphically with deviationsin isentropic compressibility later on.

The binary values were fitted with a Redlich–Kister-type equation:

1Qi j = xi x j

M∑p=0

Bp(xi − xj )p, (7)

where1Qi, j is the excess property,x is the mole fraction,Bp is the fitting parameter, and


TABLE 4. ParametersBp of equation (7) and standard root-mean-square deviationsσ at T =288.15 K, T = 293.15 K, andT = 298.15 K

x(CH3)3COCH3 + (1− x)CH3OHT = 298.15 K

VEm/(cm3 ·mol−1) B0 = −2.5821 B1 = −0.0910 B2 = −0.3578 σ = 0.0021mixnD B0 = 0.0490 B1 = −0.0249 B2 = 0.0128 σ = 0.000051κS/(TPa−1) B0 = −275.6 B1 = 121.9 B2 = −142.0 B3 = 49.7 σ = 0.3

T = 293.15 KVE

m/(cm3 ·mol−1) B0 = −2.5318 B1 = −0.2244 B2 = −0.5231 σ = 0.0041mixnD B0 = 0.0493 B1 = −0.0245 B2 = 0.0134 σ = 0.000021κS/(TPa−1) B0 = −250.6 B1 = 111.2 B2 = −99.0 B3 = 41.4 σ = 0.3

T = 288.15 KVE

m/(cm3 ·mol−1) B0 = −2.4261 B1 = −0.2814 B2 = −0.2085 σ = 0.0041mixnD B0 = 0.0502 B1 = −0.0252 B2 = 0.0123 σ = 0.000011κS/(TPa−1) B0 = −232.7 B1 = 99.2 B2 = −98.2 B3 = 35.2 σ = 0.2

x(CH3)3COCH3 + (1− x)C2H5OHT = 298.15 K

VEm/(cm3 ·mol−1) B0 = −2.0489 B1 = −0.0116 B2 = −0.2273 σ = 0.0031mixnD B0 = 0.0122 B1 = −0.0035 B2 = 0.0033 B3 = 0.0010 σ = 0.000021κS/(TPa−1) B0 = −256.6 B1 = 92.0 B2 = −93.1 σ = 0.2

T = 293.15 KVE

m/(cm3 ·mol−1) B0 = −1.9939 B1 = −0.1139 B2 = −0.2807 σ = 0.0021mixnD B0 = 0.0127 B1 = −0.0027 B2 = 0.0036 B3 = −0.0013 σ = 0.000021κS/(TPa−1) B0 = −233.2 B1 = 87.1 B2 = −59.6 B3 = 22.1 σ = 0.2

T = 288.15 KVE

m/(cm3 ·mol−1) B0 = −1.9469 B1 = −0.0439 B2 = −0.2477 σ = 0.0031mixnD B0 = 0.0131 B1 = −0.0042 B2 = −0.0042 σ = 0.000021κS/(TPa−1) B0 = −220.3 B1 = 86.0 B2 = −59.7 σ = 0.4

x(CH3)3COCH3 + (1− x)C3H7OHT = 298.15 K

VEm/(cm3 ·mol−1) B0 = −2.6472 B1 = −0.0648 B2 = −0.3270 σ = 0.0041mixnD B0 = 0.0028 B1 = 0.0011 σ = 0.000011κS/(TPa−1) B0 = −63.6 B1 = −14.6 B2 = −66.2 B3 = −25.4 σ = 0.2

T = 293.15 KVE

m/(cm3 ·mol−1) B0 = −2.6276 B1 = −0.1067 B2 = −0.0314 σ = 0.0051mixnD B0 = 0.0032 B1 = 0.0004 B2 = 0.0006 σ = 0.000011κS/(TPa−1) B0 = −51.0 B1 = −6.2 B2 = −36.0 σ = 0.4

T = 288.15 KVE

m/(cm3 ·mol−1) B0 = −2.4755 B1 = −0.0413 B2 = −0.2054 σ = 0.0041mixnD B0 = 0.0023 B1 = −0.0016 σ = 0.000021κS/(TPa−1) B0 = −44.8 B1 = −11.0 B2 = −20.5 σ = 0.2


TABLE 4—continued

x(CH3)3COCH3 + (1− x)C4H9OHT = 298.15 K

VEm/(cm3 ·mol−1) B0 = −2.9301 B1 = −0.3388 B2 = −0.3297 σ = 0.0041mixnD B0 = 0.0033 B1 = 0.0002 B2 = 0.0011 σ = 0.000011κS/(TPa−1) B0 = −141.4 B1 = −34.6 B2 = −65.9 B3 = −27.1 σ = 0.4

T = 293.15 KVE

m/(cm3 ·mol−1) B0 = −2.8586 B1 = −0.2912 B2 = −0.4107 σ = 0.0061mixnD B0 = 0.0023 B1 = 0.0004 B2 = 0.0003 σ = 0.000011κS/(TPa−1) B0 = −121.6 B1 = −18.9 B2 = −46.5 B3 = −16.1 σ = 0.2

T = 288.15 KVE

m/(cm3 ·mol−1) B0 = −2.7126 B1 = −0.2308 B2 = −0.0907 B3 = 0.1061 σ = 0.0021mixnD B0 = 0.0024 B1 = −0.0006 σ = 0.000031κS/(TPa−1) B0 = −106.8 B1 = −17.7 B2 = −41.7 B3 = −15.3 σ = 0.2

0–40

–30

–20

–10

0

10

0.5

x1

1

1κ

S /(

TPa

–1)

FIGURE 3. Curves of deviation in isentropic compressibility1κS/(TPa−1) at: - - -, T =298.15 K; —, T = 293.15 K; – –, T = 288.15 K for: ◦, {x(CH3)3COCH3 + (1− x)CH3OH};✩, {x(CH3)3COCH3 + (1− x)C4H9OH}; ¤, {x(CH3)3COCH3 + (1− x)C2H5OH}; 4,{x(CH3)3COCH3+ (1− x)C3H7OH}.

M is the degree of the polynomic expansion. The degree of this equation was optimizedby applying the F-test.(6) The correlation parameters calculated by using equation (7) are


TA

BL

E5

.Par

amet

ersA

ijof

equa

tion

(9)

and

root

-mea

n-sq

uare

devi

atio

nsσ

x(C

H3) 3

CO

CH 3+(1−

x)C

H3O

HV

E m/(c

m3·m

ol−1)

A11=−2.5

223

A12=−0.0

530

A13=

0.00

04A

21=−0.1

659

A22=

0.09

04A

23=

0.00

32σ=

0.01

31

mix

n DA

11=

0.09

750

A12=

0.00

034

A13=

0.00

004

A21=−0.0

6731

A22=−0.0

0060

A23=

0.00

005

σ=

0.00

017

1κ

S/(T

Pa−

1)

A11=

42.7

A12=−2.3

763

A13=−0.2

0794

A21=−7

7.8

A22=

0.91

84A

23=−0.0

030

σ=

1.0

x(C

H3) 3

CO

CH 3+(1−

x)C

2H

5O

HV

E m/(c

m3·m

ol−1)

A11=−2.0

895

A12=−0.0

762

A13=−0.0

061

A21=

0.00

87A

22=

0.09

72A

23=

0.00

90σ=

0.00

81

mix

n DA

11=

0.01

866

A12=

0.00

005

A13=

0.00

004

A21=−0.0

0856

A22=−0.0

0020

A23=−0.0

0005

σ=

0.00

008

1κ

S/(T

Pa−

1)

A11=

46.3

A12=

3.94

3A

13=

0.19

41A

21=−5

5.0

A22=−8.5

36A

23=−0.6

040

σ=

1.1

x(C

H3) 3

CO

CH 3+(1−

x)C

3H

7O

HV

E m/(c

m3·m

ol−1)

A11=−2.6

214

A12=−0.0

309

A13=−0.0

015

A21=−0.1

091

A22=

0.05

97A

23=

0.00

64σ=

0.01

01

mix

n DA

11=

0.00

302

A12=

0.00

034

A13=

0.00

005

A21=−0.0

0012

A22=−0.0

0079

A23=−0.0

0012

σ=

0.00

003

1κ

S/(T

Pa−

1)

A11=−3

8.7

A12=

4.64

9A

13=

0.55

21A

21=−5

0.4

A22=−1

2.7

A23=−1.0

14σ=

1.5

x(C

H3) 3

CO

CH 3+(1−

x)C

4H

9O

HV

E m/(c

m3·m

ol−1)

A11=−2.3

983

A12=

0.01

28A

13=

0.00

14A

21=−0.8

435

A22=−0.0

168

A23=

0.00

19σ=

0.01

21

mix

n DA

11=

0.00

323

A12=

0.00

063

A13=

0.00

007

A21=

0.00

034

A22=−0.0

0044

A23=−0.0

0006

σ=

0.00

003

1κ

S/(T

Pa−

1)

A11=−7

6.6

A12=

4.80

4A

13=

0.48

94A

21=−1

08.8

A22=−1

4.8

A23=−0.9

396

σ=

1.8


0–100

–75

–50

–25

0a

0.5x1

1

κS /(

TPa

–1)

E

0–100

–75

–50

–25

0b

0.5x1

1

κS /(

TPa

–1)

E

FIGURE 4. Curves of excess isentropic compressibilityκES/(TPa−1) at: - - - T = 298.15 K;

—, T = 293.15 K; – –, T = 288.15 K for: a, ◦, {x(CH3)3COCH3 + (1− x)CH3OH};✩, {x(CH3)3COCH3 + (1− x)C4H9OH}; and b,¤, {x(CH3)3COCH3 + (1− x)C2H5OH}; 4,{x(CH3)3COCH3+ (1− x)C3H7OH}.

listed in table 4, together with the root-mean-square deviationsσ . This one is calculated byapplying the following expression:

σ ={ nDAT∑

i

(Zexp− Zpred)2/

nDAT

}1/2

, (8)

where property values and the number of experimental data are represented byZ andnDAT,respectively.

The excess molar volumes were fitted as a function of the mole fraction and temperaturewith a polynomial of the form:

VE = x(1− x)2∑

i=1

2∑j=1

Ai j x(i−1/2)(T − 298.15 K) j−1, (9)

where Ai j and root-mean-square deviations are given in table 5. The fitted curves,as well as excess changes on mixing and deviations values fromT = 288.15 K toT = 298.15 K are shown in figures 1 to 4. Excess molar volumes are negative over theentire composition rangex. Changes of refractive index on mixing are positive for the binarymixtures at the above temperatures. Deviations in isentropic compressibilities are negativeover the range of temperatures discussed, for the binary mixtures{x(CH3)3COCH3 +(1− x)C3H7OH} and {x(CH3)3COCH3 + (1− x)C4H9OH}. However, if the binary


TABLE 6. Partial excess molar volumes at infinite

dilution VE,∞

of the binary mixtures

T/K VE,∞1 /(cm3 ·mol−1) V

E,∞2 /(cm3 ·mol−1)

x(CH3)3COCH3 + (1− x)CH3OH298.15 −2.849 −3.031293.15 −2.830 −3.279288.15 −2.353 −2.916

x(CH3)3COCH3 + (1− x)C2H5OH298.15 −2.264 −2.288293.15 −2.161 −2.388288.15 −2.151 −2.239

x(CH3)3COCH3 + (1− x)C3H7OH298.15 −2.909 −3.039293.15 −2.834 −3.048288.15 −2.640 −2.722

x(CH3)3COCH3 + (1− x)C4H9OH298.15 −2.921 −3.599293.15 −2.978 −3.560288.15 −2.679 −2.928

mixture is{x(CH3)3COCH3+ (1− x)CH3OH}and{x(CH3)3COCH3+ (1− x)C2H5OH},the fitted curve of deviations in isentropic compressibilities is sigmoidal in nature with aninitial positive region followed by a negative lobe at low alcohol mole fraction. Excessisentropic compressibilities show the same behaviour as excess molar volumes.

Negative excess molar volumes are observed when the mixture is (t-butyl methyl ether +alcohols). The magnitude and sign of excess molar volumes are a reflection of the type ofinteractions taking place in the mixture. The packing effect in the (ether + butanol) mixtureis higher than in the (ether + methanol) mixture, and the same observation was foundbetween (ether + propanol) and (ether + methanol) mixtures. However, the packing effect isgreater in the (ether + methanol) mixture compared with that in the (ether + ethanol) mixture{figures 1(a) and 1(b)}. This reverse trend seems to be attributed to the opposite effects of themolecular size and the intramolecular interaction (hydrogen bonding, or self-association) inthe four alcohols, which directly interfere in the packing effect as well as in the interactivebehaviour between ether and alcohol. The above findings lend support, using the data ofheats of mixing of those mixtures available in the literature,(12) to the proposal above As thetemperature is lowered, the packing effect in all four mixtures is also lowered, accordingto figure 1, probably due to the increase in the intramolecular interaction in the alcoholcomponent. This trend of temperature effect is also observed in the results of isentropiccompressibility, figures 3 and 4.

In table 6, values of partial excess molar volumes at infinite dilution(7) fromT = 298.15 Kto T = 288.15 K, calculated for the Redlich–Kister equation as a function of mole fraction,


for the four binary mixtures are shown. In general terms, a negative trend is observedcorresponding to the binary mixture (t-butyl methyl ether+ alcohols). These results suggestthe different packing of molecules depending on the length of the main chains.

REFERENCES

1. Letcher, T. M.; Govender, P. U.Fluid Phase Equilib.1997, 140, 207–222.2. Arce, A.; Rodil, E.; Soto, A.J. Chem. Eng. Data1997, 42, 721–7263. Redlich, O.; Kister, A. T.Ind. Eng. Chem.1948, 40, 345–348.4. Roman´ı, L.; Peleteiro, J.; Iglesias, T. P.; Carballo, E.; Escudero, R.; Legido, J. L.J. Chem. Eng.

Data1994, 39, 19–22.5. Daubert, T. E.; Danner, R. P.Data Compilation Tables of Properties of Pure Compounds.

American Institute of Chemical Engineers: New York.1984.6. Bevington, P.Data Reduction and Error Analysis for the Physical Sciences. McGraw-Hill: New

York. 1969.7. Canosa, J.; Rodr´ıguez, A.; Iglesias, M.; Orge, B.; Tojo, J.J. Chem. Eng. Data1997, 42, 1121–

1125.8. Das, A.; Frenkel, M.; Gadalla, N. M.; Marsh, K.; Wilhoit, R. C.TRC Thermodynamic Tables.

Texas Engineering Experimental Station, Texas A&M University System: College Station, TX.1994.

9. Riddick, J. A.; Bunger, W. B.; Sakano, T. K.Organic Solvents Techniques of Chemistry:4thedition, Vol. II. Wiley: New York.1986.

10. Daubert, T. E.; Danner, R. P.Physical and Thermodynamic Properties of Pure Chemicals: Datacompilation. Library of Congress Cataloging-in Publication Data: New York.1989.

11. Aminabhavi, T. M.; Aralaguppi, M. I.; Harogoppad, S. B.; Balundgi, R. H.J. Chem. Eng. Data1993, 38, 31–39.

12. Letcher, T. M.; Govender, P. U.J. Chem. Eng. Data1995, 40, 997–1000.

(Received 22 December 1998; in final form 15 February 1999)

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Physical properties of binary mixtures of (t-butyl methyl ether + alcohols) fromT = 288.15K...

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Transcript of Physical properties of binary mixtures of (t-butyl methyl ether + alcohols) fromT = 288.15K...