Article pubs.acs.org/jced
Excess Molar Volumes and Speed of Sound in Bromotrichloromethane + n‑Heptane, Dibromomethane + n‑Heptane, Bromotrichloromethane + Dibromomethane, and Bromotrichloromethane + Bromochloromethane at Temperatures from (293.15 to 313.15) K Lourdes Martínez-Baños, Clara Rivas, José Muñoz Embid, and Santos Otín* Departamento de Química Física, Facultad de Ciencias, Universidad de Zaragoza, 50009-Zaragoza, Spain ABSTRACT: Density and speed of sound of four binary mixtures bromotrichloromethane + n-heptane, dibromomethane + n-heptane, bromotrichloromethane + dibromomethane, and bromotrichloromethane + bromochloromethane were measured over the entire range of composition in the temperature range from T = 293.15 K to T = 313.15 K. Excess molar volumes and deviation in isentropic compressibility have been calculated from experimental measurements and fitted to a Redlich−Kister equation to derive binary coefficients and the standard deviation.
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INTRODUCTION This work is a part of our studies on the thermodynamics of the halogen−halogen interaction in binary liquid mixtures containing haloalkanes. The thermodynamic study of different haloalkanes and their mixtures has a theoretical and industrial interest. In this way, to correlate the structures of molecules with the thermodynamic properties of their mixtures, it is necessary to have systematic information on the behavior of substances with different specific groups. On the other hand, monohaloalkanes and different types of polyhaloalkanes represent a class of technically important compounds, used in industry as intermediates or as final products, with special applications in organic synthesis, chemistry of surfaces, manufacturing of pharmaceuticals, and so forth. From a theoretical viewpoint, systems containing mono- or poly haloalkanes are of great interest because of the variety and complexity of the intermolecular interactions present in the mixture (including dipole−dipole and specific interactions) or because of the intramolecular effects (proximity effects, etc.). Therefore the applicability of theoretical predictive methods is of great interest. In this occasion, we report molar excess volumes, VEm, and deviations in isentropic compressibility, ΔκS, obtained from density and speed of sound measurements, respectively, at five temperatures between 293.15 K and 313.15 K and atmospheric pressure, for binary systems bromotrichloromethane or dibromomethane + n-heptane and bromotrichloromethane + dibromomethane or bromochloromethane. The only previous measurements of these mixtures are those of Boquera et al. reporting densities of bromotrichloromethane + dibromomethane or bromochloromethane at 298.15 K1 and those of Przybyla and Chorazewski on densities and speeds of sound of dibromomethane + heptane within the temperature range from 288.15 K to 318.15 K.2 Our results agree satisfactorily with theirs. © 2013 American Chemical Society
EXPERIMENTAL SECTION Materials. Liquids employed in present work are included in Table 1. All of the liquids were used directly without further Table 1. Sample Information Table chemical name
source
mole fraction purity
bromotrichloromethane dibromomethane bromochloromethane n-heptane
Aldrich Chemistry Aldrich Chemistry Aldrich Chemistry Fluka AG Buchs
> 0.99 > 0.99 > 0.99 > 0.995
purification. To check the purity of the substances, their density and speed of sound values at 298.15 K were compared with literature data in Table 2. Apparatus and Procedure. The density and the speed of sound of the pure liquids and mixtures were measured at atmospheric pressure with a digital density and sound velocity analyzer Anton Paar DSA-5000 M automatically thermostatted by a built-in solid state thermostat. The instrument was calibrated using air8 and double-distilled water8,9 prepared especially for the calibration and verified using tetrachloromethane (better than 0.999 in mole fraction supplied by Fluka AG Buchs). The liquid were partially degassed to prevent the formation of gas bubbles in the densimeter capillary at higher temperatures. The samples were prepared by weighing (Sartorius BP210S Received: July 12, 2012 Accepted: December 28, 2012 Published: January 11, 2013 248
dx.doi.org/10.1021/je300775u | J. Chem. Eng. Data 2013, 58, 248−256
Journal of Chemical & Engineering Data
Article
Table 2. Density (ρ), Speed of Sound (u), and Dipole Moment ( μ) of Pure Liquids at T = 298.15 Ka 10−3·ρ/kg·m−3 component
exptl
bromotrichloromethane dibromomethane bromochloromethane n-heptane
lit.
Standard uncertainties u are u(T) = 0.001 K, u(ρ) = 2·10 Reference 7. gIn benzene. hGas.
2.012 2.4842c 1.92292d 0.67960e −2
μ/D
exptl
b
2.00214 2.47861 1.92171 0.67960
a f
c/m·s−1 lit.
0.59f,g 1.43f,h 1.66f,g
903.6 949.2 986.1 1130.9
−3
lit.
1128.5e
−1 b
c
kg·m , and u(c) = 0.5 m·s . Reference 3. Reference 4. dReference 5. eReference 6.
Table 3. Values of Density ( ρ), Speed of Sound (u), Excess Molar Volumes (VEm), and Deviation in Isentropic Compressibility (ΔκS) for the Binary Mixtures at Various Temperatures and 0.1 MPaa x1
10−3·ρ
c
106·VEm
1012·ΔκS
kg·m−3
m·s−1
m3·mol−1
Pa−1
x1
10−3·ρ
c
106·VEm
1012·ΔκS
kg·m−3
m·s−1
m3·mol−1
Pa−1
966.7 958.4 948.0 940.1 934.8 929.0 924.6 920.6 918.0 917.1
0.194 0.184 0.163 0.146 0.135 0.116 0.097 0.064 0.049 0.000
−36.80 −36.48 −35.30 −33.25 −30.90 −27.09 −22.48 −15.92 −7.97 0.00
950.6 942.8 932.8 925.2 920.0 914.5 910.4 906.7 904.4 903.6
0.185 0.173 0.153 0.137 0.125 0.108 0.091 0.060 0.047 0.000
−40.13 −40.13 −38.80 −36.48 −33.68 −29.50 −24.56 −17.45 −8.85 0.00
1.27134 1.32829 1.41254 1.48986 1.55071 1.63270 1.70838 1.80152 1.89858 1.99120
934.7 927.1 917.4 910.3 905.3 900.1 896.2 892.8 890.7 890.2
0.173 0.162 0.143 0.127 0.116 0.101 0.085 0.056 0.045 0.000
−43.89 −43.68 −42.02 −39.78 −36.66 −32.11 −26.64 −18.94 −9.51 0.00
1.26388 1.32053 1.40437 1.48130 1.54185 1.62344 1.69877 1.79147 1.88806
918.8 911.3 902.2 895.4 890.7 885.8 882.2 879.0 877.2
0.161 0.152 0.133 0.118 0.108 0.094 0.079 0.052 0.043
−48.03 −47.38 −45.94 −43.42 −40.12 −35.14 −29.27 −20.75 −10.55
0.0000 0.0527 0.1116 0.1520 0.2038 0.2512 0.2988 0.3556 0.4027 0.4603 0.4989
0.68384 0.73154 0.78688 0.82609 0.87808 0.92729 0.97853 1.04197 1.09665 1.16630 1.21482
1152.6 1126.6 1100.3 1083.8 1064.1 1047.4 1031.9 1015.0 1001.9 987.5 978.4
0.0000 0.0527 0.1116 0.1520 0.2038 0.2512 0.2988 0.3556 0.4027 0.4603 0.4989
0.67960 0.72703 0.78207 0.82109 0.87278 0.92175 0.97269 1.03581 1.09021 1.15950 1.20780
1131.0 1105.8 1080.2 1064.4 1045.2 1028.9 1013.7 997.3 984.7 970.6 962.0
Bromotrichloromethane (1) + n-Heptane (2) T = 293.15 K 0.000 0.00 0.5537 1.28616 0.042 −5.35 0.5961 1.34368 0.081 −11.33 0.6562 1.42879 0.114 −15.34 0.7088 1.50686 0.136 −20.09 0.7486 1.56829 0.162 −23.88 0.8001 1.65109 0.170 −27.44 0.8456 1.72753 0.186 −31.17 0.8990 1.82157 0.197 −33.26 0.9521 1.91955 0.200 −35.62 1.0000 2.01306 0.193 −36.32 T = 298.15 K 0.000 0.00 0.5537 1.27876 0.041 −6.08 0.5961 1.33600 0.077 −12.59 0.6562 1.42068 0.106 −17.47 0.7088 1.49838 0.131 −22.51 0.7486 1.55953 0.153 −26.48 0.8001 1.64191 0.164 −30.00 0.8456 1.71798 0.178 −34.02 0.8990 1.81156 0.187 −36.48 0.9521 1.90909 0.191 −38.69 1.0000 2.00214 0.180 −39.84
0.0000 0.0527 0.1116 0.1520 0.2038 0.2512 0.2988 0.3556 0.4027 0.4603 0.4989
0.67533 0.72250 0.77725 0.81604 0.86743 0.91616 0.96684 1.02961 1.08375 1.15266 1.20071
1109.6 1085.1 1060.4 1044.9 1026.0 1010.4 995.8 979.7 967.5 953.9 945.5
0.000 0.037 0.070 0.100 0.126 0.144 0.152 0.168 0.176 0.180 0.172
0.0000 0.0527 0.1116 0.1520 0.2038 0.2512 0.2988 0.3556 0.4027
0.67104 0.71794 0.77239 0.81096 0.86207 0.91053 0.96093 1.02338 1.07723
1088.2 1064.5 1040.5 1025.3 1007.0 992.0 977.7 962.2 950.4
0.000 0.035 0.065 0.094 0.120 0.137 0.145 0.159 0.166
T = 303.15 K 0.00 0.5537 −6.72 0.5961 −14.26 0.6562 −19.22 0.7088 −24.14 0.7486 −28.98 0.8001 −33.13 0.8456 −37.02 0.8990 −39.70 0.9521 −42.15 1.0000 −43.18 T = 308.15 K 0.00 0.5537 −7.63 0.5961 −15.87 0.6562 −20.91 0.7088 −26.41 0.7486 −31.94 0.8001 −36.10 0.8456 −40.55 0.8990 −43.44 0.9521 249
dx.doi.org/10.1021/je300775u | J. Chem. Eng. Data 2013, 58, 248−256
Journal of Chemical & Engineering Data
Article
Table 3. continued 10−3·ρ x1
kg·m
−3
106·VEm
c −1
m·s
−1
m ·mol 3
10−3·ρ
1012·ΔκS −1
x1
Pa
kg·m
−3
106·VEm
c m·s
−1
m ·mol 3
−1
1012·ΔκS Pa−1
0.4603 0.4989
1.14580 1.19357
937.2 929.2
0.170 0.163
T = 308.15 K −45.96 1.0000 −47.27
1.98024
876.8
0.000
0.00
0.0000 0.0527 0.1116 0.1520 0.2038 0.2512 0.2988 0.3556 0.4027 0.4603 0.4989
0.66671 0.71335 0.76750 0.80584 0.85667 0.90488 0.95501 1.01712 1.07068 1.13890 1.18641
1067.1 1044.0 1020.7 1005.8 988.3 973.6 959.8 944.8 933.3 920.7 912.9
0.000 0.034 0.060 0.090 0.113 0.129 0.135 0.149 0.156 0.159 0.154
T = 313.15 K 0.00 0.5537 −8.16 0.5961 −17.18 0.6562 −22.32 0.7088 −28.95 0.7486 −34.57 0.8001 −39.24 0.8456 −44.05 0.8990 −46.97 0.9521 −50.03 1.0000 −51.22
1.25637 1.31274 1.39616 1.47271 1.53296 1.61416 1.68912 1.78135 1.87749 1.96925
902.9 895.9 887.1 880.6 876.2 871.5 868.2 865.3 863.7 863.6
0.150 0.141 0.122 0.108 0.100 0.086 0.073 0.049 0.042 0.000
−52.04 −51.77 −49.98 −47.14 −43.67 −38.06 −31.76 −22.52 −11.34 0.00
969.3 959.2 953.4 948.0 944.6 942.9 943.8 947.2 953.1 961.8
0.492 0.445 0.410 0.360 0.319 0.259 0.191 0.136 0.064 0.000
−64.28 −66.95 −67.97 −67.36 −65.04 −59.87 −52.10 −40.61 −23.59 0.00
Dibromomethane (1) + n-Heptane (2) T = 293.15 K 0.00 0.5532 1.34790 −5.07 0.6119 1.45249 −12.09 0.6543 1.53418 −18.57 0.7032 1.63575 −25.07 0.7514 1.74418 −31.71 0.8024 1.86964 −38.00 0.8518 2.00309 −44.60 0.9004 2.14705 −50.57 0.9502 2.31037 −56.11 1.0000 2.49167 −59.65
0.0000 0.0504 0.1039 0.1552 0.2037 0.2532 0.3019 0.3540 0.4022 0.4552 0.4962
0.68384 0.72759 0.77680 0.82684 0.87702 0.93138 0.98809 1.05294 1.11705 1.19254 1.25487
1152.2 1128.1 1104.9 1084.0 1065.7 1048.3 1032.4 1016.7 1003.5 990.1 980.6
0.000 0.157 0.288 0.390 0.460 0.505 0.549 0.561 0.555 0.540 0.523
0.0000 0.0504 0.1039 0.1552 0.2037 0.2532 0.3019 0.3540 0.4022 0.4552 0.4962
0.67960 0.72309 0.77201 0.82177 0.87166 0.92572 0.98212 1.04661 1.11037 1.18546 1.24747
1130.9 1107.3 1084.7 1064.4 1046.5 1029.7 1014.2 999.1 986.1 973.2 964.2
0.000 0.161 0.292 0.394 0.466 0.510 0.555 0.566 0.560 0.544 0.527
T = 298.15 K 0.00 0.5532 −5.30 0.6119 −12.87 0.6543 −19.97 0.7032 −26.75 0.7514 −34.13 0.8024 −40.75 0.8518 −48.05 0.9004 −54.00 0.9502 −60.03 1.0000 −64.10
1.33998 1.44409 1.52537 1.62646 1.73439 1.85925 1.99214 2.13543 2.29808 2.47861
953.3 943.8 938.2 933.3 930.2 928.9 930.2 933.8 940.1 949.2
0.499 0.447 0.412 0.361 0.319 0.259 0.190 0.136 0.064 0.000
−68.89 −71.98 −72.83 −72.35 −69.74 −64.19 −55.87 −43.35 −25.18 0.00
0.0000 0.0504 0.1039 0.1552 0.2037 0.2532 0.3019 0.3540 0.4022 0.4552 0.4962
0.67533 0.71856 0.76719 0.81667 0.86626 0.92003 0.97609 1.04023 1.10365 1.17834 1.24003
1109.1 1086.4 1064.4 1044.8 1027.3 1010.9 995.8 981.2 968.8 956.4 947.8
0.000 0.162 0.294 0.396 0.471 0.515 0.561 0.572 0.565 0.549 0.530
T = 303.15 K 0.00 0.5532 −6.41 0.6119 −14.56 0.6543 −22.53 0.7032 −29.57 0.7514 −37.29 0.8024 −44.24 0.8518 −52.09 0.9004 −58.79 0.9502 −65.29 1.0000 −69.71
1.33206 1.43565 1.51652 1.61714 1.72455 1.84885 1.98112 2.12378 2.28574 2.46553
937.4 928.3 923.1 918.6 915.8 915.0 916.5 920.3 927.1 936.6
0.501 0.449 0.414 0.361 0.319 0.259 0.190 0.136 0.063 0.000
−74.83 −77.93 −78.88 −78.32 −75.31 −69.42 −60.15 −46.43 −27.01 0.00
0.0000 0.0504 0.1039 0.1552 0.2037
0.67104 0.71400 0.76236 0.81154 0.86084
1088.1 1065.7 1044.3 1025.2 1008.2
0.000 0.165 0.297 0.401 0.474
T = 308.15 K 0.00 0.5532 −6.29 0.6119 −15.15 0.6543 −23.64 0.7032 −31.28 0.7514
1.32408 1.42716 1.50763 1.60776 1.71466
921.4 912.9 908.0 903.9 901.5
0.506 0.452 0.416 0.362 0.320
−79.98 −83.58 −84.54 −83.98 −80.81
250
dx.doi.org/10.1021/je300775u | J. Chem. Eng. Data 2013, 58, 248−256
Journal of Chemical & Engineering Data
Article
Table 3. continued 10−3·ρ
c
106·VEm
1012·ΔκS
x1
kg·m−3
m·s−1
m3·mol−1
Pa−1
0.2532 0.3019 0.3540 0.4022 0.4552 0.4962
0.91430 0.97004 1.03382 1.09688 1.17115 1.23254
992.3 977.6 963.5 951.5 939.6 931.2
0.0000 0.0504 0.1039 0.1552 0.2037 0.2532 0.3019 0.3540 0.4022 0.4552 0.4962
0.66671 0.70941 0.75748 0.80636 0.85537 0.90853 0.96395 1.02738 1.09009 1.16395 1.22500
1066.9 1045.1 1024.3 1005.6 989.0 973.7 959.6 946.0 934.5 923.0 914.8
0.0000 0.0506 0.0993 0.1491 0.1991 0.2473 0.2986 0.3465 0.3979 0.4468 0.4967
2.49167 2.45557 2.42417 2.39298 2.36317 2.33559 2.30734 2.28189 2.25564 2.23141 2.20774
961.8 957.0 953.0 948.9 945.3 942.1 939.1 936.3 933.6 931.3 929.1
0.0000 0.0506 0.0993 0.1491 0.1991 0.2473 0.2986 0.3465 0.3979 0.4468 0.4967
2.47861 2.44267 2.41140 2.38034 2.35066 2.32321 2.29508 2.26975 2.24364 2.21949 2.19591
949.2 944.4 940.3 936.2 932.6 929.3 926.2 923.3 920.7 918.3 916.1
0.0000 0.0506 0.0993 0.1491 0.1991 0.2473 0.2986 0.3465 0.3979 0.4468 0.4967
2.46553 2.42969 2.39859 2.36761 2.33813 2.31080 2.28277 2.25758 2.23157 2.20752 2.18402
936.6 931.7 927.6 923.4 919.8 916.5 913.2 910.5 907.7 905.3 903.1
0.0000 0.0506
2.45242 2.41674
924.0 919.1
x1
10−3·ρ
c
106·VEm
1012·ΔκS
kg·m−3
m·s−1
m3·mol−1
Pa−1
901.1 902.9 907.1 914.1 924.0
0.258 0.189 0.131 0.063 0.000
−74.51 −64.47 −49.85 −28.83 0.00
905.5 897.5 893.0 889.2 887.2 887.0 889.3 893.8 901.1 911.4
0.509 0.455 0.418 0.364 0.321 0.259 0.189 0.134 0.062 0.000
−86.14 −90.03 −91.17 −90.39 −87.02 −79.92 −69.31 −53.48 −30.87 0.00
927.2 925.3 923.7 922.4 921.0 919.9 918.8 918.0 917.4 917.1
0.195 0.192 0.190 0.183 0.165 0.146 0.133 0.117 0.078 0.000
−0.28 0.03 0.25 0.38 0.60 0.71 0.91 0.97 0.76 0.00
914.1 912.2 910.6 909.2 907.7 906.6 905.5 904.6 904.0 903.6
0.197 0.193 0.190 0.183 0.165 0.148 0.134 0.118 0.082 0.000
−0.41 −0.15 0.03 0.25 0.57 0.64 0.81 0.96 0.72 0.00
901.1 899.1 897.4 896.0 894.5 893.4 892.2 891.3 890.6 890.2
0.199 0.200 0.192 0.185 0.167 0.150 0.135 0.118 0.079 0.000
−0.60 −0.20 0.03 0.23 0.51 0.56 0.82 0.94 0.77 0.00
888.0 886.1
0.201 0.196
−0.67 −0.51
T = 308.15 K −39.63 0.8024 1.83840 −46.99 0.8518 1.97007 −55.50 0.9004 2.11221 −62.64 0.9502 2.27336 −69.72 1.0000 2.45242 −74.21 T = 313.15 K 0.000 0.00 0.5532 1.31609 0.169 −6.87 0.6119 1.41862 0.300 −16.47 0.6543 1.49869 0.407 −25.29 0.7032 1.59832 0.482 −33.31 0.7514 1.70472 0.526 −42.61 0.8024 1.82787 0.573 −50.87 0.8518 1.95896 0.582 −60.08 0.9004 2.10038 0.577 −67.92 0.9502 2.26095 0.561 −75.37 1.0000 2.43926 0.541 −79.88 Bromotrichloromethane (1) + Dibromomethane (2) T = 293.15 K 0.000 0.00 0.5462 2.18538 0.076 −0.17 0.5975 2.16289 0.091 −0.76 0.6479 2.14149 0.117 −0.83 0.6947 2.12235 0.133 −1.03 0.7469 2.10190 0.145 −1.12 0.7959 2.08333 0.158 −1.27 0.8494 2.06355 0.171 −1.07 0.8980 2.04620 0.181 −0.88 0.9469 2.02971 0.195 −0.67 1.0000 2.01306 0.202 −0.40 T = 298.15 K 0.000 0.00 0.5462 2.17366 0.076 −0.25 0.5975 2.15129 0.092 −0.85 0.6479 2.13001 0.118 −0.99 0.6947 2.11096 0.134 −1.26 0.7469 2.09059 0.147 −1.32 0.7959 2.07208 0.159 −1.42 0.8494 2.05239 0.172 −1.16 0.8980 2.03513 0.181 −1.13 0.9469 2.01865 0.197 −0.84 1.0000 2.00214 0.204 −0.61 T = 303.15 K 0.000 0.00 0.5462 2.16190 0.078 −0.23 0.5975 2.13950 0.093 −0.92 0.6479 2.11846 0.121 −1.01 0.6947 2.09949 0.135 −1.37 0.7469 2.07921 0.148 −1.48 0.7959 2.06079 0.161 −1.41 0.8494 2.04121 0.173 −1.43 0.8980 2.02404 0.183 −1.21 0.9469 2.00769 0.199 −0.95 1.0000 1.99120 0.207 −0.75 T = 308.15 K 0.000 0.00 0.5462 2.15012 0.078 −0.32 0.5975 2.12800 0.520 0.567 0.577 0.572 0.556 0.535
251
dx.doi.org/10.1021/je300775u | J. Chem. Eng. Data 2013, 58, 248−256
Journal of Chemical & Engineering Data
Article
Table 3. continued 10−3·ρ
c
106·VEm
1012·ΔκS
x1
kg·m−3
m·s−1
m3·mol−1
Pa−1
0.0993 0.1491 0.1991 0.2473 0.2986 0.3465 0.3979 0.4468 0.4967
2.38575 2.35494 2.32548 2.29833 2.27045 2.24537 2.21948 2.19550 2.17216
914.8 910.7 907.1 903.7 900.4 897.6 894.8 892.4 890.1
0.094 0.121 0.139 0.150 0.163 0.175 0.185 0.202 0.209
0.0000 0.0506 0.0993 0.1491 0.1991 0.2473 0.2986 0.3465 0.3979 0.4468 0.4967
2.43926 2.40373 2.37287 2.34221 2.31293 2.28584 2.25808 2.23311 2.20734 2.18350 2.16025
911.4 906.4 902.2 898.1 894.4 891.0 887.7 884.8 882.0 879.5 877.1
0.000 0.079 0.095 0.122 0.139 0.152 0.165 0.177 0.187 0.204 0.211
x1
T = 308.15 K −0.89 0.6479 −1.17 0.6947 −1.58 0.7469 −1.66 0.7959 −1.65 0.8494 −1.60 0.8980 −1.43 0.9469 −1.20 1.0000 −0.92 T = 313.15 K 0.00 0.5462 −0.28 0.5975 −1.04 0.6479 −1.39 0.6947 −1.77 0.7469 −1.88 0.7959 −1.91 0.8494 −1.77 0.8980 −1.64 0.9469 −1.31 1.0000 −0.92
10−3·ρ
c
106·VEm
1012·ΔκS
kg·m−3
m·s−1
m3·mol−1
Pa−1
2.10690 2.08796 2.06783 2.04947 2.03002 2.01293 1.99665 1.98024
884.4 882.8 881.4 880.2 879.0 878.1 877.3 876.8
0.193 0.189 0.169 0.152 0.136 0.118 0.080 0.000
−0.25 0.21 0.31 0.46 0.68 0.76 0.70 0.00
2.13831 2.11630 2.09525 2.07647 2.05641 2.03817 2.01879 2.00178 1.98557 1.96925
875.1 873.1 871.4 869.9 868.4 867.1 865.9 865.0 864.1 863.6
0.204 0.197 0.197 0.189 0.170 0.152 0.136 0.119 0.081 0.000
−0.83 −0.54 −0.31 −0.03 0.19 0.45 0.66 0.71 0.77 0.00
938.2 935.8 932.3 929.6 926.9 924.5 922.3 920.3 919.8 917.1
0.202 0.198 0.191 0.181 0.167 0.158 0.125 0.099 0.078 0.000
8.37 8.07 7.71 7.04 6.35 5.59 4.50 3.41 2.28 0.00
1.96989 1.97267 1.97674 1.98021 1.98388 1.98720 1.99096 1.99438 1.99617 2.00214
924.2 921.9 918.5 915.8 913.2 910.8 908.7 906.8 906.3 903.6
0.205 0.201 0.192 0.185 0.169 0.160 0.126 0.100 0.080 0.000
8.81 8.43 8.00 7.39 6.60 5.87 4.66 3.45 2.30 0.00
1.95874 1.96152 1.96563 1.96915 1.97283 1.97620 1.97993 1.98339 1.98515 1.99120
910.3 908.0 904.7 902.0 899.5 897.2 895.1 893.3 892.9 890.2
0.206 0.203 0.194 0.186 0.171 0.159 0.128 0.102 0.082 0.000
9.23 8.91 8.42 7.85 6.98 6.14 4.96 3.63 2.32 0.00
Bromotrichloromethane (1) + Bromochloromethane (2) T = 293.15 K 0.000 0.00 0.5665 1.98104 0.035 1.85 0.6027 1.98379 0.071 3.49 0.6567 1.98781 0.101 4.67 0.7046 1.99131 0.130 5.76 0.7543 1.99491 0.151 6.71 0.8025 1.99820 0.171 7.45 0.8516 2.00194 0.179 7.47 0.8996 2.00535 0.192 8.46 0.9228 2.00714 0.200 8.51 1.0000 2.01306 0.202 8.49
0.0000 0.0520 0.1030 0.1538 0.2031 0.2551 0.3050 0.3522 0.4063 0.4553 0.5058
1.93323 1.93820 1.94279 1.94734 1.95155 1.95605 1.96019 1.96398 1.96854 1.97241 1.97640
1001.2 992.8 985.2 978.4 972.2 966.1 960.7 956.4 950.8 946.7 942.7
0.0000 0.0520 0.1030 0.1538 0.2031 0.2551 0.3050 0.3522 0.4063 0.4553 0.5058
1.92171 1.92672 1.93134 1.93588 1.94016 1.94471 1.94882 1.95266 1.95730 1.96120 1.96521
986.1 977.9 970.4 963.6 957.5 951.6 946.3 942.1 936.7 932.6 928.6
0.000 0.036 0.073 0.105 0.133 0.153 0.176 0.193 0.195 0.203 0.205
T = 298.15 K 0.00 0.5665 1.88 0.6027 3.64 0.6567 5.03 0.7046 6.17 0.7543 7.06 0.8025 7.84 0.8516 7.83 0.8996 8.73 0.9228 8.88 1.0000 8.95
0.0000 0.0520 0.1030 0.1538 0.2031 0.2551 0.3050 0.3522 0.4063 0.4553
1.91015 1.91519 1.91985 1.92446 1.92876 1.93331 1.93749 1.94128 1.94602 1.94996
971.0 962.9 955.5 948.9 942.8 937.0 931.8 927.8 922.4 918.4
0.000 0.037 0.074 0.105 0.134 0.156 0.178 0.198 0.198 0.206
T = 303.15 K 0.00 0.5665 2.04 0.6027 3.93 0.6567 5.29 0.7046 6.64 0.7543 7.60 0.8025 8.42 0.8516 8.29 0.8996 9.35 0.9228 9.48 1.0000 252
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Table 3. continued 10−3·ρ
c
106·VEm
1012·ΔκS
x1
kg·m−3
m·s−1
m3·mol−1
Pa−1
0.5058
1.95400
914.5
0.207
0.0000 0.0520 0.1030 0.1538 0.2031 0.2551 0.3050 0.3522 0.4063 0.4553 0.5058
1.89851 1.90360 1.90830 1.91293 1.91727 1.92186 1.92618 1.92999 1.93468 1.93865 1.94275
955.9 947.9 940.7 934.2 928.1 922.6 917.3 913.5 908.2 904.2 900.5
0.000 0.037 0.075 0.107 0.137 0.159 0.177 0.198 0.201 0.210 0.211
0.0000 0.0520 0.1030 0.1538 0.2031 0.2551 0.3050 0.3522 0.4063 0.4553 0.5058
1.88682 1.89194 1.89667 1.90144 1.90574 1.91036 1.91472 1.91858 1.92330 1.92729 1.93142
940.8 933.0 925.9 919.1 913.6 908.1 903.0 898.9 894.0 890.3 886.5
0.000 0.038 0.077 0.106 0.139 0.162 0.180 0.201 0.205 0.214 0.215
x1
T = 303.15 K 9.53 T = 308.15 K 0.00 0.5665 2.21 0.6027 4.12 0.6567 5.59 0.7046 7.16 0.7543 7.92 0.8025 9.02 0.8516 8.74 0.8996 9.88 0.9228 10.14 1.0000 10.02 T = 313.15 K 0.00 0.5665 2.29 0.6027 4.37 0.6567 6.49 0.7046 7.53 0.7543 8.51 0.8025 9.54 0.8516 9.82 0.8996 10.61 0.9228 10.58 1.0000 10.73
10−3·ρ
c
106·VEm
1012·ΔκS
kg·m−3
m·s−1
m3·mol−1
Pa−1
1.94752 1.95031 1.95445 1.95812 1.96175 1.96514 1.96892 1.97242 1.97422 1.98024
896.4 894.1 891.0 888.3 885.9 883.7 881.6 879.9 879.4 876.8
0.210 0.207 0.198 0.184 0.172 0.161 0.128 0.101 0.080 0.000
9.69 9.43 8.73 8.19 7.23 6.29 5.13 3.64 2.45 0.00
1.93626 1.93910 1.94326 1.94695 1.95061 1.95405 1.95785 1.96138 1.96319 1.96925
882.6 880.3 877.2 874.7 872.3 870.2 868.3 866.5 865.9 863.6
0.213 0.209 0.201 0.187 0.175 0.162 0.130 0.102 0.081 0.000
10.23 10.03 9.43 8.66 7.77 6.71 5.28 3.96 2.90 0.00
x1 is the mole fraction of component 1. Standard uncertainties u are u(T) = 0.001 K, u(x1) = 1·10−4, u(ρ) = 2·10−2 kg·m−3, u(c) = 0.5 m·s−1, and the combined expanded uncertainties Uc are Uc(VEm) = 2·10−9 m3·mol−1, Uc(ΔκS) = 5·10−14 Pa−1 (level of confidence = 0.95). a
κS1 and κS2 are the isentropic compressibility of the pure components and ϕi (i = 1, 2) are the volume fraction of pure components calculated from the individual pure molar volumes Vi, using the equation
balance). Attention was paid to changes in the composition of the samples during weighing. To diminish this effect, the used vessels are a negligibly small vapor space.
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RESULTS Table 3 list the measured density ρ, and speed of sound c, together with the calculated excess molar volume VEm, and deviation in isentropic compressibility ΔκS for binary mixtures bromotrichloromethane + n-heptane, dibromomethane + n-heptane, bromotrichloromethane + dibromomethane, and bromotrichloromethane + bromochloromethane at T = (293.15, 298.15, 303.15, 308.15, and 313.15) K along with the mole fraction. The excess molar volumes VEm have been calculated from density using
ϕi = xiVi /(∑ xiVi )
The excess molar volumes, VEm, and the deviations in isentropic compressibility, ΔκS, data were fitted by the method of nonlinear least-squares to the Redlich−Kister type polynomial equation10 Q = x1x 2 ∑ Ai (x1 − x 2)i
(1)
σ(Q ) = [∑(Q obs − Q cal)2 /(N − k)]1/2
where ρ is the density of the mixture and x1, M1, ρ1, and x2, M2, ρ2 are the mole fraction, molar mass, and density of pure components. Subscript 1 refers to the first component of the binary, and subscript 2 to the respective second component. The deviations in isentropic compressibility ΔκS have been calculated using the equation 1012 ·ΔκS /(Pa−1) = κS − (ϕ1κS1 + ϕ2κS 2)
(6)
where N is the number of experimental data points and k is the number of the fitting coefficients of the Redlich−Kister polynomial. The coefficients Ai and standard deviations σ(Q) of the fit are listed in Table 4.
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DISCUSSION Excess molar volumes VEm of the studied systems (Figure 1) are positive and increase with increasing temperature in the interval studied (298.15 K to 313.15 K) except for bromotrichloromethane + n-heptane.
(2)
where κS is the observed isentropic compressibility of the liquid mixture calculated by using the relation kS = c −2ρ−1
(5)
where Ai are adjustable binary coefficients. For each system the optimum number of coefficients is determined from the examination of the variation of standard deviation (σ) calculated by
106 ·V E m/(m 3·mol−1) = (x1M1 + x 2M 2)/ρ − (x1M1/ρ1 + x 2M 2 /ρ2 )
(4)
(3) 253
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Table 4. Parameters Ai of eq 5 and Standard Deviations σ function 106· VEm/m3·mol−1
1012·ΔκS/Pa−1
106·VEm/m3·mol−1
1012·ΔκS/Pa−1
106·VEm/m3·mol−1
1012·ΔκS/Pa−1
106·VEm/m3·mol−1
1012·ΔκS/Pa−1
T/K 293.15 298.15 303.15 308.15 313.15 293.15 298.15 303.15 308.15 313.15 293.15 298.15 303.15 308.15 313.15 293.15 298.15 303.15 308.15 313.15 293.15 298.15 303.15 308.15 313.15 293.15 298.15 303.15 308.15 313.15 293.15 298.15 303.15 308.15 313.15 293.15 298.15 303.15 308.15 313.15
A0
A1
A2
Bromotrichloromethane (1) + n-Heptane (2) 0.7891 −0.1766 −0.1440 0.7482 −0.1875 −0.1618 0.7035 −0.1965 −0.1514 0.6630 −0.2091 −0.1550 0.6201 −0.2129 −0.1850 −145.60 −37.302 0.620 −159.07 −39.141 −3.741 −173.21 −41.561 −4.670 −189.01 −44.966 −7.496 −205.38 −49.326 −7.531 Dibromomethane (1) + n-Heptane (2) 2.0883 −1.0494 0.521 2.1069 −1.0695 0.495 2.1218 −1.1027 0.491 2.1454 −1.1252 0.445 2.1616 −1.1506 0.459 −239.98 −167.35 −72.90 −257.44 −179.53 −77.07 −279.38 −194.88 −84.88 −298.63 −211.18 −89.13 −322.39 −226.25 −92.36 Bromotrichloromethane (1) + Dibromomethane (2) 0.7973 0.1132 −0.241 0.8036 0.1027 −0.272 0.8164 0.1238 −0.285 0.8200 0.1129 −0.240 0.8289 0.1143 −0.258 −2.2010 9.8278 4.774 −2.8235 10.2392 4.242 −3.3066 10.5678 4.665 −4.0668 10.8439 4.151 −4.5485 11.6411 3.371 Bromotrichloromethane (1) + Bromochloromethane (2) 0.8055 0.0625 0.185 0.8224 0.0302 0.188 0.8329 0.0131 0.188 0.8446 0.0226 0.172 0.8592 0.0166 0.165 33.960 −0.7568 3.771 35.505 −1.0974 3.987 37.757 −1.8966 3.748 39.792 −3.0890 3.123 42.384 −3.6836 5.214
σ
A3
A4
0.209 0.225 0.258 0.281 0.278
0.31 0.34 0.30 0.29 0.36
0.0055 0.0051 0.0052 0.0050 0.0052 0.2 0.2 0.2 0.2 0.2
0.052 0.033 0.058 0.042 0.034 −54.93 −58.86 −49.92 −55.90 −60.38
−0.31 −0.26 −0.27 −0.24 −0.22
0.0045 0.0051 0.0055 0.0054 0.0056 0.3 0.3 0.3 0.3 0.3
−0.037 −0.005 −0.072 −0.049 −0.053
1.31 1.39 1.40 1.35 1.37
0.0055 0.0055 0.0054 0.0058 0.0058 0.1 0.1 0.1 0.1 0.2
0.210 0.266 0.306 0.262 0.272
0.0027 0.0030 0.0030 0.0029 0.0029 0.1 0.2 0.2 0.2 0.1
contribution of the configurational effects coming from the special geometry of the haloalkane. In Table 2 we present the dipole moment values of the haloalkanes. The values shown explain that the VEm for the equimolar mixtures of the mentioned systems decrease with decreasing difference of dipole moments of the components of the mixtures. In this respect, excess molar enthalpies HEm of these mixtures,12 where the most important contribution is the interactional, follow the same order. However one has to bear in mind that there will be also a contribution to the excess volume arising from the different geometry of the components of the mixtures, more significant in the haloalkane + n-heptane mixtures, the “solvent” molecule nheptane being linear and the other component, the haloalkane, with certain spherical symmetry.
It is well-known that it is difficult to interpret excess volume in liquid mixtures in terms of molecular interactions since it is the result of at least two contributions: a first one due to breaking and formation of molecular interactions in pure components and in the mixture, respectively, and another one coming from geometrical and configuration effects (“free volume”). Both in the systems studied here as in two others related, found in the literature, bromochloromethane + n-heptane11 or + dibromomethane,1 the most important contribution to the excess volume will be coming from the break of dipole−dipole interactions between the haloalkane molecules. The temperature coefficients of VEm could be explained in terms of the decreasing strength of dipolar interactions in haloalkanes with increasing temperature and, in the case of bromotrichloromethane + n-heptane, the 254
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compressibility in both haloalkane + n-heptane systems studied is similar but of opposite sign to the excess molar volume. The greatest deviation of the isentropic compressibility of the mixtures from the values arising from volume fraction mixture law is for the dibromomethane + n-heptane system (nearly double that of bromotrichloromethane + n-heptane), which has a negative temperature coefficient. In principle this behavior could be explained as due to the decrease in the polarity of the mixture with respect to the pure haloalkane, but it is not clear in the case of the haloalkane + haloalkane studied mixtures, since ΔκS is positive for bromotrichloromethane + bromochloromethane and shows S-shaped curves in the case of bromotrichloromethane + dibromomethane, with a negative temperature coefficient for ΔκS. Experimental studies on HEm of binary mixtures containing different monohaloalkanes carried out previously in our laboratory13−15 led to the conclusion that the strength of the interaction between two different halogen atoms follows the sequence: I−F > I−Cl > Br−F, and that the weakest interactions are those between atom couples of halogen next to each other in the periodic table, that is I−Br, Br−Cl, and Cl−F. From previous values of VEm, HEm, and GEm some conclusions can be drawn when the two halogen atoms are on the same molecule: (a) Increasing the number of chlorine substituents produces a decrease in the mentioned excess properties of mixture with nalkane in the sequence: + CH2Cl2 > + CHCl3 > + CCl4. It can be explained as a consequence of the decrease in the dipole moment of the halogenated compound. (b) Excess property values for HEm and GEm in polybromoalkanes containing mixtures are bigger than the corresponding mixtures with polychloralkanes. However, it is not the case of VEm, for which property values are slightly lower, that showing that the “free volume effect” is not the same but different. (c) Changing a bromine atom for a chlorine atom in the same molecule (from bromochloromethane and bromotrichloromethane to dibromomethane and tetrachloromethane) does not have a very remarkable effect in the excess properties, then showing, as has been explained above, that in dihaloalkanes molecules weaker interactions are those between halogen-atom pairs contiguous in the periodic table, Br−Cl in our case.
Figure 1. Excess molar volumes VEm plotted against mole fraction x1 of ●, bromotrichloromethane (1) + n-heptane (2); ■, dibromomethane (1) + n-heptane (2); ▲, bromotrichloromethane (1) + dibromomethane (2); ◆, bromotrichloromethane (1) + bromochloromethane (2) at 298.15 K.
■
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Funding
The authors gratefully acknowledge financial support received from the Spanish MICINN-FEDER (Project CTQ2008-02037) and Gobierno de Aragón (RYM052/09). Figure 2. Deviation in isentropic compressibility ΔκS plotted against mole fraction x1 of ●, bromotrichloromethane (1) + n-heptane (2); ■, dibromomethane (1) + n-heptane (2); ▲, bromotrichloromethane (1) + dibromomethane (2); ◆, bromotrichloromethane (1) + bromochloromethane (2) at 298.15 K.
Notes
The authors declare no competing financial interest.
■
REFERENCES
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On the other hand, deviations of the isentropic compressibilities, ΔκS, are negative for both haloalkane + n-heptane systems (Figure 2) and show negative temperature coefficients. For bromotrichloromethane + dibromomethane the deviations of isentropic compressibilities, ΔκS, showed S-shaped curves (Figure 2) with negative temperature coefficients. Finally, ΔκS values are positive for bromotrichloromethane + bromochloromethane (Figure 2) with positive temperature coefficients. The behavior of isentropic 255
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