J. Chem. Eng. Data 2005, 50, 1095-1098
1095
Temperature Dependence of the Speed of Sound, Densities, and Isentropic Compressibilities of Hexane + Hexadecane in the Range of (293.15 to 373.15) K Mikhail F. Bolotnikov,* Yurij A. Neruchev, Yurij F. Melikhov, Vyacheslav N. Verveyko, and Marina V. Verveyko Department of General Physics, Laboratory of Molecular Acoustics, Kursk State University, Kursk, Radishcheva 33, Russia
The speed of sound u and density F for the binary mixture hexane + hexadecane has been measured as a function of composition and temperature along the saturation line between 293.15 K and 373.15 K. The speed of sound was measured by a pulse-phase echo ultrasonic device at a frequency of (1 to 5) MHz with an uncertainty of (0.1%. The density was measured by an Ostwald-Sprengel-type pycnometer with an uncertainty of (3 × 10-5 g‚cm-3. The experimental results were used to calculate deviations of the speed of sound ∆u, excess molar volume VE, and isentropic compressibility kS. The values ∆u and VE were fitted by the Redlich-Kister equation.
Introduction Experimental data of n-alkane binary liquid mixtures at room temperatures are widely covered in the literature.1-3 However, information about the composition and temperature dependence of the thermophysical properties of n-alkane binary liquid systems is rather limited. The aim of the present work is to report data for the speed of sound u and density F for the binary mixture of hexane + hexadecane over the whole range of composition, at the saturation line, and in the temperature range of (293.15 to 373.15) K. In this work, we report the calculated values of isentropic compressibilities kS, excess molar volumes VE, and changes in the speed of sound for these mixtures. The excess molar volumes were compared with those measured by Marsh et al.4 at 313. 15 K and Dymond et al.5 at 298.15 K. This paper is part of a program in our laboratory of molecular acoustics aimed at providing reliable acoustic data of binary liquid mixtures. Experimental Section Materials. Hexane and hexadecane (mole fraction >0.99) were supplied from Sigma-Aldrich Ltd. All chemicals were partially degassed and dried over Fluka 0.4 nm molecular sieves. The purity of the products was checked by gas chromatography (GC). The mole fractions of hexane and hexadecane were 99.7% and 99.5%, respectively. The mixtures were prepared by mass with a precision of (5 × 10-5 g. The uncertainty in the mole fraction is less than 1 × 10-4. All molar quantities are based on the IUPAC relative atomic mass table (IUPAC, 1986).6 Measurements. The ultrasonic speed was measured along the saturation line with our pulse-phase echo ultrasonic device, with a precision of (1 m‚s-1. The details of the method and technique used to determine the speed of sound have been described previously.7 The speed of sound was measured at a frequency of (1 to 5) MHz. Dispersion was not observed. The speed-of-sound measuring cell was * To whom correspondence should be addressed. E-mail: bolotnikov@ mail.ru.
Table 1. Comparison of Experimental Densities G and Speed of Sound u with Literature Data for Pure Liquids at Different Temperatures F/kg‚m-3 liquid
u/m‚s-1
T/K
this work
lit
this work
lit
293.15 298.15
659.44 654.93
1098 1076
1099.816 1078.117 1085.688
303.15
650.36
659.409 654.8910 654.811 654.9812 655.0813 650.211
1054
1052.217 1054.616
308.15 323.15
645.74 631.61
1032 966
333.15
621.95
hexadecane 298.15
769.97
303.15 323.15 333.15
766.55 752.79 745.86
348.15 373.15
735.42 717.88
645.8613 631.511 631.8213 621.914 621.811 769.9415 770.25 770.011 766.511 753.05 745.911 746.115 735.85 717.911 718.65
hexane
1338
971.428 964.716 920.717 920.616 1339.228
1319 1247 1211
1320.017 1248.118 1211.417
1159 1073
1160.598 1076.217 1074.998
921
thermostated with a temperature stability of (0.01 K. The temperature was measured with a platinum resistance thermometer with an uncertainty of (0.01 K. Densities were measured with an Ostwald-Sprengel-type pycnometer, with a capacity of approximately 50 cm3. The uncertainty in the density measurements was estimated to be (3 × 10-5 g‚cm-3. Experimental values of the density and speed of sound for hexane and hexadecane were compared with those found in the literature, and they were found to be in fairly good agreement (with the exception of speedof-sound data for hexane presented in ref 8), as shown in Table 1. The experimental results of the speed of sound u and density F in the liquid phase for hexane and hexadecane are listed in Table 2. The values of the speed of sound from (293.15 to 373.15) K and density from (293.15 to
10.1021/je050060q CCC: $30.25 © 2005 American Chemical Society Published on Web 04/14/2005
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Journal of Chemical and Engineering Data, Vol. 50, No. 3, 2005
Table 2. Speed of Sound u and Density G of Hexane and Hexadecane from (293.15 to 373.15) K T/K
u/m‚s-1
F/kg‚m-3
u/m‚s-1
293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15
1098 1076 1054 1032 1010 988 966 944 921
Hexane 659.44 338.15 654.93 343.15 650.36 348.15 645.74 353.15 641.08 358.15 636.37 363.15 631.61 368.15 626.81 373.15 621.95
900 878 856 834 812 790 768 747
293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15
1357 1338 1312 1301 1283 1265 1246 1228 1211
Hexadecane 773.38 338.15 769.97 343.15 766.55 348.15 763.12 353.15 759.68 358.15 756.24 363.15 752.79 368.15 749.33 373.15 745.86
1193 1176 1158 1141 1124 1107 1090 1074
T/K
F/kg‚m-3
742.39 738.91 735.42 731.93 728.43 724.92 721.4 717.88
x1
293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 368.15 373.15
0.1 1341 1322 1304 1285 1266 1248 1230 1211 1193 1176 1158 1140 1123 1106 1088 1072 1055
0.2 1327 1308 1289 1270 1251 1232 1214 1196 1177 1160 1142 1124 1106 1089 1071 1054 1037
0.3 1314 1295 1275 1256 1237 1219 1200 1182 1163 1145 1127 1109 1092 1074 1057 1039 1022
0.4
0.5
u/m‚s-1 1297 1277 1277 1257 1258 1237 1238 1217 1219 1198 1200 1178 1181 1159 1163 1140 1144 1122 1126 1103 1108 1084 1089 1066 1072 1048 1054 1030 1036 1012 1019 995 1002 977
Table 5 along with the standard deviation σ defined by
[{∑ n
σ)
(uobsd - ucalcd)2
i)1
Table 3. Speed of Sound u of Hexane (1) + Hexadecane (2) from (293.15 to 373.15) K T/K
Figure 1. Deviation of the speed of sound u for hexane (1) + hexadecane (2) for the data of Ye at al.18 from eq 1: +, x1 ) 0.2; 0, x1 ) 0.4; O, x1 ) 0.6; 4, x1 ) 0.8.
0.6
0.7
0.8
0.9
1254 1234 1215 1195 1175 1156 1136 1117 1098 1079 1060 1042 1023 1005 986 968 950
1228 1207 1187 1167 1146 1126 1107 1087 1067 1048 1029 1010 991 972 953 935 916
1196 1175 1154 1133 1112 1091 1071 1050 1030 1010 990 971 951 932 912 893 874
1151 1129 1108 1086 1065 1044 1023 1002 981 960 939 918 898 877 857 837 816
333.15) K of the binary mixture hexane (1) + hexadecane (2) are given in Tables 3 and 4, respectively. Results and Discussion The speed of sound, u, values are fitted by the method of least squares using the polynomial
u ) A0 + A1T + A2T2
}]
(2)
where uobsd and ucalcd are the observed and calculated quantities as defined earlier, n is the total number of experimental points, and p is the number of parameters. We have compared our results for the speed of sound of the researched mixture at 298.35 K, 313.15 K, 323.15 K, and 333.15 K with the data reported by Ye et al.18 As shown in Figure 1, it was found that their results at 298.35 K typically deviated by 0.5 m‚s-1 from the values calculated with eq 1 with the exception of the value -12.3 m‚s-1 at x1 ) 0.2. By analogy to the data at 298.35 K, a typically deviation of the data of Ye at al. from eq 1 is 1 m‚s-1, except for the value -8 m‚s-1 at x1 ) 0.2. However, an increase of the temperature difference between our data and the data of Ye et al. increases significantly. The excess molar volume VE and deviations in the speed of sound ∆u of the mixtures have been calculated using the following equations
VE ) V - (x1V1 + x2V2)
(3)
∆u ) u - (x1u1 + x2u2)
(4)
where x1 and x2 are the mole fractions; u1, u2, and u are the speeds of sound of pure components and mixture; and V1, V2, and V are the molar volumes of the pure components and mixture, respectively. The molar volume V is defined by the relation
(1)
Here, T is the absolute temperature and A0, A1, and A2 are adjustable parameters. The parameters are presented in
n-p
1/2
V)
x1M1 + x2M2 F
where M1 and M2 are the molar masses of the pure
Table 4. Density G of Hexane (1) + Hexadecane (2) from (293.15 to 333.15) K x1 T/K 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15
0.1 768.10 764.70 761.25 757.78 754.31 750.84 747.36 743.88 740.37
0.2 762.36 758.88 755.40 751.90 748.41 744.91 741.40 737.89 734.36
0.3 756.02 752.56 749.09 745.61 741.92 738.42 734.92 731.41 727.88
0.4
0.5
F/kg‚m-3 748.67 740.14 745.03 736.52 741.49 732.90 737.93 729.25 734.37 725.59 730.80 721.92 727.21 718.23 723.62 714.52 720.01 710.80
0.6
0.7
0.8
0.9
729.79 726.08 722.32 718.63 714.88 711.12 707.34 703.55 699.74
717.46 713.68 709.86 706.03 702.18 698.30 694.38 690.44 686.47
702.30 698.40 694.47 690.50 686.49 682.45 678.36 674.25 670.09
683.23 679.04 674.80 670.53 666.22 661.87 657.47 653.04 648.56
Journal of Chemical and Engineering Data, Vol. 50, No. 3, 2005 1097 Table 5. Values of the Parameters of Equation 1 and Standard Deviation for Hexane (1) + Hexadecane (2) from (293.15 to 373.15) K x1
A1
A2
A3
σ/m‚s-1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
2660.3 2698.5 2695.2 2718.2 2718.4 2749.8 2665.1 2706.8 2700.4 2575.8 2437.9
-5.1612 -5.4528 -5.4943 -5.6897 -5.7649 -6.0346 -5.6053 -5.9471 -6.0088 -5.3921 -4.7075
2.435 × 10-3 2.8065 × 10-3 2.8168 × 10-3 3.0671 × 10-3 3.1187 × 10-3 3.4422 × 10-3 2.7049 × 10-3 3.0789 × 10-3 2.9886 × 10-3 1.8132 × 10-3 4.6904 × 10-3
0.08 0.23 0.17 0.09 0.22 0.09 0.23 0.20 0.11 0.37 0.43
Figure 2. Excess molar volumes VE for hexane (1) + hexadecane (2) at 313.15 K: b, this work; 4, ref 4.
Table 6. Values of ∆u for the Binary Mixture Hexane (1) + Hexadecane (2) from (293.15 to 373.15) K x1 T/K 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 368.15 373.15
0.1 11 11 11 11 11 11 11 11 11 12 12 12 12 13 13 14 14
0.2 22 22 22 22 23 23 23 24 24 25 25 26 26 27 28 29 29
0.3 35 35 35 36 36 37 38 38 39 40 41 41 42 43 44 46 47
0.4
0.5
0.6
0.7
0.8
0.9
∆u/m‚s-1 43 49 44 50 44 50 45 51 45 51 46 52 47 53 48 54 49 55 50 56 51 58 52 59 53 60 55 62 56 64 57 65 59 67
53 53 54 55 56 57 58 59 61 62 63 65 66 68 69 71 73
52 53 53 54 55 56 57 58 59 60 62 63 64 66 68 70 72
46 46 46 47 47 48 49 50 51 52 53 54 56 57 59 61 62
27 27 27 28 28 29 29 29 30 31 32 32 33 34 35 36 37
Figure 3. Excess molar volumes VE for hexane (1) + hexadecane (2): 4, 298.15 K (this work); 0, 323.15 K (this work); 2, 298.15 K (ref 5); ×, 323.15 (ref 5).
components and F is the density of the mixture. Experimental values ∆u and VE at various temperatures are reported in Tables 6 and 7. Uncertainty in the changes ∆u and VE were estimated to be better than (2 m‚s-1 and (0.02 cm3‚mol, respectively. The excess molar volume VE and the change in the speed of sound upon mixing ∆u were fitted by a Redlich-Kister-type equation19 k
- 1)j (5)
Figure 4. Deviation of the speed of sound for hexane (1) + hexadecane (2): 2, 298.15 K; 4, 333.15 K; 9, 353.15 K; 0, 373.15 K.
The coefficient Bj in eq 5 was estimated by the leastsquares fitting method. The values of parameters Bj and standard deviation σ(∆u) are given in Table 8 at temperatures from (293.15 to 373.15) K. σ(∆u) values were calculated for a ratio of the type seen in eq 2. As can be seen from Figure 2, our composition dependence of VE at 313.15 K is in reasonably good agreement with data
presented by Marsh at al.4 The experimental results of the excess molar volume VE and deviations of the speed of sound ∆u for hexane + hexadecane at various temperatures are plotted as a function of composition in Figures 3 and 4. It is interesting that extreme values of deviations of the speed of sound and excess molar volume are at x1 ≈ 0.6.
∑B (2x
∆u/m‚s-1 or VE/cm3‚mol-1 ) x1x2
j
2
j)0
Table 7. Excess Molar Volumes VE of the Binary Mixture Hexane (1) + Hexadecane (2) from (293.15 to 333.15) K x1 T/K 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15
0.1 -0.037 -0.065 -0.079 -0.091 -0.108 -0.127 -0.146 -0.171 -0.190
0.2 -0.143 -0.167 -0.197 -0.226 -0.265 -0.303 -0.344 -0.392 -0.439
0.3 -0.303 -0.359 -0.420 -0.486 -0.487 -0.557 -0.635 -0.717 -0.801
0.4
0.5
VE/cm3‚mol -0.432 -0.550 -0.459 -0.610 -0.524 -0.681 -0.592 -0.751 -0.667 -0.827 -0.746 -0.907 -0.827 -0.991 -0.916 -1.078 -1.009 -1.173
0.6
0.7
0.8
0.9
-0.563 -0.626 -0.685 -0.774 -0.855 -0.942 -1.034 -1.133 -1.238
-0.552 -0.624 -0.698 -0.780 -0.866 -0.954 -1.043 -1.137 -1.237
-0.454 -0.525 -0.602 -0.680 -0.759 -0.841 -0.923 -1.010 -1.099
-0.232 -0.267 -0.303 -0.343 -0.384 -0.427 -0.469 -0.515 -0.562
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Journal of Chemical and Engineering Data, Vol. 50, No. 3, 2005 Literature Cited (1) Cooper, E. F.; Asfour, A.-F. A. Densities and Kinematic Viscosities of Some C6-C16 n-Alkane Binary Liquid Systems at 293.15 K. J. Chem. Eng. Data 1991, 36, 285-288. (2) Garcia Sanchez, M.; Rey Losada, C. Excess Volumes of n-Hexane + n-Undecane between 288.15 and 308.15 K. J. Chem. Eng. Data 1991, 36, 75-77. (3) Sims, M. J.; Winnick, J. Excess Volumes of Binary Liquid Mixtures of n-Alkanes. J. Chem. Eng. Data 1969, 14, 164-166. (4) Marsh, K. N.; Organ, P. P. Excess Molar Enthalpies and Excess Volumes for Three- and Four-component n-Alkane Mixtures Simulating (n-Hexane + n-Hexadecane). J. Chem. Thermodyn. 1985, 17, 835-841.
Figure 5. Isentropic compressibility kS as a function of temperature for hexane (1) + hexadecane (2) from (293.15 to 333.15) K: [, x1 ) 0; 9, x1 ) 0.2; 2, x1 ) 0.4; O, x1 ) 0.6; 4, x1 ) 0.8; b, x1 ) 0.9; 0, x1 ) 1. Table 8. Parameters Bj of Equation 5 and Standard Deviation σ T/K
B0
293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 368.15 373.15
200.235 201.909 204.246 207.034 209.914 213.480 217.297 221.383 226.677 230.547 236.029 241.189 246.625 253.173 259.297 266.378 273.467
293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15
-2.158 -2.374 -2.653 -2.972 -3.296 -3.606 -3.968 -4.351 -4.763
B1
B2
B3
σ
∆u 104.215 105.178 108.376 109.394 110.167 113.516 115.480 117.850 122.306 123.630 127.646 130.857 133.010 137.121 141.694 145.889 150.256
25.895 24.134 21.250 20.150 20.850 20.603 19.292 18.332 18.512 19.883 19.706 19.436 21.080 23.303 23.999 26.900 29.136
29.333 28.406 22.630 24.895 24.697 23.352 24.208 23.989 23.040 23.769 23.614 23.373 27.096 28.179 27.103 28.165 28.017
2.43 2.39 2.14 2.19 2.20 2.25 2.26 2.34 2.31 2.43 2.38 2.44 2.41 2.43 2.52 2.65 2.71
VE -1.531 -1.781 -1.828 -1.977 -2.149 -2.483 -2.575 -2.670 -2.774
0.911 0.665 0.562 0.532 0.268 0.422 0.375 0.292 0.281
0.997 0.339 0.055 -0.076 -0.319 0.127 -0.040 -0.185 -0.379
0.032 0.057 0.077 0.083 0.110 0.072 0.081 0.096 0.108
Isentropic compressibilities kS of the binary mixtures were calculated from the Laplace equation
kS )
1 Fu2
(6)
where u is the sound velocity and F is the density. The values of isentropic compressibility kS for hexane + hexadecane as a functions of temperature from (293.15 to 333.15) K are plotted in Figure 5. The uncertainty in the calculated values of kS was (0.1 to 0.2)%.
(5) Dymond, J. H.; Young, K. J.; Isdale J. D. P, F, T Beheviour for n-Hexane + n-Hexadecane in the Range 298 to 373 K and 0.1 to 500 MPa. J. Chem. Thermodyn. 1979, 11, 887-895. (6) IUPAC Commission on Atomic Weights and Isotopic Abundances, 1985. Pure Appl. Chem. 1986, 58, 1677-1692. (7) Bolotnikov, M. F.; Neruchev, Yu. A. Speed of Sound of Hexane + 1-Chlorohexane, Hexane + 1-Iodohexane, and 1-Chlorohexane + 1-Iodohexane at Saturation Condition. J. Chem. Eng. Data 2003, 48, 411-415. (8) Ball, S. J.; Trusler, J. P. M. Speed of Sound of n-Hexane and n-Hexadecane at Temperatures Between 298 and 373 K and Pressures up to 100 MPa. Int. J. Thermophys. 2001, 22, 427443. (9) Nath, J. Speeds of Sound in and Isentropic Compressibilities of (n-Butanol + n-Pentane, or n-Hexane, or n-Heptane, or 2,2,4Trimethylpentane, or Carbon tetrachloride) at T ) 293.15 K. J. Chem. Thermodyn. 1997, 29, 853-863. (10) Marsh, K. N. TRC Data Bases for Chemistry and EngineeringTRC Thermodynamic Tables; Texas A&M University: College Station, TX, 1995. (11) Vargaftik, N. B. Handbook of the Thermophysical Properties of Liquids and Gases; FM: Moscow, 1963. (12) Postigo, M.; Mariano, A.; Mussari, L.; Canzonieri, S. Viscosities for Binary Mixtures of 1-Decanol, Hexane, and Diethylamine at 10, 25, and 40 °C. J. Solution Chem. 2001, 30, 1081-1090. (13) Heintz, A.; Schmittecker, B.; Wagner, D.; Lichtenthaler, N. Excess Volumes of Binary 1-Alkanol/Hexane Mixtures at Temperatures between 283.15 and 323.15 K. J. Chem. Eng. Data 1986, 31, 487492. (14) Krestov, G. A.; Afanasiev, W. N.; Jefriemova, L. S. Physicochemical Properties of Binary Solvents; Khimia: Leningrad, 1988. (15) TRC Thermodynamic Tables. Hydrocarbons; Thermodynamics Research Center: College Station, TX, 1996. (16) Daridon, J. L.; Lagourette, B.; Grolier J.-P. E. Experimental Measurements of the Speed of Sound in n-Hexane from 293 to 373 K and up to 150 MPA. Int. J. Thermophys. 1998, 19, 145160. (17) Khasanshin, T.; Shchemelev, A. Speed of Sound in Liquid n-Alkanes. High Temp. 2001, 39, 60-68. (18) Ye, S.; Lagourette, B.; Alliez, J.; Saint-Guirons, H.; Xans, P.; Montel, F. Speed of Sound in Binary Mixtures as a Function of Temperature and Pressure. Fluid Phase Equilib. 1992, 74, 177202. (19) Redlich, O.; Kister, A. T. Algebraic Representation of Thermodynamic Properties and the Classification of Solutions. Ind. Eng. Chem. 1948, 40, 345-348.
Received for review February 8, 2005. Accepted March 3, 2005.
JE050060Q
