FULL PAPER Acoustical Properties of Binary Mixtures of Heptane with Ethyl Acetate or Butyl Acetate Shukla, Divya Singh, Shashi Parveen, Shahla Gupta, Manisha* Shukla, Jagdish Prasad Department of Physics, University of Lucknow, Lucknow-226 007, India Mixed solvents rather than single pure liquids are of utmost practical importance in chemical and industrial processes as they provide an ample opportunity for the continuous adjustment of desired properties of the medium. Therefore, ultrasonic velocity (u) and density (ρ) were measured for the binary mixtures formed by heptane with ethyl acetate or butyl acetate at temperatures 293, 298 and 303 K over the entire composition range. Deviation in ultrasonic velocity (∆u), deviation in isentropic compressibility (∆κs), and excess intermolecular free length ( LEf ) have been evaluated using the ultrasonic velocity data and the computed results were fitted to the Redlich-Kister polynomial equation. The values of ∆u, ∆κs and LEf were plotted against the molar fraction of heptane. The observed positive and negative values of excess parameters were discussed in terms of molecular interaction between the components of the mixtures. Experimental values of ultrasonic velocity and density were compared with the results obtained by theoretical estimation procedures. The results were discussed in terms of average absolute deviation (AAD). Keywords
density, ultrasonic velocity, excess property, mixing rule, density model
Introduction The knowledge of the thermodynamic properties of organic liquid mixtures is very important for understanding the molecular interactions between the components. This also helps to evolve theoretical models and is useful in industrial applications.1-4 Excess properties of liquid systems, such as deviation in ultrasonic velocity (∆u), deviation in isentropic compressibility (∆κs), and excess intermolecular free length ( LEf ), are needed for the design of separation equipment and to test the theories of the solution.5 In addition, excess properties provide information about the molecular interactions and macroscopic behaviour of fluid mixtures and can be used to test and improve the thermodynamical models for calculating and predicting the fluid phase equilibria. In recent years, there has been considerable upsurge in the theoretical and experimental investigation of the excess thermodynamic properties of binary liquid mixtures.6,7 Heptane is employed in organic synthesis and is an ingredient of gasoline and aviation. Esters are used as artificial perfumes or scents as they emit a sweet smell. The experimental data on the mixtures of heptane with esters are scarce. Also, the molecular association in these solvent pairs provides valuable information regarding solute-solvent interaction taking place within the constituents present in the mixture. Therefore, as a
continuation of our ongoing studies on thermo-acoustical properties of binary liquid mixtures, we report here the ultrasonic velocity and density of binary mixtures of heptane with ethyl acetate or butyl acetate over the entire composition range at temperatures 293, 298 and 303 K. The experimental results were used to calculate ∆u, ∆κs and LEf , and the computed results were fitted to Redlich-Kister polynomial equation. The Rackett and Hankinson-Brobst-Thomson (HBT) models8,9 have been applied to compare the difference between predicted and experimental density. Vangeel’s, Nomoto’s and Junjie’s relation and Collision Factor Theory (CFT)10 were also used to correlate the ultrasonic velocity data. The results have been discussed in terms of average absolute deviation (AAD).
Experimental Ultrasonic velocity (u) was measured using an ultrasonic interferometer (Model F81) provided by Mittal Enterprises, New Delhi, which was calibrated by measuring the velocity in standard liquids, e.g. AR grade benzene and carbon tetrachloride (CCl4). Our measured values of u at 20, 25, 30 and 40 ℃ for benzene and CCl4 agree closely with the literature values.11 Maximum possible experimental error in u has been found to be ±0.08%. The temperature was controlled by circulating water around the liquid cell from thermostatically controlled adequately stirred water bath (accuracy±0.1
* E-mail:
[email protected] Received August 9, 2007; revised October 18, 2007; accepted March 1, 2008. Chin. J. Chem. 2010, 28, 371—377
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Shukla et al.
FULL PAPER ℃). The density of various systems has been measured using a single capillary calibrated pyknometer as described earlier.12 Mixtures were prepared by weighing the liquids in specially designed ground glass stoppered bottles, taking extreme precautions to minimize preferential evaporation. An OHAUS (AR 2140) single pan balance having a stated precision of 0.1 mg was used throughout. The maximum possible error in the molar fraction was estimated to be ±0.0001. The chemicals used were obtained from Ranbaxy Fine Chemical Ltd. All the chemicals used were purified by distillation technique.13,14 Distillation of liquids was carried out in a simple pear-shaped distillation flask. The distillate was collected in the centrifuge-tube placed in the bottom of the vessel. Distillation was performed very slowly to ensure efficient condensation and collection of the distillate in the centrifuge-tube. The purities of all the chemicals were ascertained by the constancy of their boiling points during final distillation and also by literature comparison11 of their densities and refractive index at 293 K. These values agreed well within the precession of experimental error.
Results and discussion Ultrasonic velocity (u), density (ρ), deviation in ultrasonic velocity (∆u), deviation in isentropic compressibility (∆κs), and excess intermolecular free length ( LEf ) of the binary systems of heptane with ethyl acetate or butyl acetate respectively at T=293, 298 and 303 K are reported in Tables 1 and 2, respectively. The ∆u, ∆κs and LEf ware calculated by the following Eqs. 1—3: 2
∆u=u- ∑ xi ui
x1
ρ/ (g•cm-3)
u/ (m•s-1)
∆u/ (m•s-1)
∆κs/ (T•Pa-1)
LEf /Å
293 K 0.0000
0.9007
1180
0.00
0.0000
0.0000
0.0892
0.8708
1168
-12.03
0.2192
0.0079
0.1802
0.8431
1148
-31.06
0.5568
0.0193
0.2735
0.8184
1132
-47.58
0.8655
0.0292
0.3696
0.7957
1118
-60.89
1.1310
0.0373
0.4679
0.7748
1116
-62.80
1.1903
0.0387
0.5688
0.7552
1123
-55.39
1.0659
0.0344
0.6727
0.7366
1131
-46.68
0.9057
0.0290
0.7786
0.7188
1164
-14.06
0.3001
0.0102
0.8878
0.7011
1168
-9.34
0.1995
0.0066
1.0000
0.6846
1177
0.00
0.0000
0.0000
0.0000
0.8944
1138
0.00
0.0000
0.0000
0.0892
0.8626
1129
-8.30
0.2039
0.0073
0.1802
0.8352
1113
-22.86
0.4999
0.0171
0.2735
0.8109
1093
-42.00
0.8851
0.0292
0.3696
0.7891
1087
-47.60
1.0176
0.0330
0.4679
0.7684
1082
-52.00
1.1267
0.0359
0.5688
0.7491
1082
-51.00
1.1197
0.0352
0.6727
0.7307
1098
-34.62
0.7773
0.0246
0.7786
0.7131
1115
-16.47
0.3939
0.0128
0.8878
0.6957
1121
-9.70
0.2395
0.0076
1.0000
0.6799
1130
0.00
0.0000
0.0000
298 K
(1)
i=1
300 K 0.0000
0.8881
1120
0.00
0.0000
0.0000
0.0892
0.8546
1116
-2.75
0.1399
0.0052
i=1
0.1802
0.8267
1107
-9.98
0.3220
0.0114
2
0.2735
0.8027
1095
-20.77
0.5507
0.0188
0.3696
0.7819
1079
-35.13
0.8386
0.0275
0.4679
0.7615
1066
-46.70
1.1013
0.0349
0.5688
0.7430
1067
-45.0
1.0664
0.0334
0.6727
0.7248
1078
-32.01
0.7790
0.0245
0.7786
0.7074
1085
-24.10
0.5966
0.0186
0.8878
0.6905
1094
-13.27
0.3407
0.0105
1.0000
0.6754
1106
0.00
0.0000
0.0000
2
∆κs=κs- ∑ xiκ s,i
(2)
LEf =Lf- ∑ xi Lf,i
(3)
i=1
where the symbols have their usual meaning. The values of ∆u, ∆κs and LEf for each mixture have been fitted to Redlich-Kister polynomial Eq. 4:15 5
YE= x1 (1-x1 )∑ ai (2 x1-1)
i-1
(4)
i=1
where YE refers to excess/deviation parameters. The values of coefficients ai were calculated by the method of least squares along with standard deviation σ(YE) which are given in Table 3. The coefficient ai is an adjustable parameter for the best fit of the excess functions. The standard deviation values were obtained from relation Eq. 5:
(
⎡ ∑ YexpE -YcalE σ(YE)= ⎢ ⎢ n-p ⎢⎣ 372
Table 1 Thermoacoustical parameters of heptane (1)+ethyl acetate (2) mixture at different temperatures
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)
2 1/ 2
⎤ ⎥ ⎥ ⎥⎦
(5)
where n is the total number of experimental points, p is E E and Ycal are the experithe number of coefficients, Yexp mental and calculated excess parameters respectively. The variation in excess parameters with composition for the binary mixtures of heptane with ethyl acetate or butyl acetate may be explained as a result of cumulative manifestation of various types of intermolecular interactions between the components. Earlier workers12 have reported that there are mainly three types of contribution to the thermodynamic properties.
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Chin. J. Chem. 2010, 28, 371—377
Acoustical Properties of Binary Mixtures Table 2 Thermoacoustical parameters of heptane (1)+butyl acetate (2) mixture at different temperatures x1
ρ/ (g•cm-3)
0.0000 0.1141 0.2247 0.3317 0.4361 0.5371 0.6349 0.7302 0.8226 0.9126 1.0000
0.8829 0.8543 0.8297 0.8074 0.7862 0.7664 0.7480 0.7305 0.7147 0.6985 0.6846
0.0000 0.1141 0.2247 0.3317 0.4361 0.5371 0.6349 0.7302 0.8226 0.9126 1.0000
0.8777 0.8476 0.8232 0.8009 0.7798 0.7605 0.7423 0.7250 0.7088 0.6930 0.6799
0.0000 0.1141 0.2247 0.3317 0.4361 0.5371 0.6349 0.7302 0.8226 0.9126 1.0000
0.8711 0.8391 0.8150 0.7929 0.7724 0.7537 0.7358 0.7187 0.7029 0.6876 0.6754
u/ ∆u/ (m•s-1) (m•s-1) 293 K 1223 0.00 1184 -33.90 1165 -48.00 1145 -63.10 1125 -77.60 1115 -83.50 1111 -82.50 1123 -66.00 1138 -47.16 1161 -20.52 1177 0.00 298 K 1204 0.00 1176 -19.30 1152 -34.90 1131 -48.00 1108 -63.10 1096 -68.00 1089 -68.00 1094 -56.00 1111 -31.95 1123 -13.18 1130 0.00 303 K 1173 0.00 1154 -10.60 1131 -27.10 1110 -40.00 1089 -55.00 1076 -60.40 1072 -58.30 1074 -50.00 1090 -28.00 1105 -6.51 1106 0.00
∆κs/ (T•Pa-1)
LEf /Å
0.0000 0.4406 0.6452 0.8949 1.1755 1.3307 1.3661 1.1045 0.7872 0.3459 0.0000
0.0000 0.0160 0.0230 0.0310 0.0394 0.0435 0.0438 0.0352 0.0250 0.0110 0.0000
0.0000 0.2756 0.4940 0.7145 1.0131 1.1482 1.2079 1.0240 0.5798 0.2524 0.0000
0.0000 0.0106 0.0183 0.0254 0.0344 0.0378 0.0387 0.0324 0.0186 0.0082 0.0000
0.0000 0.1655 0.4076 0.6325 0.9397 1.0852 1.0933 0.9727 0.5407 0.1284 0.0000
0.0000 0.0067 0.0153 0.0225 0.0317 0.0355 0.0349 0.0306 0.0173 0.0045 0.0000
Physical: Due to non-specific van der Waals type dispersive forces leading to a positive contribution towards ∆κs and LEf and negative contribution towards ∆u. Chemical: Due to hydrogen bonding and other complex forming interactions making negative contribution towards ∆κs and LEf and positive contribution towards ∆u. Structural: Due to changes in interstitial accommodation, molar volume and free volume. Thus, the sign and magnitude of ∆u, ∆κs and LEf play an important role in assessing the molecular rearrangement as a result of molecular interaction between the component molecules in the liquid mixtures. As can be seen from Figure 1, ∆u is negative for both the mixtures at all the three temperatures. Experimental error bars of Figure 1 i.e. deviation in ultrasonic velocity vs. Chin. J. Chem. 2010, 28, 371—377
Figure 1 Deviation in ultrasonic velocity vs. molar fraction of heptane for binary mixtures: (a) heptane (1)+ethyl acetate and (b) heptane+butyl acetate at varying temperature.
Figure 2 Experimental error bars of Figure 1 i.e. deviation in ultrasonic velocity vs. molar fraction of heptane for binary mixtures: (a) heptane (1)+ethyl acetate and (b) heptane+butyl acetate at varying temperature.
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FULL PAPER
Table 3 The values of co-efficient αi from Eq. 4 for Δu, ∆κs and LEf and standard deviation σ(YE) for both the binary mixtures at different temperatures Parameter
a2
a1
a3
a4
a5
σ(YE)
Heptane (1)+Ethyl acetate (2) T=293 K -1
∆u/(m•s )
-234.706
-217.040
324.9566
284.856
-245.970
2.4640
∆κs/(T•Pa-1)
4.577
2.106
-5.396
-0.2854
0.4195
0.0446
0.1144
-0.2132
0.3516
3.520
3.3655
0.0010
-203.208
-162.709
253.521
249.533
-157.913
2.5328
∆κs/(T•Pa )
4.7866
-1.8617
-16.3963
2.2898
19.6667
0.0463
LEf /Å
0.1513
-0.0474
-0.4810
0.0661
0.5768
0.0014
∆u/(m•s-1)
-189.859
1.7860
253.129
92.066
-140.478
0.7349
∆κs/(T•Pa )
4.6077
-1.8666
-8.9921
1.0260
8.9285
0.0253
LEf /Å
0.1449
-0.0452
-0.2584
0.0239
0.2526
0.0007
LEf
/Å
T=298 K - ∆u/(m•s 1) -1
T=303 K -1
Heptane (1)+Butyl acetate (2) T=293 K -1
∆u/(m•s )
-340.374
162.125
144.003
-332.673
-147.888
1.0590
∆κs/(T•Pa-1)
5.1600
-3.3840
-2.0390
5.364
1.5240
0.0194
0.1718
-0.0947
-0.0697
0.1698
0.0617
0.0006
-175.766
691.321
714.138
1177.842
1222.381
1.1510
∆κs/(T•Pa )
2.193
-17.121
-16.542
28.183
30.059
0.0222
LEf /Å
0.0849
-0.4727
-0.4708
0.7930
0.8494
0.0007
∆u/(m•s-1)
-233.211
132.206
87.591
-204.460
187.383
1.4210
∆κs/(T•Pa )
4.1030
-3.4789
-1.7215
5.0569
-2.9454
0.0294
LEf /Å
0.0698
-0.3956
-0.2474
0.6554
0.4240
0.0027
LEf
/Å
T=298 K ∆u/(m•s-1) -1
T=303 K -1
Figure 3 Deviation in isentropic compressibility vs. molar fraction of heptane for binary mixtures: (a) heptane (1)+ethyl acetate and (b) heptane+butyl acetate at varying temperature. 374
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molar fraction of heptane for binary mixtures of heptane +ethyl acetate and heptane+butyl acetate at varying temperature is given in Figure 2. However, ∆κs and LEf are positive for both the mixtures (Figures 3 and 4). As the temperature is increased the negative and positive values of deviation decrease for both the mixtures. This is in accordance with the view proposed by Resa et al.,16 according to which when molecules of two components are mixed, interactions between them occur. Esters are weakly polar, when non-polar molecules of a hydrocarbon intersperse among the ether molecules, there is a decrease in interaction among the dipoles of the acetate molecules resulting in positive ∆κs and LEf and negative ∆u values. Negative values of ∆u and positive values of ∆κs and LEf or both the mixtures may be attributed to the presence of weak interaction between the component molecules in the mixture, thereby indicating the predominance of long range dispersive forces. However, the interaction of heptane—a hydrocarbon is stronger with ethyl acetate than with butyl acetate as observed experimentally. Since ethyl acetate has a smaller molecule size than butyl acetate, it is thought that the heptane molecule could establish a better rela-
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Chin. J. Chem. 2010, 28, 371—377
Acoustical Properties of Binary Mixtures
tion by way of some sort of bonding than butyl acetate that has a comparatively longer alkyl chain. Alternatively because of longer size of butylacetate, the interaction is weaker which may be probably due to steric hindrance not allowing the heptane molecules to have a stronger interaction. Similar trends in ∆u, ∆κs and LEf ere also reported earlier by other workers17-19 for binary mixtures.
where values of the constants are: a=-1.52816, b= 1.43907, c=-0.81446, d=0.190454, e=-0.296123, f=0.386914, g=-0.04273, h=-0.04806. ZRA is a unique constant for each compound, Tr is the reduced temperature, Tc and Pc are the pseudo critical properties* of a mixture, M is the average weight in a mixture, V* is the characteristic volume and ωSRK is the acentric factor respectively. The critical values for pure components are listed in Table 4a. A comparison between the experimental and predicted densities is shown in Table 4b in terms of AAD. As evident from Table 4b, Rackett model seems to be more suitable in the case of heptane+butyl acetate mixture with minimum AAD of 0.0813. However the HBT model is more suitable for heptane+ethyl acetate mixtures. These models require only critical values and molecular weights of pure components for the prediction of density. Thus, one can determine density of pure liquids and liquid mixtures theoretically and also can check the accuracy of experimental data. Since mixtures of liquids with different molecular sizes were considered, a particular model provided good agreement in one system but deviated in other. Table 4a Critical values for pure compounds for the estimation of density
Figure 4 Deviation in excess intermolecular free length vs. molar fraction of heptane for binary mixtures: (a) heptane (1)+ ethyl acetate and (b) heptane+butyl acetate at varying temperature.
Modelling Due to strong dependence of design and optimization of chemical processes on computer calculations, the availability of accurate simple and tested method, as well as related parameters is of increasing relevance. In this case, consideration was given to the Rackett equation of state and HBT model in order to analyze how accurate densities are predicted. According to Rackett model (8), the density could be described as Eq. 6: (6) 9
The Hankinson equation of state for density could be described as Eq. 7: M V
*
VR(o)
(7)
(δ) SRKVR ⎤ ⎦
⎡1-ω ⎣
where VR(o) =1+a(1-Tr)1/3 +b(1-Tr)2/3 +c(1-Tr)+ d(1-Tr)4/3 0.25<Tr<0.95 and
VR(δ)=
(e+fTr+gTr2+hTr3 )
Tr-1.00001
Chin. J. Chem. 2010, 28, 371—377
Pc/Bar
ZRA
V*
VC
Heptane
27.4
540.3 0.2604 0.3507 0.4304 432
Ethyl acetate
38.3
523.2 0.2539 0.3595 0.2853 286
Butyl acetate
31.4
579.0 0.2540 0.4170 0.4000 400
Table 4b Average absolute values for the estimation of density with respect to corresponding experimental data for both binary mixtures at different temperatures T/K
Rackett
Hankinson
Heptane (1)+Ethyl acetate (2) 293
0.9862
0.6722
298
1.1820
0.6725
303
1.4010
0.6712
Heptane (1)+Butyl acetate (2)
-{1+(1-Tr )2 / 7 } ⎛ MP ⎞ ρ=⎜ c ⎟ Z RA ⎝ RTc ⎠
ρ=
Tc/K
ωSRK
Compound
0.25<Tr<1.0
293
0.0813
1.9700
298
0.0950
1.8010
303
0.3967
1.4930
Mixing rules for ultrasonic velocity Van Dael and Vangeel20 proposed the following ideal mixing relation for predicting speed of sound of a binary liquid mixture (Eq. 8): 2
1 2
∑ xi M ium
2
xi M i ui i=1
=∑
(8)
i=1
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FULL PAPER Nomoto21 assuming the linearity of the molar sound velocity and the additivity of the molar volumes in liquid solutions, gave the following relation Eq. 9: 3
⎡ 2 ⎤ 3 ⎢ ∑ xi Ri ⎥ ⎡R ⎤ ⎥ um= ⎢ m ⎥ = ⎢ i=21 ⎢ ⎥ ⎣ Vm ⎦ ⎢ ∑ xi Ri ⎥ ⎣ i=1 ⎦
(9)
Zhang22 gave following relation (Eq. 10) for the ultrasonic velocity in binary mixture: 2
um=
∑ xiVi i=1
(10)
1/ 2
2 ⎡ 2 xiVi ⎤ i x M ⎢∑ i i ∑ 2⎥ i=1 ρi ui ⎦ ⎣ i=1
Nutsch-Kuhnkies23 extended the relation given by Schaaffs for predicting ultrasonic velocity in pure liquids on the basis of Collision factor theory, to the binary liquid mixtures. The relation is as Eq. 11: 2
2
∑ xi Bi
i=1
Vm
um=U ∞ ∑ xi Si
i=1
(11)
where the symbols have their usual meanings. Ultrasonic velocities of both the binary mixtures were theoretically evaluated using these relations and compared with the experimental velocities. In Table 5, a comparison between the experimental and predicted ultrasonic velocity is shown in terms of AAD. It can be seen from Table 5 that the values of the ultrasonic velocity (u), as predicted by the four mixing rules for two mixtures at three temperatures, show deviations from the respective measured values in terms of AAD. The approximations and assumptions incorporated in the theories on which these mixing rules are based, may have a bearing on these deviations. The assumption that Table 5 Average absolute values for the estimation of ultrasonic velocity with respect to experimental data for the binary mixtures at different temperatures T/K
Van Dael & Vangeel
Nomoto
Junjie
the liquid molecules in the mixtures are of spherical shape is not true every time. The van Dael and Vangeel mixing rule assumes a mixture to be an ideal one with components having molar specific heat ratios equal to that of the mixture (i.e. γ1=γ2=γ). Also their molar volumes were assumed to be equal. Both of these assumptions do not hold good for either of the two mixtures. Similarly, Nomoto based his mixing rule on the conditions of the linearity of the molar sound velocity and the additivity of the molar volumes in the liquid mixture. Thus, both the mixing rules do not take into account the interactions between the component molecules. Vangeel’s and Nomoto’s relations provide moderate AAD values for either of two mixtures. However, on the other hand AAD values obtained using a CFT theory are quite higher in both the mixtures. The predictions made using Zhang’s relation show quite a good agreement with the respective experimentally observed values with minimum AAD of 1.2336 in the binary mixture of heptane+ethyl acetate at 303 K and maximum AAD of 3.2768 in the binary mixture of heptane+butyl acetate at 293 K. Thus, in terms of relative merits of the mixing rules for ultrasonic velocity, it appears that the Zhang’s rule is best suited for predicting the speed of sound, as it gives an overall smaller AAD than that given by rest of the mixing rules.
Conclusion The observed positive and negative values of ∆u, ∆κs and LEf indicate the presence of weak dispersive forces on mixing and the progressive occultation of the polar effect of ester molecular group. Due to strong dependence of adequate industrial design on computation and simulation, an estimation of physical properties was made by different theoretical procedures, showing the practical application suitability of the simple models used.
References 1 2 3
CFT
4 5 6 7
Heptane (1)+Ethyl acetate (2) 293
2.6117
2.7192
2.1297
4.0990
298
2.2501
2.3208
1.7158
3.1789
303
1.8298
1.8571
1.2336
2.4973
8
Heptane (1)+Butyl acetate (2) 293
3.8942
3.4306
3.2768
3.7951
298
2.8870
2.3480
2.2646
2.7461
303
2.4214
1.9054
1.8451
2.5688
376
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9
10
Vesovic, V. Fluid Phase Equilib. 2002, 199, 295. Takogi, T. J. Chem. Eng. Data 1996, 41, 1061. Otto, J. B.; Sipowska, J. T.; Marchart, B. G. J. Chem. Thermodyn. 1994, 26, 717. Krahn, U. G.; Luft, G. J. Chem. Eng. Data 1994, 39, 670. Rivas, M. A.; Pereira, S. M.; Iglesias, T. P. J. Chem. Thermodyn. 2002, 34, 1897. Ali, A.; Nain, A. K. Pramana J. Phys. 2002, 58, 695. Pandey, J. D.; Rai, R. D.; Shukla, R. K.; Shukla, A. K.; Misra, N. Ind. J. Pure Appl. Phys. 1993, 31, 84. Resa, J. M.; Gonzalez, C.; Prieto, S.; Diez, E.; Iglesias, M. Korean J. Chem. Eng. 2006, 23, 93. Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids, 4th ed., Mc Graw-Hill Book Co., New York, 1987. Misra, A.; Vibhu, I.; Singh, R. K.; Gupta, M.; Shukla, J. P. Phys. Chem. Liq. 2007, 45, 93.
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Chin. J. Chem. 2010, 28, 371—377
Acoustical Properties of Binary Mixtures 11
12 13 14 15 16 17
CRC Handbook of Chemistry and Physics, 76th ed., Eds: Lide, D. R.; Frederikse, H. P. R., CRC Press, Boca Raton, 1995—1996. Gupta, M.; Vibhu, I.; Shukla, J. P. Fluid Phase Equilib. 2006, 26, 244. Perrin, D. D.; Armarego, W. L. F. Purification of Laboratory Chemistry, 3rd ed., Pregamon Press, Oxford, 1988. Glasstone, S. Textbook of Physical Chemistry, Macmillan India Limited, New Delhi, 1981, p. 717. Redlich, O.; Kister, A. T. Ind. Eng. Chem. 1948, 40, 345. Resa, J. M.; Gozalez, C.; Landaluce, S. O.; Lanz, J. J. Chem. Thermodyn. 2002, 34, 995. Resa, J. M.; Gozalez, C.; Landaluce, S. O.; Lanz, J. J. Chem. Thermodyn. 2005, 50, 319.
18 19 20 21 22 23
Gonzalez, B.; Dominguez, A.; Tojo, J. J. Chem. Thermodyn. 2004, 36, 267. Chandraasekher, G.; Venkatesu, P.; Rao, M. V. P. J. Chem. Thermodyn. 2000, 45, 590. Van Dael, W.; Van Geel Thermodynamics Properties and Velocity of Sound Wave, Worths, London, 1975, Chapter II. (a) Nomoto, O. J. Phys. Soc. Japan 1956, 11, 1146. (b) Nomoto, O. J. Phys. Soc. Japan 1958, 13, 1528. Junjie, Z. J. Chem. Univ. Sci. Technol. 1984, 14, 298. (a) Schaaffs, W. Molekuiarakustik, Springer-Verlag, Berlin, 1963, Chapters XI and XII. (b) Schaaffs, W. Acustica 1974, 30, 275. (c) Schaaffs, W. Acustica 1975, 33, 272. .
(E0708092 Zhu, H.; Pan, B.)
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