Acoustical Properties of Binary Mixtures of ... - Wiley Online Library

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

© 2010 SIOC, CAS, Shanghai, & WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

371

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

www.cjc.wiley-vch.de

)

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.


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.



373

Shukla et al.

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


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-


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



375

Shukla et al.

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


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.


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.)

Chin. J. Chem. 2010, 28, 371—377



377