Molecular interactions in binary mixtures of ethyl benzoate + ethers at (303.15, 308.15 and 313.15) K

Journal of Molecular Liquids 187 (2013) 58–65

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Molecular interactions in binary mixtures of ethyl benzoate + ethers at (303.15, 308.15 and 313.15) K Manapragada V. Rathnam a,⁎, Devappa R. Ambavadekar a,1, Manapragada Nandini b,2 a b

Physical Chemistry Research Laboratory, B.N. Bandodkar College of Science, Thane 400601, India Department of Chemistry, Dr. P.R. Ghogrey Science College, Deopur, Dhule 424005, India

a r t i c l e

i n f o

Article history: Received 30 March 2013 Received in revised form 22 May 2013 Accepted 10 June 2013 Available online 21 June 2013 Keywords: Density Viscosity Speed of sound Ethyl benzoate Isentropic compressibility

a b s t r a c t The density, viscosity and speed of sound at temperatures (303.15, 308.15 and 313.15) K were measured for the binary mixtures of ethyl benzoate with tetrahydrofuran, 1,4-dioxane, anisole, and butyl vinyl ether over the entire range of mixture composition. From these data excess volume, VE, isentropic compressibility, Ks, intermolecular free length, Lf, internal pressure, πi and free volume, Vf, have been calculated. The computed excess quantities were fitted to the Redlich–Kister equation. This work also provides a test of Katti and Chaudhri and McAllister's (3-body and 4-body) equations for correlating the viscosities of the binary mixtures. © 2013 Elsevier B.V. All rights reserved.

1. Introduction The study on physico-chemical behaviour and molecular interactions of liquid mixtures is of considerable importance in several industrial, engineering and technological processes. Acoustic properties have been extensively applied in understanding physicochemical behaviour and molecular interactions in liquid mixtures [1,2]. Acoustic sonograms have become an important medicinal diagnostic tool which is widely used now a days [3,4]. It includes the detection of wide variety of anomalies such as tumour, bloodless sugar, and kidney stone fragmentation [5]. There have been a number of reports on thermodynamic, transport and acoustic properties of liquid mixtures consisting of oxygenated compounds [6–16]. As a further contribution in this area, in continuation of our earlier work [17–20] we report the density, ρ, viscosity, η and speed of sound, u, for the binary mixtures of ethyl benzoate + tetrahydrofuran or 1,4-dioxane or anisole or butyl vinyl ether at 303.15,308.15 and 313.15 K over the entire range of composition. Tetrahydrofuran a cyclic ether is an aprotic solvent often used in polymer science to dissolve polymers. It is also an industrial solvent for PVC and varnishes. Anisole is a precursor to perfumes, insect

⁎ Corresponding author. Tel.: +91 8976545095; fax: +91 22 25337672. E-mail addresses: [email protected] (M.V. Rathnam), [email protected] (D.R. Ambavadekar), [email protected] (M. Nandini). 1 Tel.: +91 9819558695; fax: +91 22 25337672. 2 Tel.: +91 2562 272562; fax: +91 2562 271340. 0167-7322/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.molliq.2013.06.002

pheromones and pharmaceuticals. 1,4-Dioxane due to its low electrical dipole moment makes it a very useful solvent in spectroscopic and dielectric works. While butyl vinyl ether is used as constituent of paint removers, it is also used in cosmetics, solvent stabilizer for pharmaceuticals. Keeping the importance of these chemicals in mind, the present research has been undertaken to study the molecular interactions of the binary mixtures reported in this paper. From the experimental data of density, viscosity and speed of sound, the excess volume, VE, deviation in isentropic compressibility, ΔKs, excess intermolecular free length, LEf , excess internal pressure, πEi , and excess free volume, VEf , were calculated. These results were fitted to the Redlich–Kister polynomial equation [21] to derive the binary coefficients and to estimate the standard errors. Further the experimental viscosities were correlated using empirical equations proposed by Katti and Chaudhri [22] and McAllister[23] three body and four body. 2. Experimental 2.1. Materials Ethyl benzoate, tetrahydrofuran, 1,4-dioxane, anisole and butyl vinyl ether all Fluka with mass fraction purity > 99.0% were supplied by Aldrich company. The purity of all these chemicals was checked by gas chromatography (GC-8610) and the analysis of the purity was found to be > 99.4%. These chemicals were stored over 0.4 nm molecular sieves to reduce water content and distilled just before the use. A comparison of pure fluid properties of density and viscosity with the literature data is shown in Table 1.

M.V. Rathnam et al. / Journal of Molecular Liquids 187 (2013) 58–65 Table 1 Comparison of experimental density (ρ), and viscosity (η), of pure liquids with literature values at (303.15, 308.15, and 313.15) K. Liquid

Ethyl benzoate

Tetrahydrofuran

1,4-Dioxane

Anisole

Butyl vinyl ether

T/K

ρ/g cm−3

η/mPa s

Exptl.

Lit.

Exptl.

Lit.

303.15

1.0378

1.758

308.15 313.15 303.15 308.15

1.0334 1.0288 0.8787 0.8730

1.751 [29] 1.751 [30] 1.591 [29] 1.453 [29] 0.438 [30] 0.4276 [13]

313.15 303.15

0.8669 1.0227

1.0373 [29] 1.03718 [30] 1.0325 [29] 1.0277 [29] 0.8771 [14] 0.87214 [14] 0.8715 [13] 0.86719 [14] 1.02271 [8] 1.02255 [31]

308.15 313.15

1.0178 1.0116

303.15 308.15 313.15 303.15 308.15 313.15

0.9853 0.9792 0.9728 0.7741 0.7682 0.7633

1.0172 [7] 1.01132 [8] 1.01130 [31] 0.984374 [12] 0.9788 [11]

1.617 1.439 0.439 0.429 0.390 1.090

0.999 0.946 0.923 0.849 0.764 0.387 0.365 0.354

1.102 [8] 1.108 [32] 1.095 [7] 1.008 [7] 0.946 [8] 0.9458 [32] 0.931 [12] 0.849 [11]

was controlled within ± 0.01 K using a constant low temperature bath (I N S R E F model IRI 016 C, India) by circulating water from thermostat. The uncertainty in the temperature was found to be ± 0.01 K. 3. Results and discussion Density ρ, viscosity η and speed of sound u of the studied binary mixtures measured at 303.15, 308.15 and 313.15 K over the entire composition range are presented in Table 2. From the density data excess volumes, VE, were calculated using the following relation E

V ¼ ðx1 Μ 1 þ x2 Μ 2 Þ=ρ12 −ðx1 Μ1 =ρ1 þ x2 Μ 2 =ρ2 Þ

2

ð3Þ 1=2

Lf ¼ K⋅ðK s Þ

ð4Þ 1=2

The binary liquid mixtures were prepared by mixing known masses of pure liquids in airtight stoppered bottles in order to minimise evaporation losses. All mass measurements were made using a Mettler one-pan balance (AE, 240, Switzerland). The resulting mole fraction uncertainty was estimated to be less than ± 0.0001. Densities of pure and their binary mixtures were determined using a density meter (DMA-4500, Anton Paar). The instrument has high precision platinum thermometer in the density sensor for the accurate measuring temperature. The instrument was calibrated frequently before the start of the actual experiments, using deionised doubly distilled water and dry air. The density measurements were accurate to ± 0.0007 g cm−3. Viscosities of the pure liquids and their mixtures were determined at the atmospheric pressure and the required temperature by using Ubbelohde viscometer. The viscometer bulb has a capacity of about 15 ml and the capillary tube with a length of about 90 mm and 0.5 mm internal diameter. The viscometer thoroughly cleaned and perfectly dried is filled with the sample liquid and its limbs were closed with Teflon caps to avoid evaporation. The viscometer is kept in a transparent walled water bath with a thermal stability of ± 0.01 K for about 20 min to obtain thermal equilibrium. An electronic digital stopwatch with an uncertainty of ±0.01 s was used for flow time measurements. At least 3–4 repetitions of each mixture reproducible to ± 0.05 s were obtained and the results were averaged. The viscosity was calculated from efflux time, t, using the following relation; η ¼ ρðAt−Bt Þ

ð1Þ

where ρ is the density and A and B are the characteristic constants of the viscometer, which were determined by taking water and benzene as the calibrating liquids. The uncertainty in the viscosity thus estimated was found to be ± 0.008 mPa s. Speed of sound of pure liquids and liquid mixtures was determined by using a single-crystal variable path interferometer (model F-81) supplied by Mittal Enterprises, New Delhi, India operating at a frequency of 2 MHz. The instrument was calibrated by measuring the velocity in standard liquids viz AR grade benzene and carbon tetrachloride. The uncertainty in speed of sound thus estimated was found to be ± 1%. In all property measurements the temperature

ð2Þ

where x1, M1 and ρ are the mole fraction, molar mass, and density respectively of pure components 1 and 2. ρ12 is the density of the binary mixture. From the speed of sound data, isentropic compressibility, Ks, intermolecular free length, Lf, internal pressure, πi, and free volume, Vf, were calculated using the following relations. K s ¼ 1=u ρ

2.2. Methods

59

πi ¼ bRT ðKη=uÞ


 2=3 7=6 ρ =Μ eff


3=2 V f ¼ Μeff u=ηΚ

ð5Þ ð6Þ

In the above Eqs. (3)–(6), K is the temperature dependent Jacobson constant, b, is the cubical packing fraction taken as 2 for all liquids. R is the universal gas constant, T is the experimental temperature, and η is the viscosity. Meff = ∑ximi where x is the mole fraction and m is the molecular weight of the ith component. These calculated properties are included in Table 2. The excess or deviation parameters such as deviation in viscosity, Δη, deviation in isentropic compressibility, ΔKs, excess intermolecular free length, LEf , excess internal pressure, πEi , and excess free volume, VEf , were obtained using the general relation E

Y ¼ Y m −x1 Y 1 −x2 Y 2 :

ð7Þ

In the above Eq. (7) YE is the deviation or excess property in question. Ym refers to the property of the mixture, and x1Y1 and x2Y2 refer to the mole fraction and specific property of the pure components 1 and 2 respectively. Further these excess or deviation properties were fitted to the Redlich–Kister polynomial equation [21] to derive the binary coefficients m Y E ðΔY Þ ¼ x1 x2 ∑Ak ðx1 −x2 Þk K¼o

ð8Þ

where, Ak, refers to the adjustable parameter and m is the degree of polynomial expansion. The variation in standard deviations, σ, was calculated by using the relation σ¼


1=2 2 = ðn−mÞ ∑ Y expt −Y cal

ð9Þ

where n represents the number of data points and m is the number of coefficients. The correlation parameters calculated using Eq. (8) along with their standard deviations (σ) obtained by Eq. (9) are listed in Table 3. The results of VE, Δη, ΔKs, LEf , πEi and VEf versus mole fraction

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Table 2 Values of density, (ρ), excess volume, (VE), viscosity,(η), speed of sound, (u), isentropic compressibility, (KS), intermolecular free length, (Lf), internal pressure,(πi) and free volume,(Vf), for the binary liquid mixtures. x1

ρ/g cm−3

VE/cm3 mol−1

Ethyl benzoate T = 303.15 K 0.0000 0.0601 0.1259 0.1980 0.2773 0.3628 0.4611 0.5719 0.6953 0.8372 1.0000 T = 308.15 K 0.0000 0.0601 0.1259 0.1980 0.2773 0.3628 0.4611 0.5719 0.6953 0.8372 1.0000 T = 313.15 K 0.0000 0.0601 0.1259 0.1980 0.2773 0.3628 0.4611 0.5719 0.6953 0.8372 1.0000

(1) + tetrahydrofuran (2)

Ethyl benzoate T = 303.15 K 0.0000 0.0639 0.1304 0.1626 0.2849 0.3735 0.4716 0.5805 0.7048 0.8402 1.0000 T = 308.15 K 0.0000 0.0639 0.1304 0.1626 0.2849 0.3735 0.4716 0.5805 0.7048 0.8402 1.0000 T = 313.15 0.0000 0.0639 0.1304 0.1626 0.2849 0.3735 0.4716 0.5805 0.7048

(1) + 1,4-dioxane (2)

η/mPa s

u/ms−1

KS/Tpa−1

Lf × 10−8 cm

πi × 106 Nm−2

Vf × 10−6 m3 mol−1

0.8787 0.8972 0.9156 0.9335 0.9508 0.9670 0.9826 0.9973 1.0108 1.0239 1.0378

−0.228 −0.459 −0.662 −0.826 −0.931 −0.928 −0.817 −0.580 −0.250

0.391 0.488 0.545 0.617 0.706 0.804 0.937 1.083 1.257 1.474 1.758

1248 1264 1276 1300 1320 1332 1352 1356 1356 1356 1352

730.7 697.6 670.8 633.9 603.6 582.9 556.8 545.3 538.0 531.2 527.1

0.5610 0.5482 0.5376 0.5226 0.5099 0.5011 0.4897 0.4847 0.4814 0.4784 0.4765

3.861 3.810 3.766 3.723 3.693 3.663 3.639 3.606 3.574 3.540 3.523

0.331 0.317 0.300 0.283 0.262 0.242 0.219 0.200 0.180 0.161 0.140

0.8730 0.8913 0.9097 0.9276 0.9450 0.9614 0.9771 0.9920 1.0056 1.0190 1.0334

−0.202 −0.425 −0.618 −0.779 −0.891 −0.882 −0.774 −0.526 −0.207

0.429 0.473 0.524 0.595 0.676 0.767 0.885 1.019 1.168 1.360 1.617

1224 1240 1252 1276 1292 1308 1320 1328 1328 1328 1336

764.6 729.7 701.3 662.1 633.9 608.0 587.4 571.6 563.9 556.5 542.1

0.5791 0.5657 0.5546 0.5389 0.5273 0.5164 0.5076 0.5007 0.4973 0.4940 0.4876

3.889 3.847 3.796 3.759 3.719 3.673 3.642 3.595 3.546 3.492 3.438

0.334 0.321 0.304 0.285 0.266 0.249 0.228 0.209 0.191 0.174 0.156

0.8670 0.8851 0.9034 0.9214 0.9389 0.9554 0.9713 0.9863 1.0002 1.0139 1.0288

−0.183 −0.387 −0.577 −0.734 −0.841 −0.834 −0.714 −0.476 −0.168

0.391 0.436 0.490 0.553 0.626 0.706 0.809 0.928 1.063 1.229 1.439

1216 1232 1244 1260 1280 1292 1304 1308 1308 1308 1320

780.1 744.4 715.3 683.6 650.1 627.0 605.5 592.6 584.4 573.0 557.9

0.5902 0.5765 0.5651 0.5525 0.5388 0.5291 0.5199 0.5144 0.5108 0.5058 0.4991

3.777 3.734 3.701 3.664 3.616 3.570 3.530 3.485 3.432 3.372 3.313

0.380 0.361 0.339 0.319 0.300 0.281 0.260 0.239 0.219 0.201 0.183

1.0228 1.0254 1.0277 1.0287 1.0318 1.0336 1.0349 1.0361 1.0369 1.0374 1.0378

−0.093 −0.172 −0.206 −0.298 −0.344 −0.341 −0.326 −0.257 −0.147

1.090 1.118 1.155 1.172 1.246 1.296 1.369 1.445 1.535 1.633 1.758

1320 1340 1348 1356 1372 1376 1384 1384 1384 1384 1352

561.1 543.1 535.5 528.7 514.9 511.0 504.5 503.9 503.5 503.2 527.1

0.4917 0.4837 0.4803 0.4772 0.4710 0.4692 0.4662 0.4659 0.4657 0.4656 0.4765

5.179 4.954 4.778 4.687 4.414 4.243 4.088 3.939 3.785 3.634 3.523

0.125 0.131 0.134 0.137 0.142 0.145 0.146 0.146 0.146 0.146 0.140

1.0178 1.0207 1.0231 1.0242 1.0275 1.0293 1.0306 1.0318 1.0326 1.0331 1.0334

−0.115 −0.199 −0.241 −0.347 −0.390 −0.382 −0.362 −0.287 −0.169

0.999 1.026 1.062 1.078 1.146 1.195 1.259 1.330 1.416 1.502 1.617

1312 1328 1336 1340 1352 1356 1360 1360 1360 1360 1336

570.8 555.5 547.6 543.8 532.4 528.4 524.6 524.0 523.6 523.3 542.1

0.5000 0.4936 0.4901 0.4884 0.4833 0.4814 0.4797 0.4794 0.4792 0.4791 0.4876

5.027 4.832 4.663 4.585 4.324 4.160 4.010 3.864 3.718 3.563 3.438

0.141 0.147 0.150 0.152 0.157 0.160 0.161 0.161 0.161 0.162 0.156

0.946 0.972 1.001 1.013 0.069 1.108 1.160 1.214 1.279

1304 1316 1324 1328 1336 1340 1340 1340 1340

581.3 568.9 560.6 556.6 548.0 543.8 543.0 542.3 541.8

0.5095 0.5040 0.5003 0.4985 0.4947 0.4927 0.4824 0.4921 0.4918

4.978 4.782 4.604 4.519 4.253 4.081 3.927 3.767 3.606

0.151 0.157 0.162 0.165 0.172 0.176 0.178 0.181 0.183

1.0116 1.0149 1.0176 1.0188 1.0223 1.0242 1.0256 1.0269 1.0279

−0.137 −0.237 −0.282 −0.388 −0.426 −0.413 −0.388 −0.318

M.V. Rathnam et al. / Journal of Molecular Liquids 187 (2013) 58–65

61

Table 2 (continued) x1

ρ/g cm−3

VE/cm3 mol−1

η/mPa s

u/ms−1

0.8402 1.0000

1.0286 1.0288

−0.206

1.348 1.439

1340 1320

Ethyl benzoate T = 303.15 K 0.0000 0.0786 0.1616 0.2448 0.3356 0.4336 0.5357 0.6386 0.7505 0.8709 1.0000 T = 308.15 K 0.0000 0.0786 0.1616 0.2448 0.3356 0.4336 0.5357 0.6386 0.7505 0.8709 1.0000 T = 313.15 K 0.0000 0.0786 0.1616 0.2448 0.3356 0.4336 0.5357 0.6386 0.7505 0.8709 1.0000

(1) + anisole (2)

Ethyl benzoate T = 303.15 K 0.0000 0.0939 0.1857 0.2804 0.3768 0.4748 0.5570 0.6781 0.7812 0.8898 1.0000 T = 308.15 K 0.0000 0.0939 0.1857 0.2804 0.3768 0.4748 0.5570 0.6781 0.7812 0.8898 1.0000 T = 313.15 0.0000 0.0939 0.1857 0.2804 0.3768 0.4748 0.5570 0.6781 0.7812 0.8898 1.0000

(1) + butyl vinyl ether (2)

KS/Tpa−1

Lf × 10−8 cm

πi × 106 Nm−2

Vf × 10−6 m3 mol−1

541.4 557.9

0.4917 0.4991

3.447 3.314

0.186 0.182

0.9853 0.9914 0.9976 1.0033 1.0089 1.0146 1.0198 1.0245 1.0291 1.0335 1.0378

−0.090 −0.192 −0.269 −0.315 −0.361 −0.356 −0.318 −0.247 −0.136

0.923 0.973 1.026 1.085 1.156 1.229 1.323 1.416 1.521 1.631 1.758

1388 1376 1368 1360 1352 1344 1344 1344 1344 1344 1352

524.6 530.8 533.9 537.3 540.9 544.5 542.0 539.7 537.5 535.5 527.1

0.4764 0.4791 0.4804 0.4818 0.4833 0.4848 0.4836 0.4825 0.4814 0.4804 0.4765

3.569 3.569 3.567 3.567 3.564 3.560 3.564 3.561 3.557 3.543 3.523

0.234 0.224 0.213 0.203 0.193 0.183 0.173 0.164 0.155 0.147 0.140

0.9792 0.9852 0.9913 0.9971 1.0028 1.0086 1.0140 1.0188 1.0237 1.0285 1.0334

−0.061 −0.133 −0.202 −0.239 −0.274 −0.270 −0.221 −0.164 −0.080

0.949 0.896 0.949 1.007 1.071 1.143 1.224 1.311 1.404 1.504 1.617

1368 1352 1344 1336 1328 1324 1324 1324 1324 1324 1336

542.7 552.5 556.0 559.7 563.5 564.0 561.4 559.0 556.7 554.4 542.1

0.4892 0.4891 0.4905 0.4920 0.4935 0.4936 0.4923 0.4911 0.4900 0.4888 0.4876

3.484 3.498 3.498 3.502 3.505 3.502 3.497 3.496 3.587 3.473 3.438

0.260 0.246 0.234 0.223 0.211 0.200 0.190 0.180 0.171 0.162 0.156

0.9728 0.9788 0.9848 0.9906 1.9966 1.0025 1.0081 1.0031 1.0185 1.0235 1.0288

−0.042 −0.082 −0.131 −0.181 −0.205 −0.202 −0.154 −0.110 −0.053

0.764 0.805 0.856 0.908 0.963 1.026 1.101 1.174 1.256 1.342 1.439

1348 1336 1324 1316 1308 1304 1304 1304 1304 1304 1320

561.5 572.4 579.3 582.9 586.5 586.6 583.4 580.5 577.5 574.6 557.9

0.5026 0.5011 0.5041 0.5056 0.5072 0.5072 0.5058 0.5046 0.5033 0.5020 0.4991

3.375 3.375 3.387 3.391 3.388 3.384 3.384 3.375 3.366 3.348 3.313

0.298 0.284 0.267 0.254 0.242 0.230 0.217 0.207 0.197 0.188 0.183

0.7743 0.8025 0.8301 0.8582 0.8859 0.9128 0.9343 0.9642 0.9882 1.0128 1.0378

−0.135 −0.357 −0.609 −0.807 −0.900 −0.885 −0.711 −0.453 −0.179

0.387 0.438 0.499 0.573 0.663 0.769 0.877 1.061 1.250 1.482 1.758

1084 1112 1144 1164 1188 1212 1230 1260 1276 1312 1352

1099.1 1007.7 920.5 860.0 799.8 745.8 707.5 653.3 621.5 577.1 527.1

0.6881 0.6589 0.6297 0.6087 0.5870 0.5668 0.5521 0.5305 0.5174 0.4986 0.4765

2.436 2.485 2.544 2.629 2.725 2.827 2.930 3.082 3.233 3.375 3.523

0.531 0.490 0.448 0.399 0.351 0.308 0.272 0.227 0.191 0.163 0.140

0.7686 0.7967 0.8243 0.8524 0.8802 0.9073 0.9289 0.9590 0.9832 1.0080 1.0334

−0.111 −0.325 −0.567 −0.767 −0.873 −0.857 −0.684 −0.427 −0.152

0.374 0.425 0.482 0.550 0.633 0.729 0.827 0.995 1.163 1.372 1.617

1072 1104 1136 1160 1184 1208 1224 1252 1268 1300 1336

1132.2 1022.4 933.5 871.8 810.4 755.3 718.6 665.2 632.6 587.0 542.1

0.7047 0.6721 0.6421 0.6184 0.5962 0.5756 0.5614 0.5402 0.5267 0.5074 0.4876

2.430 2.483 2.543 2.612 2.699 2.792 2.889 3.032 3.169 3.305 3.438

0.549 0.508 0.465 0.422 0.375 0.332 0.294 0.247 0.211 0.181 0.156

0.7637 0.7917 0.8192 0.8473 0.8751 0.9022 0.9238 0.9539 0.9782 1.0032 1.0288

−0.098 −0.300 −0.544 −0.745 −0.849 −0.828 −0.646 −0.394 −0.136

0.354 0.404 0.458 0.519 0.592 0.678 0.762 0.907 1.054 1.231 1.439

1060 1096 1128 1156 1176 1200 1216 1240 1256 1286 1320

1165.4 1051.5 959.4 883.3 826.5 769.7 732.1 681.8 648.1 602.7 557.9

0.7213 0.6852 0.6545 0.6280 0.6074 0.5862 0.5717 0.5517 0.5379 0.5188 0.4991

2.412 2.459 2.512 2.572 2.652 2.735 2.816 2.946 3.070 3.189 3.313

0.586 0.543 0.500 0.458 0.410 0.366 0.330 0.280 0.241 0.210 0.183

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Table 3 Derived parameters of Eq. (8) for various functions and standard deviation (σ) of the binary mixtures. Function

T/K

A0

A1

A2

σ

Ethyl benzoate (1) + tetrahydrofuran (2) 303.15 −3.6230 VE 308.15 −3.4478 313.15 −3.2389 Δη 303.15 −0.45360 308.15 −0.3358 313.15 −0.2632 303.15 −30.414 ΔKS 308.15 −29.179 313.15 −27.427 303.15 −0.1222 LfE 308.15 −0.1148 313.15 −0.1073 303.15 −0.2621 πEi 308.15 0.1585 313.15 0.1283 303.15 −0.0917 VEf 308.15 −0.0951 313.15 −0.0811

1.7408 1.7690 1.7839 0.0248 0.0014 0.0119 11.088 14.911 15.479 0.0386 0.0562 0.0577 0.1417 0.1152 0.0506 −0.0094 −0.0021 −0.0012

1.3668 1.6822 1.8619 −0.1400 −0.1461 −0.0600 6.7581 8.1520 6.5898 0.0298 0.0443 0.0332 −0.2369 −0.1313 −0.0137 0.0398 0.0376 0.0147

0.004 0.007 0.007 0.002 0.002 0.001 0.281 0.210 0.216 0.001 0.001 0.001 0.002 0.003 0.004 0.000 0.001 0.001

Ethyl benzoate (1) + 1,4-dioxane (2) 303.15 −1.3779 VE 308.15 −1.5425 313.15 −1.6575 Δη 303.15 −0.1451 308.15 −0.1208 313.15 −0.0784 303.15 −15.818 ΔKS 308.15 −12.590 313.15 −10.791 E 303.15 −0.0697 Lf 308.15 −0.0569 313.15 −0.0476 303.15 −1.2118 πEi 308.15 −1.0482 313.15 −1.0572 303.15 0.0559 VEf 308.15 0.0510 313.15 0.0498

0.2989 0.3838 0.4222 0.0598 0.0418 0.0155 −0.0948 0.7700 1.3406 −0.0114 0.0010 0.0069 0.3956 0.3462 0.3100 −0.0093 −0.0132 −0.0071

0.1482 0.0490 −0.3050 −0.0348 −0.0272 −0.0165 −10.068 −8.9603 −8.5333 −0.0413 −0.0421 −0.0383 −0.3690 −0.2017 −0.2460 0.0245 0.0210 0.0221

0.004 0.005 0.005 0.003 0.003 0.002 0.209 0.140 0.118 0.001 0.001 0.001 0.006 0.005 0.004 0.001 0.001 0.001

Ethyl benzoate (1) + anisole (2) 303.15 −1.4412 VE 308.15 −1.0848 313.15 −0.8045 Δη 303.15 −0.1990 308.15 −0.1760 313.15 −0.1052 303.15 6.6236 ΔKS 308.15 7.8762 313.15 9.8612 303.15 0.0287 LfE 308.15 0.0622 313.15 0.0686 303.15 0.0646 πEi 308.15 0.1552 313.15 0.1615 E 303.15 −0.0433 Vf 308.15 −0.0596 313.15 −0.0756

0.1133 0.1900 0.1400 0.0541 0.0614 0.0397 −0.7070 −1.5671 −1.7211 −0.0022 −0.0156 −0.0114 0.0725 0.0480 0.0520 −0.0023 0.0032 0.0070

0.2794 0.4794 0.5529 0.0485 0.0661 0.0104 0.0771 4.3958 6.6871 0.0042 0.0885 0.0927 0.0505 0.1217 0.0541 −0.0044 −0.0062 −0.0121

0.006 0.006 0.008 0.003 0.002 0.002 0.146 0.154 0.163 0.001 0.002 0.001 0.002 0.002 0.003 0.000 0.000 0.001

Ethyl benzoate (1) + butyl 303.15 VE 308.15 313.15 Δη 303.15 308.15 313.15 303.15 ΔKS 308.15 313.15 303.15 LfE 308.15 313.15 303.15 πEi 308.15 313.15

−0.0410 −0.0912 −0.0421 −0.2351 −0.2103 −0.1810 20.423 25.570 27.540 0.0604 0.0709 0.0854 0.2087 0.1698 0.1358

3.0712 3.3001 3.4422 −0.0070 0.0023 0.0226 2.2816 −7.2318 −5.8566 0.0158 0.0148 0.0017 0.0604 0.1939 0.1060

0.003 0.003 0.005 0.001 0.001 0.001 0.391 0.394 0.192 0.001 0.001 0.001 0.005 0.003 0.003

vinyl ether (2) −3.6236 −3.5037 −3.3934 −1.0844 −0.9461 −0.7758 −31.878 −36.855 −41.298 −0.0799 −0.0993 −0.1140 −0.4704 −0.4486 −0.4091

Table 3 (continued) Function

T/K

A0

A1

A2

σ

Ethyl benzoate (1) + butyl vinyl ether (2) VEf

303.15 308.15 313.15

−0.1564 −0.1323 −0.1172

−0.0954 −0.0905 −0.0811

0.0503 0.0187 −0.0050

0.001 0.001 0.001

x1 were graphically represented in Figs. 1–6. In all the plots, points represent the quantities calculated from Eqs. 2 and 7 while the smooth curves are drawn from the best fitted values calculated from Eq. 8 Fig. 1 shows the variation of the VE with x1 for the studied binary mixtures. The values of VE were found to be negative over the entire range of composition. The observed negative VE values suggest the presence of significant donor–acceptor interactions between the mixtures. Ethyl benzoate with its dipole moment (μ = 1.99) behaves as a normal polar liquid with dipole–dipole interactions. When ethyl benzoate is mixed with ether some of the bonds present in the pure component are broken and new bonds are formed. These effects mainly contribute VE to its sign and magnitude. It was observed that the variation of VE with x1 for the mixtures of tetrahydrofuran and butyl vinyl ether is almost similar, except a shift in minima. For ethyl benzoate + tetrahydrofuran the minima occurred at x1 = 0.4, whereas for ethyl benzoate + butyl vinyl ether maxima occurred at x1 = 0.5. Further it was observed that there is an effect of temperature on VE, as the negative VE values for ethyl benzoate + 1,4-dioxane increase with increase in temperature and for the remaining studied systems they decrease with increase in temperature systematically. Fig. 2 shows graphical variation of Δη with x1 for the binary mixtures of ethyl benzoate with ethers. The values of Δη were found to be negative over the entire range of composition for all the systems at studied temperatures. These negative values indicate weaker interactions [24] involving dispersion forces. These forces are dominant where the component molecules have different molecular sizes and shapes [25,26] and as a result the forces between pairs of unlike molecules are less than the forces between like molecules. The negative Δη values in our present study may indicate the inclusion of smaller molecules in the structure of larger molecules where there is no specific interaction between the components [27]. The Δη values increase in the following order Butyl vinyl ether b tetrahydrofuran b anisole b 1,4-dioxane. The

Fig. 1. Curves of excess volumes, VE versus mole fraction x1 for the binary mixtures. Ethyl benzoate + tetrahydrofuran at (□, 303.15; ◊, 308.15; Δ, 313.15) K. Ethyl benzoate + 1,4-dioxane at (O, 303.15; ж, , 308.15; __, 313.15) K. Ethyl benzoate + anisole at (×, 303.15; +, 308.15; ■, 313.15) K. Ethyl benzoate + butyl vinyl ether (▲, 303.15; ♦, 308.15; ●, 313.15) K.

M.V. Rathnam et al. / Journal of Molecular Liquids 187 (2013) 58–65

Fig. 2. Curves of deviation in viscosity, Δη Vs mole fraction for the binary mixtures. Ethyl benzoate + tetrahydrofuran at (□, 303.15; ◊, 308.15; Δ, 313.15) K. Ethyl benzoate + 1,4-dioxane at (×, 303.15; ж, , 308.15; __, 313.15) K. Ethyl benzoate + anisole at (O, 303.15; +, 308.15; ■, 313.15) K. Ethyl benzoate + butyl vinyl ether at (♦, 303.15; ▲,308.15; ●, 313.15) K.

effect of temperature on Δη was found to be systematic as the magnitude of negative Δη values decrease with an increase in temperature for all the mixtures studied. The effect of composition on ΔKs is shown in Fig. 3. It was observed that the ΔKs values for the system ethyl benzoate + anisole are positive, while for the remaining studied systems the ΔKs values are negative over the entire composition range. The positive ΔKs values suggest that the interactions between ethyl benzoate and anisole molecules are weaker as compared to the interactions between like molecules, while the negative ΔKs values indicate the presence of specific interactions.

Fig. 3. Curves of deviations in isentropic compressibilities, ΔKS Vs mole fraction for the binary mixtures ethyl benzoate + tetrahydrofuran at (□, 303.15; ◊, 308.15; Δ, 313.15) K. Ethyl benzoate + 1,4-dioxane (×, 303.15; ж, , 308.15; __, 313.15) K. Ethyl benzoate + anisole at (O, 303.15; +, 308.15; ■, 313.15) K. Ethyl benzoate + butyl vinyl ether (♦, 303.15; ▲, 308.15; ●, 313.15) K.

63

Fig. 4. Curves of excess intermolecular free length, LEf Vs mole fraction for the binary mixtures ethyl benzoate + tetrahydrofuran at (□, 303.15; ◊, 308.15; Δ, 313.15) K. Ethyl benzoate + 1,4-dioxane at (×, 303.15; ж, , 308.15; __, 313.15) K. Ethyl benzoate +anisole at (O, 303.15; +, 308.15; ■, 313.15) K. Ethyl benzoate + butyl vinyl ether (♦, 303.15; ▲, 308.15; ●, 313.15) K.

Like ΔKs the variation in excess intermolecular free length, LEf and excess internal pressure, πiE, with mole fraction as shown in Figs. 4 and 5 for the system ethyl benzoate + anisole shows positive deviations while the remaining systems show negative deviations. The negative values of LEf substantiate the fact that the specific interactions are being operative between the molecules of solvent and co-solvent in the mixture. Generally internal pressure increases with an increase in intermolecular attraction. However it was observed from Table 1 that the values of internal pressure for ethyl benzoate + butyl vinyl ether increase uniformly with an increase in the mole fraction of ethyl benzoate, suggesting that the strength of interactions increases with an increase in the concentration of ester component, while in case of other studied systems the internal

Fig. 5. Curves of excess internal pressure, πEi Vs mole fraction for the binary mixtures. Ethyl benzoate + tetrahydrofuran at (□, 303.15; ◊, 308.15; Δ, 313.15) K. Ethyl benzoate + 1,4-dioxane at (×, 303.15; ж, , 308.15; __, 313.15) K. Ethyl benzoate + anisole at (O, 303.15; +, 308.15; ■, 313.15) K. Ethyl benzoate + butyl vinyl ether (♦, 303.15; ▲, 308.15; ●, 313.15) K.

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M.V. Rathnam et al. / Journal of Molecular Liquids 187 (2013) 58–65

3.2.2. McAllister (3-body) model [23] McAllister 3-body equation is a cubic equation which can have a maximum, a minimum, or both for v as a function of x. The equation has only two adjustable parameters and is of the form lnv ¼ x31 lnv1 þ 3x21 x2 1nZ 12 þ 3x1 x22 lnZ 21 þ x2 lnv2 − ln½x1 þ x2 ðΜ 2 =Μ1 Þ ð13Þ þ3x21 x2 ln½f2 þ ðΜ 2 =Μ1 Þg=3 þ3x1 x22 ln½f1 þ 2ðM2=M1Þg=3þx23 lnðM2=M1Þ where Z12 and Z21 are the interaction parameters. McAllister (4-body) model is a quadratic equation having three interaction parameters. This model is mostly applied to the case of mixtures having large differences in their molecular size. The form of the equation applied to kinematic viscosity is as follows lnv ¼ x1 4 lnv1 þ 4x1 3 x2 lnv1112 þ 6x1 2 x2 2 lnv1122 þ4x1 x2 3 lnv2221 þ x2 4 lnv2 –ln½x1 þ ðx2 M 2 =M1 Þ ð14Þ

þ4x1 3 x2 ln½f3 þ ðM 2 =M1 Þg=4 2 2

þ6x1 x ln½f1 þ ðM 2 =M1 Þg=2

VEf

Fig. 6. Curves of excess free volume, Vs mole fraction for the binary mixtures of binary mixtures ethyl benzoate + tetrahydrofuran at (□, 303.15; ◊, 308.15; Δ, 313.15) K. Ethyl benzoate + 1,4-dioxane at (×, 303.15; ж, , 308.15; __, 313.15) K. Ethyl benzoate +anisole at (O, 303.15; +, 308.15; ■, 313.15) K. Ethyl benzoate + butyl vinyl ether (♦, 303.15; ▲, 308.15; ●, 313.15) K.

pressure either decreases or remains constant with the mole fraction of ester component. Fig. 6 shows the variation in excess free volume, VEf , with the mole fraction of ethyl benzoate x1. It was observed that for ethyl benzoate + 1,4-dioxane the VEf values show positive deviation, while the other systems show negative deviation over the entire composition range. The negative values of VEf indicate strong molecular interactions [28] suggesting that the mixtures have a tendency for closer packing and there is a decrease in free volume in intermediate composition due to strong heteromolecular interactions. 3.1. Correlation of viscosity models Models available in the literature for calculating the viscosities of liquid mixtures may be divided into two categories viz: a) correlative and b) predictive. Correlative models contain adjustable parameters whose values are determined from fitting those models to the experimental mixture data. Predictive models employ molecular properties for the prediction of the dependence of a physical property e.g. viscosity on composition. The predictive models can further be classified into either semi-theoretical or empirical. In our present study the two viscosity models viz. Katti–Chaudhri and McAllister's (3-body and 4-body) were subjected to testing. 3.1.1. Katti–Chaudhri [22] Katti and Chaudhri proposed an equation of the form: 1n η12 V 12 ¼ x1 1nη1 V 1 þ x2 1nη2 V 2 þ x1 x2 ðW visc =RT Þ

ð10Þ

where V12 is the molar volume of the mixture defined by equation V ¼ ðx1 Μ1 þ x2 Μ 2 Þ=ρ:

ð11Þ

Wvisc is an interaction parameter calculated at equimolar concentration for each system as E

W visc ¼ ΔG =x1 x2 :

ð12Þ

þ4x1 x2 3 ln½f1 þ ð3M 2 =M1 Þg=4 þ x2 4 lnðM2 =M 1 Þ where υ, υ1, and υ2 are the kinematic viscosities of binary mixtures and those of the pure components 1 and 2 respectively. υ1112, υ1122 and υ2221 are the model parameters which are obtained by non-linear regression. The correlating ability of Eqs (10), (13) and (14) was tested by calculating the standard percentage deviation σ(%) between the experimental and calculated viscosities as

σ ð% Þ ¼

 n
 o2 1=2 1=n  ka ˚ 100 nexp −ncal =nexp

ð15Þ

where, n, represents the number of data points in each set and, k, is the number of numerical coefficients in the equation. The interaction parameters and standard percentage deviations σ% of the studied models at 303.15, 308.15 and 313.15 K are presented in Table 4. The analysis of these results indicates that McAllister (4-body) with 3 adjustable parameters predicts the mixture viscosities more satisfactorily as compared to Katti–Chaudhri and McAllister (3-body) models. This is mainly attributed to the more number of adjustable parameters present in the equation. Table 4 Adjustable parameters and standard percentage deviations of viscosity models for binary liquid mixtures. T/K

Katti–Chaudhri McAllister (3-body) Wvisc

σ%

Z12

Z21

McAllister (4-body) σ%

v1112

v1122

v2221

σ%

Ethyl benzoate (1) 303.15 0.155 308.15 0.160 313.15 0.168

+ tetrahydrofuran (2) 0.06 −3.5431 −4.6217 0.01 0.07 −3.5379 −4.6155 0.01 0.09 −3.5326 −4.6089 0.01

4.876 4.745 4.615 0.009 4.882 4.750 4.622 0.009 4.888 4.755 4.629 0.009

Ethyl benzoate (1) 303.15 0.0034 308.15 0.0037 313.15 0.0036

+ 1,4-dioxane (2) 0.03 −3.6937 −4.7898 0.01 0.03 −3.6893 −4.7062 0.01 0.01 −3.6845 −4.7020 0.01

4.881 4.762 4.636 0.006 4.885 4.766 4.640 0.006 4.656 4.760 4.656 0.009

Ethyl benzoate (1) 303.15 0.0021 308.15 0.0029 313.15 0.0035

+ anisole (2) 0.05 −3.7999 −4.6876 0.003 4.911 4.853 4.778 0.005 0.03 −3.7941 −4.6813 0.003 4.917 4.859 4.785 0.006 0.03 −3.7886 −4.6746 0.004 4.865 4.791 4.795 0.006

Ethyl benzoate (1) 303.15 −0.0037 308.15 −0.0029 313.15 −0.0018

+ butyl vinyl ether (2) 0.08 −3.6995 −4.5574 0.01 0.05 −3.6940 −4.4506 0.01 0.04 −3.6886 −4.5445 0.01

4.952 4.910 4.900 0.008 4.958 4.915 4.907 0.008 4.964 4.920 4.914 0.008

M.V. Rathnam et al. / Journal of Molecular Liquids 187 (2013) 58–65

4. Conclusions Density, viscosity and speed of sound for binary mixtures of ethyl benzoate + tetrahydrofuran, + 1,4-dioxane, + anisole, and + butyl vinyl ether have been reported at 303.15, 308.15 and 313.15 K. The excess or deviation properties such as excess volume, V E, deviation in viscosity, Δη, deviation in isentropic compressibility, ΔKs, excess intermolecular free length, LEf , excess internal pressure, π Ei and excess free volume, VfE, were evaluated from the experimental data at the respective temperatures and discussed in terms of the interaction between the components of the mixtures. These excess or deviation properties were correlated by Redlich–Kister type polynomial equation to derive the coefficients and standard errors. Both, V E, and Δη, exhibit completely negative deviation for all the studied systems, while, ΔKs, LEf , and π Ei , exhibit positive deviations for binary mixture ethyl benzoate + anisole and the remaining studied systems exhibit negative deviations. Viscosity results were analysed using Katti– Chaudhri and McAllister's three body and four body models. From the analysis it was observed that McAllister four body model predicts mixture viscosities more satisfactorily. Acknowledgements One of the authors (M.V.R.) sincerely acknowledge UGC, New Delhi (India) for financial assistance through Major Research Project [No: 38-24/2009(SR)]. The authors also gratefully acknowledge the Hon'ble Editor-in-Chief of Journal of Molecular Liquids and the reviewers for their valuable suggestions. References [1] A. Ali, A.K. Nain, V.K. Sharma, S. Ahmad, Acoust. Lett. 24 (2000) 9–16. [2] V. Kannapan, R. Jaya Santhi, Indian J. Pure Appl. Phys. 43 (2005) 750–754.

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