# Studies on Excess Volume, Viscosity, and Speed of Sound of Binary Mixtures of Methyl Benzoate in Ethers atT=(303.15,308.15, and 313.15) K

Authors: M. V. Rathnam; Devappa R. Ambavadekar; M. Nandini
Journal: Journal of Thermodynamics
 (2013)

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## Abstract

Densities, viscosities, and speed of sound have been determined atT = (303.15, 308.15, and  313.15) K for the binary mixtures of methyl benzoate with tetrahydrofuran, 1,4-dioxane, anisole, and butyl vinyl ether over the entire range of composition. Using these measured values, excess volume VE, deviation in viscosities Δη, excess Gibb’s free energy of activation for viscous flow ΔG*E, and deviation in isentropic compressibility Δks have been calculated. These calculated binary data have been fitted to Redlich-Kister equation to determine the appropriate coefficients. The values of excess volume VE and deviation in viscosities Δη are negative over the entire range of composition for all the binary systems at the studied temperatures. The behavior of these parameters with composition of the mixture has been discussed in terms of molecular interactions between the components of liquids.


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## Body

## 1. Introduction

The excess or deviation properties of liquid-liquid mixtures are useful in several industrial applications owing to their influence upon the effectiveness of the operations. Nowadays, the determination of ultrasonic velocity and the related acoustical parameters derived from it has attracted the attention of several researchers. Much work has been done in solutions of polymers [1–3], pharmamaterials [4], electrolytes [5–7], and nonelectrolytes [8–10].Tetrahydrofuran is a polar(μ=1.75D), aprotic solvent. It’s main use is a precursor to polymers. It is also used as an industrial solvent for PVC and in varnishes. Dye carrier formulations based on methyl benzoate are useful in textile processing. Further methyl benzoate finds its primary uses as a perfume or flavouring agent and also used as a source of benzoyl radical. While ethers are excellent solvents, because they are relatively unreactive, yet they solvate a wide variety of compounds. Tetrahydrofuran, a cyclic ether which is one of the most polar simple ethers, is used as a solvent for polymers and also commercially used for the production of several compounds. Anisole, an aryl ether, is a major constituent of essential oil of anise seed.In view of the abovementioned significances, these solvents are chosen with an aim to investigate the effect of the presence of two lone pairs of electrons on the oxygen atom of ether, when it is mixed with methyl benzoate. Moreover, it would be interesting to know the behavior of ether in an environment of aromatic ester molecules. The main objective of the present study is to determine the densityρ, viscosity η, and speed of sound u for the binary mixtures formed by the methyl benzoate with ether compounds.In our earlier papers [11–13], we have reported some data on thermodynamic, transport, acoustical, and optical properties on mixtures of methyl benzoate with hydrocarbons and ketones and analysed the data in terms of molecular interactions. Several authors have also published density, viscosity, and speed of sound data [14–20] of binary mixtures of methyl benzoate with different types of organic solvents. In the present study, we report the results of density ρ, viscosity η, and speed of sound u for the binary mixtures of methyl benzoate with ethers, namely, tetrahydrofuran, 1,4-dioxane, anisole, and butyl vinyl ether measured at (303.15, 308.15, and 313.15) K over the entire mixture composition. To the best of our knowledge, such data on the abovementioned mixtures are not available in the earlier literature. Using the experimental data of  ρ,  η, and u, various parameters such as excess volume VE, deviation in viscosity Δη, excess Gibb’s free energy of activation for viscous flow ΔG*E, and deviation in isentropic compressibility Δks were determined. These computed data are discussed to study the nature of behaviors between the components of the mixtures.


## 2. Experimental

### 2.1. Materials

Methyl benzoate (Fluka AG >0.996), tetrahydrofuran, 1,4-dioxane, anisole, and butyl vinyl ether (all Sigma-Aldrich, AR grade) of mass purity >0.997 were used without further purification. These chemicals were kept over molecular sieves for several days before use. The mass fraction purities as determined by gas chromatography (HP 8610) using FID were as follows: methyl benzoate (>0.996), tetrahydrofuran, (>0.996), 1,4-dioxane, (>0.998), anisole, (>0.998), and butyl vinyl ether (>0.997). The purity of the samples was further checked by comparing the measured densityρ and viscosity η with the literature values [18–28] as shown in Table 1.Table 1
Comparison  of  experimental  densityρ and viscosity η  of pure liquids with the  literature values at (303.15, 308.15, and 313.15) K.
Liquid
T/K
ρ/g·cm−3
η/mPa·s
Exptl.
Lit.
Exptl.
Lit.
Methyl benzoate
303.15
1.0785
1.0788 [18]
1.678
1.673 [28]
1.0790 [22]
1.656 [18]
308.15
1.0743
1.0740 [18]
1.517
1.510 [18]
1.0741 [19]
1.504 [20]
1.07399 [20]
1.510 [21]
313.15
1.0696
1.0690 [27]
1.373
1.365 [27]
Tetrahydrofuran
303.15
0.8787
0.8771 [22]
0.439
308.15
0.8730
0.87214 [22]
0.429
313.15
0.8669
0.86719 [22]
0.390
1,4-Dioxane
303.15
1.0227
1.02271 [23]
1.090
1.102 [23]
1.095 [24]
308.15
1.0178
1.0172 [24]
0.999
1.008 [24]
313.15
1.0116
1.01132 [23]
0.946
0.946 [23]
Anisole
303.15
0.9853
0.984374 [25]
0.923
0.931 [25]
308.15
0.9792
0.9788 [26]
0.849
0.849 [26]
313.15
0.9728
0.764
Butyl vinyl ether
303.15
0.7741
0.387
308.15
0.7682
0.365
313.15
0.7633
0.354


### 2.2. Methods

Binary mixtures were prepared by mass in airtight ground stoppered bottles. Mass measurements accurate to ±0.01 mg were made on a digital electronic balance (Mettler AE 240, Switzerland). The resulting uncertainty in mole fraction was estimated to be less than ±0.0001. Each mixture was immediately used after it was well mixed by shaking. The densities of the pure and their binary mixtures were determined by using an Anton Paar density meter (DMA 4100). The uncertainty in the density measurements was found to be less than ±0.0004 g·cm−3.Viscosities were determined using an Ubbelohde viscometer with an uncertainty of ±0.008 mPa.s. The detailed method of measurement of viscosity has been reported earlier [11]. The speeds of sound were measured with a single crystal variable path interferometer (Mittal Enterprises, New Delhi, India) at an operating frequency of 2 MHz that had been calibrated with double distilled water and benzene. The uncertainty in speed of sound was estimated to be ±1 m·s−1.


## 2.1. Materials

Methyl benzoate (Fluka AG >0.996), tetrahydrofuran, 1,4-dioxane, anisole, and butyl vinyl ether (all Sigma-Aldrich, AR grade) of mass purity >0.997 were used without further purification. These chemicals were kept over molecular sieves for several days before use. The mass fraction purities as determined by gas chromatography (HP 8610) using FID were as follows: methyl benzoate (>0.996), tetrahydrofuran, (>0.996), 1,4-dioxane, (>0.998), anisole, (>0.998), and butyl vinyl ether (>0.997). The purity of the samples was further checked by comparing the measured densityρ and viscosity η with the literature values [18–28] as shown in Table 1.Table 1
Comparison  of  experimental  densityρ and viscosity η  of pure liquids with the  literature values at (303.15, 308.15, and 313.15) K.
Liquid
T/K
ρ/g·cm−3
η/mPa·s
Exptl.
Lit.
Exptl.
Lit.
Methyl benzoate
303.15
1.0785
1.0788 [18]
1.678
1.673 [28]
1.0790 [22]
1.656 [18]
308.15
1.0743
1.0740 [18]
1.517
1.510 [18]
1.0741 [19]
1.504 [20]
1.07399 [20]
1.510 [21]
313.15
1.0696
1.0690 [27]
1.373
1.365 [27]
Tetrahydrofuran
303.15
0.8787
0.8771 [22]
0.439
308.15
0.8730
0.87214 [22]
0.429
313.15
0.8669
0.86719 [22]
0.390
1,4-Dioxane
303.15
1.0227
1.02271 [23]
1.090
1.102 [23]
1.095 [24]
308.15
1.0178
1.0172 [24]
0.999
1.008 [24]
313.15
1.0116
1.01132 [23]
0.946
0.946 [23]
Anisole
303.15
0.9853
0.984374 [25]
0.923
0.931 [25]
308.15
0.9792
0.9788 [26]
0.849
0.849 [26]
313.15
0.9728
0.764
Butyl vinyl ether
303.15
0.7741
0.387
308.15
0.7682
0.365
313.15
0.7633
0.354


## 2.2. Methods

Binary mixtures were prepared by mass in airtight ground stoppered bottles. Mass measurements accurate to ±0.01 mg were made on a digital electronic balance (Mettler AE 240, Switzerland). The resulting uncertainty in mole fraction was estimated to be less than ±0.0001. Each mixture was immediately used after it was well mixed by shaking. The densities of the pure and their binary mixtures were determined by using an Anton Paar density meter (DMA 4100). The uncertainty in the density measurements was found to be less than ±0.0004 g·cm−3.Viscosities were determined using an Ubbelohde viscometer with an uncertainty of ±0.008 mPa.s. The detailed method of measurement of viscosity has been reported earlier [11]. The speeds of sound were measured with a single crystal variable path interferometer (Mittal Enterprises, New Delhi, India) at an operating frequency of 2 MHz that had been calibrated with double distilled water and benzene. The uncertainty in speed of sound was estimated to be ±1 m·s−1.


## 3. Results and Discussion

The experimental values of densitiesρ, excess volumes VE, viscosities η, speeds of sound u,   and isentropic compressibility ks of the binary mixtures of methyl benzoate with tetrahydrofuran, 1,4-dioxane, anisole, and butyl vinyl ether at temperatures 303.15, 308.15, and 313.15 K are listed in Table 2.Table 2
Values of   densityρ, excess volume VE, viscosity η, speeds of sound u, and isentropic compressibility
ks
for the binary  liquid   mixtures.
x
1
ρ/g·cm−3
V
E/cm3·mol−1
η/mPa·s
u/m·s−1
k
s/Tpa−1
Methyl benzoate (1) + tetrahydrofuran (2)
T
=
303.15 K
0.0689
0.9020
-
0.261
0.496
1260
698
0.1417
0.9246
-
0.496
0.562
1272
669
0.2202
0.9468
-
0.699
0.638
1284
641
0.3030
0.9680
-
0.858
0.727
1296
615
0.3932
0.9885
-
0.943
0.829
1308
591
0.4930
1.0084
-
0.938
0.951
1320
569
0.6018
1.0272
-
0.822
1.096
1332
549
0.7225
1.0452
-
0.590
1.262
1344
530
0.8535
1.0623
-
0.277
1.446
1356
512
T
=
308.15 K
0.0689
0.8964
-
0.269
0.484
1232
735
0.1417
0.9192
-
0.510
0.546
1236
712
0.2202
0.9413
-
0.719
0.616
1244
686
0.3030
0.9627
-
0.882
0.699
1256
659
0.3932
0.9833
-
0.969
0.790
1268
633
0.4930
1.0033
-
0.964
0.904
1284
605
0.6018
1.0222
-
0.847
1.032
1300
679
0.7225
1.0403
-
0.612
1.181
1316
555
0.8535
1.0575
-
0.294
1.343
1336
530
T
=
313.15 K
0.0689
0.8905
-
0.283
0.443
1216
759
0.1417
0.9134
-
0.538
0.505
1220
736
0.2202
0.9358
-
0.749
0.567
1228
709
0.3030
0.9572
-
0.913
0.641
1240
679
0.3932
0.9779
-
0.999
0.729
1252
652
0.4930
0.9980
-
0.990
0.830
1268
623
0.6018
1.0171
-
0.877
0.943
1284
596
0.7225
1.0354
-
0.645
1.078
1300
572
0.8535
1.0527
-
0.317
1.220
1320
545
Methyl benzoate (1) + 1,4-dioxane (2)
T
=
303.15 K
0.0898
1.0307
-
0.059
1.130
1328
550
0.1468
1.0355
-
0.105
1.157
1336
541
0.2280
1.0421
-
0.185
1.198
1344
531
0.3145
1.0485
-
0.254
1.244
1352
521
0.4054
1.0543
-
0.281
1.293
1360
513
0.5056
1.0599
-
0.278
1.352
1368
504
0.6161
1.0653
-
0.242
1.418
1372
499
0.7316
1.0701
-
0.161
1.491
1372
496
0.8597
1.0749
-
0.062
1.573
1372
494
T
=
308.15 K
0.0898
1.0261
-
0.093
1.038
1324
556
0.1468
1.0311
-
0.157
1.066
1332
547
0.2280
1.0377
-
0.237
1.106
1340
537
0.3145
1.0440
-
0.297
1.147
1348
530
0.4054
1.0499
-
0.333
1.192
1352
521
0.5056
1.0555
-
0.329
1.246
1356
515
0.6161
1.0608
-
0.282
1.308
1360
510
0.7316
1.0655
-
0.189
1.376
1360
507
0.8597
1.0702
-
0.077
1.449
1360
505
T
=
313.15 K
0.0898
1.0205
-
0.132
0.984
1320
562
0.1468
1.0257
-
0.207
1.006
1328
553
0.2280
1.0326
-
0.304
1.040
1336
543
0.3145
1.0390
-
0.363
1.075
1340
536
0.4054
1.0450
-
0.398
1.110
1348
527
0.5056
1.0507
-
0.392
1.157
1352
521
0.6161
1.0560
-
0.331
1.208
1356
515
0.7316
1.0608
-
0.234
1.263
1356
513
0.8597
1.0655
-
0.106
1.324
1356
510
Methyl benzoate (1) + Anisole (2)
T
=
303.15 K
0.0860
0.9950
-
0.052
0.974
1388
522
0.1821
1.0056
-
0.113
1.038
1380
522
0.2756
1.0157
-
0.179
1.101
1372
523
0.3978
1.0282
-
0.229
1.187
1368
520
0.4637
1.0347
-
0.248
1.234
1368
516
0.5659
1.0442
-
0.238
1.307
1368
512
0.6701
1.0534
-
0.202
1.391
1368
507
0.7776
1.0624
-
0.140
1.480
1368
503
0.8850
1.0710
-
0.063
1.572
1368
499
T
=
308.15 K
0.0860
0.9891
-
0.062
0.894
1368
540
0.1821
1.0000
-
0.145
0.949
1356
544
0.2756
1.0102
-
0.209
1.007
1352
542
0.3978
1.0229
-
0.264
1.086
1348
538
0.4637
1.0295
-
0.285
1.129
1348
535
0.5659
1.0392
-
0.282
1.195
1348
530
0.6701
1.0485
-
0.242
1.272
1348
525
0.7776
1.0576
-
0.175
1.355
1348
520
0.8850
1.0663
-
0.093
1.439
1348
516
T
=
313.15 K
0.0860
0.9830
-
0.082
0.800
1356
553
0.1821
0.9941
-
0.170
0.850
1344
557
0.2756
1.0045
-
0.241
0.902
1340
554
0.3978
1.0174
-
0.297
0.972
1336
551
0.4637
1.0241
-
0.317
1.012
1336
547
0.5659
1.0340
-
0.318
1.074
1336
541
0.6701
1.0435
-
0.282
1.144
1336
537
0.7776
1.0528
-
0.218
1.220
1336
532
0.8850
1.0616
-
0.127
1.301
1336
528
Methyl benzoate (1) + Butyl vinyl ether (2)
T
=
303.15 K
0.1026
0.8056
-
0.108
0.437
1104
1019
0.2055
0.8375
-
0.260
0.497
1128
938
0.3060
0.8690
-
0.423
0.571
1152
867
0.4047
0.8999
-
0.544
0.657
1176
804
0.5057
0.9313
-
0.605
0.761
1204
741
0.6065
0.9623
-
0.596
0.891
1232
685
0.7061
0.9926
-
0.524
1.038
1260
635
0.8034
1.0218
-
0.388
1.205
1292
586
0.9021
1.0511
-
0.201
1.422
1328
540
T
=
308.15 K
0.1026
0.8001
-
0.141
0.421
1092
1048
0.2055
0.8322
-
0.320
0.478
1116
965
0.3060
0.8637
-
0.476
0.546
1136
891
0.4047
0.8947
-
0.602
0.657
1160
825
0.5057
0.9261
-
0.651
0.626
1188
760
0.6065
0.9572
-
0.639
0.720
1216
702
0.7061
0.9875
-
0.550
0.974
1248
650
0.8034
1.0168
-
0.408
1.124
1280
600
0.9021
1.0462
-
0.212
1.319
1316
552
T
=
313.15 K
0.1026
0.7954
-
0.182
0.400
1084
1070
0.2055
0.8275
-
0.367
0.452
1108
984
0.3060
0.8591
-
0.541
0.515
1132
908
0.4047
0.8901
-
0.667
0.585
1156
841
0.5057
0.9215
-
0.713
0.671
1184
774
0.6065
0.9526
-
0.697
0.778
1212
715
0.7061
0.9829
-
0.601
0.897
1244
657
0.8034
1.0121
-
0.439
1.034
1276
607
0.9021
1.0414
-
0.221
1.205
1308
561The excess volumeVE of the mixtures was deduced from the measured densities using the following relation:
(1)VE=(x1M1+x2M2)ρ12-(x1M1ρ1+x2M2ρ2),
where x, M, and ρ are the mole fraction, molar mass, and density, respectively, of pure components 1 and 2. ρ12 is the density of the liquid mixture. The Gibb’s free energy of activation for viscous flow ΔG*E was calculated from the viscosity data using the following relation:
(2)ΔG*E=RT[ln(ηv)-{x1ln(η1v1)+x2ln(η2v2)}],
where v=(x1M1/ρ1+x2M2)/ρ12 is the molar volume of the mixture and v1 and v2 are the molar volumes of the pure components.The isentropic compressibilitiesks were calculated from the densities ρ and speeds of sound u using the Newton-Laplace equation:
(3)ks=1u2ρ.
The deviation in viscosity Δη and deviation in isentropic compressibility Δks were calculated using the general equation:
(4)ΔY=Ym-x1Y1-x2Y2,
where ΔY is the deviation 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. The results of these excess or deviation properties were fitted by the method of least squares to the Redlich-Kister [29] polynomial type equation:
(5)Y=x1x2∑j=1paj-1(x1-x2)j-1,
where Y is VE, Δη, ΔG*E, or Δks and x1 and x2 are the mole fractions of pure components 1 and 2, respectively. aj-1 is the polynomial coefficient, and p is the polynomial degree. The degree of (5) was optimised by applying the F-test. The correlated results are shown in Table 3 in which the tabulated standard deviation σ was calculated using the following relation:
(6)σ=[∑(yexpE-ycalE)2(n-J)]0.5,
where n is the number of data points and j is the number of coefficients. The subscripts exp and cal denote experimental and calculated values, respectively.Table 3
Derived parameters of  excess functions by Redlich-Kister equation   and standard deviationsσ  of  binary liquid mixtures.
Function
T/K
a
0
a
1
a
2
a
3
σ
Methyl benzoate (1) + tetrahydrofuran (2)
V
E
303.15
-
3.7342
1.2905
1.1561
—
0.003
308.15
-
3.8390
1.2879
1.1173
—
0.003
313.15
-
3.9542
1.2921
1.9336
—
0.004
Δ
η
303.15
-
0.3703
0.0783
-
0.0054
—
0.002
308.15
-
0.2820
0.0762
-
0.0017
—
0.002
313.15
-
0.2206
0.0052
-
0.0013
—
0.001
Δ
G
*
E
303.15
1303.56
9.2800
-
47.1207
-
173.82
2.5
308.15
1332.27
-
4.3204
-
21.9964
-
216.76
3.3
313.15
1442.68
-
177.56
50.2305
-
79.613
3.8
Δ
k
s
303.15
-
17.457
7.2762
-
0.2584
1.4106
0.008
308.15
-
11.729
-
0.0066
3.5145
-
0.134
0.093
313.15
-
11.726
0.5719
4.7747
1.1539
0.090
Methyl benzoate (1) + 1,4-dioxane (2)
V
E
303.15
-
1.144
0.290
0.846
—
0.002
308.15
-
1.326
0.425
0.753
—
0.002
313.15
-
1.568
0.552
0.575
—
0.003
Δ
η
303.15
-
0.122
0.018
-
0.011
—
0.001
308.15
-
0.096
0.007
0.009
—
0.001
313.15
-
0.062
0.019
0.045
—
0.001
Δ
G
*
E
303.15
152.594
48.243
-
4.7463
-
34.315
0.7
308.15
191.571
23.232
37.394
-
27.738
2.8
313.15
201.888
29.749
100.81
-
116.35
2.4
Δ
k
s
303.15
-
8.7386
1.8216
3.7965
-
1.7238
0.094
308.15
-
9.2275
2.7930
-
0.9078
-
0.8437
0.044
313.15
-
11.303
2.1793
-
5.0991
-
0.8657
0.048
Methyl benzoate (1) + anisole (2)
V
E
303.15
-
0.9866
0.2637
0.5566
—
0.003
308.15
-
1.1427
-
0.0217
0.4368
—
0.003
313.15
-
1.2778
-
0.0899
0.2005
—
0.002
Δ
η
303.15
-
0.1440
0.0055
0.0234
—
0.002
308.15
-
0.1774
-
0.0067
-
0.0351
—
0.001
313.15
-
0.1602
-
0.0069
-
0.0270
—
0.002
Δ
G
*
E
303.15
177.724
-
46.913
99.649
70.211
2.2
308.15
116.959
-
70.397
12.737
80.252
2.5
313.15
56.636
-
50.389
-
50.388
63.520
1.2
Δ
k
s
303.15
3.5076
-
3.8057
0.9701
5.8130
0.036
308.15
4.7056
-
4.2092
5.0184
4.5773
0.053
313.15
5.3764
-
4.7277
6.5667
2.5075
0.050
Methyl benzoate (1) + butyl vinyl ether (2)
V
E
303.15
-
2.4161
-
0.7060
1.0922
—
0.004
308.15
-
2.6110
-
0.5335
0.9973
—
0.004
313.15
-
2.8690
-
0.4280
0.9846
—
0.005
Δ
η
303.15
-
1.0856
-
0.3096
-
0.1033
—
0.002
308.15
-
0.9534
-
0.2594
-
0.0654
—
0.003
313.15
-
0.8261
-
0.2221
-
0.0264
—
0.003
Δ
G
*
E
303.15
-
663.33
174.93
-
102.07
-
27.064
5.8
308.15
-
627.07
153.92
-
43.740
-
3.6493
7.2
313.15
-
596.84
106.49
131.85
-
19.948
5.7
Δ
k
s
303.15
-
20.411
5.1677
5.1277
-
1.1243
0.080
308.15
-
22.018
5.1564
3.8155
-
3.0159
0.085
313.15
-
25.224
3.8500
-
3.2901
2.8527
0.072The variations of excess volumeVE with mole fraction x1 of methyl benzoate at the studied temperatures for the binary mixtures are displayed in Figure 1. It is observed that all the studied systems exhibit negative deviations. The VE data for different components of the mixtures vary in the sequence:tetrahydrofuran > butyl vinyl ether > 1,4-dioxane > anisoleThe effect of temperature on VE as displayed in Figure 1 is quite significant, as the negative VE values increase with increase in temperature. The behavior of VE can be explained by considering the type of component molecules in pure state and in mixture. In the present case, the negative VE values may be attributed to the differences in the dielectric constants of the components. The dielectric constants of methyl benzoate, tetrahydrofuran, 1,4-dioxane, anisole, and butyl vinyl ether are ϵ=6.02,7.261,2.209,4.33,3.9, respectively. Further, there is a possibility of electron donor-acceptor type or charge transfer interactions [30] between the highly electronegative oxygen of ether and the π-electron of ring of aromatic ester molecule resulting in negative VE values. The less negative VE values in case of methyl benzoate + anisole may be due to the presence of methyl (–CH3) group in anisole. This observation suggests that with an increase in methyl group in mixture, the donor-acceptor interactions between the unlike molecules tend to decrease.Figure 1
Curves of excess volumes (VE) versus mole fraction for the binary mixtures of methyl benzoate + tetrahydrofuran at (□, 303.15;  ◊, 308.15; Δ, 313.15) K, methyl benzoate + 1,4-dioxane at (×, 303.15;  *, 308.15; —, 313.15)  K, methyl benzoate + anisole at  (O, 303.15;  +, 308.15;  ■, 313.15) K, and methyl benzoate + butyl vinyl ether at (◆, 303.15; ▲, 308.15; ●, 313.15) K.The results ofΔη as displayed in the Figure 2 are all negative over the entire range of composition and the magnitude values of Δη vary according to the following sequence: butyl vinyl ether > tetrahydrofuran > anisole > 1,4-dioxaneIt is observed that negative values of Δη decrease with increase in the temperature indicating the effect of temperature on Δη. Fort and Moore [31] observed that the negative Δη values indicate the dispersion forces without involving the formation of any hetero-molecular complexes. A perusal of Figures 1 and 2 reveals that both VE and Δη exhibit the negative deviations over the entire range of composition; however, the magnitude values of the studied mixtures follow a different sequence. This type of behavior supports the observation of Rastogi et al. [32] and Kaulgud [33], suggesting that the strength of specific or dispersion forces is not the only factor influencing the Δη, but the molecular size and shape of the components are also equally important.Figure 2
Curves of deviation in viscosity (Δη) versus mole fraction for the binary mixtures of methyl benzoate + tetrahydrofuran at (□, 303.15;  ◊, 308.15; Δ, 313.15) K, methyl benzoate + 1,4-dioxane at (×, 303.15;  *, 308.15; —, 313.15)  K, and methyl benzoate + anisole at  (O, 303.15;  +, 308.15;  ■, 313.15) K.The dependence ofΔG*E on the mole fraction is shown in Figure 3, where it was observed that ΔG*E is positive for mixtures of methyl benzoate with tetrahydrofuran, 1,4-dioxane, and anisole, whereas for mixtures of methyl benzoate + butyl vinyl ether, the values of ΔG*E are negative over the entire range of composition. The positive ΔG*E values may be an indicative of specific interactions [31, 34, 35] and the negative ΔG*E values indicate the presence of dispersive forces in these mixtures.Figure 3
Curves of excess Gibb’s free energy of activation of viscous flow (ΔG*E) versus mole fraction for the binary mixtures of methyl benzoate + tetrahydrofuran at (□, 303.15; ◊, 308.15; Δ, 313.15) K, methyl benzoate + 1,4-dioxane at (×, 303.15; *, 308.15; —, 313.15) K, methyl benzoate + anisole at  (O, 303.15;  +, 308.15; ■, 313.15) K, and methyl benzoate + Butyl vinyl ether at (◆, 303.15; ▲, 308.15; ●, 313.15) K.The plots ofΔks, as displayed in Figure 4, show that  for methyl benzoate with tetrahydrofuran, 1,4-dioxane, and butyl vinyl ether, the values of Δks exhibit negative deviation over the entire range of mixture composition; while for methyl benzoate + anisole, the values of Δks exhibit positive deviations. The positive Δks values are a sign of weak interaction between component molecules, which may be attributed to the mutual disruption in molecules associated with pure liquids. These positive Δks values are accompanied by a decrease in sound velocity over the entire range of composition of ester. The negative values of Δks may be attributed to the formation of weak bonds [36–38] by dipole-induced dipole interaction between unlike molecules and the geometrical fitting of component molecules in to each other’s structure.Figure 4
Curves of deviation in isentropic compressibility (Δks) versus mole fraction for the         binary mixture of methyl benzoate + tetrahydrofuran at (□, 303.15; ◊, 308.15; Δ, 313.15) K, methyl benzoate + 1,4-dioxane at (×, 303.15; *, 308.15; —, 313.15) K, methyl benzoate + anisole at (O, 303.15; +, 308.15; ■, 313.15) K, and methyl benzoate + Butyl vinyl ether at (◆, 303.15; ▲, 308.15; ●, 313.15) K.


## 4. Conclusions

The densitiesρ, excess volumes VE, viscosities η, speeds of sound u, and data of binary mixtures methyl benzoate with tetrahydrofuran, 1,4-dioxane, anisole, and butyl vinyl ether have been reported at (303.15, 308.15 and 313.15) K. The excess molar volumes VE, deviation in viscosity Δη, excess Gibb’s free energies of activation for viscous flow ΔG*E, and deviation in isentropic compressibility Δks were evaluated using the experimental data of ρ, η, and u and discussed in terms of the interactions between the components of the mixtures. Both VE and Δη  exhibit negative deviations, while ΔG*E and Δks exhibit both positive and negative deviations. It is concluded that the negative VE may be attributed to the differences in the dielectric constants of the components and the possibility of the electron donor-acceptor type or charge transfer interactions between the electronegative oxygen of ether and the π-electrons of aromatic ester resulting into contraction in volumes.



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*Source: 413878-2013-08-26.xml*