# Thermodynamic and Acoustic Study on Molecular Interactions in Certain Binary Liquid Systems Involving Ethyl Benzoate

Authors: B. Nagarjun; A. V. Sarma; G. V. Rama Rao; C. Rambabu
Journal: Journal of Thermodynamics
 (2013)

---

## Abstract

Speeds of sound and density for binary mixtures of ethyl benzoate (EB) with N,N-dimethylformamide (NNDMF), N,N-dimethyl acetamide (NNDMAc), and N,N-dimethylaniline (NNDMA) were measured as a function of mole fraction at temperatures 303.15, 308.15 K, 313.15 K, and 318.15 K and atmospheric pressure. From the experimental data, adiabatic compressibility (βad), intermolecular free length (Lf), and molar volume (V) have been computed. The excess values of the above parameters were also evaluated and discussed in light of molecular interactions. Deviation in adiabatic compressibilities and excess intermolecular free length (LfE) are found to be negative over the molefraction of ethyl benzoate indicating the presence of strong interactions between the molecules. The negative excess molar volume VE values are attributed to strong dipole-dipole interactions between unlike molecules in the mixtures. The binary data of Δβad, VE, and LfE were correlated as a function of molefraction by using the Redlich-Kister equation.


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## Body

## 1. Introduction

The thermophysical study of esters is of increasing interest due to their wide range in flavouring, perfumery, artificial essences, and cosmetics. Esters are also important solvents in pharmaceutical, paint, and plastic industries [1]. Recently, interest in the study of liquid mixtures containing esters as one of the components [2–5] has increased. These studies are of great significance because one can get information regarding structural changes that occur in pure ester because of mixing.Among the different types of esters, ethyl benzoate (aromatic ester) is a polar solvent (μ=1.8D) and is not a strongly associated liquid. On the other hand, NNDMF, to some extent, is associated by means of dipole-dipole interactions. Significant structural effects are absent due to the lack of hydrogen bonds. Therefore, it acts as an aprotic protophilic solvent [6]. NNDMAc is a dipolar aprotic solvent and is moderately structured [7]. The N,N-dialkylamides have no significant intermolecular hydrogen bonding capability but are highly polar with high percentage of ionic character, making oxygen of C=O group strongly negative [8]. NNDMA is a unassociated liquid [9]. The interactions of ethyl benzoate with N,N-dialkylamides and N,N-dimethylaniline are important to enable analysis of their dissimilar geometric structures on mixture properties.Rao [10] calculated the excess isentropic compressibilities for the binary mixtures of N,N-dimethylformamide and N,N-dimethylacetamide and various normal and branched esters. The negative excess values are attributed to the presence of n-n interactions between unlike molecules. Aminabhavi et al. [11] studied the physicochemical behavior of binary mixtures of ethyl benzoate with diethylene glycol and dimethyl ether. Rathnam et al. [12] reported the densities, viscosities, and refractive indices of ethyl benzoate with o-xylene, m-xylene, p-xylene, and ethyl benzene. Lien et al. [13] have measured the excess molar enthalpies of the binary mixture of ethyl benzoate with 1-Octanol at 298.15 K. Joshi et al. [14] measured the densities and viscosities of the binary mixture of bromoform with ethyl benzoate.We report herein the experimental values of densities and ultrasonic velocities of mixtures of ethyl benzoate with NNDMF, NNDMAc, and NNDMA at temperatures 303.15, 308.15, 313.15, and 318.15 K covering the whole miscibility range to enable analysis of the effect of their dissimilar geometric structures on the mixture properties. The non-rectilinear behavior of ultrasonic velocity, compressibility, and other thermodynamic parameters of liquid mixtures reveal the strength of interactions. To get additional information about the nature and strength of molecular interactions, other parameters such as free length, adiabatic compressibility, and their excess parameters have been calculated in the liquid mixtures. These results were correlated with the Redlich-Kister polynomial equation [15] to derive the coefficients and standard deviation.


## 2. Materials and Experimental Details

Ethyl benzoate (SD Fine Chemicals, purity > 99%) was used without any further treatment. NNDMF, NNDMAc, and NNDMA were purchased from SD Fine or Merck and were purified by the recommended methods [16, 17]. Further, the purities were ascertained from their ultrasonic speed and density values at 303.15 K which agreed with the literature values (Table 1).Table 1
Comparison of experimental velocities and  densities  of pure  liquids with the literature values at 303.15 K.
Component
U (m/s)
ρ
×
10
3 (kg·m−3)
Expt
Lit
Expt
Lit
Ethyl benzoate
1347.00
1346.50a
1.0456
1.0455a
N,N dimethyl formamide
1438.53
1438.32b
0.9392
0.9393b
N,N dimethyl acetamide
1438.00
1435.55b
0.9319
0.9317b
N,N dimethyl aniline
1470.50
1470.00c
0.9482
0.94815d
aData taken from [18]. bData taken from [19]. cData taken from [20]. dData taken from [21].Mixtures were prepared by mixing appropriate volumes of liquids in airtight bottles and weighed in a single-pan Mettler balance to an accuracy of ±0.001 mg. Preferential evaporation losses of solvents from mixtures were kept to a minimum as evidenced by repeated measurement of the physical properties over an interval of 2-3 days, during which no changes in physical properties were observed. The possible error in mole fractions is estimated to be around ±0.0001.The densities of liquids and their mixtures were measured by a 25 mL specific gravity bottle, calibrated with redistilled water. The average uncertainty in measurement in the measured density is ±0.05 kgm−3. With the fluctuation of ±0.05 K, temperature was controlled by a water thermostat. Ultrasonic velocity was measured using the ultrasonic interferometer (Model M-83) provided by Mittal Enterprises, New Delhi. The values agree closely with the values given in the literature.The experimental values of ultrasonic speeds (u), densities (ρ), adiabatic compressibilities (βad), molar volumes (V), and free length (Lf) of pure ethyl benzoate, NNDMF, NNDMAc, NNDMA, and those of their binary mixtures over the entire composition range and at 303.15 K, expressed by mole fraction x1 of ethyl benzoate, are listed in Table 2.Table 2
Experimental ultrasonic velocities,u, densities, ρ,  and related thermodynamic parameters for ethyl benzoate + NNDMF system.
x
1
U ms−1
ρ
×
10
3 kgm−3
β
ad
×
10
-
12 m2N−1
V
×
10
-
6 m3mol−1
L
f Å
Δ
β
ad
×
10
-
12 m2N−1
V
E
×
10
-
6 m3mol−1
L
f
E Å
T
=
303.15 K
0.0000
1438.53
0.9392
51.4522
77.8216
0.4497
0.0000
0.0000
0.0000
0.0568
1433.50
0.9529
51.0688
81.2961
0.4481
−0.4549
−0.2620
−0.0019
0.1193
1427.94
0.9663
50.7512
85.1516
0.4467
−0.8511
−0.5200
−0.0037
0.1885
1421.80
0.9793
50.5133
89.4680
0.4456
−1.1761
−0.7540
−0.0051
0.2654
1414.94
0.9922
50.3414
94.2800
0.4449
−1.4448
−1.0030
−0.0063
0.3514
1407.25
1.0045
50.2715
99.7325
0.4446
−1.6230
−1.2130
−0.0071
0.4484
1398.50
1.0158
50.3334
105.9725
0.4448
−1.6831
−1.3510
−0.0073
0.5584
1388.25
1.0249
50.6279
113.3098
0.4461
−1.5271
−1.2520
−0.0066
0.6843
1376.50
1.0327
51.1051
121.8471
0.4482
−1.2084
−1.0000
−0.0052
0.8298
1362.89
1.0395
51.7198
131.8472
0.4512
−0.7048
−0.5770
−0.0030
1.0000
1347.00
1.0456
52.7108
143.6209
0.4552
0.0000
0.0000
0.0000
T
=
308.15 K
0.0000
1420.69
0.9345
53.0178
78.2129
0.4598
0.0000
0.0000
0.0000
0.0568
1416.24
0.9498
52.4916
81.5612
0.4575
−0.5600
−0.3950
−0.0024
0.1193
1411.27
0.9639
52.0884
85.3661
0.4558
−1.0003
−0.7110
−0.0043
0.1885
1405.75
0.9773
51.7820
89.6557
0.4544
−1.3478
−0.9800
−0.0059
0.2654
1399.58
0.9900
51.5655
94.4878
0.4535
−1.6100
−1.2180
−0.0070
0.3514
1392.69
1.0023
51.4383
99.9475
0.4529
−1.7883
−1.4310
−0.0078
0.4484
1384.81
1.0134
51.4578
106.2300
0.4530
−1.8265
−1.5380
−0.0080
0.5584
1375.55
1.0226
51.6827
113.5634
0.4540
−1.6669
−1.4560
−0.0073
0.6843
1364.87
1.0304
52.0990
122.1266
0.4558
−1.3254
−1.1930
−0.0058
0.8298
1352.50
1.0368
52.7261
132.1880
0.4585
−0.7848
−0.7260
−0.0034
1.0000
1338.00
1.0419
53.6120
144.1309
0.4624
0.0000
0.0000
0.0000
T
=
313.15 K
0.0000
1398.00
0.9294
55.0533
78.6421
0.4719
0.0000
0.0000
0.0000
0.0568
1394.18
0.9463
54.3682
81.8657
0.4690
−0.6765
−0.5300
−0.0029
0.1193
1389.85
0.9609
53.8719
85.6300
0.4668
−1.1633
−0.8980
−0.0050
0.1885
1385.04
0.9742
53.5109
89.9392
0.4652
−1.5137
−1.1600
−0.0065
0.2654
1379.64
0.9870
53.2289
94.7763
0.4640
−1.7840
−1.4070
−0.0077
0.3514
1373.59
0.9990
53.0536
100.2767
0.4632
−1.9462
−1.5950
−0.0084
0.4484
1366.70
1.0101
52.9994
106.5688
0.4630
−1.9856
−1.7100
−0.0086
0.5584
1358.48
1.0191
53.1703
113.9502
0.4638
−1.7980
−1.6000
−0.0078
0.6843
1349.00
1.0267
53.5206
122.5584
0.4653
−1.4285
−1.3150
−0.0061
0.8298
1337.99
1.0331
54.0707
132.6663
0.4677
−0.8562
−0.8280
−0.0037
1.0000
1325.00
1.0375
54.9010
144.7422
0.4712
0.0000
0.0000
0.0000
T
=
318.15 K
0.0000
1380.74
0.9299
56.4079
78.5998
0.4810
0.0000
0.0000
0.0000
0.0568
1377.12
0.9487
55.5820
81.6576
0.4775
−0.8276
−0.7380
−0.0035
0.1193
1373.00
0.9638
55.0381
85.3744
0.4752
−1.3733
−1.2000
−0.0059
0.1885
1368.39
0.9770
54.6608
89.6770
0.4735
−1.7527
−1.5200
−0.0075
0.2654
1363.20
0.9888
54.4219
94.6046
0.4725
−1.9938
−1.7337
−0.0085
0.3514
1357.36
0.9998
54.2883
100.2006
0.4719
−2.1300
−1.8900
−0.0091
0.4484
1350.64
1.0098
54.2828
106.5998
0.4719
−2.1383
−1.9700
−0.0092
0.5584
1342.70
1.0184
54.4667
114.0329
0.4727
−1.9577
−1.8900
−0.0084
0.6843
1333.49
1.0256
54.8316
122.6897
0.4743
−1.5965
−1.6500
−0.0069
0.8298
1322.72
1.0310
55.4405
132.9388
0.4769
−0.9919
−1.1300
−0.0043
1.0000
1310.00
1.0325
56.4374
145.4431
0.4812
0.0000
0.0000
0.0000


## 3. Results and Discussion

The experimental density (ρ) values of binary mixtures were used to calculate the excess molar volumes as
(1)VE=x1M1(1ρ-1ρ1)+x2M2(1ρ-1ρ2),
where  M  is the molar mass; subscripts 1 and 2 stand for pure components, ethyl benzoate and NNDMF, NNDMAc, and NNDMA, respectively. The uncertainty in VE is estimated to be within ±2×10-6m3·mol-1.Assuming that ultrasonic absorption is negligible, adiabatic compressibility (βad) can be obtained from the density and velocity of ultrasonic sound (U) using the relation
(2)βad=1ρU2.
Deviation in adiabatic compressibility was calculated using the relation
(3)Δβ=βad-(β1x1+β2x2),
where βad is the compressibility of the mixture.Intermolecular free length (Lf) has been calculated using the relation
(4)Lf=K(βad)1/2,
where  K  is Jacobson’s temperature-dependant constant and is equal to (93.875+0.375T)·10-8.The excess intermolecular free length (LfE) at a given mole fraction is the difference between mean free length and the sum of the fractional contributions of the two liquids given by
(5)LfE=Lf-(Lf1x1+Lf2x2),
where Lf1 and Lf2 are the individual intermolecular free length values of pure liquids in the binary mixtures.The experimental values of ultrasonic velocity (U) and values of density (ρ), at the four temperatures, namely, T=303.15 K, 308.15 K, 313.15 K, and 318.15 K, along with the derived values of adiabatic compressibility (βad), intermolecular free length (Lf), and molar volume (V) and their excess parameters are given in Tables 2, 3, and 4.Table 3
Experimental ultrasonic velocities,u, densities, ρ,  and related thermodynamic parameters for ethyl benzoate + NNDMAc.
x
1
U ms−1
ρ
×
10
3 kgm−3
β
ad
×
10
-
12 m2N−1
V
×
10
-
6 m3mol−1
L
f Å
Δ
β
ad
×
10
-
12 m2N−1
V
E
×
10
-
6 m3mol−1
L
f
E Å
T
=
303.15 K
0.0000
1438.00
0.9319
51.8935
93.4864
0.4517
0.0000
0.0000
0.0000
0.0674
1432.95
0.9480
51.3740
96.3878
0.4494
−0.5747
−0.4800
−0.0025
0.1400
1427.32
0.9635
50.9473
99.5830
0.4475
−1.0606
−0.9200
−0.0047
0.2181
1421.01
0.9782
50.6271
103.1217
0.4461
−1.4447
−1.3000
−0.0063
0.3026
1414.06
0.9925
50.3887
107.0031
0.4451
−1.7521
−1.6553
−0.0077
0.3943
1406.27
1.0058
50.2747
111.3334
0.4446
−1.9410
−1.9200
−0.0085
0.4940
1397.57
1.0175
50.3173
116.2342
0.4448
−1.9800
−2.0200
−0.0087
0.6030
1387.19
1.0274
50.5796
121.7970
0.4459
−1.8068
−1.9200
−0.0079
0.7225
1375.40
1.0358
51.0348
128.0889
0.4479
−1.4492
−1.6200
−0.0063
0.8542
1362.17
1.0419
51.7277
135.3109
0.4510
−0.8639
−1.0000
−0.0037
1.0000
1347.00
1.0456
52.7108
143.6209
0.4552
0.0000
0.0000
0.0000
T
=
308.15 K
0.0000
1425.00
0.9282
53.0553
93.8591
0.4600
0.0000
0.0000
0.0000
0.0674
1414.43
0.9533
52.4328
96.6298
0.4573
−0.6600
−0.6200
−0.0029
0.1400
1407.10
0.9757
51.7632
99.7749
0.4543
−1.3700
−1.1200
−0.0060
0.2181
1400.06
0.9955
51.2467
103.3044
0.4521
−1.9300
−1.5200
−0.0085
0.3026
1392.49
1.0127
50.9238
107.2326
0.4506
−2.3000
−1.8400
−0.0101
0.39 43
1385.16
1.0275
50.7248
111.5802
0.4498
−2.5500
−2.1000
−0.0112
0.4940
1378.23
1.0390
50.6703
116.4747
0.4495
−2.6600
−2.2200
−0.0117
0.6030
1370.45
1.0463
50.8910
122.0725
0.4505
−2.5000
−2.1000
−0.0109
0.7225
1362.13
1.0499
51.3375
128.3908
0.4525
−2.1200
−1.7900
−0.0093
0.8542
1351.69
1.0489
52.1808
135.6309
0.4562
−1.3500
−1.1700
−0.0059
1.0000
1338.00
1.0419
53.6120
144.1309
0.4624
0.0000
0.0000
0.0000
T
=
313.15 K
0.0000
1405.50
0.9238
54.7974
94.3061
0.4708
0.0000
0.0000
0.0000
0.0674
1403.10
0.9419
53.9280
97.0079
0.4671
−0.8764
−0.7000
−0.0038
0.1400
1400.00
0.9589
53.2064
100.0549
0.4639
−1.6055
−1.3100
−0.0069
0.2181
1396.00
0.9743
52.6688
103.5372
0.4616
−2.1512
−1.7700
−0.0093
0.3026
1390.60
0.9883
52.3255
107.4594
0.4601
−2.5033
−2.1100
−0.0109
0.3943
1384.40
1.0015
52.0988
111.8120
0.4591
−2.7395
−2.3800
−0.0119
0.4940
1377.50
1.0138
51.9853
116.6629
0.4586
−2.8632
−2.5600
−0.0124
0.6030
1368.80
1.0237
52.1359
122.2385
0.4592
−2.7239
−2.4800
−0.0118
0.7225
1358.10
1.0314
52.5672
128.6366
0.4611
−2.3051
−2.1100
−0.0100
0.8542
1345.00
1.0365
53.3302
136.0082
0.4645
−1.5557
−1.3800
−0.0067
1.0000
1325.00
1.0375
54.9010
144.7422
0.4712
0.0000
0.0000
0.0000
T
=
318.15 K
0.0000
1385.00
0.9194
56.7017
94.7575
0.4823
0.0000
0.0000
0.0000
0.0674
1384.98
0.9396
55.4839
97.2461
0.4771
−1.2000
−0.9300
−0.0051
0.1400
1381.08
0.9573
54.7647
100.2213
0.4740
−1.9000
−1.6300
−0.0082
0.2181
1376.75
0.9726
54.2441
103.7130
0.4717
−2.4000
−2.1000
−0.0103
0.3026
1371.70
0.9871
53.8417
107.5884
0.4700
−2.7800
−2.5078
−0.0120
0.3943
1366.33
1.0002
53.5575
111.9618
0.4687
−3.0400
−2.7800
−0.0131
0.4940
1359.66
1.0121
53.4475
116.8575
0.4683
−3.1236
−2.9400
−0.0135
0.6030
1352.00
1.0220
53.5323
122.4504
0.4686
−3.0100
−2.8700
−0.0130
0.7225
1342.03
1.0295
53.9307
128.8682
0.4704
−2.5800
−2.5100
−0.0111
0.8542
1330.16
1.0320
54.7659
136.6042
0.4740
−1.7100
−1.4485
−0.0074
1.0000
1310.00
1.0325
56.4374
145.4431
0.4812
0.0000
0.0000
0.0000Table 4
Experimental ultrasonic velocities,u, densities, ρ,  and related thermodynamic parameters for ethyl benzoate + NNDMA system.
x
1
U ms−1
ρ
×
10
3 kgm−3
β
ad
×
10
-
12 m2N−1
V
×
10
-
6 m3mol−1
L
f Å
Δ
β
ad
×
10
-
12 m2N−1
V
E
×
10
-
6 m3mol−1
L
f
E Å
T
=
303.15 K
0.0000
1470.50
0.9482
48.7719
127.8106
0.4379
0.0000
0.0000
0.0000
0.0900
1463.99
0.9605
48.5763
128.8888
0.4370
−0.5500
−0.3445
−0.0025
0.1820
1455.87
0.9724
48.5187
130.0539
0.4367
−0.9700
−0.6340
−0.0043
0.2761
1446.91
0.9841
48.5394
131.2837
0.4368
−1.3200
−0.8920
−0.0058
0.3724
1436.85
0.9957
48.6486
132.5568
0.4373
−1.5900
−1.1410
−0.0070
0.4709
1425.42
1.0070
48.8766
133.9043
0.4383
−1.7500
−1.3510
−0.0077
0.5717
1413.22
1.0176
49.2038
135.3745
0.4398
−1.8200
−1.4750
−0.0080
0.6750
1398.88
1.0268
49.7705
137.0818
0.4423
−1.6600
−1.4000
−0.0072
0.7807
1383.14
1.0347
50.5169
138.9865
0.4456
−1.3300
−1.1670
−0.0058
0.8890
1366.09
1.0412
51.4636
141.1360
0.4498
−0.8100
−0.7300
−0.0035
1.0000
1347.00
1.0456
52.7108
143.6209
0.4552
0.0000
0.0000
0.0000
T
=
308.15 K
0.0000
1453.40
0.9439
50.1538
128.3928
0.4472
0.0000
0.0000
0.0000
0.0900
1448.57
0.9571
49.7950
129.3529
0.4456
−0.6700
−0.4560
−0.0029
0.1820
1441.85
0.9691
49.6332
130.4900
0.4449
−1.1500
−0.7670
−0.0051
0.2761
1433.31
0.9810
49.6186
131.6920
0.4448
−1.4900
−1.0460
−0.0066
0.3724
1423.92
0.9925
49.6915
132.9731
0.4452
−1.7500
−1.2800
−0.0077
0.4709
1413.61
1.0038
49.8522
134.3235
0.4459
−1.9300
−1.4800
−0.0085
0.5717
1402.59
1.0144
50.1109
135.8035
0.4470
−2.0200
−1.5870
−0.0089
0.6750
1389.28
1.0236
50.6179
137.5103
0.4493
−1.8700
−1.5050
−0.0082
0.7807
1374.46
1.0316
51.3136
139.4123
0.4524
−1.5400
−1.2670
−0.0067
0.8890
1358.23
1.0383
52.2081
141.5350
0.4563
−1.0200
−0.8490
−0.0044
1.0000
1338.00
1.0419
53.6120
144.1309
0.4624
0.0000
0.0000
0.0000
T
=
313.15 K
0.0000
1435.20
0.9398
51.6583
128.9530
0.4571
0.0000
0.0000
0.0000
0.0900
1431.88
0.9534
51.1601
129.8537
0.4549
−0.7900
−0.5200
−0.0035
0.1820
1425.32
0.9658
50.9684
130.9465
0.4541
−1.2800
−0.8800
−0.0056
0.2761
1417.25
0.9777
50.9236
132.1433
0.4539
−1.6300
−1.1690
−0.0071
0.3724
1408.35
0.9892
50.9658
133.4173
0.4540
−1.9000
−1.4150
−0.0083
0.4709
1398.80
1.0004
51.0852
134.7768
0.4546
−2.1000
−1.6110
−0.0092
0.5717
1388.45
1.0109
51.3122
136.2689
0.4556
−2.2000
−1.7110
−0.0096
0.6750
1375.74
1.0199
51.8070
138.0100
0.4578
−2.0400
−1.6000
−0.0088
0.7807
1361.81
1.0279
52.4598
139.9134
0.4606
−1.7300
−1.3660
−0.0075
0.8890
1345.54
1.0345
53.3911
142.0506
0.4647
−1.1500
−0.9390
−0.0049
1.0000
1325.00
1.0375
54.9010
144.7422
0.4712
0.0000
0.0000
0.0000
T
=
318.15 K
0.0000
1412.00
0.9356
53.6093
129.5319
0.4690
0.0000
0.0000
0.0000
0.0900
1409.96
0.9497
52.9638
130.3486
0.4661
−0.9000
−0.6150
−0.0040
0.1820
1404.50
0.9624
52.6740
131.4026
0.4649
−1.4500
−1.0250
−0.0064
0.2761
1397.05
0.9743
52.5901
132.6049
0.4645
−1.8000
−1.3200
−0.0079
0.3724
1389.02
0.9857
52.5824
133.8966
0.4645
−2.0800
−1.5600
−0.0091
0.4709
1380.54
0.9967
52.6410
135.2781
0.4647
−2.3000
−1.7460
−0.0100
0.5717
1371.38
1.0071
52.7962
136.7845
0.4654
−2.4300
−1.8440
−0.0106
0.6750
1359.31
1.0160
53.2681
138.5332
0.4675
−2.2500
−1.7380
−0.0098
0.7807
1345.99
1.0239
53.9072
140.4535
0.4703
−1.9100
−1.5000
−0.0083
0.8890
1330.79
1.0303
54.8035
142.6280
0.4742
−1.3200
−1.0490
−0.0057
1.0000
1310.00
1.0325
56.4374
145.4431
0.4812
0.0000
0.0000
0.0000The excess properties were fitted to a Redlich, Kister-type [14] polynomial equation
(6)YE=x1x2∑i=0jAi(1-2x1)i.
The optimum number of coefficients,  j, was ascertained from an examination of the variation of the standard deviation  σ. The values of coefficients, Ai, were evaluated by using the method of least squares, with all points weighted equally. The coefficients A0, A1, and A2 along with standard deviations,  σ  of fit for all the mixtures are listed in Table 5.Table 5
Coefficients,Ai, of (6) and standard deviations, σ, for binary systems at different temperatures.
T
/
K
A
0
A
1
A
2
σ
Ethyl benzoate + NNDMF
Δ
β
ad
×
10
-
12/m2N−1
303.15
−6.4467
2.2499
−0.0638
0.0171
308.15
−6.8775
2.8689
−1.3139
0.0391
313.15
−7.2181
3.6083
−2.8140
0.0767
318.15
−7.6186
4.2860
−5.1293
0.1145
V
E
×
10
-
6/m3mol−1
303.15
−5.1947
0.8178
1.3098
0.0259
308.15
−5.8404
1.3461
−0.4321
0.0456
313.15
−6.1729
2.0602
−2.4103
0.0899
318.15
−7.0606
−2.4146
−5.8222
0.1234
L
f
E
/
Å
303.15
−0.0285
0.0096
0.0020
0.0001
308.15
−0.0301
0.0123
−0.0047
0.0002
313.15
−0.0312
0.0154
−0.0118
0.0003
318.15
−0.0328
0.0177
−0.0215
0.0005
Ethyl benzoate + NNDMAc
Δ
β
ad
×
10
-
12/m2N−1
303.15
−7.8289
1.3767
−0.1647
0.0155
308.15
−10.7235
−0.2065
0.0599
0.0681
313.15
−11.2398
0.4350
−3.1080
0.0260
318.15
−11.9293
2.3285
−6.8757
0.1496
V
E
×
10
-
6/m3mol−1
303.15
−8.0967
−0.1873
0.3985
0.0196
308.15
−8.7131
0.0699
−1.4562
0.0315
313.15
−9.9358
−0.2638
−1.9087
0.0390
318.15
−11.1717
1.5314
−3.0602
0.1497
L
f
E
/
Å
303.15
−0.0342
0.0064
0.0000
0.0001
308.15
−0.0471
−0.0007
0.0004
0.0003
313.15
−0.0488
0.0022
−0.0131
0.0001
318.15
−0.0516
0.0093
−0.0287
0.0007
Ethyl benzoate + NNDMA
Δ
β
ad
×
10
-
12/m2N−1
303.15
−7.0776
−0.9608
−0.6333
0.0256
308.15
−7.8226
−1.4455
−2.2954
0.0322
313.15
−8.4985
−1.4000
−3.4138
0.0474
318.15
−9.3139
−1.6851
−4.5462
0.0618
V
E
×
10
-
6/m3mol−1
303.15
−5.5381
−2.0172
−0.4794
0.0310
308.15
−6.0491
−1.9707
−1.6874
0.0364
313.15
−6.5792
−2.0734
−2.1865
0.0427
318.15
−7.1185
−2.0844
−3.1230
0.0440
L
f
E
/
Å
303.15
−0.0311
−0.0032
−0.0031
0.0001
308.15
−0.0344
−0.0061
−0.0089
0.0001
313.15
−0.0372
−0.0049
−0.0143
0.0003
318.15
−0.0404
−0.0064
−0.0203
0.0003TheΔβad, VE, and LfE values plotted against mole fraction of ethyl benzoate (x1) are shown in Figures 2, 3, and 4.In this investigation, the values of ultrasonic velocity decrease with increase in the concentration of ethyl benzoate and decrease with increase in temperature at any particular concentration for all the three systems (Figure1). The ultrasonic velocity values decrease with increase of temperature due to the breaking of hetero-and homomolecular clusters at high temperatures [22]. Lagemann and Duban [23] were the first to point out the ultrasonic velocity approach for qualitative estimation of the interaction in liquids.Figure 1
Ultrasonic velocities (U) plotted against the mole fractions of ethyl benzoate (X) in binary mixtures of ethyl benzoate + NNDMF (◆), ethyl benzoate + NNDMAc (■), and ethyl benzoate + NNDMA (▲).Figure 2
Excess intermolecular free lengths (LfE) plotted against the mole fractions of ethyl benzoate (X) in binary mixtures of ethyl benzoate + NNDMF (◆), ethyl benzoate + NNDMAc (■), and ethyl benzoate + NNDMA (▲).Figure 3
Deviation in adiabatic compressibilities (Δβad) plotted against the mole fractions of ethyl benzoate (X) in binary mixtures of ethyl benzoate + NNDMF (◆), ethyl benzoate + NNDMAc (■), and ethyl benzoate + NNDMA (▲).Figure 4
Excess molar volumes (VE) plotted against the mole fractions of ethyl benzoate (X) in binary mixtures of ethyl benzoate + NNDMF (◆), ethyl benzoate + NNDMAc (■), and ethyl benzoate + NNDMA (▲).The intermolecular free length is the distance between the surfaces of the neighboring molecules. The variation of ultrasonic velocity in a solution depends upon the increase or decrease of intermolecular free length after mixing the components. The interdependence of intermolecular free length and ultrasonic velocity was evolved from a model for sound propagation proposed by Kincaid and Eyring  [24]. The ultrasonic velocity should decrease if the intermolecular free length increases as a result of mixing of components. This fact is observed in the present investigation for ethyl benzoate + NNDMF, ethyl benzoate + NNDMAc, and ethyl benzoate + NNDMA systems. Figure 2 represents the variation of excess intermolecular free length with mole fraction of ethyl benzoate. The excess intermolecular free length values are negative, and the curves appear to reach negative peak value at about 0.45 mole fraction of ethyl benzoate. According to Ramamurthy and Sastry [25], the negative LfE values indicate that sound wave has to travel a longer distance. This may be attributed to the dominant nature of interactions between unlike molecules.The compressibility behavior of solutes, which is the second derivative of the Gibbs energy, is a very sensitive indicator of molecular interactions and can provide useful information about this phenomenon [26–28]. The structural change of molecules takes place due to the existence of electrostatic field between interacting molecules. The change in adiabatic compressibility value in liquids and liquid mixtures may be ascribed to the strength of intermolecular attraction. The effect of depolymerization increases the compressibility of the system [29]. Electrostatic attraction and association decrease the compressibility. The compressibility of the mixtures is the result of these two effects depending upon the predominance [30]. According to Jacobson [31, 32], the adiabatic compressibility can be studied more through intermolecular free length.Figure3 represents the deviation in adiabatic compressibility with the mole fraction of ethyl benzoate. In the present investigation, deviation in adiabatic compressibilities is found to be negative over the mole fraction of ethyl benzoate indicating the presence of strong interactions between the molecules. The negative deviation in adiabatic compressibility reaches a peak at about 0.45 mole fraction of ethyl benzoate in all the three systems chosen.The deviation in adiabatic compressibility can be explained by taking into consideration the following factors.(a)
Loss of dipolar association and difference in size and shape of component molecules which lead to decrease in velocity and increase in compressibility.(b)
Dipole-dipole interaction or hydrogen-bonded complex formation between unlike molecules which lead to increase in sound velocity and decrease of compressibility.The actual deviation depends on the resultant effect. The strength of the interaction between the components increases when excess values tend to become increasingly negative. This may be qualitatively interpreted in terms of closer approach of unlike molecules leading to reductions in compressibility and volume [33, 34]. This type of interactions for the binary mixtures has been already reported previously [35]. The deviations in adiabatic compressibilities are found to increase with increasing temperature which is in agreement with the previously reported results [36]. The Δβad and LfE minima occur at the same concentrations further strengthen the occurrence of molecular associations [37].The values ofVE calculated by using (1) are included in Tables 2–4.The sign ofVE of a system depends upon the relative magnitude of expansion and contraction of the two liquids due to mixing [38].The negativeVE arises due to dominance of the following factors.(a)
Chemical interaction between constituent molecules such as heteromolecular association through the formation of H-bond, often termed as strong specific interaction.(b)
Association through weaker physical forces such as dipolar force or any other forces of this kind.(c)
Accommodation of molecules of one component into the interstitial positions of the structural network of molecules of the other component.(d)
Geometry of the molecular structure that favors fitting of the component molecules with each other.TheVE values are negative over the entire mole fraction range and at all temperatures investigated for all binary systems under study (Figure 4). The observed negative values of VE for the three mixtures indicate the presence of specific interactions between ethyl benzoate and amide molecules. The negative VE values are attributed to strong dipole-dipole interactions between unlike molecules in the mixtures. The VE values are more negative for ethyl benzoate + DMAc than those for other two systems.The electron density at oxygen atom of the carbonyl atom of DMAc is greater than that of DMF due to the presence of methyl group at carbon atom of carbonyl group in DMF resulting in stronger interaction in thesystem [39, 40]. The VE values of ethyl benzoate + DMA are in between these two. The strength of interactions between ethyl benzoate + DMA is stronger than ethyl benzoate + DMF due to the fact that negative charge on nitrogen in DMA is more than that of nitrogen in DMF due to conjugation with C=O group (this is also evident from the fact that the DMA is more basic than DMF).Rao and Reddy [41] reported increased negative values of excess molar volumes with the increase in carbon chain length of the ester, in the binary mixtures of DMF, and aliphatic esters. The observed higher negative values of VE (-1.35cm3mol-1) for aromatic ester with DMF in the present investigation, when compared to that of ethyl acetate and DMF (VE=-0.375) at the same temperature (303.15 K), indicate much stronger interactions between the unlike molecules of components in this binary mixture due to the formation of not only dipole-dipole interactions but also of induced polar interaction like dipole-induced dipole and dipole interactions between aromatic ester and DMF. Similar interactions are reported in the mixtures of DMF and polycyclic aromatic hydrocarbons by Nikam and Kharat [42, 43] and by Ramadevi and Prabhakara Rao [44]. Also, formation of induced polar interactions like dipole-induced dipole interactions between polycyclic aromatic hydrocarbons and NMP (acyclic amide) is reported by Sugiura and Ogawa [45]. This further supports that amides react with aromatic compounds more strongly than the corresponding aliphatic counter parts.TheVE values decrease (become more negative) with increase in temperature for all the 3 systems. This is attributed due to the dissociation of self-associated amide molecules resulting in the more favorable fitting of the smaller molecules into large voids of bigger ethyl benzoate molecules leading to contraction in volume and hence resulting in more negative VE values with rise in temperature.


## 4. Conclusions

The adiabatic compressibility (βad) and intermolecular free length (Lf) both have an inverse relationship with ultrasonic velocity (U). Occurrence of U maxima, βad, and Lf minima at the same concentrations indicates the strong interaction through dipole-dipole interactions between the components. The negative VE values are attributed to strong dipole-dipole interactions between unlike molecules in the mixtures.



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*Source: 285796-2013-03-25.xml*