# Thermoacoustic, Volumetric, and Viscometric Investigations in Binary Liquid System of Cyclohexanone with Benzyl Benzoate atT = 308.15, 313.15, and 318.15 K

Authors: Sk. Md Nayeem; M. Kondaiah; K. Sreekanth; D. Krishna Rao
Journal: Journal of Thermodynamics
 (2014)

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## Abstract

Ultrasonic velocities (u), densities (ρ), and viscosities (η) of binary liquid mixtures of cyclohexanone with benzyl benzoate, including pure liquids, over the entire composition range have been measured at 308.15 K, 313.15 K, and 318.15 K. Using the experimental results, parameters such as molar volume (Vm), isentropic compressibility (ks), intermolecular free length (Lf), acoustic impedance (Z), internal pressure (πi), enthalpy (H), Gibbs free energy of activation of viscous flow (G*E), and excess/deviation properties of these including partial molar volumes (V-m,1 and V-m,2), excess partial molar volumes (V-m,1E and V-m,2E), partial molar volume of the components at infinite dilution (V-m,1∞, V-m,2∞), and excess partial molar volume at infinite dilution (V-m,1E,∞and V-m,2E,∞) have been computed. The observed negative values of VmE, Δks, LfE, and πiE and positive values of zE, HE, ΔG*E, Δη, and Δu for all the liquid mixtures studied clearly indicate the presence of strong dipole-dipole-type interactions, fitting of smaller molecules into bigger molecules. Further theoretical values of sound velocity and viscosity in the mixtures have been evaluated using various theories and have been compared with experimental values to verify the applicability of such theories to the systems studied.


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## Body

## 1. Introduction

Volumetric, viscometric, and ultrasonic investigations of liquid mixtures are of considerable importance in understanding the intermolecular interactions occurring among component molecules and they find application in several industrial and technological processes [1, 2]. The work on medicinally used chemical compounds requires the attention of the society in all aspects including ultrasonic behaviour. Benzyl benzoate is a carboxylate ester which is used in oily injections and as an insect repellent and as acaricide and pediculicide in veterinary hospitals. It is an effective and inexpensive topical treatment for human scabies. It is a polar (μ=2.06D) molecule (C+=O−) with the structure shown in Figure 12. Behaviour of benzyl benzoate in many liquids such as aliphatic alkanes, aromatic alkanes, aliphatic alcohols, substituted benzenes, acetates, ketones, and DMSO (super solvent) has been thoroughly studied ultrasonically [3–6].Ketone is an organic compound that contains a carbonyl group and two aliphatic or aromatic substituents containing the chemical formula RCOR1. Here, R and R1 may be same or different incorporated into a ring (alkyl, aryl, and heterocyclic radicals). Cyclohexanone is a ketone liquid. The chemical reactivity of the carbonyl group (C+=O−) plays important role in chemical reactions and is influenced considerably by steric effects. The greater electronegativity of O− and high dipole moment make ketones polar (μ=3.25D). The resonance structure shown in Figure 12 illustrates this polarity. Thus a study on thermophysical properties data of binary liquid mixtures has attracted considerable interest in the literature [7–10]. Cyclohexanone and its derivatives are used for the synthesis of pharmaceuticals, dyes, herbicides, pesticides, plasticizers, and rubber chemicals.The liquids under investigation have been chosen on the basis of their medicinal and industrial applications. These applications have greatly stirred the need for extensive information on the thermodynamic, acoustic, and transport properties of these solvents and their mixtures [11–13]. Ultrasonic and density data for binary mixtures of benzyl benzoate with Isomers of butanol have been studied previously in our laboratory [14]. The literature survey reveals that Madhuri et al. [15] have reported ultrasonic, volumetric, and viscometric studies of benzyl benzoate with acetonitrile and benzonitrile. Recently, Sri et al. [16] reported ultrasonic velocity and density in binary liquids of certain aldehydes and esters. In the present investigation, a detailed study of the binary mixture of benzyl benzoate (BB) with cyclohexanone (CH) at three temperatures 308.15 K, 313.15 K, and 318.15 K is aimed. From the experimentally measured data of ultrasonic velocity (u), densities (ρ), and viscosities (η), thermodynamic and other related parameters like molar volume, isentropic compressibility, acoustic impedance, free length, relaxation time, internal pressure, enthalpy, and Gibbs free energy of activation of viscous flow are computed and in terms of some of these excess/deviation parameters, the nature of molecular interactions is predicted in the binary mixtures. An evaluation of velocities and viscosities using three different empirical theories is also attempted at all the three temperatures.


## 2. Experimental Section

Benzyl benzoate (BB) and cyclohexanone (CH) used in the present study were the AR grade products from LOBA Chemicals, India, and were purified by standard methods described in the literature [17–19]. The mass fraction purity of liquids obtained is >0.995. Before use, the chemicals were stored over 0.4 nm molecular sieves approximately for 72 h to remove water content and degassed and latter kept in air tight bottles. The mass measurements are performed with a METTLER TOLEDO (Switzerland make) AB135-S/FACT digital balance with an accuracy of ±0.01 mg. The uncertainty in the mole fraction is 10−4. The ultrasonic velocity of pure liquids and their binary mixtures has been measured by using a multifrequency ultrasonic interferometer (M-82 model) supplied by Mittal Enterprises, New Delhi, at a fixed frequency of 2 MHz with an accuracy of ±0.2%. The temperature of liquid sample in the interferometer cell is maintained constant by circulating water pumped from constant temperature water bath. In the present study, the constant temperature water bath (digital electronic) supplied by Concord Instruments Co., Ltd., Chennai (RAAGA type), has been used. The instrument can maintain temperature to ±0.01 K as per its specifications.Densities and viscosities of pure liquids and liquid solutions are determined using 5 cm3 two stem double walled Parker & Parker-type pycnometer [20] and Ostwald viscometer which is standardized as described by Naidu and Prasad [21] using triply distilled water, respectively. The estimated accuracy in measuring the density is 3 in 105 parts. The uncertainty in the viscosity measurement is ±0.2%. The detailed description of measurement of density and viscosity is discussed in our previous papers [22–25]. The densities, velocities, and viscosities of pure liquids in this investigation at temperature of 308.15 K, 313.15 K, and 318.15 K are compiled in Table 1 together with the literature data [15, 26] available. These results are found to be in good agreement with reported data.Table 1
Comparison of experimental values of ultrasonic velocity  (u), density (ρ), and viscosity, (η) of pure liquids with the literature values concerned at 308.15, 313.15, and 318.15 K.
Liquid
Temp/K
ρ/(kg⋅m−3)
η/(10−3 N⋅s⋅m−2)
u/(m⋅s−1)
Exptl.
Lit.
Exptl.
Lit.
Exptl.
Lit.
Cyclohexanone
308.15
939.60
939.6    (26)
1.594
1.6013 (26)
1362.00
1362.0 (26)
313.15
934.70
934.7    (26)
1.472
1.4561 (26)
1348.20
1348.2 (26)
318.15
922.30
922.5    (26)
1.370
1.3101 (26)
1275.00
1272.8 (26)
Benzyl benzoate
308.15
1114.54
1114.5 (15)
7.118
—
1493.30
1493.3 (15)
313.15
1109.70
1109.7 (15)
6.261
—
1471.40
1471.4 (15)
318.15
1104.80
—
5.550
—
1440.00
—


## 3. Results and Discussion

The measured values of density, velocity, and viscosity and the calculated values of molar volume, isentropic compressibility, free length, acoustic impedance, internal pressure, relaxation time, enthalpy, and Gibbs free energy of activation of viscous flow are calculated using standard relations and are presented in Table2 with mole fraction of cyclohexanone in benzyl benzoate. In the present investigation, the values of u and z increase and those of ks and Lf decrease as the mole fraction increases. The variation of ultrasonic speed in a solution depends upon the increase or decrease of Lf after mixing the components. This is due to the fact that ultrasonic speed increases if the intermolecular free length decreases and vice versa. The decrease in the values of ks and Lf with mole fraction in the present study indicates significant interactions between CH and BB molecules.Table 2
Experimental values of densities (ρ), velocities (u), and viscosities (η)  with calculated properties of  molar volume, (Vm), acoustic impedance, (Z), isentropic compressibility, (ks), free length, (Lf),  internal pressure, (πi), enthalpy, (H), and  Gibbs free energy of activation of viscous flow, (G*E), with mole fraction, x, of cyclohexanone (x) in benzyl benzoate at T  =  308.15 K, 313.15 K, and 328.15 K.
L
L
L
L
x
ρ/(kg⋅m−3)
u
/(m⋅s−1)
η/(10−3 N⋅s⋅m−2)
V
m/(10−5 m3⋅mol−1)
Z
E/(106 kg⋅m−2⋅s−1)
k
s/(10−10 Pa−1)
L
f/(10−10 m)
π
i
E/(106 Pa)
H/(J⋅mol−1)
G
*
E/(kJ⋅mol−1)
308.15 K
1.0000
939.60
1362.00
1.594
10.4459
1.2797
5.7372
0.5016
521.97
54525.20
−39.9867
0.9021
969.35
1385.94
1.878
11.2775
1.3435
5.3706
0.4853
505.62
57021.57
−39.3711
0.8443
984.74
1397.80
2.071
11.7709
1.3765
5.1973
0.4775
499.07
58745.42
−39.0100
0.7852
999.11
1409.21
2.289
12.2765
1.4080
5.0400
0.4702
493.94
60639.08
−38.6459
0.6470
1028.33
1433.09
2.879
13.4610
1.4737
4.7349
0.4557
486.22
65450.91
−37.8231
0.5522
1045.47
1447.20
3.347
14.2748
1.5130
4.5670
0.4476
483.19
68975.81
−37.2863
0.4789
1057.32
1456.83
3.746
14.9058
1.5403
4.4563
0.4421
481.64
71793.50
−36.8876
0.3232
1079.23
1473.61
4.696
16.2491
1.5904
4.2669
0.4326
479.88
77976.77
−36.0876
0.2112
1092.84
1482.60
5.466
17.2160
1.6203
4.1629
0.4273
479.51
82553.29
−35.5502
0.1035
1104.50
1488.79
6.276
18.1468
1.6444
4.0847
0.4233
479.63
87038.88
−35.0614
0.0000
1114.54
1493.30
7.118
19.0428
1.6643
4.0236
0.4201
479.96
91398.24
−34.6154
313.15 K
1.0000
934.70
1348.89
1.472
10.5007
1.2608
5.8800
0.5078
502.22
52736.76
−40.1779
0.9021
964.24
1377.00
1.707
11.3373
1.3278
5.4694
0.4898
481.96
54641.93
−39.6016
0.8443
979.69
1390.87
1.870
11.8317
1.3626
5.2763
0.4811
473.72
56050.30
−39.2590
0.7852
994.09
1401.82
2.054
12.3385
1.3935
5.1190
0.4738
467.57
57692.00
−38.9103
0.6470
1023.27
1422.33
2.558
13.5275
1.4554
4.8306
0.4603
458.59
62036.14
−38.1127
0.5522
1040.41
1434.12
2.962
14.3443
1.4921
4.6733
0.4527
455.16
65289.63
−37.5869
0.4789
1052.26
1442.36
3.307
14.9774
1.5178
4.5680
0.4476
453.41
67909.90
−37.1940
0.3232
1074.26
1457.01
4.135
16.3243
1.5652
4.3849
0.4386
451.48
73702.04
−36.4016
0.2112
1087.89
1464.42
4.809
17.2944
1.5931
4.2863
0.4336
451.19
78030.81
−35.8666
0.1035
1099.62
1468.85
5.520
18.2273
1.6152
4.2150
0.4300
451.53
82303.37
−35.3788
0.0000
1109.70
1471.40
6.261
19.1259
1.6328
4.1623
0.4273
452.17
86483.25
−34.9328
318.15 K
1.0000
933.20
1275.00
1.370
10.5176
1.1898
6.5918
0.5377
497.80
52356.76
−40.3579
0.9021
962.12
1309.97
1.567
11.3623
1.2604
6.0568
0.5154
472.78
53719.01
−39.8149
0.8443
977.21
1326.76
1.704
11.8617
1.2965
5.8133
0.5050
462.25
54831.30
−39.4904
0.7852
991.40
1342.23
1.860
12.3720
1.3307
5.5988
0.4956
453.82
56147.48
−39.1584
0.6470
1020.06
1372.34
2.290
13.5702
1.3999
5.2053
0.4778
440.75
59810.82
−38.3889
0.5522
1036.87
1388.73
2.639
14.3933
1.4399
5.0008
0.4683
435.57
62693.06
−37.8743
0.4789
1048.47
1399.38
2.940
15.0316
1.4672
4.8705
0.4622
432.95
65079.84
−37.4865
0.3232
1070.00
1417.30
3.668
16.3892
1.5165
4.6525
0.4517
430.03
70478.74
−36.6981
0.2112
1083.31
1427.23
4.265
17.3675
1.5461
4.5317
0.4458
429.22
74544.92
−36.1631
0.1035
1094.79
1435.30
4.895
18.3077
1.5714
4.4338
0.4410
428.90
78523.17
−35.6752
0.0000
1104.80
1440.00
5.550
19.2107
1.5909
4.3651
0.4376
429.05
82424.53
−35.2306Study of deviation/excess properties plays vital role in the study of molecular interactions. The nonlinear variation of excess/deviation properties with mole fraction of BB is responsible for nonideality in the systems of binary liquid mixture [15]. The factors responsible for such departure from ideality may either be due to the presence of intermolecular forces between the constituents in the mixture or due to compound formation between solute and solvent, or as a result of association of either to form complex molecules [27]. These excess parameters throw light upon the strength of interaction and their variation with mole fraction finds application in typifying the physicochemical behaviour of liquid mixtures [28].The deviation/excess properties have been calculated using the relation(1)YE=Yreal-Yideal,
where YE represent deviation/excess value of the parameter, Yreal is the experimental value of the parameter of liquid mixture, and Yideal is the ideal value of the parameter computed theoretically. The YE=VmE is excess molar volume, ZE is excess specific acoustic impedance, Δks is deviation in isentropic compressibility, LfE is excess intermolecular free length, πiE is excess internal pressure, HE is excess enthalpy, ΔG*E is excess Gibbs free energy of activation of viscous flow, Δη is deviation in viscosity, and Δu is deviation in velocity.The deviation in isentropic compressibility(Δks) has been calculated from
(2)Δks=ks-Φ1ks1+Φ2ks2,
where Φ1, Φ2 and ks1, ks2 are the volume fractions and isentropic compressibilities of components 1 and 2, respectively. Since ks is not additive on mole fraction but is additive on volume fraction, hence such values are calculated using volume fraction Фi:
(3)Фi=xiVi∑xiVi.
The excess/deviation properties have been fitted to a Redlich-Kister-type polynomial equation [29]:
(4)YE=x1-x∑i=0jAi1-2xi,
where x is the mole fraction of CH and for evaluating Δks, x is replaced by volume fraction (Фi) and Ai are the adjustable parameters of the function and are determined using the least square method. In the present investigation “i” values taken are from 0 to 4. The corresponding standard deviations σ(YE) were calculated using the expression
(5)σYE=∑Yexp⁡E-YcalE2m-n1/2,
where “m” is the total number of experimental points and “n” is the number of coefficients in (4). The calculated values of the coefficients Ai along with the standard deviations (σ) are given in Table 3.Table 3
CoefficientsAi of Redlich-Kister-type polynomial equation and the corresponding standard deviations, σ, of the system CH + BB at T=308.15 K, 313.15 K, and 318.15 K.
Property
A
0
A
1
A
2
A
3
A
4
σ
At 308.15 K
VmE/(10−5 m³⋅mol−1)
−0.1852
−1.2716
−0.6378
5.1475
1.5786
0.0442
ZE/(106 kg⋅m−2⋅s−1)
0.2425
−0.0386
0.0089
0.0046
0.1483
0.0001
Δks/(10−10 Pa−1)
−1.5704
0.4932
−0.1605
0.0213
−0.1559
0.0003
LfE/(10−10 m)
−0.0727
0.0009
0.1215
0.2317
−0.3916
0.0060
πiE/(106 Pa)
−81.96
72.84
222.75
−575.16
−400.46
6.1774
HE/(J⋅mol−1)
−7945.70
3556.51
−1661.40
519.50
−462.21
0.4439
ΔG*E/(k J⋅mol−1)
1.2005
0.0541
−0.1314
0.0720
−0.0263
0.0001
Δη/(m N⋅s⋅m−2)
−2.912
−0.001
0.001
0.003
−0.002
0.0002
Δu/(m⋅s−1)
106.13
−6.91
0.50
3.72
11.64
0.03
At 313.15 K
VmE/(10−5m³⋅mol−1)
−0.0473
−0.0514
−0.1583
0.4146
0.1953
0.0046
ZE/(106 kg⋅m−2⋅s−1)
0.255
−0.0511
0.0606
−0.0826
−0.0177
0.0002
Δks/(10−10 Pa−1)
−1.6905
0.6082
−0.5890
0.6564
0.0583
0.0012
LfE/(10−10 m)
−0.0738
0.0240
−0.0262
0.0258
0.0073
0.0001
πiE/(106 Pa)
−93.42
55.97
−36.68
24.88
−2.77
0.0259
HE/(J⋅mol−1)
−9845.27
4398.17
−3040.88
2073.36
435.13
3.1835
ΔG*E/(k J⋅mol−1)
0.9980
0.1547
−0.1695
0.0906
−0.0263
0.0001
Δη/(m N⋅s⋅m−2)
−2.644
−0.001[
0.001
0.001
−0.001
0.0003
Δu/(m⋅s−1)
119.47
−21.79
58.41
−74.26
−24.87
0.15
At 318.15 K
VmE/(10−5m³⋅mol−1)
−0.0656
0.0232
0.0195
0.0245
0.0006
0.0002
ZE/(106 kg⋅m−2⋅s−1)
0.2772
−0.0793
−0.0024
0.0463
0.0444
0.0003
Δks/(10−10 Pa−1)
−2.2868
1.0124
−0.3349
0.1037
−0.3589
0.0006
LfE/(10−10 m)
−0.0952
0.0378
−0.0091
−0.0011
−0.0163
0.0001
πiE/(106 Pa)
−119.32
72.47
−29.02
9.38
−10.37
0.0120
HE/(J⋅mol−1)
−10268.50
8865.00
−13730.10
−17705.21
15648.81
2.5820
ΔG*E/(k J⋅mol−1)
0.7885
0.2677
−0.1434
0.0399
0.0029
0.0001
Δη/(m N⋅s⋅m−2)
−2.436
0.007
0.068
−0.001
0.003
0.0005
Δu/(m⋅s−1)
156.09
−49.22
2.17
4.21
37.00
0.06Figure1 represents the variation of excess molar volume (VmE) with mole fraction of CH. The sign of VmE depends upon the contraction and expansion of volume of the liquids due to mixing. The excess molar volume is the resultant contribution from several opposing effects, namely, chemical, physical, and structural [30]. The chemical or specific interactions result in volume contractions, leading to negative excess molar volume, and these include charge-transfer complexes, dipole-dipole, dipole-induced dipole interactions and formation of H-bonding between component molecules. The physical interactions or nonspecific interactions are weak and these include breaking of the structure of one or both of the components in a solution, that is, the loss of dipolar association between the molecules (dispersion forces), steric hindrance of the molecules and H-bond rupture, and stretching of self-associated molecules (like alcohols). The structural contributions are mostly negative and arise from several effects such as interstitial accommodation and geometrical fitting of one component into another due to the differences in the molar volume and free volume between components. In the present investigation, the sign of VmE is found to be negative over the entire composition range.Figure 1
Variation of excess molar volume,VmE, with mole fraction, x, of CH in BB at (◆) 308.15 K, (■) 313.15 K, and (▲) 318.15 K.The nature of existing interaction in a binary liquid can also be analysed by knowing their individual chemical and physical properties. It is well known that BB and CH are polar and their dipole moment values follow:μCH = 3.25 D > μBB = 2.06 D. In the present study, possibility of Keesom dipole-dipole van der Waals forces which arise due to the dipole moment of the components gives strong interactions leading to negative values of VmE [31]. Moreover, the liquids BB and CH lack hydroxyl groups; hence the possibility for formation of intermolecular hydrogen bonds is trifling. Further, the molar volumes of CH and BB are 10.4459 and 19.0428 (×10−5 m3·mol−1), respectively, at 308.15 K. This implies that geometrical fitting of smaller molecules into the voids created by the bigger molecules is most favorable. The VmE values in binary mixture are thereby decreased with increasing temperature. Negative VmE values indicate strong interactions following the order 318.15K>313.15K>308.15K. According to Rastogi et al. [32], such behaviour may arise due to the fact that, as temperature increases, thermal energy activates the molecule; this would increase the rate of association of unlike molecules. Similar type of trend was observed by Baragi et al. [33] in methyl cyclohexane with alkanes.The strong molecular interactions in the presented binary system are well reflected in the properties of partial molar volumes. The partial molar volumesV-m,1 of component 1 (CH) and V-m,2 of component 2 (BB) in the mixtures have been calculated by using the following equations:
(6)V-m,1=VmE+V1*+x2∂VmE∂xT,P,V-m,2=VmE+V2*+x1∂VmE∂xT,P,
where V1* and V2* are the molar volumes of the pure components of CH and BB, respectively. By differentiating (4) and then rearranging one can get the following equations for V-m,1 and V-m,2.The derivates in the above equations are obtained by differentiating Redlich-Kister equation (8) which leads to the following equations for V-m,1 and V-m,2:
(7)V-m,1=V1*+x22∑i=0jAix2-x1i-2x1x22∑i=1jAix2-x1i-1,(8)V-m,2=V2*+x12∑i=0jAix2-x1i-2x2x12∑i=1jAix2-x1i-1.
The excess partial molar volumes are then given by
(9)V-m,1E=V-m,1-V1*,V-m,2E=V-m,2-V2*.
The values of V-m,1 and V-m,2 are tabulated in Table 4. This table reproduces the values of V-m,1 and V-m,2 for both the components in the mixtures are smaller than their individual molar volumes in the pure state; this indicates that shrinkage of volume takes place on mixing CH with BB. Figures 2 and 3 represent the disparity of excess partial molar volumes of V-m,1E and V-m,2E, respectively, in the binary mixture. Examination of these figures not only reveals the existence of strong forces between the unlike molecules but also supports the deductions drawn from excess molar volume.Table 4
Mole fraction (x) and values of partial molar volume V-m,2/(10−5 m3⋅mol−1),  V-m,1/(10−5 m3⋅mol−1) of the binary system at 308.15, 313.15, and 318.15 K.
x
T= 308.15 K
T = 313.15 K
T = 318.15 K
V
-
m
,
2
V
-
m
,
1
V
-
m
,
2
V
-
m
,
1
V
-
m
,
2
V
-
m
,
1
1.0000
16.5603
10.4459
18.9107
10.5007
19.0979
10.5176
0.9021
19.1068
10.3190
19.1066
10.4880
19.1381
10.5161
0.8443
19.6593
10.2239
19.1608
10.4759
19.1540
10.5144
0.7852
19.7480
10.1852
19.1786
10.4667
19.1663
10.5123
0.6470
19.1208
10.4029
19.1386
10.4730
19.1864
10.5058
0.5522
18.7192
10.6493
19.1017
10.4931
19.1966
10.4996
0.4789
18.6383
10.7183
19.0898
10.5035
19.2030
10.4935
0.3232
19.0412
10.0898
19.1175
10.4635
19.2123
10.4792
0.2112
19.3430
9.3218
19.1459
10.3961
19.2141
10.4735
0.1035
19.2619
9.9694
19.1433
10.4335
19.2124
10.4826
0.0000
19.0428
15.0774
19.1259
10.8536
19.2107
10.5198Figure 2
Variation of excess partial molar volume,V-m,2E, with mole fraction, x,  of CH in BB (◆) 308.15 K, (■) 313.15 K, and (▲) 318.15 K.Figure 3
Variation of excess partial molar volume,V-m,1E, with mole fraction, x,  of CH in BB (◆) 308.15 K, (■) 313.15 K, and (▲) 318.15 K.The partial molar volumes and excess partial molar volumes of the components at infinite dilution,V-m,1∞, V-m,2∞, V-m,1E,∞, and V-m,2E,∞, respectively, were obtained by putting x=0 in (7) and x=1 in (8):
(10)V-m,1E,∞=A0+A1+A2+A3+⋯=V-m,1∞-V1*,V-m,2E,∞=A0-A1+A2-A3+⋯=V-m,2∞-V2*.
The pertinent values of V-m,1∞, V-m,2∞, V-m,1E,∞, and V-m,2E,∞ are reported in Table 5. This table shows that these values are negative, from which we conclude that strong interactions exist among the unlike molecules of the mixtures, which support the trends of VmE values observed in these mixtures.Table 5
Values of partial molar volume of the components at infinite dilution (V-m,1∞,V-m,2∞) and excess partial molar volume at infinite dilution (V-m,1E,∞,V-m,2E,∞) for the system CH + BB at 308.15, 313.15, and 318.15 K.
Temp. (K)
L
L
L
L
V
-
m
,
1
E
,
∞
V
-
m
,
2
E
,
∞
V
-
m
,
1
∞
V
-
m
,
2
∞
/(10−5 m3⋅mol−1)
308.15
4.6315
−3.1203
15.0774
15.9225
313.15
0.3529
−0.3735
10.8536
18.7524
318.15
0.0022
−0.0933
10.5197
19.1173Figures4 and 5 represent the deviation in isentropic compressibility (Δks) and excess intermolecular free length LfE, respectively. These values are found to be negative for the system under investigation at all temperatures. The nature of Δks, LfE plays vivacious role in assessing the compactness due to molecular rearrangement. The extent of molecular interactions in liquid mixtures may be due to charge transfer, dipole-induced-dipole, dipole-dipole interactions, and interstitial accommodation, leading to more compact structure making Δks and LfE negative. The values of the excess functions Δk, LfE depend upon several physical and/or chemical contributions [34–37]. The physical contribution consists of dispersion forces or weak dipole-dipole interaction that leads to positive values of Δks and LfE. Another factor, which involves a physical contribution, is the geometrical effect allowing the fitting of molecules of two different sizes into each other’s structure resulting in negative Δks, LfE values. The strength of the interactions increases with temperatures as observed from more negative values of the excess parameters. They are negative throughout and become more negative at all concentrations as the temperature is increased. In heteromolecular interaction between the component molecules of the mixtures, Fort and Moore [38] found that the negative value of excess compressibility indicates greater interaction between the components of the mixtures due to the formation of hydrogen bond. Thus the negative Δks values for binary mixtures indicate strong interactions between BB and CH.Figure 4
Variation of deviation in isentropic compressibility,Δks, with mole fraction, x, of CH in BB (◆) 308.15 K, (■) 313.15 K, and (▲) 318.15 K.Figure 5
Variation of excess free length,LfE, with mole fraction, x, of CH in BB (◆) 308.15 K, (■) 313.15 K, and (▲) 318.15 K.According to Singh et al. [39], negative values of excess intermolecular free length LfE indicate that sound waves cover longer distances due to decrease in intermolecular free length ascribing the dominant nature of hydrogen bond interaction between unlike molecules. Fort and Moore indicated that the positive values of excess free length should be attributed to the dispersive forces, and negative excess values should be due to hydrogen bond formation or dipole-dipole interactions between solute and solvent. In the present study the negative contribution in all the systems prevails in the existence of greater interactions. Nain et al. [40] also concluded a similar observation. From Figure 6, the excess values of ZE are found to be positive for the system at all temperatures under investigation. According to Kondaiah and Rao [41], the nature of the positive values of ZE is attributed to specific interaction between the heteromolecules. This further supports our earlier finding.Figure 6
Variation of excess acoustic impedance,ZE, with mole fraction, x, of CH in BB (◆) 308.15 K, (■) 313.15 K, and (▲) 318.15 K.The variations of excess internal pressure(πiE) and excess enthalpy (HE) are presented in Figures 7 and 8 for the present system at all the three temperatures, respectively. From these figures it is observed that πiE is negative and HE is positive over the entire composition range of CH. In accordance with Kondaiah et al. [42], the negative values of πiE indicate the existence of strong specific interactions and according to Kumar and Rao [43], positive value of ΔH suggests strong bonding and exothermic reactions. Thus, it can be concluded that strong specific interactions are operative in the systems investigated. These conclusions support our earlier findings of strong interactions. The variation of excess Gibbs free energy of activation of viscous flow ΔG*E with mole fraction of CH has been presented in Figure 9 at all temperatures. These values are positive over the entire range of composition of CH. According to Iloukhani et al. [44, 45], negative values of ΔG*E indicate the presence of weak physical forces such as dispersive forces in the system. On the other hand positive values of it suggest strong specific interactions. This also supports the conclusions drawn from our earlier findings.Figure 7
Variation of excess internal pressure,πiE, with mole fraction, x, of CH in BB (◆) 308.15 K, (■) 313.15 K, and (▲) 318.15 K.Figure 8
Variation of excess enthalpy,HE, with mole fraction, x, of CH in BB (◆) 308.15 K, (■) 313.15 K, and (▲) 318.15 K.Figure 9
Variation of excess Gibbs free energy of activation of viscous flow,ΔG*E, with mole fraction, x, of CH in BB (◆) 308.15 K, (■) 313.15 K, and (▲) 318.15 K.According to Fort and Moore [46], deviation in viscosity tends to become more positive as the strength of the interaction increases. The deviation in viscosity variation gives a qualitative estimation of the strength of the intermolecular interactions. The deviation in viscosities may be generally explained by considering the following factors. (i) The difference in size and shape of the component molecules and the loss of dipolar association in pure component may contribute to a decrease in viscosity and (ii) specific interactions between unlike components such as hydrogen bond formation or dipole-dipole interactions or charge-transfer complexes may cause increase in viscosity in mixtures compared to in pure components [47]. The former effect produces negative deviation in viscosity and latter effect produces positive deviation in viscosity. A perusal of Figure 10 shows that the values of Δη are positive for the present system at three temperatures. The positive Δη values decrease with increasing temperature. The positive Δη values indicate specific interactions while the negative Δη values indicate dispersion forces [48–50]. In the present investigation, the positive values of all binary systems may be attributed to the dipole-dipole interactions. The sign and magnitude of Δu play important roles in describing molecular rearrangements as a result of molecular interactions occurring among the component molecules in the mixtures. The excess ultrasonic speed with mole fraction of CH is shown in Figure 11. Here we observed that the Δu values are positive for all binary systems over the entire range of composition at all the studied temperatures. Positive deviations indicate the increasing strength of interaction between component molecules of binary liquid mixtures. According to Reddy et al. [51], strong interactions among the components of a mixture lead to the formation of molecular aggregates and more compact structures; then sound will travel faster through the mixture by means of longitudinal waves and hence the ultrasonic speed deviations with respect to a linear behaviour will be positive while if the structure-breaking factor in the mixture predominates resulting expansion, then the speed of sound through the mixture will be slower resulting in negative deviation in the speed of sound. According to Ali et al. [52], more positive values mean much more strong interactions between the molecules. Therefore, based on the above references for the present scenario, interactions are found to be in the order 318.15K>313.15K>308.15K; this again emphasizes our view regarding the interaction between CH and BB.Figure 10
Variation of deviation in viscosity,Δη, with mole fraction, x, of CH in BB (◆) 308.15 K, (■) 313.15 K, and (▲) 318.15 K.Figure 11
Variation of deviation in ultrasonic velocity,Δu, with mole fraction, x, of CH in BB (◆) 308.15 K, (■) 313.15 K, and (▲) 318.15 K.Figure 12In the present study, theoretical sound velocities have been evaluated by considering CH as one component and BB as the other component in the binary mixture at all the three temperatures. Such an evaluation of theoretical sound velocity is useful to verify the applicability of various assumes of the theories of liquid mixtures and to arrive at some useful implications regarding the (strength of) molecular interactions between component liquids in some cases. The theoretical values of ultrasonic velocity obtained using various theories along with the experimental velocity and percentage deviation are summarized in Table6. Nomoto [53] established the following relation for sound velocity based on the supposition of the linearity of the molecular sound velocity and the additives of molar volume:
(11)UN=∑xiRi∑xiVi3.
Van Dael [54] obtained the ideal mixture relation
(12)∑xiMiui2=1∑xiMi1UV2.
The impedance dependence relation used by Baluja and Parsania [55] is given below:
(13)Uimp=∑xiZi∑xiρi,
where xi is mole fractions, Mi is molecular weight, R is the molar sound speed, and Zi is acoustic impedance of CH and BB, respectively, at three temperatures.Table 6
Experimental and theoretical velocities from various empirical relations and percentage deviation in velocities with molefraction,x, of CH with BB at T =  308.15, 313.15, and 318.15 K.
x
u
expt
U
N
U
V
U
I
%UN
%UV
%UI
308.15 K
1.0000
1362.00
1362.00
1362.00
1361.96
0.00
0.00
0.00
0.9021
1385.94
1383.13
1331.26
1376.93
−0.20
−3.95
−0.65
0.8443
1397.80
1394.27
1318.02
1385.52
−0.25
−5.71
−0.88
0.7852
1409.21
1404.79
1307.85
1394.13
−0.31
−7.19
−1.07
0.6470
1433.09
1426.46
1296.25
1413.55
−0.46
−9.55
−1.36
0.5522
1447.20
1439.35
1297.68
1426.33
−0.54
−10.33
−1.44
0.4789
1456.83
1448.39
1304.03
1435.94
−0.58
−10.49
−1.43
0.3232
1473.61
1465.38
1333.84
1455.57
−0.56
−9.49
−1.22
0.2112
1482.60
1476.03
1371.26
1469.08
−0.44
−7.51
−0.91
0.1035
1488.79
1485.25
1423.35
1481.61
−0.24
−4.40
−0.48
0.0000
1493.30
1493.30
1493.30
1493.26
0.00
0.00
0.00
313.15 K
1.0000
1348.89
1348.89
1348.89
1348.88
0.00
0.00
0.00
0.9021
1377.00
1368.65
1318.18
1362.86
−0.61
−4.27
−1.03
0.8443
1390.87
1379.07
1304.90
1370.88
−0.85
−6.18
−1.44
0.7852
1401.82
1388.91
1294.64
1378.91
−0.92
−7.65
−1.63
0.6470
1422.33
1409.16
1282.67
1397.04
−0.93
−9.82
−1.78
0.5522
1434.12
1421.20
1283.67
1408.97
−0.90
−10.49
−1.75
0.4789
1442.36
1429.65
1289.58
1417.93
−0.88
−10.59
−1.69
0.3232
1457.01
1445.52
1318.07
1436.24
−0.79
−9.54
−1.43
0.2112
1464.42
1455.48
1354.08
1448.84
−0.61
−7.53
−1.06
0.1035
1468.85
1464.09
1404.28
1460.53
−0.32
−4.40
−0.57
0.0000
1471.40
1471.60
1471.61
1471.38
0.00
0.00
0.00
318.15 K
1.0000
1275.00
1275.00
1275.00
1275.22
0.00
0.00
0.00
0.9021
1309.97
1301.37
1247.66
1293.99
−0.66
−4.76
−1.22
0.8443
1326.76
1315.31
1236.19
1304.75
−0.86
−6.83
−1.66
0.7852
1342.23
1328.49
1227.68
1315.54
−1.02
−8.53
−1.99
0.6470
1372.34
1355.68
1219.56
1339.89
−1.21
−11.13
−2.36
0.5522
1388.73
1371.88
1223.20
1355.93
−1.21
−11.92
−2.36
0.4789
1399.38
1383.27
1231.24
1367.99
−1.15
−12.02
−2.24
0.3232
1417.30
1404.69
1265.00
1392.63
−0.89
−10.75
−1.74
0.2112
1427.23
1418.15
1306.03
1409.60
−0.64
−8.49
−1.23
0.1035
1435.30
1429.81
1362.97
1425.35
−0.38
−5.04
−0.69
0.0000
1440.00
1440.00
1440.00
1439.98
0.00
0.00
0.00Percentage deviation in ultrasonic speed is given by(14)%Δu=100*1-Ucaluexpt.On observing Table6, among all the empirical theories, Nomoto’s relation gives the best estimate of experimental values of sound velocity in the system followed by impedance’s relation. In the present binary systems, the difference between experimental and theoretical velocities is greater where the mole fraction of CH varies in the region 0.4 to 0.7. Hence it can be qualitatively inferred that the strength of interaction in the binary mixtures is more in this range of composition of binary mixtures.The dynamic viscosities of the liquid mixtures have been calculated using the several empirical relations.Grunberg and Nissan [56] proposed the following equation for the measurement of viscosity of liquid mixtures:
(15)ln⁡⁡η=x1ln⁡⁡η1+x2ln⁡⁡η2+x1x2G12,
where G12 is an interaction parameter and it is the function of components 1, 2 and temperature.Hind et al. [57] suggested an equation for the viscosity of binary liquid mixtures as
(16)η=x12η1+x22η2+2x1x2H12,
where H12 is an interaction parameter and is attributed to unlike pair interaction.Katti and Chaudhri [58] proposed the following equation:
(17)ln⁡⁡ηV=x1ln⁡⁡η1V1+x2ln⁡⁡η2V2+x1x2WvisRT,
where (Wvis/RT) is an interaction parameter.The theoretical viscosity values using (15) to (17) along with the percentage error are compiled in Table 7. The evaluated values of parameters G12, H12, and Wvis/RT and standard deviations σ  (10−3kg−1·s−1) are presented in Table 8. The estimated values of σ are indicating that the viscosities are well correlated by all the three viscosity models. Prolongo et al. [59] reported positive values of interaction parameters corresponding to systems with negative excess molar volumes. This is consistent with our results. Among all of these models, the viscosity representations obtained from the Hind model are in best agreement with the experimental viscosity data.Table 7
Experimental and theoretical values of viscosity from various empirical relations and percentage deviation in viscosity in CH + BB atT = 308.15, 313.15, and 318.15 K.
T (K)
Exptl. viscosity
Gruenberg
Hind
Katti
%G
%H
%K
308.15 K
1.594
1.594
1.594
1.595
0.000
0.000
0.000
1.878
1.891
1.878
1.891
0.698
0.005
0.692
2.071
2.086
2.071
2.086
0.685
−0.014
0.676
2.289
2.302
2.289
2.302
0.537
−0.009
0.524
2.879
2.877
2.879
2.877
−0.052
0.007
−0.069
3.347
3.333
3.347
3.333
−0.445
−0.006
−0.448
3.746
3.721
3.746
3.721
−0.649
0.003
−0.667
4.696
4.658
4.695
4.658
−0.794
−0.002
−0.809
5.460
5.430
5.466
5.431
−0.662
−0.009
−0.658
6.276
6.253
6.276
6.253
−0.362
0.006
−0.366
7.118
7.118
7.118
7.118
0.000
0.000
0.000
313.15 K
1.472
1.472
1.472
1.472
0.000
0.000
0.000
1.707
1.724
1.707
1.724
0.966
−0.023
0.937
1.870
1.890
1.870
1.890
1.075
0.021
1.070
2.054
2.073
2.055
2.073
0.886
0.005
0.876
2.558
2.560
2.559
2.560
0.070
0.004
0.039
2.962
2.947
2.963
2.947
−0.513
0.007
−0.540
3.307
3.279
3.308
3.278
−0.871
0.006
−0.907
4.135
4.084
4.135
4.084
−1.214
0.010
−1.233
4.809
4.757
4.809
4.756
−1.094
−0.006
−1.123
5.520
5.484
5.520
5.484
−0.665
−0.005
−0.670
6.261
6.261
6.261
6.262
0.000
0.000
0.000
318.15 K
1.370
1.370
1.370
1.370
0.000
0.000
0.000
1.567
1.585
1.566
1.586
1.122
−0.128
1.148
1.704
1.726
1.703
1.728
1.344
−0.059
1.408
1.860
1.883
1.860
1.884
1.237
0.000
1.290
2.290
2.298
2.294
2.301
0.380
0.175
0.480
2.639
2.629
2.644
2.632
−0.345
0.189
−0.265
2.940
2.914
2.945
2.917
−0.867
0.170
−0.782
3.668
3.612
3.671
3.615
−1.548
0.055
−1.472
4.265
4.202
4.265
4.205
−1.496
−0.023
−1.430
4.895
4.848
4.893
4.850
−0.974
−0.061
−0.940
5.550
5.550
5.550
5.550
0.000
0.000
0.000Table 8
Various interaction parameters calculated from various empirical relations and the corresponding standard deviations (σ/10−3 N⋅s⋅m−2) of the present system CH + BB at T = 308.15, 313.15, and 318.15 K.
Temp. (K)
G
12
σ
H
12
σ
W
vis/RT
σ
308.15
0.272
0.020
0.003
0.003
0.004
0.020
313.15
0.186
0.028
0.003
0.003
0.003
0.028
318.15
0.103
0.032
0.002
0.030
0.003
0.031


## 4. Conclusions

(i)
Ultrasonic velocities, densities, and viscosities for binary liquids of CH with BB are determined experimentally atT = 308.15 K, 313.15 K, and 318.15 K over the entire composition range.
(ii)
The values ofVmE, Δks, LfE, ZE, πiE, HE, ΔG*E, and Δu are calculated from experimental results at all three temperatures. The excess/deviation properties are fitted to Redlich-Kister-type polynomial and corresponding standard deviations are evaluated. The observed negative values of VmE, Δks,LfE, and πiE and positive values of ZE, HE, ΔG*E, Δη, and Δu for all the liquid mixtures studied clearly indicate dipole-dipole-type interactions and the geometrical fitting of molecules leading to strong molecular interactions between CH and BB. These strong interactions increase with temperature.
(iii)
The values ofV-m,1, V-m,2 and V-m,1E, V-m,2E are calculated from experimental data. The observed lower partial molar volumes in the liquid mixture when compared to the respective molar volumes of pure components indicate that strong interactions present in the system support the trends of VmE values very well.
(iv)
The ultrasonic velocities/viscosities computed from three different velocity/viscosity theories were correlated with the experimentally measured ultrasonic velocities and their percentage deviations were evaluated. Among all the empirical theories Nomoto’s velocity/Hind viscosity relation gives the best estimate of experimental values of sound velocity/viscosity in the system at all temperatures.



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*Source: 487403-2014-12-29.xml*