# Thermophysical Properties of Binary Mixtures of Dimethylsulfoxide with 1-Phenylethanone and 1,4-Dimethylbenzene at Various Temperatures

Authors: Harmandeep Singh Gill; V. K. Rattan
Journal: Journal of Thermodynamics
 (2014)

---

## Abstract

This research article reports the experimental results of the density, viscosity, refractive index, and speed of sound analysis of binary mixtures of dimethylsulfoxide (DMSO) + 1-phenylethanone (acetophenone) and + 1,4-dimethylbenzene (para-xylene) over the whole composition range at 313.15, 318.15, 323.15, and 328.15 K and at atmospheric pressure. The excess molar volumes (V
E), viscosity deviations (Δ
η), excess Gibbs energy of activation (G
E), deviations in isentropic compressibility (K
S
E), deviations in speed of sound (u
E), and deviations in the molar refraction (Δ
R) were calculated from the experimental data. The computed quantities were fitted to the Redlich-Kister equation to derive the coefficients and estimate the standard error values. The viscosities have also been correlated with two, and three-parameter models, that is, Heric correlation, McAllister model, and Grunberg-Nissan correlation, respectively.


---

## Body

## 1. Introduction

This paper is a continuation of our ongoing research on the solution properties. Studies of the thermodynamic properties of binary mixtures play an important role in the fundamental understanding of different molecules and the interactions prevalent in them. In the present study, data on density, viscosity, refractive index, and speed of sound of binary mixtures of dimethylsulfoxide (DMSO) + 1-phenylethanone (acetophenone) and 1,4-Dimethylbenzene (para-xylene) at 313.15, 318.15, 323.15, and 328.15 K has been measured experimentally. From these results, the excess molar volumes, viscosity deviations, deviations in molar refraction, deviations in speed of sound, and isentropic compressibility have been derived. Dimethylsulfoxide is a versatile nonaqueous dipolar aprotic solvent having wide range of applications like in veterinary medicine, dermatology, microbiology, experimental immunology, and enzyme catalyzed reactions. It can easily pass through membranes, a quality which has been verified by numerous researchers. It has the ability to penetrate through living tissues without damaging them. Therefore an anesthetic or penicillin can be carried through the skin without using a needle which makes it paramount in medicinal field. Acetophenone is the simplest aromatic ketone organic compound. It can easily dissolve in water, but, since it is denser than water, it tends to sink. Its vapor is heavier than air and when inhaled in high concentrations it can be narcotic and also mild irritant to the eyes and skin. It is mostly used to create fragrances that smell like cherry, almond, strawberry, or other fruits. Acetophenone can also be found naturally occurring in fruits such as apple and banana. Para-xylene is an aromatic hydrocarbon based on benzene with two methyl substituents, opposite to each other. It is a colorless, flammable liquid and is insoluble in water. It is used as a thinner for paint and in paints and varnishes. The study of the thermodynamic properties of DMSO + 1-phenylethanone (acetophenone) and + 1,4-dimethylbenzene (para-xylene) mixtures is of interest mainly in industrial fields where solvent mixtures could be used as selective solvents for numerous reactions. In principle, interactions between the molecules can be established from the study of the deviations from ideal behavior of physical properties such as molar volume and isentropic compressibility. The negative or positive deviations from the ideal value depend on the type and the extent of the interactions between the unlike molecules, as well as on the composition and the temperature. The variation of the isentropic compressibility is analogous of that of the excess molar volume, whereas the change of the deviation in speed of sound tends to become the inverse [1]. Physical and transport properties of liquid mixtures also affect most separation procedures, such as liquid-liquid extraction, gas absorption, and distillation [2]. The mixture DMSO-p-xylene has been earlier reported twice in literature at different temperatures [1, 3].


## 2. Experimental Section

### 2.1. Materials

The chemicals used are of analytical reagent grade. Dimethylsulfoxide (DMSO) is from Riedel, Germany; 1-phenylethanone (acetophenone) and 1,4-dimethylbenzene (para-xylene) are from S-D Fine Chemicals, Mumbai. The chemicals were purified using standard procedure [4] and were stored over molecular sieves. The purity of the chemicals was verified by comparing density, viscosity, and refractive index with the known values reported in the literature as shown in Table 1. All the compositions were prepared by using SARTORIUS balance. The possible uncertainty in the mole fraction is estimated to be less than ±1 × 10−4.Table 1
Physical properties of the components at 298.15 K.
Component
ρ (g·cm−3)
η (mPa·s)
n
D
Exptl.
Lit.
Exptl.
Lit.
Exptl.
Lit.
Acetophenone
1.0283
1.026317
0.01681
0.0168117
1.5050
1.500517
DMSO
1.0940
1.09537
1.9834
1.9910
1.4798
1.4775
p-Xylene
8.5661
8.566216
0.609
0.61116
1.4933
1.493316


### 2.2. Viscosity

Kinematic viscosities were measured by using a calibrated modified Ubbelohde viscometer [5]. The calibration of viscometer was done at each temperature in order to determine the constants A and B of the following equation:
(1)
ν
=
η
ρ
=
A
t
+
B
t
.
The viscometer was kept vertically in a transparent-walled water bath with a thermal stability of ±0.05 K for about 30 minutes to attain thermal equilibrium. Flow time was measured with an electronic stop watch with precision of ±0.01 s. The corresponding uncertainty in the kinematic viscosity is ±0.001 × 10−6 m2 s−1. The efflux time was repeated at least three times for each composition and the average of these readings was taken. The temperature of the bath was maintained constant with the help of a circulating type cryostat (type MK70, MLW, Germany). The dynamic viscosities were found out after the DSA analysis, that is, by dividing the above found kinematic viscosity by density. The uncertainty in the values of dynamic viscosity is within ±0.003 mPa·s.


### 2.3. Density and Speed of Sound

Density and speed of sound were measured with the help of an ANTON PAAR density meter (DSA 5000). The accuracy in the measurement of density and speed of sound is ±0.000005 g cm−3 and ±0.5 ms−1, respectively. The density meter was calibrated by using triply distilled degassed water.


### 2.4. Refractive Index

Refractive indices were measured for sodium D-line by ABBE-3L refractometer having Bausch and Lomb lenses. The temperature was maintained constant with the help of water bath used for the viscosity measurement. A minimum of three independent readings were taken for each composition, and the average value was considered in all the calculations. Refractive index values are accurate up to ±0.0001 units.


## 2.1. Materials

The chemicals used are of analytical reagent grade. Dimethylsulfoxide (DMSO) is from Riedel, Germany; 1-phenylethanone (acetophenone) and 1,4-dimethylbenzene (para-xylene) are from S-D Fine Chemicals, Mumbai. The chemicals were purified using standard procedure [4] and were stored over molecular sieves. The purity of the chemicals was verified by comparing density, viscosity, and refractive index with the known values reported in the literature as shown in Table 1. All the compositions were prepared by using SARTORIUS balance. The possible uncertainty in the mole fraction is estimated to be less than ±1 × 10−4.Table 1
Physical properties of the components at 298.15 K.
Component
ρ (g·cm−3)
η (mPa·s)
n
D
Exptl.
Lit.
Exptl.
Lit.
Exptl.
Lit.
Acetophenone
1.0283
1.026317
0.01681
0.0168117
1.5050
1.500517
DMSO
1.0940
1.09537
1.9834
1.9910
1.4798
1.4775
p-Xylene
8.5661
8.566216
0.609
0.61116
1.4933
1.493316


## 2.2. Viscosity

Kinematic viscosities were measured by using a calibrated modified Ubbelohde viscometer [5]. The calibration of viscometer was done at each temperature in order to determine the constants A and B of the following equation:
(1)
ν
=
η
ρ
=
A
t
+
B
t
.
The viscometer was kept vertically in a transparent-walled water bath with a thermal stability of ±0.05 K for about 30 minutes to attain thermal equilibrium. Flow time was measured with an electronic stop watch with precision of ±0.01 s. The corresponding uncertainty in the kinematic viscosity is ±0.001 × 10−6 m2 s−1. The efflux time was repeated at least three times for each composition and the average of these readings was taken. The temperature of the bath was maintained constant with the help of a circulating type cryostat (type MK70, MLW, Germany). The dynamic viscosities were found out after the DSA analysis, that is, by dividing the above found kinematic viscosity by density. The uncertainty in the values of dynamic viscosity is within ±0.003 mPa·s.


## 2.3. Density and Speed of Sound

Density and speed of sound were measured with the help of an ANTON PAAR density meter (DSA 5000). The accuracy in the measurement of density and speed of sound is ±0.000005 g cm−3 and ±0.5 ms−1, respectively. The density meter was calibrated by using triply distilled degassed water.


## 2.4. Refractive Index

Refractive indices were measured for sodium D-line by ABBE-3L refractometer having Bausch and Lomb lenses. The temperature was maintained constant with the help of water bath used for the viscosity measurement. A minimum of three independent readings were taken for each composition, and the average value was considered in all the calculations. Refractive index values are accurate up to ±0.0001 units.


## 3. Experimental Results and Correlations

At least three independent readings of all the physical property measurements of density (ρ), viscosity (η), refractive index (n
D), and speed of sound (u) were taken for each composition and the averages of these experimental values are presented in Tables 2 and 3 for both systems. The experimentally determined values are used for the deviation calculations.Table 2
Refractive indices,n
D, density, ρ, speed of sound, u, and viscosity, η, for DMSO(1) + acetophenone(2) system at different temperatures.
x
1
n
D
ρ (g·cm−3)
u (m·s−1)
η (mPa·s)
DMSO(1) + acetophenone(2)
313.15 K
0.00000
1.5142
1.0106
1421.81
1.2920
0.17422
1.5090
1.0173
1424.53
1.3093
0.31320
1.5046
1.0238
1426.25
1.3150
0.43453
1.5001
1.0300
1427.15
1.3180
0.54292
1.4955
1.0361
1427.99
1.3609
0.63921
1.4915
1.0430
1428.88
1.4000
0.72696
1.4877
1.0502
1430.33
1.4295
0.80600
1.4841
1.0578
1432.57
1.4515
0.87681
1.4806
1.0651
1434.55
1.4721
0.94521
1.4771
1.0730
1436.77
1.4959
1.00000
1.4742
1.0802
1438.85
1.5169
318.15 K
0.00000
1.5102
1.0072
1403.51
1.1161
0.17422
1.5055
1.0144
1406.42
1.1362
0.31320
1.5011
1.0208
1408.41
1.1459
0.43453
1.4967
1.0271
1409.52
1.1633
0.54292
1.4921
1.0332
1410.57
1.2100
0.63921
1.4880
1.0400
1411.59
1.2550
0.72696
1.4843
1.0476
1413.17
1.2873
0.80600
1.4807
1.0549
1415.38
1.3150
0.87681
1.4772
1.0623
1417.55
1.3400
0.94521
1.4735
1.0700
1419.97
1.3707
1.00000
1.4703
1.0768
1422.30
1.3968
323.15 K
0.00000
1.5061
0.9987
1385.35
1.0645
0.17422
1.5019
1.0064
1388.33
1.0659
0.31320
1.4978
1.0134
1390.60
1.0735
0.43453
1.4933
1.0199
1391.91
1.0870
0.54292
1.4887
1.0261
1393.10
1.1275
0.63921
1.4847
1.0332
1394.32
1.1675
0.72696
1.4810
1.0408
1396.05
1.1969
0.80600
1.4775
1.0486
1398.30
1.2205
0.87681
1.4739
1.0560
1400.55
1.2425
0.94521
1.470
1.0636
1403.10
1.2675
1.00000
1.4665
1.0702
1405.68
1.2972
328.15 K
0.00000
1.5030
0.9856
1367.34
0.9873
0.17422
1.4991
0.9944
1370.47
0.9815
0.31320
1.4950
1.0024
1372.93
0.9875
0.43453
1.4904
1.0095
1374.35
1.0010
0.54292
1.4859
1.0168
1375.75
1.0405
0.63921
1.4817
1.0245
1377.15
1.0770
0.72696
1.4780
1.0331
1379.00
1.1065
0.80600
1.4744
1.0417
1381.30
1.1305
0.87681
1.4707
1.0498
1383.50
1.1505
0.94521
1.4668
1.0583
1386.10
1.1755
1.00000
1.4630
1.0655
1389.12
1.2086Table 3
Refractive indices,n
D, density, ρ, speed of sound, u, and viscosity, η, for DMSO(1) + p-xylene(2) system at different temperatures.
x
1
n
D
ρ (g·cm−3)
u (m·s−1)
η (mPa·s)
DMSO(1) + p-xylene(2)
313.15 K
0.00000
1.4850
0.8445
1247.96
0.5175
0.15820
1.4843
0.8720
1264.82
0.5979
0.30056
1.4839
0.8999
1281.64
0.6777
0.42694
1.4828
0.9293
1297.89
0.7389
0.52448
1.4813
0.9577
1310.14
0.8106
0.62739
1.4790
0.9923
1325.23
0.8875
0.72506
1.4778
1.0233
1346.79
0.9889
0.80799
1.4765
1.0477
1373.38
1.0997
0.87462
1.4747
1.0557
1395.79
1.2275
0.94123
1.4727
1.0723
1418.20
1.3757
1.00000
1.4717
1.0802
1439.15
1.5116
318.15 K
0.00000
1.4831
0.8395
1227.99
0.4923
0.15820
1.4823
0.8665
1246.38
0.5675
0.30056
1.4816
0.8942
1263.94
0.6422
0.42694
1.4803
0.9233
1281.67
0.6971
0.52448
1.4789
0.9517
1295.39
0.7555
0.62739
1.4767
0.9870
1310.77
0.8179
0.72506
1.4754
1.0183
1331.90
0.9090
0.80799
1.4737
1.0417
1358.39
1.0220
0.87462
1.4719
1.0497
1380.68
1.1401
0.94123
1.4701
1.0668
1404.05
1.2705
1.00000
1.4690
1.0768
1423.09
1.3822
323.15 K
0.00000
1.4812
0.8348
1207.94
0.4603
0.15820
1.4802
0.8610
1226.95
0.5401
0.30056
1.4794
0.8882
1245.22
0.6030
0.42694
1.4777
0.9167
1263.54
0.6550
0.52448
1.4761
0.9443
1277.98
0.7107
0.62739
1.4744
0.9804
1292.79
0.7697
0.72506
1.4727
1.0110
1314.76
0.8557
0.80799
1.4710
1.0333
1340.33
0.9776
0.87462
1.4690
1.0410
1363.23
1.0895
0.94123
1.4675
1.0590
1385.97
1.1999
1.00000
1.4665
1.0702
1404.14
1.2972
328.15 K
0.00000
1.4793
0.8298
1188.15
0.4385
0.15820
1.4781
0.8553
1208.59
0.5150
0.30056
1.4771
0.8823
1227.53
0.5707
0.42694
1.4754
0.9106
1247.59
0.6092
0.52448
1.4736
0.9377
1262.23
0.6579
0.62739
1.4715
0.9733
1278.99
0.7175
0.72506
1.4699
1.0045
1300.23
0.7917
0.80799
1.4683
1.0261
1325.12
0.9158
0.87462
1.4663
1.0341
1348.21
1.0109
0.94123
1.4652
1.0530
1370.98
1.1152
1.00000
1.4640
1.0655
1388.57
1.1974


### 3.1. Excess Molar Volume

Density values are used to evaluate excess molar volume by the equation(2)
V
E
=
x
1
M
1
+
x
2
M
2
ρ
-
x
1
M
1
ρ
1
-
x
2
M
2
ρ
2
,
where ρ
1, ρ
2 are the densities of pure components and ρ is the density of the mixture. M
1, M
2 are the molar mass of the two components and x
1, x
2 are the mole fraction of DMSO.Excess Gibbs’ free energy of activation has been also calculated using the viscosity and density of the mixture by the equation(3)
Δ
G
E
=
R
T
[
ln
⁡
⁡
(
η
V
)
-
∑
i
=
1
2
x
i
ln
⁡
⁡
(
η
i
V
i
)
]
,
where R is a universal gas constant, T is the temperature of the mixture, and η and η
i are the viscosities of the mixture and pure compound, respectively. V, V
i refer to the molar volume of the mixture and pure components, respectively.


### 3.2. Viscosity Calculations

The deviation in viscosity is obtained by the following equation:(4)
Δ
η
=
η
-
η
1
x
1
-
η
2
x
2
,
where η is the viscosity of mixture and η
1, η
2 refer to the viscosities of pure components.McAllister [6] model
(5)
ln
⁡
⁡
ν
=
x
1
3
ln
⁡
⁡
ν
1
+
x
2
3
ln
⁡
⁡
ν
2
+
3
x
1
2
x
2
ln
⁡
⁡
η
12
+
3
x
1
x
2
2
ln
⁡
⁡
η
21
-
ln
⁡
[
x
1
+
x
2
M
2
M
1
]
+
3
x
1
2
x
2
ln
⁡
[
2
+
M
2
/
M
1
3
]
+
3
x
1
x
2
2
ln
⁡
[
1
+
(
2
M
2
/
M
1
)
3
]
+
x
2
3
ln
⁡
[
M
2
M
1
]
.
Herric [6] correlation
(6)
ln
⁡
⁡
ν
=
x
1
ln
⁡
⁡
ν
1
+
x
2
ln
⁡
⁡
ν
2
+
x
1
x
2
[
α
12
+
α
´
12
(
x
1
-
x
2
)
]
-
ln
⁡
⁡
M
mix
+
x
1
ln
⁡
⁡
M
1
+
x
2
ln
⁡
⁡
M
2
,
and Grunberg-Nissan [7] equation
(7)
ln
⁡
(
η
)
=
x
1
ln
⁡
(
η
1
)
+
x
2
ln
⁡
(
η
2
)
+
d
12
x
1
x
2
have been fitted to viscosity data and it was found that both have the same standard errors at each temperature.


### 3.3. Isentropic Compressibility

The experimental results for the speed of sound of binary mixtures are listed in Tables2 and 3. The isentropic compressibility was evaluated by using K
S
=
u
-
2
ρ
-
1 and the deviation in isentropic compressibility is calculated using the following equation:
(8)
K
S
E
=
K
S
-
K
S
id
,
where K
S
id stands for isentropic compressibility for an ideal mixture calculated using Benson-Kiyohara model [8, 9]:
(9)
K
S
id
=
∑
i
=
1
2
Φ
i
[
K
S
,
i
+
T
V
i
(
α
i
2
)
C
p
,
i
]
-
{
T
(
∑
i
=
1
2
x
i
V
i
)
(
∑
i
=
1
2
Φ
i
a
i
)
2
∑
i
=
1
2
x
i
C
p
,
i
}
,
where a
i and C
p are the thermal expansion coefficient and molar heat capacity of the ith components, respectively.The deviation in speed of sound is given by(10)
Δ
u
=
u
-
x
1
u
1
-
x
2
u
2
.


### 3.4. Molar Refraction

Refractive indices have been used for the calculation of molar refraction (R
m) that is obtained by using Lorentz-Lorenz equation [8].Deviation in molar refraction (Δ
R) is calculated by the following equation:
(11)
R
=
R
m
-
∑
Φ
i
R
i
,
Φ
i
=
x
i
∑
x
j
V
j
,
where n
D refers to the refractive index, R
m is molar refraction of the mixture, R
i is molar refraction of the ith component, and Φ is ideal state volume fraction.All the deviations (V
E, Δ
R, Δ
η, Δ
u, and K
S
E) have been fitted to Redlich-Kister polynomial regression of the type
(12)
Δ
Y
=
x
1
x
2
∑
i
=
1
m
A
i
(
1
-
2
x
1
)
i
-
1
to derive the constant A
i using the method of the least square.Standard deviation for each case is calculated by(13)
σ
=
[
∑
(
Δ
Y
exptl
-
Δ
Y
calcd
)
2
m
-
n
]
0.5
,
where m is the number of data points and n is the number of coefficients. Derived parameters of the Redlich-Kister equation (12) and standard deviations (13) are presented in Tables 4 and 5.Table 4
Derived parameters of Redlich-Kister equation (12) and standard deviation (13) for various functions of the binary mixtures at different temperatures (DMSO-acetophenone).
T
/
K
A
0
A
1
A
2
A
3
σ
V
E (cm3·mol−1)
313.15
1.2005
0.741
−0.1784
−0.6838
0.01377
318.15
1.0176
0.7493
−0.5481
−0.7711
0.01379
323.15
0.7709
0.8700
−0.7689
−1.2620
0.01527
328.15
0.6714
0.9374
−0.9528
−1.3257
0.01381
Δ
η (mPa·s)
313.15
−0.2371
0.2135
0.2487
−0.4972
0.00461
318.15
−0.2575
0.2259
0.1846
−0.4935
0.00323
323.15
−0.2722
0.2375
0.0974
−0.4693
0.00309
328.15
−0.2887
0.2407
0.0508
−0.4755
0.00290
K
s
E (TPa−1)
313.15
4.8515
15.4271
−1.3121
−12.5359
0.11076
318.15
3.5099
15.7048
−1.8315
−12.902
0.09236
323.15
2.0047
21.1502
−4.7008
−34.8976
0.44672
328.15
0.0146
15.1308
−2.0538
−11.8737
0.17247
ΔR
313.15
0.06817
0.039577
−0.06186
−0.09945
0.006271
318.15
0.102475
0.056959
−0.00441
−0.06411
0.003073852
323.15
0.147987
0.106458
0.080891
−0.10664
0.005976
328.15
0.175329
0.134545
0.138756
−0.14317
0.008927
ΔG
E (J·mol−1)
313.15
−66.3882
516.3512
492.0794
−981.8602
9.00998
318.15
−141.309
625.565
410.846
−1119.199
7.38255
323.15
−234.912
700.1368
230.6251
−1143.3850
7.33602
328.15
−321.946
780.1317
132.3463
−1256.91
7.21134Table 5
Derived parameters of Redlich-Kister equation (12) and standard deviation (13) for various functions of the binary mixtures at different temperatures (DMSO-p-xylene).
T
/
K
A
0
A
1
A
2
A
3
σ
V
E (cm3·mol−1)
313.15
−8.5850
−15.1234
−6.084
12.8652
0.15687
318.15
−8.2010
−15.9715
−5.4345
15.6022
0.17024
323.15
−7.7110
−16.483
−4.7908
17.7396
0.19337
328.15
−7.1898
−16.3123
−4.0863
18.0512
0.20482
Δ
η (mPa·s)
313.15
−0.9028
−0.7268
−0.2127
0.25
0.00553
318.15
−0.8069
−0.7852
−0.1061
0.5942
0.00475
323.15
−0.7589
−0.7364
0.093
0.6582
0.00619
328.15
−0.7126
−0.6943
0.2137
0.6476
0.0067
K
s
E (TPa−1)
313.15
−119.0039
−64.4234
−74.9361
−36.2431
1.03835
318.15
−137.2976
−76.3846
−70.5856
−21.5844
0.97745
323.15
−148.0003
−81.8649
−67.7606
−17.6011
0.84832
328.15
−166.5237
−92.1709
−61.6439
−2.9525
0.87227
Δ
R
313.15
−3.25811
4.787247
−1.77213
−3.9986
0.226222
318.15
−3.20078
4.955419
−1.49922
−4.5735
0.239049
323.15
−3.14001
5.033874
−1.26969
−4.89488
0.245337
328.15
−3.0793
5.147192
−1.01287
−5.28097
0.254675
ΔG
E (J·mol−1)
313.15
−1022.2560
−1753.98
−140.348
1173.282
15.8755
318.15
−1013.8590
−2190.4
88.3584
2252.137
14.30563
323.15
−1011.6820
−2200.58
769.1765
2310.619
22.20041
328.15
−1113.8360
−2249.67
1294.863
2307.221
24.1139


## 3.1. Excess Molar Volume

Density values are used to evaluate excess molar volume by the equation(2)
V
E
=
x
1
M
1
+
x
2
M
2
ρ
-
x
1
M
1
ρ
1
-
x
2
M
2
ρ
2
,
where ρ
1, ρ
2 are the densities of pure components and ρ is the density of the mixture. M
1, M
2 are the molar mass of the two components and x
1, x
2 are the mole fraction of DMSO.Excess Gibbs’ free energy of activation has been also calculated using the viscosity and density of the mixture by the equation(3)
Δ
G
E
=
R
T
[
ln
⁡
⁡
(
η
V
)
-
∑
i
=
1
2
x
i
ln
⁡
⁡
(
η
i
V
i
)
]
,
where R is a universal gas constant, T is the temperature of the mixture, and η and η
i are the viscosities of the mixture and pure compound, respectively. V, V
i refer to the molar volume of the mixture and pure components, respectively.


## 3.2. Viscosity Calculations

The deviation in viscosity is obtained by the following equation:(4)
Δ
η
=
η
-
η
1
x
1
-
η
2
x
2
,
where η is the viscosity of mixture and η
1, η
2 refer to the viscosities of pure components.McAllister [6] model
(5)
ln
⁡
⁡
ν
=
x
1
3
ln
⁡
⁡
ν
1
+
x
2
3
ln
⁡
⁡
ν
2
+
3
x
1
2
x
2
ln
⁡
⁡
η
12
+
3
x
1
x
2
2
ln
⁡
⁡
η
21
-
ln
⁡
[
x
1
+
x
2
M
2
M
1
]
+
3
x
1
2
x
2
ln
⁡
[
2
+
M
2
/
M
1
3
]
+
3
x
1
x
2
2
ln
⁡
[
1
+
(
2
M
2
/
M
1
)
3
]
+
x
2
3
ln
⁡
[
M
2
M
1
]
.
Herric [6] correlation
(6)
ln
⁡
⁡
ν
=
x
1
ln
⁡
⁡
ν
1
+
x
2
ln
⁡
⁡
ν
2
+
x
1
x
2
[
α
12
+
α
´
12
(
x
1
-
x
2
)
]
-
ln
⁡
⁡
M
mix
+
x
1
ln
⁡
⁡
M
1
+
x
2
ln
⁡
⁡
M
2
,
and Grunberg-Nissan [7] equation
(7)
ln
⁡
(
η
)
=
x
1
ln
⁡
(
η
1
)
+
x
2
ln
⁡
(
η
2
)
+
d
12
x
1
x
2
have been fitted to viscosity data and it was found that both have the same standard errors at each temperature.


## 3.3. Isentropic Compressibility

The experimental results for the speed of sound of binary mixtures are listed in Tables2 and 3. The isentropic compressibility was evaluated by using K
S
=
u
-
2
ρ
-
1 and the deviation in isentropic compressibility is calculated using the following equation:
(8)
K
S
E
=
K
S
-
K
S
id
,
where K
S
id stands for isentropic compressibility for an ideal mixture calculated using Benson-Kiyohara model [8, 9]:
(9)
K
S
id
=
∑
i
=
1
2
Φ
i
[
K
S
,
i
+
T
V
i
(
α
i
2
)
C
p
,
i
]
-
{
T
(
∑
i
=
1
2
x
i
V
i
)
(
∑
i
=
1
2
Φ
i
a
i
)
2
∑
i
=
1
2
x
i
C
p
,
i
}
,
where a
i and C
p are the thermal expansion coefficient and molar heat capacity of the ith components, respectively.The deviation in speed of sound is given by(10)
Δ
u
=
u
-
x
1
u
1
-
x
2
u
2
.


## 3.4. Molar Refraction

Refractive indices have been used for the calculation of molar refraction (R
m) that is obtained by using Lorentz-Lorenz equation [8].Deviation in molar refraction (Δ
R) is calculated by the following equation:
(11)
R
=
R
m
-
∑
Φ
i
R
i
,
Φ
i
=
x
i
∑
x
j
V
j
,
where n
D refers to the refractive index, R
m is molar refraction of the mixture, R
i is molar refraction of the ith component, and Φ is ideal state volume fraction.All the deviations (V
E, Δ
R, Δ
η, Δ
u, and K
S
E) have been fitted to Redlich-Kister polynomial regression of the type
(12)
Δ
Y
=
x
1
x
2
∑
i
=
1
m
A
i
(
1
-
2
x
1
)
i
-
1
to derive the constant A
i using the method of the least square.Standard deviation for each case is calculated by(13)
σ
=
[
∑
(
Δ
Y
exptl
-
Δ
Y
calcd
)
2
m
-
n
]
0.5
,
where m is the number of data points and n is the number of coefficients. Derived parameters of the Redlich-Kister equation (12) and standard deviations (13) are presented in Tables 4 and 5.Table 4
Derived parameters of Redlich-Kister equation (12) and standard deviation (13) for various functions of the binary mixtures at different temperatures (DMSO-acetophenone).
T
/
K
A
0
A
1
A
2
A
3
σ
V
E (cm3·mol−1)
313.15
1.2005
0.741
−0.1784
−0.6838
0.01377
318.15
1.0176
0.7493
−0.5481
−0.7711
0.01379
323.15
0.7709
0.8700
−0.7689
−1.2620
0.01527
328.15
0.6714
0.9374
−0.9528
−1.3257
0.01381
Δ
η (mPa·s)
313.15
−0.2371
0.2135
0.2487
−0.4972
0.00461
318.15
−0.2575
0.2259
0.1846
−0.4935
0.00323
323.15
−0.2722
0.2375
0.0974
−0.4693
0.00309
328.15
−0.2887
0.2407
0.0508
−0.4755
0.00290
K
s
E (TPa−1)
313.15
4.8515
15.4271
−1.3121
−12.5359
0.11076
318.15
3.5099
15.7048
−1.8315
−12.902
0.09236
323.15
2.0047
21.1502
−4.7008
−34.8976
0.44672
328.15
0.0146
15.1308
−2.0538
−11.8737
0.17247
ΔR
313.15
0.06817
0.039577
−0.06186
−0.09945
0.006271
318.15
0.102475
0.056959
−0.00441
−0.06411
0.003073852
323.15
0.147987
0.106458
0.080891
−0.10664
0.005976
328.15
0.175329
0.134545
0.138756
−0.14317
0.008927
ΔG
E (J·mol−1)
313.15
−66.3882
516.3512
492.0794
−981.8602
9.00998
318.15
−141.309
625.565
410.846
−1119.199
7.38255
323.15
−234.912
700.1368
230.6251
−1143.3850
7.33602
328.15
−321.946
780.1317
132.3463
−1256.91
7.21134Table 5
Derived parameters of Redlich-Kister equation (12) and standard deviation (13) for various functions of the binary mixtures at different temperatures (DMSO-p-xylene).
T
/
K
A
0
A
1
A
2
A
3
σ
V
E (cm3·mol−1)
313.15
−8.5850
−15.1234
−6.084
12.8652
0.15687
318.15
−8.2010
−15.9715
−5.4345
15.6022
0.17024
323.15
−7.7110
−16.483
−4.7908
17.7396
0.19337
328.15
−7.1898
−16.3123
−4.0863
18.0512
0.20482
Δ
η (mPa·s)
313.15
−0.9028
−0.7268
−0.2127
0.25
0.00553
318.15
−0.8069
−0.7852
−0.1061
0.5942
0.00475
323.15
−0.7589
−0.7364
0.093
0.6582
0.00619
328.15
−0.7126
−0.6943
0.2137
0.6476
0.0067
K
s
E (TPa−1)
313.15
−119.0039
−64.4234
−74.9361
−36.2431
1.03835
318.15
−137.2976
−76.3846
−70.5856
−21.5844
0.97745
323.15
−148.0003
−81.8649
−67.7606
−17.6011
0.84832
328.15
−166.5237
−92.1709
−61.6439
−2.9525
0.87227
Δ
R
313.15
−3.25811
4.787247
−1.77213
−3.9986
0.226222
318.15
−3.20078
4.955419
−1.49922
−4.5735
0.239049
323.15
−3.14001
5.033874
−1.26969
−4.89488
0.245337
328.15
−3.0793
5.147192
−1.01287
−5.28097
0.254675
ΔG
E (J·mol−1)
313.15
−1022.2560
−1753.98
−140.348
1173.282
15.8755
318.15
−1013.8590
−2190.4
88.3584
2252.137
14.30563
323.15
−1011.6820
−2200.58
769.1765
2310.619
22.20041
328.15
−1113.8360
−2249.67
1294.863
2307.221
24.1139


## 4. Discussions

The excess molar volume from 313.15 to 328.15 K versus the mole fraction of both mixtures with respect to DMSO is shown in Figure1. The molar volume of the mixtures and the viscosity data have been used for the calculation of Gibbs’ free energy presented in Figure 5. The V
E values decrease with increasing temperatures for the systems but are positive in case of DMSO-acetophenone mixture and negative for DMSO-p-xylene mixture. Treszczanowicz et al. [10] and Roux and Desnoyers [11] suggested that V
E is the resultant contribution from several opposing effects. These effects can be primarily divided into three types, namely, chemical, physical, and structural. A physical contribution, that is, specific interactions between the real species present in the mixture, contribute in negative terms to V
E. The chemical or specific intermolecular interactions result in a volume decrease, and these include charge transfer type forces and other complex forming interactions. This effect also contributes in negative values to V
E. The structural contributions are mostly negative and can arise from several effects, especially from changes of free volume and interstitial accommodation. In other words, structural contributions arising from geometrical fitting of one component into the other due to the differences in the free volume and molar volume between components lead to a negative contribution to V
E. The viscosity and deviations are presented in Table 2 and plotted in Figure 2, respectively, for both systems. The viscosity deviations decrease with the increase in temperature for both systems. The negative Δ
η values are generally observed for systems where dispersion or weak dipole-dipole forces are primarily responsible for interaction between the component molecules. The viscosity data is also fitted to the two, and the three-parameter models, that is, Herric correlation, the McAllister model, and Grunberg-Nissan correlation, and the evaluated parameters are presented in Tables 6 and 7. The deviations in molar refraction for both systems are shown in Figure 3. The Δ
R values are positive for acetophenone system for the whole composition range which goes on increasing as the temperature of the solution increases. The Δ
R values are negative for para-xylene system for the whole composition range which goes on decreasing as the temperature of the solution increases. In general, the negative values of Δ
R suggest that we have weak interactions between the component molecules in the mixture. The results of excess isentropic compressibility (K
S
E) are also plotted in Figure 4. The deviations for DMSO-acetophenone system are initially negative and then become positive when mole fraction is around 0.5, whereas for DMSO-p-xylene system they are negative over the entire composition range. Deviation in Gibbs free energy for DMSO-acetophenone system follows an arbitrary path, going from negative to positive and vice versa twice, while for DMSO-p
a
r
a-xylene system the deviations are negative and increase with increasing temperature.Table 6
Interaction parameters for the McAllister model (5), Herric correlation (6), and Grunberg-Nissan correlation (7) for viscosity at different temperatures (DMSO-acetophenone).
McAllister model
T
/
K
η
12
η
21
σ(η)/mPa·s
313.15
1.3242
1.3473
0.00016
318.15
1.350624
1.334886
0.00025
323.15
1.377883
1.314174
0.00038
328.15
1.348994
1.240874
0.00042
Herric correlation
T
/
K
α
12
α
´
12
σ(η)/mPa·s
313.15
−0.02338
−0.01368
0.00016
318.15
−0.026
−0.01677
0.00025
323.15
−0.02874
−0.01993
0.00038
328.15
−0.03047
−0.02084
0.00042
Grunberg-Nissan correlation
T
/
K
d
12
σ(η)/mPa·s
313.15
−0.0956181
0.156414
318.15
−0.1201454
0.095161
323.15
−0.1618181
0.124392
328.15
−0.1988545
0.2077Table 7
Interaction parameters for the McAllister model (5), Herric correlation (6), and Grunberg-Nissan correlation (7) for viscosity at different temperatures (DMSO-p-xylene).
McAllister model
T
/
K
η
12
η
21
σ(η)/mPa·s
313.15
1.04511700
0.88014850
0.00304
318.15
1.03668800
0.87514410
0.00310
323.15
1.02613100
0.87012170
0.00325
328.15
1.01597400
0.86517980
0.00327
Herric correlation
T
/
K
α
12
α
´
12
σ(η)/mPa·s
313.15
0.04364338
0.13563440
0.00304
318.15
0.03664824
0.13067020
0.00310
323.15
0.03026920
0.12422880
0.00325
328.15
0.02245963
0.11706220
0.00327
Grunberg-Nissan correlation
T
/
K
d
12
σ(η)/mPa·s
313.15
−0.408281
0.01591
318.15
−0.377472
0.025161
323.15
−0.320472
0.01239
328.15
−0.312945
0.02016Figure 1
Experimental and calculated excess molar volume for (i) DMSO(
1
) + acetophenone(
2
) and (ii) DMSO(
1
) + p-Xylene(
2
) at 313.15 K, ♦, 318.15 K, ■, 323.15 K, ▲, 328.15 K, ●; symbols represent the experimental values; dotted lines represent DMSO-acetophenone mixture and solid lines represent DMSO-p-Xylene mixture, both optimised by Redlich-Kister parameters.Figure 2
Experimental and calculated deviations in viscosity for (i) DMSO(
1
) + acetophenone(
2
) and (ii) DMSO(
1
) + p-xylene(
2
) at 313.15 K, ♦, 318.15 K, ■, 323.15 K, ▲, 328.15 K, ●; symbols represent the experimental values; dotted lines represent DMSO-acetophenone mixture and solid lines represent DMSO-p-xylene mixture, both optimised by Redlich-Kister parameters.Figure 3
Experimental and calculated deviations in molar refraction for (i) DMSO(
1
) + acetophenone(
2
) and (ii) DMSO(
1
) + p-xylene(
2
) at 313.15 K, ♦, 318.15 K, ■, 323.15 K, ▲, 328.15 K, ●; and symbols represent the experimental values; dotted lines represent DMSO-acetophenone mixture and solid lines represent DMSO-p-xylene mixture, both optimised by Redlich-Kister parameters.Figure 4
Experimental and calculated deviations in isentropic compressibility for (i) DMSO(
1
) + acetophenone(
2
) and (ii) DMSO(
1
) + p-xylene(
2
) at 313.15 K, ♦, 318.15 K, ■, 323.15 K, ▲, 328.15 K, ●; and symbols represent the experimental values; dotted lines represent DMSO-Acetophenone mixture and solid lines represent DMSO-p-xylene mixture, both optimised by Redlich-Kister parameters.Figure 5
Experimental and calculated deviations in Gibbs free energy of activation for (i) DMSO(
1
) + acetophenone(
2
) and (ii) DMSO(
1
) + p-xylene(
2
) at 313.15 K, ♦, 318.15 K, ■, 323.15 K, ▲, 328.15 K, ●; and symbols represent the experimental values; solid lines represent DMSO-Acetophenone mixture and dotted lines represent DMSO-p-xylene mixture, both optimised by Redlich-Kister parameters.



---

*Source: 607052-2014-02-24.xml*