# Thermo Physical Properties for Binary Mixture of Dimethylsulfoxide and Isopropylbenzene at Various Temperatures

Authors: Maninder Kumar; V. K. Rattan
Journal: Journal of Thermodynamics
 (2013)

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## Abstract

Density, refractive index, speed of sound, and viscosity have been measured of binary mixture dimethylsulfoxide (DMSO) + isopropylbenzene (CUMENE) over the whole composition range at 298.15, 303.15, 308.15, and 313.15 K and atmospheric pressure. From these experimental measurements the excess molar volume, deviations in viscosity, molar refractivity, speed of sound, and isentropic compressibility have been calculated. These deviations have been correlated by a polynomial Redlich-Kister equation to derive the coefficients and standard error. The viscosities have furthermore been correlated with two or three parameter models, that is, herric correlation and McAllister model, respectively.


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## Body

## 1. Introduction

This paper contributes in part to our ongoing research on the solution properties. In the present study, data on density, viscosity, refractive index and speed of sound of binary mixture dimethylsulfoxide (DMSO) + isopropylbenzene at 298.15, 303.15, 308.15, and 313.15 K have been measured experimentally. From these results the excess molar volumes, viscosity deviations, and deviations in molar refraction and isentropic compressibility have been derived. Dimethylsulfoxide is a versatile nonaqueous dipolar aprotic solvent having wide range of applications. It is used as a solvent in many nucleophilic substitutions reactions. It has the ability to pass through membranes, an ability that has been verified by numerous subsequent researchers. It can penetrate through living tissues without damaging them. Therefore local anesthetic or penicillin can be carried through the skin without using a needle which makes it a paramount in medicinal field.Isopropylbenzene is a naturally occurring substance present in coal tar and petroleum, insoluble in water, but is soluble in many organic solvents. It is used as a feedback for the production of Phenol and its coproduct acetone. It is also used as a solvent for fats and raisins.The study of the thermodynamic properties of DMSO + isopropylbenzene mixtures is of interest in industrial fields where solvent mixtures could be used as selective solvents for numerous reactions.


## 2. Experimental Section

### 2.1. Materials

The chemicals used are of AR grade, dimethylsulfoxide (DMSO) and isopropylbenzene (CUMENE) are from Riedel, Germany. The chemicals are purified using standard procedure [1] and are stored over molecular sieves. The purity of the chemicals was verified by comparing viscosity, density, and refractive index with the known values reported in the literature as shown in Table 1. All the compositions are prepared by using SARTOIS balance. The possible error in the mole fraction is estimated to be less than ±1×10-4.Table 1
Physical properties of components at 298.15 K.
Component
T
/
K
ρ/g·cm−3
η/mPa·s
n
D
exptl
lit
exptl
lit
exptl
lit
DMSO
298.15
1.0940
1.095379
1.9834
1.99109
1.4798
1.47759
CUMENE
298.15
0.8581
0.857439
0.7388
0.73909
1.4928
1.48899


### 2.2. Density and Speed of Sound

Density and Speed of sound were measured by ANTON PAAR densimeter (DSA 5000) to an accuracy of±0.000005 g/cm−3  and ±0.5 m/s, respectively. The densimeter was calibrated with bi-distilled degassed water.


### 2.3. Viscosity

Viscosities were measured by using calibrated modified Ubbelohde viscometer [2] as described earlier. The calibration of viscometer was done at each temperature in order to determine constants A and B of equation
(1)ν=ηρ=At+Bt.Flow time was measured with an electronic stop watch with precision of±0.01 s. For each measurement viscometer was kept vertically in water bath for half an hour at constant temperature in order to attain thermodynamic equilibrium. The temperature of the bath was maintained constant with the help of circulating type cryostat where the temperature is controlled to ±0.02 K. The efflux time was repeated at least three times for each composition. The uncertainty in the values is within ±0.003 mPa·s.


### 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 water bath as described 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 data are accurate to ±0.0001 units.


## 2.1. Materials

The chemicals used are of AR grade, dimethylsulfoxide (DMSO) and isopropylbenzene (CUMENE) are from Riedel, Germany. The chemicals are purified using standard procedure [1] and are stored over molecular sieves. The purity of the chemicals was verified by comparing viscosity, density, and refractive index with the known values reported in the literature as shown in Table 1. All the compositions are prepared by using SARTOIS balance. The possible error in the mole fraction is estimated to be less than ±1×10-4.Table 1
Physical properties of components at 298.15 K.
Component
T
/
K
ρ/g·cm−3
η/mPa·s
n
D
exptl
lit
exptl
lit
exptl
lit
DMSO
298.15
1.0940
1.095379
1.9834
1.99109
1.4798
1.47759
CUMENE
298.15
0.8581
0.857439
0.7388
0.73909
1.4928
1.48899


## 2.2. Density and Speed of Sound

Density and Speed of sound were measured by ANTON PAAR densimeter (DSA 5000) to an accuracy of±0.000005 g/cm−3  and ±0.5 m/s, respectively. The densimeter was calibrated with bi-distilled degassed water.


## 2.3. Viscosity

Viscosities were measured by using calibrated modified Ubbelohde viscometer [2] as described earlier. The calibration of viscometer was done at each temperature in order to determine constants A and B of equation
(1)ν=ηρ=At+Bt.Flow time was measured with an electronic stop watch with precision of±0.01 s. For each measurement viscometer was kept vertically in water bath for half an hour at constant temperature in order to attain thermodynamic equilibrium. The temperature of the bath was maintained constant with the help of circulating type cryostat where the temperature is controlled to ±0.02 K. The efflux time was repeated at least three times for each composition. The uncertainty in the values is within ±0.003 mPa·s.


## 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 water bath as described 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 data are accurate to ±0.0001 units.


## 3. Experimental Results and Correlations

At least three independent readings of all the physical property measurements onρ, η, nD, and u were taken for each composition and the averages of these experimental values are presented in Table 2. The experimentally determined values are used for the deviation calculations.Table 2
Density,ρ, viscosity, η, speed of Sound, u, and refractive indices, nD, for DMSO(1) + CUMENE(2) at different temperatures.
ρ
η
u
n
D
x
1
g·cm−3
mPa·s
m·s−1
Dimethylsulfoxide(1) + isopropylbenzene(2)
298.15 K
0.0000
0.8581
0.7388
1325
1.4928
0.1047
0.8721
0.8025
1336
1.4918
0.1866
0.8842
0.8603
1348
1.4909
0.3013
0.9031
0.9610
1365
1.4897
0.3835
0.9180
1.0397
1378
1.4887
0.5032
0.9421
1.1661
1400
1.4871
0.5858
0.9610
1.2692
1417
1.4859
0.6972
0.9895
1.4337
1442
1.4841
0.7926
1.0178
1.5896
1467
1.4829
0.8929
1.0519
1.7648
1493
1.4811
1.0000
1.0940
1.9834
1523
1.4798
303.15 K
0.0000
0.8538
0.6806
1313
1.4915
0.1047
0.8676
0.7519
1327
1.4905
0.1866
0.8797
0.8143
1339
1.4898
0.3013
0.8984
0.9064
1356
1.4885
0.3835
0.9132
0.9814
1369
1.4875
0.5032
0.9372
1.1086
1391
1.4859
0.5858
0.9559
1.2075
1408
1.4848
0.6972
0.9843
1.3691
1434
1.4829
0.7926
1.0122
1.5230
1459
1.4815
0.8929
1.0459
1.6943
1485
1.4796
1.0000
1.0890
1.8949
1512
1.4781
308.15 K
0.0000
0.8495
0.6167
1301
1.4896
0.1047
0.8632
0.6962
1317
1.4888
0.1866
0.8751
0.7616
1329
1.4881
0.3013
0.8936
0.8565
1346
1.4869
0.3835
0.9083
0.9294
1359
1.4859
0.5032
0.9322
1.0493
1381
1.4844
0.5858
0.9508
1.1459
1398
1.4833
0.6972
0.9788
1.3059
1425
1.4814
0.7926
1.0064
1.4565
1449
1.4799
0.8929
1.0404
1.6131
1473
1.4784
1.0000
1.0840
1.7979
1498
1.4765
313.15 K
0.0000
0.8452
0.5588
1289
1.4871
0.1047
0.8587
0.6434
1306
1.4864
0.1866
0.8705
0.7103
1319
1.4857
0.3013
0.8887
0.8063
1337
1.4846
0.3835
0.9033
0.8756
1349
1.4836
0.5032
0.9270
0.9947
1372
1.4821
0.5858
0.9454
1.0872
1389
1.4809
0.6972
0.9732
1.2459
1416
1.4792
0.7926
1.0008
1.3888
1439
1.4778
0.8929
1.0348
1.5402
1462
1.4762
1.0000
1.0786
1.7054
1486
1.4742


### 3.1. Excess Molar Volume

Density is used to evaluate excess molar volume calculated by the equation(2)VE=x1M1+x2M2ρ-x1M1ρ1-x2M2ρ2,
where ρ1, ρ2 are the densities of pure components and ρ is the density of mixture. M1, M2 are the molecular weight of the two components. x1, x2 are the mole fraction of DMSO.Excess gibb’s free energy of activation has been also calculated using the viscosity and density of the mixture by the equation(3)ΔGE=RT[ln(ηV)-∑i=12xiln(ηiVi)]R is a universal gas constant; T is the temperature of the mixture. η, ηi are the viscosity of the mixture and pure compound, respectively. V, Vi  refers to the molar volume of the mixture and pure components, respectively.


### 3.2. Viscosity Calculations

The deviation in viscosity is obtained by equation(4)Δη=η-x1η1-x2η2.η1, η2 refers to the viscosity of pure components and η is the viscosity of mixture. McAllister [3] model
(5)lnν=x13lnν1+x23lnv2+3x12x2lnη12+3x1x22lnη21-ln[x1+x2M2M1]+3x12x2ln[2+(M2/M1)3]+3x1x22ln[1+(2M2/M1)3]+x23ln[M2M1]
and herric correlation
(6)lnv=x1lnv1+x2lnν2+x1x2[α12+α12′(x1-x2)]-lnMmix+x1lnM1+x2lnM2
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 mixture are listed in Table2. The isentropic compressibility was evaluated by KS=u-2ρ-1 and the deviation in isentropic compressibility is calculated using the below equation:
(7)KSE=KS-KSid
and deviation in speed of sound by
(8)Δu=u-x1u1-x2u2,
where KSid stands for isentropic compressibility for an ideal mixture calculated using the relation
(9)KSid=∑i=12Φi[KS,i+TVi(ai2)Cp,i]-{T(∑i=12xiVi)(∑i=12Φiai)2∑i=12xiCp,i}
recommended by Kiyohara and Benson [4]. (1979) and Douhe´ret et al. [5] (1997), where ai and Cp,i are the volume expansion coefficient and heat capacity of the ith components.


### 3.4. Molar Refraction

Refractive indices have been used for the calculation of Molar refraction (Rm) obtained by using Lorenz-Lorenz [6] equation
(10)Rm=[nD2-1][nD2-2]∑xiMiρm,Ri=[nD2-1][nD2-2]Miρi.
Deviation in molar refraction (ΔR) is calculated by equation
(11)ΔR=Rm-∑ΦiRi,Φ=xi∑xjVj,
where nD refers to refractive index, Rm is molar refraction of the mixture, Ri is molar refraction of the ith component, and Φ is ideal state volume fraction.All the deviations (VE, ΔR, Δη, Δu, KSE) have been fitted to Redlich-Kister [7] polynomial regression of the type
(12)ΔY=x1x2∑i=1mAj-1(1-2x1)j-1
to derive the constant Aj using the method of least square. Standard deviation for each case is calculated by
(13)σ=[∑(ΔYexptl-ΔYcalcd)2m-n]0.5,
where m is the number of data points and n is the number of coefficients. Derived parameters of the redlich-Kister (12) equation and standard deviations (13) are presented in Table 3Table 3
Derived parameters of Redlich-Kister equation (12) and standard deviation (13) for various functions of the binary mixtures at different temperatures.
T
/K
A
0
A
1
A
2
A
3
σ
V
E/cm3·mol−1
298.15
-
1.6771
-
0.2071
-
0.0446
-
0.6836
0.00561
303.15
-
1.5289
-
0.2059
0.5117
-
0.0903
0.0055
308.15
-
1.3339
-
0.0698
0.7925
0.1613
0.0046
313.15
-
1.0884
0.0276
0.8186
0.1259
0.00549
Δη/mPa·s
298.15
-
0.7847
-
0.1293
0.0065
0.0645
0.00296
303.15
-
0.7328
-
0.1197
0.1384
0.0587
0.00178
308.15
-
0.6393
-
0.1245
0.2208
0.0967
0.00359
313.15
-
0.5606
-
0.1118
0.2922
0.141
0.00333
K
S
E
/TPa−1
298.15
-
121.777
-
64.3513
-
24.8534
-
29.8607
0.37123
303.15
-
133.145
-
66.2282
-
46.6216
-
17.4037
0.21847
308.15
-
144.714
-
73.4879
-
59.3712
4.1751
0.27323
313.15
-
157.833
-
74.2561
-
62.2923
10.1465
0.51612
ΔR
298.15
-
0.7478
0.2009
−0.1111
0.2177
0.0089
303.15
-
0.6486
0.1994
0.0606
0.045
0.0056
308.15
-
0.5417
0.2093
0.2408
-
0.0917
0.0127
313.15
-
0.4454
0.1947
0.3148
-
0.1187
0.0167
Δ
G
E/J·mol−1
298.15
133.9592
209.2619
16.9998
168.234
64.9657
303.15
246.905
198.0077
349.8235
15.7865
3.63471
308.15
488.086
69.5143
603.5378
59.8815
7.55398
313.15
724.2593
-
0.9946
832.3713
64.9657
8.13559


## 3.1. Excess Molar Volume

Density is used to evaluate excess molar volume calculated by the equation(2)VE=x1M1+x2M2ρ-x1M1ρ1-x2M2ρ2,
where ρ1, ρ2 are the densities of pure components and ρ is the density of mixture. M1, M2 are the molecular weight of the two components. x1, x2 are the mole fraction of DMSO.Excess gibb’s free energy of activation has been also calculated using the viscosity and density of the mixture by the equation(3)ΔGE=RT[ln(ηV)-∑i=12xiln(ηiVi)]R is a universal gas constant; T is the temperature of the mixture. η, ηi are the viscosity of the mixture and pure compound, respectively. V, Vi  refers to the molar volume of the mixture and pure components, respectively.


## 3.2. Viscosity Calculations

The deviation in viscosity is obtained by equation(4)Δη=η-x1η1-x2η2.η1, η2 refers to the viscosity of pure components and η is the viscosity of mixture. McAllister [3] model
(5)lnν=x13lnν1+x23lnv2+3x12x2lnη12+3x1x22lnη21-ln[x1+x2M2M1]+3x12x2ln[2+(M2/M1)3]+3x1x22ln[1+(2M2/M1)3]+x23ln[M2M1]
and herric correlation
(6)lnv=x1lnv1+x2lnν2+x1x2[α12+α12′(x1-x2)]-lnMmix+x1lnM1+x2lnM2
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 mixture are listed in Table2. The isentropic compressibility was evaluated by KS=u-2ρ-1 and the deviation in isentropic compressibility is calculated using the below equation:
(7)KSE=KS-KSid
and deviation in speed of sound by
(8)Δu=u-x1u1-x2u2,
where KSid stands for isentropic compressibility for an ideal mixture calculated using the relation
(9)KSid=∑i=12Φi[KS,i+TVi(ai2)Cp,i]-{T(∑i=12xiVi)(∑i=12Φiai)2∑i=12xiCp,i}
recommended by Kiyohara and Benson [4]. (1979) and Douhe´ret et al. [5] (1997), where ai and Cp,i are the volume expansion coefficient and heat capacity of the ith components.


## 3.4. Molar Refraction

Refractive indices have been used for the calculation of Molar refraction (Rm) obtained by using Lorenz-Lorenz [6] equation
(10)Rm=[nD2-1][nD2-2]∑xiMiρm,Ri=[nD2-1][nD2-2]Miρi.
Deviation in molar refraction (ΔR) is calculated by equation
(11)ΔR=Rm-∑ΦiRi,Φ=xi∑xjVj,
where nD refers to refractive index, Rm is molar refraction of the mixture, Ri is molar refraction of the ith component, and Φ is ideal state volume fraction.All the deviations (VE, ΔR, Δη, Δu, KSE) have been fitted to Redlich-Kister [7] polynomial regression of the type
(12)ΔY=x1x2∑i=1mAj-1(1-2x1)j-1
to derive the constant Aj using the method of least square. Standard deviation for each case is calculated by
(13)σ=[∑(ΔYexptl-ΔYcalcd)2m-n]0.5,
where m is the number of data points and n is the number of coefficients. Derived parameters of the redlich-Kister (12) equation and standard deviations (13) are presented in Table 3Table 3
Derived parameters of Redlich-Kister equation (12) and standard deviation (13) for various functions of the binary mixtures at different temperatures.
T
/K
A
0
A
1
A
2
A
3
σ
V
E/cm3·mol−1
298.15
-
1.6771
-
0.2071
-
0.0446
-
0.6836
0.00561
303.15
-
1.5289
-
0.2059
0.5117
-
0.0903
0.0055
308.15
-
1.3339
-
0.0698
0.7925
0.1613
0.0046
313.15
-
1.0884
0.0276
0.8186
0.1259
0.00549
Δη/mPa·s
298.15
-
0.7847
-
0.1293
0.0065
0.0645
0.00296
303.15
-
0.7328
-
0.1197
0.1384
0.0587
0.00178
308.15
-
0.6393
-
0.1245
0.2208
0.0967
0.00359
313.15
-
0.5606
-
0.1118
0.2922
0.141
0.00333
K
S
E
/TPa−1
298.15
-
121.777
-
64.3513
-
24.8534
-
29.8607
0.37123
303.15
-
133.145
-
66.2282
-
46.6216
-
17.4037
0.21847
308.15
-
144.714
-
73.4879
-
59.3712
4.1751
0.27323
313.15
-
157.833
-
74.2561
-
62.2923
10.1465
0.51612
ΔR
298.15
-
0.7478
0.2009
−0.1111
0.2177
0.0089
303.15
-
0.6486
0.1994
0.0606
0.045
0.0056
308.15
-
0.5417
0.2093
0.2408
-
0.0917
0.0127
313.15
-
0.4454
0.1947
0.3148
-
0.1187
0.0167
Δ
G
E/J·mol−1
298.15
133.9592
209.2619
16.9998
168.234
64.9657
303.15
246.905
198.0077
349.8235
15.7865
3.63471
308.15
488.086
69.5143
603.5378
59.8815
7.55398
313.15
724.2593
-
0.9946
832.3713
64.9657
8.13559


## 4. Discussions

The deviations in excess molar volume at 298.15 to 313.15 K versus the mole fraction of DMSO are shown in Figure1. The molar volume of the mixture and the viscosity data have also been used for the calculation of Gibb’s free energy presented in Figure 5. The negative values of VE indicate an interaction between the molecules which decreases with an increase of temperature. The large negative VE values indicate a contraction of the volume and can be explained in terms of the heteroassociation in the mixture and suggest the strongest association occurs in this binary system [8].Figure 1
Experimental and calculated excess molar for the DMSO(1) + CUMENE(2) at ♦, 298.15 K; ■, 303.15 K; ▲, 308.15 K; ×, 313.15 K; symbols represent the experimental values; lines are optimised by Redlich-Kister parameters.The viscosity and deviations are presented in Table2 and plotted in Figure 2, respectively. The negative values of Δη obtained for the investigated mixture suggest that there may be reduction in the strength of H-bonds upon mixing. The viscosity data can be qualitatively explained by considering that the Cumene has a branching CH3 group, leading to packing of molecules in the pure state and a consequent lower density and larger mobility (lower viscosity) of the structure. This may be because interaction of Cumene with DMSO is less [6].Figure 2
Experimental and calculated deviations in viscosity for DMSO(1) + CUMENE(2) at ♦, 298.15 K; ■, 303.15 K; ▲, 308.15 K; ×, 313.15 K; symbols represent the experimental values; lines are optimised by Redlich-Kister parameters.The viscosity data is also fitted to the two- and the three-parameter model, that is, herric correlation and the McAllister model and the evaluated parameters are presented in Table4. The deviations decrease with the increase in temperature.Table 4
Interaction parameters for the McAllister model (5) and herric correletion (6) for viscosity at different temperatures.
T/K
η
12
η
21
σ(η)/mPa·s
McAllister model
298.15
0.975300
0.909494
0.00014
303.15
0.968905
0.905236
0.00032
308.15
0.962426
0.900935
0.00044
313.15
0.958670
0.900372
0.00051
T/K
α
12
α
12
′
σ(η)/mPa·s
Herric correlation
298.15
-
0.02338
-
0.01368
0.00014
303.15
-
0.02600
-
0.01677
0.00032
308.15
-
0.02874
-
0.01993
0.00044
313.15
-
0.03047
-
0.02084
0.00052The deviations in molar refraction are shown in Figure3. The ΔR values are negative for the whole composition range which goes on decreasing as the temperature of the solution increases.Figure 3
Experimental and calculated deviations in molar refraction for DMSO(1) + CUMENE(2) at ♦, 298.15 K; ■, 303.15 K; ▲, 308.15 K; ×, 313.15 K; symbols represent the experimental values; lines are optimised by Redlich-Kister parameters.The results of derivedKSE are also plotted in Figure 4. The deviations are negative over the whole composition range. The KSE is negative near the composition of x1=0.7 and then abruptly goes to zero.Figure 4
Experimental and calculated deviations in isentropic compressibility for DMSO(1) + CUMENE(2) at ♦, 298.15 K; ■, 303.15 K; ▲, 308.15 K; ×, 313.15 K; symbols represent the experimental values; lines are optimised by Redlich-Kister parameters.Figure 5
Experimental and calculated deviations in Gibbs free energy of activation for DMSO(1) + CUMENE(2) at ♦, 298.15 K; ■, 303.15 K; ▲, 308.15 K; ×, 313.15 K; symbols represent the experimental values; Lines are optimised by Redlich-Kister parameters.



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*Source: 353841-2013-04-29.xml*