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

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.

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.

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 𝜂𝜈=𝜌𝐵=𝐴𝑡+𝑡. (1)

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 on 𝜌, 𝜂, 𝑛_𝐷, 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, 𝑛_𝐷, for DMSO(1) + CUMENE(2) at different temperatures.

3.1. Excess Molar Volume

Density is used to evaluate excess molar volume calculated by the equation 𝑉^𝐸=𝑥₁𝑀₁+𝑥₂𝑀₂𝜌−𝑥₁𝑀₁𝜌₁−𝑥₂𝑀₂𝜌₂, (2) 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 Δ𝐺^𝐸=𝑅𝑇ln𝜂𝑉−²_𝑖=1𝑥_𝑖ln𝜂_𝑖𝑉_𝑖 (3)𝑅 is a universal gas constant; 𝑇 is the temperature of the mixture. 𝜂, 𝜂_𝑖 are the viscosity of the mixture and pure compound, respectively. 𝑉, 𝑉_𝑖 refers to the molar volume of the mixture and pure components, respectively.

3.2. Viscosity Calculations

The deviation in viscosity is obtained by equation Δ𝜂=𝜂−𝑥₁𝜂₁−𝑥₂𝜂₂. (4)𝜂₁, 𝜂₂ refers to the viscosity of pure components and 𝜂 is the viscosity of mixture. McAllister [3] model ln𝜈=𝑥³₁ln𝜈₁+𝑥³₂ln𝑣₂+3𝑥²₁𝑥₂ln𝜂₁₂+3𝑥₁𝑥²₂ln𝜂₂₁−ln𝑥₁+𝑥₂𝑀₂𝑀₁+3𝑥²₁𝑥₂𝑀ln2+₂/𝑀₁3+3𝑥₁𝑥²₂ln1+2𝑀₂/𝑀₁3+𝑥³₂𝑀ln²𝑀₁ (5) and herric correlation ln𝑣=𝑥₁ln𝑣₁+𝑥₂ln𝜈₂+𝑥₁𝑥₂𝛼₁₂+𝛼^′₁₂x₁−x₂−ln𝑀_mix+𝑥₁ln𝑀₁+𝑥₂ln𝑀₂ (6) 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 Table 2. The isentropic compressibility was evaluated by 𝐾_𝑆=𝑢⁻²𝜌⁻¹ and the deviation in isentropic compressibility is calculated using the below equation: 𝐾^𝐸_𝑆=𝐾_𝑆−𝐾_𝑆^𝑖𝑑 (7) and deviation in speed of sound by Δ𝑢=𝑢−𝑥₁𝑢₁−𝑥₂𝑢₂, (8) where 𝐾_𝑆^𝑖𝑑 stands for isentropic compressibility for an ideal mixture calculated using the relation 𝐾_𝑆^𝑖𝑑=²_𝑖=1Φ_𝑖𝐾_𝑆,𝑖+𝑇𝑉_𝑖𝑎²_𝑖𝐶_𝑝,𝑖−𝑇∑²_𝑖=1𝑥_𝑖𝑉_𝑖∑²_𝑖=1Φ_𝑖𝑎_𝑖²∑²_𝑖=1𝑥_𝑖𝐶_𝑝,𝑖 (9) recommended by Kiyohara and Benson [4]. (1979) and Douhéret et al. [5] (1997), where 𝑎_𝑖 and 𝐶_𝑝,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 (𝑅_𝑚) obtained by using Lorenz-Lorenz [6] equation 𝑅_𝑚=𝑛²_𝐷−1𝑛²_𝐷𝑥−2^𝑖𝑀_𝑖𝜌_𝑚,𝑅_𝑖=𝑛²_𝐷−1𝑛²_𝐷𝑀−2𝜌^𝑖_𝑖. (10) Deviation in molar refraction (Δ𝑅) is calculated by equation Δ𝑅=𝑅_𝑚−Φ_𝑖𝑅_𝑖,𝑥Φ=^𝑖,∑𝑥𝑗𝑉𝑗 (11) where 𝑛_𝐷 refers to 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, Δ𝑅, Δ𝜂, Δ𝑢, 𝐾^𝐸_𝑆) have been fitted to Redlich-Kister [7] polynomial regression of the type Δ𝑌=𝑥₁𝑥₂^𝑚_𝑖=1𝐴_𝑗−11−2𝑥₁^𝑗−1 (12) to derive the constant 𝐴_𝑗 using the method of least square. Standard deviation for each case is calculated by ∑𝜎=Δ𝑌_expt𝑙−Δ𝑌_calc𝑑²𝑚−𝑛^0.5, (13) 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 3

Table 3 

Derived parameters of Redlich-Kister equation (12) and standard deviation (13) for various functions of the binary mixtures at different temperatures.

4. Discussions

The deviations in excess molar volume at 298.15 to 313.15 K versus the mole fraction of DMSO are shown in Figure 1. 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 𝑉^𝐸 indicate an interaction between the molecules which decreases with an increase of temperature. The large negative 𝑉^𝐸 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 Table 2 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 Table 4. 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.

The deviations in molar refraction are shown in Figure 3. 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 derived 𝐾^𝐸_𝑆 are also plotted in Figure 4. The deviations are negative over the whole composition range. The 𝐾^𝐸_𝑆 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.

Symbols

𝐴0, 𝐴1, 𝐴2, 𝐴3:	Parameters of Redlich-Kister equation
𝐴12,  𝐴21:	Interaction coefficient of McAllister model
𝛼12,  𝛼′12:	Coefficients of Herric’s correlation
𝑣:	Kinematic viscosity (m2/s)
𝜌:	Density (g/cm³)
𝜎:	Standard deviation
𝛼:	Expansion coefficient
𝜂:	Viscosity (cP)
Δ𝐺𝐸:	Excess Gibbs free energy (J/mol)
𝑉𝐸:	Excess molar volume
Δ𝐾𝐸𝑆:	Excess isentropic compressibility
𝑅:	Universal gas constant (8.314 J/mol.K)
𝑇:	Absolute temperature (K)
Φ𝑖:	Volume fraction (dimensionless).