Studies on Excess Volume , Viscosity , and Speed of Sound of Binary Mixtures of Methyl Benzoate in Ethers at T = ( 303 .

Densities, viscosities, and speed of sound have been determined at T = (303.15, 308.15, and 313.15) K for the binary mixtures of methyl benzoate with tetrahydrofuran, 1,4-dioxane, anisole, and butyl vinyl ether over the entire range of composition. Using these measured values, excess volume V, deviation in viscosities Δη, excess Gibb’s free energy of activation for viscous flow ΔG, and deviation in isentropic compressibility Δk s have been calculated. These calculated binary data have been fitted to Redlich-Kister equation to determine the appropriate coefficients. The values of excess volume VE and deviation in viscosities Δη are negative over the entire range of composition for all the binary systems at the studied temperatures. The behavior of these parameters with composition of the mixture has been discussed in terms of molecular interactions between the components of liquids.


Introduction
The excess or deviation properties of liquid-liquid mixtures are useful in several industrial applications owing to their influence upon the effectiveness of the operations.Nowadays, the determination of ultrasonic velocity and the related acoustical parameters derived from it has attracted the attention of several researchers.Much work has been done in solutions of polymers [1][2][3], pharmamaterials [4], electrolytes [5][6][7], and nonelectrolytes [8][9][10].
Tetrahydrofuran is a polar ( = 1.75), aprotic solvent.It's main use is a precursor to polymers.It is also used as an industrial solvent for PVC and in varnishes.Dye carrier formulations based on methyl benzoate are useful in textile processing.Further methyl benzoate finds its primary uses as a perfume or flavouring agent and also used as a source of benzoyl radical.While ethers are excellent solvents, because they are relatively unreactive, yet they solvate a wide variety of compounds.Tetrahydrofuran, a cyclic ether which is one of the most polar simple ethers, is used as a solvent for polymers and also commercially used for the production of several compounds.Anisole, an aryl ether, is a major constituent of essential oil of anise seed.
In view of the abovementioned significances, these solvents are chosen with an aim to investigate the effect of the presence of two lone pairs of electrons on the oxygen atom of ether, when it is mixed with methyl benzoate.Moreover, it would be interesting to know the behavior of ether in an environment of aromatic ester molecules.The main objective of the present study is to determine the density , viscosity , and speed of sound  for the binary mixtures formed by the methyl benzoate with ether compounds.
In our earlier papers [11][12][13], we have reported some data on thermodynamic, transport, acoustical, and optical properties on mixtures of methyl benzoate with hydrocarbons and ketones and analysed the data in terms of molecular interactions.Several authors have also published density, viscosity, and speed of sound data [14][15][16][17][18][19][20] of binary mixtures of methyl benzoate with different types of organic solvents.In the present study, we report the results of density , viscosity , and speed of sound  for the binary mixtures of methyl benzoate with ethers, namely, tetrahydrofuran, 1,4-dioxane, 308.15 1.0743 1.0740 [18] 1.517 1.510 [18] 1.0741 [19] 1.504 [20] 1.07399 [20] 1 .5 1 0 [ 21] 313.15 [18][19][20][21][22][23][24][25][26][27][28] as shown in Table 1. .The resulting uncertainty in mole fraction was estimated to be less than ±0.0001.Each mixture was immediately used after it was well mixed by shaking.The densities of the pure and their binary mixtures were determined by using an Anton Paar density meter (DMA 4100).The uncertainty in the density measurements was found to be less than ±0.0004 g⋅cm −3 .Viscosities were determined using an Ubbelohde viscometer with an uncertainty of ±0.008 mPa.s.The detailed method of measurement of viscosity has been reported earlier [11].The speeds of sound were measured with a single crystal variable path interferometer (Mittal Enterprises, New Delhi, India) at an operating frequency of 2 MHz that had been calibrated with double distilled water and benzene.The uncertainty in speed of sound was estimated to be ±1 m⋅s −1 .

Results and Discussion
The experimental values of densities , excess volumes   , viscosities , speeds of sound , and isentropic compressibility   of the binary mixtures of methyl benzoate with tetrahydrofuran, 1,4-dioxane, anisole, and butyl vinyl ether at temperatures 303.15, 308.15, and 313.15K are listed in Table 2.
The excess volume   of the mixtures was deduced from the measured densities using the following relation: where , , and  are the mole fraction, molar mass, and density, respectively, of pure components 1 and 2.  12 is the density of the liquid mixture.The Gibb's free energy of activation for viscous flow Δ *  was calculated from the viscosity data using the following relation: where V = ( 1  1 / 1 +  2  2 )/ 12 is the molar volume of the mixture and V 1 and V 2 are the molar volumes of the pure components.
The isentropic compressibilities   were calculated from the densities  and speeds of sound  using the Newton-Laplace equation: The deviation in viscosity Δ and deviation in isentropic compressibility Δ  were calculated using the general equation: where Δ is the deviation property in question,   refers to the property of the mixture, and  1  1 and  2  2 refer to the mole fraction and specific property of the pure components 1 and 2, respectively.The results of these excess or deviation properties were fitted by the method of least squares to the Redlich-Kister [29] polynomial type equation: where  is   , Δ, Δ *  , or Δ  and  1 and  2 are the mole fractions of pure components 1 and 2, respectively. −1 is the polynomial coefficient, and  is the polynomial degree.The degree of ( 5) was optimised by applying the test.The correlated results are shown in Table 3 in which the tabulated standard deviation  was calculated using the following relation: where  is the number of data points and  is the number of coefficients.The subscripts exp and cal denote experimental and calculated values, respectively.The variations of excess volume   with mole fraction  1 of methyl benzoate at the studied temperatures for the binary mixtures are displayed in Figure 1.It is observed that all the studied systems exhibit negative deviations.The   data for different components of the mixtures vary in the sequence: The effect of temperature on   as displayed in Figure 1 is quite significant, as the negative   values increase with increase in temperature.The behavior of   can be explained  by considering the type of component molecules in pure state and in mixture.In the present case, the negative   values may be attributed to the differences in the dielectric constants of the components.The dielectric constants of methyl benzoate, tetrahydrofuran, 1,4-dioxane, anisole, and butyl vinyl ether are  = 6.02, 7.261, 2.209, 4.33, 3.9, respectively.Further, there is a possibility of electron donor-acceptor type or charge transfer interactions [30] between the highly electronegative oxygen of ether and the -electron of ring of aromatic ester molecule resulting in negative   values.The less negative   values in case of methyl benzoate + anisole may be due to the presence of methyl (-CH 3 ) group in anisole.This observation suggests that with an increase in methyl group in mixture, the donor-acceptor interactions between the unlike molecules tend to decrease.The results of Δ as displayed in the Figure 2   It is observed that negative values of Δ decrease with increase in the temperature indicating the effect of temperature on Δ.Fort and Moore [31] observed that the negative Δ values indicate the dispersion forces without involving the formation of any hetero-molecular complexes.A perusal of Figures 1 and 2 reveals that both   and Δ exhibit the negative deviations over the entire range of composition; however, the magnitude values of the studied mixtures follow a different sequence.This type of behavior supports the observation of Rastogi et al. [32] and Kaulgud [33], suggesting that the strength of specific or dispersion forces is not the only factor influencing the Δ, but the molecular size and shape of the components are also equally important.
The dependence of Δ *  on the mole fraction is shown in Figure 3, where it was observed that Δ *  is positive for mixtures of methyl benzoate with tetrahydrofuran, 1,4-dioxane, and anisole, whereas for mixtures of methyl benzoate + butyl vinyl ether, the values of Δ *  are negative over the entire range of composition.The positive Δ *  values may be an indicative of specific interactions [31,34,35] and the negative Δ *  values indicate the presence of dispersive forces in these mixtures.The plots of Δ  , as displayed in Figure 4, show that for methyl benzoate with tetrahydrofuran, 1,4-dioxane, and butyl vinyl ether, the values of Δ  exhibit negative deviation over the entire range of mixture composition; while for methyl benzoate + anisole, the values of Δ  exhibit positive deviations.The positive Δ  values are a sign of weak interaction between component molecules, which may be attributed to the mutual disruption in molecules associated with pure liquids.These positive Δ  values are accompanied by a decrease in sound velocity over the entire range of composition of ester.The negative values of Δ  may be attributed to the formation of weak bonds [36][37][38] by dipoleinduced dipole interaction between unlike molecules and the geometrical fitting of component molecules in to each other's structure.

Conclusions
The densities , excess volumes   , viscosities , speeds of sound , and data of binary mixtures methyl benzoate  with tetrahydrofuran, 1,4-dioxane, anisole, and butyl vinyl ether have been reported at (303.15, 308.15 and 313.15)K.The excess molar volumes   , deviation in viscosity Δ, excess Gibb's free energies of activation for viscous flow Δ *  , and deviation in isentropic compressibility Δ  were evaluated using the experimental data of , , and  and discussed in terms of the interactions between the components of the mixtures.Both   and Δ exhibit negative deviations, while Δ *  and Δ  exhibit both positive and negative deviations.It is concluded that the negative   may be attributed to the differences in the dielectric constants of the components and the possibility of the electron donor-acceptor type or charge transfer interactions between the electronegative oxygen of ether and the -electrons of aromatic ester resulting into contraction in volumes.
are all negative over the entire range of composition and the magnitude values of Δ vary according to the following sequence: butyl vinyl ether > tetrahydrofuran > anisole > 1,4

Table 1 :
Comparison of experimental density  and viscosity  of pure liquids with the literature values at (303.15, 308.15, and 313.15)K.
These computed data are discussed to study the nature of behaviors between the components of the mixtures.
anisole, and butyl vinyl ether measured at (303.15, 308.15, and 313.15)K over the entire mixture composition.To the best of our knowledge, such data on the abovementioned mixtures are not available in the earlier literature.Using the experimental data of , , and , various parameters such as excess volume   , deviation in viscosity Δ, excess Gibb's free energy of activation for viscous flow Δ *  , and deviation in isentropic compressibility Δ  were determined.

Table 3 :
Derived parameters of excess functions by Redlich-Kister equation and standard deviations  of binary liquid mixtures.