Studying of Acoustical Parameters of Some Binary Liquid Mixture at 303.15 K and 3 M. Hz

.


Introduction
The ultrasonic properties of liquid-liquid mixtures play vital role in understanding the thermodynamics, acoustic and transport aspects (Buddiga et al., 2020).Ultrasonic velocities are of liquid mixture are of considerable importance in studying intermolecular interaction between component molecules and used to compute various physical and chemical parameters which have wide applications in several Industrial and engineering processes (Ali, & Nain, 2002;Nath, Sahu, & Paikaray, 2009;Sahu, Nath, & Paikaray, 2012;Nath, Tripathy, & Paikaray, 2013;Natrajan, & Ramesh, 2011).The study of molecular interaction in binary liquid mixtures plays an important role in the development of molecular Sciences.A large number of studies have been made on the intermolecular interaction in the liquid system by various methods like Ultraviolet, Dielectric constant, Infrared, Raman effect, Nuclear Magnetic resonance and Ultrasonic method.In recent years the ultrasonic method has become a powerful tool in providing information regarding the physicochemical-properties of the liquid system.Departure from linearity in the velocity versus concentration in liquid mixture is

Suggested Citation
Sharma, D.K., Mishra, R.K. & Prajapati, C.P. (2023).Studying of Acoustical Parameters of Some Binary Liquid Mixture at 303.15 K and 3 M. Hz.European Journal of Theoretical and Applied Sciences, 1(5), 1155-1178. DOI: 10.59324/ejtas.2023.1(5).1(5).101taken as an indication of the existence of molecular interaction between different species.The Physico -chemical properties of liquid mixture can be studied by the non-linear variation of ultrasonic velocity and other related parameters with the variation of concentration in the liquid mixture.
The present work is a continuation of systematic experimental studies on thermodynamic properties of binary liquid mixtures of 1,4-Dioxane with alkanols at 303.15 K.In recent years, there has been considerable development in the experimental investigation of the thermodynamic properties of liquid and liquid mixtures are used to study the molecular interactions between the various components of the mixtures.An ultrasonic technique has become a powerful tool for studying the molecular behaviour of liquid mixtures.The ultrasonic velocity along with density and viscosity furnish wealth of information about the interaction between ions, dipoles, hydrogen bonding, multi-polar and dispersive forces (Rawat, & Sangeeta, 2008).The1,4-Dioxine is selected as a solvent in the present work since it finds a variety of application.Alcohols play an important role in many chemical reactions due to the ability to undergo self association with internal structures.1,4-dioxane cyclic Ether is used as a degreasing agent, as a component of paint and varnish removers and as a wetting and dispersion agent in the textile industries.1,4-Dioxane is also used as a solvent in the Chemical synthesis.Ultrasonic studies of the solution of the alcohols with 1,4-Dioxane have yielding valuable information regarding the association between the monomers of alcohols and free oxygen of dioxane through hydrogen bonding.Ultrasonic propagation parameters field valuable information regarding the behaviour of liquid systems because intermolecular and intermolecular association, complex formation, dipolar interactions and related structural charges effect the compressibility of the system which in turn produces corresponding variations in ultrasonic velocity (Jasmine et al., 2012).The different acoustical parameters interpret the nature and strength of molecular interaction that exist in the system (Singh, & Bhatt, 2010).The intermolecular interaction that influence the structured arrangement along with the shape of the molecules (Tabhane et al., 2012;Wadekar, 2013;Kaur, & Juglan, 2013).In the present study, density, viscosity and ultrasonic velocity of binary mixture 1,4-dioxane with alkanols at 303.15K at frequencies 3 M.Hz .These measured values are used to calculate different parameters like acoustic impedance (Z), adiabatic compressibility (βad), intermolecular free length (Lf), Rao's constant (R) , internal pressure (Pi),viscous relaxation time (Ԏ) and relaxation strength (r).The excess parameters of ultrasonic velocity (u E ), molar volume (V E ), acoustic impedance (Z E ), adiabatic compressibility (βad E ), intermolecular free length (Lf E ), excess viscosity (η E ) excess internal pressure (Pi E ) are computed, which are highly useful in understanding the nature and stand of molecular interaction, internal structure and aggregation behaviour.

Density
Density of pure liquids and their binary mixture were determined by using a double-arm pycnometer (Boodida et al., 2007) with a bulb of 25 cm 3 and a capillary of an internal diameter of about 1 mm is used to measure the densities (ρ) of pure liquids and their binary mixtures.The pycnometer is calibrated by using conductivity water (having specific conductance less than 1 X10 6 ohm -1 ) with 0.9970 and 0.9940gcm -3 , as its densities at T = 303.15K,respectively.The pycnometer filled with air bubbled free liquids is kept in a thermostate water bath (MSI Goyal scientific, Meerut, India.)controlled with a thermal equilibrium.The precision of the density measurements was estimated to be ± 0.0002 g cm -3 .The observed values of densities of pure 1,4-Dioxane, methanol, ethanol, propanol, butanol, hexanol and octanol at 3:03.15 K were1.0108,0.7840,0.7720, 0.8070, 0.8040, 0.8128 and 0.8242 g cm -3 which compare well with corresponding literature values respectively.

Viscosity
The viscosity of pure liquids and their binary mixture were measured using suspended ubbelohde type viscometer (Swindells, Coe, & Godfrey, 1952;Nikam, Shirsat, & Hasan, 1998) having a capacity of about 15 ml and the capillary having a length of about 90 mm and 0.5 mm internal diameter has been used to measure the flow time of pure liquids and liquid mixtures and it was celebrated with triply distilled water, methanol and benzene at 303.15 K.The details of the methods and techniques have been described by researchers (Roy, Dey, & Jha, 2001;Roy, Jha, & Choudhury, 2003)

Theoretical
The ultrasonic velocity (u), density (ρ) and viscosity (η) in pure liquids and liquid mixtures of various concentrations have been measured at 303.15 K.
Thermodynamics and acoustical parameters such as adiabatic compressibility, (  ) free length ( ƒ ), acoustic impedance (Z), relaxation strength (r), molar compressibility or Wada constant (W), relaxation time (τ) and internal pressure ( i ) were determined using the observed values of sound velocity, density and viscosity using the standard relations given below.
The adiabatic compressibility(  ) has been determined by using experimentally measured ultrasonic velocity (u) and density (ρ) by using the following relation: The Mean molar volume (V) of binary liquid mixtures at a given mole fraction is given by: The excess volume (V E ) at a given mole fraction is the difference between mean molar volume and the average volume is calculated using the given formula: Where V1 and V2 are the mean molar volumes of pure liquids 1 and 2 respectively.
The excess adiabatic compressibility (   ) at a given mole fraction is the difference between adiabatic compressibility (  ) and the sum of the fractional contributes of the two liquids is: Where  1 and  2 are the individual values of pure liquid in the binary mixtures at that temperature.
The molar sound velocity or Rao's constant has been calculating using formula: R = (M/ρ)  1/3   (5) Where M is the molecular weight of the solution which can be calculated according to the equation Where X1 and X2 are mole fraction of solvent and solute, respectively, M1 and M2 are the molecular weight of the solvent and solute respectively.
Molar compressibility or Wada constant (W) can be calculated by the following equation Intermolecular free length (  ) is calculated using the standard expression Where K is Jacobson's constant which is temperature dependent parameter.
The excess viscosity (  ) at a given mole fraction is the difference between viscosity and the sum of the fraction contribution of the liquid are given by Fort and Moore (Fort, & Moore, 1966) is: Where   ,  1 &  2 are the individual viscosity values of pure liquid in the binary mixture and viscosity of mixture: The excess mean free length (   ) at given mole fraction is the difference between mean free length and sum of the fraction contribution of the two liquid are given by: Where   ,  1 and  2 are the individual mean free length values of pure liquid in the binary mixture and mean free length of the mixture.
Specific acoustic impedance (Z) is also calculated using the below relation: 1160 Where ρ is the density and u is the sound validity of the mixture.
Excess acoustic impedance (  ) is difference between the ideal acoustic impedance and acoustic impedance of the pure components i.e.
=   -  (12) Excess sound velocity is the difference between the ideal velocity and velocity of pure components.
=   - Relaxation strength (r) has been calculated by the following relations: Where  ∞ = 1600 m/s Relaxation time (τ) has been calculated by the following relation: Suryanarayana & Kuppuswami (1976) suggested a method for evaluation of internal pressure from the knowledge of ultrasonic velocity, u, density and viscosity, the relation proposed is expressed as Where b is packing factor, which is assumed to be 2 for all liquids and solution.K is a constant, independent of temperature and its value is 4.28 × 10 9 for all liquids, R is universal gas constant and T is absolute temperature.

Results and Discussion
The experimental values of density, viscosity and sound velocity for the binary liquid mixtures of All the seven organic compounds namely 1,4dioxane, methanol, ethanol, propanol, butanol, hexanol and octanol are a polar organic compounds having dipole moment 0.45 D, 1.70 D,1.69 D, 1.68 D, 1.66 D, 1.60D and 1.68 D respectively.Normally, more the dipole moment, stronger is the intermolecular interaction, which result is decreasing of free space between molecules and an increase in the ultrasonic velocity.
Various type of interaction which are possible and which can operate in the binary liquid mixtures containing 1,4-Dioxane are hydrogen bonded complex formation, that can produce negative deviation in excess viscosity, excess molar volume, excess adiabatic compressibility, excess internal pressure and excess free length.This may be fact that O-H Hydrogen bonded complex formation.
Alkanols are liquids which are associated through the hydrogen bonding and in the pure state, they exhibit an equilibrium between the monomer and multimer species.Also they can be associated with any other group having some degree of polar attraction.Due to polar nature of 1,4-Dioxane and alkanols, the dipole -dipole interaction of hydrogen bombs in pure Ethyl Acetate and also, dipole -dipole interaction equilibria are evidently rupture of hydrogen bonds in pure 1,4-Dioxane and alkanols, dipoledipole interactions and the formation of O-H………O hydrogen bonds between the components.
The alkanols are associated through hydrogen bonding and 1,4-Dioxane-alkenols interactions are due to hydrogen bonding between the oxygen atom of the cyclic ether and the proton of hydrogen group of alkanols.
Excess thermodynamic parameters like excess viscosity, excess molar volume, excess adiabatic compressibility, excess internal pressure and excess intermolecular free length were calculated and listed in Table 5 (Appendix 1).Excess viscosity, excess molar volume, excess adiabatic compressibility, excess internal pressure and excess intermolecular free length were shows that the similar behaviour i.e. these are increase up to x = 0.59 continuous increasing mole fraction (X1).The negative sign due to contractive factors dominate the expensive factors.This is similar to S. Sahakal Ahmed et al (1976) measured excess molar volume values, excess viscosity of binary mixture of 1butylamine with ethanol and heptanol.Plot of excess viscosity versus mole fraction (X1) in figure 1.It decreases with an increase in concentration of 1,4-dioxane.It is observed that the converse on the behaviour of adiabatic compressibility and intermolecular free length from the table 4 (Appendix 1).This may be due to self association of the solute molecules and very weak dipole-induced dipole interaction between the component molecules (Rodríguez, Canosa, & Tojo, 2001).The adiabatic compressibility decreases with increasing concentration which is due to the strong molecular interaction among the solute and solvent molecules shown in figure 2. The excess adiabatic compressibility shows the similar behaviour i.e. these are increase up to x = 0.59 then decrease with continuous increasing mole fraction (X1).In Table 5  values are negative for lower mono alcohols, but the magnitude of the negative values diminishes and the negative values increase with increasing chain length of the alcohols.the order it follow is: These results can be explained in terms of molecular interactions and structural effects.
Interactions between the molecules of cyclic diether and mono alcohol are broken in the mixing process, the breaking of strong dipoledipole interaction in 1,4-dioxane, which can be considered as a polar fluid.The donor-acceptor interaction between the oxygen and hydrogen atoms of the cyclic diether and the alcohols play and important part for the mixture containing lower alcohols, like Me-OH and Et-OH,, where there is a strong Specific interaction between the component molecules leading to negative value of excess adiabatic compressibility (   ).From the figure 3 it is clear that the excess adiabatic compressibility values negative indicates the increased strength of interactions between component molecules of liquid mixtures.This negative sign of excess adiabatic compressibility clearly shows the strong interaction through formation of hydrogen bonding between the components.Figure 4 depicts the variation in intermolecular free length.This decrease in free length is due to the decreased adiabatic compatibility which brings the molecules to be closer packing (Nikam, Mahale, & Hasan, 1996).The value of excess free length (   ) are negative over the entire range of composition in system    ) that they must show opposite behaviour and adiabatic compressibility and intermolecular free length (   = K   1/2 ) should exhibit same behaviour which is in agreement with the experimental results (Roy, Sinka, &Biswajit, 2005).Specific acoustic impedance is defined as the impedance offered to the sound wave by the components of the mixture.Acoustic impedance increases with increase in concentration.
Increasing trend of acoustic impedance further support the possibility of molecular interaction due to hydrogen bonding between the 1,4dioxane and alcohol molecule.Specific acoustic impedance is directly proportional to ultrasonic velocity and inversely proportional to adiabatic compressibility and shows similar behaviour to that of ultrasonic velocity and opposite to that of adiabatic compressibility.variation in Wada constant Rao's constant is linear then it shows that there is an absence of complex formation in two mixtures and so is found in the present investigation which means that there is no complex formation in the mixture of 1, 4-dioxane and alkanols.The Rao's constant increase with increase in concentration which indicates that the magnitude of interactions is enhanced.This increasing trend of Rao's constant indicate that availability of more number of components in a given region of space.Alcohols are strongly self -associated liquids with a three dimensional network of hydrogen bonds and can be associated with any other group having some degree of Polar attractions.
The associative alcohol molecule acts as a proton donor in enabling hydrogen bonding with 1, 4-dioxane molecule.In the system studied, the complex formation is likely to occur between Hδ + of alcohol and Oδ -of -O group of 1,4-dioxane.Hence in the present study there is existence of solute-solvent interaction which are discussed in the above calculated acoustical parameters.

Conclusion
The ultrasonic velocity study of binary liquid mixtures of 1,4-dioxane with alkanlols shows the presence of molecular interaction between the molecules of the mixture.The ultrasonic velocity Increases with increase in concentration which is due to the decrease in intermolecular free length of the mixture.The density increases with increase in mole fraction.Adiabatic compressibility, intermolecular free length, internal pressure, relaxation time and relaxation strength decreases with increase in concentration.This decrease in acoustical parameters indicates that there is a weak interaction between the molecules of the mixture.Wada constant and Rao's constant show linear variation with increase in mole fraction which indicates the absence of complex formation in the mixture.The study of excess property along with the speed of sound has been found to be very useful in understanding the nature of the interactions within binary liquid mixtures.The parameters obtained from the correlating equations have also provided us with valuable information.

Figure 9
Figure 9 and 10 illustrate the linear-behaviour of relaxation time and relaxation strength with mole fraction at the trend of these parameters is almost same with best results obtained between 0.2-0.8range of mole fraction.As seen from the experimental results ultrasonic velocity increase which results in the decrease of relaxation strength.Viscous relaxation time is the time taken for the excitation energy to appear as transnational energy.The variations in specific relaxation time are mainly due to the change in viscosity of solution due to both concentration and temperature.The non-linear variation of relaxation time with increase in molar concentration is due to the existence of significant molecular interaction between the solute and solvent molecules.The decrease in relaxation time indicates that the viscous force has no effect on it.All the two constant Wada constant and Rao's constant are increasing with increases in mole fraction and display in figure 11 and 12 respectively.It was reported that if the

Table 1 . Provenance and Purity of the Materials Used
prepared by weight covering the entire mole fraction range.The components of binary mixture were injected by means of syringe in to the glass vials sealed with rubber topper in order to check evaporation losses during sample preparation.The mass measurements were carried out using a single pan analytical balance (Model K -15 Deluxe, K-Roy Instruments Pvt.

Table 2 . Physical Properties of Pure Components at 303.15K
The values of excess viscosity (η E ), excess molar volume (V E ), excess adiabatic compressibility (   ), excess internal pressure (Pi E ) and excess free length (   ) are listed in table 5 (Appendix 1).