Ultrasonic studies on molecular interactions in strong electrolytes-Metal chlorides in aqueous medium at different temperatures and 2 MHz frequency

Bidyadhar Swain. Values of ultrasonic velocity (U), density (d) and viscosity (η) have been measured in aqueous solutions of magnesium chloride, zinc chloride, strontium chloride, cadmium chloride and barium chloride in different concentrations over the temperature range 298.15K to 313.15K at 5K interval. The thermo-acoustical parameters, such as acoustic impedance (Z), isentropic compressibility (Κs), apparent isentropic compressibility (Κs,ф), intermolecular free length (Lf), relative association (RA), relaxation time (τ), Gibb’s free energy change (∆G), solvation number (Sn), ultrasonic attenuation (α f 2 ), internal pressure (πi), free volume (Vf) and van der Walls constant (b) have been computed to assess the ion-solvent and ion-ion interactions in these solutions. It is found that the ion-solvent and ion-ion interactions depend on concentration, temperature, ionic size, ionic field strength and nature of the ion. The structural arrangement of molecules in electrolyte solutions has been discussed on the basis of electrostatic field (ionic field) of ion. The qualitative intermolecular elastic forces between the solute and solvent molecules are explained in terms of compressibility. The variation of solvation number with respect to temperature and concentration of electrolyte solution has been explained in the light of dipolar interaction between solute and solvent.


Bidyadhar Swain.
Values of ultrasonic velocity (U), density (d) and viscosity (η) have been measured in aqueous solutions of magnesium chloride, zinc chloride, strontium chloride, cadmium chloride and barium chloride in different concentrations over the temperature range 298.15K to 313.15K at 5K interval. The thermo-acoustical parameters, such as acoustic impedance (Z), isentropic compressibility (Κ ), apparent isentropic compressibility (Κ ,ф ), intermolecular free length (L f ), relative association (R A ), relaxation time (τ), Gibb's free energy change (∆G), solvation number (S n ), ultrasonic attenuation ( f 2 ), internal pressure (π i ), free volume (V f ) and van der Walls constant (b) have been computed to assess the ion-solvent and ion-ion interactions in these solutions. It is found that the ion-solvent and ion-ion interactions depend on concentration, temperature, ionic size, ionic field strength and nature of the ion. The structural arrangement of molecules in electrolyte solutions has been discussed on the basis of electrostatic field (ionic field) of ion. The qualitative intermolecular elastic forces between the solute and solvent molecules are explained in terms of compressibility. The variation of solvation number with respect to temperature and concentration of electrolyte solution has been explained in the light of dipolar interaction between solute and solvent.

Introduction:-
Ultrasonic method is a versatile non-destructive technique, which provides useful information for understanding the physico-chemical characteristics and the structural properties of electrolyte solutions (Johnson et al., 2001, Osamu et al., 1978. Since ultrasonic wave is low amplitude and high frequency wave, due to its penetrating nature through liquid medium, it is of interest to study its interaction with matter to throw light into the molecular interaction and molecular kinetic properties of the materials. Hence, the bulk properties of solutions like density, viscosity and ultrasonic velocity provides insight into the intermolecular arrangement of the components in solutions and assists to understand the thermo-acoustics and thermodynamics properties of the electrolyte solutions (Ranga Nayakulu et al., 2005, Kannappan et al., 2005, Ravichandran et al., 2010. It is desirable that any discussion about thermo-acoustical and thermodynamic parameters of electrolytes is connected to ions as ions are playing important role in an electrolyte solution. The effect of concentrations and temperatures of electrolyte solutions help to understand ion-ion (electrostatic) and ion-solvent (solvation) interactions.
In continuous of our previous work in aqueous medium (Swain et al., 2016), the present investigation aims at studying various thermo-acoustical parameters, such as acoustic impedance (Z), isentropic compressibility (Κ ), apparent isentropic compressibility (Κ ,ф ), intermolecular free length (L f ), solvation number (S n ), relative association (R A ), relaxation time (τ), Gibb's free energy change (∆G), ultrasonic attenuation ( f 2 ), internal pressure (π i ), free volume (V f ) and van der Walls constant (b) in different concentrations and at different temperatures ranging from 298.15K to 313.15K at 5K interval to examine the ion-ion and ion-solvent interactions in the aqueous solutions of magnesium chloride, zinc chloride, strontium chloride, cadmium chloride and barium chloride, which have wide applications in pharmaceutical, medicinal, agricultural, environmental, industry, etc. in desiccator before use. All solutions were prepared in conductivity water (Sp. cond. ~10 -6 S.cm -1 ). The solutions were prepared on the molal basis and conversion of molality to molarity was done by using standard expression (Robinson et al., 1955) and using the density data at the corresponding temperature. The solute content of the solutions varied over a concentration range of 6.0x10 -3 to 8.0x10 -2 mol.dm -3 for all measurements.

Theoretical aspects:-
The experimentally measured values of ultrasonic velocity (U), density (d) and viscosity (η) in aqueous solutions of magnesium chloride, zinc chloride, strontium chloride, cadmium chloride and barium chloride at different temperatures have been used to compute the values of different parameters, such as acoustic impedance (Z), isentropic compressibility (Κ ), apparent isentropic compressibility (Κ ,ф ), intermolecular free length (L f ), solvation number (S n ), relative association (R A ), relaxation time (τ), Gibb's free energy change (∆G), ultrasonic attenuation ( f 2 ), internal pressure (π i ), free volume (V f ) and van der Walls constant (b) from the following relations ) 1000 ( 1000   (12) where M eff = ∑ m i x i is the effective molecular weight, m i is the effective molecular weight of the individual constituent, x i is the mole fraction of the individual constituent, K T is the temperature dependent Jacobson's constant {(93.875+0.375T)x10 -8 }, M is the molecular mass of the solute, c is the molar concentration, d o and d are the densities of pure solvent and solution, respectively, U 0 and U are the velocities of pure solvent and solution, respectively, n 1 and n 2 are the number of moles of solvent and solute, respectively, Κ and Κ 0 are the isentropic compressibility of the solution and solvent, respectively, b' is the cubic packing factor having value '2' for all liquids, T is the temperature in Kelvin, is the attenuation co-efficient and 'f' is the frequency of ultrasonic wave (2MHz), k B is the Boltzmann's constant (1.38x10 -23 JK -1 ), h is the Planck's constant (6.626x10 -34 Js), R is the Universal gas constant (8.3143JK -1 .mol -1 ), K is the dimensionless constant (4.281x10 9 ) independent of temperature and nature of liquid.

Results and discussions:-
As previously (Swain et al., 2016), the sound velocity (U) increases with concentration of aqueous solutions of magnesium chloride, zinc chloride, strontium chloride, cadmium chloride and barium chloride. It also increases with increase in temperature. Typical plot of ultrasonic velocity versus concentration of magnesium chloride electrolyte at different temperatures are shown in Fig. 1.
As observed, the values of sound velocity in aqueous solutions of all the metal chlorides are in the order: BaCl 2 > CdCl 2 > ZnCl 2 > MgCl 2 > SrCl 2 at all temperatures. The values of U were fitted to an equation of the form, U = U 0 + A'c + B'c 3/2 + C'c 2 (13) where U 0 is the sound velocity in water, c is the molar concentration, and A', B' and C' are the empirical constants. These constants are given in Table 1. The variation of (U-U 0 )/c vs c 1/2 are parabolic for lower concentration and decreases linearly for the higher concentration in aqueous solutions of all the metal chlorides at all temperatures agreeing fairly well with the Eq. (13). Typical plots are shown in Fig. 2 over the concentration range at 298.15K. From Table 2, it is observed that the acoustic impedance (Z), which assesses the absorption of sound wave in a medium and determines the elastic behaviour (i.e., the bulk modulus of elasticity) of the medium increases with increase in concentration of electrolytes (Moharatha et al., 2011). This is well agreeing with the theoretical requirement as density and ultrasonic velocity increase with increase in the concentration of electrolytes. The increase in Z values with concentration of electrolytes at all given temperatures may be attributed to the effective solute-solvent interactions. The Z values also increase with increase in temperature due to structural properties of electrolyte in the solution and there occurs a structural rearrangement as a result of hydration (Solvation) leading to a comparatively more ordered state (Singh et al., 2008, Palani et al., 2008. Therefore, ultrasound speed increases with increase in temperature and the resistance offered by the solution to the sound velocity increases resulting in an increase in Z. The values of isentropic compressibility, K s as calculated by Eq. (2) were fitted to an equation of the form, Κ = Κ 0 + A"c + B"c 3/2 + C"c 2 (14) where A", B" and C" are constants and Κ 0 is the isentropic compressibility of water. The values of the constants A", B" and C" are given in Table 1 for the aqueous solutions of all the metal chlorides at 298.15K. Typical plots of (Κ -Κ 0 )/c versus c 1/2 are shown in Fig. 3. As observed, the value of Κ decreases with increase in concentration of the solute at all temperatures. The reason is that, when an electrolyte (solute) dissolves in water (solvent) some of the surrounding solvent molecules are closely attached to the ions due to the influence of electrostatic field of the ions. Since the solvent molecules are oriented in the ionic field (electrostatic field), the solvent molecules are more compactly packed in the primary solvation shell as compared to the compactness in the absence of the ions. Thus, the electrostatic field of the ion causes compactness of the medium due to ion-solvent interaction giving rise to a phenomenon called electrostriction. The interstitial spaces in water are occupied by the solute molecules making the medium harder to compress, i.e., providing greater electrostriction. The medium does not respond to further application of pressure. So, the 430 compressibility and internal pressure increase. Hence, isentropic compressibility as well as internal pressure describes the molecular arrangement in the electrolyte solutions (Moharatha et al., 2011). Also the values of Κ decrease with increase in temperature for all concentrations of aqueous solutions of the metal chlorides due to the fact that, with increase in temperature, the compression of the medium becomes more prominent, resulting a decrease in Κ values. As observed, the isentropic compressibility values of all the metal chlorides solution are in the order: BaCl 2 < CdCl 2 < ZnCl 2 < SrCl 2 < MgCl 2 at all temperatures. The values of apparent molar isentropic compressibility, Κ ,ф computed by means of Eq. (3) were fitted into Eq. (15) Κ ,ф = Κ ,ф 0 + A"'c 1/2 + B"'c (15) to obtain Κ ,ф 0 , the limiting apparent molar isentropic compressibility, A"' and B"' are constants, and are given in Table 1.
As observed, the values of apparent isentropic compressibility (Κ ,ф ) initially decrease (for lower concentrations) and then increase (for higher concentrations) with increase in concentration of the solutions. The negative values of Κ ,ф and Κ ,ф 0 are due to loss of compressibility of surrounding solvent molecules due to strong electrostrictive forces in the vicinity of the ions causing electrostrictive solvation of the ions. As seen, the values of Κ ,ф of all the metal chlorides solution follow the same order as of Κ discussed earlier.
From Table 3, it is observed that the intermolecular free length (L f ) decreases with increase in concentration of solution at all temperatures in all the electrolytes. It indicates that, there is a significant interaction between solute and solvent suggesting the structure promoting behaviour on addition of electrolytes (Kanhekar et al., 2010). The increase of temperature increases the thermal energy of the system and decreases the intermolecular forces thereby causing an expansion in volume and decrease in density, and hence, free length increases. Therefore, intermolecular free length increases with increase in temperatures. The intermolecular free length of one aqueous electrolyte is less than the other is due to the less isentropic compressibility value of former than the latter.  Table 4, it is clear that, relaxation time ( ) increases with increase in concentration of electrolytes (MgCl 2 , ZnCl 2 and SrCl 2 ) at all temperatures suggesting the rearrangement of molecules due to co-operation process and reinforcement of H-bonds (Ali et al., 2000), but it decreases with concentration of electrolytes (CdCl 2 and BaCl 2 ) which may be due to less stronger molecular interaction. Further, with rise in temperature, H-bonds become weak due to thermal vibration resulting in structure breaking effect that predominates over H-bond formation, and hence,  decreases in all the electrolyte solutions (Wadekar, 2013).
Gibb's free energy change (∆G) increases with increase in concentration of MgCl 2 , ZnCl 2 and SrCl 2 , but it decreases with concentration of CdCl 2 and BaCl 2 at all temperatures. The former suggests shorter time and latter suggests longer time for rearrangement of molecules. Moreover, ∆G decreases with increase in temperature as given in Table  4 due to increase in kinetic energy of the molecules by thermal energy and takes longer time for rearrangement of molecules for a given concentration (Fort et al., 1965).
Ultrasonic attenuation ( f 2 ) is a measure of spatial rate of decrease in the intensity level of the ultrasonic wave. Attenuation co-efficient ( ) is characteristic of the medium which depends on the external conditions like temperature, pressure and frequency of the measurement. Ultrasonic attenuation decreases with increase in concentration as well as rise in temperature (except in few cases). The decrease in isentropic compressibility or increase in velocity of ultrasonic wave indicates that the wave is less attenuated in the electrolyte solutions. The free volume (V f ) is the effective volume accessible to the centre of a molecule in a liquid. The structure of a liquid is determined by strong repulsive forces in the liquid with the relatively weak attractive forces providing the internal pressure which held the liquid molecules together. The free volume seems to be conditional by repulsive forces whereas the internal pressure is more sensitive to attractive forces. These two factors together uniquely determine the entropy of the system. Thus, the internal pressure, free volume and temperature seem to be the thermodynamic variables that describe the liquid system of fixed composition (Moharatha et al., 2011). From Table  5, it is observed that the free volume (V f ) decreases with increase in concentration of electrolyte and internal pressure (π i ) changes in a manner opposite to that of free volume at all experimental temperatures. The decrease of V f (or increase of π i ) at a given temperature indicates the formation of hard and/or tight solvation layer around the ion (Syal et al., 1998) due to more ion-solvent interaction. With increase in temperature, thermal energy of the molecules increase, hence available free volume (V f ) increases (or i  decreases).
It is also found that van der Walls constant (b) is increasing almost linearly with concentrations at all the experimental temperatures as well as with rise in temperature which indicates the binding forces between the solute and solvent in the solution becomes stronger and there exist a strong molecular interaction and binding forces between the solute and solvent molecules (Nithiyanantham et al., 2009).

Conclusion:-
The results of the present study reveal that specific ion-ion and ion-solvent interactions play an important role for explaining the different thermo-acoustical parameters of strong electrolytes in aqueous medium at four different temperatures 298.15K, 303.15K, 308.15K and 313.15K. These interactions result in attractive forces which promote the structure forming tendency. It is also noticed that the strength of molecular interaction weakens with rise of temperature which may be due to weak intermolecular forces and thermal energy of the system. However, any deviation from the usual behaviour is probably due to characteristic structural changes in the system.