Study of Molecular Interaction in Aqueous KCl at Different Temperatures

Ultrasonic velocity, density, viscosity, and electrical conductivity have been measured for an aqueous solution of KCl at different concentrations and temperatures, the frequency is maintained at a constant value. Using the above experimental data, parameters such as Rao's constant, Wada's constant, solvation number, and surface tension were calculated and the molecular interactions between molecules of KCl and water at different temperatures was studied. Using Walden's plot, the ionicity of the solution was also studied.


Introduction
The ultrasonic technique has been effectively employed to study the nature of molecular interaction in pure liquids [1], liquid mixtures [2] and ionic liquids and ionic interactions in electrolytic solutions [3,4]. Since ionic liquids are attracting growing interest as alternative to molecular liquids, it is important to study the various properties of ionic liquids through ultrasonic studies. Ionic liquids have unusual properties including nonvolatility, non-flammability, high ionic density, conductivity, chemical, and electrochemical stability. Room-temperature ionic liquids have been currently applied as a novel solvent in organic synthesis [5][6][7], catalysis [8][9][10], electrochemistry [11] and chemical separation [12].
Human body needs many essential minerals, which are divided in two groups, major minerals (like Na, K ...) and micro minerals (like Fe, Si,...). The latter is required in small amounts than the former. K is a very significant body mineral, important to both cellular and electrical function. It is one of the main blood minerals called "electrolytes". This means it carries a tiny electrical charge (potential). K is the primary positive ion found within the cells, where 98 % of the 120 g of K contained in the body is found. The blood serum contains about 4-5 mg. (per 100 mL) of the total K; the red blood cells contain 420 mg. This is why a red-blood-cell level is a better indication of an individual's K status than the commonly used serum level. Conductivity is the ability of an aqueous solution to carry an electrical current. Conductivity measurement is an extremely widespread and useful method for quality control purposes. Surveillance of feed water purity, control of drinking water quality, estimation of total number of ions in a solution can all be performed using conductivity measurements. The measurement of conductivity is a rapid and inexpensive way of determining the ionic strength of a solution. The present paper deals the study of interaction between molecules of KCl and water at different temperatures for various concentrations of KCl.

Experimental
Fresh distilled water has been used as a solvent for preparing KCl solutions of different concentrations. KCl used as a solute for the solution is of analytical reagent (Tradewell International Pvt. Ltd, India, purity -99.9 %) grade. The density, viscosity, and ultrasonic velocity were measured as a function of the concentration of KCl at 288, 298 and 318K respectively. Conductivity measurements were carried out using conductivity meter (Labline, India). Before and after measurements, the instrument was calibrated with NaCl solution. Each measurement was repeated three times and the average values were reported.Ultrasonic velocity was measured by using an ultrasonic interferometer (M-84, New Delhi) with the accuracy of ±0.1 m·s −1 . The densities of the mixture were measured using a 10 mL specific gravity bottle by relative measurement method with an accuracy of ±0.01 kg·m −3 . An Oswald viscometer (10 mL) with an accuracy of ±0.001 Ns·m −2 was used for the viscosity measurement. The flow time was determined using a digital racer stopwatch with an accuracy of ±0.1 s.

Theoretical Aspects
Rao's constant (R): Rao"s constant is also known as molar sound velocity and it is an additive property and can be evaluated by an equation [13], Wada's constant: Wada"s constant also known as Molar compressibility is dependent on adiabatic compressibility and density is given by [14], Surface tension: Surface tension can be calculated by using the relation [15],

X 1 (3)
Solvation number: Solvation number is determined by using the formula [16], Where M and Mo are molecular weight of solvent and solution respectively, and are adiabatic compressibility"s of solvent and solution respectively and "x" is the number of grams of salt in 100 g of the solution.

Results and Discussion
Experimental values of density [17], viscosity, ultrasonic velocity and electrical conductivity are presented in Table 1. Calculated values of molar electrical conductivity and Rao's constant are shown in Table 2. Calculated values of Wada's constant and surface tension are shown in Table 3. Calculated values of solvation number and Gibb's free energy are shown in Table 4. Acoustic impedance and free volume are presented in Table 5. At constant temperature, velocity increases as concentration increases. With the increase in the concentration of KCl the H-bonded structure of water is disrupted. Electrolytes occupy the interstitial space and tend to break the original ordered structure of water. Interaction between solute and solvent molecules results in a decrease in free length and increase in density, viscosity, and velocity. Velocity increases, when temperature increases at a particular concentration. The increase in the ultrasonic velocity usually indicates a greater association of the component molecules. The greater association is due to ionic hydration of the solute. KCl is strong electrolytes which dissolve in water to form K+, Clions respectively.
Concentration remaining constant as temperature increases, the intermolecular distance increases. This results in a decrease in density and viscosity. KCl in solution breaks into K + and Clions which are hydrated by water molecules. The hydrated moles are strongly held by electrostatic forces and are thus highly incompressible. This results in a decrease in the compressibility of the solution and an increase in ultrasonic velocity through it. The change in viscosity with temperature can be shown through an Arrhenius dependence.

( ) ( ) ( )
Where η is viscosity at any temperature T and η 0 is a constant defined as the maximum viscosity which would be the viscosity at infinite temperature, K B is the Boltzmann's constant and E n is the activation energy for the viscous flow. Analogous to the viscosity data, the electrical conductivity data of ionic liquids at various temperatures were fitted to Arrhenius equation, where is the conductivity at any temperature, is maximum conductivity at infinite temperature, is the activation energy for electrical conduction. Arrhenius plots ( ) and ( ) are shown in the Fig. 1  Electrical conductivity increases both as temperature increases for a particular concentration and as concentration increases at a particular temperature. The increase in conductivity depends on the solvent added and also the extent to which the ions are dissociated. As temperature or concentration increases more K + ions are available in KCL solution. As K + ions are less hydrated, their mobility is more. This leads to an increase in the conductivity of the KCl solution.
Rao's and Wada's constant remain almost constant when the temperature increases. This may be due to the increase in conductivity of the KCl solution with an increase in temperature. Because of this, there is no accumulation of solute molecules in a given region. However, the above two constants increase, when concentration increases.
Surface tension increases rapidly with the increase of concentration of KCl (when the temperature remains constant). At higher concentrations, there is a strong molecular association between adjacent molecules causing strong surface film. However, when concentration remains constant, the surface tension changes slowly even when the temperature increases. This is because the weak electrostatic interaction of the ions does not affect the surface tension appreciably.   is the molar conductivity and is the viscosity. Walden's plot comes out to be a straight line. These plots indicate the ionicity of the ionic liquids. For 0.01 M KCl the straight-line graph should pass through the origin. For other ionic liquids, the linear graph may be above the KCl graph or below it. Those lying above are more ionic and those below are less ionic. For the same concentration (S-1) the ordinate of the Walden plot in KCl solution is larger than that of the NaCl solution, indicating KCl is more ionic than NaCl.
Just as the relation between conductivity and viscosity has been studied through Walden's plot, an equation relating viscosity and surface tension can be obtained by combining the following equations of Batchinski and MacLeod [15]. (5) and ( ) Where " " is the viscosity and "v" is the specific volume, w is the limiting volume, S is the surface tension, D is the density of the liquid, d is the density of the vapor. C and are constants for a given liquid. Below the boiling point, the density of vapor may be neglected as compared with the density of the liquid "D" Equating v to 1/D in equations (5) and (6) we get, where A and B are constants In the present paper, the graph between "S -1/4 " and "1/η" comes out to be a straight line as shown in the Fig. 2(b), confirming the above equation. The solvation number is an important parameter to study the interaction between the solute and solvent. It can be defined as the number of solvent molecules per ion which remains attached to a given ion long enough to experience its translational motion when the solution is formed [16].
The positive value of the solvation number suggests that the compressibility of the solution under all circumstances will be more than that of the solvent. The zero value of the solvation number indicates that no change occurs in the compressibility of the solvent when the solution is formed. The negative value of the solvation number emphasizes that the compressibility of the solution is less than that of the solvent. In our case, the solvation number is always negative. When an ion is added to water, it attracts some water molecule towards itself and is thus hydrated by a water molecule. The hydrated molecules are held strongly by electrostatic force. These are highly incompressible and the compressibility of the solution is due to the remaining solvents. This indicates the negative value of the solvation number. With increases in the ionic concentration of KCl the additional ions take up water molecules that are not bound strongly to the ion-water complex. This effect, in turn, increases the compressibility. This is evident in our observation where the negative value of the solvation number decreases rapidly with the increase of concentration. For a given concentration as the temperature increases, the hydrated ions become more mobile and hence compressibility of the solution decreases slowly. This is obvious from our observation where the negative solvation number decreases slowly.

Conclusion
Ultrasonic and conductometric studies of KCl solution are done to study certain important parameters of the solution for different concentrations and temperatures. It has been seen that KCl has structure forming tendency in the solvent system. The increased cohesion between the molecules in the solution is due to ionic hydration or solvation. Ionicity of KCl is studied through the Walden plot.