Theoretical evaluation of ultrasonic velocities in binary liquid mixtures at different temperatures

Ultrasonic velocities calculated from various theories and relations like Nomoto’s relation, Van dael ideal mixing relation, Impedance relation, Rao’s specific velocity relation and Jungie’s theory are compared with experimental values in binary liquid mixtures o-anisidine with o-cresol at temperatures 303.15, 308.15, 313.15 and 318.15 K over the entire mole fraction range. The relative applicability of these theories to the present system is checked and discussed. A good agreement is observed between experimental and theoretical values. The results are explained in the light of molecular interactions occuring in these mixtures.


INTRODUCTION
Results of theoretical evaluation of ultrasonic velocities are used for the better understanding of molecular arrangements in liquid mixtures. In assessing the nature of molecular interactions and investigating the physico-chemical behaviour, ultrasonic study of liquid mixtures gained more importance during the last few decades. Several researchers [1][2][3][4] carried out ultrasonic investigations on binary and ternary liquid mixtures and compared the experimental values with theoretical relations [5][6][7][8][9] of Nomoto, Van Dael and Vangeel, Impedance dependence, Rao's specific velocity and Junjie's equations and the results are explained in terms of molecular interactions. o-anisidine is mainly used in the manufacture of dyes for tattooing and coloration of paper. Cresols are used to dissolve other chemicals, as disinfectants and deodorizers, and to make specific chemicals that kill insect pests. Ultrasonic velocities calculated in binary liquid mixture o-anisidine with o-cresol using the above relations are compared with the experimental values at temperatures 303.15, 308.15, 313.15 and 318.15 K for the entire mole fraction range.

EXPERIMENTAL
The chemicals used in this work are obtained from Loba (o-anisidine, purity 98 %) and SDFCL (o-cresol, purity 99 %) and were used as such without further purification. The purity of the samples was checked by comparing the experimental values of density with the values reported in literature [10]. The mixtures of required proportions are prepared by using Job's method of continuous variation and are preserved in well-stoppared conical flasks. The flasks are left free to allow them to attain thermal equilibrium after they are prepared.
Using ultrasonic interferometer (Mittal enterprises, India; Model: F-80X) ultrasonic velocities were measured. It consists of a high frequency generator and a measuring cell and the measurements were made at a fixed frequency of 3MHz. The calibration of the equipment was done by measuring the velocity in water and benzene, and the results were compared with the literature values [11]. The ultrasonic velocity has an accuracy of ±0.5 %. Temperature was controlled by circulating water around the liquid cell from thermostatically controlled constant temperature water bath. Using specific gravity bottle, the densities of pure liquids and liquid mixtures were measured. Weights were measured with an electronic balance (Shimadzu AUY220, Japan) capable of measuring up to 0.1mg. An average of 4-5 measurements was taken for each sample.

RESULTS AND DISCUSSION
Theoretical values of ultrasonic velocities were calculated using different theories and empirical relations. Comparison of theoretical values of ultrasonic velocities with those obtained experimentally in the present binary liquid mixtures is expected to reveal the nature of interaction between the component molecules in the mixture. Such theoretical study is useful in building the comprehensive theoretical model for the liquid mixtures. Theoretical values of ultrasonic velocities in the mixtures o-anisidine + o-cresol at different mole fractions of o-anisidine for different temperatures were calculated using the following theories and relations: Nomoto relation for ultrasonic velocity in binary liquid mixtures, Where R is molar sound velocity, x 1 and x 2 are the mole fractions of 1 st and 2 nd components of the liquid mixture and V is molar volume. Van Dael and Vangeel Ideal mixing relation, where U imx is the ideal mixing ultrasonic velocity in liquid mixture. U 1 and U 2 are ultrasonic velocities of the individual compounds. Impedance dependent relation,

ILCPA Volume 10
where x i is the mole fraction,  i the density of the mixture and Z i is the acoustic impedance. Rao's specific velocity, where x i is the mole fraction,  i the density of the mixture and r i is the Rao's specific sound velocity. Jungie equation,  [12,13] between the unlike molecules in the liquid mixture. From Table 2, more deviations are observed in case of Nomoto theory and less deviation are observed in case of Van dael ideal mixing relation. On increasing temperature, it was observed that the ultrasonic velocity values decrease in the liquid mixtures chosen. This is probably due to the fact that the thermal energy activates the molecule, which would increase the rate of association of unlike molecules.