Comparative Study of Experimental and Theoretical Ultrasonic Velocities in Binary Mixtures of Cyclohexanone with Aliphatic Esters at Different Temperatures

Ultrasonic velocity evaluated by various theoretical relations viz., Nomoto, Free Length Theory (FLT), Van deal and Vangeel ideal mixing relation (IMR), Impedance Dependence Relation (IDR), and Junjie in three binary liquid mixtures of cyclohexanone as a common component with aliphatic esters (isopropyl acetate, isobutyl acetate and isoamyl acetate) at 303, 308, 313 and 318K over the entire composition range. An attempt has been made to compare the merits of the relations and the relative applicability of these theories to the present systems have been checked and discussed. The results are explained in terms of intermolecular interactions occurring in these binary systems. The deviation in the variation of U 2exp / U 2 imx from unity has also been evaluated for explaining the non-ideality in the mixtures.


INTRODUCTION
Ultrasonic velocity is one of the important parameters, frequently used to investigate intermolecular interactions in binary liquid mixtures [1][2][3][4] . Theoretical evaluation of ultrasonic velocity in binary liquid mixtures and its correlation to study molecular interaction has been successfully done in recent years. Ultrasonic velocities of liquid mixtures are of considerable importance in understanding intermolecular interaction between component molecules, and they find applications in several industrial and technological processes. Ultrasonic velocity measurements have been successfully employed to detect and assess weak and strong molecular interactions, present in binary liquid mixtures 5,6 . More over the measurement of ultrasonic velocity gives the valuable information about the physico-chemical behaviour of the liquid mixtures such as molecular association and dissociation. Several relations, semiempirical formula and theories are available for the theoretical computation of ultrasonic velocity in liquid and liquid mixtures [7][8][9][10][11][12][13][14][15] . Using the theories available in literature, ultrasonic velocities in liquid mixtures have been calculated and compared with those obtained experimentally. The comparison of theoretical ultrasonic velocities with those obtained experimentally reveals the nature of interactions between the component molecules in the mixtures.
The aim of the present investigation is to compare the ultrasonic sound velocity in six binary liquid mixtures from various theoretical relations of Nomoto, Free Length Theory (FLT), Van deal and Vangeel ideal mixing relation (IMR), Impedance Dependence Relation (IDR), and Junjie. An attempt has been made to compare the merits of the relations for the binary liquid mixtures investigated at four different temperatures. The relative applicability of these theories to the present systems have been checked and discussed. The results are explained in terms of intermolecular interactions occurring in these binary systems. The deviation in the variation of U 2 exp / U 2 imx from unity has also been evaluated for explaining the non-ideality the mixtures.

EXPERIMENTAL
Three liquid mixtures taken for study are: System-1: Cyclohexanone + Isopropyl Acetate (CY + IPA) System-2: Cyclohexanone + Isobutyl Acetate (CY + IBA) System-3: Cyclohexanone + Isoamyl Acetate (CY + IAA) All the chemicals used in the present research work are analytical reagent (AR) of minimum assay of 99.9% obtained from E-Merck, Germany and Sd. Fine Chemicals, India, which were used without further purification. The liquid mixtures were prepared by mixing calculated amount of pure liquids. The ultrasonic velocities in the liquid mixtures were measured using a single crystal variable path interferometer operating at a frequency of 2MHz (MITTAL ENTERPRISES, New Delhi, Model: F-81) with an overall accuracy of ± 0.1%. The temperature during the experiment was controlled by circulating water around the liquid cell from the thermostatically controlled adequately stirred water bath (accurately ± 0.1 ºC). The densities of pure liquids and liquid mixtures were determined from the weight measurements using 10 ml specific gravity bottle by the standard procedure with an accuracy of ±0.1kg m -3 .

1 Nomoto's Relation
Rao found experimentally that 7 , for pure liquids, the ratio of temperature coefficients of sound velocity U and molar volume remains almost constant: Where T is the absolute temperature. On Integrating this equation we get 14 ILCPA Volume 42 Where M is molecular weight and ρ is density. The constant R is called the molar sound velocity or Rao's constant. It was found to be additive i.e., it can be calculated as a sum of increments from the atoms or atom groups in the molecule and from the chemical bonds.
On assuming the additivity of molar sound velocity (R) and no volume change on mixing, Nomoto established the following relation for a liquid mixture Where U 1 and U 2 are the ultrasonic velocities of the pure liquid components.

4. Impedance Dependence Relation
The ultrasonic velocity can be evaluated by the Impedance Dependence Relation 11 of the following form Where X 1 and X 2 are the mole fractions, ρ 1 and ρ 2 are the densities and Z 1 and Z 2 are the acoustic impedances of the liquid components.

5. Junjie's Relation
Junjie's Relation 12 for ultrasonic velocity is given by   Here, U mix(obs) is experimental value of ultrasonic velocity and U mix(cal) is computed value of ultrasonic velocity. The worst-case error is the maximum value of deviation of the theoretical values from experimental values of ultrasonic velocity.

7. Degree of interaction, α
The deviation of the ratio U 2 exp / U 2 imx from unity is called degree of interaction, α.

RESULT AND DISCUSSION
The theoretical relations used to calculate ultrasonic velocity in all the above liquid mixtures are (i) Nomoto's relation, (ii) Free Length Theory, (iii) Van Deal and Vangeel Ideal Mixture Relation, (IMR) (iv) Impedance Dependence Relation (IDR) and (v) Junjie's Relation at the temperatures 303, 308, 313 and 318K and the values along with the experimental values are given in the Tables from 1.1 to 1.3. Also the validity of different theoretical formulae is checked by percentage deviation for all the mixtures and at all the temperatures are shown.
It is observed from the tabulated values that the theoretical values of ultrasonic velocities evaluated by the above mentioned relations show deviations from the experimental values. The reason for the deviation maybe the limitations and approximations incorporated in these theories. The effect of volume change due to mixing was not considered in the Nomoto's relation. That is interaction between the molecules was not taken into account. In Free Length theory, it was assumed that the molecules are of spherical shape but it is not true at all times. In the case of Ideal mixing relation, it was assumed that, the ratio of specific heats and volumes are equal. Again no molecular interactions were considered.
Upon mixing two liquids, the interaction between the molecules of the two liquids take place because of the presence of various types of forces such as dispersion forces, charge transfer, hydrogen bonding, dipole-dipole and dipole-induced-dipole interactions. Thus, the observed deviation of theoretical values of velocity from the experimental values shows the molecular interactions between the unlike molecules in the liquid mixture.

1. Cyclohexanone + Isopropyl acetate (CY + IPA)
Tables 1. show that there is a slight deviation between experimental and theoretical values calculated by Junjie's relation, followed by ideal mixing relation and Nomoto's relation. More over the deviation in values evaluated by Junjie's relation increases with increase in temperature except at 308 K, at the same time the deviations observed for the values evaluated by other theories are continuously increase with increase in temperature. However, Junjie's relation provides the best result than the other relations., where as a large deviations are observed in Free length theory and Impedance dependence relation.

2. Cyclohexanone + Isobutyl acetate (CY + IBA)
A close look at Table 2 reveals that a very slight deviation for the values obtained by Junjie's relation, increase with increase in temperature.

ILCPA Volume 42
The deviation in values calculated by Nomoto's relation and Ideal mixing relation follows the deviation of the values obtained by Junjie's relation.
The evaluated values by the mentioned theories have a little more deviation at middle concentrations is observed. For this binary mixture also larger deviations are observed for the values obtained by Free length theory and Impedance dependence relation. In this case, the Junjie's relation provides more appropriate result than the other relations.

3. Cyclohexanone + Isoamyl acetate (CY + IAA)
A perusal of Table 3  Velocities were determined on the basis of different theories and relations are discussed by other researchers earlier [13][14][15][16] and the validity of different theoretical formulae is checked by percentage deviation at different temperatures. As per the earlier studies, the limitations and approximations incorporated in these theories are responsible for the deviations between theoretical and experimental values.
In the present study, in the three binary mixtures viz., cyclohexanone with aliphatic esters, the velocities predicted by the Junjie's relation are in better agreement than the other relations. When two liquids are mixed various types of forces play a vital role due to interactions. Thus, the observed deviations between theoretical and experimental values of velocity shows that there is molecular interaction between the unlike molecules in the liquid mixture. The FLT assumes that molecules are rigid spheres with no interaction between them and it is not valid in all the cases. Hence the deviation from the experimental ultrasonic velocity values is maximum in the FLT. It is assumed that all the molecules are spherical in shape, which is not true every time. According to Nomoto's theory, it is assumed that the volume does not change on mixing. Therefore, no interaction between the components of liquid mixtures has been taken into account. Similarly, the assumption for the formation of ideal mixing relation is that, the ratios of specific heats of ideal mixtures and the volumes are also equal. Again, no molecular interaction is taken into account. But on mixing two liquids, the interaction takes place because of various forces such as dispersion forces, charge transfer, hydrogen bonding, dipole-dipole and dipole-induced dipole interactions. Thus the observed deviation of theoretical values of velocity from the experimental values shows that the molecular interaction is taking place between the unlike molecules in the liquid mixture The deviation of the ratio U 2 exp / U 2 imx from unity (degree of interaction, α) and its variation as a function of mole fraction of cyclohexanone is a direct measure of the nonideality of the system as a consequence of association or other type of interactions. The positive values of α in all the system clearly indicate the existence of tendency for the formation of association in mixture through hydrogen bonded complexes 17,18 . Figs. 1, 2 and 3 represent the variation of U 2 exp / U 2 imx with mole fraction of cyclohexanone . It is observed that the curves are similar in all the three systems with minimum approximately at 0.5 mole fraction of cyclohexanone at all temperatures. They decrease with increase in temperature.

International Letters of Chemistry, Physics and Astronomy Vol. 42
The trend of the curves reveal a fact that the mixtures tend move towards ideality up to the middle mole fraction of cyclohexanone.

CONCLUSION
In the binary liquid mixtures, Cyclohexanone + Isopropyl acetate, Cyclohexanone + Isobutyl acetate, Cyclohexanone + Isoamyl acetate it is observed that there is a close agreement between experimental and theoretical values calculated by Junjie's relation, followed by Ideal Mixing Relation and Nomoto's relation.It may be concluded that out of the five theories and relations discussed above, the Junjie's relation, Impedance Dependence Relation and Nomoto's relation for estimation of velocities show good agreement with the respective measured values of ultrasonic velocity.