Theoritical Evaluation of Ultrasonic Velocities in Binary Liquid Mixtures of N-Methyl-2-pyrrolidone at Different Temperatures with Some Cyclic Compounds

Ultrasonic velocities and densities of the binary liquid mixtures of N-methyl-2-Pyrrolidone (NMP) with Cyclohexylamine (CHA), Cyclohexanol (CHOL) and Cyclohexene(CHE) at a temperature range of 303.15 to 318.15 K over the entire composition range were measured. The theoretical values of ultrasonic velocity were evaluated using the Nomoto's relation(UNR), Impedence relation(UIR), Ideal mixing relation(UIMR), Jungie's relation(UJR) and Rao's specific velocity relation(UR).The molecular interaction parameter (α) was computed by using the experimental and theoretical ultrasonic velocity values. The variation of interaction parameter with the composition of the mixture has been discussed in terms of molecular interactions.


Introduction
In resent years measurement of ultrasonic investigations find extensive applications in determining the physicho-chemical behavior of liquid mixtures [1][2][3][4][5] .Several researchers [6][7][8][9] carried out ultrasonic investigations and correlated the experimental results of ultrasonic velocity with the theoretical relations of Nomoto 10 , Van Deal and Vangeel 11 , impedence relation 12 , Rao's Specific Velocity 13 and Junjie 14 and interpreted the results in terms of molecular interactions.There has been an increasing interest in the study of intermolecular interactions from last two decades and number of experimental techniques have been used to investigate the interactions between the binary liquid mixture components.The ultrasonic sound speed and the thermodynamical parameters derived from it have been widely used to interpret the interactions between unlike molecules in the binary liquid mixtures.This investigation presents the evaluation of ultrasonic velocity using Nomoto's relation, ideal mixtures relation, impedence relation, Rao's specific velocity relation and Junjie's relation for cyclohexylamine, cyclohexanol, cyclohexene with N-Methyl-2-Pyrrolidone at temperatures of 303.15-318.15K with an intrevel of 5K.An attempt has been made to study the molecular interactions from the deviation in the values of U 2 exp /U 2 mix from unity based on earlier studies [15][16] and percentage deviation.

Experimental
NMP (Merck India >0.995 purity) was distilled at low pressure and over freshly activated 0.3 nm molecular sieves 17 .CHOL and CHA (Both SD Fine Chemicals, India, >0.995) were purified by using the methods described in the literature 18 .Cyclohexene (Sigma Aldrich >0.995 purity) used without further purification.The purity of the chemicals was verified by measuring the densities, and speed of sounds which were in good agreement with literature values.

Apparatus and procedure
The densities of the pure compounds and their mixtures were measured by means of an Anton Paar DMA 4500 vibrating tube density meter with an accuracy of ±.01 kgm -3 .All the measurements were made from 303.15 K to 318.15 K at an interval of 5 K and at atmospheric pressure where the temperature stability was better than  0.002 K and the accuracy  0.01 K.The speeds of sound, u, were measured using an ultrasonic interferometer (Mittal Enterprises, New Delhi, India, model F 05) operating at 2 MHz.The measured speeds of sound have a precision of 0.8 ms -1 and an uncertainty better than  1.0 ms -1 .The temperature stability was maintained within  0.01 K by circulating thermostatic water around the cell with a circulating pump.

Nomoto's Relation (U NR )
On assuming the additivity of molar sound velocity(R) and no volume change on mixing, Nomoto established the following relation for the ultrasonic velocity of binary liquid mixtures.
Where x 1 and x 2 are the mole fractions of the species and R is related to molecular weight (M) and density (ρ) as Where U is the sound velocity and V is the molar volume of the mixture.The molar volume of the mixture is given by Where M 1 and M 2 are molecular weights of constituent components.

Impedance relation (U IR )
The product of ultrasonic velocity (U) and density (ρ) of the mixture is termed as acoustic impedance (z) of the mixture.Hence the sound velocity in the mixture can be predicted from the knowledge of acoustic impedance and the density of the pure components.

Ideal mixing relation(U IMR )
Van Deal and Vangeel (1969) suggested the following relation for the velocity of sound Where U imx is the ideal mixing ultrasonic velocity in liquid mixture.U 1 and U 2 are the velocities of pure components.

Junjies Relation (U JR )
Where M 1 and M 2 are the molecular weights and ρ 1 and ρ 2 are the densities of the constituent components of binary liquid mixtures.
Rao's Specific Sound Velocity (U R ) Where x i is the mole fraction, r i is the Rao's specific sound velocity =u i 1/3 /ρ i , ρ is the density of the mixture, ρ i is the density and u i is the velocity of the i th component of the mixture.

Results and Discussion
It is assumed that all the molecules are spherical in shape, which is not true every time.
According to Nomoto's theory there is an assumption that the volume of the molecules does not change on mixing of the components and hence there is no possibility of interaction between the components of the liquid mixture.Similarly for the formation of ideal mixing relation, there is an assumption that the ratio of specific heats of ideal mixtures and the volumes are equal, which indicates that there is no possibility of molecular interactions.But actually there is a possibility of interactions between the components of liquid mixtures on mixing of two liquids.The interaction takes place due to various forces such as dispersion forces, hydrogen bonding, charge transfer, dipole-dipole interactions and dipole-induced dipole interactions.The deviation in the experimental velocity with the theoretical values of velocity shows that there are intermolecular interactions between unlike molecules on mixing of the components.
In general the predictive ability of various ultrasonic theories depends upon the strength of interactions that are existing in a binary system.In case strong interactions exist between the molecules of the mixtures there is much deviation in theoretical prediction of velocity than the molecules of the mixture where less interaction are present.
From table 1, it is observed that for the system NMP+CHA, there is good agreement between the experimental and theoretical values in impedance relation, Rao's specific velocity, and ideal mixing relation where as higher deviations are observed in Nomoto relation and Junjie's relation.The interaction parameter is positive for the system at all measured temperatures over the entire composition range and the values are more positive in the middle composition range suggesting strong molecular interaction between unlike molecules.The higher deviations in the intermediate composition range suggests the existence of strong intermolecular interactions as a result of hydrogen bonding 19,20 .In the present system the C=O group of NMP is polar and it forms hydrogen bonding with -NH 2 group of CHA.
Table 2, indicates that for the system NMP+CHOL, good agreement between experimental and theoretical velocities is observed in Impedance relation, Ideal mixing relation, Nomoto's relation where as higher deviations are observed in Rao's specific velocity and Junjie's relation.For this system interaction parameter is positive at all measured temperatures over the entire composition range.It is observed that at the mid composition range the interaction parameter values are higher and the percentage deviation in velocity is also more suggesting that the variation in the velocity is non linear and the interaction between unlike molecules are more at this composition range may be due to the formation of hydrogen bonding between the C=O group of NMP and -OH group of CHOL.Analogously a similar trend of hydrogen bonding is reported between DMSO and cyclohexanol molecules based on excess acoustical parameters by Ali et.al 21,22 A general survey of the Table 3 suggests that for the system NMP+CHE, a good agreement in experimental and theoretical values of velocity is observed in Ideal mixing relation, Jungie's relation and Nomoto's relation where as higher deviation is observed in Rao's specific velocity and Impedance relation.For this system an opposite trend in interaction parameter is observed at all measured temperatures and over the entire composition range which suggests the interaction between unlike molecules are very less compared to the above two systems..4985-0.0040 1.0000 1474.5 1474.5 1474.5 1474.5 1474.5 1474.5 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 Keeping in view the behavior of the three aforementioned systems under the present investigation, it can be said that the positive deviations in velocity are attributed to 1) molecular association and 2) complex formation , where as negative deviation in velocity are attributed to the molecular dissociation of an associated species composed by addition of solvent.The lack of smoothness of deviations is due to interactions between the component molecules.In our present investigation for the system NMP+CHA the maximum deviation in velocity is observed in the middle composition range at a mole fraction of 0.5442 at all measured temperatures due to more complex formation between unlike molecules through hydrogen bonding.For the system NMP+CHOL the maximum deviation is observed at 0.5235 mole fraction at all measured temperatures due to the formation of hydrogen bonding complex between them.For the system NMP+CHE the maximum deviation is observed at a mole fraction of 0.6420 with an opposite sign in all the theoretical deviations in velocity.From this we can conclude that weak interactions or dispersive forces are present in the binary components for the system NMP+CHE where as strong intermolecular interactions are present in the systems NMP+CHA and NMP+CHOL.
The degree of molecular interaction for the binary systems NMP+CHA and NMP+CHOL are positive and for the binary system NMP+CHE is negative.It changes from negative to positive and becomes more positive in the increasing order NMP+CHE< NMP+CHOL< NMP+CHA.This suggest that the molecular interactions are more in NMP+CHA system due to hydrogen bonding and forms more compact structure than the system NMP+CHOL though hydrogen bonding is present in the later also.For the system NMP+CHE the interactions are very weak and no possibility of formation of strong hydrogen bonding only dispersive forces are operating.
Figure 1 represents the variation of U 2 exp /U 2 imx with the mole fraction of NMP.It is observed that for the systems NMP+CHA and NMP+CHOL with a maximum at around 0.5 mole fraction and for the system NMP+CHE the maximum is observed at around 0.6 mole fraction at all measured temperatures.The percentage deviations of the ultrasonic velocity are both positive and negative which indicates the non-ideal behavior of liquid mixtures.The ratio of U 2 exp /U 2 imx is an important tool to measure the non-ideality in the mixtures where the properties other than sound velocity are not known 23 .It is observed that all the three binary systems under investigation the increase in temperature the experimental and theoretical velocities decreases perhaps due to breaking of hetero and homo molecular clusters at higher temperatures 24 .

Conclusion
In the binary systems of cyclic compounds with NMP, Rao's specific velocity holds well for the systems NMP+CHA, Impedance relation for the system NMP+CHOL and Ideal mixing relation best suited for the binary system NMP+CHE.The observed deviations of theoretical values of velocity from the experimental values are attributed to the presence of intermolecular interactions in the systems under investigation.The interaction parameter also inferred the same conclusion.

Figure 1 .
Variation of U 2 exp /U 2 imx with the mole fraction of N-Methyl-2-pyrrolidone.

Table 1 .
The experimental velocity(U), the theoretical velocity, percentage deviation and molecular interaction parameter (α) for the system N-Methyl-2-pyrrolidone with cyclohexylamine ay different temperatures.

Table 2 .
The experimental velocity(U), the theoretical velocity, percentage deviation and molecular interaction parameter (α) for the system N-Methyl-2-pyrrolidone cyclohexanol at different temperatures.