Experimental and Theoretical Studies of Ultrasonic Velocity in Binary Liquid Mixtures of Ethyl Benzoate

Ultrasonic velocity is measured at 2MHz frequency in the binary mixtures of Ethyl Benzoate with 1-Propanol, 1-Butanol, 1-Pentanol and theoretical values of ultrasonic velocity have been evaluated at 303K using Nomoto’s relation, Impedance relation, Ideal mixture relation, Junjie’s method and free length theory. Theoretical values are compared with the experimental values and the validity of the theories is checked by applying the chi-square test for goodness of fit and by calculating the average percentage error (APE). A good agreement has been found between experimental and Nomoto’s ultrasonic velocity.


Introduction
Measurement of ultrasonic velocity gives the valuable information about the physicochemical behavior 1,2 of the liquid and liquid mixtures.Several relations, semiempirical formulas and theories are available for the theoretical computation of ultrasonic velocity in liquid and liquid mixtures [3][4][5][6][7] .In continuation of our dielectric work [8][9][10] we report the ultrasonic velocity evaluated using Nomoto's relation 3 , Impedance relation 4 , Ideal mixture relation 5 , Junjie's method 6 and free length theory 7 for the binary mixtures of Ethyl benzoate with 1-Propanol, 1-Butanol, 1-Pentanol.Further, the best suitable theory for the given molecular system under study is also picked out by calculating the average percentage error and chi-square test.

Experimental
The compounds Ethyl benzoate, 1-Propanol, 1-Butanol, 1-Pentanol of 99% AR grade were supplied by Merck Co. Inc., Germany.The ultrasonic velocity was measured at 303K using a single crystal ultrasonic interferometer (M/s Mittal Enterprises, India) operating at a frequency of 2 MHz with an accuracy of ±0.1m/s.The density was measured at 303K using specific gravity bottle method by the standard procedure.

Theory
The following relations/theories are used for the prediction of ultrasonic velocity in the binary liquid mixtures.Surface area per mole, ; Where, 1, 2, represents the first and second component of the liquid mixture and the other symbols have their usual meanings.

Results and Discussion
The experimental values along with the values calculated theoretically using Nomoto's relation, collision factor theory, free length theory, ideal mixture relation and Junjie's method for the systems Ethyl benzoate+1-propanol, Ethyl benzoate+1-butanol and Ethyl benzoate+1-pentanol at 303K are given in Table 1.The validity of the theories is checked by applying Chi-square test and by calculating average percentage error.

Chi-square test for goodness of fit
According to Karl Pearson 11 , the Chi-square value is calculated using the formula, For (n-1) degrees of freedom, where, n is the number of data used.

Average percentage error (APE)
The average percentage Error 12 is calculated using the relation, Where, nnumber of data used.Umix(obs) = experimental values of ultrasonic velocities.Umix(cal) = computed values of ultrasonic velocities.
It can be seen from Table 1 that the theoretical values of ultrasonic velocity computed by various theories show deviation from experimental values.The predictive abilities of various ultrasonic therories depend upon the strength of interaction prevailing in a system.These theories generally fail to predict accurately the ultrasonic velocities where strong interactions are supposed to exist.  1 shows that the Chi-square value and APE value are minimum for Nomoto's relation and Free length theory than those obtained by other theories.An important reason for deviation from experimental values of ultrasonic velocity is that the molecular association effects are not taken into account in these theories.When two liquids are mixed, the interaction between the molecules of the two liquids takes place because of the presence of various forces like dispersive force, charge transfer, hydrogen bonding dipole-dipole and dipole-induced dipole interactions.Hence the observed deviation shows that the molecular interaction is taking place between the unlike molecules in the liquid mixture 13 .Similar kinds of results were obtained by earlier workers [14][15][16] .The agreement between experimental and theoretical velocities of Nomoto relation in all the three binary systems, suggests that R is additive property in all the systems.Higher deviations are observed in some intermediate concentration range.This suggests the existence of strong tendency for the association between component molecules as a result of Hydrogen bonding 17,18 .

Conclusion
Ultrasonic velocities predicted using NOM, IMR, JM, IMP and FLT were compared with experimentally measured velocity values at 303K for the binary mixtures of Ethyl benzoate with 1-Propanol, 1-Butanol, 1-Pentanol.It may be concluded that Nomoto's relation is best suited for all the binary mixtures under study.The observed deviation of theoretical values of velocity from the experimental values is attributed to the presence of intermolecular interactions in the systems studied.

Table 1 .
Experimental and computed values of Ultrasonic velocity for different systems at 303K.