Ultrasonic Relative percentage deviations with respect to the

Ultrasonic
velocity of the binary liquid mixtures is the best tool to measure the
mechanical stability of liquids and to understand the molecular interactions in
pure, binary and higher order multi component liquid mixtures. 1-3. It also
gives better information on the physico-chemical behavior of liquids and their
mixtures 4-7. Theoretical evaluation of ultrasonic velocity values of binary
mixtures with the experimental data indicates the behavior of molecular
interactions and it is used to develop theoretical models for liquids. Literature
survey reveals that some studies were reported by other researchers on the measurement
of ultrasonic speeds, densities, viscosities, relative permittivity etc., of
binary mixtures containing Xylenes with other components at different
temperatures 8-14. Apparently no
study has been reported on the theoretical evaluation of ultrasonic velocity by
using velocity theories such as Nomato’s relation, Van Dael and Vangeel’s relation,
Junjie’s relation, Impedance dependence relation and Rao’s specific velocity
relation for the Propiophenone with Xylene binary mixtures at temperatures from
303.15 to 318.15K. The results were discussed further in terms of molecular
interaction parameter (?) values for the non-ideality in the liquid mixture,
relative deviation percentage error with respect to experimental data and
Chi-square (?2) test for the goodness of fit.  Propiophenone is widely
used component in perfumes industries and also in the synthesis of
ketoamphetamines such as cathinone and methcathinone 15. Xylenes with other
components used as chemical intermediates. Xylenes also used as solvent in
leather, rubber and printing industries data research, Worldofchemicals.com.

Based on the observed relative
percentage deviations in ultrasonic velocities, the positive deviations in
velocity are a result of (a) molecular association and (b) complex formation
whereas negative deviations in velocity are due to molecular dissociation of
associated species as a result of addition of inner solvent or an active
solvent 22. Relative percentage deviations with respect to the experimental
data indicate the presence of molecular interactions between the unlike
molecules in the studied binary mixtures and it is supported by Sk.Fakruddin
et.al 23. Respective theories own the responsibility for its limitations and
approximations. Figure-01-03 shows the relative percentage deviations in the
ultrasonic velocities with respect to experimental data are positive in UNOM,
UVDV, UJUN, URAO, and negative in UIMP
relations at all four temperatures for the studied binary mixtures. Percentage
deviation values of UNOM, UIMP, & URAO
values are in good agreement with the experimental values, whereas UVDV
& UJUN values are deviating away from the experimental
values. It indicates the non-ideal behavior in the liquid mixtures. Interaction
parameter (?) is the best tool to measure the non-ideality in the liquid
mixtures. Figure-04-06 shows the molecular interaction parameter values of the
binary mixtures at temperatures from 303.15 to 318.15K. The ‘?’ values are having
the parabolic trend which indicates the non-ideality.  Positive values of ‘?’ are observed at the
entire composition range at all four temperatures and they are increasing with
increase in temperatures. It shows strong interactions between the component
molecules.   

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Validity
of the applied theories is checked by using Chi square test for the goodness of
fit. The values of average relative percentage error and Chi square are
tabulated in Table-04. If there is no significant difference between the
experimental and the calculated values, then the Chi square values are closer
to zero, therefore those binary mixtures are in agreement with goodness of fit
(Null hypothesis), if the Chi-square values are deviating away from zero it
comes under alternative hypothesis. The Chi square values of UNOM
followed by UIMP, URAO are closer to zero and are in good
agreement under the studied binary mixtures.