Theoretical Values, Percentage Deviations and Calculated Values by Polynomial Equations of the Liquid Mixture with Equimolar Mixture of Ethanol and Formamide
Authors: Patel Bhavi , Salvi Bhavya , Mishra Vivekanand , Yadav Ritesh 
Published: July 2020

Background:
The binary mixtures of isopropanol/isobutanol/isoamyl alcohol with
an equimolar mixture of ethanol and formamide consist of different ultrasonic properties, which
have been studied at room temperature at a fixed frequency of 2 MHz. The ultrasonic-related
physical parameters like velocity (U), density (ρ), adiabatic compressibility (βad), intermolecular
free length (Lf), acoustic impedance (Z), etc., have been studied. The theoretical evaluation
of ultrasonic velocity in liquid mixtures offers a transparent method for the study of the nature
of molecular interactions in the mixtures besides verifying the applicability of different theories
such as Nomoto’s, Van Dael and Vangeel’s, Impedance Dependence relation, Junjie’s relation,
Rao’s specific sound velocity relation, and Jacobson’s relations, Percentage deviations of theoretical
ultrasonic velocities from experimental values in the mixtures of all liquid mixture and
also calculated values of ultrasonic velocity from polynomials for all the schemes with mole
fraction (x) of isopropanol/isobutanol/ isoamyl alcohol.

Objective:
The main focus of the present work was to prepare the structural changes associated
with the liquid mixtures having weakly interacting components and strongly interacting components.
The study of molecular association in mixtures providing exact information of thermodynamic
mixing properties, such as adiabatic compressibility, intermolecular free length, free volume,
internal pressure, and molar volume, has significant importance in theoretical and applied
areas of research. The ultrasonic study has been a subject of keen interest during the past many
years. This branch of physical sciences has played a significant role in deciding the interactions
between the molecules of compounds under study. It has a potential tool for evaluating energy
exchange between various degrees of freedom and nonlinear properties in binary liquid mixtures.

Methods:
The binary liquid mixtures were prepared by mixing two components, by weight, using
an electronic analytical balance (Reptech RA-2012), accurate up to ±0.0001 g. The average
uncertainty in mole fraction of binary mixtures was estimated to be ±0.0001. To avoid loss of
solvent due to evaporation, mixtures were stored in specially designed ground-glass airtight
ampoules and placed in a dark place to prevent photolytic effects.

Results:
These empirical fittings of data are described qualitatively and quantitatively using experimental
speed data even in the specific interaction predominant region where non-ideal behavior
of the mixture is observed. The values of sound velocities and percentage deviation (after
determining the co-efficient of the polynomial equations by applying the least squares method)
are compiled in the tables, respectively.

Conclusion:
The ultrasonic velocities and densities for all three mixtures were measured, and
the values were calculated. The observed trends of VEm, ΔkS and LEf indicate the presence of
weak interactions, and the strength of these interactions follows the order EMM+IPA>EMM
+IBA>EMM+IAA. Besides, the ultrasonic velocities measured from different velocity theories
were found to be consistent with the experimentally measured ultrasonic velocities. Among these
theories, Jacobson’s velocity equation showed a good result for the experimental and theoretical
ultrasonic velocity values for all the binary mixtures used.