INTRODUCTION
Measurement of ultrasonic study gives information about physicochemical
behaviour of solutions and liquid mixtures and molecular interactions
of multicomponent liquid mixtures. In this context Ramaswamy et al.
(1980) carried out ultrasonic investigation on some binary and ternary
liquid mixtures and correlated the experimental findings of ultrasonic
velocity with the theoretical relations suggested by Nomoto (1958) and
Van Deal and Vangeel (1969) and interpreted the results in terms of molecular
interactions. Kannappan et al. (2003) have also computed the ultrasonic
velocity of liquid mixtures using both the relations and discussed the
applicability of the same. The Free Length Theory (FLT) based upon Jacobson
(1952) concept of intermolecular free length has been successfully applied
by many workers to evaluate ultrasonic velocities in liquids. All the
four theories have been successfully applied by Kannappan and Rajendran
(1990). Palaniappan and Ramesh (2001) have calculated the sound velocity
and interpreted the results in terms of molecular interactions. This investigation
presents the evaluation of ultrasonic velocity using Nomoto`s relation,
ideal mixtures relation, free length theory and impedence dependance relation
for propanol, butanol, pentanol and hexanol with TEA in nhexane and comparison
with experimentally observed values.
THEORY
Nomoto`s Relation (NR): The empirical formula for sound velocity
in liquid mixtures given by Nomoto can be written as:
where, X_{1}, X_{2} and X_{3} are the mole fractions
of pure liquids, R and V represents the molar sound velocity and molar
volume.
Impedence Dependance Relation (IDR): The product of sound velocity
(U) and the density (ρ) of the mixture is termed as the acoustic
impedance (z) of the mixture. Hence, the sound velocity in the mixture
can be predicted from the knowledge of the acoustic impedance and the
density of pure components. This relation for ternary system (Kalidoss
and Srinivasamoorthy, 1997) may be given as:
where, the symbols refer to their usual meaning.
Free Length Theory (FLT): Free Length concept in ternary liquid
mixtures is introduced by Jacobson (1952) as:
where, V_{01}, V_{02} and V_{03} represent the
volume at absolute zero of the three pure components with (V_{0}=V_{mix}
U_{exp}/U_{α}), V_{mix} is the molar volume
of the mixture and Y is the surface area per mole and is defined as:
Where:
U_{α} = 1600 m sec^{1 }and also he has given the
expression for L_{f} as:
where, U_{exp} and ρ_{exp} are experimentally determined
values of the sound velocity and density, respectively and K is the temperature
dependent Jacobson`s constant. The sound velocity in a mixture (U_{mix})
can be calculated from the formula:
Ideal Mixture Relation (IMR): Van Deal and Vangeel (1969) suggested
the following expression for the ultrasonic velocity (U_{imr}):
The degree of molecular interaction (α) is given by:
Chisquare test for goodness of fit: According to Pearson (1978)
the Chisquare is given by:
where, O_{i} (i = 1, 2, 3, …n) is a set of observed or
experimental frequencies and E_{i} (i = 1, 2, 3…n) is the
set of expected or theoretical frequencies.
RESULTS AND DISCUSSION
Table 1 shows that the deviations between experimental
and theoretical velocity values obtained using four methods for 1propanol
system are as: Nomoto (1.93 to 0.48), IMR (1.31 to 0.59), FLT (37.8
to 2.07) and IDR (2.95 to 1.29). The deviations observed in the remaining
systems are also more or less in the same range.
Table 1: 
The experimental velocity (U), the theoretical velocity,
percentage deviation and molecular interaction parameter (α) 

Table 2: 
The greatest percentage deviation and values of Chisquare
for four theories 

The extent of deviation in velocities
may be attributed to the presumption made in the theories for nonpolarnonpolar
and nonpolarpolar interaction between the molecules. A general survey
of the Table 1 shows that α is positive and small which indicates
the absence of complex formation in all the systems studied. Also α
is maximum at 0.2999 mf with 1propanol (0.0119), 1butanol (0.0037),
1pentanol (0.0082) and 1hexanol (0.0383). The maximum value of α
indicates larger deviations from ideality, which may be due to the formation
of association in mixtures through hydrogen bonding.
This result is in accordance with those of Kannappan et al. (2003) and
Jayakumar et al. (1996). It is inferred from the Table
2 that the percentage deviation using the relation for system IV is minimum
(Chisquare is also minimum) whereas for system III it is greatest (Chisquare
is also maximum).
Hexane is a nonpolar chain molecule, only Van der Waals` type interactions
are present in nhexane, while alcohols are polar and associate strongly
through hydrogen bonding. In alcohols + nhexane mixtures, the alcohol
molecules associate in inert hexane medium and form clusters. Such self
association factors are not taken into account in FLT or Nomoto`s relation
which may thus lead to the maximum percentage deviation from experimental
values of the ultrasonic velocity.
An important reason for deviation is the molecular association effects
that are not taken into account in these theories. This association is
mainly due to hydrogen bond formation between like molecules. An associated
molecular cluster in a liquid may be called as a quasimolecule or a pseudo
molecule. The present theories of liquids are inadequate to account comprehensively
for the experimental manifestation of molecular interactions in various
ultrasonic processes. It is obvious that the intermolecular interaction
potential for a liquid will require for its full description; the knowledge
of at least the dipoledipole interactions, the collision factors, the
hydrogen bond forces and the relative strengths of various interactions
in like and unlike molecules. Such a comprehensive expression for the
intermolecular potential including all these factors has not yet been
developed.
CONCLUSION
It may be pointed out NR is best suited among the above theories for
the prediction of ultrasonic velocity and hence molecular interaction
in liquid mixtures. The chisquared test values also support the NR theory.
ACKNOWLEDGMENT
One of the authors (Shailaja) is thankful to Dr. AN. Kannappan, Professor
and Head, Department of Physics, Annamalai University (India), for the
award of University Research Fellowship.