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Theoretical Evaluation of Ultrasonic Velocity in Organic Liquid Mixtures



P. Vasantharani, S. Muthu Shailaja, A.N. Kannappan and R. Ezhil Pavai
 
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ABSTRACT

Theoretical values of ultrasonic velocity in four ternary liquid mixtures of 1-propanol, 1-butanol, 1-pentanol and 1-hexanol with TEA in n-hexane for different proportions have been evaluated using Nomoto`s Relation, Ideal Mixture Relation, Free Length Theory and Impedence Dependance Relation. Theoretical values are compared with experimental values and the Chi-square test for goodness of fit is applied to check the validity of the theories.

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  How to cite this article:

P. Vasantharani, S. Muthu Shailaja, A.N. Kannappan and R. Ezhil Pavai, 2008. Theoretical Evaluation of Ultrasonic Velocity in Organic Liquid Mixtures. Journal of Applied Sciences, 8: 2329-2332.

DOI: 10.3923/jas.2008.2329.2332

URL: https://scialert.net/abstract/?doi=jas.2008.2329.2332
 

INTRODUCTION

Measurement of ultrasonic study gives information about physico-chemical 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 n-hexane 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:

Image for - Theoretical Evaluation of Ultrasonic Velocity in Organic Liquid Mixtures
(1)

where, X1, X2 and X3 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:

Image for - Theoretical Evaluation of Ultrasonic Velocity in Organic Liquid Mixtures
(2)

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:

Image for - Theoretical Evaluation of Ultrasonic Velocity in Organic Liquid Mixtures
(3)

where, V01, V02 and V03 represent the volume at absolute zero of the three pure components with (V0=Vmix Uexp/Uα), Vmix is the molar volume of the mixture and Y is the surface area per mole and is defined as:

Image for - Theoretical Evaluation of Ultrasonic Velocity in Organic Liquid Mixtures
(4)

Where:
Uα = 1600 m sec-1 and also he has given the expression for Lf as:

Image for - Theoretical Evaluation of Ultrasonic Velocity in Organic Liquid Mixtures
(5)

where, Uexp and ρexp 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 (Umix) can be calculated from the formula:

Image for - Theoretical Evaluation of Ultrasonic Velocity in Organic Liquid Mixtures
(6)

Ideal Mixture Relation (IMR): Van Deal and Vangeel (1969) suggested the following expression for the ultrasonic velocity (Uimr):

Image for - Theoretical Evaluation of Ultrasonic Velocity in Organic Liquid Mixtures
(7)

The degree of molecular interaction (α) is given by:

Image for - Theoretical Evaluation of Ultrasonic Velocity in Organic Liquid Mixtures
(8)

Chi-square test for goodness of fit: According to Pearson (1978) the Chi-square is given by:

Image for - Theoretical Evaluation of Ultrasonic Velocity in Organic Liquid Mixtures
(9)

where, Oi (i = 1, 2, 3, …n) is a set of observed or experimental frequencies and Ei (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 1-propanol 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)
Image for - Theoretical Evaluation of Ultrasonic Velocity in Organic Liquid Mixtures

Table 2: The greatest percentage deviation and values of Chi-square for four theories
Image for - Theoretical Evaluation of Ultrasonic Velocity in Organic Liquid Mixtures

The extent of deviation in velocities may be attributed to the presumption made in the theories for non-polar-non-polar and non-polar-polar 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 1-propanol (0.0119), 1-butanol (-0.0037), 1-pentanol (0.0082) and 1-hexanol (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 (Chi-square is also minimum) whereas for system III it is greatest (Chi-square is also maximum).

Hexane is a nonpolar chain molecule, only Van der Waals` type interactions are present in n-hexane, while alcohols are polar and associate strongly through hydrogen bonding. In alcohols + n-hexane 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 quasi-molecule 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 dipole-dipole 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 chi-squared 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.

REFERENCES
1:  Jacobson, B., 1952. Intermolecular free length in the liquid state I adiabatic and isothermal compressibilities. Acta Chem. Scand. (Denmark), 6: 1485-1487.

2:  Jayakumar, S., N. Karunanidhi and V. Kannappan, 1996. Ultrasonic study of molecular interaction in binary liquid mixtures. Ind. J. Pure Applied Phys., 34: 761-763.

3:  Kalidoss, M. and R. Srinivasamoorthy, 1997. Ultrasonic study of ternary liquid mixtures of cyclohexane + 1, 2- dichloroethene + n-propanol, + n-butanol. J. Pure Applied Ultrason, 19: 9-15.

4:  Kannappan, A.N. and V. Rajendran, 1990. Ultrasonic studies on molecular interaction and theoretical evaluation of sound velocity in ternary liquid mixture. Ind. J. Acoust Soc. India, 25: 137-140.

5:  Kannappan, A.N., V. Arumugam and P. Vasantharani, 2003. Evaluation of sound velocity in ternary liquid systems. J. Curr. Sci., 3: 277-280.

6:  Nomoto, O., 1958. Empirical formula for sound velocity in liquid mixture. J. Phys. Soc. Jpn., 13: 1528-1532.
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7:  Palaniappan, L. and K. Ramesh, 2001. Estimation of sound velocity in ternary liquid mixtures of isobutanol in cyclohexane with toluene. J. Acoust Soc. India, 29: 149-153.

8:  Pearson, K., 1978. Fundamentals of Mathematical Statistics. AS Chand and Company, New Delhi, India, pp: 903.

9:  Ramaswamy, K., D. Anbanathan and A.N. Kannappan, 1980. Study of intermolecular interaction by ultrasonic method. Acustica. (Germany), 44: 342-344.

10:  Van, D. and E. Vangeel, 1969. Proceedings of the 1st international conference on calorimetry and thermodynamics. Warsaw, pp: 556.

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