Ultrasonic Velocity Determination in Binary Liquid Mixtures

Transcription

1 J. Pure Appl. & Ind. Phys. Vol.1 (4), (2011) Ultrasonic Determination in Binary Liquid Mixtures R. NATARAJAN* and P. RAMESH *Department of Physics, A. M. Jain College, Meenambakkam, Chennai , Tamil Nadu, India ABSTRACT Ultrasonic velocity, density and viscosity of binary liquid mixtures of acetone and carbon tetra chloride, Acetonitrile and aniline, acetone and iso-propyl alcohol, methyl ethyl ketone and Acetonitrile have been measured at room temperature 303K. value of parameters such as adiabatic compressibility (β), internal pressure (π i ), acoustic impedance (Z), (V E ), viscosity ( η ) and adiabatic compressibility (β E ) have been calculated. Ultrasonic velocities evaluated using Nomoto,Van Deal equation and Free length theory have been compared with Experimental values. It has been established that ultrasonic velocity increases with decrease in free length. Also Rao s shows a non linear variation confirming the associative nature of liquids. Keywords: Ultrasonic velocity, binary mixtures, molecular interaction. INTRODUCTION A Knowledge of densities, viscosities and ultrasonic velocities of liquids and liquid mixtures is essential to understand interaction between molecules. Ultrasonic study plays an important role to analyse physio-chemical behavior of molecular interaction. A knowledge of variation of velocity with concentration provides vital information about molecular interaction. The ultrasonic studies are extensively carried out to measure the thermodynamic properties and predict the intermolecular interaction of liquid mixtures. Ultrasonic data can be utilized to deduce some useful thermodynamic properties of liquid mixtures. The present study deals with the study of the following binary liquid mixtures. (i) Acetone + Carbon Tetra Chloride (ii) Acetonitile + Aniline A comparison has also been made between experimental and theoretical values of acoustical parameters evaluated at room temperature. EXPERIMENTAL DETAILS The liquids used were of pure analytical grade. The ultrasonic velocities(u)

2 253 R. Natarajan, et al., J. Pure Appl. & Ind. Phys. Vol.1 (4), (2011) were measured using ultrasonic interferometer at the frequency 1MHz. Densities of pure liquids and binary mixtures were found using specific gravity bottle. measurements were made using Ostwald s viscometer. THEORY AND CALCULATION The equations which are relevant for our study are given below Ultrasonic velocity U = nλ m/s (1) Adiabatic compressibility β = 1/ (U 2 ρ) ms 2 kg -1 (2) Acoustic impedance Z = ρ U kg m -2 s -1 (3) Molar sound velocity or Rao s R = (M eff / ρ) U 1/3 m 3 (m/s) 1/3 (4) Internal pressure Π i = b RT (kη/u) 1/2 (ρ 2/3 /M eff 7/6 ) Nm -2 (5) V = V ( X 1 V 1 + X 2 V 2 ) (6) viscosity η = η (X 1 η 1 + X 2 η 2 ) (7) adiabatic compressibility β = β (X 1 β 1 + X 2 β 2 ) (8) Vandael s equation for ultrasonic velocity [1/ (X 1 M 1 + X 2 M 2 )] [1 / U id 2 ] = (X 1 /M 1 U 1 2 ) + (X 2 / M 2 U 2 2 ) m/s (9) Nomoto s equation for ultrasonic velocity U = [ (X 1 R 1 + X 2 R 2 ) / (X 1 V 1 + X 2 V 2 )] 3 m/s (10) WADA S CONSTANT M W = (11) ρβ 1/7 FREE LENGTH THEORY U L f ρ 1/2 = K T (12) where U ultrasonic velocity n the frequency of the ultrasonic wave in Hertz λ wavelength in metres ρ density in kg m -3 R Rao s Meff effective molecular weight. Πi internal pressure b packing factor assumed as two in liquid system R universal gas T temperature in Kelvin k 4.28 x 10 9 a which is independent of the nature of the liquids and temperature. η viscosity of the liquid mixture V, V 1, V 2 molar of the mixture and the X 1, X 2 mole fraction of individual η 1, η 2 viscosity of pure liquids β,β 1,β 2 Adiabatic compressibility of binary mixture and the pure M 1, M 2 molecular weight of the U 1,U 2 ultrasonic velocity in the U id velocity of sound in the ideal mixture R 1, R 2 molecular sound velocity of the individual

3 R. Natarajan, et al., J. Pure Appl. & Ind. Phys. Vol.1 (4), (2011) 254 W M Wada s effective molecular weight of the L fmix and ρ - free length and density of the mixture K T - temperature dependent Jacobson s, 200 x 10-8 at 303K. Table 1. Properties of Binary Mixture (Acetone + Carbon Tetra Chloride ) at 303k fraction of acetone (X 1) fraction of carbon tetra chloride (X 2) Effective cula r Weight x 10-3 kg Density (Kg m -3 ) x 10-3 [Exp] [Van deal] [Nomoto] [Free Length Theory] Internal pressure π i x 10 6 (N m -2 ) RESULTS AND DISCUSSION The experimental values of density, viscosity, ultrasonic velocity and related acoustical parameters for different liquid mixtures are shown in tables (1 to 4). Further, figures (1 to 3) show the variation of ultrasonic velocity (U), Rao s (R), Internal pressure (π i ), at temperature 303K. Moreover the experimental values of ultrasonic velocity are compared with those calculated using Nomoto s, Vandeal s and Free length theory. A close examination of velocity Table (1) for Acetone + Carbon tetra chloride shows that the variation of ultrasonic velocity is almost linear. This may be assumed due to the fact that when nonpolar solvents are mixed there are only weak interactions between the liquid and hence it is expected that ultrasonic velocity variation should be linear. Conversely the linear dependence in the ultrasonic velocity confirms the non-polar nature of carbon tetra chloride and acetone 1. Since velocity and Adiabatic compressibility are inversely related, Adiabatic compressibility decreases as velocity increases. Rao s shows a nonlinear variation (Fig. 1) confirming the associative nature of liquids.

4 255 R. Natarajan, et al., J. Pure Appl. & Ind. Phys. Vol.1 (4), (2011) The Ultrasonic velocity decreases with increase in concentration of acetonitrile. This is in accordance with the view that the ultrasonic speed increases with decrease in free length and vice versa 9. Density is the measure of liquid-liquid interaction. Increase in density with increase in concentration of one of the indicates solvent-solvent interactions while decrease in density indicates lesser-solvent interactions. It may be also be assumed that solvent-solvent interaction bring about a bonding between them. So the sizes of the molecules increase and hence there will be a decrease in density. Table 2. Properties of Binary Mixture (Acetone + Carbon Tetra Chloride ) at 303k Rao s R x 10-4 m 3 (m s - ) 1/3 Acoustic impedance (Z) ( kg m -2 s -1 ) Volume x 10 6 (m 3 ) Free ml/mol V x 10 6 m 3 ηx 10-3 Adiabatic compressibility βx10-10 Wada Adiabatic compressibil ity βx Table 3. Properties of Binary Mixture (Acetonitrile + Aniline ) at 303k fraction of acetonitrile (X 1) fraction of aniline (X 2) Effective cular Weight x 10-3 kg Density (Kg m -3 ) x 10-3 [Experim -ental] [Van deal] [Nomoto] Adiabatic compressibility βx10-10 Internal pressure π i x 10 6 (N m -2 )

5 R. Natarajan, et al., J. Pure Appl. & Ind. Phys. Vol.1 (4), (2011) 256 Table 4. Properties of Binary Mixture (Acetonitrile + Aniline ) at 303k Rao s R x 10-4 m 3 (m s -1 ) 1/3 Acoustic impedance (Z) ( kg m -2 s -1 ) Volume x 10 6 (m 3 ) Free ml/mol V x 10 6 m 3 ηx 10-3 Adiabatic compressibility βx10-10 Wada Free Length x m [Free Length Theory]

6 257 R. Natarajan, et al., J. Pure Appl. & Ind. Phys. Vol.1 (4), (2011)

7 R. Natarajan, et al., J. Pure Appl. & Ind. Phys. Vol.1 (4), (2011) 258 CONCLUSION Ultrasonic velocity has been determined in Binary liquid mixtures of Acetone + Carbon Tetra Chloride and Acetonitrile + Aniline. The molecular interaction has been analysed in terms of acoustical parameters. REFERENCES 1. Sharma S.J., and Rajagopalan S. Jour. Pure and Applied Ultrasonic Vol.15 (No.4) pp , October (1993). 2. Vasumathi. V., Subramnyam B., and Sobhandri, Jour. Pure and Applied Ultrasonics, Vol.15 pp October (1993). 3. Singh Sudhanshu S. N., Kiran Kumar Baral and Ramesh Kumar Mandal, Jour. Pure and Applied Physics, Vol. 20 (2), pp 39-43, April June (1998). 4. M. Meyappan and P. Sethupathy., Jour. Pure and Applied Ultrasonics Vol. 25, pp 1-5 (2003). 5. K. Ramanathan and S. Ravichandran., Jour. Pure and Applied Ultrasonics., Vol 26, pp (2004). 6. R. R. Yadav and D. K. Pandey., Jour. Pure and Applied Ultrasonics, Vol 28, pp 4-11 (2006). 7. M.I. Aralaguppi, C.V. Jadar and T.M. Aminabhavi., Jour. Chem. Eng. Data Col. 44, pp (1999). 8. G. Venkataramana, E.Rajagopal and N. Manohara Murthy., Jour. Pure and Applied Ultrasonics., Vol 25, pp 33-37, (2003). 9. Eyring H., and Kinciad J.F., Jour. Chemical Phyics, Vol 6, pp 680, (1938).