Available online at http://www.urpjournals.com International Journal of Research in Pure and Applied Physics Universal Research Publications. All rights reserved ISSN 2278-134X Original Article Study of Acoustical and Thermodynamic Properties of Aqueous Solution of NaCl at different Concentrations and Frequencies through Ultrasonic Technique M. K. Praharaj *, P. R. Mishra, S. Mishra, A. Satapathy Department of Physics, ABIT, CDA, Sector-1, Cuttack, Odisha-753014, * E-mail.: abitphysics@rediffmail.com Received 25 April 2012; accepted 20 June 2012 Abstract The Ultrasonic velocity, density, and viscosity have been measured for aqueous solution of NaCl at different concentrations, at different frequencies at constant temperature (293 0 K). These experimental data have been used to estimate the thermodynamic parameters such as adiabatic compressibility, free length, free volume, internal pressure, relaxation time, acoustic impedance, Gibb s free energy and absorption coefficient for the solution. This kind of study is important for both humans as well as plants. 2011 Universal Research Publications. All rights reserved Key words: Ultrasonic velocity, Acoustical and thermodynamical properties 1. INTRODUCTION The ultrasonic studies find extensive applications in characterizing aspects of physic-chemical behavior involving molecular interactions in liquid mixtures [1-2]. Ultrasonic velocity measurements are considerably importance in understanding the molecular interactions and can be used to provide qualitative information about the physical nature and strength of molecular interaction in the liquid mixtures [3-5]. Recent studies [6-8] have also found to use of ultrasonic energy in engineering, agriculture and medicine. In engineering it is used to study the structure of materials. Ultrasonic pulses can speedup certain chemical reactions and act as a catalytic agent on wheat germinations. The magnitude of density as well as velocity of ultrasonic wave in human body fluids or organs is of vital importance for carrying out acoustical analysis of human system or organs [9-12]. Further we know that sodium potassium levels in human blood are of considerable importance for several reasons. Sodium maintains the normal distribution of water and the osmotic pressure in various fluid components of the body. Potassium influences the acid base balance and osmotic pressure including water retention. Since sodium salt is important to human as well as plants, we have done ultrasonic study of sodium chloride solution of different concentration at different frequencies. Variation in frequencies leads to variation in velocity and the different thermodynamics parameters. This gives an idea about the nature of molecular interaction in the solutions of different concentration at different frequencies. To our knowledge, these kinds of measurements have not been made so far. 2. MATERIALS AND METHODS: Fresh distilled water has been used as solvent for preparing sodium chloride (NaCl) solutions of different concentrations. Sodium chloride used as solute for the solution is of analytical reagent (AR) grade, manufactured by reputed firm E-Merk Ltd. (India). 2.1 Velocity Measurement:- The velocity of ultrasonic wave in the NaCl solutions (Molality- 0.8562, 1.711, 2.566, 3.422) have been measured using multi-frequency ultrasonic interferometer with a high degree of accuracy operating at 11 different frequencies (Model M-84) supplied by M/s Mittal Enterprises, New Delhi. The measuring cell of interferometer is a specially designed double walled vessel with provision for temperature constancy. An electronically operated digital constant temperature bath (Model SSI-03spl) supplied by M/s Mittal Enterprises, New Delhi, operating in the temperature range -10 o c to 85 o c with an accuracy of ± 0.1K has been used to circulate water through the outer jacket of the double walled measuring cell containing the experimental liquid. 2.2 Density Measurement:- The densities of solutions are measured using a 10ml specific gravity bottle. The specific gravity bottle with the 15
Figure-1: Variation of Ultrasonic velocity with frequency Figure-3: Variation of Viscous Relaxation Time with frequency Figure-2: Variation of Adiabatic Compressibility with frequency experimental liquid is immersed in a temperature controlled water bath. The density was measured using the formula ρ 2 = (w 2 /w 1 ). ρ 1 Where, W 1 and W 2 are the weights of distilled water and NaCl solution respectively. ρ 1 and ρ 2 are densities of water and NaCl solution respectively. 2.3 Viscosity measurement:- The viscosities of solutions are measured using an Oswald s viscometer calibrated with double distilled water. The Oswald s viscometer with the experimental liquid is immersed in a temperature controlled water bath. The time of flow was measured using a racer stop watch with an accuracy of 0.1 sec. The viscosity was determined using the relation, Figure-4. Variation of Free Length with frequency η2= η1.(t2/t1).(ρ2/ρ1) Where, η 1 is the viscosity of water, η 2 is the viscosity of experimental liquid, ρ 1 is the density of water, ρ 2 is the density of experimental liquid, t 1 is the time of flow of water and t 2 is the time of flow of experimental liquid. 3. THEORETICAL ASPECT The following thermodynamic parameters were calculated from Jacobson s relation [13 15]. The adiabatic compressibility has been calculated from the speed of sound (U) and the density (ρ) of the medium by using the equation of Newton Laplace as, β = 1/U 2. ρ ---------------------------------- (1) The intermolecular free length has been determined 16
Figure-5: Variation of Internal Pressure with frequency Figure-7: Variation of Gibb s Free Energy with frequency Figure-6: Variation of Acoustic Impedance with frequency as, L f = K T β 1/2 --------------------------------- (2) Where K T is the temperature dependent constant and β is the adiabatic compressibility. Suryanarayana [16] obtained a relation for free volume in terms of ultrasonic velocity (U) and the viscosity (η) of liquid is V f = ( M eff.u / k.η ) 3/2 -------------------- (3) Where M eff is the effective mass of the mixture, k is a dimensionless constant independent of temperature and liquid. Its value is 4.281 x 10 9. On the basis of statistical thermodynamics, Suryanarayana [17] derived an expression for the Figure-8: Variation of Absorption coefficient with frequency determination of internal pressure by the use of free volume concept as, П i = brt (kη/u) 1/2 (ρ 2/3 /M 7/6 ) ---------- (4) Where, b stands for cubic packing, which is assumed to be 2 for all liquids, k is a dimensionless constant independent of temperature and nature of liquids. Its value is 4.281x10 9. T is the absolute temperature in Kelvin, M is the effective molecular weight, R is the Universal gas constant, η is the viscosity of solution in N.S.m -2, U is the ultrasonic velocity in m.s -1 and ρ is the density in Kg.m -3 of solution. Relaxation time is the time taken for the excitation energy to appear as translational energy and it depends on 17
Figure-9: Variation of ultrasonic velocity with Molality Figure-11: Variation of Viscous Relaxation Time with Molality Figure-10: Variation of Adiabatic Compressibility with Molality temperature and impurities. The relaxation time can be calculated from the relation, τ = 4/3. (β.η) ------- (5) Where β is the adiabatic compressibility and η is the viscosity of the mixture. The specific acoustic impedance is given by, Z = U.ρ ------- (6) Where U and ρ are velocity and density of the mixture respectively. The Gibb s free energy is calculated by using the relation Figure-12: Variation of Free Length with Molality G = KT.Ln (KTτ/h) ------- (7) Where, τ is the viscous relaxation time, T is the absolute temperature, K is the Boltzmann s constant and h is the Planck s constant. Absorption coefficient or attenuation coefficient is a characteristic of the medium and it depends on the external condition like temperature, pressure and frequency of measurement. It is given by the following relation [18]. α = 8π 2 ηf 2 / 3ρU 2 ----- (8) Where η is the viscosity in NS.m -2, U is the ultrasonic velocity in m.s -2, ρ in Kg.m -3 and f is the frequency in Hz. 18
Figure-13: Variation of Internal Pressure with Molality Figure-15: Variation of Gibb s Free Energy with Molality Figure-14: Variation of Acoustic Impedance with Molality 6. RESULT AND DISCUSSION The Ultrasonic velocity, density and viscosity of aqueous solution of NaCl of different concentrations are presented in table-i at frequencies 3 MHz, 6 MHz, 9 MHz and 12 MHz It is observed that, for a particular concentration of the solution, velocity decreases when frequency increases [fig.1]. Increase in frequency leads to increase in local density and hence consequent decrease in velocity. Decrease Figure-16: Variation of Absorption coefficient with Molality in velocity is also due to increase in free length [Fig.-4] and adiabatic compressibility [19] [Fig.-2] of the liquid as these two factors are the deciding factors of the ultrasonic velocity in the liquid system. The same has been presented in table-ii. The increase in density with increasing concentration of solute suggests a moderate strong electrolytic nature in which the solute tends to attract the solvent molecules. The intermolecular free length however decreases with molar concentration of solute [Fig.12]. The 19
Table I: Values of density (ρ), viscosity (η) and Ultrasonic velocity (U) at frequencies 3 MHz, 6 MHz, 9 MHZ and 12 MHz. Molality of Density(ρ) Viscosity (η) Velocity (U) m.s -2 NaCl Kg.m -3 x 10-3 (N.s.m -2 ) 3 MHz 6 MHz 9 MHz 12 MHz 0.8562 1040.5 1.0532 1562.36 1561.45 1560.52 1559.12 1.711 1078.7 1.0973 1592.4 1591.8 1590.3 1588.8 2.566 1116.3 1.1386 1630.8 1627.2 1624.5 1622.4 3.422 1158.8 1.1798 1667.4 1666.5 1665 1662 TABLE II: Values of Adiabatic compressibility (β), Free length (L f ) and free volume(v f ) at frequencies 3 MHz, 6 MHz, 9 MHZ and 12 MHz. Molality of NaCl Adiabatic compressibility (β) (10-10 N -1.m 2 ) TABLE III: Values of Internal pressure (πi ), viscous relaxation time (τ) and Gibb s free energy (ΔG) at frequencies 3 MHz, 6 MHz, 9 MHZ and 12 MHz. TABLE IV: Values of Acoustic impedance (Z) and absorption coefficient (α) at frequencies 3 MHz, 6 MHz, 9 MHZ and 12 MHz. decrease in adiabatic compressibility [Fig.10] with molality is attributed to the influence of the electrostatic field of the ions on the surrounding solvent molecules. Acoustic impedance is governed by the inertial and elastic properties of the medium. In the present investigation, acoustic impedance decreases with increase in frequency [Fig.6] but increases with increase in molality [Fig.-14]. Viscous relaxation time increases with increase in frequency [Fig.3]. This relaxation time which is of the order of 10-10 sec is due to the structural relaxation process [20] showing the presence of molecular interaction. Gibb s free energy confirms the same [Fig.7]. Viscous relaxation time [Fig.11] and Gibb s free energy [Fig.15] decreases with increase in molality. The reduction in Gibb s free energy with molality indicates smaller time for the cooperative process. Free length (L f) (10-10 m) Free volume (V f) (10-7 m 3.mol -1 ) 3 MHz 6 MHz 9 MHz 12 MHz 3 MHz 6 MHz 9 MHz 12 MHz 3 MHz 6 MHz 9 MHz 12 MHz 0.8562 3.937 3.942 3.947 3.954 0.391 0.391 0.392 0.392 1.996 1.994 1.992 1.990 1.711 3.656 3.659 3.666 3.672 0.377 0.377 0.377 0.378 1.895 1.893 1.891 1.888 2.566 3.368 3.383 3.395 3.403 0.362 0.363 0.363 0.364 1.827 1.821 1.816 1.813 3.422 3.104 3.107 3.113 3.124 0.347 0.347 0.348 0.348 1.766 1.765 1.763 1.758 Molality of NaCl Internal pressure ( π i ) (x 10 6 N.m- 2 ) Viscous relaxation time (τ) ( x 10-12 s ) Gibb s free energy (ΔG) ( x 10-20 k.j.mol -1 ) 3 MHz 6 MHz 9 MHz 12 12 12 3 MHz 6 MHz 9 MHz 3 MHz 6 MHz 9 MHz MHz MHz MHz 0.8562 401.23 401.35 401.47 401.65 0.553 0.554 0.554 0.555 0.492 0.493 0.493 0.494 1.711 421.75 421.83 422.03 422.23 0.535 0.535 0.536 0.537 0.479 0.479 0.480 0.481 2.566 440.00 440.49 440.86 441.14 0.511 0.514 0.515 0.517 0.461 0.462 0.464 0.465 3.422 458.98 459.11 459.31 459.73 0.488 0.489 0.490 0.491 0.442 0.442 0.443 0.444 Molality of NaCl Acoustic impedance (Z) ( x 10 6 Kg.m 2.s -1 ) Absorption coefficient (α) np.m -1 3 MHz 6 MHz 9 MHz 12 MHz 3 MHz 6 MHz 9 MHz 12 MHz 0.8562 1.626 1.625 1.624 1.622 62.89 251.98 567.97 1012.45 1.711 1.718 1.717 1.715 1.714 59.69 239.02 539.33 961.53 2.566 1.820 1.816 1.813 1.811 55.72 224.36 507.34 905.44 3.422 1.932 1.931 1.929 1.926 52.04 208.48 470.35 840.72 These parameters are presented in Table-III. Internal pressure represents the resultant cohesive force between the molecules. The increase in internal pressure with increase in frequency as well as molality of solution [Fig.-5 & 13] may be due to stronger cohesive force. It also gives an idea about the solubility characteristics. We find that for a particular concentration, internal pressure increases slowly with increase in frequency where as for a particular frequency the variation is rapid when concentration varies. Finally we find that the absorption coefficient or the attenuation coefficient varies as desired [Fig.8 & 16]. It decreases with increase in density and velocity where as increases with increase in frequency. 20
7. CONCLUSION It is concluded that ultrasonic studies provide a comprehensive investigations of molecular association in liquid solution. When an acoustic wave travels in a medium, there is a variation in pressure from particle to particle. When the frequency of the wave changes, the pressure also changes leading to a change in the velocity as well as the associated thermodynamics parameters. Summarising the trends and variation of thermodynamic parameters with frequency of the ultrasonic wave has been studied in detail which will give us an idea about the nature of molecular interactions in the sodium chloride solution. ACKNOWLEDGEMENT: We are thankful to Dr. J. C. Mohanty, Ex-Principal, Govt. Science College, Chatrapur for his effort in guiding us in the right direction, Mrs. Jayashree Mohanty for her support in preparing this article. And above all we are thankful to the Management of Ajay Binay Institute of technology, CDA, Cuttack for providing the infrastructure as an initiation for the improvement of research activities in the Institute and Department of Physics, Ravenshaw University for providing guidance through their experienced faculty members. 8. REFERENCE 1. Dash S. K & Swain B. B, Chem. Papers. 48 146, (1994). 2. Dash S. K, Chakravortty V & Swain B. B, Acoustic Lett, 19, 142, (1996). 3. Kincaid J. F, Eyring H, J Chem Physics, 5, 587, (1973). 4. Meheta S. K, Chauhan R.K, J Solution Chem, 26, 295, (1996). 5. Dewan R. K, Meheta S. K, Parashar R, Bala K, J. Chem. Soc. Faraday, Trans,, 87,1561, (1991). 6. Megremis S, Chatziioannou M, Tritou L, JUM, January, 29, 145-147, (2010). 7. Zhong Y, Longman R, Bradshaw R, Odibo A O, JUM, 30, 463-459, (April 2011). 8. Jambrack A. R, Mason T. J, Paniwnyk L, Lelas V, Czech J Food Sci, 25, 90-99, (2007). 9. Ludwig G. D, J Acoust Soc. Amer, 22, 862, (1950). 10. Singh J, & Bhatti S, Indian j Pure & Appl Phys, 36, 43. (1998). 11. Singh A. K, Bihari J, Indian j Pure & Appl Phys, 32, (1994). 12. Gandhi K, Singh V. R, Bansal M. C, & Bhatia S, Indian j Pure & Appl Phys, 40, 515, (2002). 13. Shashikant A. Ikhe & Narwade M. L, Indian J. Chem, 44A, 1203, (2005). 14. Palani R., Sarvanan S. & Geetha A., Asian J. of Chem., 19 No 7, 5113, (2007). 15. Thiyagarajan R. & Palaniappan L., Indian J. Pure & Appl. Phys, 46, 852, (2008). 16. Suryanarayana C. V, J acoust Soc India, 7, 107, (1976). 17. Suryanarayana C. V, J acoust Soc India, 7, 131, (1976). 18. Varada Rajulu A, Mabu Sab, Bull mater P, Sci,, 3,18, 247-253. (1995). 19. Eyring H, & Kincaud J F, J. Chem Phys, DOI: 10.1063/1.1750134, 6, 620-629, (1938). 20. Bender J. M, Pecora R, J Phys. Chem, DOI: 10.1021/ j 100399a048, 90, 1700-1706, (1986). Source of support: Nil; Conflict of interest: None declared 21