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 Interrelationship between Surface Tension and Sound Velocity & Thermodynamical studies of binary liquid mixtures Mathana Gopal.A., Poongodi.J.,* *Department of Physics, Kamaraj College, Thoothukudi-628003, Tamilnadu Email-id: poongodinagaraj@gmail.com Received 23 April 2015; accepted 05 May 2015 Abstract To understand the intermolecular interactions in organic liquids and liquid mixtures, the study of ultrasonic and thermodynamic parameters are of due importance. Thermodynamic interaction in ethanol with benzene have been studied extensively using experimental results of density, viscosity and velocity at different temperatures ranging from 308K to 323K. Various ultrasonic measurements are made using ultrasonic interferometer (2MHz). The internal pressure, free volume, adiabatic compressibility and other related parameters of ethanol for different concentrations of benzene are presented. In addition to this, acoustical parameters such as specific acoustical impedance, relaxation time, Rao s constant, Wada s constant are computed. Also by using the ultrasonic velocity data, the values of surface tension (σ Aur & σ Mod) at different temperature are computed and the results are discussed. The variations in ultrasonic velocity and other parameters play a significant role in understanding the solute-solvent, intra and intermolecular interactions between the constituent molecules. 2015 Universal Research Publications. All rights reserved Keywords: Ultrasonic velocity;viscosity; free volume; internal pressure; adiabatic compressibility, Rao s constant, Wada s constant; surface tension; molecular interactions. I. Introduction Ultrasonic speed and its related thermodynamic properties have been extensively used to study physicochemical behaviour and molecular interactions in a variety of binary liquid systems. Excess sound velocity is found to be highly useful in understanding the solute-solvent interactions in binary aqueous and non-aqueous liquid mixtures 1,2. Ultrasonic study of intermolecular interactions between the component molecules in binary liquid mixtures are of considerable theoretical and industrial importance. 3 The dependence of ultrasonic velocity and those of derived parameters such as isentropic compressibility, intermolecular free length, relative association, acoustic impedance, excess isentropic compressibility, excess intermolecular free length and other excess parameters on composition of the binary mixtures throw light on the nature and extent of interaction between the component molecules of these mixtures 4-6. With this aim, we determined densities and ultrasonic velocities of the binary mixture of ethanol with benzene at 308K, 313K, 318K, 323K over the entire concentration range. Using experimental values of density and velocity, a number of acoustical parameters were calculated in order to study the intermolecular interactions in these systems. In addition to this, two empirical interrelationships between the Surface Tension and Ultrasonic velocity are available in Literature. The First due to Auerbach 7 has been widely used by various workers during the recent years. The Second relation due to Altenberg 8 could not gain much importance and has been successfully applied to pure liquids 9, binary 10 and multi component liquid mixtures 11, liquid metals and alloys 12, molten salts and electrolytes and their mixtures. In one of the Research papers an attempt has been made to modify this relation by including temperature as an additional factor in the equation. Both the results are compared and are interpreted in the light of molecular interactions. II. EXPERIMENTAL Chemicals used for our study were of AR grade and are used without further purification. All the binary mixtures were prepared and were kept in special air-tight bottles. The density of pure liquid and mixtures was determined with a specific gravity bottle with 10 ml capacity. The ultrasonic velocities in pure liquid and liquid mixtures were measured using single-crystal variable path ultrasonic interferometer operating at 2 MHz frequency, supplied by 1
M/s. Mittal Enterprises, New Delhi. The temperature stability is maintained by circulating thermostat water around the interferometer cell that contains experimental liquid. III.THEORY The experimentally measured ultrasonic velocity (U) and density (ρ) are used to calculate the derived parameters such as isentropic compressibility (β a) intermolecular free length (L f), molar volume (V), acoustic impedance (Z), Wada s constant, Rao s constant, Surface Tension (σ) and other related parameters are calculated using the following expressions: 1. Adiabatic compressibility β a = 1/ ρ U 2 (1) 2. Free Length L f = k (β a ) 1/2 (2) 3. Molar Volume V m = M/ρ (3) 4. Acoustic Impedance Z = U ρ (4) 5. Free Volume V f = (M U/ K η ) 3/2 (5) 6. Internal pressure π i= brt.(v fv m 2 ) -1/3 (6) 7. Enthalpy H = π i V m (7) 8. Rao s Constant R m = (M/ρ) U 1/3 (8) 9. Wada s Constant W = (M/ρ) β a -1/7 (9) 10. Relaxation Time τ = (4/3) βη (10) The empirical relation due to Auerbach to calculate the Surface Tension is given by, σ = 6.3 10-4 U 3/2 ρ (11) All the three parameters σ, U, ρ show strong temperature dependence. Hence the modified relation to calculate the surface Tension is σ = 10-4 U 3/2 ρt 1/3 (12) Where T is in K, U and ρ are the corresponding sound velocity and density at that particular temperature. IV. RESULTS AND DISCUSSION Ultrasonic velocities, densities and viscosities have been measured experimentally in the mixture of ethanol with benzene at 308K, 313K, 318K & 323K over the entire concentration range and are presented in Table 1. With the view to understand the molecular interactions occurring in the binary mixtures, some acoustical parameters such as free volume, internal pressure, adiabatic compressibility, acoustical impedance, Rao s constant, Wada s constant, relaxation time have been calculated by using the experimental values of ultrasonic velocity, density and viscosity at different temperatures ranging from 308K to 323K with different mole fractions of ethanol in benzene and are presented in Table 1. The variation of ultrasonic velocity, adiabatic compressibility, acoustic impedance and other related parameters for this binary liquid have been shown in Table 2 and the variation in free volume, internal pressure, adiabatic compressibility with the mole fraction are plotted in Fig.1 to Fig.3. From the tables and figures it is observed that ultrasonic velocity slightly decreased with increase of mole fraction and as well as for the temperature. The study of these acoustic parameters in binary liquid mixtures may be of much importance in assessing the nature of molecular interactions and investigating the physico-chemical behaviour of liquid system 13,14. The increase in adiabatic compressibility is due to solute solvent interaction in this mixture. This is also confirmed with the variation of acoustic impedance (Z) values, which is also observed to decrease here. The Fig (1): Variation of free volume with temperature Fig (2): Variation of Adiabatic Compressibility with temperature Fig (3): variation of Internal Pressure with Temperature Fig (4): Variation of Surface Tension(σ Aur & σ Mod) with Temperature for Ethanol Fig (5): Variation of Surface Tension (σ Aur Temperature for Benzene & σ Mod) with 2
Fig (6): Variation of Surface Tension(σ Aur & σ Mod) in Ethanol+Benzene at different temperature Table 1: Values of U, ρ, ɳ & Vm for Ethanol with Benzene at 308K,313K, 318K, 323K 308K 313K 318K 323K X2 Velocity U ms -1 Density ρ K kg/m 3 Viscosity ɳ mnsm -2 Vm μm 3 (10-6 ) 0.000 1248 0.864 0.567 90.42 0.201 1209 0.846 0.628 84.73 0.403 1187 0.832 0.690 78.37 0.602 1172 0.812 0.751 72.45 0.795 1140 0.794 0.810 66.30 1.000 1110 0.777 0.872 59.29 0.000 1228 0.858 0.497 91.05 0.201 1196 0.84 0.557 85.33 0.403 1172 0.823 0.617 79.23 0.602 1168 0.805 0.676 73.08 0.795 1122 0.788 0.733 66.80 1.000 1100 0.772 0.794 59.68 0.000 1212 0.852 0.466 91.69 0.201 1168 0.834 0.519 85.95 0.403 1148 0.817 0.573 79.81 0.602 1132 0.8 0.626 73.53 0.795 1109 0.783 0.677 67.23 1.000 1080 0.767 0.732 60.06 0.000 1184 0.847 0.437 92.23 0.201 1152 0.829 0.484 86.46 0.403 1120 0.812 0.531 80.30 0.602 1116 0.798 0.577 73.72 0.795 1089 0.779 0.622 67.57 1.000 1060 0.763 0.670 60.38 3
Table 2 : Values of Vf, πi, βa, Z, R, W & τ for Ethanol with Benzene at 308K, 313K, 318K, 323K Acoustical Rao s Internal Adiabatic Mole Free Impedance Constant Pressure Compressibility Fraction Volume Vf Z R X2 (µ m 3 πi βa ) (M Pa) (10-10 Nm -2 (10 ) 5 kg m -2 [10-4 m 3 mol -1 s -1 ) (m/s) 1/3 ] 308K Wada s Constant W (10-4 m 3 mol -1 kg -1 ms 2 ) Relaxation Time τ (10-13 sec) 0.000 0.254 401.44 7.43 10.78 9.73 18.21 5.62 0.201 0.669 303.56 8.09 10.23 9.03 16.86 6.77 0.403 0.846 295.69 8.53 9.88 8.30 15.48 7.85 0.603 0.885 306.96 8.97 9.52 7.64 14.21 8.98 0.795 0.829 332.83 9.69 9.05 6.93 12.86 10.46 1.000 0.715 376.68 10.45 8.62 6.14 11.38 12.14 313K 0.000 0.303 382.88 7.73 10.54 9.75 18.24 5.12 0.201 0.788 290.72 8.32 10.05 9.06 16.91 6.18 0.403 0.981 283.96 8.85 9.65 8.35 15.57 7.28 0.603 1.035 294.37 9.11 9.40 7.69 14.30 8.21 0.795 0.956 320.91 10.08 8.84 6.94 12.88 9.85 1.000 0.816 364.72 10.71 8.49 6.16 11.41 11.02 318K 0.000 0.327 377.47 7.99 10.33 9.78 18.28 4.96 0.201 0.845 287.19 8.79 9.74 9.05 16.90 6.08 0.403 1.065 279.33 9.29 9.38 8.36 15.57 7.09 0.603 1.108 291.14 9.76 9.06 7.66 14.25 8.14 0.795 1.039 315.77 10.38 8.68 6.96 12.91 9.37 1.000 0.898 357.36 11.18 8.28 6.16 11.41 10.91 323K 0.000 0.347 374.42 8.42 10.03 9.76 18.25 4.91 0.201 0.919 282.53 9.09 9.55 9.06 16.92 5.86 0.403 1.151 275.35 9.82 9.09 8.34 15.54 6.95 0.603 1.226 285.44 10.06 8.91 7.65 14.22 7.74 0.795 1.148 309.18 10.82 8.48 6.95 12.90 8.97 1.000 0.998 349.20 11.66 8.09 6.16 11.40 10.42 measurement of internal pressure (π i) is due to the forces of attraction and repulsion between the molecules in a solution. There is a decrease in π i, due to predominance of repulsive forces. There is a slight decrease in internal pressure as the mole fraction increases, and approximately at 0.403 mole fraction of ethanol, π i is minimum and it begins to increase. The same trend is also observed for different temperature range. This suggests the existence of molecular interactions in these mixture. The free volume of a solute molecule at a particular temperature and pressure depends only on the internal pressure of the liquid in which it is dissolved 15 The weakening of molecular association leads to a larger free volume available for molecular motion and the reverse effect gives rise to smaller free volume. In this binary mixture, both type of positive and negative values are obtained for the acoustical parameters which suggest the dominance of solute solute interactions and as well as solute-solvent interactions. Eqn 12 has been utilized to calculate the surface tension from the experimental values of Ultrasonic velocity, Density and Temperature. The values of Surface Tension obtained from eqn 12 are compared with values obtained from eqn11 for the pure liquids ethanol and benzene and also the binary mixtures of ethanol and benzene with different temperatures 308K, 313K, 318K, 323K. The Calculated values of Surface Tension using these two equations for the pure liquids and their mixtures are given in Table 3. Referring to the Table 3 it is inferred that the values of surface tension obtained from equation 12 are higher than the obtained from equation 11. This is in agreement with the previous results also. In general Auerbach Relation yields better results when compared to the modified relations, since it is simply an empirical relation. As a whole the deviation between these two equations are very less in the case of mixtures when compared to the pure liquids. Here our aim is to compare both the relations in our liquid systems and it is observed that the new modified relation has an edge over the classical relation which can be easily observed from the 4
Table 3: Values of Surface tension( σaur & σmod ) for Ethanol with Benzene at 308K,313K, 318K, 323K X2 Velocity U ms -1 Density ρ K kg/m 3 Auerbach Relation σaur N/m-1 Modified relation σmod N/m-1 308K 0.000 1248 0.864 23998.06 25724.83 0.201 1209 0.846 22405.28 24017.44 0.403 1187 0.832 21435.81 22978.21 0.602 1172 0.812 20525.23 22002.11 0.795 1140 0.794 19253.88 20639.29 1.000 1110 0.777 18102.81 19405.39 313K 0.000 1228 0.858 23260.84 25068.77 0.201 1196 0.840 21888.53 23589.80 0.403 1172 0.823 20803.28 22420.19 0.602 1168 0.805 20244.20 21817.66 0.795 1122 0.788 18657.61 20107.76 1.000 1100 0.772 17986.32 19122.93 318K 0.000 1212 0.852 22648.22 24537.82 0.201 1168 0.834 20973.50 22723.37 0.403 1148 0.817 20020.52 21690.89 0.602 1132 0.800 19195.53 20797.06 0.795 1109 0.783 18217.96 19737.92 1.000 1080 0.767 17150.29 18581.18 323K 0.000 1184 0.847 21739.60 23676.19 0.201 1152 0.829 20420.85 22239.97 0.403 1120 0.812 19174.48 20882.57 0.602 1116 0.798 18743.03 20412.68 0.795 1089 0.779 17636.80 19207.91 1.000 1060 0.763 16589.14 18066.92 graphs (Figs 4,5,6). ACKNOWLEDGEMENT One of the authors, Dr. J. Poongodi, gratefully acknowledged University Grants Commission, for the financial support under Minor Research Project scheme, during the year 2013. REFERENCE 1. Manohara Murthy,N., and Nagabhushanam, G., Excess sound velocity behaviour of aqueous mixtures of nonelectrolytes, J.Acoust.Soc.India, 12(1984)32. 2. Manohara Murthy, N., and Nagabhushanam, G., Excess sound velocity behaviour of n-alkanol+heptane and 2-ethoxy ethanol + n-heptane mixtures, J. Pure. Appl. Ultrason. 8 (1986) 1. 3. Asghar,J., Liakath Ali Khan, F., Subramani, K., Thermodynamic studiesof molecular interactionsin ternary liquid mixtures at various temperatures, Rasayan.J.Chem.,3(4),(2010), 697. 4. Gagwar,M., Saxena, A., Srivastava, P., Ultrasonic velocities and Thermo-Acoustical Parameters of Cumene with P-Xylene at 303K and 308K, Archives of Physics Research, 4(1), (2013), 29. 5. Mehta, S.K., & Chauhan, R.K., Ultrasonic velocity and apparent isentropic compressibility in mixtures of nonelectrolytes, J. Sol. Chem., 26 (1996) 295. 6. Dewan, R.K., Gupta, C.M., & Mehta, S.K., Ultrasonic study of ethylbenzene + n-alkanols, Acoustica, 65, (1988)245. 7. R. Auerbach, oberflachen Sannung and Schallgeschwinding keit, Experimentia & (1984) 473. 8. K. Altenberg physics chem., 195 (1950) 145. 9. J.D. Pandey, Sound velocity and surface tension from Flory s statistical theory J.Chem Soc. Fara Trans I, 75 (1979) 2160. 10. J.D. Pandey, R.D.Rai and R.K. Shukla, Pressure dependent study of Ultrasonic velocity of benzene + nitrobenzene system at 293.15, 303.15 and 313.15k Can J.Chem, 67 (1989) 437. 11. M.S. Khanwalker, J.S. Murthy and D.D. Deshpande, ultrasonic velocity in binary liquid mixtures, Acoustic Lett, 13 (1990) 121. 12. J.D.Pandey, Surface tension and sound velocity of Pb- Sn alloys in the liquid state, Phys. Chem. Liquid 14 (1985) 253. 13. Semwal, H.K., Bhatt, S.C., and Semwal, B.S., Acoustical study of binary liquid mixture of Acetic acid and Isopropyl sulphide, J.Pure.Appl.Ultrason., 25 (2003) 6. 14. Pandey, J. D., Shukla, A. K., Tripathi, Neelima and. 5
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