Investigation of molecular interactions in ternary liquid mixtures using ultrasonic velocity

Transcription

1 Indian Journal of Chemistry Vol. 46A, February 007, pp Investigation of molecular interactions in ternary liquid mixtures using ultrasonic velocity R Palani a, b, * & K Meenakshi a a Department of Physics, b Distance ducation Wing Annamalai niversity, Annamalainagar , India mail: palani_physics06@yahoo.co.in Received 9 April 006; revised 6 December 006 ltrasonic velocity (), density (ρ) and viscosity (η) measurement have been carried out in three ternary liquid mixtures of benzene, toluene and CCl 4 with ethane, diol in a polar component of acetone at 0 K. The experimental data have been used to calculate adiabatic compressibility, free length, free volume, internal pressure, Gibb s energy and available volume. The excess values of the above parameters and the d parameter Grunberg and Nission equation have also been evaluated and discussed in the light of molecular interaction in the mixtures. An attempt has been made to evaluate the experimental ultrasonic velocity with that predicted on the basis of Nomotos Relations (NR), Ideal Mixing Relation (IMR), Free Length Theory (FLT) and Collision Factor Theory (CFT) with a view to compare the merits of the above three ternary liquid mixtures. The modulus of percentage deviation in ultrasonic velocity and the Chi-square test (χ ) for goodness of fit is applied to check the validity of the theories. IPC Code: Int. Cl. 8 G0N/00 Molecular interaction studies play an important role in understanding the structure and properties of liquids and gases. The interaction can be classified as long range forces and short range forces. A large number of studies have been made on the interaction in liquid systems by various physical methods like infrared, Raman effect, nuclear magnetic resonance ultraviolet 4 and ultrasonic methods 5. The ultrasonic velocity measurements find wide applications in characterising the physico-chemical behaviour of liquid mixtures 6 and in the study of molecular interaction. The method of studying the molecular interaction from the knowledge of variation of thermodynamic parameters and their excess values with composition gives an insight into the molecular process 7. The investigations regarding the molecular association in organic ternary mixtures having aromatic group as one of the components is of particular interest, since aromatic group is highly non-polar and can associate with any other group having some degree of polar attractions. Owing to these considerations, an attempt has been made to elucidate the molecular interactions in the mixtures of benzene, toluene and CCl 4 with ethane, diol in acetone at 0 K. In recent years, various theories 8-0 have been in use for computing ultrasonic velocity in liquid mixtures and the deviation in theoretical ultrasonic velocity has been attributed mainly to the molecular interactions in the mixtures. As an additional confirmation for the presence of specific interaction, an attempt has been made to correlate the experimental findings with those predicted theoretically on the basis of molecular models. Such comparisons help to understand the thermodynamics of the mixtures and provide a better means to test the validity of the various empirical and semi-empirical theories. Materials and Methods All the chemicals used were AR/SR grade (minimum assay of 99.9%) obtained from -Merck and Sd.fines. Fresh conductivity water was used throughout the investigation. The purities of these chemicals were checked by density determination at 0 K ± 0. K which showed an accuracy of ± gcm as compared to the reported values,. The ternary liquid mixtures of different known compositions were prepared in stopper measuring flasks. The density, viscosity and velocity were measured as a function of composition of the ternary liquid mixture at 0 K. The density was determined

2 PALANI & MNAKSHI: MOLCLAR INTRACTIONS IN TRNARY LIQID MIXTRS 5 using a specific gravity bottle by relative measurement method. The weight of the sample was measured using electronic digital balance with an accuracy of ±0. mg (model Shimadzu AX-00). An Ostwald s viscometer (0 ml) was used for the viscosity measurement. fflux time was determined using a digital chronometer to within ±0.0 s. An ultrasonic interferometer having the frequency MHz with an overall accuracy of ± ms was used for ultrasonic velocity measurement. An electronically digital operated constant temperature bath (Raaga Industries) was used to circulate water through the double walled measuring cell made up of steel containing the experimental solution at the desired temperature (accuracy in the temperature measurement ±0. K). Theoretical Various physical and thermodynamical parameters were calculated from the measured data such as Adiabatic compressibility Intermolecular free length β = () ρ L f = K β () where K is a temperature dependent constant. Its values are 6 0 6, at 0 K. / M eff Free volume V f = () Kη where M eff is the effective molecular weight (M eff =Σm i x i, in which m i and x i are the molecular weight and the mole fraction of the individual constituents respectively). K is a temperature independent constant which is equal to for all liquids. ½ / Kη Internal pressure ρ π = i brt (4) 7/6 M eff where b is the cubic packing which is assumed to be for all liquids and solutions, η the viscosity and C, the concentration in gram moles/litre. R is a gas constant and T absolute temperature. The Gibb s energy can be estimated from: KTτ ΔG = KT ln h (5) where, K is the Boltzmaan s constant (. 0 JK ), T the absolute temperature, h the Planck s constant and τ is the relaxation time 4 (τ = ηβ ). Available volume can be calculated using the relation: Va = VT (6) where V T is the molar volume at T K and is the limiting ultrasonic velocity and is taken as 600 m s. xcess values of the above parameters can be determined using: A = A A (7) exp id where A id = Σ A i Xi, A i is any acoustical parameters and X i the mole fraction of the liquid component. Grunberg and Nissan put forward a logarithmic relation between the viscosity of a binary liquid mixture and pure components: ln ηmix = Xln η + Xln η + XX d (8) On applying to a ternary liquid mixture, this equation takes up the form: ln ηmix = Xln η + Xln η + Xln η + XX Xd (9) where d is a constant regarded as a measure of the strength of molecular interactions between the mixing components. Nomoto 4 established an empirical formula for ultrasonic velocity in ternary liquid mixtures on the assumption of linear dependence of the molar ultrasonic velocity on concentration in mole fractions and the additivity for molar volume as, XR + X R + X R = XV X V X V (0) + + where R = V / and V is the molar volume obeys the additivity. V = X + V + X V X V VanDeal and Vengeal 5 suggested the following relation for ultrasonic velocity in ternary liquid mixture: IMR = ( X m + X m + X m ) ½ X m X + m X + m ½ ()

3 54 INDIAN J CHM, SC A, FBRARY 007 ltrasonic velocity is calculated using Jacobson s formula, ½ mix Lmix ρmix = K () where K is the temperature dependent constant mix, ρmix and L mix are the velocity, density and free length in mixtures. According to Schaaffs 6, the ultrasonic velocity in ternary liquid mixtures is given by: S mixbmix mix = () Vmix where S is collision factor and B is the actual volume of molecule/mole. B can be computed from the knowledge of Van der Waal s Constant b as it is related as follows: b = 4B (4) Van der Waal s Constant b can be expressed as: M RT M b = + (5) ρ M RT The modulus of percentage deviation in ultrasonic velocity between experimental and computed values can be calculated as: Δ exp -the % = 00 (6) exp Chi-square test for goodness of fit (χ ) is given by: ( ) ( ) = n Oi i χ (7) i= i Chi-square follows Chi-square distribution with (n-) degree of freedom where O i are the experimental frequencies and i is the corresponding theoretical frequencies. Results and Discussion The values of density, viscosity, ultrasonic velocity, adiabatic compressibility, free length, free volume, internal pressure, Gibb s energy, available volume and d constant of all the pure liquids and for the three ternary mixtures are listed in Tables and. The respective excess values of these parameters have been evaluated and are presented in Table. The theoretical values of ultrasonic velocity in ternary liquid mixtures calculated on the basis of Nomoto s Relation (NR) and Ideal Mixing Relation (IMR), Free Length Theory (FLT) and Collision Factor Theory (CFT) along with the experimental values, the modulus of percentage deviations in velocity and the chi-square deviations of the theoretical velocities from the experimental values are provided in Table 4. The measurement of viscosity in ternary mixture provides some reliable information in the study of molecular interaction. Table shows that the viscosity decreases with increase in concentration of acetone. According to Fort and Moore 7, the excess viscosity gives the strength of the molecular interaction between the interacting molecules. For systems where dispersion, induction and dipolar forces are operating, the values of excess viscosity are found to be negative, whereas the existence of specific interactions leading to the formation of complexes in mixtures tends to make excess viscosity positive. The excess viscosity is negative through the whole range of concentration in all the studied systems and increases with increase in concentration of the second component. The large negative values of excess viscosity for all systems can be attributed to the presence of dispersion, induction and dipolar forces between the components. It is observed from the Table that the value of adiabatic compressibility and free length increases as the concentration of second component increases. Further, Table shows that the values of excess adiabatic compressibilities are positive (except System III). Table Values of density (ρ), viscosity (η), ultrasonic velocity () adiabatic compressibility (β), free length (L f ), internal pressure (π i ), Gibb s energy (ΔG), and available volume (V a ) of pure liquids at 0 K Liquids ρ η β L f V f π ΔG V a (kg m ) ( 0 (ms ) ( 0 0 m N - ) ( 0 0 m) ( 0 8 m mol ) ( 0 6 Nm ) ( 0-0 kjmol - ) ( 0-6 m mol - ) Nsm ) thane, diol Acetone Benzene Toluene CCl

4 PALANI & MNAKSHI: MOLCLAR INTRACTIONS IN TRNARY LIQID MIXTRS 55 Table Values of density (ρ), viscosity (η), and ultrasonic velocity (), adiabatic compressibility (β), free length (L f ), free volume (V f ), internal pressure (π i ), Gibb s energy (ΔG), available volume (V a ) and d constant at 0 K Mole fraction ρ η β L f V f π I ΔG V a 'd' X X (kg m ) ( 0 Nsm ) (ms ) ( 0 0 m N - ) ( 0 0 m) ( 0 8 m mol ) ( 0 6 Nm ) ( 0-0 kjmol - ) ( 0-6 m mol - ) System I [thane, diol (X ) + Acetone (X ) + Benzene (X )] System II [thane, diol (X ) + Acetone (X ) + Toluene (X )] System III [thane, diol (X ) + Acetone (X ) + CCl 4 (X )] Table Values of excess viscosity (η ) adiabatic compressibility (β ), free length (L f ), free volume (V f ), internal pressure (π i ), Gibb's energy (ΔG ) and available volume (V a ) at 0 K Mole fraction η β L f V f π i ΔG V a X X ( 0 Nsm ) ( 0 0 m N - ) ( 0 0 m) ( 0 8 m mol ) ( 0 6 Nm ) ( 0-0 kjmol - ) ( 0-6 m mol - ) System I: [thane, diol (X ) + Acetone (X ) + Benzene (X )] System II: [thane, diol (X ) + Acetone (X ) + Toluene (X )] System III: [thane, diol (X ) + Acetone (X ) + CCl 4 (X )]

5 56 INDIAN J CHM, SC A, FBRARY 007 Δ Table 4 Values of experimental, theoretical ultrasonic velocity, the modulus of percentage deviation in velocity % and chi-square test (χ ) at 0 K Δ Mole fraction (ms ) (%) (χ ) X X exp NR IMR FLT CFT NR IMR FLT CFT NR IMR FLT CFT System I: [thane, diol (X ) + Acetone (X ) + Benzene (X )] System II: [thane, diol (X ) + Acetone (X ) + Toluene (X )] System III: [thane, diol (X ) + Acetone (X ) + CCl 4 (X )] Fort and Moore 7 found that the increasing negative value of excess compressibility indicates greater interaction between the components of the mixtures. Positive values in excess properties correspond mainly to the existence of dispersive forces. Dispersive forces, which are generally present in Systems I and II would make positive contribution. Negative value of β is associated 7 with a structure forming tendency while a positive value is taken to indicate a structure breaking tendency due to heteromolecular interaction between the component molecules of the mixtures. The shape and size of the molecules in the mixture are loosely packed which is due to the positive excess adiabatic compressibility. In the present investigation, the positive deviation in β in ternary systems has been attributed to dispersive forces that show weak interaction between the unlike molecules. Table shows that the values of excess free length are positive in Systems I and II and negative in System III. The positive excess values indicate the existence of molecular interaction in the mixtures. According to Ramamoorthy and Sastry 8, negative value of excess intermolecular free length indicates that ultrasonic waves cover longer distances due to decrease in intermolecular free length ascribing the dominant nature of hydrogen bond interaction between unlike molecules. Fort and Moore indicated that the positive values of excess free length should be attributed to the dispersive forces and negative excess values should be due to charge transfer for all the systems. Table gives the value of the excess free volume for the ternary liquid mixtures. The excess values are found to be positive in all the systems studied. Adgaonkar et al. 9 showed positive value in the excess free volume and indicated the existence of weak molecular interaction in the liquid mixtures. The decrease in internal pressure (Table ) and the behaviour of negative excess values (Table ) show that the strength of interaction decreases gradually as the concentration of acetone increases in all mixtures. The negative values of π i indicate that only dispersion and dipolar forces are operating with complete absence of specific interaction. Table L f

6 PALANI & MNAKSHI: MOLCLAR INTRACTIONS IN TRNARY LIQID MIXTRS 57 shows the variation of excess Gibb s energy, which is found to be negative in all the three systems studied. The reduction of negative excess values with increase in concentration of second component in all the systems indicates the need for smaller time for the cooperative process; or the rearrangement of molecules in mixtures decreases energy that leads to dissociation. Recently, Ali and Nain 0 have attributed the increasing positive values of Gibb s energy in a few ternary liquid mixtures to hydrogen bond formation between unlike molecules, which supports the present investigations. The excess available volumes are positive (Table ) for all mixtures. It is observed from the study of Fort and Moore 7 when interaction occurs between the molecules of the two species, the excess available volume becomes increasingly negative. This is due to closer approach of unlike molecules. The positive excess available volume obtained in the present study reflects the absence of stronger interaction. Dissociation also leads to positive contribution. The interaction parameters d in Grunburg and Nission equation is a measure of the strength of interaction between the mixing components. Table shows that the value of d is negative in all the systems studied. It is seen that values of d vary appreciably with the composition, which indicates the presence of specific interaction. The negative values of d may be attributed to the dominance of dispersion forces 6 arising from the breaking of hydrogen bonds in the associated components of the mixtures. It is evident from Table 4 that there is good agreement between the experimental and calculated ultrasonic velocities even though assumption and approximation are made in the theory. In all the three systems, collision factor theory (CFT) shows that the percentage deviation between experimental and theoretical values is minimum compared to other theories. The extent of deviation in velocities may be attributed to be presumption made in the theories for polar non-polar interactions between the molecules. Moreover from Table 4, it is interesting to note that in all the three systems, the values of Chi-square are much smaller in CFT than other theories. The tabulated value of chi-squared at 5% level of significant is.455, if the Chi-square value calculated using q. 7 is less than the tabulated value of chi-square for the same degrees of freedom, then there is good correspondence between theory and experiment. Thus, it is clear that CFT is found to give an excellent prediction of ultrasonic velocity in all the three systems, which is justified by the earlier predications. Conclusions The present investigations show that weak molecular interactions exist in the mixtures which may be due to the dominance of dispersion forces and dipolar interaction between the unlike molecules. The existence of molecular interaction in the mixture is in the order: CCl 4 > toluene > benzene. Among the four theories taken up for the prediction of ultrasonic velocity, CFT is found to yield excellent comparison with the experimental values for the systems investigated. The greatest percent deviations indicate the maximum departure of theory from experiment at particular concentration, and the Chisquared value indicates the overall validity of theory. References Fletcher A, J Phy Chem, 7 (969) 7. Ramasamy K & Ranganathan V, Indian J Pure Appl Phys, 8 (970) 44. Venkateswaran K, Krishanapillai M G & Ramasamy K, Proc Indian Acad, 5 (96)95. 4 Nagakuva S, J Am Chem Soc, (954). 5 Gupta A K & Agarwal V C, Indian J Pure Appl Phys, (975)74. 6 Kincaid J F & yring H, J Chem Phys, 5 (97) Hemmes P, Mayershi A A, Buckin V A & Saravazyan, J Chem Phys, 84 (980) Pandey J D, Pant N, Shukla A K, Sarika & Krishan V, Indian J Pure Appl Phys, 7 (989) Khanwalkar M S, Acoust Lett, (989) Kannappan A N, Palani R & Ramalaingam K, Indian J Pure Appl Phys, 9 (99) 4. Dean J A, Lange s Hand Book of Chemistry, th dn (Mcgraw-Hill, New York) 979. David R L, CRC Hand Book of Chemistry & Physics, 7 nd dn (CRC Press, Boston) 99. Grunberg L & Nissan A H, Nature, 64 (949) Nomoto O, J Phys Soc Japan, (958) VanDeal W & Vengeal, Proc First Int Conf on Calorimetry & Thermodynamics, Warsaw, 969, pp Schaaffs W, Molekutarakustik, Chap. XI & XII (Springer- Verlag-Berlin-Gottingen Heidelberg) Fort R J & Moore W R, Trans Faraday Soc, 6 (965) 0. 8 Ramamurthy M & Sastry O S, Indian J Pure Appl Phys, (98) Adganokar C S Tajoo S N & Deogaonkar V S, Indian J Pure Appl Phys, 7 (979) Ali A & Nain A K, Indian J Phys, 74 (000) 6. Kannappan A N & Palani R Indian J Pure Appl Phys, 70B (996) 59.