Thermodynamic Parameters and Their Excess Values for Binary Mixtures of Cyclohexane Plus Benzene and Substituted Benzenes at Different Ultrasonic Frequencies

Thermodynamic Parameters and Their Excess Values for Binary Mixtures of Cyclohexane Plus Benzene and Substituted Benzenes at Different Ultrasonic Frequencies

Manoj Kumar Praharaj Department of Physics, ABIT, CDA, Sector-1,

Cuttack, Odisha-753014, India

Jayashree Mohanty Department of Physics, ABIT, CDA, Sector-1,

Cuttack, Odisha-753014,India

Abhiram Satapathy Department of Physics, ABIT, CDA, Sector-1,

Cuttack, Odisha-753014, India

Sarmistha Mishra Department of Physics, ABIT, CDA, Sector-1,

Cuttack, Odisha-753014, India

Abstract: Different thermodynamic parameters like acoustic impedance, Gibbs free energy, adiabatic compressibility, free length, free volume, internal pressure and their excess values are studied at various ultrasonic frequencies keeping temperature constant at 318K.

Keywords: Gibbs free energy, acoustic impedance, free length and free volume.

1. INTRODUCTION

   Ultrasonic investigations of liquid mixtures, consisting of polar and non-polar components are of considerable importance in understanding the intermolecular interactions between the component molecules, which finds applications in several industrial and technological processes [1-10]

   In the present paper we have studied the various thermodynamic parameters along with their excess values from the study of variation in ultrasonic velocity at different frequencies for the following binary mixtures.

   Mixture – I: Cyclohexane + Benzene Mixture – II: Cyclohexane + Chlorobenzene Mixture – III: Cyclohexane + Nitrobenzene Mixture – IV: Cyclohexane + Pyridine

   The temperature has been maintain at a constant value (318K).

   Cyclohexane belongs to the group of alicyclic hydrocarbons. It is non-polar, unassociated, inert hydrocarbon and has a globular structure. It is highly inert towards an electrophille or nucleophille at ordinary temperature. Due to the above properties dispersive types of interactions are possible between cyclohexane and other components.

   Benzene is a non-polar solvent. It is a cyclic hydrocarbon with a continuous pi bond. Chlorobenzene is a poor electron donor towards the electron seeking proton of any group. It has low dielectric constant and dipole moment. The chlorine atom being an electron withdrawing atom attracts the –

   electron of benzene ring and thus a decrease of electron density of the

   ring takes place. This makes the benzene ring a relatively poor electron donor towards the Cyclohexane molecules.

   Nitrobenzene is a polar solvent with high dielectric constant and dipole moment. Hence intermolecular interaction in this case is large.

   Pyridine is a basic heterocyclic organic compound with a lower dielectric constant and dipole moment. Pyridine molecules are spherical in shape and tightly packed.

2. EXPERIMENTAL TECHNIQUE:

   The liquid mixtures of fixed concentration (6:4) in mole fraction were prepared by taking analytical reagent grade and spectroscopic reagent grade chemicals with minimum assay of 99.9% and obtained from E.Merck Ltd (India).

   The density, viscosity, and ultrasonic velocity of all liquid mixtures were measured at temperature 318K and for different frequencies 2 MHz, 4 MHz, 6 MHz, 8 MHz.

   Ultrasonic velocity measurements were made using an ultrasonic interferometer (Model M-84, supplied by M/S Mittal Enterprises, New Delhi), at different temperatures and different frequencies with the accuracy of ±0.1m·s1. 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-03 Spl, supplied by M/S Mittal Enterprises, New Delhi), operating in the temperature range of10°C to 85°C with an accuracy of ±0.1°C has been used to circulate water through the outer jacket of the double- walled measuring cell containing the experimental liquid.

   The densities of the mixture were measured using a 10-ml specific gravity bottle by relative measurement method with an accuracy of ±0.01 kg·m3. The specific gravity bottle

   with the experimental mixture was immersed in the temperature-controlled water bath. The weight of the sample was measured using an electronic digital balance with an accuracy of ±0.1 mg (Model: SHIMADZU AX-200, Kyoto, Japan).

   An Oswald viscometer (10 ml) with an accuracy of ± 0.001 Ns·m2 was used for the viscosity measurement. The flow time was determined using a digital racer stopwatch with an accuracy of ±0.1s.

3. THEORY

   1. Adiabatic compressibility: The ultrasonic velocity

   1. Acoustic impedance (Z): The specific acoustic impendence is given by [18]

      = . . Kg. m2. s 1 .

   2. Excess Parameters (AE)

   In order to study the non-ideality of the liquid mixtures, the difference between the values of the real mixture (Aexp) and those corresponding to an ideal mixture (Aid), namely the excess parameters (AE) of some of the acoustic parameters, were computed using the equation

   E

   in a liquid medium, in terms of Bulk modulus (B) and density

   A = A

   n

   exp

   – Aid (7)

   of the medium is given by the Newton-Laplace equation [11]. Where A = A X , A is any parameters and X the mole

   id i i i i

   B 1

   U = =

   fraction of the liquid components of i.

   Or, =

   .

   .

   . . (1)

4. RESULT AND DISCUSSION:

   1. Intermolecular free length: Intermolecular free length (L ), is calculated using the standard expression [12]

      f

      The experimental values of density, viscosity and velocity are presented in table-1. Calculated values of acoustic and

      thermodynamic parameters are presented in table-2 and 3.

      T

      Where, K

      =

      . (m) ()

      {=(93.875 + 0.375.T) x 10

      } is Jacobsons

      -8

      Excess values of the parameters are shown in table-4 and 5. Variations of these parameters and their excess values with

      temperature dependent constant and is the adiabatic

      compressibility.

   2. Free Volume: Suryanarayana et al [13,14] obtained a relation for free volume in terms of ultrasonic velocity (U) and the viscosity of the liquid () as,

      frequency are shown in fig.1 to fig.12.

      Ultrasonic velocity increases in the following order. It is maximum for mixture-I and increases from mixture-II to mixture-III and finally to mixture-IV. Since benzene and cyclohexane both are non-polar, their intermolecular interaction is weak; hence ultrasonic velocities in such

      =

      .

      . ()

      mixtures are minimum.

      In the cyclohexane chlorobenzene mixture, the intermolecular

      .

      Where Meff is the effective mass of the mixture, K is a dimensionless constant independent of temperature and liquid. Its value is 4.281 x 109.

   3. Internal Pressure: Internal pressure can be calculated by using the relation [15,16]

      = (. ) ()

      interaction is also weak as mentioned before; hence velocity is less than that in the mixtures III and IV.

      Nitrobenzene has a larger dipole moment compared to pyridine but the intermolecular interaction is weaker in mixture-III compared to mixture-IV because of steric hindrance in nitrobenzene (Nitrobenzene being a complex and big molecule).

      When frequency increases, velocity in each case decreases

      Where, b stands for the cuic packing factor, which is assumed to be 2 for all liquids and solutions. K is a dimensionless constant independent of temperature and nature of liquids. Its value is 4.281×109, R is the gas constant, T is the absolute temperature, is the viscosity, U is the ultrasonic velocity, is the density and M is the effective molecular weight.

   4. Gibbs free energy: The variation of with temperature can be expressed in the form of Eyring salt process theory [17].

   indicating weakening of intermolecular interaction. Intermolecular free length (Lf) is maximum for mixture-I. This is obvious as the molecular interaction in this case is weakest. For the mixture-III, Lf is the next as the interaction in this case is next as expected due to steric hindrance. Lf for mixture-IV comes the next. Lf is minimum for mixture-II. Although intermolecular interaction in this case (mixture-II) is small, the molecules in the mixture fit in to each other yielding minimum intermolecular space.

   Excess free length (LfE) is positive for system-I, III and IV and decreases in the same order. Positive LfE indicates weak

   interaction.This may be due to the non-polar nature of

   = ()

   The above equation can be rearranged as

   molecules or steric hindrance or expansion in volume from additivity. However because of comparatively stronger

   interaction in mixture-IV, LfE is positive but small. In

   = . .

   . (k. J. mol 1) . ()

   mixture-II, LfE is negative. This may be due to the fact that

   Where, is the viscous relaxation time, T is the absolute temperature, K is the Boltzmanns constant and h is the Plancks constant.

   the molecules fit well into each other and Lf decreases in the mixture. LfE does not vary with frequency in all the cases.

   Adiabatic compressibility () decreases in the following order of the mixture-I, III, IV and II. It changes in the same way as free length changes. At low frequencies Lf and are small for

5. TABULATION

   TABLE 1: Values of Density (), Viscosity () and velocity (U) in binary mixtures for different frequencies.

   Binary mixture	Density () Kg.m-3	Viscosity x10-3 (N.s.m-2)	Velocity (U) m.s-2
   			2 MHz	4 MHz	6 MHz	8 MHz
   M-I: Ben+C.H	818.226	0.455	1168.6	1167.2	1165.1	1164.4
   M-I: C.Ben+C.H	975.25	0.549	1172	1169	1166	1165.9
   M-I: N.Ben+C.H	856.69	0.646	1170	1169	1166	1164.5
   M-I: Pyr.+C.H	869.56	0.571	1247	1238	1225	1209.7

   TABLE 2: Calculated values of , Lf, and Vf in binary mixtures for different frequencies.

   Binary mixture	Adiabatic compressibility () (10-10N-1.m2)				Free length (Lf) (10-10 m)				Free volume (Vf) (10-7 m3.mol-1)
   	2 MHz	4 MHz	6 MHz	8 MHz	2 MHz	4 MHz	6 MHz	8 MHz	2 MHz	4 MHz	6 MHz	8 MHz
   M-I: Ben+C.H	8.949	8.971	9.003	9.014	0.608	0.608	0.609	0.610	3.364	3.358	3.349	3.346
   M-I: C.Ben+C.H	7.462	7.501	7.537	7.543	0.555	0.556	0.558	0.558	3.590	3.576	3.563	3.561
   M-I: N.Ben+C.H	8.524	8.549	8.584	8.608	0.593	0.594	0.595	0.596	3.069	3.062	3.053	3.046
   M-I: Pyr.+C.H	7.393	7.499	7.669	7.859	0.552	0.556	0.562	0.569	2.663	2.635	2.591	2.544

   TABLE 3: Calculated values of G, Z and i in binary mixtures for different frequencies.

   Binary mixture	Gibbs free energy ( G ) ( x 10- 20 k.J.mol-1)				Acoustic impedance (Z) ( x 106 Kg.m2.s-1)				Internal pressure( i ) ( x 106 N.m-2 )
   	2 MHz	4 MHz	6 MHz	8 MHz	2 MHz	4 MHz	6 MHz	8 MHz	2 MHz	4 MHz	6 MHz	8 MHz
   M-I: Ben+C.H	0.562	0.563	0.564	0.565	0.956	0.955	0.953	0.953	356.7	356.9	357.2	357.3
   M-I: C.Ben+C.H	0.564	0.567	0.569	0.569	1.143	1.140	1.138	1.137	336.9	337.4	337.8	337.9
   M-I: N.Ben+C.H	0.695	0.696	0.698	0.699	1.002	1.001	0.999	0.998	312.8	313.0	313.3	313.5
   M-I: Pyr.+C.H	0.578	0.584	0.594	0.605	1.085	1.077	1.065	1.052	399.6	401.0	403.2	405.7

   TABLE 4: Excess values E, LfE , VfE in binary mixtures for different frequencies.

   Binary mixture	Excess Adiabatic comp. (E) (10-10 N-1.m2)				Excess Free length (LfE) (10-10 m)				Excess Free volume (VfE) (10-7 m3.mol-1)
   	2 MHz	4 MHz	6 MHz	8 MHz	2 MHz	4 MHz	6 MHz	8 MHz	2 MHz	4 MHz	6 MHz	8 MHz
   M-I: Ben+C.H	0.3138	0.3119	0.3238	0.3127	0.012	0.011	0.012	0.011	0.9438	0.9427	0.9379	0.9395
   M-I: C.Ben+C.H	-0.31	-0.291	-0.274	-0.287	-0.008	-0.008	-0.007	-0.008	0.266	0.260	0.253	0.257
   M-I: N.Ben+C.H	1.965	1.975	1.999	2.009	0.083	0.083	0.084	0.084	0.391	0.388	0.382	0.379
   M-I: Pyr.+C.H	0.03	0.115	0.265	0.422	0.006	0.009	0.014	0.020	-0.451	-0.471	-0.508	-0.544

   TABLE 5: Excess values iE, ZE AND GE in binary mixtures for different frequencies.

   Binary mixture	Excess internal pressure( E ) i ( x 106 N.m-2 )				Excess acoustic impedance (ZE) ( x 106 Kg.m2.s-1)				Excess Gibbs free energy (GE) ( x 10- 20 k.J.mol-1)
   	2 MHz	4 MHz	6 MHz	8 MHz	2 MHz	4 MHz	6 MHz	8 MHz	2 MHz	4 MHz	6 MHz	8 MHz
   M-I: Ben+C.H	-47.829	-47.892	-47.808	-47.951	-0.024	-0.024	-0.025	-0.024	-0.092	-0.092	-0.091	-0.092
   M-I: C.Ben+C.H	-2.998	-2.833	-2.638	-2.771	0.012	0.011	0.010	0.011	-0.031	-0.031	-0.030	-0.030
   M-I: N.Ben+C.H	-52.69	-52.64	-52.44	-52.38	-0.330	-0.330	-0.331	-0.332	0.072	0.073	0.074	0.074
   M-I: Pyr.+C.H	16.523	17.594	19.571	21.555	-0.045	-0.050	-0.061	-0.071	0.056	0.061	0.069	0.078

   mixture-IV compared to mixture-II but is just the opposite when frequency increases.

   Excess adiabatic compressibility (E) is positive for mixture- I, III and IV and decreases in the same order. E is negative for mixture-II. E changes in the same way as LfE.

   i

   i

   i

   i

   Free volume (Vf) at any frequency is maximum for mixture-II and decreases successively from mixture-I o III to IV. Since Lf decreases in the order mixture-I. III. IV and II, Vf should change accordingly but for system-II it is maximum. When

   Excess internal pressure ( E) is negative for mixture-I, II and III at all frequencies. It is maximum negative for mixture-III and then for mixture-I and II. For mixture-II the negative value is much less than that of mixture-III and I. This is obvious as internal pressure is minimum in mixture-III and increases for mixture-II and I. However E is very small for mixture-II. The variation in E with change in frequency is negligible. i is positive for system-IV. This is because i is larger for system-IV. In this case, E increases considerably,

   chlorobenzene and cyclohexane are mixed, Lf is minimum. The molecules in this case are close to each other and the vibrations are transmitted through the molecules to a large distance increasing the apparent free volume. Free volume decreases very slowly with increase in frequency.

   Excess free volume (VfE) is positive for mixture-I, III and IV and decreases in that order. In case of mixture-I, positive VfE is due to expansion in volume because of additivity.

   VfE decreases with increase in frequency. In mixture-III, VfE is less than that in mixture-I. The interaction in system-III being stronger, the expansion is less. However VfE is less in mixture-IV than system-III as the interaction in mixture-III is less compared to mixture-IV because of steric hindrance in nitrobenzene solution. In mixture-II, VfE is negative and becomes more and more negative as frequency increases.

   When molecules are subjected to larger frequencies they vibrate rapidly, increasing the interaction between the molecules, which is of dispersive type. This reduces the free volume and hence the above observation.

   Internal pressure is maximum for mixture-IV and then decreases in the order mixture-I, II and III at any frequency. Pyridine molecules are spherical in shape, closely packed and have a finite dipole moment. Hence the intra-molecular as well as intermolecular interaction is maximum in case of mixture-IV. In case of system-III, it is the minimum. Nitrobenzene has a high dipole moment, but the complex structure of nitrobenzene molecules leads to less intermolecular forces and for the same reason also gives a less force of cohesion. Mixture-I and II show more internal pressure compared to mixture-III because of the molecular arrangement even though benzene is non-polar and dipole moment of chlorobenzene is low. Internal pressure increases very slowly with increase in frequency for mixture-I, II and III, but comparatively more in mixture-IV. This is because, when frequency increases molecular motion increases and the molecular interaction increases.

   when frequency increases.

6. FIGURES:

   Gibbs free energy (G) is maximum for mixture-III and then for mixture-IV, II & I in that order. In all the cases, G increases slowly with increase in frequency. Increase in G suggests shorter time for rearrangement of molecules in the mixture. This may be due to the fact that, when frequency increases, the energy imparted to the molecules expedites the rearrangement procedure.

   Excess Gibbs free energy (GE) is negative for mixture-I & II and is positive for mixture-III & IV. In mixture-I & II G decreases in the mixture indicating longer time for rearrangement of molecules, as the intermolecular interaction in both of them are comparatively small. In mixture-III and IV, G was large and hence GE is positive. In the above two mixtures, interaction being stronger, shorter time is required for rearrangement of molecules in the mixture. GE changes rapidly with frequency for mixture-IV.

7. CONCLUSION:

   Variation of ultrasonic velocity with frequency in the binary mixture of cyclohexane and benzene group of liquids enabled us to study the thermodynamic parameters and their excess values. These indicated the nature of the interaction between the components of the mixture. Although cyclohexane is non- polar the intermolecular interaction is evident through the excess values of the thermodynamic parameters.

   It has been observed that, the change in velocity with change in frequency is conspicuous in mixture-IV. This leads to large variation in the parameters and their excess values with change in frequency compared to the other mixtures.

8. REFERENCE:

1. M.K. Praharaj, A. Satapathy, P.R. Mishra and S. Mishra Study of thermodynamic and transport properties of ternary liquid mixture at different temperatures. Advances in Applied Science Research, vol. 3(3), pp. 1518-153, 2012.

2. M.K. Praharaj, A. Satapathy, P.R. Mishra and S. Mishra Study of thermodynamic and transport properties of ternary liquid mixture at different frequencies, Journal of Chemical and Pharmaceutical Research, vol. 4(4), pp. 1910-1920, 2012.

3. M.K. Praharaj, A. Satapathy, P.R. Mishra and S. Mishra Ultrasonic Study of Ternary Liquid Mixture Containing Substituted Benzene, Archives of Physics Research, vol. 3 (3), pp. 192-200, 2012.

4. Ashok Kumar Dash and Rita Paikaray, Research Journal of Physical Scieces, vol. 1(3), pp. 12-20, 2013.

5. M.K. Praharaj, A. Satapathy, P.R. Mishra and S. Mishra, Ultrasonic studies of molecular interactions in pyridine + N-N dimethylformamide

   + cyclohexane ternary liquid mixtures at different temperatures, International Journal of Chemical and Pharmaceutical Sciences, vol. 3 (3), pp. 6-14, 2012.

6. M.K. Praharaj, A. Satapathy, P.R. Mishra and S. Mishra, Ultrasonic analysis of intermolecular interaction in the mixtures of benzene with N.N-dimethylformamide and cyclohexane at different temperatures, Journal of Chemical and Pharmaceutical Research, vol. 5(1), pp. 49-56, 2013.

7. M.K. Praharaj, A. Satapathy, P.R. Mishra and S. Mishra, Study of molecular interaction in mixture of n, n-dimethylformamide, cyclohexane and benzene for different frequencies of ultrasonic waves, Golden Research Thoughts, vol. 2(8), pp. 1-10, 2013.

8. Prashant Dabrase, B.M. Suryavanshi, R.A. Patil, International journal of advanced scientific and technical research, vol. 2(6), pp. 541-549, 2012.

9. M.K. Praharaj, A. Satapathy, P.R. Mishra and S. Mishra, Ultrasonic studies of ternary liquid mixtures of N-N-dimethylformamide, nitrobenzene, and cyclohexane at different frequencies at 318 K, Journal of Theoretical and Applied Physics, vol. 7, 23, 2013.

10. Manoj kumar praharaj & Sarmistha Mishra, Comparative study of molecular interaction in ternary liquid mixtures of polar and non-polar solvents, National Symposium on Ultrasonics, pp. 24-25, Jan. 2014.

11. D.N. Rao, A. Krishnaiah and P.R. Naidu, Acta Chim. Acad. Sci. Hung, vol. 107(1), pp. 49-55, 1981.

12. B. Jacobson. J. Chem. Phys., vol. 20, pp. 927, 1952.

13. C.V. Suryanarayana,. and J. Kuppusamy, J. Acoust. Soc. Ind., vol. 4, pp. 75, 1976.

14. C.V. Surayanarayana and T. Kuppusamy, J.Acou.s oc.Ind, vol. 4, pp. 75. 1976,

15. J.d Vanderwaals, Essay on the continuity of the gaseous and liquid States London, 1873.

16. S. Glasstone, Thermodynamic for chemist, D. van Mostrand Co., Inc., Newyork, vol. 62, 1947.

17. Kemal Hassun Subhi, Acoustics Letters, vol. 11(10), pp. 195, 1988.

18. J.P Woodcock., Ultrasonics, Medical Physics Handbook, Published by Adam Hilger Ltd, 1979.