# Ultrasonic velocity and isentropic compressibility of binary fluid mixtures at 298.15 K.

IntroductionPhysicochemical behavior and molecular interactions occurring in a variety of liquid mixtures and solutions can be studied with the help of ultrasonic velocity. There has been an increasing interest in the study of molecular interactions and a number of experimental techniques have been used to investigate the same in binary liquid mixtures, since data on sound velocity offers a convenient method for determining certain thermodynamical properties of liquids and liquid mixtures, which are not obtained by other methods. Ultrasonic investigations are important in elucidating internal structure of fluid mixtures involving heat transfer, mass transfer etc. which are applicable in many ndustrial applications.

Extensive work has been carried out by Pereira et al. [1], Dzida and Ernest [2], Al-Kandary et al. [3], Pandey et al. [4] and Pan et al. [5] to investigate liquid state through analysis of ultrasonic propagation parameters and to correlate ultrasonic velocity with other physical and thermodynamic parameters. Substantial amount of work have also been done by Shukla et al. [6-12] successfully for the theoretical evaluation of ultrasonic velocity in binary and multicomponent non polar liquid mixtures by various empirical, semi-empirical and statistical mechanical concepts. Shukla et al. [11-12] have further applied these concepts to polar and ionic liquids. As a part of research concerning the thermochemical studies on new working fluid pair, we present here some useful data on speed of sound and isentropic compressibility for the mixture of trimethylbenzene with tetrahydrofuran, tetrachloromethane and dimethyl sulfoxide. These properties have been determined over the whole composition range. The major objective of the present work is to find out the applicability of Prigogine-Flory-Patterson (PFP) theory in polarnonpolar cyclic liquid binary mixtures. The necessary parameters for computation have been taken from the work of Pan et al. [5] and CRC hand book of chemistry & physics [13]. To the best of our knowledge, this is the first report in which PFP model has been applied in polar-nonpolar cyclic liquid mixtures.

Theoretical

In dealing with liquid state, Flory et al. [14-16] defined an element (or segment) as an arbitrary chosen portion of the molecules. Considering such segments in a molecule and following Prigogine's treatment of (y-mer) chain molecules and representing the number of external degree of freedom per segment by 3C, he was able to derive a partition function of the form:

Z = [Z.sub.comb][[[gamma][([v.sup.1/3] - [v.sup.*1/3]).sup.3]].sup.[gamma]nc]exp(-[E.sub.0]/kT) (1)

where k, N, T and [E.sub.0] are, respectively, the Boltzmann constant, number of particles, absolute temperature and excess intermolecular energy. [Z.sub.comb] is combinatorial factor which takes into account the number of ways in which [gamma]N elements intersperse among one another. Flory obtained the following expressions for the intermolecular free energy.

[E.sub.0] = Nrs [eta]/2v (2)

Here [eta] is a constant characterizing the energy of interaction for a pair of neighboring sites, s is the number of intermolecular contact sites per segment and v is the volume per segment. The reduced partition function thus takes the form as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

the reduced equation of state obtained from the resulting partition function is given by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

Changing from the molecular to molar units per segment for v, v* and jj, one gets,

[??] = v/[v.sup.*] = V/[V.sup.*] (5)

[??] = T/[T.sup.*] = 2[v.sup.*]ckT/[S.sub.[eta]] (6)

and

[??] = p/[p.sup.*] = 2[pv.sup.*]/[S.sub.[eta]] (7)

The reduced equation of state at zero pressure becomes,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)

[??] = [[[alpha]T/3 + 3[alpha]T) + 1].sup.3] (9)

Where [alpha] is the coefficient of thermal expansion at P = 0. Thus the reduced volume [v.sup.~] and reduced temperature [??] can be obtained from the experimental values of [alpha]. The values of [v.sup.~], [??], [v.sup.*] and [T.sup.*] can be computed using eqs (5) and (6). From the reduced equation of state it follows that:

[P.sup.*] = [[alpha]/[[beta].sub.T]]T[[??].sup.2] = [gamma]T[[??].sup.2] (10)

where [[gamma].sub.p] = [([delta]P/[delta]T).sub.V] is the thermal pressure coefficient at P = 0. Characteristic pressure [P.sup.*] is evaluated from this equation for binary liquid mixtures with the component subscript 1 and 2, Flory obtained the following expressions for binary liquid mixtures as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)

and

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)

where [[PSI].sub.1] and [[PSI].sub.2] are the segment fractions and [[theta].sub.1] and [[theta].sub.2] are the site fractions given by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (13)

where [x.sub.1] and [x.sub.2] are the mole fractions, [X.sub.12] is the interaction parameter and [v.sub.1] and [v.sub.2] are the molar volumes of the components 1 and 2, respectively. The ration ([s.sub.1]/[s.sub.2]) = [([v.sup.*.sub.1]/ [v.sup.*.sub.2]).sup.-1/3] = [([r.sub.1]/[r.sub.2]).sup.-1/3] for spherical molecules. The interaction parameter ([X.sub.12]) can be expressed as:

[X.sub.12] = [P.sup.*.sub.1][[1 - [([P.sup.*.sub.2]/[P.sup.*.sub.1]).sup.1/2][([v.sup.*.sub.2]/[v.sup.*.sub.1]).sup.1/6]].sup.2] (14)

12 is the energy parameter and it is measured of the difference of interaction energy between the unlike pairs and the mean of the like pairs.

The surface tension of binary liquid mixture in terms of Flory's statistical theory can be described by the expression:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15)

Where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are the characteristic and reduced parameters involved in the eqn.

Patterson and Rastogi [17] in their extension of the corresponding state theory dealt with the surface tension by using as a reduction parameter:

[[sigma].sup.*] = [k.sup.1/3][P.sup.*2/3][T.sup.*1/3] (16)

called the characteristic surface tension of the liquid. Here k is Boltzmann constant and [P.sup.*] and [T.sup.*] are the characteristic pressure and temperature, respectively. Starting from the work of Prigogine and Saraga [18] 1952 and Prigogine and Bellmas [19] they derived a reduced surface equation for Van der Waals liquids:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (17)

Where M is the fraction of the nearest neighbor that a molecule loses on moving from the bulk of the liquid to the surface. Its most suitable value ranges from 0.25 to 0.29.

Although Flory's statistical theory is not directly related with ultrasonic velocity but its evaluation needed the use of well-known and well-tested Auerbach relation which can be successfully used for the evaluation of ultrasonic velocity in binary liquid mixtures represented as:

u = [([sigma]/6.3 x [10.sup.-4][rho]).sup.2/3] (18)

where [sigma] and [rho] are the surface tension and density of the liquid mixture respectively.

Isentropic compressibility is related to speed of sound and density by the relation: [[beta].sub.s] = [u.sup.-2][[rho].sup.-1] (19)

Material and Methods

Experimental surface tension and experimental density data have been utilized to evaluate experimental sound velocity with the help of well known and well tested relation of Auerbach for six cyclic binary liquid mixtures over the whole composition range at 298.15K. Parameters of pure components are listed in Table 1 along with the literature values. Values of density ([rho]), molar volume ([V.sub.m]), theoretical and experimental speed of sound ([u.sub.cal] and [u.sub.exp]), percent deviation in speed of sound (%[DELTA]u) and isentropic compressibility ([[beta].sub.s]) for six binary mixtures; tetrahydrofuran (THF) + 1,2,4-trimethyl benzene (TMB), tetrahydrofuran (THF) + 1,2,3-trimethyl benzene (TMB), tetrachloromethane (TCM) + 1,2,4-trimethyl benzene (TMB), tetrachloromethane (TCM) + 1,3,5-trimethylbenzene, dimethyl sulfoxide (DMSO) + 1,2,4-trimethyl benzene + dimethyl sulfoxide (DMSO) + 1,3,5-trimethyl benzene at 298.5 K are presented in tables 2-7.

All the necessary data for computation were taken from the work of Pan et al. [5]. A close observation of all the tables reveal that experimental and calculated values of speed of sound are very close to each other indicating the success of PFP model in TMB with THF, TCM and DMSO liquid mixtures.

Results and Discussions

The percent deviations in speed of sound at 298.15 K from figures 1 and 2 shows that they are positive for THF and TCM with 1,2,4-TMB and are negative for THF, TCM and DMSO with 1,3,5-TMB while DMSO with 1,2,4-TMB has both positive and negative values. The maximum positive value of percent deviation in speed of sound follow the order DMSO + 1,2,4-TMB > TCM + 1,2,4-TMB > THF + 1,2,4-TMB and maximum negative values of percent deviation in speed of sound follow the order DMSO + 1,3,5TMB > TCM + 1,3,5-TMB > THF + 1,3,5-TMB. In both the cases, the trend is similar except for the system DMSO + 1,2,4-TMB where both positive and negative deviations are observed. The possible reason may be that there are no strong intermolecular forces between DMSO and TMB because 1,3,5-TMB is a symmetrical nonpolar molecule. Conversely, stronger forces exists for the systems with 1,2,4-TMB, so the values are positive. Negative values of the systems with 1,3,5-TMB are possibly owing to the greater repulsion due to bulky methyl group as compared to 1,2,4-TMB. These short range repulsive forces are responsible for less compact structure of 1,3,5 TMB. With the increase of concentration, density increases and molar volume decreases due to shrinkage in the volume of DMSO and TCM. Hence, an increase in the speed of sound may be correlated to the structure former of the 1,3,5-TMB. Positive deviations are due to dipolar-dipolar interactions because 1,2,4-TMB is a polar molecule.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

The lack of smoothness in deviations is due to the interaction between the component molecules. Isentropic compressibility increases regularly with the increase of mole fraction. Increment becomes larger with 1,2,4-TMB. Strong discrepancy is observed in Table 6 where the value of isentropic compressibility decreases. Possibly, it is due to dipolar repulsion which lowers the energy hence regular trend is not observed, while density and speed of sound show regular behavior.

Conclusion

Thus it can be concluded from the preceding discussion that PFP model can be applied successfully to polar-nonpolar cyclic liquid binary mixtures.

Acknowledgements

One of author (R. K. Shukla) is thankful to U.G.C. for financial assistance and Department of Chemistry of V. S. S. D. College for cooperation and help.

References and Notes

[1] Pereira, S. M.; Rivas, M. A.; Iglesias, T. P. J. Chem. Eng. Data 2005, 47, 1363.

[2] Dzida, M.; Ernest, S. J. Chem. Eng. Data 2003, 48, 1453.

[3] Al-Kandary, J. A.; Al-Jimaz, A. S.; Latiq, H. M. A. J. Chem Eng. Data 2006, 51, 2074.

[4] Pandey, J. D.; Singh, A. K.; Day, R. Indian J. Chem. Tech. 2005, 12, 588.

[5] Pan, C.; Ke, Q.; Ouyang, G.; Zhan, X.; Yang, Y.; Huang, Z. J. Chem. Eng. Data 2004, 49, 1839.

[6] Shukla R. K.; Kumar, A.; Srivastava, K.; Yadava, S. J. Mol. Liq. 2008, 140, 25.

[7] Shukla, R. K.; Kumar, A.; Singh, N.; Shukla, A. J. Mol. Liq. 2008, 140, 117.

[8] Shukla, R. K.; Kumar, A.; Srivastava, K.; Singh, N. J. Soln. Chem. 2007, 36, 1103.

[9] Shukla, R. K.; Rai, R. D.; Shukla, A. K.; Mishra, N.; Pandey, J. D. Indian J. Pure Appl. Phys. 1993, 31, 54.

[10] Shukla, R. K.; Rai, R. D.; Shukla, A. K.; Pandey, J. D. J. Chem. Thermodyn. 1989, 21, 125.

[11] Shukla, R. K.; Rai, R. D.; Pandey, J. D. Can. J. Chem. 1989, 67, 437.

[12] Shukla, R. K.; Shukla, S.; Pandey, V.; Awasthi, P. J. Phys. Chem. Liq. 2007, 45, 169.

[13] Chemical Rubber Publishing Company Handbook of Chemistry and Physics, Florida: CRC, Boca Raton, 1979.

[14] Flory, P. J. J. Am. Chem. Soc. 1965, 82, 1833.

[15] Abe, A.; Flory, P. J. J. Am. Chem. Soc. 1965, 82, 1838.

[16] Flory, P. J.; Orwoll, R. A.; Vrij, A. J. Am. Chem. Soc. 1964, 86, 3515.

[17] Patterson, D.; Rastogi, A. K. J. Phys. Chem. 1970, 74, 1067.

[18] Prigogine, I.; Saraga, L. J. Chem. Phys. 1952, 49, 399.

[19] Prigogine, I.; Bellmas, A.; Method, V. Molecular Theory of Solutions. Amsterdam: North-Holland, 1957.

[20] Riddick, J.; Bunger, W. B.; Sakano, T. K. Technique of Chemical Organic Solvent; Physical Properties and Methods of Purification, 4th ed. John Willy and Sons. 1986

[21] Nair, A. K. J. Phy. Chem. Liq. 2007, 45, 371.

[22] Moattar, M. T. Z.; Cegineara, R. M. J. Chem. Eng. Data 2007, 52, 2359.

Rajeev Kumar Shukla (a) *, S. N. Dixit (b), Pratima Jain (b), Preeti Mishra (b) and Sweta Sharma (b)

(a) Department of Chemistry, V. S. S. D. College, Kanpur--208002, India

(b) Department of Chemistry, Govt. Science College, Gwalior, M. P. India

Received: 28 August 2010; accepted: 31 November 2010.

* Corresponding author. E-mail: rajeevshukla47@rediffmail.com. Phone: +91 9838516217

Table 1. Parameters of pure components at 298.15 K Liquid p (a) p (a) [10.sup.4] [[beta].sub.T]/ (exp) (lit) a/K-1 [TPa.sup.-1] 1,2,4-TMB 0.87164 087174 11.168 81.445 1,3,5-TMB 0.86103 0.86109 11.320 85.961 THF 0.88206 0.88197 11.464 90.440 TCM 1.58380 1.58429 11.504 91.704 DMSO 1.09554 1.095560 9.8922 50.134 Liquid [V.sub.m]/ u/[ms.sup.-1] [cm.sup.3] (exp) [mol.sup.-1] 1,2,4-TMB 137.893 1415.7 1,3,5-TMB 139.592 1389.3 THF 81.752 1291.2 TCM 97.121 921.6 DMSO 71.316 1480.9 Liquid u/[ms.sup.-1] u/[ms.sup.-1] (cal) (lit) 1,2,4-TMB 1412.3 1421 (b) 1,3,5-TMB 1390.8 1397 (c) THF 1283.6 1278 (d) TCM 916.6 926 (e) DMSO 1498.4 1487 (d) (a)--ref [5], (b)--ref [20], (c)--ref [21], (d)--ref [22], (e)--ref [7] Table 2. Values of mole fraction ([X.sub.1]), density ([rho]), molar volume ([V.sub.m]), theoretical and experimental speed of sound (u-cal, u-exp), %[DELTA]u and isentropic compressibility of tetrahydrofuran and 1,2,4-trimethyl benzene [X.sub.1] [[rho].sub.m]/ [V.sub.m]/ u(cal)/ g.[cm.sup.-3] c.c.[mol.sup.-1] [ms.sup.-1] 0.0988 0.8727 132.3 1404.5 0.2018 0.8737 126.6 1396.5 0.3003 0.8748 121.0 1388.8 0.3995 0.8758 115.5 1381.1 0.5002 0.8769 109.8 1373.3 0.6005 0.8779 104.2 1365.7 0.6986 0.8789 98.67 1358.5 0.7996 0.8800 93.00 1351.4 0.9006 0.8810 87.33 1344.6 [X.sub.1] u(exp)/ (%[DELTA]u) [beta]s/ [ms.sup.-1] [Mpa.sup.-1] 0.0988 1410.1 0.390 0.5809 0.2018 1405.3 0.632 0.5869 0.3003 1400.4 0.828 0.5927 0.3995 1394.4 0.958 0.5986 0.5002 1386.8 0.974 0.6047 0.6005 1377.9 0.885 0.6107 0.6986 1367.8 0.677 0.6165 0.7996 1355.9 0.336 0.6223 0.9006 1343.7 -0.067 0.6278 Table 3. Values of mole fraction ([X.sub.1]), density ([rho]), molar volume ([V.sub.m]), theoretical experimental speed of sound (u-cal, u-exp), %[DELTA]u and isentropic compressibility of tetrahydrofu and 1,3,5-trimethylbenzene [X.sub.1] [[rho].sub.m]/ [V.sub.m]/ u(cal)/ g.[cm.sup.-3] c.c.[mol.sup.-1] [ms.sup.-1] 0.0481 0.8620 136.8 1388.0 0.2021 0.8653 127.9 1379.0 0.3002 0.8673 122.2 1373.4 0.4000 0.8694 116.5 1367.8 0.5004 0.8716 110.6 1362.3 0.6010 0.8737 104.8 1356.9 0.7003 0.8758 99.09 1351.8 0.7989 0.8778 93.38 1347.0 0.9000 0.8800 87.54 1342.5 [X.sub.1] u(exp)/ (%[DELTA]u) [beta]s/ [ms.sup.-1] [Mpa.sup.-1] 0.0481 1381.3 -0.484 0.60217 0.2021 1372.6 -0.473 0.60769 0.3002 1365.4 -0.587 0.61121 0.4000 1358.9 -0.653 0.61475 0.5004 1352.8 -0.702 0.61826 0.6010 1347.6 -0.687 0.62167 0.7003 1342.9 -0.665 0.62488 0.7989 1338.8 -0.615 0.62784 0.9000 1335.6 -0.515 0.63054 Table 4. Values of mole fraction ([X.sub.1]), density ([rho]), molar volume ([V.sub.m]), theoretical and experimental speed of sound (u-cal, u-exp), %[DELTA]u, isentrtopic compressibility of tetrachloromethane and 1,2,4-trimethyl benzene [X.sub.1] [[rho].sub.m]/ [V.sub.m]/ u(cal)/ g.[cm.sup.-3] c.c.[mol.sup.-1] [ms.sup.-1] 0.0496 0.9070 135.9 1371.8 0.0996 0.9426 133.8 1333.6 0.1986 1.0131 129.8 1264.4 0.3001 1.0854 125.7 1201.2 0.4006 1.1569 121.6 1145.1 0.5987 1.2980 113.5 1049.6 0.6986 1.3692 109.4 1007.6 0.7985 1.4403 105.3 969.2 0.9011 1.5134 101.2 932.9 [X.sub.1] u(exp)/ (%[DELTA]u) [beta]s/ [ms.sup.-1] [Mpa.sup.-1] 0.0496 1374.9 0.222 0.58587 0.0996 1337.3 0.277 0.59654 0.1986 1270.1 0.449 0.61742 0.3001 1208.3 0.588 0.63854 0.4006 1152.0 0.604 0.65921 0.5987 1060.5 1.029 0.69938 0.6986 1014.9 0.721 0.71937 0.7985 973.0 0.394 0.73918 0.9011 932.1 -0.088 0.75929 Table 5. Values of mole fraction ([X.sub.1]), density ([rho]), molar volume ([V.sub.m]), theoretical and experimental speed of sound (u-cal, u-exp), %[DELTA]u, isentropic compressibility of tetrachloromethane and 1,3,5-trimethyl benzene [X.sub.1] [[rho].sub.m]/ [V.sub.m]/ u(cal)/ g.[cm.sup.-3] c.c.[mol.sup.-1] [ms.sup.-1] 0.1009 0.9340 137.5 1311.8 0.2014 1.0066 133.3 1242.8 0.2994 1.0774 129.0 1183.2 0.4007 1.1506 124.7 1128.2 0.4998 1.2223 120.5 1080.1 0.5995 1.2943 116.2 1036.5 0.6988 1.3661 112.0 997.3 0.7970 1.4371 107.8 962.4 0.9012 1.5124 103.5 929.0 [X.sub.1] u(exp)/ (%[DELTA]u) [beta]s/ [ms.sup.-1] [Mpa.sup.-1] 0.1009 1306.0 -0.445 0.62221 0.2014 1235.2 -0.615 0.64319 0.2994 1173.6 -0.818 0.66299 0.4007 1118.0 -0.912 0.68274 0.4998 1071.0 -0.847 0.70131 0.5995 1028.8 -0.744 0.71914 0.6988 991.3 -0.613 0.73592 0.7970 957.6 -0.494 0.75134 0.9012 925.1 -0.418 0.76616 Table 6. Values of mole fraction ([X.sub.1]), Density ([rho]), molar volume ([V.sub.m]), theoretical and experimental speed of sound (u-cal, u-exp), %[DELTA]u, isentropic compressibility of dimethylsulfoxide and 1,2,4-trimethylbenzene [X.sub.1] [[rho].sub.m]/ [V.sub.m]/ u(cal)/ g.[cm.sup.-3] c.c.[mol.sup.-1] [ms.sup.-1] 0.1007 0.8942 131.2 1259.5 0.2007 0.9166 124.5 1264.7 0.3007 0.9390 117.9 1270.4 0.3995 0.9611 111.3 1276.6 0.5011 0.9838 104.5 1283.7 0.6012 1.0062 97.9 1291.4 0.6992 1.0282 91.3 1300.0 0.7992 1.0506 84.7 1309.9 0.9013 1.0734 77.9 1321.7 [X.sub.1] u(exp)/ (%[DELTA]u) [beta]s/ [ms.sup.-1] [Mpa.sup.-1] 0.1007 1367.2 7.88 0.70503 0.2007 1354.0 6.59 0.68209 0.3007 1333.6 4.74 0.65984 0.3995 1321.9 3.42 0.63841 0.5011 1312.2 2.17 0.61685 0.6012 1289.1 -0.18 0.59588 0.6992 1271.0 -2.28 0.57552 0.7992 1272.4 -2.95 0.55474 0.9013 1407.5 6.10 0.53331 Table 7. Values of mole fraction ([X.sub.1]), density ([rho]), molar volume ([V.sub.m]), theoretical and experimental speed of sound (u-cal, u-exp), %[DELTa]u, isentropic compressibility of dimethylsulfoxide and 1,3,5-trimethylbenzene [X.sub.1] [[rho].sub.m]/ [V.sub.m]/ u(cal)/ g.[cm.sup.-3] c.c.[mol.sup.-1] [ms.sup.-1] 0.1023 0.8850 132.6 1399.7 0.1987 0.9076 126.0 1408.4 0.3027 0.9320 118.9 1418.1 0.401 0.9551 112.2 1427.7 0.4999 0.9783 105.5 1437.7 0.6003 1.0018 98.6 1448.5 0.6990 1.0250 91.9 1459.7 0.8003 1.0487 85.0 1471.9 0.8998 1.0720 78.2 1484.6 [X.sub.1] u(exp)/ (%[DELTA]u) [beta]s/ [ms.sup.-1] [Mpa.sup.-1] 0.1023 1338.4 -4.58 0.57675 0.1987 1303.8 -8.02 0.55548 0.3027 1274.0 -11.31 0.53355 0.401 1275.5 -11.93 0.51371 0.4999 1285.3 -11.86 0.49452 0.6003 1314.8 -10.17 0.47575 0.6990 1350.6 -8.08 0.45791 0.8003 1404.3 -4.81 0.44016 0.8998 1466.3 -1.25 0.42321

Printer friendly Cite/link Email Feedback | |

Title Annotation: | Full Paper |
---|---|

Author: | Shukla, Rajeev Kumar; Dixit, S.N.; Jain, Pratima; Mishra, Preeti; Sharma, Sweta |

Publication: | Orbital: The Electronic Journal of Chemistry |

Date: | Oct 1, 2010 |

Words: | 3669 |

Previous Article: | Synthesis and biological activities of some 3-chloro-4-(substituted phenyl)-1-{[2-oxo-2-(5-phenyl-1H-tetrazol-1-yl) ethyl] amino} azetidin-2-one as... |

Next Article: | Chalcones: compounds possessing a diversity in applications. |