Excess and deviation properties for the binary mixtures of methylcyclohexane with benzene, toluene, p-xylene, mesitylene, and anisole at T = (298.15, 303.15, and 308.15) K

J. Chem. Thermodynamics 38 (2006) 1717–1724 www.elsevier.com/locate/jct

Excess and deviation properties for the binary mixtures of methylcyclohexane with benzene, toluene, p-xylene, mesitylene, and anisole at T = (298.15, 303.15, and 308.15) K Jagadish G. Baragi, Mrityunjaya I. Aralaguppi

*

Department of Chemistry, Karnatak University, Dharwad 580 003, India Received 19 November 2004; received in revised form 26 November 2005; accepted 11 December 2005 Available online 6 October 2006

Abstract Experimental data on density, viscosity, and refractive index at T = (298.15, 303.15, and 308.15) K, while speed of sound values at T = 298.15 K are presented for the binary mixtures of (methylcyclohexane + benzene), methylbenzene (toluene), 1,4-dimethylbenzene (p-xylene), 1,3,5-trimethylbenzene (mesitylene), and methoxybenzene (anisole). From these data of density, viscosity, and refractive index, the excess molar volume, the deviations in viscosity, molar refraction, speed of sound, and isentropic compressibility have been calculated. The computed values have been fitted to Redlich–Kister polynomial equation to derive the coefficients and estimate the standard errors. Variations in the calculated excess quantities for these mixtures have been studied in terms of molecular interactions between the component liquids and the effects of methyl and methoxy group substitution on benzene ring.  2006 Elsevier Ltd. All rights reserved. Keywords: Excess molar volume; Deviations in viscosity; Molar refraction; Speed of sound; Isentropic compressibility; Methylcyclohexane; Aromatic hydrocarbons; Molecular interactions

1. Introduction In the earlier literature, excess molar properties of binary mixtures of variety of aromatic liquids with different types of liquids have been studied. Aminabhavi et al. and Aralaguppi et al. [1–5] have studied molecular interactions and thermodynamic properties of several binary mixtures containing a variety of liquids. Different excess properties of the binary mixtures of the aromatic hydrocarbons of our study with a variety of other liquids at different temperatures have also been studied by different authors [6–13]. Different excess properties of binary mixtures containing methylcyclcohexane as one of the components with a large number of liquids have also been studied [14–19] by large number of researchers.

*

Corresponding author. Tel.: +91 95836 2772696. E-mail address: [email protected] (M.I. Aralaguppi).

0021-9614/$ - see front matter  2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2005.12.005

As a part of our ongoing program of research [1–3,5], we present here the experimental data on density, q, viscosity, g, refractive index, nD, at T = (298.15, 303.15, and 308.15) K and speed of sound, u, at 298.15 K for the binary mixtures of (methylcyclohexane with benzene, + toluene, + p-xylene, + mesitylene, and + anisole). These systems have not been studied earlier as found from the literature survey. Most of the aromatic liquids used in this research are important in petrochemical industries. Methylcyclohexane is a toxic organic compound [20]. Measurement of physicochemical property data on such mixtures will be useful in process engineering. We are not aware of any such data in the earlier literature on the mixtures of this study and hence, an attempt has been made to present the data on q, g, nD, and u, and to compute the excess molar volume, VE, and deviations in viscosity, Dg, molar refraction, DR, speed of sound, Du and isentropic compressibility, Dks for the mixtures of (methylcyclohexane + benzene, + toluene, + p-xylene, + mesitylene, and + anisole)

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over the entire range of mixture composition. These results have been fitted to the Redlich–Kister equation [21] to derive the binary coefficients and estimate the standard errors. The results are displayed graphically. 2. Experimental 2.1. Materials Methylcyclohexane and toluene were AR grade samples procured from S.D. fine Chemicals, Mumbai, India. Mesitylene was also AR grade sample purchased from E. Merck, Mumbai, India. Extrapure grade sample of anisole was procured from Sisco Research Lab. Pvt. Ltd., Mumbai, India. HPLC grade sample of benzene and pure sample of p-xylene were procured from S.D. fine chemicals, Mumbai, India. 2.2. Methods Densities of pure components and their mixtures were determined at atmospheric pressure by using density meter DMA 4500 (Anton Paar). The DMA 4500 is the oscillating U-tube density meter, which measures density with an uncertainty of ±0.0001 g Æ cm3 in wide viscosity and temperature ranges. By measuring the damping of the U-tube’s oscillation caused by the viscosity of the filled-in sample, the DMA 4500 automatically corrects viscosity related errors. To perform the measurement, we select one out of a total of 10 individual measuring methods, and fill the sample into the measuring cell. An acoustic signal will inform us when the measurement is completed. The results are automatically converted (including temperature compensation wherever necessary) into concentration, specific gravity or other density-related units using the built-in conversion tables and functions. The uncertainties in the densities measured were ±0.0001 g Æ cm3. The density results, including sample number or name, shown on the programmable LC display, is transferred to the data memory. Viscosities were measured using a Cannon Fenske viscometer (size 75, ASTM D 445, Industrial Research Glass-

ware Ltd., Roselle, NJ). An electronic digital stopwatch with a readability of ± 0.01 s was used for the flow time measurements. The measured viscosity values are precise up to ±0.001 mPa Æ s. Calibration procedures are as described previously [2,23]. Refractive indices for the sodium D-line were measured using a thermostatically controlled Abbe refractometer (Atago 3T, Japan). Minimum of three independent readings were taken for each composition, and the average value was considered in all the calculations. Refractive index data are accurate to ±0.0001 U. Speed of sound was measured using a variable path single-crystal interferometer (Mittal Enterprises, Model M-84, New Delhi). A crystal-controlled high-frequency generator was used to excite the transducer at a frequency of 1 MHz. Frequency was measured within an accuracy of 1 in 104 using a digital frequency meter. Interferometer cell was filled with the test liquid and water was circulated around the measuring cell from a constant temperature bath maintained at T = (298.15 ± 0.01) K. Details of the speed of sound measurements have been given earlier [2,23] and these data are precise up to ±2 in 1000 m Æ s1. In all the property measurements, temperature was controlled within an uncertainty of ±0.01 K using a constant temperature bath. A Julabo immersion cooler (FT 200, Julabo Labortechnik, Gmbh, Germany) was used to cool water bath. This unit was installed at the intake of a heating circulator to draw the heat away from the circulating bath liquid. Immersion probe was connected to the instrument with a flexible and insulated tube, which maintained the constant temperature of the bath. 3. Results and discussion In table 1 experimental data of density and refractive index at T = 298.15 K for pure liquids are compared with the literature values. By taking the average values of three concurrent measurements of the physical properties studied viz., density, viscosity, refractive index and speed of sound, at each composition and at different temperatures, are tabulated in table 2. Excess molar volume, VE, is calculated using equation (1) from the experimental data

TABLE 1 Comparison of experimental densities (q) and refractive indices (nD) of pure liquids with the literature values at 298.15 K Liquid

(Mol.% purity)

q/(kg Æ m3) Experimental

Methyl cyclohexane Benzene Toluene p-Xylene Mesitylene Anisole a b c d

Riddick et al. [24]. Marsh [25]. Isaias [26]. Zutao [27].

(>99.0) (>99.8) (>99.5) (>98.5) (>98.0) (>99.0)

764.99 873.42 862.26 856.70 861.20 989.18

nD Literature c

765.06 873.60b 862.19a 856.60a 861.11a 989.32a

Experimental

Literature

1.4217 1.4971 1.4931 1.4926 1.4961 1.5136

1.4206d 1.4979a 1.4932a 1.4932a 1.4968a 1.5143a

J.G. Baragi, M.I. Aralaguppi / J. Chem. Thermodynamics 38 (2006) 1717–1724 TABLE 2 Densities (q), viscosity (g), refractive indices (nD), and speed of sound (u) of (methylcyclohexane + aromatic hydrocarbon) mixtures at different temperatures x1

q/(kg Æ cm3)

0.0000 0.1040 0.2045 0.3020 0.4006 0.5007 0.6004 0.7056 0.8033 0.8982 1.0000

Methylcyclohexane (1) + Benzene (2) T = 298.15 K 873.4 0.602 1.4971 855.9 0.584 1.4840 840.8 0.566 1.4728 827.6 0.561 1.4628 815.8 0.556 1.4550 805.0 0.559 1.4475 795.3 0.571 1.4410 785.9 0.597 1.4341 778.5 0.617 1.4290 771.4 0.647 1.4245 765.0 0.676 1.4217

0.0000 0.1040 0.2045 0.3020 0.4006 0.5007 0.6004 0.7056 0.8033 0.8982 1.0000

868.1 850.7 835.8 822.7 811.0 800.3 790.6 781.4 774.0 767.0 760.7

T = 303.15 K 0.560 0.546 0.530 0.527 0.523 0.527 0.537 0.564 0.853 0.607 0.631

1.4936 1.4810 1.4702 1.4604 1.4524 1.4448 1.4384 1.4316 1.4262 1.4219 1.4192

0.0000 0.1040 0.2045 0.3020 0.4006 0.5007 0.6004 0.7056 0.8033 0.8982 1.0000

862.7 845.5 830.7 817.8 806.2 795.6 786.0 776.8 769.5 762.6 756.3

T = 308.15 K 0.523 0.509 0.494 0.492 0.490 0.496 0.504 0.531 0.549 0.567 0.590

1.4903 1.4779 1.4675 1.4580 1.4499 1.4422 1.4357 1.4292 1.4235 1.4192 1.4163

0.0000 0.1027 0.2050 0.3034 0.4043 0.5031 0.5988 0.7061 0.8005 0.8984 1.0000

Methylcyclohexane (1) + Toluene (2) T = 298.15 K 862.3 0.559 1.4931 849.5 0.551 1.4838 837.5 0.547 1.4750 826.6 0.548 1.4666 816.0 0.556 1.4586 806.3 0.564 1.4511 797.3 0.577 1.4443 787.8 0.592 1.4373 780.0 0.614 1.4315 772.4 0.643 1.4261 765.0 0.676 1.4217

0.0000 0.1027 0.2050 0.3034 0.4043 0.5031

857.6 844.9 832.9 822.0 811.5 801.8

g/(mPa Æ s)

T = 303.15 K 0.526 0.520 0.518 0.517 0.523 0.532

nD

1.4902 1.4811 1.4723 1.4641 1.4561 1.4486

u/(m Æ s1)

1302 1293 1284 1276 1267 1259 1250 1242 1234 1225 1217

1314 1304 1295 1285 1275 1266 1256 1246 1237 1227 1217

1719

TABLE 2 (continued) 0.5988 0.7061 0.8005 0.8984 1.0000

792.8 783.4 775.6 768.0 760.7

0.544 0.558 0.577 0.603 0.631

1.4418 1.4347 1.4289 1.4234 1.4192

0.0000 0.1027 0.2050 0.3034 0.4043 0.5031 0.5988 0.7061 0.8005 0.8984 1.0000

852.9 840.3 828.3 817.5 807.0 797.3 788.4 779.0 771.2 763.7 756.3

T = 308.15 K 0.497 0.490 0.489 0.487 0.491 0.500 0.510 0.524 0.540 0.563 0.590

1.4874 1.4783 1.4696 1.4615 1.4537 1.4461 1.4392 1.4321 1.4263 1.4208 1.4163

0.0000 0.0993 0.2037 0.3028 0.4047 0.5382 0.6035 0.7030 0.8037 0.8981 1.0000

Methylcyclohexane (1) + p-Xylene (2) T = 298.15 K 856.7 0.611 1.4926 846.6 0.597 1.4848 836.2 0.590 1.4767 826.4 0.587 1.4690 816.7 0.586 1.4615 804.2 0.593 1.4519 798.3 0.597 1.4473 789.5 0.608 1.4405 780.8 0.625 1.4338 773.0 0.646 1.4279 765.0 0.676 1.4217

0.0000 0.0993 0.2037 0.3028 0.4047 0.5382 0.6035 0.7030 0.8037 0.8981 1.0000

852.3 842.3 831.8 822.1 812.3 799.9 794.0 785.1 776.5 768.7 760.7

T = 303.15 K 0.572 0.566 0.557 0.553 0.553 0.559 0.562 0.573 0.588 0.607 0.631

1.4893 1.4820 1.4743 1.4668 1.4594 1.4498 1.4451 1.4384 1.4314 1.4253 1.4192

0.0000 0.0993 0.2037 0.3028 0.4047 0.5382 0.6035 0.7030 0.8037 0.8981 1.0000

848.0 837.9 827.5 817.8 808.0 795.5 789.6 780.8 772.2 764.4 756.3

T = 308.15 K 0.540 0.536 0.523 0.520 0.520 0.525 0.528 0.537 0.550 0.569 0.590

1.4867 1.4793 1.4718 1.4646 1.4572 1.4476 1.4430 1.4362 1.4290 1.4228 1.4163

0.0000 0.1007 0.1993 0.3035 0.4063

Methylcyclohexane (1) + Mesitylene (2) T = 298.15 K 861.2 0.667 1.4960 851.6 0.653 1.4890 842.0 0.638 1.4817 832.0 0.629 1.4740 822.0 0.622 1.4663 (continued on next

1326 1315 1303 1293 1282 1268 1261 1250 1239 1228 1217

1346 1328 1312 1295 1280 page)

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TABLE 2 (continued)

TABLE 2 (continued) 1

x1

q/(kg Æ cm )

g/(mPa Æ s)

nD

u/(m Æ s )

0.4974 0.6085 0.7027 0.7973 0.9020 1.0000

813.1 802.2 793.1 784.0 774.1 765.0

0.620 0.621 0.627 0.638 0.654 0.676

1.4593 1.4508 1.4436 1.4363 1.4285 1.4217

1267 1253 1244 1235 1225 1217

0.0000 0.1007 0.1993 0.3035 0.4063 0.4974 0.6085 0.7027 0.7973 0.9020 1.0000

857.1 847.5 837.9 827.9 817.9 808.9 798.1 788.9 779.7 769.8 760.7

T = 303.15 K 0.622 0.612 0.600 0.592 0.584 0.603 0.582 0.588 0.598 0.622 0.631

1.4936 1.4865 1.4809 1.4730 1.4647 1.4565 1.4529 1.4421 1.4347 1.4265 1.4192

0.0000 0.1007 0.1993 0.3035 0.4063 0.4974 0.6085 0.7027 0.7973 0.9020 1.0000

853.0 843.3 833.8 823.7 813.7 804.8 793.9 784.7 775.5 765.6 756.3

T = 308.15 K 0.586 0.577 0.569 0.559 0.553 0.547 0.548 0.553 0.566 0.575 0.590

1.4913 1.4843 1.4771 1.4692 1.4614 1.4544 1.4459 1.4386 1.4312 1.4233 1.4163

0.0000 0.1025 0.2009 0.3006 0.4060 0.5043 0.6058 0.7026 0.8023 0.9053 1.0000

Methylcyclohexane (1) + Anisole (2) T = 298.15 K 989.2 1.008 1.5136 962.1 0.924 1.5023 936.5 0.854 1.4917 911.8 0.793 1.4813 886.7 0.750 1.4706 864.4 0.717 1.4609 842.2 0.689 1.4516 821.9 0.675 1.4431 801.8 0.667 1.4351 782.1 0.666 1.4278 765.0 0.676 1.4217

0.3006 0.4060 0.5043 0.6058 0.7026 0.8023 0.9053 1.0000

0.0000 0.1025 0.2009

984.5 957.4 931.8 907.2 882.2 860.1 837.8 817.3 797.4 777.8 760.7

979.8 952.7 927.2

T = 303.15 K 0.929 0.905 0.792 0.734 0.694 0.664 0.645 0.634 0.621 0.622 0.631 T = 308.15 K 0.861 0.808 0.737

1.5112 1.5036 1.4890 1.4801 1.4701 1.4586 1.4497 1.4408 1.4323 1.4242 1.4192

0.693 0.654 0.627 0.605 0.593 0.584 0.583 0.590

1.4766 1.4659 1.4563 1.4467 1.4382 1.4301 1.4226 1.4163

ð1Þ

Here, Vm is molar volume of the mixture, V1 and V2 are molar volumes of the respective pure components; xi represents the mole fraction of the ith component of the mixture. Using equation (2) deviations in viscosity, qg, molar refraction, qR, speed of sound, Du, and isentropic compressibility, Dks, have been calculated as DY ¼ Y m  ðY 1 x1 þ Y 2 x2 Þ.

1410 1391 1372 1352 1333 1314 1294 1275 1256 1236 1217

ð2Þ

In the above equation, DY represents Dg, DR, Du, and Dks, respectively, while Ym represents the respective mixture properties viz., viscosity, g, molar refractivity, R (calculated from the Lorentz–Lorentz relation), speed of sound, u, and isentropic compressibility, ks(=1/u2q), of the binary mixture; the symbol Y1 and Y2 refers to the same properties for pure components of the mixture. P While P calculating DR and Dks, volume fraction, /i ð¼ xi vi = 2i¼1 xi vi Þ, was used but, for calculating Dg and Du, the mole fraction, xi was used. The results of excess molar volume at T = 298.15 K for methylcyclohexane + benzene, + toluene, + p-xylene, + anisole, or + mesitylene are displayed in figure 1. The variations in VE, depend upon the nature of the aromatic liquid components in the mixture. For instance, large 0.6

0.5

-1

0.0000 0.1025 0.2009 0.3006 0.4060 0.5043 0.6058 0.7026 0.8023 0.9053 1.0000

902.6 877.6 855.4 833.3 813.0 792.9 773.4 756.3

V E ¼ V m  ðV 1 x1 þ V 2 x2 Þ.

E -6 3 V /10 (m ·mol )

3

0.4

0.3

0.2

0.1

0 0

0.2

0.4

0.6

0.8

1

x1 1.5088 1.4978 1.4870

FIGURE 1. Plot of excess molar volume (VE) against mole fraction of methylcyclohexane with (r) benzene, (j) toluene, (m) xylene, ( ) mesitylene, and (·) anisole at 298.15 K.

J.G. Baragi, M.I. Aralaguppi / J. Chem. Thermodynamics 38 (2006) 1717–1724

same dependencies, but their magnitudes increase systematically with increasing temperature. A representative plot of Dg vs. x1 showing the effect of temperature on methylcyclohexane (1) + p-xylene (2) mixture is displayed in figure 3. For other mixtures, a similar trend is observed. The plots of DR vs. /1 (volume fraction of methylcyclohexane) at T = 298.15 K for (methylcyclohexane + benzene, + toluene, + p-xylene, + mesitylene or + anisole) are shown in figure 4. A large negative deviation is observed for (methyl cyclohexane + benzene), while for (methylcyclohexane + toluene or + mesitylene), these values are

0

-0.01

-0.02

Δη /(mPa·s-1)

positive deviation is observed in the case of methylcyclohexane (1) + benzene (2). This may be due to the strong dispersion type interactions between methylcyclohexane and benzene molecules. Positive values of VE are also observed for mixtures of (methylcyclohexane + toluene, + p-xylene, + anisole, or + mesitylene). But the values are less and are almost same. In (methylcyclohexane + toluene, or + anisole) mixtures, due to the introduction of – CH3 and –OCH3 groups on the benzene ring, p-electron donating capacity increases, thereby increasing the attractive interactions between the two components. However in the case of mesitylene, the steric hindrance by three – CH3 groups on benzene ring compensates the strong interactions between the liquid components, making theVE contribution the same as those for the mixtures with other methyl group substituted benzenes. Hence the curves for these mixtures overlap in the graphs. These binary mixtures exhibit almost identical trends over the whole of the mixture composition, because of the identical nature of the molecules. It is observed that there is no effect of temperature on excess molar volume for all these mixtures. The plots of deviations in viscosity vs. mole fraction (Dg vs. x1) at T = 298.15 K for methylcyclohexane + benzene, + toluene, + p-xylene, + mesitylene, or + anisole are presented in figure 2. The negative values of Dg are seen for all the mixtures over the entire mole fraction range. It is observed that the behavior is almost identical for methylcyclohexane, + toluene, + p-xylene, or + mesitylene. Large negative deviation is observed for methylcyclohexane + anisole and a slightly less negative deviation is observed for (methylcyclohexane + benzene) mixture as compared to (methylcyclohexane + anisole) mixture. In general, negative values of Dg vary as per the sequence: anisole > benzene > toluene > p-xylene > mesitylene. At higher temperatures, deviations in viscosity exhibit the

1721

-0.03

-0.04

-0.05

-0.06

0

0.2

0.4

0.6

0.8

1

x1 FIGURE 3. Plot showing the effect of temperature on Dg for methylcyclohexane + p-xylene mixture: (s) 298.15 K, (h) 303.15 K, (n) 308.15 K.

0.1

0 0

-0.02

-0.1 -1 Δ R 10 /(m ·mol )

3

-0.06

6

Δη /mPa·s

-0.04

-0.08

-0.2 -0.3 -0.4 -0.5

-0.1 -0.6

-0.12 -0.7

-0.14

0

0.2

0.4

0.6

0.8

1

x1 FIGURE 2. Plot of deviations in viscosity (Dg) against mole fraction at 298.15 K for mixtures of methylcyclohexane with (r) benzene, (j) toluene, (m) xylene, ( ) mesitylene, and (·) anisole.

-0.8

0

0.2

0.4

φ1

0.6

0.8

1

FIGURE 4. Plot of deviations in molar refraction (DR) against volume fraction at 298.15 K for mixtures of methylcyclohexane with (r) benzene, (j) toluene, (m) p-xylene, ( ) mesitylene, and (·) anisole.

1722

J.G. Baragi, M.I. Aralaguppi / J. Chem. Thermodynamics 38 (2006) 1717–1724

slightly negative and almost overlap on one another on the higher composition side. The DR curve for methylcyclohexane + p-xylene is slightly positive in the whole volume fraction range. For mixtures of (methylcyclohexane + anisole), the DR curve is sigmoidal, i.e., slightly positive for lower compositions of methylcyclohexane, but changes to slightly negative trend at about /1 = 0.5 and for higher compositions of methylcyclohexane. Deviations in excess molar refraction, DR, increase with increasing temperature for (methylcyclohexane + p-xylene) mixture as displayed in figure 5, while for others, no systematic trend is observed.

0.12

6

Function VE/106

0.08

A1

0

0.2

0.4

0.6

0.8

1

φ1 FIGURE 5. Plot showing the effect of temperature on molar refraction (DR) against volume fraction for mixtures of methylcyclohexane + pxylene at (r) 298.15 K, (j) 303.15 K, and (m), 308.15 K.

Δ K s /TPa-1

-15

0.002 0.003 0.004 0.034

DR · 106/(m3 Æ mol1)

303.15 308.15

2.565 2.429

0.852 0.852

0.774 0.758

0.034 0.026

Du/(m Æ s1) Dks/(TPa1)

298.15 298.15

0.53 8.75

2.30 0.53

0.418 0.318

1.72 55.14

(1) + Toluene (2) 1.545 0.223 1.545 0.214 1.548 0.213

0.2

0.4

φ1

0.6

0.8

1

FIGURE 6. Plot of deviations in speed of sound (Dks) against volume fraction for methylcyclohexane with (r) benzene, (j) toluene, (m) pxylene, ( ) mesitylene, and (·) anisole at 298.15 K.

0.031 0.046 0.033

0.006 0.006 0.007

Dg/(mPa Æ s)

298.15 303.15 308.15

0.216 0.189 0.178

0.016 0.015 0.011

0.028 0.003 0.019

0.002 0.001 0.001

DR · 106/(m3 Æ mol1)

298.15 303.15 308.15

0.388 0.340 0.255

0.496 0.531 0.474

0.260 0.374 0.380

0.015 0.016 0.010

Du/(m Æ s1) Dks/(TPa1)

298.15 298.15

1.55 3.60

1.04 0.93

0.334 0.567

1.16 51.53

Methylcyclohexane 298.15 VE/106 (m3 Æ mol1) 303.15 308.15

(1) + p-Xylene (2) 1.431 0.423 1.435 0.423 1.429 0.403

0.082 0.069 0.049

0.005 0.004 0.004

Dg/(mPa Æ s)

298.15 303.15 308.15

0.213 0.184 0.173

0.024 0.028 0.026

0.036 0.012 0.015

0.001 0.001 0.002

DR · 106/(m3.mol1)

298.15 303.15 308.15

0.117 0.330 0.513

0.048 0.158 0.054

0.017 0.040 0.162

0.002 0.004 0.006

Du/(m Æ s1) Dks/(TPa1)

298.15 298.15

2.48 3.37

6.85 8.35

0.579 0.404

1.93 39.66

0.175 0.092 0.145

0.009 0.008 0.009

Dg/(mPa Æ s)

298.15 303.15 308.15

0.207 0.157 0.159

0.034 0.030 0.039

0.002 0.011 0.057

0.001 0.007 0.002

DR · 106/(m3 Æ mol1)

298.15 303.15 308.15

0.506 0.026 0.467

0.237 0.105 0.233

0.095 0.185 0.006

0.006 0.136 0.007

Du/(m Æ s1) Dks /(TPa1)

298.15 298.15

-35

0

0.025 0.026 0.026

0.089 0.098 0.074 0.697

-25

-45

0.013 0.013 0.009

0.023 0.038 0.050 0.734

Methylcyclohexane (1) + Mesitylene (2) 298.15 1.492 0.546 VE/106 (m3 Æ mol1) 303.15 1.475 0.532 308.15 1.415 0.506

-5

r

0.315 0.271 0.242 2.670

15

5

A3

298.15 303.15 308.15 298.15

0.04

0.02

A2 (1) + Benzene (2) 2.417 0.003 2.440 0.003 2.458 0.010

Dg/(mPa Æ s)

0.06

0

T/(K)

Methylcyclohexane (m3 Æ mol1) 298.15 303.15 308.15

Methylcyclohexane 298.15 VE/106 (m3 Æ mol1) 303.15 308.15

3

ΔR 10 / (m ·mol-1)

0.1

TABLE 3 Estimated parameters of equation (3) for various functions of the binary mixtures at different temperatures

58.64 40.34

Methylcyclohexane VE/106 (m3 Æ mol1) 298.15 303.15 308.15

0.80 9.59

15.99 19.97

(1) + Anisole (2) 1.526 0.704 0.106 1.490 0.737 0.245 1.517 0.698 0.126 (continued on next

0.535 0.895

0.030 0.034 0.031 page)

J.G. Baragi, M.I. Aralaguppi / J. Chem. Thermodynamics 38 (2006) 1717–1724 TABLE 3 (continued) A2

A3

r

0.063 0.014 0.021

0.025 0.250 0.037

0.003 0.016 0.006

0.057

0.435

0.219

0.008

0.260 0.166

1.002 0.427

0.097 0.133

0.112 0.006

0.62 6.54

0.423 0.745

Function

T/(K)

Dg/(mPa Æ s)

298.15 303.15 308.15

0.500 0.476 0.396

DR · 106/ (m3 Æ mol1)

298.15 303.15 308.15

Du/(m Æ s1) Dks/(TPa1)

A1

298.15 298.15

2.05 32.32

3.26 164.21

The results of Dks vs. /1 at T = 298.15 K for mixtures of methylcyclohexane + benzene, + toluene, + p-xylene, + mesitylene, or + anisole are shown in figure 6. For mixtures of (methylcyclohexane + benzene, + toluene, + p-xylene, or + anisole), a negative deviation in Dks is observed whereas for methylcyclohexane (1) + mesitylene (2), the values are positive. However, the Dks values increase in the order for benzene < toluene < p-xylene < mesitylene, while the mixture with anisole shows very large negative deviation. The Dks values are almost identical for mixtures of methylcyclohexane with benzene and toluene. The results of Du vs. x1 do not show systematic behaviour and hence the graphs are not presented. All the quantities (VE, Dg, DR, Du and Dks) have been fitted to Redlich–Kister equation [21] by the method of least-squares using the Marquardt algorithm [22] equation (3) to derive the binary coefficients, Ai and standard deviation, r. In each case, the optimum number of coefficients, Aj was ascertained from an examination of the variation of the standard deviation, r, using equation (4). V E ðDY Þ ¼ x1 x2 r¼

X 

k X

Aj ðx2  x1 Þ

j1

ð3Þ

;

j¼1

1=2    2 . V Ecal or DY cal  V Eobs or DY obs =ðn  mÞ ð4Þ E

The estimated values of Aj and r for V , Dg, DR, Du, and Dks are summarized in table 3. In all cases, the best fit was obtained by using only three fitting coefficients. In all the figures, the points represent the experimental values calculated from equation (1) or equation (2), while smooth curves are drawn from the best fitted data calculated from equation (3). 4. Conclusion In this paper, an attempt has been made to measure densities, viscosities, and refractive indices at T = 298.15, 303.15, and 308.15 K, while speed of sound values at T = 298.15 K over the entire range of mixture composition of {methylcyclohexane + benzene, + toluene (methylbenzene), + p-xylene(1,4-dimethylbenzene), + mesitylene(1,3,

1723

5-trimethylbenzene) or + anisole(methoxybenzene)} mixtures. From these measured physical property data, excess molar volume, deviations in viscosity, molar refraction, speed of sound and isentropic compressibility have been calculated and correlated by a Redlich–Kister type polynomial equation to derive the coefficients and standard deviation. Only positive deviations are observed in case of excess molar volume and only negative deviations in Dg were observed for all binary mixtures of methyl cyclohexane, however, deviations in DR is negative for the binary mixtures of methylcyclohexane with benzene, toluene and mesitylene, while the reverse trend is observed for the mixture (methylcyclohexane + p-xylene) except for the mixture with anisole which shows sigmoidal trend. The deviations in isentropic compressibility are negative for the mixtures of (methylcyclohexane with benzene, toluene, p-xylene, and anisole) except for mesitylene where positive deviation is observed. Acknowledgements The authors thank the Department of Science and Technology, DST, New Delhi for the research Grant No. SP/ S1/H-09/2000. References [1] M.I. Aralaguppi, T.M. Aminabhavi, R.H. Balundgi, Fluid Phase Equilibria 71 (1992) 99–112. [2] M.I. Aralaguppi, T.M. Aminabhavi, S.B. Haragoppad, R.H. Balundgi, J. Chem. Eng. Data 37 (1992) 298–303. [3] M.I. Aralaguppi, C.V. Jadar, T.M. Aminabhavi, J. Chem. Eng. Data 44 (1999) 446–450. [4] T.M. Aminabhavi, K. Banarjee, J. Chem. Eng. Data 44 (3) (1999) 547–552. [5] J.N. Nayak, M.I. Aralaguppi, T.M. Aminabhavi, J. Chem. Eng. Data 47 (2002) 964–969. [6] G.C. Allred, J.W. Beets, W.R. Parrish, J. Chem. Eng. Data 40 (5) (1995) 1062–1066. [7] T. Avraam, G. Moumouzias, G. Ritzoulis, J. Chem. Eng. Data 43 (1) (1998) 51–54. [8] M.A. Wahab, A.M. Azhar, Mohammad A. Mottaleb, Bull. Korean Chem. Soc. 23 (7) (2002) 953–956. [9] Jagan Nath, Jai Gopal Pandey, J. Chem. Eng. Data 41 (1996) 844– 847. [10] N.G. Tsierkezos, M.M. Palaiologou, I.E. Molinou, J. Chem. Eng. Data 45 (2000) 272–275. [11] N. Swain, D. Panda, S.R. Singh, V. Chakravorty, J. Mol. Liq. 75 (3) (1998) 211–218. [12] P. Venkatesu, D. Venkasulu, M.V. Prabhakara Rao, Indian J. Pure Appl. Phys. 31 (11) (1993) 818–822. [13] T.S. Prasad, P. Venkateshwarulu, Acoust. Lett. 18 (1) (1994) 5–8. [14] J.B. Monton, M.P. Peria, V.M. Soria, J. Chem. Eng. Data 45 (4) (2000) 518–522. [15] S.C.P. Hwa, W.T. Ziegler, J. Phys. Chem. 70 (8) (1996) 2572– 2593. [16] S. Loras, J.B. Monton, F. Espana, J. Chem. Eng. Data 42 (1997) 914–918. [17] D. Venkatesulu, B.B. Goud, M.V. Prabhakara Rao, J. Chem. Eng. Data 36 (4) (1991) 473–474.

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[18] S.L. Oswal, P. Oswal, R.P. Phalak, Int. J. Thermophys. 17 (6) (1996) 1255–1267. [19] M.C.S. Subha, G. Narayanaswamy, S. Rao, Brahmaji Rao, K. Chowdoji, Indian J. Theor. Phys. 38 (3) (1990) 217–224. [20] fifth ed. J. Buckingham (Ed.), Dictionary of Organic Compounds, vol. 3, Chapman & Hall, London, England, 1982. [21] O. Redlich, A.T. Kister, Ind. Eng. Chem. 40 (1948) 345. [22] D.W. Marquardt, J. Soc. Ind. Appl. Math. 11 (1961) 431. [23] M.I. Aralaguppi, T.M. Aminabhvi, R.H. Balundgi, S. Joshi, J. Phys. Chem. 95 (1991) 5299.

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JCT 04-247