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Molecular interactions and theoretical estimation of ultrasonic speeds using scaled particle theory in binary mixtures of 3-chloroaniline and 1-alkanols (C6–C10) at different temperatures
Journal of Molecular Liquids 212 (2015) 618–628
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Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq
Molecular interactions and theoretical estimation of ultrasonic speeds using scaled particle theory in binary mixtures of 3-chloroaniline and 1-alkanols (C6–C10) at different temperatures D. Rahul a, T. Srinivasa Krishna b, M. Gowrisankar a, D. Ramachandran c,⁎ a b c
Department of Chemistry, J.K.C.C., Acharya Nagarjuna University, Guntur 522510, AP, India Department of Physics, Raylaseema University, Kurnool, Andhra Pradesh, India Department of Chemistry, Acharya Nagarjuna University, Guntur 522510, AP, India
a r t i c l e
i n f o
Article history: Received 15 July 2015 Received in revised form 25 September 2015 Accepted 26 September 2015 Available online 11 November 2015 Keywords: 3-Chloroaniline Excess thermodynamic parameters Scaled particle theory
a b s t r a c t Density (ρ), speed of sound (u) and viscosity (η) have been measured for the binary mixtures of 3-chloroaniline with 1-alkanols (1-hexanol, 1-heptanol, 1-octanol, 1-decanol) over the entire composition range at (303.15, 308.15, 313.15, and 318.15) K. By using this data, the excess volume (VE), excess isentropic compressibility (κEs ), deviation in viscosity (Δη) and excess Gibbs free energy of activation of viscous flow (G⁎E) have been calculated and were fitted to Redlich–Kister polynomial equation. The excess molar volumes, excess isentropic compressibility, deviation in viscosity and excess Gibbs energy of activation of viscous flow have been analyzed in terms of declustering and breaking of H-bonds in alkanols and alkyl chain of the 1-alkanols between unlike molecules. Moreover, the theoretical ultrasonic speeds are computed based on the scaled particle theory and compared with the experimentally measured values. © 2015 Elsevier B.V. All rights reserved.
1. Introduction It has been reported by several researchers, that not only the difference in size and shape of molecules will influence significantly the excess thermodynamic functions, but also the chemical nature of the components play an important role [1–3]. Further, the study of thermodynamic properties of liquid mixtures is of great importance because of their extensive use in garment industry, tannery industry, pharmaceutical industry and in many others. A survey of literature has shown that a few attempts have been made to investigate the excess thermodynamic properties of liquid mixtures containing 3-chloroaniline [4–6]. The main theme of the present article is to characterize the molecular interactions between 3-chloroaniline and 1-hexanol, 1-heptanol, 1-octanol and 1decanol binary systems and to subsequently evaluate the effect of chain length of 1-alkanols on excess functions of these mixtures. The liquids were chosen in the present investigation on the basis of their industrial importance. 3-Chloroaniline is used as an intermediate in the production of a number of products, including agricultural chemicals, azo dyes and pigments, bactericide or biocide and pharmaceuticals. It is dipolar and associated liquid, whereas alkanols are protic, have relatively high value of dielectric constant and are self-associated through hydrogen bond [7,8]. The degree of association in alkanols decreases ⁎ Corresponding author. E-mail addresses: [email protected] (M. Gowrisankar), [email protected] (D. Ramachandran).
http://dx.doi.org/10.1016/j.molliq.2015.09.046 0167-7322/© 2015 Elsevier B.V. All rights reserved.
as the carbon chain length increases from 1-hexanol to 1-decanol due to steric factors [9]. In this paper, we report densities (ρ), speeds of sound (u) and viscosities (η) of pure 3-chloroaniline, 1-alkanols(1hexanol, 1-heptanol, 1-octanol and 1-decanol) and those of their binary mixtures over the entire composition range at T = (303.15 K to 318.15) K. From these experimental data, the values of excess volume (VE), excess isentropic compressibility (κEs ), deviation in viscosity (Δη) and excess Gibbs free energy of activation of viscous flow (G⁎E) are calculated and discussed in terms of molecular interactions between the unlike molecules. Furthermore, theoretical ultrasonic speeds of these mixtures are evaluated by considering the different shapes of the participating components using the scaled particle theory and compared with the experimental values. 2. Experimental 2.1. Materials All the chemicals used in the present work were of analytical reagent grade produced from Merck and their purities were as follows: 3chloroaniline 99.5%, 1-hexanol 99.5%, 1-heptanol 99.5%, 1-octanol 99.5%, and 1-decanol 99.5%. Prior to experimental measurements, all the liquids were purified as described in the literature [10,11]. Further the water content of solvents used in this work was measured by Analab (MicroAqua Cal 100) Karl Fischer Titrator and Karl Fisher reagent from Merck. It can detect water content from less than 10 ppm to 100% by
D. Rahul et al. / Journal of Molecular Liquids 212 (2015) 618–628 Table 1 Provenance and purity of the materials used. Chemical name
CAS number
Supplier Purity in mass Purity (after Water fraction (as received purification) content from supplier) (%)
3-Chloroaniline 1-Hexanol 1-Heptanol 1-Octanol 1-Decanol
108–42–9 111–27–3 111–70–6 111–87–5 112–30–1
Merck Merck Merck Merck Merck
0.99 0.98 0.98 0.99 0.97
0.995 0.985 0.995 0.995 0.995
0.042 0.048 0.044 0.045 0.043
conductometric titration with dual platinum electrode and given in Table 1 along with their CAS number and purity. The purity of the sample was further confirmed by GLC single sharp peak. Before use, the chemicals were stored over 0.4 nm molecular sieves for about 72 h to remove water and were later degassed. Density (ρ), speed of sound (u) and viscosity (η) data of pure component liquids are compared with the available literature values [12–18] and were found in good agreement as shown in Table 2.
2.2. Apparatus and procedure All the binary liquid mixtures are prepared by weighing an amount of pure liquids in an electric balance (Afoset, ER-120A, and India) with a precision of ±0.1 mg by syringing each component into air-tight stopper bottles to minimize evaporation losses. The uncertainty of the mole fraction was ±1 × 10−4. After mixing the sample, the bubble-free homogeneous sample was transferred into the U-tube of the densimeter through a syringe. The density measurements were performed with a Rudolph Research Analytical digital densimeter (DDH-2911 Model), equipped with a built-in solid-state thermostat and a resident program with accuracy of temperature of 303.15 K ± 0.03 K. The uncertainty in density measurement liquid mixtures was found to be ±5 × 10−5 g/cm3. Proper calibration at each temperature was achieved with doubly distilled, deionized water and with air as standards. The
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viscosities of pure liquids and their mixtures were determined at atmospheric pressure and at temperature 303.15, 308.15, 313.15, and 318.15 K by using an Ubbelohde viscometer, which was calibrated with benzene, carbon tetrachloride, acetonitrile, and doubly distilled water. The viscometer was thoroughly cleaned and perfectly dried, is filled with the sample liquid by fitting the viscometer to about 30° from the vertical and its limbs are closed with Teflon caps to avoid the evaporation. The viscometer is kept in a transparent walled bath with a thermal stability of ±0.01 K for about 20 min to obtain thermal equilibrium. An electronic digital stopwatch with an uncertainty ±0.01 s was used for flow time measurements. The uncertainty of viscosity thus estimated was found to be ± 0.005 mPa ∙ s. The ultrasonic speed in pure liquids and in their mixtures were measured by using a multi frequency ultrasonic interferometer (M-82 Model, Mittal Enterprise, New Delhi, India) single-crystal variable path, operated at 2 MHz. from 303.15 K to 318.15 K by using a digital constant temperature water bath. The uncertainty in the measurement of ultrasonic speed is ±0.3%. The interferometer is immersed in a thermostatic water bath, whose temperature can be maintained at any desired value with an accuracy of ± 0.01 K. The present investigation has been devoted to the study of densities, speed of sounds and viscosities of binary liquid mixtures at different temperatures and at a pressure of 0.1 MPa. 3. Results and discussion The measured density of binary mixtures of 3-chloroaniline with 1akanols were given in Table 3 from 303.15 K to 318.15 K. The excess volume data of all the liquid mixtures were computed by using the following formula: VE =cm3 mol
−1
¼ ½x1 M1 þ x2 M2 =ρ–½x1 M1 =ρ1 þ x2 M2 =ρ2
ð1Þ
where x1 and x2 are the mole fractions of 3-chloroaniline and 1-alkanol respectively; M1, M2 and ρ1 and ρ2 are the molecular weights and density of components 1 and 2 respectively and ρ is the density of the
Table 2 Densities and viscosities data of pure components at different temperatures and p = 0.1 MPa. Component
Density (ρ/g·cm−3)
Speed of sound (u/m·s−1)
Viscosity (η/mPa·s)
Experimental
Literature
Experimental
Literature
Experimental
Literature
3-Chloroaniline 303.15 K 308.15 K 313.15 K 318.15 K
1.20532 1.20075 1.19602 1.19125
1.20530 [12] – 1.19600 [12] –
4.2554 3.8420 3.4302 3.0224
4.2556 [13] – – –
1517.5 1501.2 1480.3 1464.8
1517.0 [12] – 1484.0 [12] –
1-Hexanol 303.15 K 308.15 K 313.15 K 318.15 K
0.81215 0.80785 0.80449 0.80015
0.81212 [14] 0.80780 [16] 0.80451 [14] 0.80018 [15]
3.883 3.355 2.911 2.6558
3.887 [17] 3.359 [17] 2.914 [17] 2.6553 [15]
1286.2 1270.2 1252.5 1245.6
1287.90 [17] 1271.14 [17] 1254.45 [17]
1-Heptanol 303.15 K 308.15 K 313.15 K 318.15 K
0.81526 0.81172 0.80814 0.80436
0.81529 [18] 0.81174 [18] 0.80816 [18] 0.80439 [15]
5.065 4.329 3.723 3.4462
5.069 [17] 4.333 [17] 3.726 [17] 3.4466 [15]
1312.5 1295.2 1275.4 1259.5
1313.58 [17] 1293.86 [17] 1277.15 [17]
1-Octanol 303.15 K 308.15 K 313.15 K 318.15 K
0.81825 0.81472 0.81007 0.80552
0.81823 [18] 0.81474 [18] 0.81009 [18] 0.80555 [15]
6.405 5.422 4.625 4.0510
6.402 [17] 5.425 [17] 4.628 [17] 4.0512 [15]
1333.5 1312.5 1295.4 1282.5
1338.02 [17] 1314.27 [17] 1297.60 [17]
1-Decanol 303.15 K 308.15 K 313.15 K 318.15 K
0.82289 0.81954 0.81595 0.81135
0.82285 [17] 0.81952 [17] 0.81598 [17] 0.81138 [15]
9.751 8.138 6.846 5.8787
9.754 [17] 8.135 [17] 6.842 [17] 5.8783 [15]
1363.5 1344.2 1328.5 1320.5
1365.0 [17] 1346.1 [17] 1329.0 [17]
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Table 3 Density (ρ), viscosity (η) and speed of sound (u) of binary liquid mixtures of 3-chloroaniline with 1-alkanols at temperatures T = (303.15 to 318.15) K. x1
ρ/gm cm−3 303.15 K
u/m s−1
η/m Pa∙s 313.15 K
318.15 K
303.15 K
308.15 K
313.15 K
318.15 K
303.15 K
308.15 K
313.15 K
318.15 K
3-Chloroaniline + hexanol-1 0.0000 0.81215 0.80785 0.1167 0.85134 0.84694 0.2291 0.89050 0.88602 0.3375 0.92968 0.92515 0.4421 0.96889 0.96431 0.5431 1.00815 1.00353 0.6407 1.04747 1.04283 0.7350 1.08685 1.08219 0.8263 1.12632 1.12167 0.9145 1.16577 1.16115 1.0000 1.20532 1.20075
308.15 K
0.80449 0.84341 0.88235 0.92133 0.96036 0.99944 1.03860 1.07781 1.11715 1.15651 1.19602
0.80015 0.83896 0.87780 0.91671 0.95568 0.99472 1.03384 1.07302 1.11234 1.15169 1.19125
3.883 3.9047 3.9251 3.9498 3.9799 4.0143 4.0561 4.1038 4.1555 4.2054 4.2554
3.355 3.3832 3.4171 3.4539 3.4970 3.5450 3.5978 3.6538 3.7146 3.7757 3.8420
2.911 2.9393 2.9758 3.0175 3.0640 3.1149 3.1700 3.2288 3.2918 3.3575 3.4302
2.6558 2.6615 2.6812 2.7071 2.7377 2.7735 2.8141 2.8574 2.9061 2.9587 3.0224
1286.2 1295.3 1305.1 1316.1 1329.0 1344.5 1363.8 1388.4 1420.2 1461.9 1517.5
1270.2 1279.5 1289.4 1300.5 1313.6 1329.5 1349.2 1374.1 1406.0 1447.2 1501.2
1252.5 1262.2 1272.1 1282.9 1295.7 1311.3 1330.8 1355.5 1387.1 1427.7 1480.3
1245.6 1254.7 1264.3 1274.9 1287.3 1302.5 1321.4 1345.3 1375.7 1414.5 1464.8
3-Chloroaniline + heptanol-1 0.0000 0.81526 0.81172 0.1306 0.85423 0.85056 0.2526 0.8932 0.8894 0.3669 0.93217 0.92825 0.4741 0.97113 0.9671 0.5749 1.01011 1.00598 0.6698 1.04911 1.04486 0.7593 1.08809 1.08375 0.8440 1.12717 1.12273 0.9241 1.16624 1.16172 1.0000 1.20532 1.20075
0.80814 0.84683 0.88553 0.92426 0.963 1.00175 1.04051 1.07929 1.11817 1.15705 1.19602
0.80436 0.84291 0.88148 0.9201 0.95873 0.99738 1.03604 1.07473 1.11353 1.15233 1.19125
5.065 4.9228 4.7942 4.6845 4.5893 4.5091 4.4415 4.3853 4.3356 4.2917 4.2554
4.329 4.2286 4.1434 4.0723 4.0135 3.9659 3.9266 3.8954 3.8694 3.8525 3.8420
3.723 3.6469 3.5854 3.5382 3.5011 3.4727 3.4510 3.4377 3.4333 3.4316 3.4302
3.4462 3.3457 3.2688 3.2068 3.1557 3.1137 3.0789 3.0511 3.0315 3.0235 3.0224
1312.5 1320.7 1328.7 1337.8 1348.4 1361.5 1378.5 1400.5 1429.4 1467.4 1517.5
1295.2 1303.5 1312.1 1321.5 1332.5 1346.0 1363.3 1385.5 1414.3 1451.9 1501.2
1275.4 1284.4 1293.0 1302.2 1312.9 1326.4 1343.7 1366.0 1394.8 1432.1 1480.3
1259.5 1268.6 1277.3 1286.6 1297.6 1311.4 1329.1 1351.7 1380.6 1417.6 1464.8
3-Chloroaniline + octanol-1 0.0000 0.81825 0.81472 0.1441 0.85703 0.85338 0.2748 0.89582 0.89203 0.3937 0.93453 0.93062 0.5026 0.97327 0.96925 0.6025 1.01196 1.00784 0.6945 1.05064 1.04641 0.7795 1.08927 1.08495 0.8584 1.12796 1.12354 0.9317 1.16664 1.16213 1.0000 1.20532 1.20075
0.81007 0.84864 0.88724 0.92579 0.96439 1.00296 1.04152 1.08006 1.11868 1.15734 1.19602
0.80552 0.84398 0.88252 0.92101 0.95958 0.99811 1.03664 1.07518 1.11383 1.15248 1.19125
6.405 6.0592 5.7543 5.4847 5.2466 5.0339 4.8441 4.6744 4.5188 4.3792 4.2554
5.422 5.1549 4.9244 4.7232 4.5471 4.3909 4.2533 4.1308 4.0201 3.9239 3.8420
4.625 4.4092 4.2292 4.0758 3.9414 3.8233 3.7209 3.6296 3.5507 3.4831 3.4302
4.051 3.8557 3.6974 3.5642 3.4483 3.3468 3.2585 3.181 3.1143 3.0605 3.0224
1333.5 1340.9 1347.6 1355.0 1363.4 1374.4 1389.2 1409.1 1435.8 1471.4 1517.5
1312.5 1320.4 1327.8 1335.4 1344.6 1356.3 1371.8 1392.4 1419.5 1455.0 1501.2
1295.4 1303.6 1310.9 1318.5 1327.5 1339.2 1354.7 1375.2 1402.1 1437.0 1482.2
1282.5 1290.8 1297.9 1305.3 1314.6 1326.4 1341.3 1361.6 1388.5 1422.9 1466.5
3-Chloroaniline + decanol-1 0.0000 0.82289 0.81954 0.1699 0.8614 0.85791 0.3153 0.89986 0.89623 0.4411 0.93823 0.93447 0.5511 0.97656 0.97267 0.6481 1.01482 1.01080 0.7342 1.05300 1.04887 0.8112 1.09114 1.08688 0.8805 1.12925 1.12488 0.9431 1.16728 1.16282 1.0000 1.20532 1.20075
0.81595 0.85417 0.89236 0.93049 0.96856 1.00658 1.04451 1.08241 1.12031 1.15816 1.19602
0.81135 0.84947 0.88761 0.92568 0.96372 1.00171 1.03964 1.07754 1.11545 1.15333 1.19125
9.751 8.7719 7.9473 7.2472 6.6414 6.1130 5.6483 5.2375 4.8712 4.5456 4.2554
8.138 7.3581 6.7099 6.1595 5.6866 5.2745 4.9120 4.5931 4.3104 4.0614 3.8420
6.846 6.2131 5.6927 5.2536 4.8780 4.5492 4.2621 4.0101 3.7884 3.5956 3.4302
5.8787 5.3385 4.8991 4.5319 4.2169 3.9431 3.7037 3.4943 3.3114 3.1530 3.0224
1363.5 1370.0 1374.5 1378.7 1384.0 1392.3 1404.5 1422.0 1445.6 1477.0 1517.5
1344.2 1351.3 1356.2 1360.6 1366.5 1375.3 1387.9 1405.6 1429.6 1461.0 1501.2
1328.5 1335.7 1340.4 1344.7 1350.4 1358.9 1371.4 1388.7 1411.9 1441.9 1480.3
1320.0 1327.1 1331.5 1335.5 1340.8 1349.0 1360.9 1377.5 1399.7 1428.3 1464.8
Standard uncertainties s are s (ρ) = ±2 × 10−5 (g·cm−3), s (u) ±0.5 (m·s−1) s (η) = ±0.005 m Pa∙s,
mixture. The VE data of all the liquid mixtures were graphically depicted over the entire composition range in Figs. 1–4. An examination of VE data in Figs. 1–4 suggest that the property is positive over the entire composition range in the binary mixtures of 3chloroaniline with 1-alkanol at all the measured temperatures. In general, the sign of excess volume (VE) depends on the relative magnitude of contractive and expansive effects which arise due to mixing of the component liquids. The factors that cause contraction on mixing are as follows: a) Strong specific interactions; usually a kind of chemical interaction. b) Strong physical interactions of the type dipole–dipole or dipole–induced dipole interactions. c) Favorable geometrical fitting of component molecules. d) Occupation of void spaces of one component by the other due to molecular sizes of two component molecules differs by a large amount.
The factors which lead to expansion in volume on mixing the two component liquids are as follows: a) Dissociation of one component or both the components. b) Steric hindrance and geometrical mismatch of the molecules. c) Formation of weaker solute-solute and solvent–solvent bonds. A perusal of curves in Figs. 1–4 reveal that the factors which are responsible for expansion in volume were dominant in all the binary mixtures of 3-chloroaniline with 1-alkanols. The algebraic VE values of all the binary mixtures fall in the following order: 1‐hexanolb1‐heptanolb1‐octanolb1‐decanol: The above order suggests that the extent of strength of molecular interactions decreases as the chain length of 1-alkanol molecule increases. The increase in positive excess volume with increase in chain length of
D. Rahul et al. / Journal of Molecular Liquids 212 (2015) 618–628
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Fig. 1. Variation of excess volume (VE) of the binary liquid mixture of 3-chloroaniline with 1-hexanol (∎), 1-heptanol (●), 1-octanol (▲) and 1-decanol (▼) at 303.15 K.
Fig. 3. Variation of excess volume (VE) of the binary liquid mixture of 3-chloroaniline with 1-hexanol (ξ), 1-heptanol (ψ), 1-octanol ({) and 1-decanol (|) at 313.15 K.
1-alkanols implies that dipole–dipole interactions are weak in higher alkanols due to the decrease in their polarizability with increasing chain length [19]. Similar type of behavior was reported for the mixtures of N,N-dimethylformamide + 1-alkanols [20] and acetonitrile + 1-alkanols [21]. Also as the increase in the chain length of the alkanols leads to decrease in the strength of hydrogen bond [8], which facilitates the disruption of associated structures in alkanols on addition of 3chloroaniline leading to positive VE values. The influence of temperature on the VE for the systems containing 1-alkanols is slightly more positive with increasing temperature. The isentropic compressibility (κs) was calculated from the Newton–Laplace equation given below.
where, κid s is the ideal value of the isentropic compressibility and was calculated from the following equation [22]:
κs ¼ u−2 ρ−1
ð2Þ
where ρ is the density and u is the speed of sound of the binary mixtures. Further, the values of excess isentropic compressibilities (κs E) were calculated from the following relation [22]: κEs ¼ κs −κid s
κid s
¼
2 X i¼1
8 9 ! !2 2 2 2 = X X 2 < X ϕi κs;i þ TVi αi =Cp;i − T xi Vi ϕi αi = xi Cp;i : ; i¼1
i¼1
i¼1
ð4Þ where, ϕi is ideal state volume fraction of component i in mixture and is defined by the following relation, ϕi ¼ xi Vi =ðΣxi Vi Þ:
ð5Þ
T is temperature and κs,i, Vi°, αi° and Cp,i are isentropic compressibility, molar volume, coefficient of isobaric thermal expansion and molar heat capacity respectively, for pure component i. αi° is calculated from measured densities by relation, αi ¼ ½ðρ1 =ρ2 Þ−1=ðT2 −T1 Þ:
ð6Þ
ð3Þ
Values of the excess isentropic compressibility (κEs ) data for the mixtures of 3-chloroaniline with 1-alkanol were graphically depicted in Figs. 5–8 and the data were given in Table 4.
Fig. 2. Variation of excess volume (VE) of the binary liquid mixture of 3-chloroaniline with 1-hexanol (▽), 1-heptanol (○), 1-octanol (△) and 1-decanol (□) at 308.15 K.
Fig. 4. Variation of excess volume (VE) of the binary liquid mixture of 3-chloroaniline with 1-hexanol (⎕), 1-heptanol (⎕), 1-ocatnol (⎕) and 1-decanol (⎕) at 318.15 K.
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Fig. 5. Variation of excess isentropic compressibility (κEs ) of the binary liquid mixture of 3chloroaniline with 1-hexanol (∎), 1-heptanol (●), 1-octanol (▲) and 1-decanol (▼) at 303.15 K.
The (κEs ) values exhibit an inversion in sign at all the temperatures for these systems over the whole composition range. The values of excess isentropic compressibility may be interpreted in terms of two opposing effects, namely (i) loss of mutual dipolar association and difference in size and shape of unlike molecules, and (ii) dipole–dipole, dipole–induced dipole, electron donor-acceptor interactions and interstitial accommodation of the non-common component in the 3chloroaniline lattice. The former effect contributes to an increase in free length, described by Jacobson [23]. This leads to negative deviations in speed of sound and positive deviations in excess isentropic compressibility. The latter effect, on the other hand, leads to positive deviations in speed of sound and a negative deviation in excess isentropic compressibility. The sign and magnitude of the actual deviation depends upon the relative strengths of the two opposing effects [24]. It is evident from Table 4 shows that the κEs values can be explained in terms of molecular interactions and structure effects. The observed negative values of kEs may be attributed to molecular association through intermolecular hydrogen bonding between the hydrogen atom of the –NH2 group of 3-chloroaniline and the oxygen atom of the –OH group of alcohols and Positive values indicates that the breaking of interactions and corresponding disruption of molecular order in the
Fig. 6. Variation of excess isentropic compressibility (κEs ) of the binary liquid mixture of 3chloroaniline with 1-hexanol (▽), 1-heptanol (○), 1-octanol (△) and 1-decanol (□) at 308.15 K.
Fig. 7. Variation of excess isentropic compressibility (κEs ) of the binary liquid mixture of 3chloroaniline with 1-hexanol (ξ), 1-heptanol (ψ), 1-octanol ({) and 1-decanol (|) at 313.15 K.
pure component molecules [25]. Similar results have also been reported [20] for N, N-dimethyl formamide + n-alkanols (C7–C10) and toluene + n-alkanols (C5–C8) binary liquid mixtures [26]. An examination of curves in Figs. 5–8 suggests that both the factors are competing with each other to varying degrees in the mixtures containing 3-chloroaniline and 1-alkanols. The algebraic values of all the binary mixtures will obey the following order: 1‐hexanolb1‐heptanolb1‐octanolb1‐decanol: The above order indicates the strength of interactions between component molecules decreases due to decrease in polarizability of alkanol molecules. Viscosity data for binary mixtures of 3-chloroaniline with 1-alkanols is given in Table 3 along with excess Gibbs energy of activation of viscous flow (G⁎E) and these were calculated by the following equations: Δη=mPa s ¼ η–½x1 η1 þ x2 η2 −1
GE =J mol
¼ RT½ ln ηV−ðx1 lnη1 V1 þ x2 ln η2 V2 Þ
ð7Þ ð8Þ
Fig. 8. Variation of excess isentropic compressibility (κEs ) of the binary liquid mixture of 3chloroaniline with 1-hexanol (⎕), 1-heptanol (⎕), 1-ocatnol (⎕) and 1-decanol (⎕) at 318.15 K.
D. Rahul et al. / Journal of Molecular Liquids 212 (2015) 618–628
where η1, η2, η, V1, V2, and V are the viscosity of components 1, 2 and mixture and molar volumes of component 1, 2, and mixture respectively. R is the gas constant and T the absolute temperature. The viscosity data of all the liquid mixtures are graphically in Figs. 9–12. The negative trend in Δη for all the mixtures of 3-chloroaniline with 1alkanols (Table 4) indicate that the viscosities of associates formed between unlike molecules are relatively less than those of pure components. Further, according to the view of Fort and Moore [27], negative Δη values are ascribed due to an increase in the dispersion forces in the mixtures. Also deviation in viscosity data in the present investigation depends on the following factors: 1) The geometrical difference in size and shape of component molecules and the loss of dipolar association in pure component may contribute decrease in viscosity and 2) specific interactions between unlike components like hydrogen bond formation and charge transfer complexes may cause for increase in viscosity in mixtures than in pure components.
623
The first factor produces negative deviation in viscosity, while the second factor leads to contribute positive deviation in viscosity. An examination of deviation in viscosity data in Figs. 9–12 reveal that the factor which is responsible for deviation in viscosity is dominant in all the binary mixtures of 3-chloroaniline with 1-alkanols. Similar negative deviations have been reported for ethanol + cyclohexane and 1hexanol + hydrocarbons [28,29]. The variation of VE, κEs and Δη with mole fraction were fitted to the Redlich–Kister polynomial equation [30] of the type, h i YE ¼ x1 x2 a0 þ a1 ðx1 −x2 Þ þ a2 ðx1 −x2 Þ2
ð9Þ
where YE is VE or κEs or Δη. The values of a0, a1 and a2 are the coefficients of the polynomial equation and the corresponding standard deviations, σ obtained by the method of least-squares with equal weights assigned
Table 4 Excess molar volume (VEm), excess isentropic compressibility (κEs ) and deviation in viscosity (Δη) of binary liquid mixtures of 3-chloroaniline with 1-alkanols at temperatures T = (303.15 to 318.15) K. x1
VEm/cm3 ∙mol−1 303.15 K
308.15 K
κEs /TPa−1
Δη/mPa∙s
313.15 K
318.15 K
303.15 K
308.15 K
313.15 K
318.15 K
303.15 K
308.15 K
313.15 K
318.15 K
3-Chloroaniline + hexanol-1 0.0000 0.0000 0.0000 0.1167 0.0202 0.0232 0.2291 0.0395 0.0440 0.3375 0.0546 0.0583 0.4421 0.0643 0.0684 0.5431 0.0677 0.0725 0.6407 0.0639 0.0685 0.7350 0.0539 0.0587 0.8263 0.0392 0.0433 0.9145 0.0206 0.0234 1.0000 0.0000 0.0000
0.0000 0.0279 0.0483 0.0631 0.0721 0.0759 0.0725 0.0634 0.0479 0.0268 0.0000
0.0000 0.0307 0.0530 0.0675 0.0762 0.0796 0.0768 0.0681 0.0521 0.0312 0.0000
0.000 −5.750 −8.189 −8.111 −6.310 −3.567 −0.627 1.813 3.111 2.682 0.000
0.000 −6.242 −8.893 −8.949 −7.298 −4.736 −1.963 0.398 1.813 1.814 0.000
0.000 −7.104 −9.920 −9.830 −7.963 −5.233 −2.384 −0.011 1.413 1.512 0.000
0.000 −7.097 −10.130 −10.326 −8.709 −6.137 −3.322 −0.859 0.769 1.162 0.000
0.000 −0.022 −0.043 −0.059 −0.068 −0.071 −0.065 −0.053 −0.035 −0.018 0.000
0.000 −0.029 −0.049 −0.065 −0.073 −0.074 −0.069 −0.059 −0.043 −0.025 0.000
0.000 −0.032 −0.054 −0.069 −0.077 −0.078 −0.074 −0.064 −0.048 −0.028 0.000
0.000 −0.037 −0.059 −0.072 −0.080 −0.081 −0.077 −0.068 −0.053 −0.032 0.000
3-Chloroaniline + heptanol-1 0.0000 0.0000 0.0000 0.1306 0.0275 0.0290 0.2526 0.0470 0.0506 0.3669 0.0622 0.0658 0.4741 0.0695 0.0738 0.5749 0.0707 0.0748 0.6698 0.0654 0.0702 0.7593 0.0563 0.0604 0.8440 0.0408 0.0453 0.9241 0.0217 0.0247 1.0000 0.0000 0.0000
0.0000 0.0330 0.0551 0.0693 0.0766 0.0782 0.0740 0.0647 0.0486 0.0284 0.0000
0.0000 0.0355 0.0593 0.0745 0.0805 0.0825 0.0787 0.0686 0.0516 0.0312 0.0000
0.000 −5.640 −7.339 −6.838 −4.672 −1.732 0.963 3.045 3.800 2.913 0.000
0.000 −5.865 −8.123 −7.764 −5.753 −2.972 −0.186 1.968 2.974 2.421 0.000
0.000 −6.915 −9.254 −8.645 −6.376 −3.448 −0.633 1.489 2.493 2.066 0.000
0.000 −7.249 −9.698 −9.174 −7.028 −4.256 −1.580 0.486 1.586 1.473 0.000
0.000 −0.028 −0.053 −0.067 −0.074 −0.073 −0.066 −0.052 −0.037 −0.020 0.000
0.000 −0.033 −0.057 −0.071 −0.077 −0.076 −0.070 −0.059 −0.045 −0.024 0.000
0.000 −0.037 −0.061 −0.075 −0.080 −0.079 −0.073 −0.061 −0.041 −0.020 0.000
0.000 −0.042 −0.065 −0.077 −0.083 −0.082 −0.077 −0.068 −0.053 −0.029 0.000
3-Chloroaniline + octanol-1 0.0000 0.0000 0.0000 0.1441 0.0339 0.0345 0.2748 0.0543 0.0570 0.3937 0.0675 0.0716 0.5026 0.0735 0.0770 0.6025 0.0737 0.0771 0.6945 0.0674 0.0709 0.7795 0.0582 0.0606 0.8584 0.0431 0.0461 0.9317 0.0228 0.0261 1.0000 0.0000 0.0000
0.0000 0.0370 0.0610 0.0743 0.0801 0.0803 0.0749 0.0655 0.0497 0.0269 0.0000
0.0000 0.0430 0.0657 0.0788 0.0841 0.0849 0.0806 0.0705 0.0526 0.0322 0.0000
0.000 −5.360 −6.799 −5.800 −3.124 −0.014 2.733 4.499 4.777 3.149 0.000
0.000 −5.924 −7.650 −6.595 −4.027 −0.993 1.709 3.496 3.963 2.848 0.000
0.000 −6.616 −8.466 −7.359 −4.724 −1.652 1.071 2.896 3.458 2.533 0.000
0.000 −7.107 −8.992 −7.871 −5.608 −2.700 0.417 2.317 2.664 1.909 0.000
0.000 −0.036 −0.060 −0.074 −0.078 −0.076 −0.068 −0.055 −0.041 −0.023 0.000
0.000 −0.039 −0.063 −0.077 −0.081 −0.079 −0.071 −0.060 −0.046 −0.026 0.000
0.000 −0.044 −0.067 −0.079 −0.083 −0.082 −0.074 −0.064 −0.049 −0.029 0.000
0.000 −0.047 −0.071 −0.082 −0.086 −0.084 −0.078 −0.068 −0.054 −0.032 0.000
3-Chloroaniline + decanol-1 0.0000 0.0000 0.0000 0.1699 0.0419 0.0433 0.3153 0.0633 0.0666 0.4411 0.0741 0.0774 0.5511 0.0769 0.0803 0.6481 0.0751 0.0789 0.7342 0.0679 0.0709 0.8112 0.0563 0.0601 0.8805 0.0419 0.0449 0.9431 0.0240 0.0243 1.0000 0.0000 0.0000
0.0000 0.0473 0.0713 0.0806 0.0838 0.0816 0.0764 0.0654 0.0489 0.0270 0.0000
0.0000 0.0530 0.0747 0.0852 0.0876 0.0866 0.0802 0.0691 0.0523 0.0289 0.0000
0.000 −5.427 −6.111 −4.063 −0.806 2.375 4.730 5.759 5.452 3.455 0.000
0.000 −6.041 −6.848 −4.659 −1.470 1.644 4.055 5.268 4.900 3.150 0.000
0.000 −6.562 −7.450 −5.357 −2.150 0.967 3.295 4.455 4.293 2.789 0.000
0.000 −7.034 −8.087 −6.072 −2.935 0.146 2.477 3.715 3.713 2.455 0.000
0.000 −0.045 −0.071 −0.080 −0.081 −0.076 −0.068 −0.055 −0.041 −0.023 0.000
0.000 −0.050 −0.074 −0.084 −0.084 −0.079 −0.072 −0.060 −0.045 −0.025 0.000
0.000 −0.053 −0.076 −0.086 −0.086 −0.083 −0.076 −0.065 −0.050 −0.029 0.000
0.000 −0.055 −0.079 −0.087 −0.088 −0.084 −0.078 −0.067 −0.052 −0.032 0.000
624
D. Rahul et al. / Journal of Molecular Liquids 212 (2015) 618–628
Fig. 9. Variation of deviation in viscosity (Δη) of the binary mixture of 3-chloroaniline with 1-hexanol (∎), 1-heptanol (●), 1-octanol (▲) and 1-decanol (▼) at 303.15 K.
to each point are calculated. The standard deviation (σ) and are defined as follows: 1=2 2 σ YE ¼ ∑ YEobs −YEcal =ðn−mÞ
ð10Þ
where n is the total number of experimental points and m is the number of coefficients. The values of a0, a1 and a2 are the coefficients is determined by a multiple-regression analysis on the least square method and summarized along with the standard deviations between the experimental and fitted values of VE, κEs , and Δη are presented in Table 5. An examination of curves Figs. 13–16 suggests that the excess Gibbs free energy of activation of viscous flow (G⁎E) are negative for binary mixtures 3-chloroaniline with 1-hexanol + 1-heptanol while for the remaining mixtures the excess Gibbs free energy of activation of viscous flow (G⁎E) is positive over the entire composition range at all temperatures. The negative values of excess Gibbs free energy of activation of viscous flow for the binary systems investigated suggest that the breaking of the self-associated molecules and weak interactions between unlike molecules, decrease systematically with an increased in chain length of alcohol. With increasing in chain length of alcohols, hydrogen bonding interaction of 3-chloroaniline with 1-alkanols is weaker due to decreased polarizability and positive values indicate that the specific
Fig. 10. Variation of deviation in viscosity (Δη) of the binary liquid mixture of 3chloroaniline with 1-hexanol (▽), 1-heptanol (○), 1-octanol (△) and 1-decanol (□) at 308.15 K.
Fig. 11. Variation of deviation in viscosity (Δη) of the binary liquid mixture of 3chloroaniline with 1-hexanol (ξ), 1-heptanol (ψ), 1-octanol ({) and 1-decanol (|) at 313.15 K.
interactions through of hydrogen bonding (O–H….N–H) resulting in the formation of complexes between the component molecules. Grunberg–Nissan provided the following empirical equation containing one adjustable parameter [31]. The equation is ln η ¼ x1 lnη1 þ x2 ln η2 þ x1 x2 d12
ð11Þ
where d12 may be regarded as a parameter proportional to the interchange energy also an approximate measure of the strength of the interaction between the components. Katti and Chaudhri derived the below equation [32]. ln ηV ¼ x1 ln V1 η1 þ x2 ln V2 η2 þ x1 x2 Wvis=RT
ð12Þ
where Wvis/RT is an interaction term. Hind et al., suggested the following equation [33], η ¼ x21 η1 þ x22 η2 þ 2x1 x2 H12
ð13Þ
where H12 is Hind interaction parameter and is attributed to unlike pair interactions.
Fig. 12. Variation of deviation in viscosity (Δη) of the binary liquid mixture of 3chloroaniline with 1-hexanol (⎕), 1-heptanol (⎕), 1-ocatnol (⎕) and 1-decanol (⎕) at 318.15 K.
D. Rahul et al. / Journal of Molecular Liquids 212 (2015) 618–628
625
Table 5 Coefficients of Redlich–Kister equation and standard deviation (σ) values. Binary mixtures 303.15 K 3-Chloroaniline + hexanol-1 3-Chloroaniline + heptanol-1 3-Chloroaniline + octanol-1 3-Chloroaniline + decanol-1 308.15 K 3-Chloroaniline + hexanol-1 3-Chloroaniline + heptanol-1 3-Chloroaniline + octanol-1 3-Chloroaniline + decanol-1 313.15 K 3-Chloroaniline + hexanol-1 3-Chloroaniline + heptanol-1 3-Chloroaniline + octanol-1 3-Chloroaniline + decanol-1 318.15 K 3-Chloroaniline + hexanol-1
3-Chloroaniline + heptanol-1 3-Chloroaniline + octanol-1 3-Chloroaniline + decanol-1
Functions
ao
σ
a1
a2
VE/cm3·mol−1 0.268 Δη/mPa·s −0.282 κEs /TPa−1 −19.26 VE/cm3·mol−1 0.281 Δη/mPa∙s −0.296 −1 E κs /TPa −15.73 VE/cm3·mol−1 0.294 Δη/mPa·s −0.308 κEs /TPa−1 −12.35 VE/cm3·mol−1 0.300 Δη/mPa∙s −0.319 −1 E κs /TPa −9.758
0.047 −0.016 55.79 0.048 −0.021 55.41 0.054 −0.030 57.19 0.062 −0.036 60.50
−0.062 0.098 10.64 −0.013 0.047 13.87 0.031 −0.020 18.50 0.116 −0.077 26.13
0.001 0.066 0.001 0.001 0.001 0.001 0.081 0.001 0.001 0.119 0.001 0.002 0.040
VE/cm3·mol−1 Δη/mPa∙s κEs /TPa−1 VE/cm3·mol−1 Δη/mPa∙s κEs /TPa−1 VE/cm3·mol−1 Δη/mPa∙s κEs /TPa−1 VE/cm3 mol−1 Δη/mPa∙s κsE/TPa−1
0.285 −0.294 −23.61 0.297 −0.308 −20.38 0.305 −0.318 −16.40 0.317 −0.332 −12.33
0.050 −0.020 52.16 0.060 −0.028 52.75 0.067 −0.039 56.36 0.069 −0.034 60.66
−0.038 −0.002 5.198 0.005 −0.013 14.10 0.052 −0.062 16.76 0.091 −0.119 22.07
0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.002 0.001 0.001 0.002 0.052
VE/cm3·mol−1 Δη/mPa∙s κsE/TPa−1 VE/cm3·mol−1 Δη/mPa∙s κEs /TPa−1 VE/cm3·mol−1 Δη/mPa∙s κEs /TPa−1 VE/cm3 mol−1 Δη/mPa∙s κEs /TPa−1
0.299 0.047 0.008 −0.311 −0.024 −0.030 −25.85 55.37 −1.036 0.308 0.061 0.052 −0.329 0.007 0.034 −22.67 56.26 6.123 0.321 0.069 0.060 −0.326 −0.033 −0.116 −19.19 57.40 12.66 0.324 0.076 0.141 −0.337 −0.049 −0.181 −14.96 59.61 17.95
0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.002 0.004
VE/cm3· mol−1 Δη/mPa∙s κEs /TPa−1 VE/cm3·mol−1 Δη/mPa∙s κEs /TPa−1 VE/cm3·mol−1 Δη/mPa∙s κEs /TPa−1 VE/cm3·mol−1 Δη/mPa∙s κEs /TPa−1
0.314
0.055
0.048
0.001
−0.321 −29.25 0.325 −0.332 −25.43 0.347 −0.336 −21.65 0.347 −0.339 −17.98
−0.022 52.40 0.064 −0.022 53.27 0.076 −0.039 55.57 0.087 −0.051 58.37
−0.093 0.982 0.072 −0.096 1.739 0.068 −0.159 6.659 0.144 −0.228 15.27
0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.238 0.001 0.001 0.002
Fig. 13. Excess Gibbs energy of activation of viscous flow (G⁎E) of the binary liquid mixture of 3-chloroaniline with 1-hexanol (∎), 1-heptanol (●), 1-octanol (▲) and 1-decanol (▼) at 303.15 K.
The interaction parameter d12 is positive for binary systems. Nigam and Mahl concluded from the study of binary mixtures that (i) if Δη N 0, d12 N 0 and magnitude of both are large then strong specific interaction (ii) if Δ η b 0, d12 N 0 then weak specific interaction (iii) if Δ η b 0, d12 b 0 magnitude of both are large then the dispersion force would be dominant. Fort and Moore [36] reported that for any binary liquid mixture, a positive value of d12 indicates the presence of specific interactions and a negative value of d12 indicates the presence of weak interactions between the unlike molecules. On this basis, we can say that there is a strong interaction in the binary system of 3-chloroaniline with 1-octanol and 1-decanol. Interaction parameter Wvis/RT shows almost the same trend as that of d12. In fact, one could say that the parameters d12 and Wvis/RT exhibit almost similar behavior, which is not unlikely in view of logarithmic nature of both equations. The values of interaction parameters Tamara and Kurata (T12) and Hind et al. (H12) do not differ appreciably from each other. This is in agreement with the view put forward by Fort and Moore [36] in regard to the nature of parameters T12 and H12.
The equation given by Heric and Brewer is as follows [34]: lnη ¼ x1 lnη1 þ x2 ln η2 þ x1 lnM1 þ x2 ln M2 – ln ðx1 M1 þx2 M2 Þ2x1 x2 Δ12
ð14Þ
where Δ12 is the interaction term and other symbols have their usual meaning. The one-parameter equation due to Tamura and Kurata [35] gave the equation of the form η ¼ x1 Φ1 η1 þ x2 Φ2 η2 þ 2ðx1 x2 Φ1 Φ2 Þ1=2 T12
ð15Þ
where Φ1 and Φ2 are the volume fractions of components 1 and 2, respectively, T12 is Tamura and Kurata constant.
Fig. 14. Excess Gibbs energy of activation of viscous flow (G⁎E) of the binary liquid mixture of 3-chloroaniline with 1-hexanol (□), 1-heptanol (○), 1-octanol (△) and 1-decanol (▽) at 308.15 K.
626
D. Rahul et al. / Journal of Molecular Liquids 212 (2015) 618–628 Table 6 Molecular assignment for different shapes. Shape Sphere Cube Tetrahedron Discs Disc A Disc B Disc C Disc D
Fig. 15. Excess Gibbs energy of activation of viscous flow (G⁎E) of the binary liquid mixture of 3-chloroaniline with 1-hexanol (ξ), 1-heptanol (ψ), 1-octanol ({) and 1-decanol (|) at 313.15 K.
3.1. Scaled particle theory The theoretical ultrasonic speed of binary mixtures may be estimated based on some empirical, semiempirical and statistical models such as Free Length Theory (FLT), Collision Factor Theory (CFT), Nomoto relation, Vandeel Vangeal relation, etc. for the binary mixtures [37,38]. The common drawback of these theoretical models is that the shapes of the participating species have not been taken into consideration. In the scaled particle theory (SPT) [39] different shapes, such as spherical, cube, tetrahedral, disc A, disc B, disc C and disc D, of the participating components are considered and when the participating components have the correct shapes the theoretical ultrasonic speed estimated based on this model will give values close to the experimental values. Generally, the chemical structure of a liquid molecule is known but no definite shape has been attached to it [40]. Ghosh et al. [40] have used the scaled particle theory for the binary mixtures of 1,1,1trichloroethane with 1-alkanols by considering different shapes such as spherical, cubical and tetrahedral. Kalidoss and Srinivasamoorthy [41] have extended the SPT for some binary mixtures and ternary liquid mixtures by considering seven shapes of the individual components that includes spherical, cube, tetrahedron, disc A, disc B, disc C and
Size
S
R
Radius = a Side = l Side = l
VH 2
A 3l/4
pffiffiffi 3l ; arctan 2=2π Radius = a and depth l l=a (π + 1)a/4 l = a/4 (π + 0.25)a/4 l = a/2 (π + 0.50)π/4 l = a/10 (π + 0.10)a/4
4πa 6l2 pffiffiffi 2 3l
4πa3/3 l3 pffiffiffi 3 ð 2=12Þl
4πa2 5πa2/2 3πa2 11πa2/5
πa3 πa3/4 πa3/2 πa3/10
disc D (the shapes are assigned by some characteristic parameters as given in Tables 6 and 7). In this paper, the theoretical ultrasonic speeds of the binary mixtures are estimated by assigning the above said seven shapes to the participating components and compared them with experimental speeds. Only when the participating molecules have particular shapes the theoretical values closely agrees with the experimental ultrasonic speed, which will be determined by chi-square fitting, χ2 [42]. The equation of state of fluid in the scaled particle theory is p 1 þ η þ η2 ¼ ρN kB T ð1−ηÞ2
ð16Þ
whereη = VHρN, VH is the hard core volume, ρN is the number density, and the other quantities have usual meanings [40].The SPT for mixtures of hard convex (not necessarily spherical) molecules gives the equation for mixture as follows [40,41]: p 1 ABρN B2 Cρ2N ¼ þ þ 2 ρN kB T ð1−VρN Þ ð1−VρN Þ 3ð1−VρN Þ3 X X X X 2 A¼ xi R i ; B ¼ xi Si ; C ¼ xi Ri ; V ¼ xi VH :
ð17Þ
Ri , Si and VH are the mean radius of curvature, surface area and volume, respectively, of a molecule of species i, ρN is the number density of mixture molecule, and xi is the mole fraction. Relating this with the equation γðdp=dρÞT ¼ u2
ð18Þ
where u is the ultrasonic speed, ρ is molecular density, and γ is the ratio of specific heats, we get Mu2 1 2ABρN B2 Cρ2N ¼ þ þ : γRT ð1−VρN Þ2 ð1−VρN Þ3 ð1−VρN Þ4
ð19Þ
Eq. (19) is used to evaluate the ultrasonic speed in the binary mixtures.
Table 7 Shape parameters.
Fig. 16. Excess Gibbs energy of activation of viscous flow (G⁎E) of the binary liquid mixture of 3-chloroaniline with 1-hexanol (⎕), 1-heptanol (⎕), 1-ocatnol (⎕) and 1-decanol (⎕) at 318.15 K.
Shape
X ¼ RS=VH
pffiffiffiffiffiffiffi Y ¼ R= 3 VH
Z ¼ S=R
Sphere Cube Tetrahedron Disc A Disc B Disc C Disc D
3.0000 4.5000 6.7035 4.1416 8.4790 5.4624 17.8274
0.6204 0.7500 0.9303 0.7070 0.9190 0.7832 1.1920
12.5664 10.6666 8.3247 11.7218 10.9244 11.3712 10.5253
2
D. Rahul et al. / Journal of Molecular Liquids 212 (2015) 618–628
627
Table 8 Ultrasonic speeds computed theoretically using SPT with behavior shape having least chi-square fit and experimentally measured values of all binary mixtures at different temperatures. x1
303.15 K u exp
308.15 K ucal
u exp
Disc D + disc A
313.15 K ucal
u exp
Disc D + disc A
318.5 K ucal
u exp
Disc D + disc A
ucal Disc D + disc A
3-Chloroaniline + 1-hexanol 0.0000 1286.20 0.1167 1295.30 0.2291 1305.10 0.3375 1316.10 0.4421 1329.00 0.5431 1344.50 0.6407 1363.80 0.7350 1388.40 0.8263 1420.20 0.9145 1461.90 1.0000 1517.50 χ2
1286.62 1294.57 1301.50 1316.10 1330.17 1345.58 1364.27 1388.30 1419.99 1461.90 1517.42 0.0753
1270.20 1279.50 1289.40 1300.50 1313.60 1329.50 1349.20 1374.10 1406.00 1447.20 1501.20
1270.14 1278.42 1288.46 1300.47 1314.66 1331.37 1351.01 1374.10 1401.40 1447.80 1501.66 0.0705
1252.5 1262.2 1272.1 1282.9 1295.7 1311.3 1330.8 1355.5 1387.1 1427.7 1480.3
1252.44 1260.56 1270.48 1282.39 1296.51 1313.12 1332.62 1355.50 1382.46 1424.30 1480.31 0.0657
1245.6 1254.7 1264.3 1274.9 1287.3 1302.5 1321.4 1345.3 1375.7 1414.5 1464.8
1245.55 1253.44 1263.10 1274.69 1288.41 1304.50 1323.32 1345.30 1371.07 1414.34 1464.25 0.0616
3-Chloroaniline + 1-heptanol 0.0000 1312.5 0.1306 1320.7 0.2526 1328.7 0.3669 1337.8 0.4741 1348.4 0.5749 1361.5 0.6698 1378.5 0.7593 1400.5 0.8440 1429.4 0.9241 1467.4 1.0000 1517.5 χ2
1312.44 1319.27 1327.47 1337.33 1349.17 1363.34 1380.28 1400.50 1427.75 1467.94 1517.36 0.3951
1295.2 1303.5 1312.1 1321.5 1332.5 1346.0 1363.3 1385.5 1414.3 1451.9 1501.2
1295.14 1301.67 1309.99 1320.27 1332.68 1347.47 1364.94 1385.50 1413.77 1450.46 1501.66 0.1156
1275.4 1284.4 1293.0 1302.2 1312.9 1326.4 1343.7 1366.0 1394.8 1432.1 1480.3
1275.34 1281.89 1290.25 1300.60 1313.08 1327.94 1345.45 1366.00 1390.16 1431.59 1480.31 0.1101
1277.3 1268.6 1277.3 1286.6 1297.6 1311.4 1329.1 1351.7 1380.6 1417.6 1464.8
1259.44 1265.86 1274.28 1284.82 1297.62 1312.87 1330.80 1351.70 1378.02 1416.28 1464.25 0.1201
3-Chloroaniline + 1-octanol 0.0000 1333.5 0.1441 1340.9 0.2748 1347.6 0.3937 1355.0 0.5026 1363.4 0.6025 1374.4 0.6945 1389.2 0.7795 1409.1 0.8584 1435.8 0.9317 1471.4 1.0000 1517.5 2 χ
1333.44 1339.64 1346.40 1354.13 1363.41 1374.95 1389.74 1409.10 1434.91 1469.75 1517.50 0.2245
1312.5 1320.4 1327.8 1335.4 1344.6 1356.3 1371.8 1392.4 1419.5 1455.0 1501.2
1312.44 1319.03 1326.30 1334.64 1344.60 1356.87 1372.38 1392.40 1418.70 1453.75 1501.20 0.2149
1295.4 1303.6 1310.9 1318.5 1327.5 1339.2 1354.7 1375.2 1402.1 1437.0 1482.2
1295.34 1301.87 1309.13 1317.50 1327.51 1339.81 1355.31 1375.20 1401.22 1435.71 1482.20 0.2074
1282.5 1290.8 1297.9 1305.3 1314.6 1326.4 1341.3 1361.6 1388.5 1422.9 1466.5
1282.44 1289.06 1296.36 1304.72 1314.65 1326.81 1342.06 1361.60 1387.12 1420.93 1466.50 0.2046
3-Chloroaniline + 1-decanol 0.0000 1363.5 0.1699 1370.0 0.3153 1374.5 0.4411 1378.7 0.5511 1384.0 0.6481 1392.3 0.7342 1404.5 0.8112 1422.0 0.8805 1445.6 0.9431 1477.0 1.0000 1517.5 χ2
1363.44 1367.06 1371.44 1376.95 1384.03 1393.30 1405.57 1422.00 1444.25 1474.78 1517.50 0.1618
1344.2 1351.3 1356.2 1360.6 1366.5 1375.3 1387.9 1405.6 1429.6 1461.0 1501.2
1344.14 1348.19 1353.02 1358.98 1366.50 1376.20 1388.85 1405.60 1428.08 1458.68 1501.20 0.1538
1328.5 1335.7 1340.4 1344.7 1350.4 1358.9 1371.4 1388.7 1411.9 1441.9 1480.3
1328.44 1332.36 1337.09 1342.96 1350.40 1359.96 1372.38 1388.70 1410.44 1439.81 1480.30 0.1491
1320.0 1327.1 1331.5 1335.5 1340.8 1349.0 1360.9 1377.5 1399.7 1428.3 1464.8
1319.94 1323.61 1328.08 1333.68 1340.80 1349.96 1361.87 1377.50 1398.29 1426.29 1464.80 0.1457
For the case of pure liquids, Eq. (19) is modified by introducing the dimensionless shape parameter, X ¼ RS=VH and η = VHρN Mu2 ½ðX−1Þη2 ¼ γRT ð1−ηÞ4
ð20Þ
Its solution is obtained as [41] qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi η ¼ K− K2 þ L−1 where K = 1 + L(X − 1)/2 and L ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi γRT=Mu2. The mean radius and the 1=3
surface area of a molecule can be written as R ¼ YVH and S ¼ ZR
2
where Y and Z are the parameters related to the shape of the molecule. If the molecule is assigned different shapes (Table 6), the corresponding values of shape parameters, X, Y and Z, can be calculated (Table 7). In the present investigation, the theoretical speed based on SPT is computed for the 3-chloroaniline + 1-alkanols binary mixtures by considering different shapes, viz. sphere, cube, tetrahedron, disc A, disc B, disc C and disc D, for both the participating components. Hence for a binary mixture there are 49 combinations of shapes at a particular temperature. By using χ2 test, the best-fitting combination of shapes of the participating component molecules is obtained. Chi-square test χ2 can be used to test the goodness of fitting, which enables us to find whether the deviations of the theoretical values from the experimental ones are due to chance or really due to the inadequacy of the theory to fit the data. The theoretical ultrasonic speeds based on SPT for the mixtures
628
D. Rahul et al. / Journal of Molecular Liquids 212 (2015) 618–628
Table 9 Volume interaction (a and b) and hard core correction (C and D) parameters. Binary mixture
3-Chloroaniline + 1-hexanol 3-Chloroaniline + 1-heptanol 3-Chloroaniline + 1-octanol 3-Chloroaniline + 1-decanol Binary mixture
3-Chloroaniline + 1-hexanol 3-Chloroaniline + 1-heptanol 3-Chloroaniline + 1-octanol 3-Chloroaniline + 1-decanol
303.15 K
308.15 K
a (C)
b (D)
Sign of VEmax
a (C)
b (D)
Sign of VEmax
−0.072 (−0.2424) −0.201 (−0.5121) −0.150 (−0.2520) −0.199 (−0.3570)
−0.057 (−0.8363) −0.253 (−0.2325) −0.155 (−0.1627) −0.251 (−0.1930)
Negative Negative Negative Negative
−0.073 (−0.0731) −0.117 (−0.1779) −0.150 (−0.2559) −0.199 (−0.3590)
−0.058 (−0.0293) −0.107 (−0.0476) −0.156 (−0.1576) −0.251 (−0.1910)
Negative Negative Negative Negative
a (C)
b (D)
Sign of VEmax
a (C)
b (D)
Sign of VEmax
−0.072 (−0.0738) −0.117 (−0.1800) −0.152 (−0.2635) −0.199 (−0.3650)
−0.058 (−0.0262) −0.107 (−0.0445) −0.157 (−0.1558) −0.251 (−0.1870)
Negative Negative Negative Negative
−0.130 (−0.0701) −0.117 (−0.1915) −0.153 (−0.2658) −0.201 (−0.3740)
−0.110 (−0.0213) −0.107 (−0.0376) −0.158 (−0.1565) −0.253 (−0.1870)
Negative Negative Negative Negative
313.15 K
318.15 K
having liquids belonging to 1-alkanols with 3-chloroaniline at different temperatures are given in Table 8 for the minimum values of χ2. From Table 8, it is seen that for all binary mixtures takes the shapes of disc D + disc A, the ultrasonic speed estimated based on SPT is found to be very close to the experimental values. Thus our theoretical analysis using SPT has proved that the temperature has no effect on the shapes of the participating components in all four binary systems [43,44]. In addition, the expansion of volume in the participating molecules can be discussed using the volume interaction parameters a and b given in Table 9. 4. Conclusions In this paper, density, speed of sound and viscosity data is reported for binary mixtures of 3-chloroaniline and 1-alkanols (1-hexanol, 1heptanol, 1-octanol, and 1-decanol) at different temperatures. The excess parameter studies such as VE, κEs , and Δη indicate that the rupture of hydrogen bonded chain of the dipolar interaction between like molecules exceed the intermolecular interaction through dipole–dipole and hydrogen bonding between 3-chloroaniline and 1-alkanol molecules. This behavior is characteristic for systems containing an associated component. Furthermore, theoretical ultrasonic speeds of these mixtures are evaluated by considering the different shapes of the participating components using the scaled particle theory. References [1] M. Chandra Sekhar, M. Gowri Sankar, A. Venkatesulu, http://dx.doi.org/10.1016/j. molliq.2015.04.034 [2] G. Praveen Chand, M. Gowri Sankar, P.N.V.V.L. Prameela Rani, C. Rambabu, J. Mol. Liq. 201 (2015) 1–9. [3] T. Srinivasa Krishna, M. Gowri Sankar, K.T.S.S. Raju, S. Govardhan Rao, B. Munibhadrayya, J. Mol. Liq. 206 (2015) 350–358. [4] M.A. Saleh, M. Habibullah, M. Shamsuddin Ahmed, M. Ashraf Uddin, S.M.H. Uddin, M. Afsar Uddin, F.M. Khan, Phys. Chem. Liq. 43 (2005) 139–148. [5] V.K. Sharma, P. Paul Singh, S. Maken, J. Chem. Eng. Data 39 (1994) 238–240. [6] V. Pandiyan, S.L. Oswal, P. Vasanthrani, Thermochim. Acta 524 (2011) 140–150. [7] Y. Marcus, Introduction to Liquid State Chemistry, Wiley Intersciences, New York, 1977.
[8] G.A. Krestov, Thermodynamics of Solvation, Ellis Horwood Limited, England, 1991. [9] W. Schaaffs, Acustica 33 (1975) 272–276. [10] J.A. Riddick, W.B. Bunger, T.K. Sakano, Organic Solvents Physical Properties and Method of Purifications, vol. 2, Wiley Intersciences, N. Y., 1986 [11] J. Timmermans, Physico-chemical Constants of Pure Organic Compounds, vol. 1, Elsevier Publications, Amsterdam, 1950. [12] S. Kumar, A. Maken, S. Agarwal, S. Maken, J. Mol. Liq. 155 (2010) 115–120. [13] P. Jeevanandham, S. Kumar, P. Periyasamy, J. Mol. Liq. 188 (2013) 203–209. [14] M.S. AlTuwaim, A. Haek, S.A. Al-Jimaz, A.A. Mohammad, J. Chem. Thermodyn. 48 (2012) 39–47. [15] A.S. Al-Jimaz, J.A. Al-Kandary, M.A.-H. Abdul-Latif, Fluid Phase Equilib. 218 (2004) 247–260. [16] J. Ortega, J.D. Garcia, Can. J. Chem. 66 (1988) 1520–1524. [17] A.S. Al-Jimaz, J.A. Al-Kandary, M. Abdul-Haq, Abdul-Latif, J. Chem. Eng. Data 52 (2007) 206–214. [18] B.D. Djordjevic, I.R. Radovic, M.L.J. Kijevcanin, A.Z. Tasica, S.P. Serbanovic, J. Serb. Chem. Soc. 74 (2009) 477–491. [19] M.N.M. Al-Hayan, J. Chem. Thermodyn. 38 (2006) 427–433. [20] M.A. Rauf, M. Arfan, F. Azizi, J. Chem. Thermodyn. 15 (1983) 1021–1023. [21] A. Ali, A.K. Nain, Abida, J. Chil. Chem. Soc. 51 (2004) 477–485. [22] G.C. Benson, O. Kiyohara, J. Chem. Thermodyn. 11 (1979) 1061–1064. [23] B. Jacobson, Ark. Kemi 2 (1950) 177–210. [24] K. Ramanjaneyulu, K.N. Surendranath, A. Krishnaiah, Acoust. Lett. 11 (1988) 152–157. [25] M.N. Roy, A. Benerjee, A. Choudhary, Phys. Chem. Liq. 47 (2009) 412–436. [26] A. Ali, K. Tiwari, A.K. Nain, V. Chakravortty, Phys. Chem. Liq. 38 (2000) 459–473. [27] R.J. Fort, W.R. Moore, Trans. Faraday Soc. 62 (1965) 2102–2111. [28] G.E. Papanastasiou, I.I. Ziogas, J. Chem. Eng. Data 36 (1961) 46–51. [29] A. Mohammad, Chowdhury, M.A. Majid, M.A. Salesh, J. Chem. Thermodyn. 33 (2001) 347–360. [30] O. Redlich, A.T. Kister, Ind. Eng. Chem. 40 (1948) 345–348. [31] L. Grunberg, A.H. Nissan, Mixture law for viscosity, Nature 164 (1949) 799–800. [32] P.K. Katti, M.H. Chaudhri, J. Chem. Eng. Data 9 (1964) 442–443. [33] R.K. Hind, E. McLaughlin, A. Ubbelohde, Trans. Faraday Soc. 56 (1960) 328–330. [34] E.L. Heric, J.G. Brewer, J. Chem. Eng. Data 12 (1967) 574–583. [35] M. Tamura, M. Kurata, Bull. Chem. Soc. Jpn. 25 (1952) 32–37. [36] R.J. Fort, W.R. Moore, Trans. Faraday Soc. 62 (1966) 1112–1129. [37] K. Rajagopal, S. Chenthilnath, A.K. Nain, J. Mol. Liq. 151 (2010) 23–29. [38] K. Rajagopal, S. Chenthilnath, Thermochim. Acta 498 (2010) 45–53. [39] H. Reiss, H.L. Frisch, J.L. Lebowitz, J. Chem. Phys. 31 (1959) 369–380. [40] S. Ghosh, K.N. Pande, Y.D. Wankhade, Indian J. Pure Appl. Phys. 42 (2004) 729–734. [41] M. Kalidoss, R. Srinivasamoorthy, Acust. Acta Acust. 83 (1997) 776–779. [42] G. Udny, An Introduction to the Theory of Statistics, 14 th edition, 1987 (New Delhi). [43] K. Rajagopal, S. Chenthilnath, Thermochim. Acta 498 (2010) 45–53. [44] K. Rajagopal, S. Chenthilnath, Chin. J. Chem. Eng. 18 (2010) 804–816.
Contents lists available at ScienceDirect
Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq
Molecular interactions and theoretical estimation of ultrasonic speeds using scaled particle theory in binary mixtures of 3-chloroaniline and 1-alkanols (C6–C10) at different temperatures D. Rahul a, T. Srinivasa Krishna b, M. Gowrisankar a, D. Ramachandran c,⁎ a b c
Department of Chemistry, J.K.C.C., Acharya Nagarjuna University, Guntur 522510, AP, India Department of Physics, Raylaseema University, Kurnool, Andhra Pradesh, India Department of Chemistry, Acharya Nagarjuna University, Guntur 522510, AP, India
a r t i c l e
i n f o
Article history: Received 15 July 2015 Received in revised form 25 September 2015 Accepted 26 September 2015 Available online 11 November 2015 Keywords: 3-Chloroaniline Excess thermodynamic parameters Scaled particle theory
a b s t r a c t Density (ρ), speed of sound (u) and viscosity (η) have been measured for the binary mixtures of 3-chloroaniline with 1-alkanols (1-hexanol, 1-heptanol, 1-octanol, 1-decanol) over the entire composition range at (303.15, 308.15, 313.15, and 318.15) K. By using this data, the excess volume (VE), excess isentropic compressibility (κEs ), deviation in viscosity (Δη) and excess Gibbs free energy of activation of viscous flow (G⁎E) have been calculated and were fitted to Redlich–Kister polynomial equation. The excess molar volumes, excess isentropic compressibility, deviation in viscosity and excess Gibbs energy of activation of viscous flow have been analyzed in terms of declustering and breaking of H-bonds in alkanols and alkyl chain of the 1-alkanols between unlike molecules. Moreover, the theoretical ultrasonic speeds are computed based on the scaled particle theory and compared with the experimentally measured values. © 2015 Elsevier B.V. All rights reserved.
1. Introduction It has been reported by several researchers, that not only the difference in size and shape of molecules will influence significantly the excess thermodynamic functions, but also the chemical nature of the components play an important role [1–3]. Further, the study of thermodynamic properties of liquid mixtures is of great importance because of their extensive use in garment industry, tannery industry, pharmaceutical industry and in many others. A survey of literature has shown that a few attempts have been made to investigate the excess thermodynamic properties of liquid mixtures containing 3-chloroaniline [4–6]. The main theme of the present article is to characterize the molecular interactions between 3-chloroaniline and 1-hexanol, 1-heptanol, 1-octanol and 1decanol binary systems and to subsequently evaluate the effect of chain length of 1-alkanols on excess functions of these mixtures. The liquids were chosen in the present investigation on the basis of their industrial importance. 3-Chloroaniline is used as an intermediate in the production of a number of products, including agricultural chemicals, azo dyes and pigments, bactericide or biocide and pharmaceuticals. It is dipolar and associated liquid, whereas alkanols are protic, have relatively high value of dielectric constant and are self-associated through hydrogen bond [7,8]. The degree of association in alkanols decreases ⁎ Corresponding author. E-mail addresses: [email protected] (M. Gowrisankar), [email protected] (D. Ramachandran).
http://dx.doi.org/10.1016/j.molliq.2015.09.046 0167-7322/© 2015 Elsevier B.V. All rights reserved.
as the carbon chain length increases from 1-hexanol to 1-decanol due to steric factors [9]. In this paper, we report densities (ρ), speeds of sound (u) and viscosities (η) of pure 3-chloroaniline, 1-alkanols(1hexanol, 1-heptanol, 1-octanol and 1-decanol) and those of their binary mixtures over the entire composition range at T = (303.15 K to 318.15) K. From these experimental data, the values of excess volume (VE), excess isentropic compressibility (κEs ), deviation in viscosity (Δη) and excess Gibbs free energy of activation of viscous flow (G⁎E) are calculated and discussed in terms of molecular interactions between the unlike molecules. Furthermore, theoretical ultrasonic speeds of these mixtures are evaluated by considering the different shapes of the participating components using the scaled particle theory and compared with the experimental values. 2. Experimental 2.1. Materials All the chemicals used in the present work were of analytical reagent grade produced from Merck and their purities were as follows: 3chloroaniline 99.5%, 1-hexanol 99.5%, 1-heptanol 99.5%, 1-octanol 99.5%, and 1-decanol 99.5%. Prior to experimental measurements, all the liquids were purified as described in the literature [10,11]. Further the water content of solvents used in this work was measured by Analab (MicroAqua Cal 100) Karl Fischer Titrator and Karl Fisher reagent from Merck. It can detect water content from less than 10 ppm to 100% by
D. Rahul et al. / Journal of Molecular Liquids 212 (2015) 618–628 Table 1 Provenance and purity of the materials used. Chemical name
CAS number
Supplier Purity in mass Purity (after Water fraction (as received purification) content from supplier) (%)
3-Chloroaniline 1-Hexanol 1-Heptanol 1-Octanol 1-Decanol
108–42–9 111–27–3 111–70–6 111–87–5 112–30–1
Merck Merck Merck Merck Merck
0.99 0.98 0.98 0.99 0.97
0.995 0.985 0.995 0.995 0.995
0.042 0.048 0.044 0.045 0.043
conductometric titration with dual platinum electrode and given in Table 1 along with their CAS number and purity. The purity of the sample was further confirmed by GLC single sharp peak. Before use, the chemicals were stored over 0.4 nm molecular sieves for about 72 h to remove water and were later degassed. Density (ρ), speed of sound (u) and viscosity (η) data of pure component liquids are compared with the available literature values [12–18] and were found in good agreement as shown in Table 2.
2.2. Apparatus and procedure All the binary liquid mixtures are prepared by weighing an amount of pure liquids in an electric balance (Afoset, ER-120A, and India) with a precision of ±0.1 mg by syringing each component into air-tight stopper bottles to minimize evaporation losses. The uncertainty of the mole fraction was ±1 × 10−4. After mixing the sample, the bubble-free homogeneous sample was transferred into the U-tube of the densimeter through a syringe. The density measurements were performed with a Rudolph Research Analytical digital densimeter (DDH-2911 Model), equipped with a built-in solid-state thermostat and a resident program with accuracy of temperature of 303.15 K ± 0.03 K. The uncertainty in density measurement liquid mixtures was found to be ±5 × 10−5 g/cm3. Proper calibration at each temperature was achieved with doubly distilled, deionized water and with air as standards. The
619
viscosities of pure liquids and their mixtures were determined at atmospheric pressure and at temperature 303.15, 308.15, 313.15, and 318.15 K by using an Ubbelohde viscometer, which was calibrated with benzene, carbon tetrachloride, acetonitrile, and doubly distilled water. The viscometer was thoroughly cleaned and perfectly dried, is filled with the sample liquid by fitting the viscometer to about 30° from the vertical and its limbs are closed with Teflon caps to avoid the evaporation. The viscometer is kept in a transparent walled bath with a thermal stability of ±0.01 K for about 20 min to obtain thermal equilibrium. An electronic digital stopwatch with an uncertainty ±0.01 s was used for flow time measurements. The uncertainty of viscosity thus estimated was found to be ± 0.005 mPa ∙ s. The ultrasonic speed in pure liquids and in their mixtures were measured by using a multi frequency ultrasonic interferometer (M-82 Model, Mittal Enterprise, New Delhi, India) single-crystal variable path, operated at 2 MHz. from 303.15 K to 318.15 K by using a digital constant temperature water bath. The uncertainty in the measurement of ultrasonic speed is ±0.3%. The interferometer is immersed in a thermostatic water bath, whose temperature can be maintained at any desired value with an accuracy of ± 0.01 K. The present investigation has been devoted to the study of densities, speed of sounds and viscosities of binary liquid mixtures at different temperatures and at a pressure of 0.1 MPa. 3. Results and discussion The measured density of binary mixtures of 3-chloroaniline with 1akanols were given in Table 3 from 303.15 K to 318.15 K. The excess volume data of all the liquid mixtures were computed by using the following formula: VE =cm3 mol
−1
¼ ½x1 M1 þ x2 M2 =ρ–½x1 M1 =ρ1 þ x2 M2 =ρ2
ð1Þ
where x1 and x2 are the mole fractions of 3-chloroaniline and 1-alkanol respectively; M1, M2 and ρ1 and ρ2 are the molecular weights and density of components 1 and 2 respectively and ρ is the density of the
Table 2 Densities and viscosities data of pure components at different temperatures and p = 0.1 MPa. Component
Density (ρ/g·cm−3)
Speed of sound (u/m·s−1)
Viscosity (η/mPa·s)
Experimental
Literature
Experimental
Literature
Experimental
Literature
3-Chloroaniline 303.15 K 308.15 K 313.15 K 318.15 K
1.20532 1.20075 1.19602 1.19125
1.20530 [12] – 1.19600 [12] –
4.2554 3.8420 3.4302 3.0224
4.2556 [13] – – –
1517.5 1501.2 1480.3 1464.8
1517.0 [12] – 1484.0 [12] –
1-Hexanol 303.15 K 308.15 K 313.15 K 318.15 K
0.81215 0.80785 0.80449 0.80015
0.81212 [14] 0.80780 [16] 0.80451 [14] 0.80018 [15]
3.883 3.355 2.911 2.6558
3.887 [17] 3.359 [17] 2.914 [17] 2.6553 [15]
1286.2 1270.2 1252.5 1245.6
1287.90 [17] 1271.14 [17] 1254.45 [17]
1-Heptanol 303.15 K 308.15 K 313.15 K 318.15 K
0.81526 0.81172 0.80814 0.80436
0.81529 [18] 0.81174 [18] 0.80816 [18] 0.80439 [15]
5.065 4.329 3.723 3.4462
5.069 [17] 4.333 [17] 3.726 [17] 3.4466 [15]
1312.5 1295.2 1275.4 1259.5
1313.58 [17] 1293.86 [17] 1277.15 [17]
1-Octanol 303.15 K 308.15 K 313.15 K 318.15 K
0.81825 0.81472 0.81007 0.80552
0.81823 [18] 0.81474 [18] 0.81009 [18] 0.80555 [15]
6.405 5.422 4.625 4.0510
6.402 [17] 5.425 [17] 4.628 [17] 4.0512 [15]
1333.5 1312.5 1295.4 1282.5
1338.02 [17] 1314.27 [17] 1297.60 [17]
1-Decanol 303.15 K 308.15 K 313.15 K 318.15 K
0.82289 0.81954 0.81595 0.81135
0.82285 [17] 0.81952 [17] 0.81598 [17] 0.81138 [15]
9.751 8.138 6.846 5.8787
9.754 [17] 8.135 [17] 6.842 [17] 5.8783 [15]
1363.5 1344.2 1328.5 1320.5
1365.0 [17] 1346.1 [17] 1329.0 [17]
620
D. Rahul et al. / Journal of Molecular Liquids 212 (2015) 618–628
Table 3 Density (ρ), viscosity (η) and speed of sound (u) of binary liquid mixtures of 3-chloroaniline with 1-alkanols at temperatures T = (303.15 to 318.15) K. x1
ρ/gm cm−3 303.15 K
u/m s−1
η/m Pa∙s 313.15 K
318.15 K
303.15 K
308.15 K
313.15 K
318.15 K
303.15 K
308.15 K
313.15 K
318.15 K
3-Chloroaniline + hexanol-1 0.0000 0.81215 0.80785 0.1167 0.85134 0.84694 0.2291 0.89050 0.88602 0.3375 0.92968 0.92515 0.4421 0.96889 0.96431 0.5431 1.00815 1.00353 0.6407 1.04747 1.04283 0.7350 1.08685 1.08219 0.8263 1.12632 1.12167 0.9145 1.16577 1.16115 1.0000 1.20532 1.20075
308.15 K
0.80449 0.84341 0.88235 0.92133 0.96036 0.99944 1.03860 1.07781 1.11715 1.15651 1.19602
0.80015 0.83896 0.87780 0.91671 0.95568 0.99472 1.03384 1.07302 1.11234 1.15169 1.19125
3.883 3.9047 3.9251 3.9498 3.9799 4.0143 4.0561 4.1038 4.1555 4.2054 4.2554
3.355 3.3832 3.4171 3.4539 3.4970 3.5450 3.5978 3.6538 3.7146 3.7757 3.8420
2.911 2.9393 2.9758 3.0175 3.0640 3.1149 3.1700 3.2288 3.2918 3.3575 3.4302
2.6558 2.6615 2.6812 2.7071 2.7377 2.7735 2.8141 2.8574 2.9061 2.9587 3.0224
1286.2 1295.3 1305.1 1316.1 1329.0 1344.5 1363.8 1388.4 1420.2 1461.9 1517.5
1270.2 1279.5 1289.4 1300.5 1313.6 1329.5 1349.2 1374.1 1406.0 1447.2 1501.2
1252.5 1262.2 1272.1 1282.9 1295.7 1311.3 1330.8 1355.5 1387.1 1427.7 1480.3
1245.6 1254.7 1264.3 1274.9 1287.3 1302.5 1321.4 1345.3 1375.7 1414.5 1464.8
3-Chloroaniline + heptanol-1 0.0000 0.81526 0.81172 0.1306 0.85423 0.85056 0.2526 0.8932 0.8894 0.3669 0.93217 0.92825 0.4741 0.97113 0.9671 0.5749 1.01011 1.00598 0.6698 1.04911 1.04486 0.7593 1.08809 1.08375 0.8440 1.12717 1.12273 0.9241 1.16624 1.16172 1.0000 1.20532 1.20075
0.80814 0.84683 0.88553 0.92426 0.963 1.00175 1.04051 1.07929 1.11817 1.15705 1.19602
0.80436 0.84291 0.88148 0.9201 0.95873 0.99738 1.03604 1.07473 1.11353 1.15233 1.19125
5.065 4.9228 4.7942 4.6845 4.5893 4.5091 4.4415 4.3853 4.3356 4.2917 4.2554
4.329 4.2286 4.1434 4.0723 4.0135 3.9659 3.9266 3.8954 3.8694 3.8525 3.8420
3.723 3.6469 3.5854 3.5382 3.5011 3.4727 3.4510 3.4377 3.4333 3.4316 3.4302
3.4462 3.3457 3.2688 3.2068 3.1557 3.1137 3.0789 3.0511 3.0315 3.0235 3.0224
1312.5 1320.7 1328.7 1337.8 1348.4 1361.5 1378.5 1400.5 1429.4 1467.4 1517.5
1295.2 1303.5 1312.1 1321.5 1332.5 1346.0 1363.3 1385.5 1414.3 1451.9 1501.2
1275.4 1284.4 1293.0 1302.2 1312.9 1326.4 1343.7 1366.0 1394.8 1432.1 1480.3
1259.5 1268.6 1277.3 1286.6 1297.6 1311.4 1329.1 1351.7 1380.6 1417.6 1464.8
3-Chloroaniline + octanol-1 0.0000 0.81825 0.81472 0.1441 0.85703 0.85338 0.2748 0.89582 0.89203 0.3937 0.93453 0.93062 0.5026 0.97327 0.96925 0.6025 1.01196 1.00784 0.6945 1.05064 1.04641 0.7795 1.08927 1.08495 0.8584 1.12796 1.12354 0.9317 1.16664 1.16213 1.0000 1.20532 1.20075
0.81007 0.84864 0.88724 0.92579 0.96439 1.00296 1.04152 1.08006 1.11868 1.15734 1.19602
0.80552 0.84398 0.88252 0.92101 0.95958 0.99811 1.03664 1.07518 1.11383 1.15248 1.19125
6.405 6.0592 5.7543 5.4847 5.2466 5.0339 4.8441 4.6744 4.5188 4.3792 4.2554
5.422 5.1549 4.9244 4.7232 4.5471 4.3909 4.2533 4.1308 4.0201 3.9239 3.8420
4.625 4.4092 4.2292 4.0758 3.9414 3.8233 3.7209 3.6296 3.5507 3.4831 3.4302
4.051 3.8557 3.6974 3.5642 3.4483 3.3468 3.2585 3.181 3.1143 3.0605 3.0224
1333.5 1340.9 1347.6 1355.0 1363.4 1374.4 1389.2 1409.1 1435.8 1471.4 1517.5
1312.5 1320.4 1327.8 1335.4 1344.6 1356.3 1371.8 1392.4 1419.5 1455.0 1501.2
1295.4 1303.6 1310.9 1318.5 1327.5 1339.2 1354.7 1375.2 1402.1 1437.0 1482.2
1282.5 1290.8 1297.9 1305.3 1314.6 1326.4 1341.3 1361.6 1388.5 1422.9 1466.5
3-Chloroaniline + decanol-1 0.0000 0.82289 0.81954 0.1699 0.8614 0.85791 0.3153 0.89986 0.89623 0.4411 0.93823 0.93447 0.5511 0.97656 0.97267 0.6481 1.01482 1.01080 0.7342 1.05300 1.04887 0.8112 1.09114 1.08688 0.8805 1.12925 1.12488 0.9431 1.16728 1.16282 1.0000 1.20532 1.20075
0.81595 0.85417 0.89236 0.93049 0.96856 1.00658 1.04451 1.08241 1.12031 1.15816 1.19602
0.81135 0.84947 0.88761 0.92568 0.96372 1.00171 1.03964 1.07754 1.11545 1.15333 1.19125
9.751 8.7719 7.9473 7.2472 6.6414 6.1130 5.6483 5.2375 4.8712 4.5456 4.2554
8.138 7.3581 6.7099 6.1595 5.6866 5.2745 4.9120 4.5931 4.3104 4.0614 3.8420
6.846 6.2131 5.6927 5.2536 4.8780 4.5492 4.2621 4.0101 3.7884 3.5956 3.4302
5.8787 5.3385 4.8991 4.5319 4.2169 3.9431 3.7037 3.4943 3.3114 3.1530 3.0224
1363.5 1370.0 1374.5 1378.7 1384.0 1392.3 1404.5 1422.0 1445.6 1477.0 1517.5
1344.2 1351.3 1356.2 1360.6 1366.5 1375.3 1387.9 1405.6 1429.6 1461.0 1501.2
1328.5 1335.7 1340.4 1344.7 1350.4 1358.9 1371.4 1388.7 1411.9 1441.9 1480.3
1320.0 1327.1 1331.5 1335.5 1340.8 1349.0 1360.9 1377.5 1399.7 1428.3 1464.8
Standard uncertainties s are s (ρ) = ±2 × 10−5 (g·cm−3), s (u) ±0.5 (m·s−1) s (η) = ±0.005 m Pa∙s,
mixture. The VE data of all the liquid mixtures were graphically depicted over the entire composition range in Figs. 1–4. An examination of VE data in Figs. 1–4 suggest that the property is positive over the entire composition range in the binary mixtures of 3chloroaniline with 1-alkanol at all the measured temperatures. In general, the sign of excess volume (VE) depends on the relative magnitude of contractive and expansive effects which arise due to mixing of the component liquids. The factors that cause contraction on mixing are as follows: a) Strong specific interactions; usually a kind of chemical interaction. b) Strong physical interactions of the type dipole–dipole or dipole–induced dipole interactions. c) Favorable geometrical fitting of component molecules. d) Occupation of void spaces of one component by the other due to molecular sizes of two component molecules differs by a large amount.
The factors which lead to expansion in volume on mixing the two component liquids are as follows: a) Dissociation of one component or both the components. b) Steric hindrance and geometrical mismatch of the molecules. c) Formation of weaker solute-solute and solvent–solvent bonds. A perusal of curves in Figs. 1–4 reveal that the factors which are responsible for expansion in volume were dominant in all the binary mixtures of 3-chloroaniline with 1-alkanols. The algebraic VE values of all the binary mixtures fall in the following order: 1‐hexanolb1‐heptanolb1‐octanolb1‐decanol: The above order suggests that the extent of strength of molecular interactions decreases as the chain length of 1-alkanol molecule increases. The increase in positive excess volume with increase in chain length of
D. Rahul et al. / Journal of Molecular Liquids 212 (2015) 618–628
621
Fig. 1. Variation of excess volume (VE) of the binary liquid mixture of 3-chloroaniline with 1-hexanol (∎), 1-heptanol (●), 1-octanol (▲) and 1-decanol (▼) at 303.15 K.
Fig. 3. Variation of excess volume (VE) of the binary liquid mixture of 3-chloroaniline with 1-hexanol (ξ), 1-heptanol (ψ), 1-octanol ({) and 1-decanol (|) at 313.15 K.
1-alkanols implies that dipole–dipole interactions are weak in higher alkanols due to the decrease in their polarizability with increasing chain length [19]. Similar type of behavior was reported for the mixtures of N,N-dimethylformamide + 1-alkanols [20] and acetonitrile + 1-alkanols [21]. Also as the increase in the chain length of the alkanols leads to decrease in the strength of hydrogen bond [8], which facilitates the disruption of associated structures in alkanols on addition of 3chloroaniline leading to positive VE values. The influence of temperature on the VE for the systems containing 1-alkanols is slightly more positive with increasing temperature. The isentropic compressibility (κs) was calculated from the Newton–Laplace equation given below.
where, κid s is the ideal value of the isentropic compressibility and was calculated from the following equation [22]:
κs ¼ u−2 ρ−1
ð2Þ
where ρ is the density and u is the speed of sound of the binary mixtures. Further, the values of excess isentropic compressibilities (κs E) were calculated from the following relation [22]: κEs ¼ κs −κid s
κid s
¼
2 X i¼1
8 9 ! !2 2 2 2 = X X 2 < X ϕi κs;i þ TVi αi =Cp;i − T xi Vi ϕi αi = xi Cp;i : ; i¼1
i¼1
i¼1
ð4Þ where, ϕi is ideal state volume fraction of component i in mixture and is defined by the following relation, ϕi ¼ xi Vi =ðΣxi Vi Þ:
ð5Þ
T is temperature and κs,i, Vi°, αi° and Cp,i are isentropic compressibility, molar volume, coefficient of isobaric thermal expansion and molar heat capacity respectively, for pure component i. αi° is calculated from measured densities by relation, αi ¼ ½ðρ1 =ρ2 Þ−1=ðT2 −T1 Þ:
ð6Þ
ð3Þ
Values of the excess isentropic compressibility (κEs ) data for the mixtures of 3-chloroaniline with 1-alkanol were graphically depicted in Figs. 5–8 and the data were given in Table 4.
Fig. 2. Variation of excess volume (VE) of the binary liquid mixture of 3-chloroaniline with 1-hexanol (▽), 1-heptanol (○), 1-octanol (△) and 1-decanol (□) at 308.15 K.
Fig. 4. Variation of excess volume (VE) of the binary liquid mixture of 3-chloroaniline with 1-hexanol (⎕), 1-heptanol (⎕), 1-ocatnol (⎕) and 1-decanol (⎕) at 318.15 K.
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Fig. 5. Variation of excess isentropic compressibility (κEs ) of the binary liquid mixture of 3chloroaniline with 1-hexanol (∎), 1-heptanol (●), 1-octanol (▲) and 1-decanol (▼) at 303.15 K.
The (κEs ) values exhibit an inversion in sign at all the temperatures for these systems over the whole composition range. The values of excess isentropic compressibility may be interpreted in terms of two opposing effects, namely (i) loss of mutual dipolar association and difference in size and shape of unlike molecules, and (ii) dipole–dipole, dipole–induced dipole, electron donor-acceptor interactions and interstitial accommodation of the non-common component in the 3chloroaniline lattice. The former effect contributes to an increase in free length, described by Jacobson [23]. This leads to negative deviations in speed of sound and positive deviations in excess isentropic compressibility. The latter effect, on the other hand, leads to positive deviations in speed of sound and a negative deviation in excess isentropic compressibility. The sign and magnitude of the actual deviation depends upon the relative strengths of the two opposing effects [24]. It is evident from Table 4 shows that the κEs values can be explained in terms of molecular interactions and structure effects. The observed negative values of kEs may be attributed to molecular association through intermolecular hydrogen bonding between the hydrogen atom of the –NH2 group of 3-chloroaniline and the oxygen atom of the –OH group of alcohols and Positive values indicates that the breaking of interactions and corresponding disruption of molecular order in the
Fig. 6. Variation of excess isentropic compressibility (κEs ) of the binary liquid mixture of 3chloroaniline with 1-hexanol (▽), 1-heptanol (○), 1-octanol (△) and 1-decanol (□) at 308.15 K.
Fig. 7. Variation of excess isentropic compressibility (κEs ) of the binary liquid mixture of 3chloroaniline with 1-hexanol (ξ), 1-heptanol (ψ), 1-octanol ({) and 1-decanol (|) at 313.15 K.
pure component molecules [25]. Similar results have also been reported [20] for N, N-dimethyl formamide + n-alkanols (C7–C10) and toluene + n-alkanols (C5–C8) binary liquid mixtures [26]. An examination of curves in Figs. 5–8 suggests that both the factors are competing with each other to varying degrees in the mixtures containing 3-chloroaniline and 1-alkanols. The algebraic values of all the binary mixtures will obey the following order: 1‐hexanolb1‐heptanolb1‐octanolb1‐decanol: The above order indicates the strength of interactions between component molecules decreases due to decrease in polarizability of alkanol molecules. Viscosity data for binary mixtures of 3-chloroaniline with 1-alkanols is given in Table 3 along with excess Gibbs energy of activation of viscous flow (G⁎E) and these were calculated by the following equations: Δη=mPa s ¼ η–½x1 η1 þ x2 η2 −1
GE =J mol
¼ RT½ ln ηV−ðx1 lnη1 V1 þ x2 ln η2 V2 Þ
ð7Þ ð8Þ
Fig. 8. Variation of excess isentropic compressibility (κEs ) of the binary liquid mixture of 3chloroaniline with 1-hexanol (⎕), 1-heptanol (⎕), 1-ocatnol (⎕) and 1-decanol (⎕) at 318.15 K.
D. Rahul et al. / Journal of Molecular Liquids 212 (2015) 618–628
where η1, η2, η, V1, V2, and V are the viscosity of components 1, 2 and mixture and molar volumes of component 1, 2, and mixture respectively. R is the gas constant and T the absolute temperature. The viscosity data of all the liquid mixtures are graphically in Figs. 9–12. The negative trend in Δη for all the mixtures of 3-chloroaniline with 1alkanols (Table 4) indicate that the viscosities of associates formed between unlike molecules are relatively less than those of pure components. Further, according to the view of Fort and Moore [27], negative Δη values are ascribed due to an increase in the dispersion forces in the mixtures. Also deviation in viscosity data in the present investigation depends on the following factors: 1) The geometrical difference in size and shape of component molecules and the loss of dipolar association in pure component may contribute decrease in viscosity and 2) specific interactions between unlike components like hydrogen bond formation and charge transfer complexes may cause for increase in viscosity in mixtures than in pure components.
623
The first factor produces negative deviation in viscosity, while the second factor leads to contribute positive deviation in viscosity. An examination of deviation in viscosity data in Figs. 9–12 reveal that the factor which is responsible for deviation in viscosity is dominant in all the binary mixtures of 3-chloroaniline with 1-alkanols. Similar negative deviations have been reported for ethanol + cyclohexane and 1hexanol + hydrocarbons [28,29]. The variation of VE, κEs and Δη with mole fraction were fitted to the Redlich–Kister polynomial equation [30] of the type, h i YE ¼ x1 x2 a0 þ a1 ðx1 −x2 Þ þ a2 ðx1 −x2 Þ2
ð9Þ
where YE is VE or κEs or Δη. The values of a0, a1 and a2 are the coefficients of the polynomial equation and the corresponding standard deviations, σ obtained by the method of least-squares with equal weights assigned
Table 4 Excess molar volume (VEm), excess isentropic compressibility (κEs ) and deviation in viscosity (Δη) of binary liquid mixtures of 3-chloroaniline with 1-alkanols at temperatures T = (303.15 to 318.15) K. x1
VEm/cm3 ∙mol−1 303.15 K
308.15 K
κEs /TPa−1
Δη/mPa∙s
313.15 K
318.15 K
303.15 K
308.15 K
313.15 K
318.15 K
303.15 K
308.15 K
313.15 K
318.15 K
3-Chloroaniline + hexanol-1 0.0000 0.0000 0.0000 0.1167 0.0202 0.0232 0.2291 0.0395 0.0440 0.3375 0.0546 0.0583 0.4421 0.0643 0.0684 0.5431 0.0677 0.0725 0.6407 0.0639 0.0685 0.7350 0.0539 0.0587 0.8263 0.0392 0.0433 0.9145 0.0206 0.0234 1.0000 0.0000 0.0000
0.0000 0.0279 0.0483 0.0631 0.0721 0.0759 0.0725 0.0634 0.0479 0.0268 0.0000
0.0000 0.0307 0.0530 0.0675 0.0762 0.0796 0.0768 0.0681 0.0521 0.0312 0.0000
0.000 −5.750 −8.189 −8.111 −6.310 −3.567 −0.627 1.813 3.111 2.682 0.000
0.000 −6.242 −8.893 −8.949 −7.298 −4.736 −1.963 0.398 1.813 1.814 0.000
0.000 −7.104 −9.920 −9.830 −7.963 −5.233 −2.384 −0.011 1.413 1.512 0.000
0.000 −7.097 −10.130 −10.326 −8.709 −6.137 −3.322 −0.859 0.769 1.162 0.000
0.000 −0.022 −0.043 −0.059 −0.068 −0.071 −0.065 −0.053 −0.035 −0.018 0.000
0.000 −0.029 −0.049 −0.065 −0.073 −0.074 −0.069 −0.059 −0.043 −0.025 0.000
0.000 −0.032 −0.054 −0.069 −0.077 −0.078 −0.074 −0.064 −0.048 −0.028 0.000
0.000 −0.037 −0.059 −0.072 −0.080 −0.081 −0.077 −0.068 −0.053 −0.032 0.000
3-Chloroaniline + heptanol-1 0.0000 0.0000 0.0000 0.1306 0.0275 0.0290 0.2526 0.0470 0.0506 0.3669 0.0622 0.0658 0.4741 0.0695 0.0738 0.5749 0.0707 0.0748 0.6698 0.0654 0.0702 0.7593 0.0563 0.0604 0.8440 0.0408 0.0453 0.9241 0.0217 0.0247 1.0000 0.0000 0.0000
0.0000 0.0330 0.0551 0.0693 0.0766 0.0782 0.0740 0.0647 0.0486 0.0284 0.0000
0.0000 0.0355 0.0593 0.0745 0.0805 0.0825 0.0787 0.0686 0.0516 0.0312 0.0000
0.000 −5.640 −7.339 −6.838 −4.672 −1.732 0.963 3.045 3.800 2.913 0.000
0.000 −5.865 −8.123 −7.764 −5.753 −2.972 −0.186 1.968 2.974 2.421 0.000
0.000 −6.915 −9.254 −8.645 −6.376 −3.448 −0.633 1.489 2.493 2.066 0.000
0.000 −7.249 −9.698 −9.174 −7.028 −4.256 −1.580 0.486 1.586 1.473 0.000
0.000 −0.028 −0.053 −0.067 −0.074 −0.073 −0.066 −0.052 −0.037 −0.020 0.000
0.000 −0.033 −0.057 −0.071 −0.077 −0.076 −0.070 −0.059 −0.045 −0.024 0.000
0.000 −0.037 −0.061 −0.075 −0.080 −0.079 −0.073 −0.061 −0.041 −0.020 0.000
0.000 −0.042 −0.065 −0.077 −0.083 −0.082 −0.077 −0.068 −0.053 −0.029 0.000
3-Chloroaniline + octanol-1 0.0000 0.0000 0.0000 0.1441 0.0339 0.0345 0.2748 0.0543 0.0570 0.3937 0.0675 0.0716 0.5026 0.0735 0.0770 0.6025 0.0737 0.0771 0.6945 0.0674 0.0709 0.7795 0.0582 0.0606 0.8584 0.0431 0.0461 0.9317 0.0228 0.0261 1.0000 0.0000 0.0000
0.0000 0.0370 0.0610 0.0743 0.0801 0.0803 0.0749 0.0655 0.0497 0.0269 0.0000
0.0000 0.0430 0.0657 0.0788 0.0841 0.0849 0.0806 0.0705 0.0526 0.0322 0.0000
0.000 −5.360 −6.799 −5.800 −3.124 −0.014 2.733 4.499 4.777 3.149 0.000
0.000 −5.924 −7.650 −6.595 −4.027 −0.993 1.709 3.496 3.963 2.848 0.000
0.000 −6.616 −8.466 −7.359 −4.724 −1.652 1.071 2.896 3.458 2.533 0.000
0.000 −7.107 −8.992 −7.871 −5.608 −2.700 0.417 2.317 2.664 1.909 0.000
0.000 −0.036 −0.060 −0.074 −0.078 −0.076 −0.068 −0.055 −0.041 −0.023 0.000
0.000 −0.039 −0.063 −0.077 −0.081 −0.079 −0.071 −0.060 −0.046 −0.026 0.000
0.000 −0.044 −0.067 −0.079 −0.083 −0.082 −0.074 −0.064 −0.049 −0.029 0.000
0.000 −0.047 −0.071 −0.082 −0.086 −0.084 −0.078 −0.068 −0.054 −0.032 0.000
3-Chloroaniline + decanol-1 0.0000 0.0000 0.0000 0.1699 0.0419 0.0433 0.3153 0.0633 0.0666 0.4411 0.0741 0.0774 0.5511 0.0769 0.0803 0.6481 0.0751 0.0789 0.7342 0.0679 0.0709 0.8112 0.0563 0.0601 0.8805 0.0419 0.0449 0.9431 0.0240 0.0243 1.0000 0.0000 0.0000
0.0000 0.0473 0.0713 0.0806 0.0838 0.0816 0.0764 0.0654 0.0489 0.0270 0.0000
0.0000 0.0530 0.0747 0.0852 0.0876 0.0866 0.0802 0.0691 0.0523 0.0289 0.0000
0.000 −5.427 −6.111 −4.063 −0.806 2.375 4.730 5.759 5.452 3.455 0.000
0.000 −6.041 −6.848 −4.659 −1.470 1.644 4.055 5.268 4.900 3.150 0.000
0.000 −6.562 −7.450 −5.357 −2.150 0.967 3.295 4.455 4.293 2.789 0.000
0.000 −7.034 −8.087 −6.072 −2.935 0.146 2.477 3.715 3.713 2.455 0.000
0.000 −0.045 −0.071 −0.080 −0.081 −0.076 −0.068 −0.055 −0.041 −0.023 0.000
0.000 −0.050 −0.074 −0.084 −0.084 −0.079 −0.072 −0.060 −0.045 −0.025 0.000
0.000 −0.053 −0.076 −0.086 −0.086 −0.083 −0.076 −0.065 −0.050 −0.029 0.000
0.000 −0.055 −0.079 −0.087 −0.088 −0.084 −0.078 −0.067 −0.052 −0.032 0.000
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Fig. 9. Variation of deviation in viscosity (Δη) of the binary mixture of 3-chloroaniline with 1-hexanol (∎), 1-heptanol (●), 1-octanol (▲) and 1-decanol (▼) at 303.15 K.
to each point are calculated. The standard deviation (σ) and are defined as follows: 1=2 2 σ YE ¼ ∑ YEobs −YEcal =ðn−mÞ
ð10Þ
where n is the total number of experimental points and m is the number of coefficients. The values of a0, a1 and a2 are the coefficients is determined by a multiple-regression analysis on the least square method and summarized along with the standard deviations between the experimental and fitted values of VE, κEs , and Δη are presented in Table 5. An examination of curves Figs. 13–16 suggests that the excess Gibbs free energy of activation of viscous flow (G⁎E) are negative for binary mixtures 3-chloroaniline with 1-hexanol + 1-heptanol while for the remaining mixtures the excess Gibbs free energy of activation of viscous flow (G⁎E) is positive over the entire composition range at all temperatures. The negative values of excess Gibbs free energy of activation of viscous flow for the binary systems investigated suggest that the breaking of the self-associated molecules and weak interactions between unlike molecules, decrease systematically with an increased in chain length of alcohol. With increasing in chain length of alcohols, hydrogen bonding interaction of 3-chloroaniline with 1-alkanols is weaker due to decreased polarizability and positive values indicate that the specific
Fig. 10. Variation of deviation in viscosity (Δη) of the binary liquid mixture of 3chloroaniline with 1-hexanol (▽), 1-heptanol (○), 1-octanol (△) and 1-decanol (□) at 308.15 K.
Fig. 11. Variation of deviation in viscosity (Δη) of the binary liquid mixture of 3chloroaniline with 1-hexanol (ξ), 1-heptanol (ψ), 1-octanol ({) and 1-decanol (|) at 313.15 K.
interactions through of hydrogen bonding (O–H….N–H) resulting in the formation of complexes between the component molecules. Grunberg–Nissan provided the following empirical equation containing one adjustable parameter [31]. The equation is ln η ¼ x1 lnη1 þ x2 ln η2 þ x1 x2 d12
ð11Þ
where d12 may be regarded as a parameter proportional to the interchange energy also an approximate measure of the strength of the interaction between the components. Katti and Chaudhri derived the below equation [32]. ln ηV ¼ x1 ln V1 η1 þ x2 ln V2 η2 þ x1 x2 Wvis=RT
ð12Þ
where Wvis/RT is an interaction term. Hind et al., suggested the following equation [33], η ¼ x21 η1 þ x22 η2 þ 2x1 x2 H12
ð13Þ
where H12 is Hind interaction parameter and is attributed to unlike pair interactions.
Fig. 12. Variation of deviation in viscosity (Δη) of the binary liquid mixture of 3chloroaniline with 1-hexanol (⎕), 1-heptanol (⎕), 1-ocatnol (⎕) and 1-decanol (⎕) at 318.15 K.
D. Rahul et al. / Journal of Molecular Liquids 212 (2015) 618–628
625
Table 5 Coefficients of Redlich–Kister equation and standard deviation (σ) values. Binary mixtures 303.15 K 3-Chloroaniline + hexanol-1 3-Chloroaniline + heptanol-1 3-Chloroaniline + octanol-1 3-Chloroaniline + decanol-1 308.15 K 3-Chloroaniline + hexanol-1 3-Chloroaniline + heptanol-1 3-Chloroaniline + octanol-1 3-Chloroaniline + decanol-1 313.15 K 3-Chloroaniline + hexanol-1 3-Chloroaniline + heptanol-1 3-Chloroaniline + octanol-1 3-Chloroaniline + decanol-1 318.15 K 3-Chloroaniline + hexanol-1
3-Chloroaniline + heptanol-1 3-Chloroaniline + octanol-1 3-Chloroaniline + decanol-1
Functions
ao
σ
a1
a2
VE/cm3·mol−1 0.268 Δη/mPa·s −0.282 κEs /TPa−1 −19.26 VE/cm3·mol−1 0.281 Δη/mPa∙s −0.296 −1 E κs /TPa −15.73 VE/cm3·mol−1 0.294 Δη/mPa·s −0.308 κEs /TPa−1 −12.35 VE/cm3·mol−1 0.300 Δη/mPa∙s −0.319 −1 E κs /TPa −9.758
0.047 −0.016 55.79 0.048 −0.021 55.41 0.054 −0.030 57.19 0.062 −0.036 60.50
−0.062 0.098 10.64 −0.013 0.047 13.87 0.031 −0.020 18.50 0.116 −0.077 26.13
0.001 0.066 0.001 0.001 0.001 0.001 0.081 0.001 0.001 0.119 0.001 0.002 0.040
VE/cm3·mol−1 Δη/mPa∙s κEs /TPa−1 VE/cm3·mol−1 Δη/mPa∙s κEs /TPa−1 VE/cm3·mol−1 Δη/mPa∙s κEs /TPa−1 VE/cm3 mol−1 Δη/mPa∙s κsE/TPa−1
0.285 −0.294 −23.61 0.297 −0.308 −20.38 0.305 −0.318 −16.40 0.317 −0.332 −12.33
0.050 −0.020 52.16 0.060 −0.028 52.75 0.067 −0.039 56.36 0.069 −0.034 60.66
−0.038 −0.002 5.198 0.005 −0.013 14.10 0.052 −0.062 16.76 0.091 −0.119 22.07
0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.002 0.001 0.001 0.002 0.052
VE/cm3·mol−1 Δη/mPa∙s κsE/TPa−1 VE/cm3·mol−1 Δη/mPa∙s κEs /TPa−1 VE/cm3·mol−1 Δη/mPa∙s κEs /TPa−1 VE/cm3 mol−1 Δη/mPa∙s κEs /TPa−1
0.299 0.047 0.008 −0.311 −0.024 −0.030 −25.85 55.37 −1.036 0.308 0.061 0.052 −0.329 0.007 0.034 −22.67 56.26 6.123 0.321 0.069 0.060 −0.326 −0.033 −0.116 −19.19 57.40 12.66 0.324 0.076 0.141 −0.337 −0.049 −0.181 −14.96 59.61 17.95
0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.002 0.004
VE/cm3· mol−1 Δη/mPa∙s κEs /TPa−1 VE/cm3·mol−1 Δη/mPa∙s κEs /TPa−1 VE/cm3·mol−1 Δη/mPa∙s κEs /TPa−1 VE/cm3·mol−1 Δη/mPa∙s κEs /TPa−1
0.314
0.055
0.048
0.001
−0.321 −29.25 0.325 −0.332 −25.43 0.347 −0.336 −21.65 0.347 −0.339 −17.98
−0.022 52.40 0.064 −0.022 53.27 0.076 −0.039 55.57 0.087 −0.051 58.37
−0.093 0.982 0.072 −0.096 1.739 0.068 −0.159 6.659 0.144 −0.228 15.27
0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.238 0.001 0.001 0.002
Fig. 13. Excess Gibbs energy of activation of viscous flow (G⁎E) of the binary liquid mixture of 3-chloroaniline with 1-hexanol (∎), 1-heptanol (●), 1-octanol (▲) and 1-decanol (▼) at 303.15 K.
The interaction parameter d12 is positive for binary systems. Nigam and Mahl concluded from the study of binary mixtures that (i) if Δη N 0, d12 N 0 and magnitude of both are large then strong specific interaction (ii) if Δ η b 0, d12 N 0 then weak specific interaction (iii) if Δ η b 0, d12 b 0 magnitude of both are large then the dispersion force would be dominant. Fort and Moore [36] reported that for any binary liquid mixture, a positive value of d12 indicates the presence of specific interactions and a negative value of d12 indicates the presence of weak interactions between the unlike molecules. On this basis, we can say that there is a strong interaction in the binary system of 3-chloroaniline with 1-octanol and 1-decanol. Interaction parameter Wvis/RT shows almost the same trend as that of d12. In fact, one could say that the parameters d12 and Wvis/RT exhibit almost similar behavior, which is not unlikely in view of logarithmic nature of both equations. The values of interaction parameters Tamara and Kurata (T12) and Hind et al. (H12) do not differ appreciably from each other. This is in agreement with the view put forward by Fort and Moore [36] in regard to the nature of parameters T12 and H12.
The equation given by Heric and Brewer is as follows [34]: lnη ¼ x1 lnη1 þ x2 ln η2 þ x1 lnM1 þ x2 ln M2 – ln ðx1 M1 þx2 M2 Þ2x1 x2 Δ12
ð14Þ
where Δ12 is the interaction term and other symbols have their usual meaning. The one-parameter equation due to Tamura and Kurata [35] gave the equation of the form η ¼ x1 Φ1 η1 þ x2 Φ2 η2 þ 2ðx1 x2 Φ1 Φ2 Þ1=2 T12
ð15Þ
where Φ1 and Φ2 are the volume fractions of components 1 and 2, respectively, T12 is Tamura and Kurata constant.
Fig. 14. Excess Gibbs energy of activation of viscous flow (G⁎E) of the binary liquid mixture of 3-chloroaniline with 1-hexanol (□), 1-heptanol (○), 1-octanol (△) and 1-decanol (▽) at 308.15 K.
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D. Rahul et al. / Journal of Molecular Liquids 212 (2015) 618–628 Table 6 Molecular assignment for different shapes. Shape Sphere Cube Tetrahedron Discs Disc A Disc B Disc C Disc D
Fig. 15. Excess Gibbs energy of activation of viscous flow (G⁎E) of the binary liquid mixture of 3-chloroaniline with 1-hexanol (ξ), 1-heptanol (ψ), 1-octanol ({) and 1-decanol (|) at 313.15 K.
3.1. Scaled particle theory The theoretical ultrasonic speed of binary mixtures may be estimated based on some empirical, semiempirical and statistical models such as Free Length Theory (FLT), Collision Factor Theory (CFT), Nomoto relation, Vandeel Vangeal relation, etc. for the binary mixtures [37,38]. The common drawback of these theoretical models is that the shapes of the participating species have not been taken into consideration. In the scaled particle theory (SPT) [39] different shapes, such as spherical, cube, tetrahedral, disc A, disc B, disc C and disc D, of the participating components are considered and when the participating components have the correct shapes the theoretical ultrasonic speed estimated based on this model will give values close to the experimental values. Generally, the chemical structure of a liquid molecule is known but no definite shape has been attached to it [40]. Ghosh et al. [40] have used the scaled particle theory for the binary mixtures of 1,1,1trichloroethane with 1-alkanols by considering different shapes such as spherical, cubical and tetrahedral. Kalidoss and Srinivasamoorthy [41] have extended the SPT for some binary mixtures and ternary liquid mixtures by considering seven shapes of the individual components that includes spherical, cube, tetrahedron, disc A, disc B, disc C and
Size
S
R
Radius = a Side = l Side = l
VH 2
A 3l/4
pffiffiffi 3l ; arctan 2=2π Radius = a and depth l l=a (π + 1)a/4 l = a/4 (π + 0.25)a/4 l = a/2 (π + 0.50)π/4 l = a/10 (π + 0.10)a/4
4πa 6l2 pffiffiffi 2 3l
4πa3/3 l3 pffiffiffi 3 ð 2=12Þl
4πa2 5πa2/2 3πa2 11πa2/5
πa3 πa3/4 πa3/2 πa3/10
disc D (the shapes are assigned by some characteristic parameters as given in Tables 6 and 7). In this paper, the theoretical ultrasonic speeds of the binary mixtures are estimated by assigning the above said seven shapes to the participating components and compared them with experimental speeds. Only when the participating molecules have particular shapes the theoretical values closely agrees with the experimental ultrasonic speed, which will be determined by chi-square fitting, χ2 [42]. The equation of state of fluid in the scaled particle theory is p 1 þ η þ η2 ¼ ρN kB T ð1−ηÞ2
ð16Þ
whereη = VHρN, VH is the hard core volume, ρN is the number density, and the other quantities have usual meanings [40].The SPT for mixtures of hard convex (not necessarily spherical) molecules gives the equation for mixture as follows [40,41]: p 1 ABρN B2 Cρ2N ¼ þ þ 2 ρN kB T ð1−VρN Þ ð1−VρN Þ 3ð1−VρN Þ3 X X X X 2 A¼ xi R i ; B ¼ xi Si ; C ¼ xi Ri ; V ¼ xi VH :
ð17Þ
Ri , Si and VH are the mean radius of curvature, surface area and volume, respectively, of a molecule of species i, ρN is the number density of mixture molecule, and xi is the mole fraction. Relating this with the equation γðdp=dρÞT ¼ u2
ð18Þ
where u is the ultrasonic speed, ρ is molecular density, and γ is the ratio of specific heats, we get Mu2 1 2ABρN B2 Cρ2N ¼ þ þ : γRT ð1−VρN Þ2 ð1−VρN Þ3 ð1−VρN Þ4
ð19Þ
Eq. (19) is used to evaluate the ultrasonic speed in the binary mixtures.
Table 7 Shape parameters.
Fig. 16. Excess Gibbs energy of activation of viscous flow (G⁎E) of the binary liquid mixture of 3-chloroaniline with 1-hexanol (⎕), 1-heptanol (⎕), 1-ocatnol (⎕) and 1-decanol (⎕) at 318.15 K.
Shape
X ¼ RS=VH
pffiffiffiffiffiffiffi Y ¼ R= 3 VH
Z ¼ S=R
Sphere Cube Tetrahedron Disc A Disc B Disc C Disc D
3.0000 4.5000 6.7035 4.1416 8.4790 5.4624 17.8274
0.6204 0.7500 0.9303 0.7070 0.9190 0.7832 1.1920
12.5664 10.6666 8.3247 11.7218 10.9244 11.3712 10.5253
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627
Table 8 Ultrasonic speeds computed theoretically using SPT with behavior shape having least chi-square fit and experimentally measured values of all binary mixtures at different temperatures. x1
303.15 K u exp
308.15 K ucal
u exp
Disc D + disc A
313.15 K ucal
u exp
Disc D + disc A
318.5 K ucal
u exp
Disc D + disc A
ucal Disc D + disc A
3-Chloroaniline + 1-hexanol 0.0000 1286.20 0.1167 1295.30 0.2291 1305.10 0.3375 1316.10 0.4421 1329.00 0.5431 1344.50 0.6407 1363.80 0.7350 1388.40 0.8263 1420.20 0.9145 1461.90 1.0000 1517.50 χ2
1286.62 1294.57 1301.50 1316.10 1330.17 1345.58 1364.27 1388.30 1419.99 1461.90 1517.42 0.0753
1270.20 1279.50 1289.40 1300.50 1313.60 1329.50 1349.20 1374.10 1406.00 1447.20 1501.20
1270.14 1278.42 1288.46 1300.47 1314.66 1331.37 1351.01 1374.10 1401.40 1447.80 1501.66 0.0705
1252.5 1262.2 1272.1 1282.9 1295.7 1311.3 1330.8 1355.5 1387.1 1427.7 1480.3
1252.44 1260.56 1270.48 1282.39 1296.51 1313.12 1332.62 1355.50 1382.46 1424.30 1480.31 0.0657
1245.6 1254.7 1264.3 1274.9 1287.3 1302.5 1321.4 1345.3 1375.7 1414.5 1464.8
1245.55 1253.44 1263.10 1274.69 1288.41 1304.50 1323.32 1345.30 1371.07 1414.34 1464.25 0.0616
3-Chloroaniline + 1-heptanol 0.0000 1312.5 0.1306 1320.7 0.2526 1328.7 0.3669 1337.8 0.4741 1348.4 0.5749 1361.5 0.6698 1378.5 0.7593 1400.5 0.8440 1429.4 0.9241 1467.4 1.0000 1517.5 χ2
1312.44 1319.27 1327.47 1337.33 1349.17 1363.34 1380.28 1400.50 1427.75 1467.94 1517.36 0.3951
1295.2 1303.5 1312.1 1321.5 1332.5 1346.0 1363.3 1385.5 1414.3 1451.9 1501.2
1295.14 1301.67 1309.99 1320.27 1332.68 1347.47 1364.94 1385.50 1413.77 1450.46 1501.66 0.1156
1275.4 1284.4 1293.0 1302.2 1312.9 1326.4 1343.7 1366.0 1394.8 1432.1 1480.3
1275.34 1281.89 1290.25 1300.60 1313.08 1327.94 1345.45 1366.00 1390.16 1431.59 1480.31 0.1101
1277.3 1268.6 1277.3 1286.6 1297.6 1311.4 1329.1 1351.7 1380.6 1417.6 1464.8
1259.44 1265.86 1274.28 1284.82 1297.62 1312.87 1330.80 1351.70 1378.02 1416.28 1464.25 0.1201
3-Chloroaniline + 1-octanol 0.0000 1333.5 0.1441 1340.9 0.2748 1347.6 0.3937 1355.0 0.5026 1363.4 0.6025 1374.4 0.6945 1389.2 0.7795 1409.1 0.8584 1435.8 0.9317 1471.4 1.0000 1517.5 2 χ
1333.44 1339.64 1346.40 1354.13 1363.41 1374.95 1389.74 1409.10 1434.91 1469.75 1517.50 0.2245
1312.5 1320.4 1327.8 1335.4 1344.6 1356.3 1371.8 1392.4 1419.5 1455.0 1501.2
1312.44 1319.03 1326.30 1334.64 1344.60 1356.87 1372.38 1392.40 1418.70 1453.75 1501.20 0.2149
1295.4 1303.6 1310.9 1318.5 1327.5 1339.2 1354.7 1375.2 1402.1 1437.0 1482.2
1295.34 1301.87 1309.13 1317.50 1327.51 1339.81 1355.31 1375.20 1401.22 1435.71 1482.20 0.2074
1282.5 1290.8 1297.9 1305.3 1314.6 1326.4 1341.3 1361.6 1388.5 1422.9 1466.5
1282.44 1289.06 1296.36 1304.72 1314.65 1326.81 1342.06 1361.60 1387.12 1420.93 1466.50 0.2046
3-Chloroaniline + 1-decanol 0.0000 1363.5 0.1699 1370.0 0.3153 1374.5 0.4411 1378.7 0.5511 1384.0 0.6481 1392.3 0.7342 1404.5 0.8112 1422.0 0.8805 1445.6 0.9431 1477.0 1.0000 1517.5 χ2
1363.44 1367.06 1371.44 1376.95 1384.03 1393.30 1405.57 1422.00 1444.25 1474.78 1517.50 0.1618
1344.2 1351.3 1356.2 1360.6 1366.5 1375.3 1387.9 1405.6 1429.6 1461.0 1501.2
1344.14 1348.19 1353.02 1358.98 1366.50 1376.20 1388.85 1405.60 1428.08 1458.68 1501.20 0.1538
1328.5 1335.7 1340.4 1344.7 1350.4 1358.9 1371.4 1388.7 1411.9 1441.9 1480.3
1328.44 1332.36 1337.09 1342.96 1350.40 1359.96 1372.38 1388.70 1410.44 1439.81 1480.30 0.1491
1320.0 1327.1 1331.5 1335.5 1340.8 1349.0 1360.9 1377.5 1399.7 1428.3 1464.8
1319.94 1323.61 1328.08 1333.68 1340.80 1349.96 1361.87 1377.50 1398.29 1426.29 1464.80 0.1457
For the case of pure liquids, Eq. (19) is modified by introducing the dimensionless shape parameter, X ¼ RS=VH and η = VHρN Mu2 ½ðX−1Þη2 ¼ γRT ð1−ηÞ4
ð20Þ
Its solution is obtained as [41] qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi η ¼ K− K2 þ L−1 where K = 1 + L(X − 1)/2 and L ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi γRT=Mu2. The mean radius and the 1=3
surface area of a molecule can be written as R ¼ YVH and S ¼ ZR
2
where Y and Z are the parameters related to the shape of the molecule. If the molecule is assigned different shapes (Table 6), the corresponding values of shape parameters, X, Y and Z, can be calculated (Table 7). In the present investigation, the theoretical speed based on SPT is computed for the 3-chloroaniline + 1-alkanols binary mixtures by considering different shapes, viz. sphere, cube, tetrahedron, disc A, disc B, disc C and disc D, for both the participating components. Hence for a binary mixture there are 49 combinations of shapes at a particular temperature. By using χ2 test, the best-fitting combination of shapes of the participating component molecules is obtained. Chi-square test χ2 can be used to test the goodness of fitting, which enables us to find whether the deviations of the theoretical values from the experimental ones are due to chance or really due to the inadequacy of the theory to fit the data. The theoretical ultrasonic speeds based on SPT for the mixtures
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Table 9 Volume interaction (a and b) and hard core correction (C and D) parameters. Binary mixture
3-Chloroaniline + 1-hexanol 3-Chloroaniline + 1-heptanol 3-Chloroaniline + 1-octanol 3-Chloroaniline + 1-decanol Binary mixture
3-Chloroaniline + 1-hexanol 3-Chloroaniline + 1-heptanol 3-Chloroaniline + 1-octanol 3-Chloroaniline + 1-decanol
303.15 K
308.15 K
a (C)
b (D)
Sign of VEmax
a (C)
b (D)
Sign of VEmax
−0.072 (−0.2424) −0.201 (−0.5121) −0.150 (−0.2520) −0.199 (−0.3570)
−0.057 (−0.8363) −0.253 (−0.2325) −0.155 (−0.1627) −0.251 (−0.1930)
Negative Negative Negative Negative
−0.073 (−0.0731) −0.117 (−0.1779) −0.150 (−0.2559) −0.199 (−0.3590)
−0.058 (−0.0293) −0.107 (−0.0476) −0.156 (−0.1576) −0.251 (−0.1910)
Negative Negative Negative Negative
a (C)
b (D)
Sign of VEmax
a (C)
b (D)
Sign of VEmax
−0.072 (−0.0738) −0.117 (−0.1800) −0.152 (−0.2635) −0.199 (−0.3650)
−0.058 (−0.0262) −0.107 (−0.0445) −0.157 (−0.1558) −0.251 (−0.1870)
Negative Negative Negative Negative
−0.130 (−0.0701) −0.117 (−0.1915) −0.153 (−0.2658) −0.201 (−0.3740)
−0.110 (−0.0213) −0.107 (−0.0376) −0.158 (−0.1565) −0.253 (−0.1870)
Negative Negative Negative Negative
313.15 K
318.15 K
having liquids belonging to 1-alkanols with 3-chloroaniline at different temperatures are given in Table 8 for the minimum values of χ2. From Table 8, it is seen that for all binary mixtures takes the shapes of disc D + disc A, the ultrasonic speed estimated based on SPT is found to be very close to the experimental values. Thus our theoretical analysis using SPT has proved that the temperature has no effect on the shapes of the participating components in all four binary systems [43,44]. In addition, the expansion of volume in the participating molecules can be discussed using the volume interaction parameters a and b given in Table 9. 4. Conclusions In this paper, density, speed of sound and viscosity data is reported for binary mixtures of 3-chloroaniline and 1-alkanols (1-hexanol, 1heptanol, 1-octanol, and 1-decanol) at different temperatures. The excess parameter studies such as VE, κEs , and Δη indicate that the rupture of hydrogen bonded chain of the dipolar interaction between like molecules exceed the intermolecular interaction through dipole–dipole and hydrogen bonding between 3-chloroaniline and 1-alkanol molecules. This behavior is characteristic for systems containing an associated component. Furthermore, theoretical ultrasonic speeds of these mixtures are evaluated by considering the different shapes of the participating components using the scaled particle theory. References [1] M. Chandra Sekhar, M. Gowri Sankar, A. Venkatesulu, http://dx.doi.org/10.1016/j. molliq.2015.04.034 [2] G. Praveen Chand, M. Gowri Sankar, P.N.V.V.L. Prameela Rani, C. Rambabu, J. Mol. Liq. 201 (2015) 1–9. [3] T. Srinivasa Krishna, M. Gowri Sankar, K.T.S.S. Raju, S. Govardhan Rao, B. Munibhadrayya, J. Mol. Liq. 206 (2015) 350–358. [4] M.A. Saleh, M. Habibullah, M. Shamsuddin Ahmed, M. Ashraf Uddin, S.M.H. Uddin, M. Afsar Uddin, F.M. Khan, Phys. Chem. Liq. 43 (2005) 139–148. [5] V.K. Sharma, P. Paul Singh, S. Maken, J. Chem. Eng. Data 39 (1994) 238–240. [6] V. Pandiyan, S.L. Oswal, P. Vasanthrani, Thermochim. Acta 524 (2011) 140–150. [7] Y. Marcus, Introduction to Liquid State Chemistry, Wiley Intersciences, New York, 1977.
[8] G.A. Krestov, Thermodynamics of Solvation, Ellis Horwood Limited, England, 1991. [9] W. Schaaffs, Acustica 33 (1975) 272–276. [10] J.A. Riddick, W.B. Bunger, T.K. Sakano, Organic Solvents Physical Properties and Method of Purifications, vol. 2, Wiley Intersciences, N. Y., 1986 [11] J. Timmermans, Physico-chemical Constants of Pure Organic Compounds, vol. 1, Elsevier Publications, Amsterdam, 1950. [12] S. Kumar, A. Maken, S. Agarwal, S. Maken, J. Mol. Liq. 155 (2010) 115–120. [13] P. Jeevanandham, S. Kumar, P. Periyasamy, J. Mol. Liq. 188 (2013) 203–209. [14] M.S. AlTuwaim, A. Haek, S.A. Al-Jimaz, A.A. Mohammad, J. Chem. Thermodyn. 48 (2012) 39–47. [15] A.S. Al-Jimaz, J.A. Al-Kandary, M.A.-H. Abdul-Latif, Fluid Phase Equilib. 218 (2004) 247–260. [16] J. Ortega, J.D. Garcia, Can. J. Chem. 66 (1988) 1520–1524. [17] A.S. Al-Jimaz, J.A. Al-Kandary, M. Abdul-Haq, Abdul-Latif, J. Chem. Eng. Data 52 (2007) 206–214. [18] B.D. Djordjevic, I.R. Radovic, M.L.J. Kijevcanin, A.Z. Tasica, S.P. Serbanovic, J. Serb. Chem. Soc. 74 (2009) 477–491. [19] M.N.M. Al-Hayan, J. Chem. Thermodyn. 38 (2006) 427–433. [20] M.A. Rauf, M. Arfan, F. Azizi, J. Chem. Thermodyn. 15 (1983) 1021–1023. [21] A. Ali, A.K. Nain, Abida, J. Chil. Chem. Soc. 51 (2004) 477–485. [22] G.C. Benson, O. Kiyohara, J. Chem. Thermodyn. 11 (1979) 1061–1064. [23] B. Jacobson, Ark. Kemi 2 (1950) 177–210. [24] K. Ramanjaneyulu, K.N. Surendranath, A. Krishnaiah, Acoust. Lett. 11 (1988) 152–157. [25] M.N. Roy, A. Benerjee, A. Choudhary, Phys. Chem. Liq. 47 (2009) 412–436. [26] A. Ali, K. Tiwari, A.K. Nain, V. Chakravortty, Phys. Chem. Liq. 38 (2000) 459–473. [27] R.J. Fort, W.R. Moore, Trans. Faraday Soc. 62 (1965) 2102–2111. [28] G.E. Papanastasiou, I.I. Ziogas, J. Chem. Eng. Data 36 (1961) 46–51. [29] A. Mohammad, Chowdhury, M.A. Majid, M.A. Salesh, J. Chem. Thermodyn. 33 (2001) 347–360. [30] O. Redlich, A.T. Kister, Ind. Eng. Chem. 40 (1948) 345–348. [31] L. Grunberg, A.H. Nissan, Mixture law for viscosity, Nature 164 (1949) 799–800. [32] P.K. Katti, M.H. Chaudhri, J. Chem. Eng. Data 9 (1964) 442–443. [33] R.K. Hind, E. McLaughlin, A. Ubbelohde, Trans. Faraday Soc. 56 (1960) 328–330. [34] E.L. Heric, J.G. Brewer, J. Chem. Eng. Data 12 (1967) 574–583. [35] M. Tamura, M. Kurata, Bull. Chem. Soc. Jpn. 25 (1952) 32–37. [36] R.J. Fort, W.R. Moore, Trans. Faraday Soc. 62 (1966) 1112–1129. [37] K. Rajagopal, S. Chenthilnath, A.K. Nain, J. Mol. Liq. 151 (2010) 23–29. [38] K. Rajagopal, S. Chenthilnath, Thermochim. Acta 498 (2010) 45–53. [39] H. Reiss, H.L. Frisch, J.L. Lebowitz, J. Chem. Phys. 31 (1959) 369–380. [40] S. Ghosh, K.N. Pande, Y.D. Wankhade, Indian J. Pure Appl. Phys. 42 (2004) 729–734. [41] M. Kalidoss, R. Srinivasamoorthy, Acust. Acta Acust. 83 (1997) 776–779. [42] G. Udny, An Introduction to the Theory of Statistics, 14 th edition, 1987 (New Delhi). [43] K. Rajagopal, S. Chenthilnath, Thermochim. Acta 498 (2010) 45–53. [44] K. Rajagopal, S. Chenthilnath, Chin. J. Chem. Eng. 18 (2010) 804–816.