Isothermal vapour pressures and thermodynamic excess properties of 3,5- and 2,6-dimethylpyridine with cyclohexane. Measurements and prediction

Fluid Phase Equilibria 373 (2014) 34–42

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Isothermal vapour pressures and thermodynamic excess properties of 3,5- and 2,6-dimethylpyridine with cyclohexane. Measurements and prediction Hamama Ben-Makhlouf-Hakem a,∗ , Ahmed Ait-Kaci a , Jacques Jose b a

Laboratoire de Thermodynamique et Modélisation Moléculaire, Faculté de Chimie, USTHB, BP, 32 El-Alia, 16111 Bab Ezzouar, Algeria Laboratoire de Chimie Analytique I, Université Claude Bernard (Lyon I), 43 Boulevard du 11 novembre 1918, Bât Raulin/2, 69622 Villeurbanne Cedex, France b

a r t i c l e

i n f o

Article history: Received 22 May 2013 Received in revised form 30 March 2014 Accepted 4 April 2014 Available online 18 April 2014 Keywords: Excess properties Vapour–liquid equilibrium Enthalpy Lutidines

a b s t r a c t The vapour pressures of liquid mixtures 3,5- and 2,6-dimethylpyridine (or lutidines) with cyclohexane were measured by a static method in the range of 283.15–353.15 K. The pure components vapour pressures data and those of corresponding mixtures were correlated using Antoine type equation. Data reduction by Barker’s method provides correlation for excess molar Gibbs energy GE . The excess molar enthalpies HE of binary liquid mixtures of 3,5- and 2,6-dimethylpyridine with cyclohexane were measured at 303.15 K using a Calvet type microcalorimeter, C80 Setaram. The experimental results, along with our previous data of GE and HE [1,2] are used for estimating interaction parameters in DISQUAC, an extended quasi-chemical group contribution model [3]. © 2014 Elsevier B.V. All rights reserved.

1. Introduction Vapor–liquid equilibrium (VLE) data are essential for engineering design of separation processes and unit operations. They are useful for an extension of some thermodynamical models commonly applied for designing petrochemical related processes. Such information can be obtained experimentally or adopted from generalized methods to calculate properties of multicomponent mixtures. Most liquid systems of industrial interest deviate from ideal behavior. Usually, densities of vapor and liquid phases are important to give proper size in the process design of many separation equipments. The present work forms a part of our investigation on binary mixtures containing nitro aromatic components with hydrocarbons. Previously, we have reported the experimental data of vapour pressures and excess enthalpies of 3,5- and 2,6-lutidines with nalkanes (C6–C8) and toluene [1,2]. As a continuation of that work, measurements of total pressure, excess molar Gibbs energy and enthalpy have been made for two further binary mixtures of 3,5-

∗ Corresponding author. Tel.: +213 771399348; fax: +213 21247107. E-mail addresses: [email protected], [email protected] (H. Ben-Makhlouf-Hakem). http://dx.doi.org/10.1016/j.fluid.2014.04.004 0378-3812/© 2014 Elsevier B.V. All rights reserved.

and 2,6-lutidines with cyclohexane. The experimental data were described using the DISQUAC model [3]. 2. Experimental 2.1. Materials The chemicals used in this study were 2,6-lutidine, 3,5-lutidine and cyclohexane. The suppliers, formulas and purities of the pure components are shown in Table 1. All liquids were used as received and thoroughly degassed before measurements. 2.2. Apparatus and procedure The experimental HE data were measured, at atmospheric pressure, by means of a microcalorimeter, C80 (SETARAM model, Lyon, France).The temperature T was maintained constant at 303.15 ± 0.02 K. The mercury is used to separate the two cells, which contained the liquids under study. The performance of the apparatus was checked by determining HE of cyclohexane + benzene at T = 298.15 K, our results differ by less than 2% from those reported by Marsh [4]. The total vapour pressure measurements were carried out with a static method described elsewhere by Blondel-Tellouk et al. [5], so, only the most salient information are given here. The

H. Ben-Makhlouf-Hakem et al. / Fluid Phase Equilibria 373 (2014) 34–42 Table 1 Provenance and purity of the chemicals used in this study. Component

Formula

2,6-Dimethylpyridine 3,5-Dimethylpyridine Cyclohexane

C7 H9 N C7 H9 N C6 H12

Source

Supplier’s purity

Sigma–Aldrich Aldrich Acros

GC purity

>98.7%

apparatus allows measurements at pressures from (133 to 200 × 103 ) Pa thanks to two pressure sensors: MKS gage (model 615D, MKS instrument, USA) for pressure between (133 and 1333) Pa and a Rosemount gage (Model 1151 DPE 2252, Minneapolis, MN, USA) for pressure between (1333 and 200 × 103 ) Pa. The pressure measurement consisted of applying the vapour pressure of the sample on the measurement side of the gauge. The reference side was submitted to a permanent-dynamic pumping; the residual pressure was 10−4 Pa and therefore can be neglected. The gauge was checked periodically by means of Hg manometer and Bouty (Paris, France) type 70298 cathetometer. Temperatures were measured with a copper–constantan thermocouple calibrated with a platinum resistance thermometer (±0.001 K, IPTS 90) a Leeds Northup bridge. The uncertainties on our measurements are estimated to be ±0.02 ◦ C for temperature range, 0.2% for mole fraction. 3% for pressure lower than 600 Pa, 1% for the pressure range 700 ≤ p (Pa) ≤ 1300 and 0.3% for the pressure range 1300 ≤ p (Pa) ≤ 200,000. Mixture compositions were prepared by mass and degassed by distillation as described previously by Blondel-Tellouk et al. [5]. The final composition of the liquid was determined after each pressure measurement by gas-liquid chromatography (Delsi instrument, Di 200, used a capillary column (Ø (100/120 mesh Hays SPQ) and length = 2 m with a FID detector). 3. Results Experimental molar excess enthalpies HE at 303.15 K are endothermic. They are reported in Table 2. The results have been fitted to the Redlich–Kister type equation: n 

H E = x1 (1 − x1 )

ai (2x1 − 1)i−1

(1)

i=1

The values of the coefficients ai and the standard deviations ı (HE ), given by:

 ∂(H E ) =

n E )2  (H E − Hexp i=1

1/2 (2)

N−n

Table 2 Experimental excess enthalpy at T = 303.15 K. x1

E

H (J mol

−1

)

x1

E

H (J mol

(a) 2,6-Lutidine (1) + cyclohexane (2) 515 0.090 1001 0.220 1124 0.275 0.308 1177 1249 0.434

0.529 0.669 0.806 0.8998

1186 945 594 313

(b) 3,5-Lutidine (1) + cyclohexane (2) 0.085 467.4 0.221 950.4 1153.5 0.312 1232.3 0.386 1282.2 0.515

0.635 0.735 0.830 0.899

1165.7 910 623.2 397.96

u(T) = 0.02 K; u(HE ) = 0.02 (J mol−1 ).

Table 3 Coefficients ai and standard deviation ı (HE ) for least-squares representation by Eq. (2) of HE at 303.15 K. Mixtures

≥99% >98+% >99.7%

−1

)

35

a1

3,5-Lutidine 5128.11 (1) + cyclohexane (2) 2,6-Lutidine 4935.74 (1) + cyclohexane (2)

a2

a3

a4

ı (HE ) (J mol−1 )

−536.83

−128.95

−827.61

14.6

−251.30

739.81

–

18.1

Table 4a Experimental vapor pressures of cyclohexane. T exp (K)

P exp (kPa)

ıP/P (%)

283.32 288.28 293.27 298.25 303.27 313.24 323.21 333.21 343.18 353.14

6.389 8.195 10.417 13.173 16.453 24.971 36.721 52.480 72.982 99.110

0.22 −0.08 −0.28 0.07 −0.03 −0.07 0.10 0.11 0.04 −0.12

Table 4b Experimental vapor pressures of 2,6-lutidine. T exp (K)

P exp (kPa)

ıP/P (%)

283.37 288.33 293.30 298.30 303.27 313.27 323.24 333.21 343.20 353.14

0.300 0.420 0.581 0.794 1.070 1.879 3.163 5.1399 8.101 12.230

−0.01 −0.06 0.02 0.04 0.15 −0.07 −0.12 −0.08 0.20 −0.07

Were determined by least-squares analysis and are reported in Table 3. N is the number of experimental points and n the number of coefficients ai . The pure components vapour pressures data used in Barker analysis are given in Table 4. They have been correlated with the Antoine equation. The results are summarized in Table 5. Vapour phase imperfection and variation of the Gibbs energy of the pure liquid components with pressure were accounted for in

Table 4c Experimental vapor pressures of 3,5-lutidine. T exp (K)

P exp (kPa)

ıP/P (%)

273.50 283.45 293.47 303.54 313.56 323.59 333.66 343.62 353.63

0.040 0.085 0.172 0.331 0.612 1.078 1.824 2.973 4.688

0.27 −0.15 −0.29 −0.35 0.20 0.42 0.12 0.12 −0.34

u(p) = 0.03 (p/Pa) for p ≤ 600 Pa. u(p) = 0.01 (p/Pa) for the pressure range700 ≤ p (Pa) ≤ 1300. u(p) = 0.003 (p/Pa) for the pressure range1300 ≤ p (Pa) ≤ 200,000. u(T) = 0.02 K and u(x) = 0.0002.

36

H. Ben-Makhlouf-Hakem et al. / Fluid Phase Equilibria 373 (2014) 34–42

Table 5 Smoothing parameters of the experimental results by the Antoine equation: Log P (mm Hg) = A − B/(t (◦ C) + C). Compound

A

B

C

ıP/P (%) mean

Cyclohexane 2,6-Lutidine 3,5-Lutidine

6.604146 ± 0.032864 7.297875 ± 0.027364 7.634883 ± 0.061927

1076.628 ± 16.447 1602.216 ± 14.359 1918.503 ± 33.640

208.45887 ± 1.89833 220.46274 ± 1.16835 234.67790 ± 2.36405

0.106 0.083 0.250

Table 6 Molar volume V* (cm3 mol−1 virial coefficients for the ij pair Bij (cm3 mol−1 ) and for pure compounds (i = j). T (K)

Cyclohexane

3,5-Lutidine

*

283.15 293.15 303.15 313.15 323.15 333.15 343.15 353.15

*

V

B11

V

105.34 106.54 107.79 109.10 110.46 111.89 113.37 114.93

−2264 −1998 −1783 −1605 −1457 −1332 −1224 −1131

111.64 112.61 113.61 114.64 115.69 116.78 117.91 119.07

2,6-Lutidine B11 −8612 −7145 −6016 −5136 −4439 −3879 −3425 −3051

B12

V*

−4223 −3615 −3137 −2755 −2445 −2190 −1977 −1798

110.62 110.62 112.79 113.93 115.11 116.33 117.59 118.90

B11

B12

−5781 −4855 −4186 −3632 −3188 −2826 −2527 −2278

−3535 −3053 −2671 −2362 −2110 −1901 −1725 −1576

terms of the 2nd molar Virial coefficients and the molar volumes under saturation pressure. 2  xi P 0 exp[g E − (Bii − V 0 )(P − P 0 ) − 2PB12 (1 − yi )2 ] i

i

i

i

RT

(3)

i=1

y=

xi Pi0 P

a

T=283,15K) T=293,15 K 303,15 K 313,15 K 323,15 K 333,15 K 343,15 K 353,15 K

100

exp[giE − (Bii − Vi0 )(P − Pi0 ) − 2PB12 (1 − yi )2 ]

BE = B12 −

B + B  11 12 2

(4) 80

;

Pi0 = P(xi =1)

(5)

where Vi0 is the molar volume of the pure compound estimated with the Rackett equation, using the literature data for acentric factor and critical properties [6]. Bii the 2nd molar Virial coefficients were evaluated with Tsonopoulos method [7,8]. The values are reported in Table 6. Vapour pressures measurements, for the two mixtures at different temperatures, are plotted in Fig. 1 and given in Table 7 together with the activity coefficients  1 and  2 and the excess molar Gibbs energies GE calculated by Barker’s method [9], on the assumption that:

 GE = x1 (1 − x1 ) Ai (2x1 − 1)i RT

P/kPa

P=

60

40

20

0 0,0

0,2

0,4

0,6

0,8

1,0

X1

m−1

(6)

b

 ı=

1 n n−m i=0

T=283,15K) T=293,15 K 303,15 K 313,15 K 323,15 K 333,15 K 343,15 K 353,15 K

100

i=0



(Pexp − Pcalc ) Pexp

2 1/2 80

where x1 is the molar fraction of 3,5- or 2,6-lutidine, n the number of experimental points and m the number of coefficients Ai . The parameters Ai and the standard deviation for the pressure ı are given in Table 8. (GE /T )x1 =0.5 was fitted with a second degree polynomial in 1/T, the correlation coefficient R is then R > 0.9995 for all cases, see Fig. 2. In the absence of independent values of activity coefficients; we cannot use the Gibbs-Duhem relation to test the thermodynamic consistency of the vapour pressure measurements. We can, however, test the consistency of the enthalpies and free energies by means of the Gibbs–Helmholtz equation. The HE values estimated from the temperature dependence of GE follow the same trend and are agreement with experimental results (Fig. 3), considering that the quantitative evaluation of HE from vapour pressure data involves great uncertainty [10].

60

P/kPa

(7)

40

20

0 0,0

0,2

0,4

0,6

0,8

1,0

x1 Fig. 1. (a, b) Vapor–liquid equilibrium data, P, as a function of molar fraction in liquid x1 . (a) 2,6-lutidine (1) + cyclohexane (2) and (b) 3,5-lutidine (1) + cyclohexane (2).

H. Ben-Makhlouf-Hakem et al. / Fluid Phase Equilibria 373 (2014) 34–42

37

Table 7 Values of vapor pressure p (kPa), relative deviation p = 100 (p − pcal )/p, activity coefficients  1 and  2 and excess molar Gibbs energies GE (J mol−1 ). T (K)

x1

GE

y1

P

2,6-Lutidine (1) + cyclohexane (2) 0.2254 283.15 0.4329 0.5446 0.6436 0.8356 0.9771 0.2254 293.15 0 .4329 0.5446 0 .6436 0.8356 0 .9771 0.2254 303.15 0.4329 0.5446 0.6436 0.8356 0.9771 0.2254 313.15 0.4329 0.5446 0.6436 0.8356 0.9771

0.01978 0.03526 0.04825 0.06451 0.12531 0.44468 0.02264 0.04176 0.05764 0.07743 0.15108 0.50530 0.02580 0.04884 0.06776 0.09125 0.17845 0.56211 0.02926 0.05646 0.07855 0.10587 0.20709 0.61419

5.296 4.448 3.952 3.509 1.960 0.668 8.640 7.208 6.386 5.651 3.157 1.147 13.560 11.254 9.946 8.783 4.927 1.908 20.566 16.997 14.994 13.226 7.474 3.081

−2.69 −2.15 0.77 5.37 −4.64 2.59 −2.80 −2.05 .86 5.27 −4.71 2.89 −2.75 −1.93 0.86 5.07 −4.65 3.13 −2.56 −1.80 0 .79 4.81 −4.51 3.32

1.5987 1.2414 1.1665 1.1184 1.0372 1.0010 1.5305 1.2200 1.1535 1.1098 1.0347 1.0009 1.4764 1.2018 1.1414 1.1012 1.0320 1.0008 1.4327 1.1858 1.1300 1.0927 1.0291 1.0008

1.0899 1.2252 1.2997 1.3828 1.7341 2.5103 1.0806 1.2000 1.2657 1.3396 1.6538 2.3362 1.0725 1.1797 1.2390 1.3059 1.5875 2.1828 1.0656 1.1632 1.2178 1.2793 1.5318 2.0468

406.0 491.5 478.5 441.4 284.9 51.9 380.1 461.8 451.0 417.4 271.0 49.5 358.1 436.8 427.4 396.2 257.8 47.1 339.1 415.3 406.9 377.2 244.9 44.7

2,6-Lutidine (1) + cyclohexane (2) 0.2254 323.15 0.4329 0.5446 0.6436 0.8356 0.9771 0.2254 333.15 0.4329 0.5446 0.6436 0.8356 0.9771 0.2254 343.15 0.4329 0.5446 0.6436 0.8356 0.9771 0.2254 353.15 0.4329 0.5446 0.6436 0.8356 0.9771

0.03300 0.06460 0.08996 0.12122 0.23670 0.66097 .03701 .07320 0.10195 0.13727 0.26698 0.70219 0.04127 0.08224 0.11451 0.15400 0.29766 0.73790 0.04573 0.09166 0.12761 0.17145 0.32850 0.76836

30.256 24.922 21.954 19.358 11.047 4.842 43.313 35.586 31.314 27.619 15.950 7.422 60.507 49.616 43.624 38.507 22.540 11.121 82.683 67.703 59.493 52.579 31.233 16.315

−2.30 −1.67 0.68 4.52 −4.30 3.46 −2.00 −1.55 .55 4.23 −4.07 3.56 −1.70 −1.45 0.42 3.96 −3.84 3.63 −1.41 −1.36 0.29 3.73 −3.63 3.69

1.3965 1.1715 1.1192 1.0845 1.0262 1.0007 1.3656 1.1583 1.1091 1.0766 1.0235 1.0006 1.3385 1.1459 1.0996 1.0694 1.0211 1.0005 1.3138 1.1339 1.0909 1.0631 1.0191 1.0005

1.0597 1.1498 1.2008 1.2578 1.4838 1.9268 1.0548 1.1388 1.1868 1.2397 1.4419 1.8222 1.0510 1.1298 1.1750 1.2240 1.4048 1.7333 1.0482 1.1226 1.1646 1.2095 1.3715 1.6602

322.9 396.8 388.7 359.8 232.4 42.2 309.0 380.4 372.2 343.8 220.4 39.7 297.3 365.7 357.1 328.8 209.2 37.5 287.7 352.3 342.9 314.7 199.0 35.5

3,5-Lutidine (1) + cyclohexane (2) 0.1771 283.15 0.2382 0.4053 0.5156

0.00732 0 .00843 0.01070 0.01233

5.648 5.451 4.985 4.780

0.78 0.07 −1.44 0.83

2.7517 2.2921 1.5885 1.3490

1.0704 1.1227 1.3328 1.5315

553.8 672.8 843.8 849.4

3,5-Lutidine (1) + cyclohexane (2) 0.7218 298.15 0.8528 0.9437 0.1771 293.15 0.2382 0.4053 0.5156 0.7218 0.8528 0.9437 0.1771 303.15 0.2382 0.4053 0.5156 0.7218 0.8528 0.9437

0.01779 0.02802 0.06063 0.00867 0.01013 0.01324 0.01549 0.02274 0.03595 0.07723 0.01024 0.01209 0.01621 0.01922 0.02861 0.04518 0.09581

3.793 2.591 1.308 9.223 8.860 8.070 7.727 6.030 4.097 2.093 14.475 13.857 12.567 12.016 9.255 6.278 3.259

0.77 −1.14 0.50 0.45 −0.45 −1.44 1.36 0.69 −1.44 0.70 0.21 −0.83 −1.47 1.77 0.66 −1.70 0.87

1.1071 1.0310 1.0048 2.6157 2.2030 1.5598 1.3359 1.1050 1.0306 1.0047 2.5079 2.1312 1.5368 1.3263 1.1044 1.0308 1.0048

2.1079 2.7476 3.4540 1.0660 1.1149 1.3104 1.4949 2.0328 2.6347 3.3036 1.0626 1.1088 1.2921 1.4646 1.9713 2.5488 3.2006

661.3 411.5 174.9 543.2 660.5 831.0 838.7 656.6 410.2 174.9 536.4 652.6 823.2 832.9 656.5 412.4 176.5

P

1

2

38

H. Ben-Makhlouf-Hakem et al. / Fluid Phase Equilibria 373 (2014) 34–42

Table 7 (Continued) T (K) 313.15

323.15

y1

P

0.1771 0.2382 0.4053 0.5156 0.7218 0.8528 0.9437 0.1771 0.2382 0.4053 0.5156

0.01204 0.01433 0.01964 0.02357 0.03547 0.05575 0.11618 0.01409 0.01688 0.02358 0.02860

21.938 20.944 18.910 18.058 13.769 9.350 4.950 32.233 30.710 27.600 26.325

0.06 −1.10 −1.52 2.09 0.66 −1.93 1.03 −0.05 −1.28 −1.59 2.35

2.4209 2.0722 1.5183 1.3195 1.1050 1.0315 1.0050 2.3494 2.0229 1.5031 1.3147

1.0602 1.1041 1.2771 1.4391 1.9203 2.4829 3.1325 1.0583 1.1005 1.2645 1.4172

532.9 648.4 819.4 831.2 660.2 417.4 179.5 531.8 647.0 818.8 832.8

0.04340 0.06770 0.13814 0.01641 0.01977 0.02807 0.03436 0.05248 0.08104 0.16145 .01901 .02300 0.03313 0.04093 0.06279 0.09578 0.18589 0.02191 0.02659 0.03880 0.04834 0.07440 0.11193 0.21125

19.923 13.574 7.348 46.066 43.823 39.204 37.351 28.114 19.254 10.682 64.222 61.031 54.347 51.721 38.787 26.738 15.232 87.560 83.152 73.708 70.073 52.429 36.422 21.334

0.70 −2.13 1.17 −0.11 −1.40 −1.67 2.54 0.75 −2.32 1.29 −0.14 −1.46 −1.76 2.69 0.82 −2.51 1.41 −0.15 −1.48 −1.86 2.81 0.91 −2.68 1.53

1.1065 1.0325 1.0052 2.2894 1.9810 1.4906 1.3116 1.1088 1.0338 1.0054 2.2378 1.9443 1.4800 1.3098 1.1118 1.0354 1.0058 2.1923 1.9116 1.4708 1.3089 1.1152 1.0371 1.0061

1.8771 2.4320 3.0906 1.0570 1.0978 1.2538 1.3980 1.8399 2.3923 3.0687 1.0561 1.0956 1.2445 1.3809 1.8069 2.3610 3.0620 1.0555 1.0940 1.2362 1.3653 1.7771 2.3358 3.0670

667.0 424.8 183.8 532.8 647.9 820.7 837.0 676.4 434.2 189.1 535.3 650.4 824.5 843.0 687.8 445.3 195.2 538.8 654.1 829.4 850.4 700.8 457.9 202.1

3,5-Lutidine (1) + cyclohexane (2) 0.7218 323.15 0.8528 0.9437 0.1771 333.15 0.2382 0.4053 0.5156 0.7218 0.8528 0.9437 0.1771 343.15 0.2382 0.4053 0.5156 0.7218 0.8528 0.9437 0.1771 353.15 0.2382 0.4053 0.5156 0.7218 0.8528 0.9437

P

1

2

GE

x1

u(p) = 0.03 (p/Pa) for p ≤ 600 Pa. u(p) = 0.01 (p/Pa) for the pressure range700 ≤ p (Pa) ≤ 1300. u(p) = 0.003 (p/Pa) for the pressure range1300 ≤ p (Pa) ≤ 200,000. u(T) = 0.02 K and u(x) = 0.0002.

Table 8a Coefficients Ai and pressure deviations ı for least-squares representation by Eq. (6) defined as: 2,6-Lutidine (1) + cyclohexane (2). T (K)

A1

A2

A3

ı

283.15 293.15 303.15 313.15 323.15 333.15 343.15 353.15

0.82828 0.7530 0.6896 0.6353 0.5882 0.5467 0 .5097 0.4762

−0.1245 −0.1026 −0.0874 −0.07779 −0.0725 −0.0706 −0.0712 −0.0735

0.3023 0.2781 0.2521 0.2255 0.2000 0.1773 0.1593 0.1476

0.0482 0.0487 0.0480 0.0465 0.0446 0.0424 0.04034 0.0386

Table 8b Coefficients Ai and pressure deviations ı for least-squares representation by Eq. (6): 3,5-Lutidine (1) + cyclohexane (2). T (K)

A1

A2

A3

ı

283.15 293.15 303.15 313.15 323.15 333.15 343.15 353.15

1.4499 1.3822 1.3268 1.2813 1.243 1.2116 1.1842 1.1601

−0.1717 −0.1469 −0.1239 −0.1024 −0.8196 −0.6236 −0.0433 −0.0244

0.1277 0.1251 0.1284 0.1364 0.1482 0.1630 0.1802 0.1995

0.0117 0.0136 0.0159 0.0181 0.0200 0.0217 0.0232 0.0244



ı=

1 n−m

n   (P

2

exp −Pcalc )

Pexp i=0



1/2 .

4. Theory The thermodynamic excess functions of organic liquid mixtures depend on the chemical structures, the sizes and the shapes of the constituent molecules. It has been suggested that additional contributions arise in systems containing molecules of anisotropic shape (orientational order) or of different degrees of internal motion (conformational effects) [11] 3,5- or 2,6-lutidine + cyclohexane systems are regarded as possessing four types of surfaces: type a, alkane (CH3 , CH2 group), type n, nitrogen (N group); type c (aromatic) and type b, (cyclohexane). The relative molecular volume ri , the surface qi , and surface ˛si (s = a, n, c or b) of all the molecular species have been calculated on the basis of group volumes and surfaces recommended by Bondi [12], taking arbitrarily the volume and surface of methane as unity [13,14]. The values utilized are shown in Tables 9 and 10. The four types of surfaces a, n, c and b generate six pairs of contact: (a,n), (a,c) (a,b), (n,c), (n,b). The equations used to calculate GE and HE are the same as in previous publications [1,2]. The temperature dependency of the interaction parameters has been expressed in term of dispersive (dis) and/or quasichemical (quac) interaction dis and C quac , where st = (a,n), (a,c), (c,n), (a,b) or (n,b), coefficients: Cst,l st,l and l = 1 (Gibbs energy) l = 2 (enthalpy). 5. Estimation of interaction parameters For each pair of binary contacts (s,t) the experimental excess functions using to adjust the parameters are as follows.

H. Ben-Makhlouf-Hakem et al. / Fluid Phase Equilibria 373 (2014) 34–42

a

39

a

1,8

1200 1,6

1,4

-1

H Jmol

-1 E

pts exp polynomial fit

E

G /T (J K )

R= 0.99977 2,6-lutidine +cyclohexane

600

1,2

1,0 0,0028

0,0030

0,0032

0,0034

0

0,0036

0,0

0,5

-1

1/T (K )

b

1,0

x1

b

1,8

1400

1200

R = 0,99965

1000

-1

pts exp Polynomial fit

E

800

600

H J mol

1,4

E

3,5-lutidine+cyclohexane

-1

G /T (J.K )

1,6

1,2

400

200 1,0 0,0028

0,0030

0,0032

0,0034

0

0,0036

0,0

0,2

0,4

-1

Fig. 2. (a, b) Polynomial fit of (GE /T )x1 =0.5 with a second degree of 1/T. (a) 2,6lutidine(1) + cyclohexane (2) and (b) 3,5-lutidine (1) + cyclohexane(2).

Table 9 Relative group increments for molecular volume, rG = VG /VCH4 , and areas qG =

AG /ACH4 , calculated by Bondi method (ref) (VCH4 = 17.12 × 10−6 m3 mol 2.90 × 10−5 m3 mol

−1

0,6

0,8

1,0

X1

1/T (K )

−1

Fig. 3. (a, b) Comparison of the HE values estimated from the temperature dependence of GE with experimental HE at 303.15 K for: Full lines, estimated values from Gibbs–Helmotz equation; points () experimental results. (a) 2,6-lutidine (1) + cyclohexane (2) and (b) 3,5-lutidine (1) + cyclohexane (2).

; ACH4 =

).

Group

rG

qG

CH4 CH3 CH2 C6 H11 C6 H5 C5 H5 C5 H4 N

1.00000 0.79848 0.59755 3.5187 2.67757 2.35396 2.20668 0.30374

1.00000 0.73103 0.46552 2.5966 1.83793 1.72413 1.48970 0.10907

Contact (a,n): lutidine + alkane [1] Contact (b,c): benzene +cyclohexane [15]

Therefore, only the contact (n,b) coefficients must be determined as the remainder parameters are already known. Calculations were carried out assuming that the quasichimical coefficients quac Can,l of the (a, n) – contact are the same as the quasichimical quac

coefficients Cbn,l of the (b, n) – contact in lutidines + cyclohexane, then, we have adjusted the dispersive coefficients Cbdisn (1,2) as it was proposed by some authors [17,18], all these coefficients are given in Table 11.

Contact (a,b): alkane + cyclohexane [15] Contact (a,c): benzene + alkane [15] Contact (n,c): pyridine +benzene [16]

Table 10 Volumes ri , total surfaces qi , and molecular surface fractions ˛si calculated from the group increments rG and qG given in Table 8. Compound

ri

qi

Benzene Pyridine 3,5-Lutidine 2,6-Lutidine Cyclohexane

2.8248 2.6577 3.9601 3.9601 3.5187

2.0724 1.8332 2.8264 2.8264 2.5966

˛ni 0.0000 0.0595 0.0386 0.0386 0.0000

˛ci

˛ai

˛bi

1.0000 0.9405 0.4441 0.4441 0.0000

0.0000 0.0000 0.5173 0.5173 0.0000

0.0000 0.000 0.0000 0.0000 1.0000

40

H. Ben-Makhlouf-Hakem et al. / Fluid Phase Equilibria 373 (2014) 34–42

Table 11 disp quac Interechange coefficients, dispersifs Cst,l and quasichimical Cst,l (l = 1, Gibbs energy; l = 2 enthalpy) for contact (s,t). disp

Contact (s,t)

disp

Cst,1

Benzene + cyclohexane (b,c)

quac

Cst,2

quac

Cst,1

Cst,2

0.2445

0.5623

0.0000

0.0000

Pyridine + alcane (b,c) (n,c) (a,n)

0.2445 19.26 21.95

0.5623 1.244 9.48

0.0000 4.502 17.13

0.0000 0.1771 27.03

Pyridine + cyclohexane (b,c) (n,c) (b,n)

0.2445 19.26 21.95

0.5623 1.244 8.50

0.0000 4.502 17.13

0.0000 0.1771 27.03

2,6-Dimethylpyridine + cyclohexane (a,c) (b,c) (c,n) (a,n) (b,n) (a,c) (b,c) (c,n) (a,n) (b,n)

0.0512 0.2445 19.26 22.80 21.90 0.0512 0.2445 19.26 28.00 31.50

0.1533 0.5619 1.244 15.00 19.00 0.1533 0.5619 1.244 21.20 23.50

0.0000 0.0000 4.502 13.22 13.22 0.0000 0.0000 4.502 13.22 13.22

0.0000 0.0000 0.1771 18.30 18.30 0.0000 0.0000 0.1771 18.30 18.30

6. Comparison with experiment and discussion

Pyridine −1

The excess enthalpies of mixing for binaries pyridines and methyl derivatives with cyclohexane have been measured by Woyciki [19]. The maximum of mixing decrease in the following order.

a

1400

E

H E G E TS

1200 1000

(HxE

1 =0.5

= 1400 J mol−1 ) > ␤-picoline −1

E (Hx1=0.5

(HxE

1 =0.5

=

= 1230 J mol ). 1320 J mol ) > ␣-picoline There are no experimental data for 3,5-lutidine with cyclohexane, so we have measured the excess enthalpies of 3,5- and 2,6-lutidine with cyclohexane at 303.15 K. The maximum heat of mixing decrease in the following order.

a

-1

G J mol

E

G ; H ; TS

E

400 800

T= 283.15K T= 303.15K T= 323.15K T= 343.15K

E

E

600 400

200

200 0 0,0

0,2

0,4

0,6

0,8

1,0

0

X1

b

0,0

b

E

H E G E TS

0,6

0,8

1,0

1000

800

800 -1

600

G J mol

E

G ; H ; TS

E

1000

0,4

X1

1400 1200

0,2

E

E

600 400 200

T= 283.15K T= 303.15K T= 323.15K T= 343.15K T= 353.15K

400

200

0 0,0

0,2

0,4

0,6

0,8

1,0

X1 Fig. 4. (a, b) Comparison of the experiment molar Gibbs energy GE , the molar enthalpy HE evaluated from temperature derivative of (GE /T) and T*SE of: (a) 2,6lutidine (1) + cyclohexane (2) and (b) 3,5-lutidine (1) + cyclohexane (2)

0 0,0

0,2

0,4

0,6

0,8

1,0

X1 Fig. 5. (a, b) Comparison of experimental data of GE at different temperatures for binaries systems formed with cyclohexane + (a) 2,6-lutidine or + (b) 3,5-lutidine.

H. Ben-Makhlouf-Hakem et al. / Fluid Phase Equilibria 373 (2014) 34–42

41

a 1600

1250

1000 -1

G ,H Jmol

750

E

800

E

E

E

G , H Jmol

-1

1200

500

400 250

0 0,0

0,2

0,4

0,6

0,8

0

1,0

0,0

X1

0,2

0,4

0,6

0,8

1,0

0,6

0,8

1,0

X1

Fig. 6. Comparison of theory with experiment for the molar excess Gibbs energy GE and the molar enthalpy HE , at 298.15 K of pyridine (1) + cyclohexane. Points, our experimental results; GE (); HE (). Lines, predicted values using DISQUAC model. disp,quac disp,quac disp disp = Cbn . Solid lines: Can = / Cbn . Dashed lines: Can

b

1500

1250

G ,H Jmol

-1

1000

750

E

a

E

1250

500

1000

750

0 0,0

E

E

G , H J mol

-1

250

0,2

0,4

X1

500

Fig. 8. (a, b) Comparison of theory with experiment for the molar excess Gibbs energy GE and the molar enthalpy HE , at 303.1515 K of 3,5-lutidine (1) + cyclohexane (2). Points, our experimental results; GE (); HE (), Lines, predicted values using disp,quac disp,quac disp disp = Cbn and (b) Can = / Cbn . DISQUAC model. (a) Can

250

0 0,0

0,2

0,4

0,6

0,8

1,0

X1

b

1400

3,5-Lutidine (HxE −1

1200

800

600

E

E

H , G J mol

-1

1000

400

200 0 0,0

0,2

0,4

0,6

0,8

1,0

X1 Fig. 7. (a, b) Comparison of theory with experiment for the molar excess Gibbs energy GE and the molar enthalpy HE , at 303.1515 K of 2,6-lutidine (1) + cyclohexane (2). Points, our experimental results; GE (); HE (). Lines, predicted values using disp,quac disp,quac disp disp = Cbn and (b) Can = / Cbn . DISQUAC model. (a) Can

1 =0.5

= 1282 J mol−1 ) > 2,6-lutidine (HxE

1 =0.5

=

1234 J mol ) The molar excess enthalpies HE and the excess Gibbs energies GE decrease with increasing steric effect (pyridine, ␣picoline + cyclohexane; 3,5-, 2,6-lutidine + cyclohexane). This is connected with the influence of the number and the position of the CH3 group on the free electron pair on the nitrogen atom and on the steric hindrance at this one. Figs. 4(a, b) and 5(a, b) show the position of methyl groups effect on the excess function (HE , GE , TSE ). TSE values are relatively important for 2,6-lutidine + cyclohexane and GE is temperature dependent. The two methyl groups in ortho positions strongly weaken the auto-association of 2,6-lutidine. This is clearly seen from the comparison of Hvap of 2,6-lutidine (37.46 kJ/mol) and 3,5-lutidine (39.46 kJ/mol) [20]. The proximity effect affects N/alkane and N/C-CH2 contact. It can be seen in Table 11, the dispersion parameters increase when the CH3 steric effect decreases. Results from the DISQUAC model are compared with experimental data for GE and HE (Figs. 6–8).

42

H. Ben-Makhlouf-Hakem et al. / Fluid Phase Equilibria 373 (2014) 34–42

7. Conclusion The intermolecular interactions in mixtures of lutidines and cyclohexane are rather complex. The steric hindrance at nitrogen atom caused by the position of methyl group and conformational effects of cyclohexane change the degree of association in those mixtures. More investigations are needed to explain the qualitative and quantitative association phenomena. References [1] H. Ben-Makhlouf–Hakem, A. Ait-Kaci, J. Jose, Fluid Phase Equilib. 232 (2005) 189–206. [2] H. Ben-Makhlouf–Hakem, A. Ait-Kaci, J. Jose, Fluid Phase Equilib. 242 (2006) 1–9. [3] M.R. Tiné, H.V. Kehiaian, Fluid Phase Equilib. 32 (1987) 211–248. [4] K.N. Marsh, Int. DATA Ser. Sel. Data Mixtures Ser. A 1 (1973) 1–3. [5] A. Blondel-Tellouk, H. Loiseleur, A. Barreau, E. Behar, J. Jose, Fluid Phase Equilib. 110 (1995) 315–339.

[6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]

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