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Isothermal vapour pressures and excess functions of 3,5- and 2,6-dimethylpyridine with toluene measurement and prediction
Fluid Phase Equilibria 242 (2006) 1–9
Isothermal vapour pressures and excess functions of 3,5- and 2,6-dimethylpyridine with toluene measurement and prediction Hamama Ben-makhlouf-Hakem a,∗ , Ahmed Ait-Kaci a , Jacques Jose b a
Laboratoire de thermodynamique des m´elanges organiques, Facult´e de chimie, USTHB, BP, 32 El-Alia 16111 Bab Ezzouar, Algeria b Laboratoire de chimie analytique I, Universit´ e Claude Bernard (Lyon I), 43 Boulvard du 11 novembre 1918, Bˆat Raulin/2, 69622 Villeurbanne Cedex, France Received 3 July 2005; received in revised form 8 November 2005; accepted 11 November 2005 Available online 3 February 2006
Abstract The vapour pressures of liquid (3,5; 2,6)-dimethylpyridine with toluene mixtures were measured by a static method in the range of 263.15–353.15 K. The pure components vapour pressures data and those of the mixtures were correlated with the Antoine equation. The excess enthalpies were measured at 303.15 K, by means of an isothermal calorimeter (C80 SETARAM model). The molar excess Gibbs energies, calculated from the vapour–liquid equilibrium data and the molar excess enthalpies compared satisfactorily with group contribution method (DISQUAC). © 2005 Elsevier B.V. All rights reserved. Keywords: Data; Excess properties; Vapour–liquid equilibria; Enthalpy; Pyridine derivatives; Lutidines
1. Introduction Previously, we have reported the experimental data of vapour pressures and excess enthalpies of (3,5; 2,6)-lutidines with nalkanes (C6 –C8 ) [1]. The experimental data were described by using the DISQUAC model [2]. To complete this study, we investigate the mixtures containing (3,5; 2,6)-lutidines and toluene. 2. Experimental 2.1. Apparatus and procedure The experimental HE data were measured at 1 atm by means of a microcalorimeter, C80 (SETARAM model, Lyon, France). The temperature T was maintained constant at 303.15 ± 0.02 K. Check measurements on (cyclohexane + benzene) are in the good agreement with the data reported by Marsh [3]. The estimated uncertainties in the mole fraction xi and HE are δ(xi ) = 0.0002 and δ(HE ) = 5 J mol−1 , respectively. The total vapour pressure measurements were carried out with a static method described elsewhere by Blondel-Tellouk et al. [4] Mixture compositions were prepared by mass and
degassed by distillation as described previously by BlondelTellouk et al. [4]. The liquid phase was analysed by chromatography (GLC). 2.2. Materials The purities of toluene and (2,6)-lutidine were 99 mol% as specified on their labels or certified by Flucka and Acros. That of (3,5)-lutidine was better than 98 mol%, it was verified by CPG. 3. Results Experimental molar excess enthalpies HE at 303.15 K are endothermic. They are reported in Table 1. The results have been fitted to the Redlich–Kister equation: E = x1 (1 − x1 ) Hi,exp
Corresponding author. E-mail address: [email protected] (H. Ben-makhlouf-Hakem).
0378-3812/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2005.11.016
ai (2x1 − 1)i
(1)
i=0
The values of the coefficients ai and the standard deviations δ(HE ), given by:
∗
n−1
δ(H E ) =
N i
1/2 E E (Hi,cal − Hi,exp )/(N − n)
(2)
2
H. Ben-makhlouf-Hakem et al. / Fluid Phase Equilibria 242 (2006) 1–9
Table 1 Experimental molar excess enthalpies HE at 303.15 K 3,5-Lutidine (1) + toluene (2)
2,6-Lutidine (1) + toluene (2)
(J mol−1 )
x1
HE
0.1248 0.1817 0.2194 0.3217 0.4079 0.5991 0.6191
55 68 78 90 106 110 107
Vapour phase imperfection and variation of the Gibbs energy of the pure liquid components with pressure were accounted for in terms of the second molar virial coefficients and the molar volumes under saturation pressure.
x1
HE (J mol−1 )
0.01445 0.2129 0.2993 0.3406 0.4340 0.4479 0.5547 0.5885 0.6718 0.7056 0.7248 0.7746 0.8563
62 83 85 88 86 87 80 76 70 68 64 50 35
P=
yi =
a1
a2
3,5-Lutidine (1) + toluene (2) 2,6-Lutidine (1) + toluene (2)
431.7842
a3 72.1172
336.9400 −101.6635
–
2.68
146.8247 −132.0229
B12 − (B11 + B12 ) ; 2
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] and Bii the second molar virial coefficients evaluated with Tsonopoulos method [7,8]. The values are reported in Table 3. The direct experimental data for total vapour pressures at different temperatures for our mixtures are given in Table 4 together with the activity coefficients γ 1 and γ 2 and the excess molar Gibbs energies GE calculated by Barker’s method [9]:
δ(HE )
a4
192.8936
xi Pi0 exp[giE − (Bii − Vi0 )(P − Pi0 ) − 2P B12 (1 − yi )2 ] P (4)
BE =
Table 2 Coefficients ai and standard deviation δ(HE ) for least-squares representation by equation of HE at 303.15 K Mixtures
2 xi Pi0 exp[giE − (Bii −Vi0 )(P − Pi0 )−2PB12 (1 − yi )2 ] RT i=1 (3)
2.53
n−1
GE = x1 (1 − x1 ) Ai (2x1 − 1)i RT
(6)
i=0
were determined by least-squares analysis and are reported in Table 2. N is the number of experimental points and n the number of coefficients ai . By fitting (GE /T)x1 = 0.5 data with a second degree polynomial in 1/T, the derivative at 303.15 K gives HE = 636 and 227 J mol−1 for 3,5-lutidine + toluene and 2,6-lutidine + toluene, respectively. The quantitative evaluation of HE from vapour pressure involves considerable uncertainty [5]. The maximum values of the enthalpy of mixing decrease in the following order:
where x1 is the liquid phase composition of 3,5- or 2,6-lutidine. 3,5-Lutidine + toluene mixtures exhibit positive deviations but those of 2,6-lutidine with toluene are negative. The values of the parameters Ai of Eq. (6) and the standard deviation for pressure are reported in Table 5. (GE /T)x1 = 0.5 was fitted to the following equation: GE = A + BX + CX2 T where X = 1/T (Fig. 1). The correlation coefficient R is then R > 0.99892 for 2,6lutidine (1) + toluene (2) and R > 0.99976 for 3,5-lutidine (1) + toluene (2).
3, 5-lutidine > 2, 6-lutdine The pure components vapour pressures data and those of mixtures were correlated with the Antoine equation.
Table 3 Molar volume V* (cm3 mol−1 ), vapour pressure P* (kPa), virial coefficients for the ij pair Bjj (cm3 mol−1 ) and for pure compounds (i = j) T (K)
263.15 273.15 283.15 293.15 303.15 313.15 323.15 333.15 343.15 353.15
Toluene
3,5-Lutidine
V*
P*
105.03 106.07 107.1 108.2 109.4 110.6 111.8 113.1 114.4 115.8
0.468 0.908 1.666 2.911 4.873 7.852 12.226 18.462 27.122 38.867
2,6-Lutidine
B11
V*
P*
B11
B12
V*
P*
B11
B12
−4842 −4055 −3452 −2983 −2610 −2310 −2065 −1861 −1691 −1545
110.6 110.7 111.7 112.7 113.61 114.64 115.69 116.78 117.91 119.07
0.016 0.038 0.830 0.169 0.325 0.596 1.049 1.775 2.904 4.603
−13150 −10550 −8612 −7145 −6016 −5136 −4439 −3879 −3425 −3051
−7820 −6404 −5337 −4518 −3879 −3373 −2966 −2635 −2362 −2133
108.57 109.6 110.6 111.7 112.79 113.93 115.11 116.33 117.59 118.90
0.065 0.143 0.296 0.575 1.061 1.868 3.154 5.129 8.066 12.31
−8500 −6950 −5781 −4885 −4186 −3632 −3188 −2826 −2527 −2278
−6391 −5286 −4447 −3799 −32891 −2883 −2553 −2282 −2057 −1868
H. Ben-makhlouf-Hakem et al. / Fluid Phase Equilibria 242 (2006) 1–9
3
Table 4 Values of vapour pressure P (kPa), relative deviation P = 100(P − Pcal )/P, activity coefficients γ 1 and γ 2 and excess molar Gibbs energies GE (J mol−1 ) T (K)
x1
2,6-Lutidine (1) + toluene (2) 263.15 0.1192 0.2311 0.3550 0.4998 0.6097 0.7102 0.8250
y1
P
P
γ1
γ2
GE
0.0162 0.0363 0.0631 0.1060 0.1595 0.2457 0.4390
0.415 0.373 0.324 0.260 0.215 0.172 0.114
−0.32 0.93 0.79 −1.55 −0.58 1.93 −0.85
0.8766 0.8974 0.8832 0.8676 0.8760 0.9029 0.9493
0.9938 0.9896 0.9966 1.0092 0.9958 0.9373 0.7895
−46 −72 −101 −145 −180 −200 −184
273.15
0.1192 0.2311 0.3550 0.4998 0.6097 0.7102 0.8250
0.0188 0.0416 0.0718 0.1197 0.1783 0.2705 0.4683
0.811 0.278 0.634 0.516 0.430 0.346 0.238
0.01 0.76 0.56 −0.1.56 −0.33 1.55 −0.73
0.8958 0.9079 0.8910 0.8742 0.8818 0.9073 0.9517
0.9946 0.9918 1.0000 1.0135 1.0013 0.9456 0.8032
−42 −65 −93 −137 −173 −194 −180
283.15
0.1192 0.2311 0.3550 0.4998 0.6097 0.7102 0.8250
0.0215 0.0470 0.0806 0.1333 0.1968 0.2943 0.4952
1.496 1.343 1.176 0.965 0.812 0.6599 0.467
0.23 0.62 0.32 −1.22 −0.15 1.26 −0.63
0.9062 0.9165 0.8975 0.8800 0.8870 0.9114 0.9538
0.9953 0.9936 1.0026 1.0167 1.0056 0.9523 0.8149
−37 −59 −86 −131 −167 −189 −176
293.15
0.1192 0.2311 0.3550 0.4998 0.6097 0.7102 0.8250
0.0241 0.0524 0.0894 0.1468 0.2150 0.3170 0.5198
2.628 2.361 2.075 1.718 1.457 1.193 0.868
0.37 0.52 0.27 −1.09 −0.02 1.03 −0.56
0.9171 0.9236 0.9032 0.8853 0.8917 0.9151 0.9558
0.9959 0.9950 1.0045 1.0189 1.0086 0.9576 0.8250
−34 −54 −81 −126 −162 −184 −173
303.15
0.1192 0.2311 0.3550 0.4998 0.6097 0.7102 0.8250
0.0268 0.0579 0.0981 0.1602 0.2326 0.3386 0.5421
4.412 3.976 3.507 2.927 2.500 2.065 1.540
0.43 0.44 0.18 90.98 0.06 0.87 −0.49
0.9256 0.9293 0.9081 0.8901 0.8961 0.9161 0.9577
0.9964 0.9961 1.0060 1.0204 1.0107 0.9617 0.8338
−31 −50 −77 −121 −158 −181 −170
2,6-Lutidine (1) + toluene (2) 313.15 0.1192 0.2311 0.3550 0.4998 0.6097 0.7102 0.8250
0.0295 0.0632 0.1067 0.1734 0.2498 0.3592 0.5626
7.129 6.441 5.705 4.795 4.123 3.438 2.620
0.44 0.38 0.12 −0.88 0.10 0.75 −0.44
0.9325 0.9340 0.9124 0.8947 0.9004 0.9220 0.9595
0.9968 0.9970 1.0069 1.0211 1.0119 0.9648 0.8417
−29 −47 −73 −118 −155 −177 −167
323.15
0.1192 0.2311 0.3550 0.4998 0.6097 0.7102 0.8250
0.03210 0.0685 0.1153 0.1863 0.2665 0.3788 0.5812
11.128 10.085 8.965 7.585 6.561 5.523 4.292
0.40 0.34 0.09 −0.79 0.11 0.66 −0.40
0.9379 0.9377 0.9163 0.8990 0.9046 0.9254 0.9613
0.9971 0.9976 1.0075 1.0211 1.0123 0.9672 0.8489
−27 −45 −71 −115 −152 −174 −165
333.15
0.1192 0.2311 0.3550 0.4998 0.6097 0.7102 0.8250
0.0347 0.0738 0.1238 0.1990 0.2827 0.3975 0.5983
16.838 15.311 13.659 11.627 10.115 8.593 6.798
0.33 0.31 0.08 −0.71 0.10 0.60 −0.37
0.9420 0.9407 0.9198 0.9033 0.9088 0.9288 0.9632
0.9974 0.9981 1.0077 1.0206 1.0120 0.9687 0.8555
−26 −43 −69 −112 −149 −171 −161
4
H. Ben-makhlouf-Hakem et al. / Fluid Phase Equilibria 242 (2006) 1–9
Table 4 (Continued ) x1
y1
P
P
γ1
γ2
GE
343.15
0.1192 0.2311 0.3550 0.4998 0.6097 0.7102 0.8250
0.0373 0.0790 0.1321 0.2116 0.2985 0.4153 0.6140
24.777 22.611 20.240 17.325 15.152 12.292 10.446
0.23 0.29 0.08 −0.64 0.07 0.57 −0.35
0.9450 0.9430 0.9229 0.9076 0.9131 0.9323 0.9651
0.9977 0.9985 1.0077 1.0197 1.0111 0.9697 0.8616
−25 −42 −67 −111 −146 −168 −158
353.15
0.1192 0.2311 0.3550 0.4998 0.6097 0.7102 0.8250
0.0399 0.0841 0.1403 0.2239 0.3139 0.4323 0.6285
35.551 32.565 29.246 25.163 22.115 19.137 15.617
0.11 0.28 0.10 −0.58 0.03 0.55 −0.33
0.9472 0.9447 0.9259 0.9119 0.9175 0.9359 0.9670
0.9979 0.9988 1.0074 1.0182 1.0096 0.9701 0.8674
−25 −41 −66 −109 −143 −164 −154
3,5-Lutidine (1) + toluene (2) 263.15 0.0472 0.1889 0.4951 0.6789 0.7326 0.8720
0.0019 0.0145 0.0341 0.0562 0.0694 0.1392
0.446 0.365 0.284 0.217 0.182 0.107
0.80 0.18 −0.49 1.51 −1.25 0.14
1.0664 1.6793 1.1792 1.0611 1.0508 1.0247
0.9904 0.9446 1.1651 1.3406 1.3722 1.5350
−14 113 347 294 265 167
T (K)
273.15
0.0472 0.1889 0.4951 0.6789 0.7326 0.8720
0.0026 0.0174 0.0401 0.0654 0.0800 0.1557
0.868 0.719 0.564 0.433 0.368 0.221
0.90 0.11 −0.39 1.24 −1.03 0.11
1.2184 1.7208 1.1903 1.0683 1.0556 1.0249
0.9921 0.9583 1.1853 1.3704 1.4103 1.6051
4 155 391 332 299 186
283.15
0.0472 0.1889 0.4951 0.6789 0.7326 0.8720
0.0034 0.0207 0.0468 0.0752 0.0913 0.1725
1.598 1.337 1.056 0.815 0.702 0.431
1.00 0.03 −0.30 0.97 −0.82 0.09
1.3537 1.7585 1.2028 1.0757 1.0605 1.0253
0.9934 0.9690 1.2010 1.3970 1.4456 1.6736
19 191 433 369 333 206
293.15
0.0472 0.1889 0.4951 0.6789 0.7326 0.8720
0.0043 0.0243 0.0542 0.0858 0.1031 0.1893
2.801 2.362 1.879 1.461 1.272 0.798
1.09 −0.05 −0.21 0.72 −0.61 0.07
1.4692 1.7920 1.2163 1.0832 1.0654 1.0258
0.9944 0.9771 1.2128 1.4207 1.4779 1.7400
31 223 474 407 368 227
303.15
0.0472 0.1889 0.4951 0.6789 0.7326 0.8720
0.0052 0.0282 0.0622 0.0969 0.1154 0.2062
4.700 3.989 3.194 2.503 2.205 1.413
1.18 −0.12 −0.13 0.47 −0.41 0.05
1.5629 1.8214 1.2307 1.0906 1.0705 1.0264
0.9952 0.9830 1.2211 1.4414 1.5074 1.8041
42 251 513 444 402 248
313.15
0.0472 0.1889 0.4951 0.6789 0.7326 0.8720
0.0062 0.0324 0.0710 0.1087 0.1283 0.2230
7.591 6.476 5.217 4.123 3.672 2.402
1.27 −0.19 −0.04 0.24 −0.22 0.03
1.6343 1.8466 1.2456 1.0982 1.0755 1.0271
0.9957 0.9870 1.2262 1.4592 1.5339 1.8658
50 274 551 481 437 269
3,5-Lutidine (1) + toluene (2) 323.15 0.0472 0.1889 0.4951 0.6789 0.7326 0.8720
0.0073 0.0369 0.0805 0.1211 0.1417 0.2398
11.845 10.143 8.222 6.556 5.899 3.937
1.36 −0.26 0.04 0.02 −0.04 0.1
1.6841 1.8674 1.2610 1.1057 1.0806 1.0279
0.9961 0.9894 1.2283 1.4742 1.5575 1.9250
56 294 586 518 471 290
H. Ben-makhlouf-Hakem et al. / Fluid Phase Equilibria 242 (2006) 1–9
5
Table 4 (Continued ) x1
y1
P
P
γ1
γ2
233.15
0.0472 0.1889 0.4951 0.6789 0.7326 0.8720
0.0083 0.0416 0.0908 0.1341 0.1555 0.2566
17.924 15.390 12.549 10.097 9.178 6.243
1.44 −0.33 0.11 −0.19 0.14 −0.01
1.7134 1.8838 1.2767 1.1132 1.0857 1.0287
0.9963 0.9904 1.2279 1.4865 1.5783 1.9815
61 310 622 554 505 311
243.15
0.0472 0.1889 0.4951 0.6789 0.7326 0.8720
0.0093 0.0466 0.1018 0.1476 0.1699 0.2732
26.383 22.697 18.610 15.111 13.871 9.612
1.53 −0.40 0.19 −0.38 0.30 −0.03
1.7240 1.8956 1.2927 1.1206 1.0907 1.030
0.9964 0.9903 1.2250 1.4961 1.5963 2.0353
64 322 655 590 538 332
253.15
0.0472 0.1889 0.4951 0.6789 0.7326 0.8720
0.0103 0.0519 0.1137 0.1618 0.1846 0.2898
37.874 32.623 26.893 22.039 20.421 14.405
1.61 −0.47 0.26 −0.57 0.46 −0.04
1.7181 1.9026 1.3088 1.1281 1.0958 1.0304
0.9964 0.9893 1.2198 1.5030 1.6116 2.0863
65 331 686 624 571 353
T (K)
GE
Table 5 Coefficients Ai and pressure standard deviations δ (Pa) for least-squares representation by Eq. (3) T (K)
263.15 273.15 283.15 293.15 303.15 313.15 323.15 333.15 343.15 353.15
3,5-Lutidine (1) + toluene (2)
2.6-Lutidine (1) + toluene (2)
A1
A2
A3
A4
δ
A1
A2
A3
δ
0.6353 0.6883 0.7356 0.7775 0.8145 0.8469 0.8750 0.8991 0.9192 0.9356
0.0040 −0.0112 −0.0166 −0.0137 −0.0040 0.0116 0.0324 0.0576 0.0869 0.1199
−0.3794 −0.3082 −0.2532 −0.2113 −0.1803 −0.1592 −0.1436 −0.1352 −0.1319 −0.1323
0.6171 0.5481 0.4918 0.4462 0.4092 0.3794 0.3553 0.3358 0.3195 0.3056
0.0155 0.0134 0.0116 0.0103 0.0096 0.0094 0.0098 0.0106 0.0118 0.0131
−0.2658 −0.2421 −0.2225 −0.2062 −0.1925 −0.1809 −0.1710 −0.1624 −0.1550 −0.1484
−0.3026 −0.2957 −0.2887 −0.2813 −0.2732 −0.2644 −0.2547 −0.2442 −0.2329 0.2207
−0.2875 −0.2708 −0.2562 −0.2429 −0.2305 −0.2186 −0.2069 −0.1952 −0.1831 −0.1708
0.0148 0.0121 0.0101 0.0087 0.0077 0.0069 0.0062 0.0055 0.0050 0.0046
4. Theory 3,5-; 2,6-Lutidine + toluene are regarded as possessing three types of surfaces: type a, alkane (CH3, CH2 group); type n, nitrogen (N group); type c (aromatic). The relative molecular volume ri , the surface qi and surface αsi (s = a, n, c) of all the molecular species have been calculated on the basis of group volumes and surfaces recommended by Bondi [10], taking arbitrarily the volume and surface of methane as unity [11,12]. The applied values are shown in Tables 6 and 7. The three types of surfaces a, n and c generate three pairs of contacts: (a,n), (a,c), (c,n). The equations used to calculate GE and HE are the same as in the other publication [2]. The temperature dependency of the interaction parameters has been expressed in term of dispersive (dis) and/or quasichemical (quac) interaction coefficients: quac dis Cst,l and Cst,l ,
where s, t = (a, n), (a, c), (c, n)
and l = 1 (Gibbs energy), l = 2 (enthaly)
Table 6 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−1 ; ACH4 = 2.90 × 10−5 m2 mol−1 ) Group
rG
qG
CH4 CH3 C6 H 5 C5 H 5 C5 H 4 N
1.00000 0.79848 2.67757 2.35396 2.20668 0.30374
1.00000 0.73103 1.83793 1.72413 1.48970 0.10907
5. Estimation of interaction parameters (a) Contact (a,c) - The dispersive interchange parameters of the contact (a,c) was already evaluated for toluene + n-alkane by Cannas et al. [13].
6
H. Ben-makhlouf-Hakem et al. / Fluid Phase Equilibria 242 (2006) 1–9 Table 7 Volumes ri , total surfaces qi and molecular surface fractions αsi calculated from the group increments rG and qG given in Table 6 Compound
ri
qi
αni
αci
αai
Toluene Benzene Pyridine Methylpyridine 3,5-Lutidine 2,6-Lutidine
3.4760 2.8248 2.6577 3.3089 3.9601 3.9601
2.0906 2.0724 1.8332 2.3298 2.8264 2.8264
0.1043 0.0000 0.0595 0.0468 0.0386 0.0386
0.5460 1.0000 0.9405 0.6394 0.4441 0.4441
0.3497 0.0000 0.0000 0.3138 0.5173 0.5173
(b) Contact (c,n) In a previous work [1] dis and quac parts of contact (c,n) were evaluated for pyridine and its methyl derivadis = 19.26; C dis = 1.244; C quac = tives + benzene (Ccn,1 cn,2 cn,1 quac 4.502; Ccn,2 = 0.177). Table 9 Molar excess Gibbs energies GE and excess molar enthalpies HE of pyridine; 2picoline; 3-picoline; 4-picoline; 2,6-lutidine; 3,5-lutidine + n-heptane mixtures at temperature T and equimolar composition: comparison of direct experimental results (Exp) with calculated values (Calc), using the interchange coefficients from Table 8 Mixture
Fig. 1. Polynomial fit of (GE /T)x1 = 0.5 with a second degree of 1/T: (a) 3,5lutidine (1) + toluene (2) (b) 2,6-lutidine (1) + toluene (2).
T (K)
Pyridine (1) + toluene (2) ␣-Picoline (1) + toluene (2) 3,5-Lutidine (1) + toluene (2) 2,6-Lutidine (1) + toluene (2) a b c d e
GE (T, x1 = 0.5) (J mol−1 )
HE (T, x1 = 0.5) (J mol−1 )
Calc
Calc
Exp
174
174b
Exp
298.15
225.1
225.1a
298.15
113.8
113.8c
75.5
75.5d
303.15
513.3
513.3e
107.9
107.9e
85
85e
303.15
−121
−121e
From Ref. [15]. From Ref. [14]. From Ref. [16]. From Ref. [17]. This work.
Table 8 quac dis Interchange coefficients, dispersive Cst,l and quasichemical Cst,l (l = 1, Gibbs energy; l = 2, enthalpy) for contact (s,t) System
Contact (a,n)
Pyridine + toluene
2-Methylpyridine
3.5-Lutidine + toluene
2,6-Lutidine + toluene
(a,c)
dis = 17.43; Can,1 quac Can,1 dis Can,1 quac Can,1 dis Can,1 quac Can,1 dis Can,1 quac Can,1
= 12.95; = 18.84; = 0000; = −1.95; = 0.000; = 39.71; = 0.00;
(c,n)
dis Can,2 = 4.823
dis = 0.320; Cac,1
dis Cac,2 = 0.620
quac Can,2 = 7.900 dis CE,2 = −31.81 quac Can,2 = 0000 dis Can,2 = −1.29 quac Can,2 = 0.00 dis Can,2 = 0.21 quac Can,2 = 0.00
quac Cac,1 = 0.000; dis Cac,1 = 0.320; quac Cac,1 = 0.000; dis = 0.320; Cac,1 quac Cac,1 = 0.00; dis = 0.320; Cac,1 quac Cac,1 = 0.000;
quac Cac,2 = 0.00 dis Cac,2 = 0.620 quac Cac,2 = 0.00 dis Cac,2 = 0.620 quac Cac,2 = 0.00 dis Cac,2 = 0.620 quac Cac,2 = 0.00
dis = 19.26; Ccn,1
dis Ccn,2 = 1.244
quac Ccn,1 dis Ccn,1 quac Ccn,1 dis Ccn,1 quac Ccn,1 dis Ccn,1 quac Ccn,1
= 9.000;
Ccn,2 = 0.257
= 19.26;
dis Ccn,2 = 1.244
= 9.000;
Ccn,2 = 0257
= 19.26;
dis Ccn,2 = 1.244
= 9.00; = 19.26; = 9.00;
quac
quac
quac
Ccn,2 = 0.257 dis Ccn,2 = 1.244 quac
Ccn,2 = 0257
H. Ben-makhlouf-Hakem et al. / Fluid Phase Equilibria 242 (2006) 1–9
From structural considerations (intramolecular inductive effect and liquid-structure breaking effect of the alkyl substituents on benzene ring and enthalpy–entropy compensation effect), the interaction parameters of the contact (c,n) for pyridine and its methyl derivatives + toluene may be different from those with benzene and, consequently, we have determined the interaction coefficients from the available experimental data [14–16] of these system. (c) Contact (a,n) - The interaction parameters for the contact (a,n) were estimated using our experimental data for HE and GE and some experimental data from literature [15–18]. Table 8 lists the final coefficients. 6. Comparison with experiment and discussion The excess enthalpies of mixing for binaries pyridine and its methyl derivatives + toluene have been measured at 298.15 K by Wilczura et al. [14,17]. The maximum of mixing decrease in the
Fig. 2. Comparison of experimental data of GE and HE at 303.15 K for binaries systems formed with (a) toluene + 3,5-lutidine (b) toluene + 2,6-lutidine.
7
following order: pyridine > ␣-picoline > ␥-picoline > 2, 4-lutidine > -picoline > 2, 6-lutidine There are no experimental data for 3,5-lutidine with toluene, so we have measured the excess enthalpies of 3,5- and 2,6lutidine with toluene at 303.15 K. Fig. 2 shows the position methyl groups effect on the excess function (HE ,GE ,TSE ). TSE values are relatively important and GE is temperature dependent. The molar excess enthalpies HE and the excess Gibbs energy GE decrease with increasing steric effect (pyridine; ␣-picoline + toluene; 3,5-; 2,6-lutidine + toluene). 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 nitrogen atom see Table 9. The molar excess enthalpies HE curves are not so symmetrical as for mixtures of pyridine derivatives with normal alkanes
Fig. 3. Comparison of theory with experiment for the molar excess Gibbs energy GE and the molar enthalpy HE , at 303.15 K, of 2,6-lutidine (1) + toluene (2) mixtures vs. x1 , the mole fraction of 2,6-lutidine. Full lines, predicted values using DISQUAC; points, experimental results; GE () (this work); HE () (this work).
8
H. Ben-makhlouf-Hakem et al. / Fluid Phase Equilibria 242 (2006) 1–9
[19–24]. This asymmetry may be due to association phenomena in the mixtures [25–29]. The excess Gibbs energy are positive for binary system formed with 3,5-lutidine + toluene and negative for 2,6-lutidine with toluene. The difference is due to the stronger – and n– interactions in solution with 2,6-lutidine + toluene than with 3,5lutidine + toluene. Nakanishi and co-workers [26] found that steric hindrance at nitrogen atom caused by the position of methyl group change degree of association of pyridines [21]. 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−1 ) [30] and 3,5-lutidine (39.46 kJ mol−1 ) [30]. Also, the presence of the two methyl groups in the 2,6-lutidine leads the n– interactions being negligible. Probably, the intermolecular interactions between different molecules (2,6-lutidine and toluene) are stronger than those between molecules of the same type.
Because of those association phenomena in (2,6)lutidine + toluene system; calculated GE and HE from DISQUAC model do not agree with experimental data Fig. 3. The model DISQUAC reproduces quite accurately the experimental measurements GE and HE for binary system of 3,5lutidine + toluene. Fig. 4 shows the experimental and theoretical curves of GE and HE at 303.15 K. 7. Conclusion The problem of intermolecular interactions in mixtures of lutidines and toluene is very complicated. The steric hindrance at nitrogen atom caused by the position of methyl group change degree and type of association in those mixtures. More investigations are needed to explain the qualitative and quantitative association phenomena. References
Fig. 4. Comparison of theory with experiment for the molar excess Gibbs energy GE and the molar enthalpy HE , at 303.15 K, of 3,5-lutidine (1) + toluene (2) mixtures vs. x1 , the mole fraction of 3,5-lutidine. Full lines, predicted values using DISQUAC; points, experimental results; GE () (this work); HE () (this work).
[1] H. Ben-makhlouf-Hakem, A. Ait-Kaci, J. Jose, Fluid Phase Equilib. 232 (2005) 189–206. [2] M.R. Tin´e, H.V. Kehiaian, Fluid Phase Equilib. 32 (1987) 211– 248. [3] K.N. Marsh, Int. Data Ser. Sel. Data Mixtures Ser. A 1 (1973) 1–3. [4] A. Blondel-Tellouk, H. Loiseleur, A. Barreau, E. Behar, J. Jose, Fluid Phase Equilib. 110 (1995) 315–339. [5] J.S. Rowlinson, F.L. Swinton, Liquids and Liquid Mixtures, third ed., Butterworth, London, 1982, p. 183. [6] W.V. Steele, R.D. Chirico, A. Nguyen, S.E. Knipmeyer, J. Chem. Thermodyn. 27 (1995) 311–334. [7] C. Tsonopoulos, AICHE J. 20 (1974) 263. [8] C. Tsonopoulos, AICHE J. 20 (1975) 827. [9] J.A. Barker, Aust. J. Chem. 6 (1953) 207. [10] A. Bondi, Physical Properties of Molecular Crystals, Liquids and Glasses, Wiley, New York, 1968. [11] H.V. Kehiaian, K. Sosnkowska-Kehiaian, R. Hryniewicz, J. Chim. Phys. 68 (1971) 922. [12] H.V. Kehiaian, J.-P.E. Grolier, G.C. Benson, J. Chim. Phys. 15 (1978) 1031–1041. [13] A. Cannas, B. Marongio, S. Porcedda, Thermochim. Acta 311 (1998) 1–19. [14] W. Woycicki, K.W. Sadowska, Bultin de l’Academie Polonaise des sciences chimiques XVI (6) (1968). [15] J. Jose, C. Michou-Saucet, M.A. Michou-Saucet, Int. Data Ser. Sel. Data Mixtures Ser. A (1) (1988) 42. [16] J.-C. Merlin, A. Ait-Kaci, Int. Data Ser. Sel. Data Mixtures Ser. A (1) (1982) 34. [17] H. Wilczura, T. Kasprzycka-Guttman, A. Myslinski, J. Therm. Anal. 4 (1995) 563–770. [18] S. Warycha, J. Chem. Eng. Data 38 (1993) 274–276. [19] T. Kasprzycka-Guttman, H. Wilczura, Thermochim. Acta 209 (1992) 25–30. [20] T. Kasprzycka-Guttman, H. Wilczura, Thermochim. Acta 198 (1992) 405–412. [21] T. Kasprzycka-Guttman, H. Wilczura, Thermochim. Acta 184 (1991) 321–327. [22] H. Wilczura, T. Kasprzycka-Guttman, M. Jarosz-Jarszewska, A. Myslinski, J. Therm. Anal. 45 (1995) 751–759. [23] R. Kechavarz, J.P. Dubes, H. Tachoire, Int. Data Ser. Sel. Data Mixtures Ser. A (1) (1992) 18–30. [24] A. Michou-Saucet, J. Jose, C. Michou-Saucet, Int. Data Ser. Sel. Data Mixtures Ser. A 2 (1986) 140–145.
H. Ben-makhlouf-Hakem et al. / Fluid Phase Equilibria 242 (2006) 1–9 [25] H. Wilczura, T. Kasprzycka-Guttman, E. Megiel, Thermochim. Acta 274 (1996) 53–59. [26] J.J. Abe, K. Nakanishi, H. Touhara, J. Chem. Thermodyn. 10 (1978) 483. [27] R.K. Nigam, S. Aggarwal, S.P. Sharma, Fluid Phase Equilib. 16 (1984) 25–39.
9
[28] E. Megiel, T. Kasprzycka-Guttman, A. Jagielska, L. Wroblewska, J. Mol. Struct. 569 (2001) 111–119. [29] P.P. Singh, D.V. Verma, Thermochim. Acta 13 (1975) 89–92. [30] David R. Lide, Hand Book of Chemistry and Physics, 84th ed., 2003/2004.
Isothermal vapour pressures and excess functions of 3,5- and 2,6-dimethylpyridine with toluene measurement and prediction Hamama Ben-makhlouf-Hakem a,∗ , Ahmed Ait-Kaci a , Jacques Jose b a
Laboratoire de thermodynamique des m´elanges organiques, Facult´e de chimie, USTHB, BP, 32 El-Alia 16111 Bab Ezzouar, Algeria b Laboratoire de chimie analytique I, Universit´ e Claude Bernard (Lyon I), 43 Boulvard du 11 novembre 1918, Bˆat Raulin/2, 69622 Villeurbanne Cedex, France Received 3 July 2005; received in revised form 8 November 2005; accepted 11 November 2005 Available online 3 February 2006
Abstract The vapour pressures of liquid (3,5; 2,6)-dimethylpyridine with toluene mixtures were measured by a static method in the range of 263.15–353.15 K. The pure components vapour pressures data and those of the mixtures were correlated with the Antoine equation. The excess enthalpies were measured at 303.15 K, by means of an isothermal calorimeter (C80 SETARAM model). The molar excess Gibbs energies, calculated from the vapour–liquid equilibrium data and the molar excess enthalpies compared satisfactorily with group contribution method (DISQUAC). © 2005 Elsevier B.V. All rights reserved. Keywords: Data; Excess properties; Vapour–liquid equilibria; Enthalpy; Pyridine derivatives; Lutidines
1. Introduction Previously, we have reported the experimental data of vapour pressures and excess enthalpies of (3,5; 2,6)-lutidines with nalkanes (C6 –C8 ) [1]. The experimental data were described by using the DISQUAC model [2]. To complete this study, we investigate the mixtures containing (3,5; 2,6)-lutidines and toluene. 2. Experimental 2.1. Apparatus and procedure The experimental HE data were measured at 1 atm by means of a microcalorimeter, C80 (SETARAM model, Lyon, France). The temperature T was maintained constant at 303.15 ± 0.02 K. Check measurements on (cyclohexane + benzene) are in the good agreement with the data reported by Marsh [3]. The estimated uncertainties in the mole fraction xi and HE are δ(xi ) = 0.0002 and δ(HE ) = 5 J mol−1 , respectively. The total vapour pressure measurements were carried out with a static method described elsewhere by Blondel-Tellouk et al. [4] Mixture compositions were prepared by mass and
degassed by distillation as described previously by BlondelTellouk et al. [4]. The liquid phase was analysed by chromatography (GLC). 2.2. Materials The purities of toluene and (2,6)-lutidine were 99 mol% as specified on their labels or certified by Flucka and Acros. That of (3,5)-lutidine was better than 98 mol%, it was verified by CPG. 3. Results Experimental molar excess enthalpies HE at 303.15 K are endothermic. They are reported in Table 1. The results have been fitted to the Redlich–Kister equation: E = x1 (1 − x1 ) Hi,exp
Corresponding author. E-mail address: [email protected] (H. Ben-makhlouf-Hakem).
0378-3812/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2005.11.016
ai (2x1 − 1)i
(1)
i=0
The values of the coefficients ai and the standard deviations δ(HE ), given by:
∗
n−1
δ(H E ) =
N i
1/2 E E (Hi,cal − Hi,exp )/(N − n)
(2)
2
H. Ben-makhlouf-Hakem et al. / Fluid Phase Equilibria 242 (2006) 1–9
Table 1 Experimental molar excess enthalpies HE at 303.15 K 3,5-Lutidine (1) + toluene (2)
2,6-Lutidine (1) + toluene (2)
(J mol−1 )
x1
HE
0.1248 0.1817 0.2194 0.3217 0.4079 0.5991 0.6191
55 68 78 90 106 110 107
Vapour phase imperfection and variation of the Gibbs energy of the pure liquid components with pressure were accounted for in terms of the second molar virial coefficients and the molar volumes under saturation pressure.
x1
HE (J mol−1 )
0.01445 0.2129 0.2993 0.3406 0.4340 0.4479 0.5547 0.5885 0.6718 0.7056 0.7248 0.7746 0.8563
62 83 85 88 86 87 80 76 70 68 64 50 35
P=
yi =
a1
a2
3,5-Lutidine (1) + toluene (2) 2,6-Lutidine (1) + toluene (2)
431.7842
a3 72.1172
336.9400 −101.6635
–
2.68
146.8247 −132.0229
B12 − (B11 + B12 ) ; 2
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] and Bii the second molar virial coefficients evaluated with Tsonopoulos method [7,8]. The values are reported in Table 3. The direct experimental data for total vapour pressures at different temperatures for our mixtures are given in Table 4 together with the activity coefficients γ 1 and γ 2 and the excess molar Gibbs energies GE calculated by Barker’s method [9]:
δ(HE )
a4
192.8936
xi Pi0 exp[giE − (Bii − Vi0 )(P − Pi0 ) − 2P B12 (1 − yi )2 ] P (4)
BE =
Table 2 Coefficients ai and standard deviation δ(HE ) for least-squares representation by equation of HE at 303.15 K Mixtures
2 xi Pi0 exp[giE − (Bii −Vi0 )(P − Pi0 )−2PB12 (1 − yi )2 ] RT i=1 (3)
2.53
n−1
GE = x1 (1 − x1 ) Ai (2x1 − 1)i RT
(6)
i=0
were determined by least-squares analysis and are reported in Table 2. N is the number of experimental points and n the number of coefficients ai . By fitting (GE /T)x1 = 0.5 data with a second degree polynomial in 1/T, the derivative at 303.15 K gives HE = 636 and 227 J mol−1 for 3,5-lutidine + toluene and 2,6-lutidine + toluene, respectively. The quantitative evaluation of HE from vapour pressure involves considerable uncertainty [5]. The maximum values of the enthalpy of mixing decrease in the following order:
where x1 is the liquid phase composition of 3,5- or 2,6-lutidine. 3,5-Lutidine + toluene mixtures exhibit positive deviations but those of 2,6-lutidine with toluene are negative. The values of the parameters Ai of Eq. (6) and the standard deviation for pressure are reported in Table 5. (GE /T)x1 = 0.5 was fitted to the following equation: GE = A + BX + CX2 T where X = 1/T (Fig. 1). The correlation coefficient R is then R > 0.99892 for 2,6lutidine (1) + toluene (2) and R > 0.99976 for 3,5-lutidine (1) + toluene (2).
3, 5-lutidine > 2, 6-lutdine The pure components vapour pressures data and those of mixtures were correlated with the Antoine equation.
Table 3 Molar volume V* (cm3 mol−1 ), vapour pressure P* (kPa), virial coefficients for the ij pair Bjj (cm3 mol−1 ) and for pure compounds (i = j) T (K)
263.15 273.15 283.15 293.15 303.15 313.15 323.15 333.15 343.15 353.15
Toluene
3,5-Lutidine
V*
P*
105.03 106.07 107.1 108.2 109.4 110.6 111.8 113.1 114.4 115.8
0.468 0.908 1.666 2.911 4.873 7.852 12.226 18.462 27.122 38.867
2,6-Lutidine
B11
V*
P*
B11
B12
V*
P*
B11
B12
−4842 −4055 −3452 −2983 −2610 −2310 −2065 −1861 −1691 −1545
110.6 110.7 111.7 112.7 113.61 114.64 115.69 116.78 117.91 119.07
0.016 0.038 0.830 0.169 0.325 0.596 1.049 1.775 2.904 4.603
−13150 −10550 −8612 −7145 −6016 −5136 −4439 −3879 −3425 −3051
−7820 −6404 −5337 −4518 −3879 −3373 −2966 −2635 −2362 −2133
108.57 109.6 110.6 111.7 112.79 113.93 115.11 116.33 117.59 118.90
0.065 0.143 0.296 0.575 1.061 1.868 3.154 5.129 8.066 12.31
−8500 −6950 −5781 −4885 −4186 −3632 −3188 −2826 −2527 −2278
−6391 −5286 −4447 −3799 −32891 −2883 −2553 −2282 −2057 −1868
H. Ben-makhlouf-Hakem et al. / Fluid Phase Equilibria 242 (2006) 1–9
3
Table 4 Values of vapour pressure P (kPa), relative deviation P = 100(P − Pcal )/P, activity coefficients γ 1 and γ 2 and excess molar Gibbs energies GE (J mol−1 ) T (K)
x1
2,6-Lutidine (1) + toluene (2) 263.15 0.1192 0.2311 0.3550 0.4998 0.6097 0.7102 0.8250
y1
P
P
γ1
γ2
GE
0.0162 0.0363 0.0631 0.1060 0.1595 0.2457 0.4390
0.415 0.373 0.324 0.260 0.215 0.172 0.114
−0.32 0.93 0.79 −1.55 −0.58 1.93 −0.85
0.8766 0.8974 0.8832 0.8676 0.8760 0.9029 0.9493
0.9938 0.9896 0.9966 1.0092 0.9958 0.9373 0.7895
−46 −72 −101 −145 −180 −200 −184
273.15
0.1192 0.2311 0.3550 0.4998 0.6097 0.7102 0.8250
0.0188 0.0416 0.0718 0.1197 0.1783 0.2705 0.4683
0.811 0.278 0.634 0.516 0.430 0.346 0.238
0.01 0.76 0.56 −0.1.56 −0.33 1.55 −0.73
0.8958 0.9079 0.8910 0.8742 0.8818 0.9073 0.9517
0.9946 0.9918 1.0000 1.0135 1.0013 0.9456 0.8032
−42 −65 −93 −137 −173 −194 −180
283.15
0.1192 0.2311 0.3550 0.4998 0.6097 0.7102 0.8250
0.0215 0.0470 0.0806 0.1333 0.1968 0.2943 0.4952
1.496 1.343 1.176 0.965 0.812 0.6599 0.467
0.23 0.62 0.32 −1.22 −0.15 1.26 −0.63
0.9062 0.9165 0.8975 0.8800 0.8870 0.9114 0.9538
0.9953 0.9936 1.0026 1.0167 1.0056 0.9523 0.8149
−37 −59 −86 −131 −167 −189 −176
293.15
0.1192 0.2311 0.3550 0.4998 0.6097 0.7102 0.8250
0.0241 0.0524 0.0894 0.1468 0.2150 0.3170 0.5198
2.628 2.361 2.075 1.718 1.457 1.193 0.868
0.37 0.52 0.27 −1.09 −0.02 1.03 −0.56
0.9171 0.9236 0.9032 0.8853 0.8917 0.9151 0.9558
0.9959 0.9950 1.0045 1.0189 1.0086 0.9576 0.8250
−34 −54 −81 −126 −162 −184 −173
303.15
0.1192 0.2311 0.3550 0.4998 0.6097 0.7102 0.8250
0.0268 0.0579 0.0981 0.1602 0.2326 0.3386 0.5421
4.412 3.976 3.507 2.927 2.500 2.065 1.540
0.43 0.44 0.18 90.98 0.06 0.87 −0.49
0.9256 0.9293 0.9081 0.8901 0.8961 0.9161 0.9577
0.9964 0.9961 1.0060 1.0204 1.0107 0.9617 0.8338
−31 −50 −77 −121 −158 −181 −170
2,6-Lutidine (1) + toluene (2) 313.15 0.1192 0.2311 0.3550 0.4998 0.6097 0.7102 0.8250
0.0295 0.0632 0.1067 0.1734 0.2498 0.3592 0.5626
7.129 6.441 5.705 4.795 4.123 3.438 2.620
0.44 0.38 0.12 −0.88 0.10 0.75 −0.44
0.9325 0.9340 0.9124 0.8947 0.9004 0.9220 0.9595
0.9968 0.9970 1.0069 1.0211 1.0119 0.9648 0.8417
−29 −47 −73 −118 −155 −177 −167
323.15
0.1192 0.2311 0.3550 0.4998 0.6097 0.7102 0.8250
0.03210 0.0685 0.1153 0.1863 0.2665 0.3788 0.5812
11.128 10.085 8.965 7.585 6.561 5.523 4.292
0.40 0.34 0.09 −0.79 0.11 0.66 −0.40
0.9379 0.9377 0.9163 0.8990 0.9046 0.9254 0.9613
0.9971 0.9976 1.0075 1.0211 1.0123 0.9672 0.8489
−27 −45 −71 −115 −152 −174 −165
333.15
0.1192 0.2311 0.3550 0.4998 0.6097 0.7102 0.8250
0.0347 0.0738 0.1238 0.1990 0.2827 0.3975 0.5983
16.838 15.311 13.659 11.627 10.115 8.593 6.798
0.33 0.31 0.08 −0.71 0.10 0.60 −0.37
0.9420 0.9407 0.9198 0.9033 0.9088 0.9288 0.9632
0.9974 0.9981 1.0077 1.0206 1.0120 0.9687 0.8555
−26 −43 −69 −112 −149 −171 −161
4
H. Ben-makhlouf-Hakem et al. / Fluid Phase Equilibria 242 (2006) 1–9
Table 4 (Continued ) x1
y1
P
P
γ1
γ2
GE
343.15
0.1192 0.2311 0.3550 0.4998 0.6097 0.7102 0.8250
0.0373 0.0790 0.1321 0.2116 0.2985 0.4153 0.6140
24.777 22.611 20.240 17.325 15.152 12.292 10.446
0.23 0.29 0.08 −0.64 0.07 0.57 −0.35
0.9450 0.9430 0.9229 0.9076 0.9131 0.9323 0.9651
0.9977 0.9985 1.0077 1.0197 1.0111 0.9697 0.8616
−25 −42 −67 −111 −146 −168 −158
353.15
0.1192 0.2311 0.3550 0.4998 0.6097 0.7102 0.8250
0.0399 0.0841 0.1403 0.2239 0.3139 0.4323 0.6285
35.551 32.565 29.246 25.163 22.115 19.137 15.617
0.11 0.28 0.10 −0.58 0.03 0.55 −0.33
0.9472 0.9447 0.9259 0.9119 0.9175 0.9359 0.9670
0.9979 0.9988 1.0074 1.0182 1.0096 0.9701 0.8674
−25 −41 −66 −109 −143 −164 −154
3,5-Lutidine (1) + toluene (2) 263.15 0.0472 0.1889 0.4951 0.6789 0.7326 0.8720
0.0019 0.0145 0.0341 0.0562 0.0694 0.1392
0.446 0.365 0.284 0.217 0.182 0.107
0.80 0.18 −0.49 1.51 −1.25 0.14
1.0664 1.6793 1.1792 1.0611 1.0508 1.0247
0.9904 0.9446 1.1651 1.3406 1.3722 1.5350
−14 113 347 294 265 167
T (K)
273.15
0.0472 0.1889 0.4951 0.6789 0.7326 0.8720
0.0026 0.0174 0.0401 0.0654 0.0800 0.1557
0.868 0.719 0.564 0.433 0.368 0.221
0.90 0.11 −0.39 1.24 −1.03 0.11
1.2184 1.7208 1.1903 1.0683 1.0556 1.0249
0.9921 0.9583 1.1853 1.3704 1.4103 1.6051
4 155 391 332 299 186
283.15
0.0472 0.1889 0.4951 0.6789 0.7326 0.8720
0.0034 0.0207 0.0468 0.0752 0.0913 0.1725
1.598 1.337 1.056 0.815 0.702 0.431
1.00 0.03 −0.30 0.97 −0.82 0.09
1.3537 1.7585 1.2028 1.0757 1.0605 1.0253
0.9934 0.9690 1.2010 1.3970 1.4456 1.6736
19 191 433 369 333 206
293.15
0.0472 0.1889 0.4951 0.6789 0.7326 0.8720
0.0043 0.0243 0.0542 0.0858 0.1031 0.1893
2.801 2.362 1.879 1.461 1.272 0.798
1.09 −0.05 −0.21 0.72 −0.61 0.07
1.4692 1.7920 1.2163 1.0832 1.0654 1.0258
0.9944 0.9771 1.2128 1.4207 1.4779 1.7400
31 223 474 407 368 227
303.15
0.0472 0.1889 0.4951 0.6789 0.7326 0.8720
0.0052 0.0282 0.0622 0.0969 0.1154 0.2062
4.700 3.989 3.194 2.503 2.205 1.413
1.18 −0.12 −0.13 0.47 −0.41 0.05
1.5629 1.8214 1.2307 1.0906 1.0705 1.0264
0.9952 0.9830 1.2211 1.4414 1.5074 1.8041
42 251 513 444 402 248
313.15
0.0472 0.1889 0.4951 0.6789 0.7326 0.8720
0.0062 0.0324 0.0710 0.1087 0.1283 0.2230
7.591 6.476 5.217 4.123 3.672 2.402
1.27 −0.19 −0.04 0.24 −0.22 0.03
1.6343 1.8466 1.2456 1.0982 1.0755 1.0271
0.9957 0.9870 1.2262 1.4592 1.5339 1.8658
50 274 551 481 437 269
3,5-Lutidine (1) + toluene (2) 323.15 0.0472 0.1889 0.4951 0.6789 0.7326 0.8720
0.0073 0.0369 0.0805 0.1211 0.1417 0.2398
11.845 10.143 8.222 6.556 5.899 3.937
1.36 −0.26 0.04 0.02 −0.04 0.1
1.6841 1.8674 1.2610 1.1057 1.0806 1.0279
0.9961 0.9894 1.2283 1.4742 1.5575 1.9250
56 294 586 518 471 290
H. Ben-makhlouf-Hakem et al. / Fluid Phase Equilibria 242 (2006) 1–9
5
Table 4 (Continued ) x1
y1
P
P
γ1
γ2
233.15
0.0472 0.1889 0.4951 0.6789 0.7326 0.8720
0.0083 0.0416 0.0908 0.1341 0.1555 0.2566
17.924 15.390 12.549 10.097 9.178 6.243
1.44 −0.33 0.11 −0.19 0.14 −0.01
1.7134 1.8838 1.2767 1.1132 1.0857 1.0287
0.9963 0.9904 1.2279 1.4865 1.5783 1.9815
61 310 622 554 505 311
243.15
0.0472 0.1889 0.4951 0.6789 0.7326 0.8720
0.0093 0.0466 0.1018 0.1476 0.1699 0.2732
26.383 22.697 18.610 15.111 13.871 9.612
1.53 −0.40 0.19 −0.38 0.30 −0.03
1.7240 1.8956 1.2927 1.1206 1.0907 1.030
0.9964 0.9903 1.2250 1.4961 1.5963 2.0353
64 322 655 590 538 332
253.15
0.0472 0.1889 0.4951 0.6789 0.7326 0.8720
0.0103 0.0519 0.1137 0.1618 0.1846 0.2898
37.874 32.623 26.893 22.039 20.421 14.405
1.61 −0.47 0.26 −0.57 0.46 −0.04
1.7181 1.9026 1.3088 1.1281 1.0958 1.0304
0.9964 0.9893 1.2198 1.5030 1.6116 2.0863
65 331 686 624 571 353
T (K)
GE
Table 5 Coefficients Ai and pressure standard deviations δ (Pa) for least-squares representation by Eq. (3) T (K)
263.15 273.15 283.15 293.15 303.15 313.15 323.15 333.15 343.15 353.15
3,5-Lutidine (1) + toluene (2)
2.6-Lutidine (1) + toluene (2)
A1
A2
A3
A4
δ
A1
A2
A3
δ
0.6353 0.6883 0.7356 0.7775 0.8145 0.8469 0.8750 0.8991 0.9192 0.9356
0.0040 −0.0112 −0.0166 −0.0137 −0.0040 0.0116 0.0324 0.0576 0.0869 0.1199
−0.3794 −0.3082 −0.2532 −0.2113 −0.1803 −0.1592 −0.1436 −0.1352 −0.1319 −0.1323
0.6171 0.5481 0.4918 0.4462 0.4092 0.3794 0.3553 0.3358 0.3195 0.3056
0.0155 0.0134 0.0116 0.0103 0.0096 0.0094 0.0098 0.0106 0.0118 0.0131
−0.2658 −0.2421 −0.2225 −0.2062 −0.1925 −0.1809 −0.1710 −0.1624 −0.1550 −0.1484
−0.3026 −0.2957 −0.2887 −0.2813 −0.2732 −0.2644 −0.2547 −0.2442 −0.2329 0.2207
−0.2875 −0.2708 −0.2562 −0.2429 −0.2305 −0.2186 −0.2069 −0.1952 −0.1831 −0.1708
0.0148 0.0121 0.0101 0.0087 0.0077 0.0069 0.0062 0.0055 0.0050 0.0046
4. Theory 3,5-; 2,6-Lutidine + toluene are regarded as possessing three types of surfaces: type a, alkane (CH3, CH2 group); type n, nitrogen (N group); type c (aromatic). The relative molecular volume ri , the surface qi and surface αsi (s = a, n, c) of all the molecular species have been calculated on the basis of group volumes and surfaces recommended by Bondi [10], taking arbitrarily the volume and surface of methane as unity [11,12]. The applied values are shown in Tables 6 and 7. The three types of surfaces a, n and c generate three pairs of contacts: (a,n), (a,c), (c,n). The equations used to calculate GE and HE are the same as in the other publication [2]. The temperature dependency of the interaction parameters has been expressed in term of dispersive (dis) and/or quasichemical (quac) interaction coefficients: quac dis Cst,l and Cst,l ,
where s, t = (a, n), (a, c), (c, n)
and l = 1 (Gibbs energy), l = 2 (enthaly)
Table 6 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−1 ; ACH4 = 2.90 × 10−5 m2 mol−1 ) Group
rG
qG
CH4 CH3 C6 H 5 C5 H 5 C5 H 4 N
1.00000 0.79848 2.67757 2.35396 2.20668 0.30374
1.00000 0.73103 1.83793 1.72413 1.48970 0.10907
5. Estimation of interaction parameters (a) Contact (a,c) - The dispersive interchange parameters of the contact (a,c) was already evaluated for toluene + n-alkane by Cannas et al. [13].
6
H. Ben-makhlouf-Hakem et al. / Fluid Phase Equilibria 242 (2006) 1–9 Table 7 Volumes ri , total surfaces qi and molecular surface fractions αsi calculated from the group increments rG and qG given in Table 6 Compound
ri
qi
αni
αci
αai
Toluene Benzene Pyridine Methylpyridine 3,5-Lutidine 2,6-Lutidine
3.4760 2.8248 2.6577 3.3089 3.9601 3.9601
2.0906 2.0724 1.8332 2.3298 2.8264 2.8264
0.1043 0.0000 0.0595 0.0468 0.0386 0.0386
0.5460 1.0000 0.9405 0.6394 0.4441 0.4441
0.3497 0.0000 0.0000 0.3138 0.5173 0.5173
(b) Contact (c,n) In a previous work [1] dis and quac parts of contact (c,n) were evaluated for pyridine and its methyl derivadis = 19.26; C dis = 1.244; C quac = tives + benzene (Ccn,1 cn,2 cn,1 quac 4.502; Ccn,2 = 0.177). Table 9 Molar excess Gibbs energies GE and excess molar enthalpies HE of pyridine; 2picoline; 3-picoline; 4-picoline; 2,6-lutidine; 3,5-lutidine + n-heptane mixtures at temperature T and equimolar composition: comparison of direct experimental results (Exp) with calculated values (Calc), using the interchange coefficients from Table 8 Mixture
Fig. 1. Polynomial fit of (GE /T)x1 = 0.5 with a second degree of 1/T: (a) 3,5lutidine (1) + toluene (2) (b) 2,6-lutidine (1) + toluene (2).
T (K)
Pyridine (1) + toluene (2) ␣-Picoline (1) + toluene (2) 3,5-Lutidine (1) + toluene (2) 2,6-Lutidine (1) + toluene (2) a b c d e
GE (T, x1 = 0.5) (J mol−1 )
HE (T, x1 = 0.5) (J mol−1 )
Calc
Calc
Exp
174
174b
Exp
298.15
225.1
225.1a
298.15
113.8
113.8c
75.5
75.5d
303.15
513.3
513.3e
107.9
107.9e
85
85e
303.15
−121
−121e
From Ref. [15]. From Ref. [14]. From Ref. [16]. From Ref. [17]. This work.
Table 8 quac dis Interchange coefficients, dispersive Cst,l and quasichemical Cst,l (l = 1, Gibbs energy; l = 2, enthalpy) for contact (s,t) System
Contact (a,n)
Pyridine + toluene
2-Methylpyridine
3.5-Lutidine + toluene
2,6-Lutidine + toluene
(a,c)
dis = 17.43; Can,1 quac Can,1 dis Can,1 quac Can,1 dis Can,1 quac Can,1 dis Can,1 quac Can,1
= 12.95; = 18.84; = 0000; = −1.95; = 0.000; = 39.71; = 0.00;
(c,n)
dis Can,2 = 4.823
dis = 0.320; Cac,1
dis Cac,2 = 0.620
quac Can,2 = 7.900 dis CE,2 = −31.81 quac Can,2 = 0000 dis Can,2 = −1.29 quac Can,2 = 0.00 dis Can,2 = 0.21 quac Can,2 = 0.00
quac Cac,1 = 0.000; dis Cac,1 = 0.320; quac Cac,1 = 0.000; dis = 0.320; Cac,1 quac Cac,1 = 0.00; dis = 0.320; Cac,1 quac Cac,1 = 0.000;
quac Cac,2 = 0.00 dis Cac,2 = 0.620 quac Cac,2 = 0.00 dis Cac,2 = 0.620 quac Cac,2 = 0.00 dis Cac,2 = 0.620 quac Cac,2 = 0.00
dis = 19.26; Ccn,1
dis Ccn,2 = 1.244
quac Ccn,1 dis Ccn,1 quac Ccn,1 dis Ccn,1 quac Ccn,1 dis Ccn,1 quac Ccn,1
= 9.000;
Ccn,2 = 0.257
= 19.26;
dis Ccn,2 = 1.244
= 9.000;
Ccn,2 = 0257
= 19.26;
dis Ccn,2 = 1.244
= 9.00; = 19.26; = 9.00;
quac
quac
quac
Ccn,2 = 0.257 dis Ccn,2 = 1.244 quac
Ccn,2 = 0257
H. Ben-makhlouf-Hakem et al. / Fluid Phase Equilibria 242 (2006) 1–9
From structural considerations (intramolecular inductive effect and liquid-structure breaking effect of the alkyl substituents on benzene ring and enthalpy–entropy compensation effect), the interaction parameters of the contact (c,n) for pyridine and its methyl derivatives + toluene may be different from those with benzene and, consequently, we have determined the interaction coefficients from the available experimental data [14–16] of these system. (c) Contact (a,n) - The interaction parameters for the contact (a,n) were estimated using our experimental data for HE and GE and some experimental data from literature [15–18]. Table 8 lists the final coefficients. 6. Comparison with experiment and discussion The excess enthalpies of mixing for binaries pyridine and its methyl derivatives + toluene have been measured at 298.15 K by Wilczura et al. [14,17]. The maximum of mixing decrease in the
Fig. 2. Comparison of experimental data of GE and HE at 303.15 K for binaries systems formed with (a) toluene + 3,5-lutidine (b) toluene + 2,6-lutidine.
7
following order: pyridine > ␣-picoline > ␥-picoline > 2, 4-lutidine > -picoline > 2, 6-lutidine There are no experimental data for 3,5-lutidine with toluene, so we have measured the excess enthalpies of 3,5- and 2,6lutidine with toluene at 303.15 K. Fig. 2 shows the position methyl groups effect on the excess function (HE ,GE ,TSE ). TSE values are relatively important and GE is temperature dependent. The molar excess enthalpies HE and the excess Gibbs energy GE decrease with increasing steric effect (pyridine; ␣-picoline + toluene; 3,5-; 2,6-lutidine + toluene). 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 nitrogen atom see Table 9. The molar excess enthalpies HE curves are not so symmetrical as for mixtures of pyridine derivatives with normal alkanes
Fig. 3. Comparison of theory with experiment for the molar excess Gibbs energy GE and the molar enthalpy HE , at 303.15 K, of 2,6-lutidine (1) + toluene (2) mixtures vs. x1 , the mole fraction of 2,6-lutidine. Full lines, predicted values using DISQUAC; points, experimental results; GE () (this work); HE () (this work).
8
H. Ben-makhlouf-Hakem et al. / Fluid Phase Equilibria 242 (2006) 1–9
[19–24]. This asymmetry may be due to association phenomena in the mixtures [25–29]. The excess Gibbs energy are positive for binary system formed with 3,5-lutidine + toluene and negative for 2,6-lutidine with toluene. The difference is due to the stronger – and n– interactions in solution with 2,6-lutidine + toluene than with 3,5lutidine + toluene. Nakanishi and co-workers [26] found that steric hindrance at nitrogen atom caused by the position of methyl group change degree of association of pyridines [21]. 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−1 ) [30] and 3,5-lutidine (39.46 kJ mol−1 ) [30]. Also, the presence of the two methyl groups in the 2,6-lutidine leads the n– interactions being negligible. Probably, the intermolecular interactions between different molecules (2,6-lutidine and toluene) are stronger than those between molecules of the same type.
Because of those association phenomena in (2,6)lutidine + toluene system; calculated GE and HE from DISQUAC model do not agree with experimental data Fig. 3. The model DISQUAC reproduces quite accurately the experimental measurements GE and HE for binary system of 3,5lutidine + toluene. Fig. 4 shows the experimental and theoretical curves of GE and HE at 303.15 K. 7. Conclusion The problem of intermolecular interactions in mixtures of lutidines and toluene is very complicated. The steric hindrance at nitrogen atom caused by the position of methyl group change degree and type of association in those mixtures. More investigations are needed to explain the qualitative and quantitative association phenomena. References
Fig. 4. Comparison of theory with experiment for the molar excess Gibbs energy GE and the molar enthalpy HE , at 303.15 K, of 3,5-lutidine (1) + toluene (2) mixtures vs. x1 , the mole fraction of 3,5-lutidine. Full lines, predicted values using DISQUAC; points, experimental results; GE () (this work); HE () (this work).
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