Paper project # 3 from Calculations 1, 3, 6, 7, 10 and 11 For Dear Researcher Students who follow these training with us, here is the third idea of paper project, we wish the success. We will show final version when it's finished and it submitted to a Journal. We will try to show more outcomes from these calculations, i.e. more other projects of papers.
Estimation of the activity coefficients from Activation of viscous flow properties for 1,2dimethoxyethane with propylene carbonate binary mixtures in the temperature interval (from 298.15 to 318.15) K. a
b
c,*
c
c
H. Salhi , N. Dhouibi , M.A. Alkhaldi , A.A. Al-Zahrani , K.Y. Alqahtani , N. Ouerfelli Hamzaoui b.
a,c
., A.H.
a
Université de Tunis El Manar, Laboratoire Biophysique et de Technologies Médicales LR13ES04, Institut Supérieur des Technologies Médicales de Tunis, 9 Avenue Dr. Zouhaier Essafi 1006 Tunis, Tunisie.; b Laboratoire de Valorisation des Matériaux Utiles, Centre National des Recherche en Sciences des Matériaux, B.P.95, 2050 Borj Cedria Hammam Lif, Tunisia.; c University of Dammam, Department of Chemistry, College of Science, P.O. Box 1982, Dammam 31441, Saudi Arabia.; * Corresponding Author: e-mail:
[email protected] (M.A. Alkhaldi). Abstract Calculation of excess properties in 1,2-dimethoxyethane + propylene carbonate binary mixtures at (298.15, 308.15 and 318.15) K from experimental density and viscosity values were presented in previous work. We have been engaged in a systematic study of the thermodynamic and transport properties of binary mixtures containing 1,2-dimethoxyethane and propylene carbonate, as the latter is an industrially important organic compound and an important mixed solvent for a number of separation processes and solutions studies. The refined measurements on viscosity lead to the determination of activation energy of viscous flow. Experimental data were used to determinate excess molar free energy of activation of viscous flow (∆G*E) over the entire mole fraction range of each studied temperature. Variation of activation parameters and partial molar Gibbs energies of activation of viscous flow against compositions are discussed, Keywords: Binary liquid mixture; viscosity; Gibbs energy; activity coefficients; Molecular interaction; 1,2dimethoxyethane ; propylene carbonate. 1. Introduction……. 16 Data DME+PPC corr
14
2
∆ G*, ∆ G* and ∆ G* / kJ.mol
-1
15
DG* 298 DG* 308 DG* 318 DG*1 298 DG*1 308 DG*1 318 DG*2 298 DG*2 308 DG*2 318
1
13
12
11
10
0
0.2
0.4
x
0.6
0.8
1
1
Figure 1 : Variation of the Molar Gibbs energy of activation of viscous flow ∆G* / kJ.mol-1 and the corresponding ∗ ∗ partial molar quantities ∆̅ and ∆̅ / kJ·mol-1 DME and PPC respectively for the system of DME (1) + PPC (2) ∗ mixtures versus mole fraction x1 at the temperatures: ∆G* : (●): 298.15K ; (○): 308.15K; (▲): 318.15K; ∆̅ : (∆): ∗ 298.15K; (■): 308.15K; (□): 318.15K and ∆̅ : (♦): 298.15K; (◊): x1 = 318.15 K; (▼): x1 = 318.15 K.
Table 1 Molar Gibbs energy of activation of viscous flow ∆G* / kJ.mol-1 and the corresponding partial molar ∗ and ∆ ∗ / kJ·mol-1 (from Eqs. 25 and 26) of DME and PPC respectively for the system of DME quantities ∆ (1) + PPC (2) mixtures versus mole fraction x1 at the temperatures: (298.15 to 318.15) K.
x1 0 0.0493 0.0999 0.1524 0.1867 0.2298 0.2769 0.3128 0.3708 0.4036 0.4686 0.5193 0.5704 0.6382 0.6767 0.7589 0.8103 0.8432 0.9035 0.9483 1.0000
∆G* / kJ.mol-1 298.15 308.15 318.15 K K K 15.538 15.597 15.673 15.288 15.351 15.438 15.011 15.107 15.206 14.760 14.869 14.969 14.604 14.717 14.817 14.425 14.528 14.636 14.201 14.329 14.431 14.060 14.174 14.293 13.827 13.944 14.064 13.699 13.817 13.939 13.455 13.567 13.692 13.271 13.388 13.518 13.092 13.202 13.343 12.854 12.971 13.117 12.706 12.847 12.990 12.437 12.579 12.733 12.260 12.410 12.574 12.149 12.301 12.474 11.970 12.127 12.291 11.834 11.995 12.164 11.676 11.851 12.016
∗ ∆̅ / kJ.mol-1 298.15 308.15 318.15 K K K 10.0259 10.6444 10.9194 10.3050 10.7540 10.9922 10.5308 10.8767 11.0906 10.7571 11.0125 11.2008 10.8888 11.0984 11.2736 11.0460 11.1993 11.3701 11.1563 11.3028 11.4600 11.2495 11.3672 11.5379 11.3599 11.4711 11.6407 11.4087 11.5222 11.6926 11.4856 11.6013 11.7751 11.5289 11.6593 11.8386 11.5633 11.6972 11.8858 11.5928 11.7441 11.9322 11.5903 11.7693 11.9510 11.6256 11.8041 11.9836 11.6352 11.8148 11.9962 11.6409 11.8175 12.0016 11.6705 11.8408 12.0066 11.6806 11.8469 12.0145 11.6764 11.8512 12.0157
∗ ∆̅ / kJ.mol-1 298.15 308.15 318.15 K K K 15.5378 15.5969 15.6733 15.5468 15.5896 15.6681 15.5087 15.5769 15.6627 15.4797 15.5624 15.6468 15.4565 15.5475 15.6303 15.4337 15.5214 15.6098 15.3671 15.4884 15.5689 15.3400 15.4520 15.5472 15.2816 15.4015 15.4926 15.2489 15.3707 15.4590 15.1920 15.3011 15.3823 15.1535 15.2556 15.3330 15.1214 15.1996 15.2776 15.0794 15.1356 15.2057 15.0401 15.1027 15.1658 14.9902 15.0179 15.0903 14.9301 14.9501 15.0441 14.8794 14.8980 15.0137 14.7715 14.8056 14.9527 14.6418 14.7071 14.9080 14.4250 14.5633 14.8395
-1 -1 -1 ∗ ∗ Table 2 The excess partial molar entropy (∆
) / J·mol ·K and enthalpy (∆ ) / kJ·mol of activation of viscous flow of DME (1) and PPC (2) respectively for the system of (DME-PPC) mixtures versus mole fraction x1 in the temperatures range (from 298.15 to 318.15) K.
x1 0 0.0493 0.0999 0.1524 0.1867 0.2298 0.2769 0.3128 0.3708 0.4036 0.4686 0.5193 0.5704 0.6382 0.6767 0.7589 0.8103 0.8432 0.9035 0.9483 1.0000
DME (1) ∗ / / ∆ -1 -1 J·mol ·K kJ·mol-1 -10.50 -4.439 -8.040 -3.579 -6.351 -2.941 -4.397 -2.207 -2.300 -1.470 -0.3703 -0.7643 -0.2517 -0.6150 -0.3190 -0.5803 -0.3281 -0.4800 -0.3148 -0.4763 -0.3156 -0.4205 -0.3508 -0.2995 -0.3491 -0.1870 -0.3613 -0.1459 -0.3648 -0.0719 -0.2224 -0.0547 -0.1901 -0.0344 -0.1700 -0.0305 -0.0736 -0.0327 -0.0447 -0.0179 0.000 0.000 ∗ ∆
PPC (2) ∗ / ∆ -1 -1 J.mol ·K kJ·mol-1 0.000 0.000 -0.1855 -0.0644 -0.4924 -0.1630 -0.8038 -0.2822 -0.9688 -0.3262 -1.178 -0.4382 -1.174 -0.4624 -1.159 -0.5017 -1.030 -0.5101 -0.9723 -0.5605 -0.8233 -0.5511 -0.6673 -0.5453 -0.8058 -0.6188 -0.9429 -0.7511 -0.9970 -0.8020 -1.900 -1.170 -2.764 -1.504 -3.694 -1.836 -5.140 -2.368 -6.445 -2.881 -7.182 -3.258 ∗ / ∆
∆S* / J.mol .K E
0
-9
-6.75
2
-1
-1
-4.5 -2.25 (x = 1) 0 i 0 (x1 = 0.75)
DH1*E
(x1 = 0.25)
DH2*E
-1 1
2
-2
-3.75
-3
E
-2.5
E
∆ H* / kJ.mol 1
(x = 0.4)
∆H* / kJ.mol
-1
-1.25
-1
(xi = 0)
Data DME+PPC corr
-4
-5 -10.5
-7
-3.5
∆S* / J.mol .K 1 E
-1
0 -1
Figure 2 The activity coefficients of activation of viscous flow lnγ1 and lnγ2 / (from Eq. 33) of DME and PPC respectively for the system of DME (1) + PPC (2) mixtures versus mole fraction x1 at the temperatures: (298.15 and 318.15) K.
Table 3 The activity coefficients of activation of viscous flow lnγ1 and lnγ2 / (from Eq. 33) of DME and PPC respectively for the system of DME (1) + PPC (2) mixtures versus mole fraction x1 at the temperatures: (301.15 and 308.15) K.
x1 0 0.0493 0.0999 0.1524 0.1867 0.2298 0.2769 0.3128 0.3708 0.4036 0.4686 0.5193 0.5704 0.6382 0.6767 0.7589 0.8103 0.8432 0.9035 0.9483 1.0000
lnγ1 298.15 K -0.47102 -0.42825 -0.38038 -0.32735 -0.29382 -0.25444 -0.21403 -0.18890 -0.14835 -0.12844 -0.09754 -0.07490 -0.06013 -0.04180 -0.03199 -0.01839 -0.01273 -0.00985 -0.00407 -0.001685 0.0000
308.15 K -0.41441 -0.38691 -0.34969 -0.30804 -0.28053 -0.24403 -0.21006 -0.18061 -0.14177 -0.12211 -0.09092 -0.07096 -0.05784 -0.04001 -0.02973 -0.01778 -0.01229 -0.009504 -0.003436 -0.001327 0.0000
lnγ2 318.15 K 0.0000 -0.003628 -0.011744 -0.017177 -0.022918 -0.035137 -0.045465 -0.062938 -0.081309 -0.096369 -0.12362 -0.13830 -0.16606 -0.18943 -0.20371 -0.24444 -0.27273 -0.29595 -0.33674 -0.38758 -0.45232
298.15 K 0.0000 -0.002844 -0.007797 -0.013460 -0.019291 -0.029488 -0.042353 -0.056559 -0.076272 -0.088267 -0.11544 -0.13322 -0.15543 -0.18004 -0.19287 -0.22599 -0.25244 -0.27277 -0.30887 -0.34731 -0.40341
308.15 K 0.0000 -0.001995 -0.004018 -0.010021 -0.016283 -0.024022 -0.039482 -0.050210 -0.068338 -0.081021 -0.10967 -0.12679 -0.14364 -0.17037 -0.18338 -0.21484 -0.23787 -0.24938 -0.28431 -0.31459 -0.36985
318.15 K -0.47102 -0.42825 -0.38038 -0.32735 -0.29382 -0.25444 -0.21403 -0.18890 -0.14835 -0.12844 -0.09754 -0.07490 -0.06013 -0.04180 -0.03199 -0.01839 -0.01273 -0.009849 -0.004074 -0.001685 0.0000
0.1
Data DME+PPC corr
0
-0.1
lnγ
1
ln gamma1 298 ln gamma1 308 ln gamma1 318
-0.2
-0.3
-0.4
-0.5
-0.6
0
0.2
0.4
0.6
x
0.8
1
1
Figure 3 : Variation of the logarithm of activity coefficient lnγ1 of DME (from Eqs. 25, 26 and 33) for DME + PPC mixtures versus molar fraction x1 in DME at the temperatures: (●): 298.15K ; (○): 308.15K and (▲): 318.15K.
0.1
Data DME+PPC corr ln gamma2 298 ln gamma2 308 ln gamma2 318
0
lnγ
2
-0.1
-0.2
-0.3
-0.4
-0.5
0
0.2
0.4
x
0.6
0.8
1
1
Figure 4 : Variation of the logarithm of activity coefficient lnγ2 of PPC (from Eqs. 25, 26 and 33) for DME + PPC mixtures versus molar fraction x1 in DME at the temperatures: (●): 298.15K ; (○): 308.15K and (▲): 318.15K.
0.1
Data DME+PPC corr ln gamma1 308
0
lnγ
1
-0.1
-0.2
-0.3
-0.4
-0.5 -0.5
-0.4
-0.3
-0.2
lnγ
-0.1
0
0.1
2
Figure 5 : Correlation between the logarithm of activity coefficients lnγ1 of DME and lnγ2 of PPC for DME + PPC mixtures at 308.15 K.
2 Correlation between activity coefficients With Gibbs–Duhem relation (At constant temperature and pressure): x1. d lnγ1,T + x2.d lnγ2,T = 0
(34)
The activity coefficient lnγi of component ‘i’ can be expressed by the Margules equation in a limiting asymptotic expansion for IBA: lnγ1,T /x22 = [A0,T + A1,T. x1 + A2,T. x12 + A3,T. x13]
(35)
lnγ2,T /x12 = [B0,T + B1,T. x2 + B2,T. x22 + B3,T. x23]
(36)
and, for water:
Considering the first Margules constants A0,T and B0,T are the limiting activity coefficients at infinite dilution, the difference of values can be attributed to the difference of size and polarity between molecules of DME and water and, to the strong molecular interaction.
Table 4: Variation of least-squares constants Ai,T and Bi,T of the fitting for the logarithm of activity coefficients lnγi /xj2 in Margules limiting expansion (Eqs. 35 and 36) with temperature and the corresponding regression coefficient (R) in DME (1) + PPC (2) mixtures. T/K
A0,T
A1,T
A2,T
A3,T
R
298.15
-0.52187 -0.13418
2.1084
-2.1617
0.95647
308.15
-0.45871 -0.33669
2.3372
-2.2178
0.95716
318.15
-0.41573 -0.33232
1.9236
-1.7241
0.96473
T/K
B0,T
B1,T
B2,T
B3,T
R
298.15
-0.36227
-1.2957
4.3009
-4.2111
0.94037
308.15
-0.33289 -0.98571
2.8003
-2.5933
0.89798
318.15
-0.31714 -0.64779
1.4673
-1.2792
0.88422
-0.2
Data DME+PPC corr
lnγγ /x 1 2
2
-0.3
-0.4
-0.5
-0.6
-0.7
ln gamma1/x2*x2 298 ln gamma1/x2*x2 308 ln gamma1/x2*x2 318
0
0.2
0.4
0.6
0.8
1
x
1
Figure 6 : Variation of the ratio lnγ1/x22 (from Eqs. 35 and 36) in DME (1) + PPC (2) mixtures versus molar fraction x1 in DME at three temperatures: for water, (●): 298.15 K ; (○): 308.15 K and (▲): 318.15 K.
-0.2
Data DME+PPC corr
-0.4
lnγγ /x 2 1
2
-0.6
-0.8
-1
-1.2 ln gamma2/x1*x1 298 ln gamma2/x1*x1 308 ln gamma2/x1*x1 318
-1.4
-1.6
0
0.2
0.4
0.6
x
0.8
1
2
Figure 7 : Variation of the ratio lnγ2/x12 (from Eqs. 35 and 36) in DME (1) + PPC (2) mixtures versus molar fraction x2 in PPC at three temperatures: for water, (●): 298.15 K ; (○): 308.15 K and (▲): 318.15 K.
-0.2 PPC high dilution region
pure DME -0.4
2
(x2 = 0.15) 1
-0.6
1
lnγ / x
2
(x = 0.15)
ln gamma2/x1*x1 308
-0.8
-1
DME high dilution region Data DME+PPC corr
pure PPC -1.2 -0.7
-0.6
-0.5
lnγ / x 2
2 -0.4
-0.3
1
Figure 8 : Correlation between the ratio lnγi/xj2 (from Eqs. 35 and 36) in DME (1) + PPC (2) mixtures at the temperature 308.15K.
