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Thermodynamic properties of disodium sebacate in different binary solvent mixtures
Journal of Molecular Liquids 252 (2018) 194–202
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Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq
Thermodynamic properties of disodium sebacate in different binary solvent mixtures Ruilin Xu a, Baohong Hou a,b, Na Wang a, Yajing Lou a, Yang Li a, Jingjing Huang a, Hongxun Hao a,b,⁎ a b
National Engineering Research Center of Industrial Crystallization Technology, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin 300072, China
a r t i c l e
i n f o
Article history: Received 24 July 2017 Received in revised form 21 October 2017 Accepted 20 December 2017 Available online 26 December 2017 Keywords: Disodium sebacate Gravimetric method Solubility Dissolution thermodynamic properties
a b s t r a c t The solubility data of disodium sebacate in three kinds of water + organic solvent mixtures, including (water + methanol), (water + acetone) and (water + DMF), were experimentally determined at temperatures from (283.15 to 328.15) K by a gravimetric method. The results show that the solubility of disodium sebacate increases with increase of temperature in binary solvent mixtures at constant solvent composition, whereas it decreases with the increase of the mole fraction of organic solvent. The modified Apelblat equation, the λh model and the NRTL model were applied to correlate the solubility data in binary solvent mixtures. In addition, the dissolution thermodynamic properties of disodium sebacate in different binary solvent mixtures, including the Gibbs energy change, entropy and enthalpy, were also calculated and discussed based on the NRTL model and experimental solubility data. © 2017 Elsevier B.V. All rights reserved.
1. Introduction Disodium sebacate (NaOOC-(CH2)8-COONa, CAS No. 17265-14-4) is a white powdered crystal and is generated in cracking process and then acidified to sebacic acid, which is extremely valuable for the production of nylon, alkyd resins, plasticizers, cosmetics, and biological agents, and so forth [1–4]. Generally, the acidization from disodium sebacate to sebacic acid is processed in water. Since the solubility of sebacic acid in water is pretty low and is prone to cause outbreak of nucleation and serious agglomeration, which will result in decanedioic acid product with small size product and uneven size distribution. Usually, decanedioic acid product with larger size and more homogeneous particle distribution will be favorite since their easier downstream processing, such as filtration, drying, and packing. As we all know, the solvent could significantly affect the crystallization process and therefore will affect the quality of final product. To overcome the burst of nucleation during acidization in water, acidization in binary solvent mixtures of water and organic solvents is one possible solution. Therefore, it is important to know the solid-liquid equilibrium data [5] of disodium sebacate in binary solvent mixtures. Apart from the effects of NaOH and ethanol on the solubility of disodium decanedioate in water studied by Qing Xia's group [6], ⁎ Corresponding author at: National Engineering Research Center of Industrial Crystallization Technology, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China. E-mail address: [email protected] (H. Hao).
https://doi.org/10.1016/j.molliq.2017.12.104 0167-7322/© 2017 Elsevier B.V. All rights reserved.
the solubility of disodium sebacate has not been reported in the literature. In this work, the solubilities of disodium sebacate in water + organic solvent mixtures at different temperatures were measured by a gravimetric method in a temperature range from (283.15 to 328.15) K. Different models were used to correlate the experimental solubility data. The dissolution thermodynamic properties were also investigated. 2. Experimental 2.1. Materials Disodium sebacate was supplied by TongTuo chromatographic technology Co., Ltd. (Tianjin, China). The organic solvents, including methanol, acetone and DMF were provided by Tianjin Guangfu Chemical Technique Co., Ltd. (Tianjin, China). Distilled–deionized water was supplied by Nankai University, China. All chemicals were used without further purification. More detailed information about the materials used in this work has been listed in Table 1. 2.2. Characterization The solid state samples in the experiments were analyzed by Xray powder diffraction [7] (type D/max-2500, Rigaku, Japan) and differential scanning calorimetry (DSC 1/500, Mettler-Toledo, Switzerland) [8] before and after the dissolution of disodium sebacate in the tested solvents. X-ray powder diffraction was used
R. Xu et al. / Journal of Molecular Liquids 252 (2018) 194–202
195
Table 1 Sources and mass fraction purity of materials. Chemical name
Source
Mass fraction purity
Purification method
Analysis method
Disodium sebacate Methanol Acetone DMF
TongTuo chromatographic technology Tianjin Guangfu Chemical Tianjin Guangfu Chemical Tianjin Guangfu Chemical
N0.99 N0.995 N0.995 N0.995
None None None None
HPLCa GCb GCb GCb
Both the analysis method and the mass fraction purity were provided by the suppliers. a High-performance liquid chromatography. b Gas chromatography.
to identify the crystal over a diffraction-angle range of 2° to 50°, at a scanning rate of 0.10°·s− 1. The melting temperature Tmelt and enthalpy of fusion ΔfusH of disodium sebacate were measured by DSC under nitrogen atmosphere.
2.3. Solubility measurements by gravimetric method The solubility of disodium sebacate in different binary solvent mixtures was determined by the gravimetric method which was described in the literature [9,10]. At first, an excess amount of disodium sebacate powder was added into the solvent mixtures. The solution was stirred in a 50 ml jacketed glass vessel for 8 h, the preliminary experiments proved that 8 h are enough for this system to reach solid-liquid equilibrium. Then the agitation was stopped and the
suspension was kept static for 6 h to make sure the undissolved particles settle down. After that, the upper clear saturated solutions were withdrawn and filtered by an organic membrane (0.2 μm) filter and dried in a vacuum oven at 313.15 K for 20 h. The temperature of the glass vessel was controlled by a thermostat (Julabo CF41, Germany) with an accuracy of ± 0.02 K. All the masses were measured by an analytical balance (Mettler ToledoML204, Switzerland). The process was repeated three times for each solubility point. Then the mean values were used to calculate the mole fraction solubility. The mole fraction solubility (x1) of disodium sebacate in binary solvent mixtures was calculated by using Eq. (1), and the initial mole fraction (x 2) of water in the binary solvent mixtures is expressed by Eq. (2): x1 ¼
m1 =M1 m1=M1 þ m2=M2 þ m3 =M3
ð1Þ
x2 ¼
m2 =M2 m2 =M 2 þ m3 =M 3
ð2Þ
where m 1, m2 and m3 represent the mass of solute (disodium sebacate), water and organic solvent (methanol, acetone or DMF) respectively. M1, M2 and M3 are the corresponding molecular mass of them. 3. Thermodynamic models In this paper, the modified Apelblat equation, the λh model and the NRTL model were applied to correlate the solubility of disodium sebacate in the binary solvent mixtures, including (water + methanol), (water + acetone) and (water + DMF). In addition, the dissolution thermodynamic properties of disodium sebacate in different Fig. 1. X-ray powder diffraction pattern of disodium sebacate. 0.020 0.5
0.019
0.0
0.018
x2
-1
HF (W g )
-0.5 -1.0
0.017 0.016
-1.5 -2.0
0.015
-2.5
0.014
-3.0 500
520
540
560
580
600
T/K Fig. 2. DSC plot of disodium sebacate.
620
640
660
280
290
300
310
320
330
340
350
T/K Fig. 3. Comparison of experimental solubility data of disodium sebacate with data from Xia [6]. in water. (● represents experimental data in water which were obtained in this work. ■ represents solubility data in water Xia).
196
R. Xu et al. / Journal of Molecular Liquids 252 (2018) 194–202
Table 2 cal Experimental (xexp 1 ) and calculated (x1 ) mole fraction solubility of disodium sebacate in water (x2) + methanol (1 − x2) binary solvent mixtures from 283.15 K to 328.15 K (0.1 MPa)a,b. T/K
104 xexp 1
xABC 1
xλh 1
xNRTL 1
23.6 24.7 25.6 29.4 31.0 34.8 36.9 40.5 42.7 46.7
23.1 24.9 26.9 29.0 31.4 34.0 36.8 39.9 43.2 46.9
24.6 24.7 24.4 29.7 30.4 35.4 36.7 41.1 42.2 47.0
25.1 25.0 24.6 29.5 30.1 34.8 35.8 39.9 40.8 45.2
x2 = 0.6000 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
31.7 36.1 40.1 41.1 46.1 51.5 56.0 58.6 64.7 68.8
32.1 35.5 39.0 42.8 46.7 50.8 55.1 59.6 64.2 69.0
30.8 36.5 41.2 39.6 45.7 52.5 57.3 57.9 65.1 68.2
30.2 35.9 40.6 39.3 45.5 52.5 57.5 58.6 66.2 69.9
x2 = 0.7000 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
49.8 51.1 54.5 59.8 66.7 72.2 75.6 84.1 91.9 96.5
48.1 51.9 56.1 60.7 65.7 71.1 77.0 83.4 90.3 97.8
52.4 50.6 52.9 58.6 67.3 72.7 73.7 84.5 93.6 95.9
51.3 50.0 52.6 58.7 67.7 73.7 75.5 87.0 96.9 100
x2 = 0.8000 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
66.3 72.0 76.2 81.3 84.8 95.3 101 107 116 120
66.2 71.1 76.3 81.8 87.6 93.7 100 107 114 122
66.5 72.9 76.0 80.8 81.9 96.9 101 107 117 119
65.0 71.1 74.2 79.0 80.2 94.9 99.4 106 116 118
x2 = 0.9000 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
98.2 103 109 114 118 126 135 141 149 157
98.3 103 108 114 120 126 133 141 149 157
99.4 103 111 113 115 126 135 140 150 157
104 107 113 115 116 126 135 139 148 155
145 147 150 153 156 160 164 168 173 178
3.1. The modified Apelblat equation
104 xcal 1
x2 = 0.5000 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
x2 = 1.0000 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
binary solvent mixtures were also calculated and discussed based on the NRTL model and experimental solubility data.
145 147 150 153 156 160 164 168 173 178
146 147 150 152 155 159 163 168 173 179
146 147 150 152 155 159 163 168 173 179
The modified Apelblat equation is a widely used semi-empirical equation which was previously used by Apelblat [11]. Due to its simplicity, it is widely used for the prediction of (solid + liquid) equilibrium. Its simplified form is shown as Eq. (3):
ln x1 ¼ A þ
B þ C ln ðT Þ T
ð3Þ
where x1 is the mole fraction solubility of disodium sebacate in the experimental solution, T is the absolute temperature and A, B and C are empirical parameters. The values of A and B represent the variation in the solution activity coefficient and the value of C represents the effect of temperature on the fusion enthalpy [12,13]. 3.2. λh model The relationship between solubility can also be analyzed by the λh model [14], which is a semi empirical model. It can be expressed as: 1−x1 1 1 ln 1 þ λ ¼ λh − T Tm x1
ð4Þ
where λ and h are the model parameters; T is the absolute temperature; and Tm is the absolute melting temperature of the solute. 3.3. NRTL model The simplified general equation for the solubility of compound in a solution is expressed as [15]:
ln x1 ¼
Δfus H 1 1 − − ln γ1 R Tm T
ð5Þ
where ΔfusH and Tm stand for the enthalpy of fusion and melting temperature of solute. To use Eq. (5) to calculate the solubility of compounds, the relationship between activity coefficient and the composition of the solution is necessary. Renon and Prausnitz proposed the nonrandom two-liquid (NRTL) model, which has been successfully used to describe various solution systems. In the binary system (in pure solvents), the activity coefficient of solute γ1 can be calculated by the NRTL model: " lnγ 1 ¼ x2 2
τ21 G21 2
τ12 G12 2 þ 2 ðx1 þ x2 G21 Þ ðx2 þ x1 G12 Þ2
# ð6Þ
Notes to table 2 a x2 is the mole fraction of water in the water + methanol binary solvent mixtures; xexp 1 is the experimentally determined solubility; xcal 1 is the calculated value of mole fraction solubility correlated by model. b The standard uncertainty of T is u (T) = 0.02 K. The relative standard uncertainty of the solubility measurement is ur (x1) = 0.04, the standard uncertainty of mole fraction of methanol in binary solvent mixture is ur (x2) = 0.001. The relative uncertainty of pressure is ur (P) = 0.05.
R. Xu et al. / Journal of Molecular Liquids 252 (2018) 194–202 Table 3 cal Experimental (xexp 1 ) and calculated (x1 ) mole fraction solubility of disodium sebacate in water (x2) + acetone (1 − x2) binary solvent mixtures from 283.15 K to 328.15 K (0.1 MPa)a,b. T/K
104 xexp 1
104 xcal 1 xABC 1
xλh 1
xNRTL 1
x2 = 0.5000 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
1.38 1.83 1.91 2.37 2.43 3.01 3.18 4.09 4.34 6.50
1.29 1.53 1.81 2.15 2.55 3.01 3.56 4.20 4.95 5.83
1.54 2.18 2.02 2.59 2.29 2.96 2.77 3.94 3.72 7.24
1.38 2.05 1.92 2.55 2.33 3.10 3.04 4.36 4.36 8.07
x2 = 0.6000 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
4.29 4.39 4.99 5.41 6.32 7.92 8.03 9.52 11.1 13.5
3.76 4.31 4.94 5.67 6.51 7.47 8.58 9.85 11.3 13.0
5.00 4.59 5.08 5.13 6.05 8.26 7.37 9.12 10.8 14.3
4.75 4.36 4.89 4.99 5.98 8.26 7.52 9.40 11.3 14.9
x2 = 0.7000 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
11.0 11.7 13.6 14.3 17.0 19.9 21.4 23.3 26.6 30.9
10.6 11.9 13.4 15.1 16.9 19.0 21.4 24.0 27.0 30.3
11.8 11.7 13.9 13.5 16.9 20.5 21.3 22.4 26.1 31.8
11.2 11.2 13.4 13.2 16.6 20.3 21.3 22.6 26.6 32.4
x2 = 0.8000 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
29.0 31.1 35.5 38.6 42.9 47.2 51.4 59.6 64.0 67.3
28.6 31.8 35.2 38.9 43.0 47.4 52.1 57.3 62.9 68.9
29.6 30.6 35.9 38.1 42.6 46.8 50.4 61.8 65.0 65.8
27.8 29.1 34.5 37.1 42.0 46.6 50.7 62.2 66.0 67.9
x2 = 0.9000 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
72.1 75.3 82.1 90.6 93.8 99.6 102 107 112 125
72.5 77.2 82.2 87.2 92.5 98.0 104 109 115 121
71.3 73.3 82.0 94.0 95.2 102 100 105 109 128
71.7 74.1 82.5 93.9 95.4 101 100 105 109 126
x2 = 1.0000 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
145 147 150 153 156 160 164 168 173 178
145 147 150 153 156 160 164 168 173 178
146 147 150 152 155 159 163 168 173 179
146 147 150 152 155 159 163 168 173 179
197
with Eq. (7): G12 ¼ expð‐α 12 τ12 Þ G21 ¼ expð‐α 12 τ21 Þ τ 12 ¼ ðg 12 ‐g 22 Þ=RT τ 21 ¼ ðg 21 ‐g 11 Þ=RT
ð7Þ
where Δg 12 (= g 12 − g 22 ) and Δg 21 (= g 21 − g 11 ) are crossinteraction energy. α12 is an empirical constant which varies from 0 to 1. For the ternary system (the binary solvent mixture system), the activity coefficient γ1 can be calculated by the following equation: Eq. (8): Gji x j þ Gkj xk τ ji Gji x j þ τki Gki xk ln γ1 ¼ 2 xi Gji x j þ Gki xk τij Gij x j 2 þ Gij Gkg x j xk τi j τ kj þ 2 x j Gij xi þ Gkj xk τjk Gjk xk 2 þ Gjk Gjk x j xk τjk τ jk þ 2 xk Gjk xi þ Gjk xk
ð8Þ
where Gij, Gik, Gji, Gjk, Gki, Gkj, τij, τik, τji, τjk, τki and τkj are parameters of this model. These terms can be defined as Eq. (9): Gij ¼ exp −α ij τij τ ij ¼ g ij −g ji =RT ¼ Δg ij =RT α ij ¼ α ji
ð9Þ
where i, j, k denote the component of i, j, k, respectively. The cross interaction energy parameters can be represented by Δgij, Δgik, Δgji , Δgjk, Δgki, and Δgkj, which are independent of the composition and temperature. Δg ji = (g ji − g ii ) is the parameter of this model and the value of αij can be adjusted from 0 to 1. 4. Results and discussion 4.1. Characterization of the compounds In this work, disodium sebacate samples were analyzed by X-ray powder diffraction before and after all experiments. And it was found that the X-ray powder diffraction pattern of all the samples used were basically the same. One of the typical X-ray powder diffraction data is shown in Fig. 1. It can be seen that the crystallinity of the sample is pretty high. It was also found that the DSC curves of all samples were basically the same. One of the typical DSC data are shown in Fig. 2. The first endothermic peak at T = 559.63 K is the melting temperature of disodium sebacate. Other endothermic peaks represent the multi-step decomposition of disodium sebacate. The enthalpy of fusion ΔfusH ΔHfusis found to be 5.04 kJ·mol−1. The standard uncertainty of melting temperature is 0.02 K while the standard uncertainty of enthalpy of fusion is 0.05 kJ·mol−1. To verify the reliability of the method used in this work, the solubility data of disodium sebacate in water obtained in this work were compared with the data from references [6]. The results are shown in Fig. 3. It can be seen that the data obtained in this work are pretty
Notes to table 3 a x2 is the mole fraction of water in the water + acetone binary solvent mixtures; xexp 1 is the experimentally determined solubility; xcal 1 is the calculated value of mole fraction solubility correlated by model. b The standard uncertainty of T is u (T) = 0.02 K. The relative standard uncertainty of the solubility measurement is ur (x1) = 0.04, the standard uncertainty of mole fraction of methanol in binary solvent mixture is ur (x2) = 0.001. The relative uncertainty of pressure is ur (P) = 0.05.
198
R. Xu et al. / Journal of Molecular Liquids 252 (2018) 194–202 0.018
Table 4 cal Experimental (xexp 1 ) and calculated (x1 ) mole fraction solubility of disodium sebacate in water (x2) + DMF (1 − x2) binary solvent mixtures from 283.15 K to 328.15 K (0.1 MPa)a,b.
0.014
0.015
104 xcal 1 xλh 1
xNRTL 1
x2 = 0.5000 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
0.547 0.635 0.735 0.848 0.978 1.12 1.29 1.47 1.68 1.91
0.553 0.638 0.735 0.846 0.972 1.12 1.28 1.47 1.68 1.92
0.594 0.676 0.769 0.874 0.995 1.13 1.28 1.46 1.65 1.87
0.481 0.569 0.671 0.787 0.925 1.08 1.26 1.46 1.69 1.95
x2 = 0.6000 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
1.85 2.08 2.35 2.64 2.97 3.34 3.74 4.18 4.67 5.21
1.87 2.10 2.35 2.63 2.95 3.31 3.71 4.17 4.67 5.24
1.88 2.10 2.35 2.63 2.95 3.32 3.73 4.17 4.68 5.24
1.65 1.88 2.16 2.46 2.80 3.19 3.64 4.10 4.64 5.23
x2 = 0.7000 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
6.04 6.63 7.29 8.02 8.83 9.71 10.6 11.7 12.9 14.1
6.03 6.63 7.30 8.02 8.82 9.70 10.7 11.7 12.9 14.1
6.17 6.69 7.28 7.98 8.77 9.64 10.6 11.7 12.9 14.2
5.64 6.23 6.90 7.66 8.52 9.46 10.4 11.7 12.9 14.3
x2 = 0.8000 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
19.6 20.9 22.4 24.3 26.2 28.4 30.6 33.0 35.8 38.6
19.5 20.9 22.5 24.3 26.2 28.3 30.6 33.0 35.7 38.6
20.0 21.0 22.3 24.2 25.9 28.2 30.4 32.8 36.0 38.8
19.3 20.6 22.1 24.1 26.1 28.5 30.8 33.3 36.5 39.5
0.012 1
xABC 1
x
104 xexp 1
0.01 0.01 0.005 0.008 0 340 320
64.7 68.2 72.0 76.2 80.6 85.5 90.7 96.4 102 109
65.7 68.7 71.6 76.2 79.1 85.3 91.4 95.7 102 111
64.9 68.5 71.9 76.6 79.9 85.9 91.6 95.9 101 109
x2 = 1.0000 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
145 147 150 153 156 160 164 168 173 178
145 147 150 153 156 160 164 168 173 178
146 147 150 152 155 159 163 168 173 179
146 147 150 152 155 159 163 168 173 179
0.8
300 280
T/k
0.004
0.7
290
0.6 0.5
x
2
Fig. 4. Mole fraction solubility (x1) of disodium sebacate versus temperature T in water (x2) + methanol (1 − x2) binary solvent mixtures.
-3
x 10 16 0.02
x
1
64.7 68.3 71.9 76.4 80.2 85.7 91.3 96.2 102 109
0.9
310
14
0.015
12
0.01
10 8
0.005 6 0 340
4 330 320
0.9
310
2
0.8
300 290 280
T/k
0.6 0.5
0.7 x2
Fig. 5. Mole fraction solubility (x1) of disodium sebacate versus temperature T in water (x2) + acetone (1 − x2) binary solvent mixtures.
-3
x 10 16 0.02 14 0.015
1
x2 = 0.9000 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
0.006
330
x
T/K
0.016
0.02
12
0.01
10 8
0.005
6
0 340 330 320
0.9
310
0.8
300 290 T/k
280
0.6 0.5
1
4 2
0.7 x2
Fig. 6. Mole fraction solubility (x1) of disodium sebacate versus temperature T in water (x2) + DMF acetone (1 − x2) binary solvent mixtures.
Notes to table 4 a x2 is the mole fraction of water in the water + DMF binary solvent mixtures; xexp 1 is the experimentally determined solubility; xcal 1 is the calculated value of mole fraction solubility correlated by model. b The standard uncertainty of T is u (T) = 0.02 K. The relative standard uncertainty of the solubility measurement is ur (x1) = 0.04, the standard uncertainty of mole fraction of methanol in binary solvent mixture is ur (x2) = 0.001. The relative uncertainty of pressure is ur (P) = 0.05.
R. Xu et al. / Journal of Molecular Liquids 252 (2018) 194–202 Table 5 Parameters of the modified Apelblat model for disodium sebacate in binary solvent mixtures from 283.15 K to 328.15 K (0.1 MPa). x2
A
Water + methanol 0.5 −82.9 0.6 15.2 0.7 −72.9 0.8 −29.8 0.9 −71.2 1 −64.6
Table 7 Parameters of the NRTL model for disodium sebacate in binary solvent mixtures from 283.15 K to 328.15 K (0.1 MPa).
B/103
C
ARD%
105RMSD
Parameter
2.25 −2.28 1.83 0.0692 2.20 2.38
12.2 −2.29 10.8 4.35 10.4 9.21
1.65 1.68 1.84 1.04 0.503 0.0242
6.07 8.60 12.7 12.8 9.27 0.542
Δg12 Δg13 Δg21 Δg23 Δg31 Δg32 ARD% 104RMSD
Water + acetone 0.5 −110 0.6 −116 0.7 −99.4 0.8 −40.5 0.9 −12.3 1 −64.6
1.96 2.77 2.38 0.0449 −0.563 2.38
16.7 17.5 14.9 6.10 1.65 9.21
8.14 4.53 2.42 1.56 1.96 0.0242
3.39 3.70 10.3 22.6 0.542 0.542
Water + DMF 0.5 −84.3 0.6 −101 0.7 −73.8 0.8 −81.6 0.9 −79.4 1 −64.6
1.22 2.42 1.53 2.22 2.47 2.38
12.4 14.9 10.8 12.0 11.6 9.21
0.443 0.583 0.100 0.226 0.314 0.0242
0.0504 0.202 0.113 0.677 3.37 0.542
consistent with the data from literature, which verify the reliability of our measurement method. 4.2. Solubility data The solubility of disodium sebacate in pure water and binary solvent mixtures at different temperatures was measured. The results are given in Tables 2–4 and graphically shown in Figs. 4–6. It can be seen that the solubility of disodium sebacate in all tested solvents increases with the rising of the temperature when the solvent composition remains constant. It also increases with the increasing of water composition in binary solvent mixtures at constant temperature. The solubility of disodium sebacate in pure
199
kJ·mol−1
Water + methanol
Water + acetone
Water + DMF
Water
20.1 1.02 5.68 −0.374 17.9 −4.16 2.27 1.99
−5.14 −1.14 20.9 22.2 39.6 −9.49 3.80 1.17
−6.88 2.72 21.0 −5.60 34.9 3.51 3.04 0.275
27.3 −1.01
0.426 0.789
water is much higher than the solubilities in other solvents. This might be explained by the higher possibility of the formation of hydrogen bond between water molecules and disodium sebacate molecules. Besides, the solubility of disodium sebacate in the binary solvent mixtures at constant temperature ranked as (methanol + water) N (acetone + water) N (DMF + water) in general, which indicates that the “like dissolves like” rule can be used to explain the solubility trend of disodium sebacate since disodium sebacate [16] is a polar molecule and the order of polarity of pure solvents is that: DMF b acetone b methanol b water. The modified Apelblat equation, the λh model and the NRTL model were applied to correlate the experimental solubility of disodium sebacate in binary solvent mixtures. The calculated solubility data are also listed in Tables 2–4. The parameters of the modified Apelblat equation, the λh model and the NRTL model are given in Tables 5–7, respectively. To evaluate the applicability of the tested models, the average relative deviation (ARD%), the root-meansquare deviations (RMSD) are used to evaluate the application of these models. The average relative deviation (ARD%) and the root-mean-square deviation (RMSD) are defined as follows:
ARD ¼
100 N
xi exp ‐xi cal
∑i¼1
exp N xi
ð10Þ
Table 6 Parameters of the λh equation for disodium sebacate in binary solvent mixtures from 283.15 K to 328.15 K (0.1 MPa). 10−4 h
ARD%
105RMSD
Water + methanol 0.5 18.3 0.6 32.1 0.7 38.7 0.8 29.5 0.9 16.4 1 −8.93
6.90 4.25 3.28 3.29 3.43 6.09
1.70 1.80 1.81 1.06 0.780 0.395
6.25 9.00 13.6 12.9 11.8 7.32
Water + acetone 0.5 3.10 0.6 31.6 0.7 40.8 0.8 50.9 0.9 17.0 1 −8.93
1.02 8.14 5.21 3.31 4.04 6.09
9.51 5.64 2.78 1.69 2.04 0.395
3.67 4.47 5.98 10.1 22.6 7.32
Water + DMF 0.5 0.6 0.7 0.8 0.9 1
44.5 31.7 17.1 8.84 4.43 6.09
3.07 0.550 0.675 0.788 0.653 0.395
0.301 0.179 0.687 2.28 6.62 7.32
x2
10−3λ
6.22 6.54 9.47 13.5 16.4 −8.93
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 N ∑i¼1 xi exp ‐xi cal RMSD ¼ N
ð11Þ
and xcal is where N is the number of experimental data points, xexp i i the experimental and the calculated solubility values. The obtained values of ARD, and RMSD are also given in Tables 5–7. It can be found from Tables 5–7 that the maximum average relative deviation (ARD%) between the experimental and calculated solubility values is below 9.51%, which indicates that the correlated values are in good agreement with experimental values at temperatures studied for the studied systems. 4.3. Dissolution thermodynamic properties In this study, the dissolution process can be assumed to consist of four energetic steps, (including heating, fusion, cooling and mixing processes) theoretically. Then it is reasonable to calculate the dissolution thermodynamic properties by the following
200
R. Xu et al. / Journal of Molecular Liquids 252 (2018) 194–202
Table 8 The dissolution thermodynamic properties of disodium sebacate in water (x2) + methanol (1 − x2) binary solvent mixtures from 283.15 K to 328.15 K (0.1 MPa)a,b. ΔdisG
ΔdisS
ΔdisH
kJ·mol−1
J·K−1·mol−1
kJ·mol−1
T = 283.15 K 0.5 0.6 0.7 0.8 0.9 1
−2.86 −2.79 −2.51 −2.02 −1.27 −0.0693
14.6 14.3 12.9 10.3 6.31 0.493
1.26 1.26 1.14 0.909 0.541 0.106
T = 288.15 K 0.5 0.6 0.7 0.8 0.9 1
−2.89 −2.81 −2.54 −2.04 −1.28 −0.0705
14.4 14.1 12.7 10.2 6.24 0.487
1.26 1.25 1.14 0.904 0.538 0.106
T = 293.15 K 0.5 0.6 0.7 0.8 0.9 1
−2.92 −2.84 −2.56 −2.06 −1.30 −0.0718
14.2 13.9 12.6 10.0 6.17 0.483
1.25 1.25 1.13 0.900 0.536 0.106
T = 298.15 K 0.5 0.6 0.7 0.8 0.9 1
−2.95 −2.87 −2.59 −2.08 −1.31 −0.0732
14.0 13.7 12.4 9.92 6.11 0.478
1.25 1.24 1.13 0.895 0.534 0.105
T = 303.15 K 0.5 0.6 0.7 0.8 0.9 1
−2.97 −2.89 −2.61 −2.10 −1.33 −0.0748
13.9 13.6 12.3 9.81 6.04 0.475
1.24 1.23 1.12 0.891 0.532 0.105
T = 308.15 K 0.5 0.6 0.7 0.8 0.9 1
−3.00 −2.92 −2.64 −2.12 −1.34 −0.0764
13.7 13.4 12.1 9.70 5.98 0.472
1.24 1.23 1.12 0.887 0.530 0.105
T = 313.15 K 0.5 0.6 0.7 0.8 0.9 1
−3.03 −2.95 −2.66 −2.14 −1.36 −0.0782
13.6 13.3 12.0 9.60 5.93 0.470
1.23 1.22 1.11 0.883 0.528 0.105
T = 318.15 K 0.5 0.6 0.7 0.8 0.9 1
−3.06 −2.98 −2.68 −2.17 −1.37 −0.0800
13.4 13.1 11.9 9.49 5.87 0.468
1.23 1.22 1.10 0.879 0.526 0.106
T = 323.15 K 0.5 0.6 0.7 0.8 0.9 1
−3.08 −3.00 −2.71 −2.19 −1.39 −0.0820
13.3 13.0 11.7 9.39 5.82 0.467
1.22 1.21 1.10 0.875 0.524 0.106
x2
Table 8 (continued) x2
0.8 0.9 1
ΔdisG
ΔdisS
ΔdisH
kJ·mol−1
J·K−1·mol−1
kJ·mol−1
−2.21 −1.40 −0.0840
9.30 5.77 0.467
0.871 0.522 0.106
a x2 is the mole fraction of water in the water + methanol binary solvent mixtures; ΔdisG, ΔdisS are the dissolution thermodynamic parameters according to Eqs. (17) to (19). b The expanded uncertainties are U (ΔdisG) = 0.02 ΔdisG, U (ΔdisS) = 0.05 ΔdisS, U (ΔdisH) = 0.01ΔdisH (0.95 level of confidence).
equations: Δdis M ¼ x Δheat M þ Δfus M þ Δcool M þ Δmix M
ð12Þ
where M can be replaced by G, S and H. x refers to the mole fraction solubility of the solute. The ΔfusM refers to the fusion thermodynamic properties; ΔmixM represents the mixing properties. ΔheatM and Δ cool M stand for the thermodynamic properties of heating and cooling process, respectively. They can be calculated by the following equations: Δheat H ¼ C pðsÞ ðT m ‐T Þ
ð13Þ
Tm T
ð14Þ
Δcool H ¼ C pðlÞ ðT‐T m Þ
ð15Þ
T Tm
ð16Þ
Δheat S ¼ C pðsÞ ln
Δcool S ¼ C pðlÞ ln
It could be assumed that the heat capacity of solid state disodium sebacate and the heat capacity of liquid state disodium sebacate are very close, and the term of ΔheatM will be offset by the term of ΔcoolM, then the sum of ΔheatM and ΔcoolM will be able to be ignored. Besides, during the phase transition of solute, the system is in equilibrium, so ΔfusG = 0. For a non-ideal solution, the mixing thermodynamic properties of the solute can be calculated by the following Eqs. (17)–(19): Δmix G ¼ GE þ Δmix Gid
ð17Þ
Δmix H ¼ HE þ Δmix H id
ð18Þ
Δmix S ¼ SE þ Δmix Sid
ð19Þ
where GE, SE and HE refer to the excess properties of Gibbs energy, entropy and enthalpy, respectively, and Δ mix Gid , Δmix S id , Δ mix Hid refer to mixing Gibbs energy, mixing entropy and mixing enthalpy of the ideal solution, respectively. The mixing thermodynamic properties of the ideal system can be calculated by the following Eqs. (20)–(22) [17]. Δmix Gid ¼ RT
N X
xi lnxi
ð20Þ
i¼1
Δmix H id ¼ 0 Δmix Sid ¼ −R
ð21Þ N X
xi lnxi
ð22Þ
i¼1
T = 328.15 K 0.5 0.6 0.7
−3.11 −3.03 −2.73
13.2 12.9 11.6
1.22 1.21 1.09
where xi indicate the mole fraction of component i in solution. N = 2 means binary solution and N = 3 means ternary solution. The excess mixing properties can be calculated by the following Eqs. (23)–(25)
R. Xu et al. / Journal of Molecular Liquids 252 (2018) 194–202 Table 9 The dissolution thermodynamic properties of disodium sebacate in water (x2) + acetone (1 − x2) binary solvent mixtures from 283.15 K to 328.15 K (0.1 MPa)a,b. ΔdisG
ΔdisS
ΔdisH
kJ·mol−1
J·K−1·mol−1
kJ·mol−1
T = 283.15 K 0.5 0.6 0.7 0.8 0.9 1
−1.65 −1.50 −1.24 −0.897 −0.521 −0.0693
13.1 11.8 9.58 6.71 3.77 0.493
2.07 1.86 1.48 1.01 0.564 0.106
T = 288.15 K 0.5 0.6 0.7 0.8 0.9 1
−1.63 −1.48 −1.22 −0.884 −0.517 −0.0705
12.7 11.3 9.12 6.35 3.56 0.487
2.02 1.79 1.41 0.953 0.528 0.106
x2
Table 9 (continued) x2
0.8 0.9 1
−1.61 −1.46 −1.20 −0.872 −0.514 −0.0718
12.2 10.9 8.68 6.01 3.38 0.483
1.96 1.73 1.35 0.899 0.497 0.106
T = 298.15 K 0.5 0.6 0.7 0.8 0.9 1
−1.59 −1.44 −1.18 −0.862 −0.513 −0.0732
11.7 10.4 8.27 5.69 3.22 0.478
1.91 1.67 1.29 0.845 0.468 0.105
T = 303.15 K 0.5 0.6 0.7 0.8 0.9 1
−1.58 −1.42 −1.17 −0.853 −0.511 −0.0748
11.3 10.0 7.88 5.40 3.05 0.475
1.85 1.61 1.22 0.794 0.436 0.105
T = 308.15 K 0.5 0.6 0.7 0.8 0.9 1
−1.56 −1.41 −1.16 −0.845 −0.511 −0.0764
10.9 9.58 7.52 5.12 2.91 0.472
1.80 1.55 1.17 0.744 0.407 0.105
T = 313.15 K 0.5 0.6 0.7 0.8 0.9 1
−1.55 −1.39 −1.14 −0.838 −0.510 −0.0782
10.5 9.20 7.17 4.86 2.76 0.470
1.75 1.49 1.11 0.696 0.377 0.105
T = 318.15 K 0.5 0.6 0.7 0.8 0.9 1
−1.54 −1.38 −1.13 −0.833 −0.511 −0.0800
10.2 8.83 6.85 4.63 2.63 0.468
1.70 1.43 1.05 0.651 0.350 0.106
T = 323.15 K 0.5 0.6 0.7 0.8 0.9 1
−1.53 −1.37 −1.12 −0.829 −0.513 −0.0820
9.82 8.48 6.54 4.40 2.51 0.467
1.65 1.38 0.995 0.606 0.323 0.106
T = 328.15 K 0.5 0.6 0.7
−1.52 −1.36 −1.12
9.49 8.15 6.25
1.60 1.32 0.942
ΔdisG
ΔdisS
ΔdisH
kJ·mol−1
J·K−1·mol−1
kJ·mol−1
−0.825 −0.516 −0.0840
4.18 2.42 0.467
0.562 0.304 0.106
a x2 is the mole fraction of water in the water + acetone binary solvent mixtures; ΔdisG, ΔdisS are the dissolution thermodynamic parameters according to Eqs. (17) to (19). b The expanded uncertainties are U (ΔdisG) = 0.02 ΔdisG, U (ΔdisS) = 0.05 ΔdisS, U (ΔdisH) = 0.01ΔdisH (0.95 level of confidence).
[18]:
GE ¼ RT
T = 293.15 K 0.5 0.6 0.7 0.8 0.9 1
201
N X
xi lnγi
ð23Þ
N X ∂lnγi xi ∂T P;x i¼1
ð24Þ
i¼1
H E ¼ −RT 2
SE ¼
HE −GE T
ð25Þ
where xi and γi are the mole fraction and activity coefficient of component i in real solution respectively. The dissolution thermodynamic properties in the three binary mixtures were calculated by using NRTL model and the experimental solubility data. The results are given in Tables 8–10. In addition, these dissolution thermodynamic data are calculated based on per mole mixture. As shown in these tables, it can be found that the values of ΔdisG are all negative, which indicates that the dissolution of disodium sebacate in all solvents investigated is a spontaneous and favorable process. The values of ΔdisS and ΔdisH are positive, which proves that the mixing process in all solvents investigated is entropy-driven and endothermic [19–21]. 5. Conclusions In this work, the solubility of disodium sebacate in binary solvent mixtures, including (methanol + water), (acetone + water), and (DMF + water), was measured from T = (283.15 to 328.15) K by the gravimetric method. It was found that the solubility data of disodium sebacate increased with increase of temperature in binary solvent mixtures at constant solvent composition, and increased with increase of mole fraction of water. Moreover, the dissolving capacity of disodium sebacate in three binary solvent mixtures at constant temperature ranked as (methanol + water) N (acetone + water) N (DMF + water). The experimental solubility data was correlated by the modified Apelblat model, the λh model and the NRTL model. It turns out that all the selected thermodynamic models can give good correlation results. Besides, the dissolution entropy, enthalpy and Gibbs energy of disodium sebacate in the tested solvents were also determined by using the NRTL model and the experimental solubility data. According to the results, it was found that the dissolution process of disodium sebacate in all solvents is spontaneous, entropy-driven and endothermic. Notes The authors declare no competing financial interest.
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R. Xu et al. / Journal of Molecular Liquids 252 (2018) 194–202
Table 10 The dissolution thermodynamic properties of disodium sebacate in water (x2) + DMF (1 − x2) binary solvent mixtures from 283.15 K to 328.15 K (0.1 MPa)a,b. ΔdisG
ΔdisS
ΔdisH
kJ·mol−1
J·K−1·mol−1
kJ·mol−1
T = 283.15 K 0.5 0.6 0.7 0.8 0.9 1
−2.45 −2.33 −2.06 −1.64 −1.03 −0.0693
12.5 11.9 10.4 8.02 4.77 0.493
1.08 1.04 0.886 0.638 0.336 0.106
T = 288.15 K 0.5 0.6 0.7 0.8 0.9 1
−2.47 −2.36 −2.08 −1.66 −1.04 −0.0705
12.3 11.7 10.3 7.93 4.72 0.487
1.06 1.03 0.879 0.633 0.332 0.106
T = 293.15 K 0.5 0.6 0.7 0.8 0.9 1
−2.50 −2.38 −2.11 −1.67 −1.06 −0.0718
12.1 11.6 10.2 7.84 4.67 0.483
1.05 1.02 0.873 0.629 0.328 0.106
T = 298.15 K 0.5 0.6 0.7 0.8 0.9 1
−2.52 −2.40 −2.13 −1.69 −1.07 −0.0732
12.0 11.5 10.0 7.75 4.62 0.478
1.04 1.01 0.866 0.624 0.325 0.105
T = 303.15 K 0.5 0.6 0.7 0.8 0.9 1
−2.55 −2.43 −2.15 −1.71 −1.09 −0.0748
11.8 11.3 9.93 7.67 4.58 0.475
1.03 1.00 0.859 0.619 0.320 0.105
T = 308.15 K 0.5 0.6 0.7 0.8 0.9 1
−2.57 −2.45 −2.18 −1.73 −1.10 −0.0764
11.7 11.2 9.82 7.60 4.53 0.472
1.02 0.994 0.853 0.614 0.317 0.105
T = 313.15 K 0.5 0.6 0.7 0.8 0.9 1
−2.60 −2.48 −2.20 −1.75 −1.11 −0.0782
11.5 11.1 9.72 7.52 4.49 0.470
1.01 0.986 0.847 0.609 0.313 0.105
T = 318.15 K 0.5 0.6 0.7 0.8 0.9 1
−2.62 −2.50 −2.22 −1.77 −1.13 −0.0800
11.4 10.9 9.62 7.45 4.45 0.468
1.00 0.978 0.840 0.604 0.308 0.106
T = 323.15 K 0.5 0.6 0.7 0.8 0.9 1
−2.64 −2.53 −2.25 −1.79 −1.14 −0.0820
11.3 10.8 9.52 7.37 4.41 0.467
0.996 0.971 0.834 0.598 0.304 0.106
T = 328.15 K 0.5 0.6 0.7
−2.67 −2.55 −2.27
11.1 10.7 9.43
0.987 0.964 0.828
x2
Table 10 (continued) x2
0.8 0.9 1
ΔdisG
ΔdisS
ΔdisH
kJ·mol−1
J·K−1·mol−1
kJ·mol−1
−1.81 −1.16 −0.0840
7.31 4.37 0.467
0.594 0.299 0.106
a x2 is the mole fraction of water in the water + DMF binary solvent mixtures; ΔdisG, ΔdisS are the dissolution thermodynamic parameters according to Eqs. (17) to (19). b The expanded uncertainties are U (ΔdisG) = 0.02 ΔdisG, U (ΔdisS) = 0.05 ΔdisS, U (ΔdisH) = 0.01ΔdisH (0.95 level of confidence).
Acknowledgment This research is financially supported by Major National Scientific Instrument Development Project (No. 21527812). References [1] S. Gouin, X.X. Zhu, S. Lehnert, New polyanhydrides made from a bile acid dimer and sebacic acid: synthesis, characterization and degradation, Macromolecules 33 (2000) 5379–5383. [2] M. Nagata, Synthesis and properties of copolyesters based on hydroquinone, sebacic acid and p-hydroxybenzoic acid, High Perform. Polym. 13 (2012) S265–S274. [3] J.C. Tang, Z.G. Zhang, Z.F. Song, L.R. Chen, X. Hou, K.D. Yao, Synthesis and characterization of elastic aliphatic polyesters from sebacic acid, glycol and glycerol, Eur. Polym. J. 42 (2006) 3360–3366. [4] M.Y. Krasko, A. Shikanov, A. Ezra, A.J. Dom, Poly(ester anhydride)s prepared by the insertion of ricinoleic acid into poly(sebacic acid), J. Polym. Sci. A Polym. Chem. 41 (2003) 1059–1069. [5] R.B. Qi, J.K. Wang, J.X. Ye, H.X. Hao, Y. Bao, The solubility of cefquinome sulfate in pure and mixed solvents, Front. Chem. Sci. Eng. 10 (2016) 245–254. [6] J. Kang, Q. Xia, L.X. Wang, M.X. Du, F.B. Zhang, G.L. Zhang, Effects of NaOH and ethanol on the solubility of disodium Decanedioate in water, J. Chem. Eng. Data 57 (2012) 994–999. [7] J.B. Ouyang, J.K. Wang, Y.L. Wang, Q.X. Yin, H.X. Hao, Thermodynamic study on dynamic water and organic vapor sorption on amorphous valnemulin hydrochloride, Front. Chem. Sci. Eng. 9 (2015) 1–11. [8] A. Maher, D. Croker, Å.C. Rasmuson, B.K. Hodnett, Solubility of form III Piracetam in a range of solvents, J. Chem. Eng. Data 55 (2010) 5314–5318. [9] P.L. Cui, Q.X. Yin, J.B. Gong, Solubility of candesartan Cilexetil in different solvents at various temperatures, J. Chem. Eng. Data 56 (1997) 658–660. [10] X. Yang, X.J. Wang, C.B. Ching, Solubility of form α and form γ of glycine in aqueous solutions, J. Chem. Eng. Data 53 (2008) 1133–1137. [11] A. Apelblat, E. Manzurola, Solubilities of L-aspartic, DL-aspartic, DL-glutamic, phydroxybenzoic, o-anisic, p-anisic, and itaconic acids in water from T = 278 K to T = 345 K, J. Chem. Thermodyn. 29 (1997) 1527–1533. [12] A. Apelblat, E. Manzurola, Solubilities of o-acetylsalicylic, 4-aminosalicylic, 3,5dinitrosalicylic, and p-toluic acid, and magnesium-DL-aspartate in water from T = (278 to 348) K, J. Chem. Thermodyn. 31 (1999) 85–91. [13] E. Manzurola, A. Apelblat, Solubilities of L-glutamic acid, 3-nitrobenzoic acid, ptoluic acid, calcium-L-lactate, calcium gluconate, magnesium-DL-aspartate, and magnesium-L-lactate in water, J. Chem. Thermodyn. 34 (2002) 1127–1136. [14] H. Buchowski, A. Ksiazczak, S. Pietrzyk, ChemInform abstract: solvent activity along a saturation line and solubility of hydrogen-bonding solids, J. Phys. Chem. 84 (1980) 975–979. [15] Y.M. Guo, Y.H. Hao, Y.N. Zhou, Z.Y. Han, C. Xie, W.Y. Su, H.X. Hao, Solubility and thermodynamic properties of vanillyl alcohol in some pure solvents, J. Chem. Thermodyn. 106 (2017) 276–284. [16] F.X. Zou, Z.G. Wei, J.L. Wu, J.W. Zhou, Q.Y. Liu, Y. Chen, J.J. Xie, C.J. Zhu, T. Guo, H.J. Ying, Experimental measurement and modelling of solubility of inosine-5′monophosphate disodium in pure and mixed solvents, J. Chem. Thermodyn. 77 (2014) 14–22. [17] F. He, Y.L. Wang, Q.X. Yin, L.G. Tao, J. Lv, Z. Xu, J.X. Wang, H.X. Hao, Effect of polymorphism on thermodynamic properties of cefamandole nafate, Fluid Phase Equilib. 422 (2016) 56–65. [18] R. Orye, J. Prausnitz, Multicomponent equilibria—the Wilson equation, Ind. Eng. Chem. Res. 57 (1965) 18–26. [19] J.Q. Li, Z. Wang, Y. Bao, J.K. Wang, Solid–liquid phase equilibrium and mixing properties of cloxacillin benzathine in pure and mixed solvents, Ind. Eng. Chem. Res. 52 (2013) 3019–3026. [20] M. Gantiva, F. Martinez, Thermodynamic analysis of the solubility of ketoprofen in some propylene glycol + water cosolvent mixtures, Fluid Phase Equilib. 293 (2010) 242–250. [21] S. Feng, T. Li, Predicting lattice energy of organic crystals by density functional theory with empirically corrected dispersion energy, J. Chem. Theory Comput. 2 (2006) 149–156.
Contents lists available at ScienceDirect
Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq
Thermodynamic properties of disodium sebacate in different binary solvent mixtures Ruilin Xu a, Baohong Hou a,b, Na Wang a, Yajing Lou a, Yang Li a, Jingjing Huang a, Hongxun Hao a,b,⁎ a b
National Engineering Research Center of Industrial Crystallization Technology, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin 300072, China
a r t i c l e
i n f o
Article history: Received 24 July 2017 Received in revised form 21 October 2017 Accepted 20 December 2017 Available online 26 December 2017 Keywords: Disodium sebacate Gravimetric method Solubility Dissolution thermodynamic properties
a b s t r a c t The solubility data of disodium sebacate in three kinds of water + organic solvent mixtures, including (water + methanol), (water + acetone) and (water + DMF), were experimentally determined at temperatures from (283.15 to 328.15) K by a gravimetric method. The results show that the solubility of disodium sebacate increases with increase of temperature in binary solvent mixtures at constant solvent composition, whereas it decreases with the increase of the mole fraction of organic solvent. The modified Apelblat equation, the λh model and the NRTL model were applied to correlate the solubility data in binary solvent mixtures. In addition, the dissolution thermodynamic properties of disodium sebacate in different binary solvent mixtures, including the Gibbs energy change, entropy and enthalpy, were also calculated and discussed based on the NRTL model and experimental solubility data. © 2017 Elsevier B.V. All rights reserved.
1. Introduction Disodium sebacate (NaOOC-(CH2)8-COONa, CAS No. 17265-14-4) is a white powdered crystal and is generated in cracking process and then acidified to sebacic acid, which is extremely valuable for the production of nylon, alkyd resins, plasticizers, cosmetics, and biological agents, and so forth [1–4]. Generally, the acidization from disodium sebacate to sebacic acid is processed in water. Since the solubility of sebacic acid in water is pretty low and is prone to cause outbreak of nucleation and serious agglomeration, which will result in decanedioic acid product with small size product and uneven size distribution. Usually, decanedioic acid product with larger size and more homogeneous particle distribution will be favorite since their easier downstream processing, such as filtration, drying, and packing. As we all know, the solvent could significantly affect the crystallization process and therefore will affect the quality of final product. To overcome the burst of nucleation during acidization in water, acidization in binary solvent mixtures of water and organic solvents is one possible solution. Therefore, it is important to know the solid-liquid equilibrium data [5] of disodium sebacate in binary solvent mixtures. Apart from the effects of NaOH and ethanol on the solubility of disodium decanedioate in water studied by Qing Xia's group [6], ⁎ Corresponding author at: National Engineering Research Center of Industrial Crystallization Technology, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China. E-mail address: [email protected] (H. Hao).
https://doi.org/10.1016/j.molliq.2017.12.104 0167-7322/© 2017 Elsevier B.V. All rights reserved.
the solubility of disodium sebacate has not been reported in the literature. In this work, the solubilities of disodium sebacate in water + organic solvent mixtures at different temperatures were measured by a gravimetric method in a temperature range from (283.15 to 328.15) K. Different models were used to correlate the experimental solubility data. The dissolution thermodynamic properties were also investigated. 2. Experimental 2.1. Materials Disodium sebacate was supplied by TongTuo chromatographic technology Co., Ltd. (Tianjin, China). The organic solvents, including methanol, acetone and DMF were provided by Tianjin Guangfu Chemical Technique Co., Ltd. (Tianjin, China). Distilled–deionized water was supplied by Nankai University, China. All chemicals were used without further purification. More detailed information about the materials used in this work has been listed in Table 1. 2.2. Characterization The solid state samples in the experiments were analyzed by Xray powder diffraction [7] (type D/max-2500, Rigaku, Japan) and differential scanning calorimetry (DSC 1/500, Mettler-Toledo, Switzerland) [8] before and after the dissolution of disodium sebacate in the tested solvents. X-ray powder diffraction was used
R. Xu et al. / Journal of Molecular Liquids 252 (2018) 194–202
195
Table 1 Sources and mass fraction purity of materials. Chemical name
Source
Mass fraction purity
Purification method
Analysis method
Disodium sebacate Methanol Acetone DMF
TongTuo chromatographic technology Tianjin Guangfu Chemical Tianjin Guangfu Chemical Tianjin Guangfu Chemical
N0.99 N0.995 N0.995 N0.995
None None None None
HPLCa GCb GCb GCb
Both the analysis method and the mass fraction purity were provided by the suppliers. a High-performance liquid chromatography. b Gas chromatography.
to identify the crystal over a diffraction-angle range of 2° to 50°, at a scanning rate of 0.10°·s− 1. The melting temperature Tmelt and enthalpy of fusion ΔfusH of disodium sebacate were measured by DSC under nitrogen atmosphere.
2.3. Solubility measurements by gravimetric method The solubility of disodium sebacate in different binary solvent mixtures was determined by the gravimetric method which was described in the literature [9,10]. At first, an excess amount of disodium sebacate powder was added into the solvent mixtures. The solution was stirred in a 50 ml jacketed glass vessel for 8 h, the preliminary experiments proved that 8 h are enough for this system to reach solid-liquid equilibrium. Then the agitation was stopped and the
suspension was kept static for 6 h to make sure the undissolved particles settle down. After that, the upper clear saturated solutions were withdrawn and filtered by an organic membrane (0.2 μm) filter and dried in a vacuum oven at 313.15 K for 20 h. The temperature of the glass vessel was controlled by a thermostat (Julabo CF41, Germany) with an accuracy of ± 0.02 K. All the masses were measured by an analytical balance (Mettler ToledoML204, Switzerland). The process was repeated three times for each solubility point. Then the mean values were used to calculate the mole fraction solubility. The mole fraction solubility (x1) of disodium sebacate in binary solvent mixtures was calculated by using Eq. (1), and the initial mole fraction (x 2) of water in the binary solvent mixtures is expressed by Eq. (2): x1 ¼
m1 =M1 m1=M1 þ m2=M2 þ m3 =M3
ð1Þ
x2 ¼
m2 =M2 m2 =M 2 þ m3 =M 3
ð2Þ
where m 1, m2 and m3 represent the mass of solute (disodium sebacate), water and organic solvent (methanol, acetone or DMF) respectively. M1, M2 and M3 are the corresponding molecular mass of them. 3. Thermodynamic models In this paper, the modified Apelblat equation, the λh model and the NRTL model were applied to correlate the solubility of disodium sebacate in the binary solvent mixtures, including (water + methanol), (water + acetone) and (water + DMF). In addition, the dissolution thermodynamic properties of disodium sebacate in different Fig. 1. X-ray powder diffraction pattern of disodium sebacate. 0.020 0.5
0.019
0.0
0.018
x2
-1
HF (W g )
-0.5 -1.0
0.017 0.016
-1.5 -2.0
0.015
-2.5
0.014
-3.0 500
520
540
560
580
600
T/K Fig. 2. DSC plot of disodium sebacate.
620
640
660
280
290
300
310
320
330
340
350
T/K Fig. 3. Comparison of experimental solubility data of disodium sebacate with data from Xia [6]. in water. (● represents experimental data in water which were obtained in this work. ■ represents solubility data in water Xia).
196
R. Xu et al. / Journal of Molecular Liquids 252 (2018) 194–202
Table 2 cal Experimental (xexp 1 ) and calculated (x1 ) mole fraction solubility of disodium sebacate in water (x2) + methanol (1 − x2) binary solvent mixtures from 283.15 K to 328.15 K (0.1 MPa)a,b. T/K
104 xexp 1
xABC 1
xλh 1
xNRTL 1
23.6 24.7 25.6 29.4 31.0 34.8 36.9 40.5 42.7 46.7
23.1 24.9 26.9 29.0 31.4 34.0 36.8 39.9 43.2 46.9
24.6 24.7 24.4 29.7 30.4 35.4 36.7 41.1 42.2 47.0
25.1 25.0 24.6 29.5 30.1 34.8 35.8 39.9 40.8 45.2
x2 = 0.6000 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
31.7 36.1 40.1 41.1 46.1 51.5 56.0 58.6 64.7 68.8
32.1 35.5 39.0 42.8 46.7 50.8 55.1 59.6 64.2 69.0
30.8 36.5 41.2 39.6 45.7 52.5 57.3 57.9 65.1 68.2
30.2 35.9 40.6 39.3 45.5 52.5 57.5 58.6 66.2 69.9
x2 = 0.7000 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
49.8 51.1 54.5 59.8 66.7 72.2 75.6 84.1 91.9 96.5
48.1 51.9 56.1 60.7 65.7 71.1 77.0 83.4 90.3 97.8
52.4 50.6 52.9 58.6 67.3 72.7 73.7 84.5 93.6 95.9
51.3 50.0 52.6 58.7 67.7 73.7 75.5 87.0 96.9 100
x2 = 0.8000 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
66.3 72.0 76.2 81.3 84.8 95.3 101 107 116 120
66.2 71.1 76.3 81.8 87.6 93.7 100 107 114 122
66.5 72.9 76.0 80.8 81.9 96.9 101 107 117 119
65.0 71.1 74.2 79.0 80.2 94.9 99.4 106 116 118
x2 = 0.9000 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
98.2 103 109 114 118 126 135 141 149 157
98.3 103 108 114 120 126 133 141 149 157
99.4 103 111 113 115 126 135 140 150 157
104 107 113 115 116 126 135 139 148 155
145 147 150 153 156 160 164 168 173 178
3.1. The modified Apelblat equation
104 xcal 1
x2 = 0.5000 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
x2 = 1.0000 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
binary solvent mixtures were also calculated and discussed based on the NRTL model and experimental solubility data.
145 147 150 153 156 160 164 168 173 178
146 147 150 152 155 159 163 168 173 179
146 147 150 152 155 159 163 168 173 179
The modified Apelblat equation is a widely used semi-empirical equation which was previously used by Apelblat [11]. Due to its simplicity, it is widely used for the prediction of (solid + liquid) equilibrium. Its simplified form is shown as Eq. (3):
ln x1 ¼ A þ
B þ C ln ðT Þ T
ð3Þ
where x1 is the mole fraction solubility of disodium sebacate in the experimental solution, T is the absolute temperature and A, B and C are empirical parameters. The values of A and B represent the variation in the solution activity coefficient and the value of C represents the effect of temperature on the fusion enthalpy [12,13]. 3.2. λh model The relationship between solubility can also be analyzed by the λh model [14], which is a semi empirical model. It can be expressed as: 1−x1 1 1 ln 1 þ λ ¼ λh − T Tm x1
ð4Þ
where λ and h are the model parameters; T is the absolute temperature; and Tm is the absolute melting temperature of the solute. 3.3. NRTL model The simplified general equation for the solubility of compound in a solution is expressed as [15]:
ln x1 ¼
Δfus H 1 1 − − ln γ1 R Tm T
ð5Þ
where ΔfusH and Tm stand for the enthalpy of fusion and melting temperature of solute. To use Eq. (5) to calculate the solubility of compounds, the relationship between activity coefficient and the composition of the solution is necessary. Renon and Prausnitz proposed the nonrandom two-liquid (NRTL) model, which has been successfully used to describe various solution systems. In the binary system (in pure solvents), the activity coefficient of solute γ1 can be calculated by the NRTL model: " lnγ 1 ¼ x2 2
τ21 G21 2
τ12 G12 2 þ 2 ðx1 þ x2 G21 Þ ðx2 þ x1 G12 Þ2
# ð6Þ
Notes to table 2 a x2 is the mole fraction of water in the water + methanol binary solvent mixtures; xexp 1 is the experimentally determined solubility; xcal 1 is the calculated value of mole fraction solubility correlated by model. b The standard uncertainty of T is u (T) = 0.02 K. The relative standard uncertainty of the solubility measurement is ur (x1) = 0.04, the standard uncertainty of mole fraction of methanol in binary solvent mixture is ur (x2) = 0.001. The relative uncertainty of pressure is ur (P) = 0.05.
R. Xu et al. / Journal of Molecular Liquids 252 (2018) 194–202 Table 3 cal Experimental (xexp 1 ) and calculated (x1 ) mole fraction solubility of disodium sebacate in water (x2) + acetone (1 − x2) binary solvent mixtures from 283.15 K to 328.15 K (0.1 MPa)a,b. T/K
104 xexp 1
104 xcal 1 xABC 1
xλh 1
xNRTL 1
x2 = 0.5000 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
1.38 1.83 1.91 2.37 2.43 3.01 3.18 4.09 4.34 6.50
1.29 1.53 1.81 2.15 2.55 3.01 3.56 4.20 4.95 5.83
1.54 2.18 2.02 2.59 2.29 2.96 2.77 3.94 3.72 7.24
1.38 2.05 1.92 2.55 2.33 3.10 3.04 4.36 4.36 8.07
x2 = 0.6000 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
4.29 4.39 4.99 5.41 6.32 7.92 8.03 9.52 11.1 13.5
3.76 4.31 4.94 5.67 6.51 7.47 8.58 9.85 11.3 13.0
5.00 4.59 5.08 5.13 6.05 8.26 7.37 9.12 10.8 14.3
4.75 4.36 4.89 4.99 5.98 8.26 7.52 9.40 11.3 14.9
x2 = 0.7000 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
11.0 11.7 13.6 14.3 17.0 19.9 21.4 23.3 26.6 30.9
10.6 11.9 13.4 15.1 16.9 19.0 21.4 24.0 27.0 30.3
11.8 11.7 13.9 13.5 16.9 20.5 21.3 22.4 26.1 31.8
11.2 11.2 13.4 13.2 16.6 20.3 21.3 22.6 26.6 32.4
x2 = 0.8000 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
29.0 31.1 35.5 38.6 42.9 47.2 51.4 59.6 64.0 67.3
28.6 31.8 35.2 38.9 43.0 47.4 52.1 57.3 62.9 68.9
29.6 30.6 35.9 38.1 42.6 46.8 50.4 61.8 65.0 65.8
27.8 29.1 34.5 37.1 42.0 46.6 50.7 62.2 66.0 67.9
x2 = 0.9000 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
72.1 75.3 82.1 90.6 93.8 99.6 102 107 112 125
72.5 77.2 82.2 87.2 92.5 98.0 104 109 115 121
71.3 73.3 82.0 94.0 95.2 102 100 105 109 128
71.7 74.1 82.5 93.9 95.4 101 100 105 109 126
x2 = 1.0000 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
145 147 150 153 156 160 164 168 173 178
145 147 150 153 156 160 164 168 173 178
146 147 150 152 155 159 163 168 173 179
146 147 150 152 155 159 163 168 173 179
197
with Eq. (7): G12 ¼ expð‐α 12 τ12 Þ G21 ¼ expð‐α 12 τ21 Þ τ 12 ¼ ðg 12 ‐g 22 Þ=RT τ 21 ¼ ðg 21 ‐g 11 Þ=RT
ð7Þ
where Δg 12 (= g 12 − g 22 ) and Δg 21 (= g 21 − g 11 ) are crossinteraction energy. α12 is an empirical constant which varies from 0 to 1. For the ternary system (the binary solvent mixture system), the activity coefficient γ1 can be calculated by the following equation: Eq. (8): Gji x j þ Gkj xk τ ji Gji x j þ τki Gki xk ln γ1 ¼ 2 xi Gji x j þ Gki xk τij Gij x j 2 þ Gij Gkg x j xk τi j τ kj þ 2 x j Gij xi þ Gkj xk τjk Gjk xk 2 þ Gjk Gjk x j xk τjk τ jk þ 2 xk Gjk xi þ Gjk xk
ð8Þ
where Gij, Gik, Gji, Gjk, Gki, Gkj, τij, τik, τji, τjk, τki and τkj are parameters of this model. These terms can be defined as Eq. (9): Gij ¼ exp −α ij τij τ ij ¼ g ij −g ji =RT ¼ Δg ij =RT α ij ¼ α ji
ð9Þ
where i, j, k denote the component of i, j, k, respectively. The cross interaction energy parameters can be represented by Δgij, Δgik, Δgji , Δgjk, Δgki, and Δgkj, which are independent of the composition and temperature. Δg ji = (g ji − g ii ) is the parameter of this model and the value of αij can be adjusted from 0 to 1. 4. Results and discussion 4.1. Characterization of the compounds In this work, disodium sebacate samples were analyzed by X-ray powder diffraction before and after all experiments. And it was found that the X-ray powder diffraction pattern of all the samples used were basically the same. One of the typical X-ray powder diffraction data is shown in Fig. 1. It can be seen that the crystallinity of the sample is pretty high. It was also found that the DSC curves of all samples were basically the same. One of the typical DSC data are shown in Fig. 2. The first endothermic peak at T = 559.63 K is the melting temperature of disodium sebacate. Other endothermic peaks represent the multi-step decomposition of disodium sebacate. The enthalpy of fusion ΔfusH ΔHfusis found to be 5.04 kJ·mol−1. The standard uncertainty of melting temperature is 0.02 K while the standard uncertainty of enthalpy of fusion is 0.05 kJ·mol−1. To verify the reliability of the method used in this work, the solubility data of disodium sebacate in water obtained in this work were compared with the data from references [6]. The results are shown in Fig. 3. It can be seen that the data obtained in this work are pretty
Notes to table 3 a x2 is the mole fraction of water in the water + acetone binary solvent mixtures; xexp 1 is the experimentally determined solubility; xcal 1 is the calculated value of mole fraction solubility correlated by model. b The standard uncertainty of T is u (T) = 0.02 K. The relative standard uncertainty of the solubility measurement is ur (x1) = 0.04, the standard uncertainty of mole fraction of methanol in binary solvent mixture is ur (x2) = 0.001. The relative uncertainty of pressure is ur (P) = 0.05.
198
R. Xu et al. / Journal of Molecular Liquids 252 (2018) 194–202 0.018
Table 4 cal Experimental (xexp 1 ) and calculated (x1 ) mole fraction solubility of disodium sebacate in water (x2) + DMF (1 − x2) binary solvent mixtures from 283.15 K to 328.15 K (0.1 MPa)a,b.
0.014
0.015
104 xcal 1 xλh 1
xNRTL 1
x2 = 0.5000 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
0.547 0.635 0.735 0.848 0.978 1.12 1.29 1.47 1.68 1.91
0.553 0.638 0.735 0.846 0.972 1.12 1.28 1.47 1.68 1.92
0.594 0.676 0.769 0.874 0.995 1.13 1.28 1.46 1.65 1.87
0.481 0.569 0.671 0.787 0.925 1.08 1.26 1.46 1.69 1.95
x2 = 0.6000 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
1.85 2.08 2.35 2.64 2.97 3.34 3.74 4.18 4.67 5.21
1.87 2.10 2.35 2.63 2.95 3.31 3.71 4.17 4.67 5.24
1.88 2.10 2.35 2.63 2.95 3.32 3.73 4.17 4.68 5.24
1.65 1.88 2.16 2.46 2.80 3.19 3.64 4.10 4.64 5.23
x2 = 0.7000 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
6.04 6.63 7.29 8.02 8.83 9.71 10.6 11.7 12.9 14.1
6.03 6.63 7.30 8.02 8.82 9.70 10.7 11.7 12.9 14.1
6.17 6.69 7.28 7.98 8.77 9.64 10.6 11.7 12.9 14.2
5.64 6.23 6.90 7.66 8.52 9.46 10.4 11.7 12.9 14.3
x2 = 0.8000 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
19.6 20.9 22.4 24.3 26.2 28.4 30.6 33.0 35.8 38.6
19.5 20.9 22.5 24.3 26.2 28.3 30.6 33.0 35.7 38.6
20.0 21.0 22.3 24.2 25.9 28.2 30.4 32.8 36.0 38.8
19.3 20.6 22.1 24.1 26.1 28.5 30.8 33.3 36.5 39.5
0.012 1
xABC 1
x
104 xexp 1
0.01 0.01 0.005 0.008 0 340 320
64.7 68.2 72.0 76.2 80.6 85.5 90.7 96.4 102 109
65.7 68.7 71.6 76.2 79.1 85.3 91.4 95.7 102 111
64.9 68.5 71.9 76.6 79.9 85.9 91.6 95.9 101 109
x2 = 1.0000 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
145 147 150 153 156 160 164 168 173 178
145 147 150 153 156 160 164 168 173 178
146 147 150 152 155 159 163 168 173 179
146 147 150 152 155 159 163 168 173 179
0.8
300 280
T/k
0.004
0.7
290
0.6 0.5
x
2
Fig. 4. Mole fraction solubility (x1) of disodium sebacate versus temperature T in water (x2) + methanol (1 − x2) binary solvent mixtures.
-3
x 10 16 0.02
x
1
64.7 68.3 71.9 76.4 80.2 85.7 91.3 96.2 102 109
0.9
310
14
0.015
12
0.01
10 8
0.005 6 0 340
4 330 320
0.9
310
2
0.8
300 290 280
T/k
0.6 0.5
0.7 x2
Fig. 5. Mole fraction solubility (x1) of disodium sebacate versus temperature T in water (x2) + acetone (1 − x2) binary solvent mixtures.
-3
x 10 16 0.02 14 0.015
1
x2 = 0.9000 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
0.006
330
x
T/K
0.016
0.02
12
0.01
10 8
0.005
6
0 340 330 320
0.9
310
0.8
300 290 T/k
280
0.6 0.5
1
4 2
0.7 x2
Fig. 6. Mole fraction solubility (x1) of disodium sebacate versus temperature T in water (x2) + DMF acetone (1 − x2) binary solvent mixtures.
Notes to table 4 a x2 is the mole fraction of water in the water + DMF binary solvent mixtures; xexp 1 is the experimentally determined solubility; xcal 1 is the calculated value of mole fraction solubility correlated by model. b The standard uncertainty of T is u (T) = 0.02 K. The relative standard uncertainty of the solubility measurement is ur (x1) = 0.04, the standard uncertainty of mole fraction of methanol in binary solvent mixture is ur (x2) = 0.001. The relative uncertainty of pressure is ur (P) = 0.05.
R. Xu et al. / Journal of Molecular Liquids 252 (2018) 194–202 Table 5 Parameters of the modified Apelblat model for disodium sebacate in binary solvent mixtures from 283.15 K to 328.15 K (0.1 MPa). x2
A
Water + methanol 0.5 −82.9 0.6 15.2 0.7 −72.9 0.8 −29.8 0.9 −71.2 1 −64.6
Table 7 Parameters of the NRTL model for disodium sebacate in binary solvent mixtures from 283.15 K to 328.15 K (0.1 MPa).
B/103
C
ARD%
105RMSD
Parameter
2.25 −2.28 1.83 0.0692 2.20 2.38
12.2 −2.29 10.8 4.35 10.4 9.21
1.65 1.68 1.84 1.04 0.503 0.0242
6.07 8.60 12.7 12.8 9.27 0.542
Δg12 Δg13 Δg21 Δg23 Δg31 Δg32 ARD% 104RMSD
Water + acetone 0.5 −110 0.6 −116 0.7 −99.4 0.8 −40.5 0.9 −12.3 1 −64.6
1.96 2.77 2.38 0.0449 −0.563 2.38
16.7 17.5 14.9 6.10 1.65 9.21
8.14 4.53 2.42 1.56 1.96 0.0242
3.39 3.70 10.3 22.6 0.542 0.542
Water + DMF 0.5 −84.3 0.6 −101 0.7 −73.8 0.8 −81.6 0.9 −79.4 1 −64.6
1.22 2.42 1.53 2.22 2.47 2.38
12.4 14.9 10.8 12.0 11.6 9.21
0.443 0.583 0.100 0.226 0.314 0.0242
0.0504 0.202 0.113 0.677 3.37 0.542
consistent with the data from literature, which verify the reliability of our measurement method. 4.2. Solubility data The solubility of disodium sebacate in pure water and binary solvent mixtures at different temperatures was measured. The results are given in Tables 2–4 and graphically shown in Figs. 4–6. It can be seen that the solubility of disodium sebacate in all tested solvents increases with the rising of the temperature when the solvent composition remains constant. It also increases with the increasing of water composition in binary solvent mixtures at constant temperature. The solubility of disodium sebacate in pure
199
kJ·mol−1
Water + methanol
Water + acetone
Water + DMF
Water
20.1 1.02 5.68 −0.374 17.9 −4.16 2.27 1.99
−5.14 −1.14 20.9 22.2 39.6 −9.49 3.80 1.17
−6.88 2.72 21.0 −5.60 34.9 3.51 3.04 0.275
27.3 −1.01
0.426 0.789
water is much higher than the solubilities in other solvents. This might be explained by the higher possibility of the formation of hydrogen bond between water molecules and disodium sebacate molecules. Besides, the solubility of disodium sebacate in the binary solvent mixtures at constant temperature ranked as (methanol + water) N (acetone + water) N (DMF + water) in general, which indicates that the “like dissolves like” rule can be used to explain the solubility trend of disodium sebacate since disodium sebacate [16] is a polar molecule and the order of polarity of pure solvents is that: DMF b acetone b methanol b water. The modified Apelblat equation, the λh model and the NRTL model were applied to correlate the experimental solubility of disodium sebacate in binary solvent mixtures. The calculated solubility data are also listed in Tables 2–4. The parameters of the modified Apelblat equation, the λh model and the NRTL model are given in Tables 5–7, respectively. To evaluate the applicability of the tested models, the average relative deviation (ARD%), the root-meansquare deviations (RMSD) are used to evaluate the application of these models. The average relative deviation (ARD%) and the root-mean-square deviation (RMSD) are defined as follows:
ARD ¼
100 N
xi exp ‐xi cal
∑i¼1
exp N xi
ð10Þ
Table 6 Parameters of the λh equation for disodium sebacate in binary solvent mixtures from 283.15 K to 328.15 K (0.1 MPa). 10−4 h
ARD%
105RMSD
Water + methanol 0.5 18.3 0.6 32.1 0.7 38.7 0.8 29.5 0.9 16.4 1 −8.93
6.90 4.25 3.28 3.29 3.43 6.09
1.70 1.80 1.81 1.06 0.780 0.395
6.25 9.00 13.6 12.9 11.8 7.32
Water + acetone 0.5 3.10 0.6 31.6 0.7 40.8 0.8 50.9 0.9 17.0 1 −8.93
1.02 8.14 5.21 3.31 4.04 6.09
9.51 5.64 2.78 1.69 2.04 0.395
3.67 4.47 5.98 10.1 22.6 7.32
Water + DMF 0.5 0.6 0.7 0.8 0.9 1
44.5 31.7 17.1 8.84 4.43 6.09
3.07 0.550 0.675 0.788 0.653 0.395
0.301 0.179 0.687 2.28 6.62 7.32
x2
10−3λ
6.22 6.54 9.47 13.5 16.4 −8.93
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 N ∑i¼1 xi exp ‐xi cal RMSD ¼ N
ð11Þ
and xcal is where N is the number of experimental data points, xexp i i the experimental and the calculated solubility values. The obtained values of ARD, and RMSD are also given in Tables 5–7. It can be found from Tables 5–7 that the maximum average relative deviation (ARD%) between the experimental and calculated solubility values is below 9.51%, which indicates that the correlated values are in good agreement with experimental values at temperatures studied for the studied systems. 4.3. Dissolution thermodynamic properties In this study, the dissolution process can be assumed to consist of four energetic steps, (including heating, fusion, cooling and mixing processes) theoretically. Then it is reasonable to calculate the dissolution thermodynamic properties by the following
200
R. Xu et al. / Journal of Molecular Liquids 252 (2018) 194–202
Table 8 The dissolution thermodynamic properties of disodium sebacate in water (x2) + methanol (1 − x2) binary solvent mixtures from 283.15 K to 328.15 K (0.1 MPa)a,b. ΔdisG
ΔdisS
ΔdisH
kJ·mol−1
J·K−1·mol−1
kJ·mol−1
T = 283.15 K 0.5 0.6 0.7 0.8 0.9 1
−2.86 −2.79 −2.51 −2.02 −1.27 −0.0693
14.6 14.3 12.9 10.3 6.31 0.493
1.26 1.26 1.14 0.909 0.541 0.106
T = 288.15 K 0.5 0.6 0.7 0.8 0.9 1
−2.89 −2.81 −2.54 −2.04 −1.28 −0.0705
14.4 14.1 12.7 10.2 6.24 0.487
1.26 1.25 1.14 0.904 0.538 0.106
T = 293.15 K 0.5 0.6 0.7 0.8 0.9 1
−2.92 −2.84 −2.56 −2.06 −1.30 −0.0718
14.2 13.9 12.6 10.0 6.17 0.483
1.25 1.25 1.13 0.900 0.536 0.106
T = 298.15 K 0.5 0.6 0.7 0.8 0.9 1
−2.95 −2.87 −2.59 −2.08 −1.31 −0.0732
14.0 13.7 12.4 9.92 6.11 0.478
1.25 1.24 1.13 0.895 0.534 0.105
T = 303.15 K 0.5 0.6 0.7 0.8 0.9 1
−2.97 −2.89 −2.61 −2.10 −1.33 −0.0748
13.9 13.6 12.3 9.81 6.04 0.475
1.24 1.23 1.12 0.891 0.532 0.105
T = 308.15 K 0.5 0.6 0.7 0.8 0.9 1
−3.00 −2.92 −2.64 −2.12 −1.34 −0.0764
13.7 13.4 12.1 9.70 5.98 0.472
1.24 1.23 1.12 0.887 0.530 0.105
T = 313.15 K 0.5 0.6 0.7 0.8 0.9 1
−3.03 −2.95 −2.66 −2.14 −1.36 −0.0782
13.6 13.3 12.0 9.60 5.93 0.470
1.23 1.22 1.11 0.883 0.528 0.105
T = 318.15 K 0.5 0.6 0.7 0.8 0.9 1
−3.06 −2.98 −2.68 −2.17 −1.37 −0.0800
13.4 13.1 11.9 9.49 5.87 0.468
1.23 1.22 1.10 0.879 0.526 0.106
T = 323.15 K 0.5 0.6 0.7 0.8 0.9 1
−3.08 −3.00 −2.71 −2.19 −1.39 −0.0820
13.3 13.0 11.7 9.39 5.82 0.467
1.22 1.21 1.10 0.875 0.524 0.106
x2
Table 8 (continued) x2
0.8 0.9 1
ΔdisG
ΔdisS
ΔdisH
kJ·mol−1
J·K−1·mol−1
kJ·mol−1
−2.21 −1.40 −0.0840
9.30 5.77 0.467
0.871 0.522 0.106
a x2 is the mole fraction of water in the water + methanol binary solvent mixtures; ΔdisG, ΔdisS are the dissolution thermodynamic parameters according to Eqs. (17) to (19). b The expanded uncertainties are U (ΔdisG) = 0.02 ΔdisG, U (ΔdisS) = 0.05 ΔdisS, U (ΔdisH) = 0.01ΔdisH (0.95 level of confidence).
equations: Δdis M ¼ x Δheat M þ Δfus M þ Δcool M þ Δmix M
ð12Þ
where M can be replaced by G, S and H. x refers to the mole fraction solubility of the solute. The ΔfusM refers to the fusion thermodynamic properties; ΔmixM represents the mixing properties. ΔheatM and Δ cool M stand for the thermodynamic properties of heating and cooling process, respectively. They can be calculated by the following equations: Δheat H ¼ C pðsÞ ðT m ‐T Þ
ð13Þ
Tm T
ð14Þ
Δcool H ¼ C pðlÞ ðT‐T m Þ
ð15Þ
T Tm
ð16Þ
Δheat S ¼ C pðsÞ ln
Δcool S ¼ C pðlÞ ln
It could be assumed that the heat capacity of solid state disodium sebacate and the heat capacity of liquid state disodium sebacate are very close, and the term of ΔheatM will be offset by the term of ΔcoolM, then the sum of ΔheatM and ΔcoolM will be able to be ignored. Besides, during the phase transition of solute, the system is in equilibrium, so ΔfusG = 0. For a non-ideal solution, the mixing thermodynamic properties of the solute can be calculated by the following Eqs. (17)–(19): Δmix G ¼ GE þ Δmix Gid
ð17Þ
Δmix H ¼ HE þ Δmix H id
ð18Þ
Δmix S ¼ SE þ Δmix Sid
ð19Þ
where GE, SE and HE refer to the excess properties of Gibbs energy, entropy and enthalpy, respectively, and Δ mix Gid , Δmix S id , Δ mix Hid refer to mixing Gibbs energy, mixing entropy and mixing enthalpy of the ideal solution, respectively. The mixing thermodynamic properties of the ideal system can be calculated by the following Eqs. (20)–(22) [17]. Δmix Gid ¼ RT
N X
xi lnxi
ð20Þ
i¼1
Δmix H id ¼ 0 Δmix Sid ¼ −R
ð21Þ N X
xi lnxi
ð22Þ
i¼1
T = 328.15 K 0.5 0.6 0.7
−3.11 −3.03 −2.73
13.2 12.9 11.6
1.22 1.21 1.09
where xi indicate the mole fraction of component i in solution. N = 2 means binary solution and N = 3 means ternary solution. The excess mixing properties can be calculated by the following Eqs. (23)–(25)
R. Xu et al. / Journal of Molecular Liquids 252 (2018) 194–202 Table 9 The dissolution thermodynamic properties of disodium sebacate in water (x2) + acetone (1 − x2) binary solvent mixtures from 283.15 K to 328.15 K (0.1 MPa)a,b. ΔdisG
ΔdisS
ΔdisH
kJ·mol−1
J·K−1·mol−1
kJ·mol−1
T = 283.15 K 0.5 0.6 0.7 0.8 0.9 1
−1.65 −1.50 −1.24 −0.897 −0.521 −0.0693
13.1 11.8 9.58 6.71 3.77 0.493
2.07 1.86 1.48 1.01 0.564 0.106
T = 288.15 K 0.5 0.6 0.7 0.8 0.9 1
−1.63 −1.48 −1.22 −0.884 −0.517 −0.0705
12.7 11.3 9.12 6.35 3.56 0.487
2.02 1.79 1.41 0.953 0.528 0.106
x2
Table 9 (continued) x2
0.8 0.9 1
−1.61 −1.46 −1.20 −0.872 −0.514 −0.0718
12.2 10.9 8.68 6.01 3.38 0.483
1.96 1.73 1.35 0.899 0.497 0.106
T = 298.15 K 0.5 0.6 0.7 0.8 0.9 1
−1.59 −1.44 −1.18 −0.862 −0.513 −0.0732
11.7 10.4 8.27 5.69 3.22 0.478
1.91 1.67 1.29 0.845 0.468 0.105
T = 303.15 K 0.5 0.6 0.7 0.8 0.9 1
−1.58 −1.42 −1.17 −0.853 −0.511 −0.0748
11.3 10.0 7.88 5.40 3.05 0.475
1.85 1.61 1.22 0.794 0.436 0.105
T = 308.15 K 0.5 0.6 0.7 0.8 0.9 1
−1.56 −1.41 −1.16 −0.845 −0.511 −0.0764
10.9 9.58 7.52 5.12 2.91 0.472
1.80 1.55 1.17 0.744 0.407 0.105
T = 313.15 K 0.5 0.6 0.7 0.8 0.9 1
−1.55 −1.39 −1.14 −0.838 −0.510 −0.0782
10.5 9.20 7.17 4.86 2.76 0.470
1.75 1.49 1.11 0.696 0.377 0.105
T = 318.15 K 0.5 0.6 0.7 0.8 0.9 1
−1.54 −1.38 −1.13 −0.833 −0.511 −0.0800
10.2 8.83 6.85 4.63 2.63 0.468
1.70 1.43 1.05 0.651 0.350 0.106
T = 323.15 K 0.5 0.6 0.7 0.8 0.9 1
−1.53 −1.37 −1.12 −0.829 −0.513 −0.0820
9.82 8.48 6.54 4.40 2.51 0.467
1.65 1.38 0.995 0.606 0.323 0.106
T = 328.15 K 0.5 0.6 0.7
−1.52 −1.36 −1.12
9.49 8.15 6.25
1.60 1.32 0.942
ΔdisG
ΔdisS
ΔdisH
kJ·mol−1
J·K−1·mol−1
kJ·mol−1
−0.825 −0.516 −0.0840
4.18 2.42 0.467
0.562 0.304 0.106
a x2 is the mole fraction of water in the water + acetone binary solvent mixtures; ΔdisG, ΔdisS are the dissolution thermodynamic parameters according to Eqs. (17) to (19). b The expanded uncertainties are U (ΔdisG) = 0.02 ΔdisG, U (ΔdisS) = 0.05 ΔdisS, U (ΔdisH) = 0.01ΔdisH (0.95 level of confidence).
[18]:
GE ¼ RT
T = 293.15 K 0.5 0.6 0.7 0.8 0.9 1
201
N X
xi lnγi
ð23Þ
N X ∂lnγi xi ∂T P;x i¼1
ð24Þ
i¼1
H E ¼ −RT 2
SE ¼
HE −GE T
ð25Þ
where xi and γi are the mole fraction and activity coefficient of component i in real solution respectively. The dissolution thermodynamic properties in the three binary mixtures were calculated by using NRTL model and the experimental solubility data. The results are given in Tables 8–10. In addition, these dissolution thermodynamic data are calculated based on per mole mixture. As shown in these tables, it can be found that the values of ΔdisG are all negative, which indicates that the dissolution of disodium sebacate in all solvents investigated is a spontaneous and favorable process. The values of ΔdisS and ΔdisH are positive, which proves that the mixing process in all solvents investigated is entropy-driven and endothermic [19–21]. 5. Conclusions In this work, the solubility of disodium sebacate in binary solvent mixtures, including (methanol + water), (acetone + water), and (DMF + water), was measured from T = (283.15 to 328.15) K by the gravimetric method. It was found that the solubility data of disodium sebacate increased with increase of temperature in binary solvent mixtures at constant solvent composition, and increased with increase of mole fraction of water. Moreover, the dissolving capacity of disodium sebacate in three binary solvent mixtures at constant temperature ranked as (methanol + water) N (acetone + water) N (DMF + water). The experimental solubility data was correlated by the modified Apelblat model, the λh model and the NRTL model. It turns out that all the selected thermodynamic models can give good correlation results. Besides, the dissolution entropy, enthalpy and Gibbs energy of disodium sebacate in the tested solvents were also determined by using the NRTL model and the experimental solubility data. According to the results, it was found that the dissolution process of disodium sebacate in all solvents is spontaneous, entropy-driven and endothermic. Notes The authors declare no competing financial interest.
202
R. Xu et al. / Journal of Molecular Liquids 252 (2018) 194–202
Table 10 The dissolution thermodynamic properties of disodium sebacate in water (x2) + DMF (1 − x2) binary solvent mixtures from 283.15 K to 328.15 K (0.1 MPa)a,b. ΔdisG
ΔdisS
ΔdisH
kJ·mol−1
J·K−1·mol−1
kJ·mol−1
T = 283.15 K 0.5 0.6 0.7 0.8 0.9 1
−2.45 −2.33 −2.06 −1.64 −1.03 −0.0693
12.5 11.9 10.4 8.02 4.77 0.493
1.08 1.04 0.886 0.638 0.336 0.106
T = 288.15 K 0.5 0.6 0.7 0.8 0.9 1
−2.47 −2.36 −2.08 −1.66 −1.04 −0.0705
12.3 11.7 10.3 7.93 4.72 0.487
1.06 1.03 0.879 0.633 0.332 0.106
T = 293.15 K 0.5 0.6 0.7 0.8 0.9 1
−2.50 −2.38 −2.11 −1.67 −1.06 −0.0718
12.1 11.6 10.2 7.84 4.67 0.483
1.05 1.02 0.873 0.629 0.328 0.106
T = 298.15 K 0.5 0.6 0.7 0.8 0.9 1
−2.52 −2.40 −2.13 −1.69 −1.07 −0.0732
12.0 11.5 10.0 7.75 4.62 0.478
1.04 1.01 0.866 0.624 0.325 0.105
T = 303.15 K 0.5 0.6 0.7 0.8 0.9 1
−2.55 −2.43 −2.15 −1.71 −1.09 −0.0748
11.8 11.3 9.93 7.67 4.58 0.475
1.03 1.00 0.859 0.619 0.320 0.105
T = 308.15 K 0.5 0.6 0.7 0.8 0.9 1
−2.57 −2.45 −2.18 −1.73 −1.10 −0.0764
11.7 11.2 9.82 7.60 4.53 0.472
1.02 0.994 0.853 0.614 0.317 0.105
T = 313.15 K 0.5 0.6 0.7 0.8 0.9 1
−2.60 −2.48 −2.20 −1.75 −1.11 −0.0782
11.5 11.1 9.72 7.52 4.49 0.470
1.01 0.986 0.847 0.609 0.313 0.105
T = 318.15 K 0.5 0.6 0.7 0.8 0.9 1
−2.62 −2.50 −2.22 −1.77 −1.13 −0.0800
11.4 10.9 9.62 7.45 4.45 0.468
1.00 0.978 0.840 0.604 0.308 0.106
T = 323.15 K 0.5 0.6 0.7 0.8 0.9 1
−2.64 −2.53 −2.25 −1.79 −1.14 −0.0820
11.3 10.8 9.52 7.37 4.41 0.467
0.996 0.971 0.834 0.598 0.304 0.106
T = 328.15 K 0.5 0.6 0.7
−2.67 −2.55 −2.27
11.1 10.7 9.43
0.987 0.964 0.828
x2
Table 10 (continued) x2
0.8 0.9 1
ΔdisG
ΔdisS
ΔdisH
kJ·mol−1
J·K−1·mol−1
kJ·mol−1
−1.81 −1.16 −0.0840
7.31 4.37 0.467
0.594 0.299 0.106
a x2 is the mole fraction of water in the water + DMF binary solvent mixtures; ΔdisG, ΔdisS are the dissolution thermodynamic parameters according to Eqs. (17) to (19). b The expanded uncertainties are U (ΔdisG) = 0.02 ΔdisG, U (ΔdisS) = 0.05 ΔdisS, U (ΔdisH) = 0.01ΔdisH (0.95 level of confidence).
Acknowledgment This research is financially supported by Major National Scientific Instrument Development Project (No. 21527812). References [1] S. Gouin, X.X. Zhu, S. Lehnert, New polyanhydrides made from a bile acid dimer and sebacic acid: synthesis, characterization and degradation, Macromolecules 33 (2000) 5379–5383. [2] M. Nagata, Synthesis and properties of copolyesters based on hydroquinone, sebacic acid and p-hydroxybenzoic acid, High Perform. Polym. 13 (2012) S265–S274. [3] J.C. Tang, Z.G. Zhang, Z.F. Song, L.R. Chen, X. Hou, K.D. Yao, Synthesis and characterization of elastic aliphatic polyesters from sebacic acid, glycol and glycerol, Eur. Polym. J. 42 (2006) 3360–3366. [4] M.Y. Krasko, A. Shikanov, A. Ezra, A.J. Dom, Poly(ester anhydride)s prepared by the insertion of ricinoleic acid into poly(sebacic acid), J. Polym. Sci. A Polym. Chem. 41 (2003) 1059–1069. [5] R.B. Qi, J.K. Wang, J.X. Ye, H.X. Hao, Y. Bao, The solubility of cefquinome sulfate in pure and mixed solvents, Front. Chem. Sci. Eng. 10 (2016) 245–254. [6] J. Kang, Q. Xia, L.X. Wang, M.X. Du, F.B. Zhang, G.L. Zhang, Effects of NaOH and ethanol on the solubility of disodium Decanedioate in water, J. Chem. Eng. Data 57 (2012) 994–999. [7] J.B. Ouyang, J.K. Wang, Y.L. Wang, Q.X. Yin, H.X. Hao, Thermodynamic study on dynamic water and organic vapor sorption on amorphous valnemulin hydrochloride, Front. Chem. Sci. Eng. 9 (2015) 1–11. [8] A. Maher, D. Croker, Å.C. Rasmuson, B.K. Hodnett, Solubility of form III Piracetam in a range of solvents, J. Chem. Eng. Data 55 (2010) 5314–5318. [9] P.L. Cui, Q.X. Yin, J.B. Gong, Solubility of candesartan Cilexetil in different solvents at various temperatures, J. Chem. Eng. Data 56 (1997) 658–660. [10] X. Yang, X.J. Wang, C.B. Ching, Solubility of form α and form γ of glycine in aqueous solutions, J. Chem. Eng. Data 53 (2008) 1133–1137. [11] A. Apelblat, E. Manzurola, Solubilities of L-aspartic, DL-aspartic, DL-glutamic, phydroxybenzoic, o-anisic, p-anisic, and itaconic acids in water from T = 278 K to T = 345 K, J. Chem. Thermodyn. 29 (1997) 1527–1533. [12] A. Apelblat, E. Manzurola, Solubilities of o-acetylsalicylic, 4-aminosalicylic, 3,5dinitrosalicylic, and p-toluic acid, and magnesium-DL-aspartate in water from T = (278 to 348) K, J. Chem. Thermodyn. 31 (1999) 85–91. [13] E. Manzurola, A. Apelblat, Solubilities of L-glutamic acid, 3-nitrobenzoic acid, ptoluic acid, calcium-L-lactate, calcium gluconate, magnesium-DL-aspartate, and magnesium-L-lactate in water, J. Chem. Thermodyn. 34 (2002) 1127–1136. [14] H. Buchowski, A. Ksiazczak, S. Pietrzyk, ChemInform abstract: solvent activity along a saturation line and solubility of hydrogen-bonding solids, J. Phys. Chem. 84 (1980) 975–979. [15] Y.M. Guo, Y.H. Hao, Y.N. Zhou, Z.Y. Han, C. Xie, W.Y. Su, H.X. Hao, Solubility and thermodynamic properties of vanillyl alcohol in some pure solvents, J. Chem. Thermodyn. 106 (2017) 276–284. [16] F.X. Zou, Z.G. Wei, J.L. Wu, J.W. Zhou, Q.Y. Liu, Y. Chen, J.J. Xie, C.J. Zhu, T. Guo, H.J. Ying, Experimental measurement and modelling of solubility of inosine-5′monophosphate disodium in pure and mixed solvents, J. Chem. Thermodyn. 77 (2014) 14–22. [17] F. He, Y.L. Wang, Q.X. Yin, L.G. Tao, J. Lv, Z. Xu, J.X. Wang, H.X. Hao, Effect of polymorphism on thermodynamic properties of cefamandole nafate, Fluid Phase Equilib. 422 (2016) 56–65. [18] R. Orye, J. Prausnitz, Multicomponent equilibria—the Wilson equation, Ind. Eng. Chem. Res. 57 (1965) 18–26. [19] J.Q. Li, Z. Wang, Y. Bao, J.K. Wang, Solid–liquid phase equilibrium and mixing properties of cloxacillin benzathine in pure and mixed solvents, Ind. Eng. Chem. Res. 52 (2013) 3019–3026. [20] M. Gantiva, F. Martinez, Thermodynamic analysis of the solubility of ketoprofen in some propylene glycol + water cosolvent mixtures, Fluid Phase Equilib. 293 (2010) 242–250. [21] S. Feng, T. Li, Predicting lattice energy of organic crystals by density functional theory with empirically corrected dispersion energy, J. Chem. Theory Comput. 2 (2006) 149–156.