Article pubs.acs.org/jced
Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Measurement and Correlation of the Solubility of Florfenicol Form A in Several Pure and Binary Solvents Pengshuai Zhang,† Chi Zhang,†,‡ Rui Zhao,†,§ Yameng Wan,† Zhongkai Yang,† Ruyi He,† Qiliang Chen,† Tao Li,*,† and Baozeng Ren*,† †
School of Chemical Engineering and Energy, Zhengzhou University, Zhengzhou 450001, PR China Key Laboratory of Green Process and Engineering, Institute of Process Engineering, Beijing 100080, PR China § Henan Chemical Technician College, Kaifeng, 475000 Henan, P. R. China ‡
S Supporting Information *
ABSTRACT: The solubility of florfenicol form A in eight pure organic solvents (propionic acid, ethanol, 1-propanol, 1-butanol, 2-propanol, 2-methyl-1-propanol, 3-methyl-1-butanol, and 2-ethyl-1-hexanol) and three binary solvents (dimethyl sulfoxide + ethanol, dimethyl sulfoxide + 1-propanol, and dimethyl sulfoxide + 1-butanol) was measured by a laser dynamic method at temperature from 283.15 to 323.15 K. The experimental results show that the mole fraction solubility of florfenicol in the pure solvents decreased according to the following order: ethanol > 1-propanol > 2-propanol > 1-butanol > 3-methyl-1butanol > 2-methyl-1-propanol ≈ propionic acid > 2-ethyl-1-hexanol. The experimental results show that the mole fraction solubility of florfenicol form A in the binary solvents increased with the increase of temperature and dimethyl sulfoxide mass fraction. The experimental solubility data were well correlated with the four thermodynamic models: modified Apelblat equation, λh equation, NRTL model equation, and Wilson model equation. The modified Apelblat model equation was regarded as the best one to fit the experimental values in the pure solvents.
■
In this study, the solubility of florfenicol form A in the solvents at atmospheric pressure was measured by using a laser dynamic method. The experimental solubility data are correlated with the modified Apelblat equation, λh equation, NRTL model equation, and Wilson model equation.
INTRODUCTION Florfenicol (CAS registry no. 73231-34-2) is one of the most commonly used antibiotics; its molecular formula is C12H14CL2FNO4S, and the molecular structure is presented in Figure 1. Florfenicol is a broad-spectrum antibiotic,1,2 and its antibacterial effect is
■
Figure 1. Chemical structure of florfenicol.
20 times more effective than chloramphenicol and thiamphenicol. Florfenicol has the characteristics of having a quick effect, no toxin, and no residue. We know that the purity of the florfenicol depends on the crystallization processes, and the purity plays a very important role on the effect of the florfenicol, so it is essential to choose a proper solvent in the crystallization process. The solubility of florfenicol form A in the pure solvents (propionic acid, 2-propanol, 2-methyl-1-propanol, 3-methyl-1-butanol, and 2-ethyl-1-hexanol) and three binary solvents (dimethyl sulfoxide + ethanol, dimethyl sulfoxide + 1-propanol, and dimethyl sulfoxide + 1-butanol) we selected has not been reported yet. © XXXX American Chemical Society
EXPERIMENTAL METHOD AND APPARATUS
Materials. Florfenicol form A (molar mass 358.21 g/mol) used in the experiments was prepared by commercial products from Aladdin Biochemical Corporation (Shanghai, China), and the mass fraction purity was higher than 0.98, confirmed by HPLC (Agilent 1100, Agilent Technologies). The sources of the materials (propionic acid, ethanol, 2-methyl-1-propanol, 3-methyl-1butanol, 2-ethyl-1-hexanol, dimethyl sulfoxide, ethanol, 1-propanol, 1-butanol, etc.) used in the experiments are listed in Table 1. Apparatus and Experimental Method. The solubility of a solid in a solvent is generally determined by two methods: a synthetic method3 and an analytical method.4 In this study, in the last crystal disappearance method,5 the laser monitoring observation technique was used to determine the disappearance of the last crystal in the solid−liquid mixture. This method is one of the synthetic methods, the apparatus and procedure were similar to Received: January 13, 2018 Accepted: April 24, 2018
A
DOI: 10.1021/acs.jced.8b00043 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
First, a certain amount of solvent (pure solvent or binary solvent) was accurately measured and then put them into the glass vessel, a certain amount of solid solute (florfenicol form A) was added, the quality of solute each time was recorded, and then the magnetic stirring was opened and accelerated the dissolution
Table 1. Sources and Purity of the Experiment Materials chemical name
CAS registry number
florfenicol
73231-34-2
ethanol
64-17-5
1-propanol
71-23-8
1-butanol
71-36-3
2-propanol
67-63-0
2-methyl-1propanol 3-methyl-1butanol 2-ethyl-1hexanol propionic acid dimethyl sulfoxide water
78-83-1 123-51-3 104-76-7 79-09-4 67-68-5 7732-18-5
source Aladdin Biochemical Co., Ltd. Sinopharm Chemical Reagent Co., Ltd. Tianjin Wind Boat Chemical Reagent Co., Ltd. Tianjin Wind Boat Chemical Reagent Co., Ltd. Tianjin Wind Boat Chemical Reagent Co., Ltd. Sinopharm Chemical Reagent Co., Ltd. Sinopharm Chemical Reagent Co., Ltd. Shanghai Macklin Biochemical Co., Ltd. Tianjin Wind Boat Chemical Reagent Co., Ltd. Tianjin Kemiou Chemical Reagent Co., Ltd. our laboratory (double distilled)
purity mass purity ≥0.98a mass purity ≥0.995b mass purity ≥0.998b mass purity ≥0.995b mass purity ≥0.997b mass purity ≥0.99b mass purity ≥0.985b mass purity ≥0.995b mass purity ≥0.995b mass purity ≥0.995b conductivity ≤0.1 μs/cm
Figure 3. DSC curve (experimental peak and integrated peak) of florfenicol form A (gray solid line: original experimental peak; blue solid line: the software fit peak I, which can represent the first endothermic peak; the red dash line: the software fit peak II, which can represent the second endothermic peak).
a
Determined by HPLC (high-performance liquid chromatography). b Determined by GC (gas chromatography) .
those described in the literature,6 and this method is described briefly here. The experimental apparatus consists of a laser monitoring system, a magnetic stirrer, and a jacketed glass vessel (60 mL) with water circulated from a super thermostat bath (type DCW0506, Shanghai Bilang Instrument Manufacturing Co., Ltd., China). The glass vessel was maintained at the desired temperature (the solution temperature was measured by a calibrated mercury in-glass thermometer, which was inserted into the inner of the vessel) through the super thermostat (uncertainty of ±0.05K). A condenser was fitted to reduce the solvent’s evaporation. The solution was stirred with a magnetic stirrer (type 85-2, Gongyi Yuhua Instrument Factory, China). The mass of the solvent and the solute were weighed by an electronic analytical balance (FA2014N, Shanghai Instrument Co., Ltd.) having an uncertainty of ±0.0001 g. The laser monitoring system consists of a laser generator, a photoelectric transformer, and a recorder, which measured the change of the light signal, and this system was designed by the Laser Institute of Zhengzhou University.
Figure 4. XRPD patterns of florfenicol form A.
Figure 2. Mole fraction solubility data of florfenicol form A in ethanol (■, experimental values; □, literature values) and 2-propanol (●, experimental values; ○, literature values) at temperatures from 283.15 to 323.15 K at atmospheric pressure.
Figure 5. Microscope pictures of florfenicol form A. B
DOI: 10.1021/acs.jced.8b00043 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
Table 2. Experimental and Calculated Solubility Values of Florfenicol Form A in the Different Pure Solvents from T= 283.15− 323.15 K at Atmospheric Pressurea 103x1,cal 3
T (K)
10 x1
283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 100RAD
1.510 1.963 2.435 3.093 3.695 4.612 5.623 7.023 8.417
283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 100RAD
0.9742 1.245 1.653 2.152 2.688 3.586 4.366 5.632 7.122
283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 100RAD
0.5123 0.6482 0.8212 1.120 1.398 1.827 2.358 3.016 3.852
283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 100RAD
0.6097 0.7605 1.008 1.333 1.692 2.182 2.778 3.633 4.572
3
10 xApel
3
10 xλh
Ethanol 1.580 1.525 1.966 1.931 2.441 2.428 3.022 3.032 3.733 3.762 4.599 4.639 5.652 5.690 6.931 6.944 8.479 8.436 1.248 1.083 1-Propanol 0.9973 0.9396 1.286 1.244 1.655 1.633 2.124 2.125 2.719 2.742 3.473 3.511 4.424 4.465 5.622 5.640 7.128 7.080 1.453 1.463 1-Butanol 0.5101 0.4698 0.6585 0.6293 0.8498 0.8349 1.096 1.098 1.412 1.431 1.819 1.851 2.341 2.376 3.009 3.029 3.865 3.838 1.160 2.243 2-Propanol 0.5975 0.5638 0.7792 0.7542 1.013 0.999 1.313 1.312 1.696 1.708 2.184 2.207 2.805 2.830 3.592 3.604 4.587 4.560 1.026 1.752
103x1,cal 3
3
3
10 xNRTL
10 xWilson
T (K)
10 x1
1.587 1.977 2.450 3.022 3.715 4.554 5.568 6.800 8.303 1.777
1.568 1.949 2.415 2.987 3.689 4.557 5.634 6.985 8.699 1.583
283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 100RAD
0.2932 0.3852 0.4969 0.6127 0.8192 1.045 1.368 1.703 2.239
1.039 1.318 1.666 2.101 2.648 3.338 4.221 5.368 6.902 3.900
1.001 1.279 1.631 2.079 2.654 3.399 4.379 5.697 7.526 2.636
283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 100RAD
0.4867 0.5862 0.7653 0.9591 1.233 1.492 1.910 2.380 2.854
0.5284 0.6766 0.863 1.097 1.391 1.765 2.242 2.860 3.680 3.689
0.5093 0.6570 0.845 1.086 1.395 1.795 2.320 3.020 3.978 1.659
283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 100RAD
0.1833 0.2541 0.3193 0.3826 0.5210 0.6353 0.8127 1.026 1.286
0.6867 0.8653 1.084 1.351 1.676 2.071 2.550 3.133 3.842 8.821
0.6111 0.7864 1.010 1.295 1.662 2.139 2.767 3.612 4.780 1.773
283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 100RAD
0.2703 0.3470 0.4475 0.5621 0.7303 0.9614 1.226 1.603 2.105
3
10 xApel
3
10 xλh
2-Methyl-1-propanol 0.2905 0.2695 0.3767 0.3611 0.4879 0.4792 0.6308 0.6302 0.8143 0.8217 1.049 1.063 1.350 1.365 1.735 1.741 2.224 2.207 1.409 2.957 3-Methyl-1-butanol 0.4858 0.4669 0.6133 0.6006 0.7718 0.7663 0.9685 0.9705 1.212 1.221 1.512 1.525 1.882 1.895 2.336 2.341 2.892 2.878 1.590 1.592 2-Ethyl-1-hexanol 0.1908 0.1819 0.2448 0.2384 0.3130 0.3098 0.3991 0.3992 0.5073 0.5105 0.6429 0.6483 0.8125 0.8179 1.024 1.026 1.287 1.279 2.017 2.166 Propionic 0.2590 0.2346 0.3363 0.3178 0.4369 0.4261 0.5676 0.5659 0.7373 0.7451 0.9574 0.9728 1.243 1.260 1.613 1.621 2.091 2.071 1.623 3.983
103xNRTL
103xWilson
0.3223 0.4105 0.5195 0.6534 0.8174 1.018 1.262 1.559 1.920 6.776
0.2948 0.3814 0.4917 0.6321 0.8114 1.041 1.339 1.728 2.247 1.227
0.4873 0.6171 0.7766 0.9718 1.210 1.500 1.853 2.282 2.804 2.162
0.4780 0.6060 0.7647 0.9612 1.205 1.506 1.880 2.347 2.933 1.597
0.1956 0.2510 0.3197 0.4047 0.5093 0.6374 0.794 0.985 1.218 3.112
0.1891 0.2439 0.3128 0.3992 0.5074 0.6427 0.812 1.024 1.292 2.000
0.2669 0.3460 0.4468 0.5752 0.7395 0.9510 1.227 1.593 2.096 0.8354
0.2668 0.3457 0.4464 0.5751 0.7401 0.9530 1.230 1.596 2.088 0.9046
a
Standard uncertainty, u, is u(T) = 0.05 K. The relative standard uncertainties, ur, are ur(xexp) = 0.02 and ur(P) = 0.05. T is the absolute temperature. The experimental pressure was about 101.3 kPa.
For the pure solvents, the following equation was used to calculate the saturated mole fraction solubility x1 of florfenicol form A
of solute until there was microsolute undissolved (when the solute was all dissolved, solute was continually added). At the beginning, when there was a lot of solute dissolved, the laser recorder on the readings changed a lot and then changed the heating rate to about 3 K/h. When the solute was unable to dissolve, the heating rate was changed to 0.3 K/h until the solute was completely dissolved, the solid−liquid phase reached a balance, and then the solution was saturated. After the saturation level was reached, the electrical signal was stable, the signal reached its maximum value, and then it recorded the sum of the total mass of the florfenicol (m1) and the temperature T. In order to ensure the accuracy of the experimental data and reduce the error, we measured at least three times per point.
x1 =
m1/M1 m1/M1 + mpure /M pure
x 2 = 1 − x1
(1) (2)
where M1 and Mpure are the molar masses of florfenicol and pure solvents (propionic acid, ethanol, 1-propanol, 1-butanol, 2-propanol, 2-methyl-1-propanol, 3-methyl-1-butanol, and 2-ethyl-1-hexanol), respectively. m1 and mpure are the masses of florfenicol and pure solvents (propionic acid, ethanol, 1-propanol, 1-butanol, 2-propanol, C
DOI: 10.1021/acs.jced.8b00043 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
peak-fit. In Figure 3, the gray solid line is the original experimental DSC line; the blue solid line is the software fit peak I, which represents the first endothermic peak; and the red dash line is the software fit peak II, which represents the second endothermic peak. The melting point temperature of florfenicol in this work was thought to be 425.15 K (the onset temperature of the first endothermic peak), and the enthalpy of fusion of florfenicol form A was calculated to be ΔfusH fit peak I = 18.98 kJ·mol−1 (since the first endothermic peak can be explained by the transition of florfenicol form A to form B during the melting process of florfenicol form A, so the enthalpy of fusion of florfenicol form A was calculated by integrating the area of the first fit peak). The XRPD (X-ray power diffraction, D8 Advance, Bruker Corporation, Germany) data of the solute in this work were measured, and the curve is shown in Figure 4. The analysis was carried out over a 2θ range of 3−50° (Figure 4). The characteristic diffraction peaks of the XRPD pattern of the solute were observed at 8.0749, 16.1894, 19.7083, 20.1153, 20.9951, 23.5161, 24.3958, 26.8643, 31.8144, 35.5959, 41.2419, and 43.5003°, which is consistent with florfenicol form A in ref 7. In addition, the morphology of the solute used in this article was measured by microscope, and the photo is shown in Figure 5, which indicates that the crystals of the solute are plate-like, which also agrees with the florfenicol form A in the literature.7 According to the DSC, XRPD, and the microscope analysis, we can confirm that the crystal form of florfenicol used in this work was florfenicol form A. Data Correlation. The measured mole fraction solubility of florfenicol form A (x1) in the pure solvents (propionic acid, ethanol, 1-propanol, 1-butanol, 2-propanol, 2-methyl-1-propanol, 3-methyl-1-butanol, 2-ethyl-1-hexanol) at temperatures from 283.15 to 323.15 K are given in Table 2 and graphically shown in Figure 6. We can conclude that the mole fraction
2-methyl-1-propanol, 3-methyl-1-butanol, and 2-ethyl-1-hexanol), respectively. For the binary solvent mixtures, the following equation was used to calculate the saturated mole fraction solubility x1 of florfenicol form A x1 =
m1/M1 m1/M1 + m2 /M 2 + m 3/M3
ω3 =
m3 m 2 + m3
(4)
x3 =
m3 /M3 m2 /M 2 + m3 /M3
(5)
(3)
where M1, M2, and M3 are the molar masses of florfenicol, (ethanol, 1-propanol, or 1-butanol), and dimethyl sulfoxide, respectively; m1, m2, and m3 are the masses of florfenicol, the pure solvents (ethanol, 1-propanol, or 1-butanol), and dimethyl sulfoxide, respectively; ω3 is the mass fraction of dimethyl sulfoxide in mixed solvents; and x3 is the mole fraction of dimethyl sulfoxide in the binary solvent. Experiment Reliability Proof. In order to identify the reliability of the measuring method and the accuracy of the experimental apparatus, the mole fraction solubility of florfenicol form A in ethanol and 2-propanol was measured by using this apparatus and compared with the literature value,7 which is shown in Figure 2, from which we can know that the mole fraction solubility deviations between the literature and the measurement used in this work were less than 5%. Therefore, it was proven that the experimental method and apparatus were reliable.
■
RESULTS AND DISCUSSION Polymorph Identification and Characterization of the Solute. The DSC and XRPD data of form A have been reported before.7 The melting properties of florfenicol in this work were determined by DSC (differential scanning calorimetry, TA Instruments, Q2000) under a nitrogen atmosphere (50.0 cm3·min−1). In this work, the DSC instrument was calibrated by using zinc (Tm = 695.65 K; ΔfusH = 6.645 kJ·mol−1) and indium (Tm = 429.75 K; ΔfusH = 3.275 kJ·mol−1). After that, about 3 mg of florfenicol was put in the closed DSC pan, and an empty DSC pan was used as a blank reference. Then, the heating rate was set to 2 K·min−1, and the heating range was carried out from 303.15 to 473.15 K. The standard uncertainty of the melting temperature of florfenicol in this work was evaluated to be 0.5 K, and the relative standard uncertainty of the enthalpy of fusion ΔfusH was evaluated to be less than 0.05. In order to ensure the accuracy of the data, the same experiment was repeated at least three times. The determined DSC curve of florfenicol is shown in Figure 3. From this curve, we can see that there were two endothermic peaks. The first endothermic peak indicated that the florfenicol crystal form A may be partially or completely transformed to florfenicol crystal form B (or mesophase, there was a lot of research about the mechanism of transformation) during the melting process of florfenicol form A. The second endothermic peak indicated that after the crystal transformation, florfenicol then became a liquid phase again. The enthalpy of fusion was obtained from integrating the melting peak. In order to calculate the enthalpy of fusion of florfenicol form A, the complex overlapping peaks were deconvoluted into two simple peaks with the help of the software PeakFit v4.12 and Origin9.3
Figure 6. Solubility of florfenicol form A in different pure solvents. x1 represents the experimental value of the mole fraction of florfenicol in the pure solvents. The solid lines are correlated values of the modified Apelblat equation.
solubility of florfenicol form A in the pure solvents decreased according to the following order: ethanol > 1-propanol > 2-propanol > 1-butanol > 3-methyl-1-butanol > 2-methyl-1propanol ≈ propionic acid > 2-ethyl-1-hexanol. The measured mole fraction solubility of florfenicol form A (x1) in DMSO + (ethanol, 1-propanol, or 1-butanol) solvent mixtures at temperatures from 283.15 to 323.15 K is given in Tables 3, 4, and 5 and graphically shown in Figures 7, 8, and 9. D
DOI: 10.1021/acs.jced.8b00043 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
Table 3. Experimental and Calculated Solubility Values of Florfenicol Form A in DMSO (ω3) + ethanol (1 − ω3) Solvents from T = 283.15−323.15 K at Atmospheric Pressurea 103x1,cal 3
T (K)
10 x1
3
10 xApel
DMSO + Ethanol ω3 = 0.000 (x3 = 0.000) 1.510 1.580 1.963 1.966 2.435 2.441 3.093 3.022 3.695 3.733 4.612 4.599 5.623 5.652 7.023 6.931 8.417 8.479 1.248 ω3 = 0.075 (x3 = 0.04562) 3.941 4.215 5.120 5.127 6.240 6.227 7.522 7.552 9.133 9.143 11.23 11.05 13.37 13.34 16.35 16.07 19.05 19.33 1.423 ω3 = 0.100 (x3 = 0.06148) 6.015 5.888 7.033 7.165 8.630 8.683 10.53 10.48 12.64 12.61 15.06 15.11 18.01 18.04 21.63 21.48 25.40 25.48 0.7507
283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 100RAD 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 100RAD 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 100RAD
103x1,cal 3
10 xλh
10 xApel
103xλh
283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 100RAD
ω3 = 0.125 (x3 = 0.07768) 8.563 8.228 9.825 9.728 11.42 11.50 13.52 13.60 16.01 16.08 18.83 19.01 22.45 22.47 26.43 26.54 31.56 31.35 0.9759
7.929 9.563 11.47 13.69 16.26 19.22 22.64 26.58 31.09 2.031
283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 100RAD
ω3 = 0.150 (x3 = 0.09424) 11.75 11.23 12.94 13.06 15.26 15.19 17.53 17.68 20.43 20.58 23.75 23.95 27.81 27.88 32.49 32.45 37.96 37.77 1.001
10.88 12.88 15.17 17.79 20.78 24.19 28.07 32.47 37.47 1.762
283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 100RAD
ω3 = 0.200 (x3 = 0.1285) 19.22 18.79 21.39 21.44 24.42 24.47 28.13 27.95 31.69 31.93 36.26 36.49 41.41 41.71 47.67 47.67 54.80 54.50 0.6692
18.34 21.22 24.47 28.12 32.21 36.79 41.92 47.66 54.08 1.254
T (K)
1.525 1.931 2.428 3.032 3.762 4.639 5.690 6.944 8.436 1.083 4.064 5.035 6.196 7.579 9.218 11.15 13.43 16.09 19.21 1.197 5.812 7.122 8.672 10.50 12.64 15.15 18.08 21.48 25.42 0.8005
3
10 x1
3
a
Standard uncertainty, u, is u(T) = 0.05 K. Relative standard uncertainties, ur, are ur(x1) = 0.02 and ur(P) = 0.05. T is the absolute temperature. The experimental pressure was about 101.3 kPa. ω3 is the mass fraction of dimethyl sulfoxide in mixed solvents. Relative standard uncertainty is ur(ω3) = 0.03. x1,cal is the calculated solubility value of florfenicol form A with a different equation model in mixed solvents.
We can conclude that the solubility of florfenicol form A in the selected solvents increased with the increasing temperature and the increase of the value ω3. The relative error (RD) in Tables S1−S4 is defined as follows:
RD =
where xi,cal and xi,exp in eqs 6, 7, and 8 represent the calculated values and the experimental values, respectively, and N represents the number of the experimental points in each solvent. The modified Apelblat model, λh model, NRTL model, and Wilson model were used to describe the dissolving behavior of florfenicol form A in the pure solvents. The modified Apelblat model and λh model were used to describe the dissolving behavior of florfenicol in DMSO + (ethanol, 1-propanol, or 1-butanol) solvent mixtures. Modified Apelblat Model. The modified Apelblat model8,9 can describe and correlate the solid−liquid equilibrium. The temperature dependence of the solubility of florfenicol form A in pure and binary mixed solvents can be well correlated by the modified Apelblat model as follows:
x i,exp − x i,cal x i,exp
(6)
The RAD in Tables 2−5 represent the average relative deviation, which is defined as follows: N
∑i = 1 RAD =
x i,cal − x i,exp x i,exp
(7)
N
The RMSD in Tables 6 and 7 represent the root-mean-square deviation, which is defined as follows: RMSD =
⎡ ∑ N (x ⎢ i = 1 i,cal ⎢⎣
− x i,exp)2 ⎤ ⎥ ⎥⎦ N
ln x = A +
B + C ln(T ) T
(9)
1/2
where x represents the experimental value of the mole fraction of florfenicol form A in the pure solvents and binary solvents at the system temperature T, and x was calculated with eqs 1 or 3,
(8) E
DOI: 10.1021/acs.jced.8b00043 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
Table 4. Experimental and Calculated Solubility Values of Florfenicol Form A in DMSO (ω3) + 1-Propanol (1 − ω3) Solvents from T = 283.15−323.15 K at Atmospheric Pressurea 103x1,cal T (K)
283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 100RAD 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 100RAD 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 100RAD
3
10 x1
3
10 xApel
DMSO + 1-Propanol ω3= 0.000 (x3 = 0.000) 0.9742 0.9973 1.245 1.286 1.653 1.655 2.152 2.124 2.687 2.719 3.586 3.473 4.366 4.424 5.632 5.622 7.122 7.128 1.453 ω3= 0.075 (x3 = 0.05870) 2.584 2.649 3.210 3.275 3.953 4.045 5.141 4.988 6.232 6.142 7.493 7.553 9.245 9.275 11.47 11.37 13.86 13.92 1.526 ω3 = 0.100 (x3 = 0.07873) 4.236 4.193 5.120 5.033 6.046 6.035 7.126 7.228 8.754 8.647 10.27 10.33 12.16 12.33 14.75 14.70 17.56 17.50 0.9226
103x1,cal 3
10 xλh
3
T (K)
0.9396 1.244 1.633 2.125 2.742 3.511 4.465 5.640 7.080 1.463 2.527 3.197 4.015 5.006 6.202 7.638 9.355 11.40 13.82 1.245
10 x1
10 xApel
103xλh
283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 100RAD
ω3= 0.125 (x3 = 0.09899) 6.106 5.870 7.003 6.992 8.380 8.324 9.965 9.906 11.70 11.78 14.02 14.00 16.10 16.63 19.87 19.74 23.62 23.41 1.214
5.670 6.881 8.302 9.963 11.90 14.15 16.75 19.77 23.24 2.066
283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 100RAD
ω3 = 0.150 (x3 = 0.1195) 9.348 9.549 11.44 11.13 13.00 12.96 15.10 15.08 17.66 17.52 20.16 20.33 23.39 23.57 27.12 27.29 31.81 31.56 1.017
9.378 11.05 12.96 15.14 17.63 20.45 23.66 27.30 31.42 1.002
ω3 = 0.200 (x3= 16.10 18.37 20.69 23.63 27.13 30.62 34.57 40.01 46.12
283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 100RAD
4.056 4.953 6.011 7.256 8.714 10.42 12.40 14.71 17.38 1.684
3
0.1613) 15.92 18.16 20.73 23.65 26.99 30.80 35.13 40.07 45.69 0.6977
15.61 18.02 20.73 23.77 27.18 31.00 35.27 40.05 45.41 1.207
a
Standard uncertainty, u, is u(T) = 0.05 K. Relative standard uncertainties, ur, are ur(x1) = 0.02 and ur(P) = 0.05. T is the absolute temperature. The experimental pressure was about 101.3 kPa. ω3 is the mass fraction of dimethyl sulfoxide in mixed solvents. Relative standard uncertainty is ur(ω3) = 0.03. x1,cal is the calculated solubility value of florfenicol form A with a different equation model in mixed solvents
NRTL Model. The NRTL model12 is widely used to correlate the solid−liquid equilibrium, and this model is based on the local composition concept. The NRTL model is an activity coefficient equation and can be expressed as follows:
where A, B, and C are the empirical constants. The values of A, B, and C are listed in Tables 6 and 7, and they were obtained from fitting the experimental solubility data with eq 9, where T is the absolute temperature (K). λh Model. Buchowski and co-workers originally proposed the λh model,10,11 and this model is widely used to correlate the solid−liquid equilibrium. The relationship between the experimental solubility and the temperature is shown as follows: ⎛1 ⎡ λ(1 − x) ⎤ 1 ⎞ ln⎢1 + ⎟ ⎥ = λh⎜ − ⎣ ⎦ x Tm ⎠ ⎝T
N
ln γi =
∑ j = 1 τjiGjixj N
∑= 1 Gijx i
N
+
∑ j=1
N ⎡ ⎤ ⎢τ − ∑i = 1 x iτijGij ⎥ ij N N ∑i = 1 Gijx i ⎢⎣ ∑ j = 1 Gijx i ⎥⎦
xjGij
(11)
(10)
where T is the absolute temperature (K); x represents the experimental value of mole fraction of florfenicol in the pure or binary solvents at the system temperature, which was calculated with eqs 1 or 3; Tm is the melting point of florfenicol, according to the DSC curve, the onset temperature Tm = 425.15 K; and λ and h are the empirical constants, they were obtained from fitting the experimental solubility data with eq 10. The values of λ and h are listed in Tables 6 and 7.
Gij = exp( − αjiτij)
(12)
αij = αji = α
(13)
τij =
g ij − g jj RT
=
Δg ij RT
(14)
where the parameter α represents the nonrandomness of the solution (the value of α generally varies from 0.2 to 0.47). Δgij stands for the equation parameters and represents the cross interaction energy. and the values of Δgij are generally considered as constant. Where T is the absolute temperature (K) and x F
DOI: 10.1021/acs.jced.8b00043 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
Table 5. Experimental and Calculated Solubility Values of Florfenicol Form A in DMSO (ω3) + 1-Butanol (1 − ω3) Solvents from T = 283.15−323.15 K at Atmospheric Pressurea 103x1,cal T (K)
283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 100RAD 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 100RAD 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 100RAD
3
10 x1
3
10 xApel
DMSO + 1-Butanol ω3= 0.0000 (x3 = 0.000) 0.5123 0.5101 0.6482 0.6585 0.8212 0.8498 1.120 1.096 1.398 1.412 1.827 1.819 2.358 2.341 3.016 3.009 3.852 3.865 1.160 ω3 = 0.075 (x3 = 0.07142) 2.445 2.384 2.988 2.902 3.525 3.535 4.341 4.309 5.287 5.255 6.219 6.412 7.765 7.826 9.584 9.554 11.73 11.66 1.304 ω3 = 0.100 (x3 = 0.09535) 3.797 3.519 4.383 4.226 5.035 5.073 6.140 6.088 7.090 7.302 8.631 8.755 10.47 10.49 12.26 12.57 15.37 15.04 2.425
103x1,cal 3
10 xλh
3
T (K)
0.4698 0.6293 0.8349 1.098 1.431 1.851 2.376 3.029 3.838 2.243 2.244 2.813 3.501 4.330 5.323 6.506 7.912 9.577 11.54 2.652 3.383 4.147 5.053 6.123 7.381 8.855 10.58 12.59 14.92 3.362
10 x1
3
10 xApel
103xλh
283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 100RAD
ω3 = 0.125 (x3 = 0.1193) 5.643 5.494 6.780 6.501 7.573 7.685 9.108 9.077 10.69 10.71 12.36 12.63 14.65 14.87 17.54 17.49 20.76 20.56 1.517
5.350 6.423 7.672 9.119 10.79 12.72 14.95 17.50 20.43 2.180
283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 100RAD
ω3 = 0.150 (x3 = 0.1434) 8.743 8.665 10.25 10.05 11.63 11.66 13.56 13.51 15.57 15.65 18.01 18.11 20.61 20.95 24.33 24.21 28.12 27.96 0.7914
8.486 9.964 11.65 13.57 15.75 18.22 21.03 24.20 27.80 1.332
283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 100RAD
ω3 = 0.200 (x3 = 0.1917) 14.01 13.58 15.53 15.47 17.65 17.62 20.11 20.09 22.86 22.92 25.70 26.15 29.56 29.84 33.91 34.06 39.38 38.88 0.9409
13.29 15.33 17.63 20.22 23.11 26.35 29.99 34.06 38.62 1.612
a
Standard uncertainty, u, is u(T) = 0.05 K. Relative standard uncertainties, ur, are ur(x1) = 0.02 and ur(P) = 0.05. T is the absolute temperature. The experimental pressure was about 101.3 kPa. ω3 is the mass fraction of dimethyl sulfoxide in mixed solvents. Relative standard uncertainty is ur(ω3) = 0.03. x1,cal is the calculated solubility value of florfenicol form A with a different equation model in mixed solvents.
equilibrium, the solubility of florfenicol in the pure solvents can be described as follows:
represents the experimental value of the mole fraction of florfenicol in the pure solvents at the system temperature, which was calculated with eq 1. The parameters α, Δg12, and Δg21 are listed in Table 6, and they were obtained from fitting the experimental solubility data with eqs 11−14. Wilson Model. According to the traditional theory of the solid−liquid phase equilibrium and the theory of Lewis, in the real mixture, such as the liquid−solid phase, the system reaches equilibrium at a given pressure and temperature. The relationship between the fugacity of the solid phase and the fugacity of the liquid phase is described as
x iLγiLfiL = x iSγiSf iS
ln(x iγi) =
⎞ ΔV Ttp ΔHtp ⎛ 1 1 ⎞ ΔCp ⎛ Ttp ⎜ − ⎟⎟ − − + 1⎟ − (p − ptp ) ⎜ln R ⎜⎝ Ttp T⎠ R ⎝ T T RT ⎠
(16)
where Ttp represents the triple-point temperature; R is the universal gas constant, the value of which is 8.314 J·mol−1·K−1; and ΔCp and ΔV represent the change of the heat capacity and the volume of a solute (in this work, it is florfenicol) between the solid states and the liquid states when the temperature is at the melting point, respectively. The values of the ΔCp and ΔV are always small, so they generally can be neglected. The triple-point Ttp is approximately equal to the melting point Tm (Ttp ≈ Tm). We can also approximately consider that the value of ΔHtp is equal to the value of the melting enthalpy ΔfusH (ΔHtp ≈ ΔfusH), so we can deduce the equation as follows:
(15)
where γi is the activity coefficient, f i represents the fugacity of the real component i, and L and S represent the liquid states and solid states, respectively. As mentioned before, based on the traditional theory of solid− liquid phase equilibrium theory, when the system (florfenicol and different organic pure solvents) reaches the solid−liquid phase
ln(x iγi) = G
ΔfusH ⎛ 1 1⎞ − ⎟ ⎜ R ⎝ Tm T⎠
(17) DOI: 10.1021/acs.jced.8b00043 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
Figure 9. Solubility of florfenicol form A in DMSO + 1-butanol mixed solutions. ω3 is the mass fraction of DMSO in mixed solvents. x1 represents the experimental value of the mole fraction of florfenicol form A in mixed solutions.
Figure 7. Solubility of florfenicol form A in DMSO + ethanol mixed solutions. ω3 is the mass fraction of DMSO in mixed solvents. x1 represents the experimental value of the mole fraction of florfenicol form A in mixed solutions.
Λ12 =
v2 ⎛ λ12 − λ11 ⎞ v2 ⎛ Δλ12 ⎞ ⎟ = exp⎜ − ⎟ exp⎜ − v1 ⎝ RT ⎠ v1 ⎝ RT ⎠
(20)
Λ 21 =
v1 ⎛ λ 21 − λ11 ⎞ v2 ⎛ Δλ 21 ⎞ ⎟ = exp⎜ − ⎟ exp⎜ − v2 ⎝ RT ⎠ v1 ⎝ RT ⎠
(21)
where V1 and V2 denote the mole volumes of the solute and solvent, respectively; γ1 and γ2 denote the activity coefficient of the solute and solvent, respectively; x1 and x2 stand for the mole fraction solubility of the solute and solvent, respectively; and Δλ12 and Δλ21 represent the interaction parameters (J·mol−1) relating to the interaction energy that can be correlated through the experimental solubility. The parameters Δλ12 and Δλ21 are listed in Table 6, and they were obtained from fitting the experimental solubility data with eqs 17−21. As mentioned before, based on the experimental data of the solubility xi,exp and the regression model, we calculated the calculation data of the solubility xi,cal, and they are listed in Tables 2−5. In order to compare the fitting effect, we introduced RAD and RSMD. For the pure solvents, we calculated that the total RAD of the modified Apelblat model, λh model, NRTL model, and Wilson model were 0.1153, 0.1724, 0.3107, and 0.1338, respectively. The total RMSD of the modified Apelblat model, λh model, NRTL model, and Wilson model were 1.962 × 10−4, 2.309 × 10−4, 8.552 × 10−4, and 4.453 × 10−4, respectively. The results show that the modified Apelblat model provided a more accurate mathematical description than the others, relatively, in the pure solvents. For the binary solvents, we calculated that the total RAD of the modified Apelblat model and λh model were 0.2104 and 0.3018, respectively. The total RMSD of the modified Apelblat model and λh model were 2.735 × 10−3 and 4.132 × 10−3, respectively. The results show that in the binary solvents, the models we selected were all able to correlate the dissolution process well.
Figure 8. Solubility of florfenicol form A in DMSO + 1-propanol mixed solutions. ω3 is the mass fraction of DMSO in mixed solvents. x1 represents the experimental value of the mole fraction of florfenicol form A in mixed solutions.
where γi is the activity coefficient. If we need to get the value of the mole fraction solubility xi, the value of the activity coefficient γi must be known first. The Wilson model equation13 is also based on the local composition concept, and the model is described as ⎤ ⎡ Λ12 Λ 21 lnγ1 = −ln(x1 + Λ12x 2) + x 2⎢ − ⎥ x 2 + Λ 21x1 ⎦ ⎣ x1 + Λ12x 2
■
(18)
CONCLUSION The solubility of florfenicol form A in the pure solvents (propionic acid, ethanol, 1-propanol, 1-butanol, 2-propanol, 2-methyl-1-propanol, 3-methyl-1-butanol, and 2-ethyl-1-hexanol)
⎤ ⎡ Λ 21 Λ12 lnγ2 = −ln(x 2 + Λ 21x1) + x1⎢ − ⎥ x1 + Λ12x 2 ⎦ ⎣ x 2 + Λ 21x1 (19) H
DOI: 10.1021/acs.jced.8b00043 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
Table 6. Regression Results in the Pure Solvents solvents
paramters
ethanol
1-propanol
1-butanol
2-propanol
2-methyl-1propanol
3-methyl-1butanol
2-ethyl-1hexanol
propionic
modified Apelblat
A B C 104RMSD λ h 104RMSD α Δg12 Δg21 104RMSD Δλ12 Δλ21 104RMSD
−103.10 1119.46 16.42 0.5239 0.1361 28037.97 0.4856 0.47 14087.48 1083.17 0.9470 595.34 518.69 1.051
−130.25 1769.62 20.74 0.4766 0.2044 22338.62 0.4994 0.62 10384.91 1218.40 1.542 902.54 333.02 1.533
−178.86 3815.72 27.95 0.1606 0.1274 37304.44 0.2419 0.62 10220.33 1405.80 0.9106 1140.76 284.84 0.4738
−123.84 1320.83 19.79 0.1996 0.1489 31766.59 0.2834 0.47 16218.05 1315.78 3.112 1039.30 334.72 0.7359
−158.79 2866.28 24.89 0.1513 0.07326 64901.01 0.2260 0.47 16092.96 1526.39 1.238 1256.46 321.81 0.1508
−106.27 1009.26 16.84 0.2550 0.05639 72186.40 0.2190 0.47 12938.08 1411.18 0.4360 1082.60 378.69 0.3268
−115.01 1120.97 18.15 0.08856 0.03198 137181.80 0.1038 0.47 13575.45 1665.78 0.2873 1440.53 288.12 0.09036
−198.21 4533.77 30.81 0.1066 0.07884 62581.29 0.2497 0.66 2790.07 1598.11 0.07923 1222.64 383.40 0.09124
λh
NRTL
Wilson
Table 7. Regression Results in the Binary Solvents λh equation
modified Apelblat equation solvent
A
B
ω3 = 0.000 ω3 = 0.075 ω3 = 0.100 ω3 = 0.125 ω3 = 0.150 ω3 = 0.200
−103.10 −108.70 −53.31 −125.99 −121.24 −110.55
1119.46 1717.58 −649.18 2883.40 2923.02 2750.35
ω3 = 0.000 ω3 = 0.075 ω3 = 0.100 ω3 = 0.125 ω3 = 0.150 ω3 = 0.200
−130.25 −126.24 −110.28 −119.56 −88.72 −100.51
1769.62 2224.06 1969.99 2490.36 1485.17 2310.89
ω3 = 0.000 ω3 = 0.075 ω3 = 0.100 ω3 = 0.125 ω3 = 0.150 ω3 = 0.200
−178.86 −165.12 −130.03 −104.62 −97.89 −110.39
3815.72 4108.39 2805.95 1937.23 1939.78 2752.75
104RMSD
C
DMSO + Ethanol 16.42 0.5239 17.21 1.729 8.939 0.8999 19.66 1.604 18.85 2.144 17.16 2.384 DMSO + 1-Propanol 20.74 0.4766 19.92 0.8588 17.33 0.8969 18.71 2.133 13.96 1.861 15.62 2.640 DMSO + 1-Butanol 27.95 0.1606 25.61 0.8102 20.27 2.030 16.40 1.757 15.28 1.552 17.07 2.889
and binary solvents (dimethyl sulfoxide + ethanol, 1-propanol, or 1-butanol) was measured by a laser dynamic method at temperatures from 283.15 to 323.15 K. The experimental results show that the mole fraction solubility of florfenicol form A in the pure solvents decreased according to the following order: ethanol > 1-propanol > 2-propanol > 1-butanol > 3-methyl-1-butanol > 2-methyl-1-propanol ≈ propionic acid > 2-ethyl-1-hexanol. The experimental results show that the mole fraction solubility of florfenicol form A in the mixed solvents increased with the increase of temperature and the dimethyl sulfoxide mass fraction. The experimental solubility data are well correlated with the modified Apelblat equation, λh equation, NRTL model equation, and Wilson model equation. The modified Apelblat model equation can correlate this dissolution process more accurately in the pure solvents, relatively.
■
■
λ
h
104RMSD
0.1361 0.2329 0.2668 0.2620 0.2392 0.2463
28037.97 14784.42 12209.09 11389.28 11073.01 9128.84
0.4856 1.239 0.9903 3.328 4.041 4.887
0.2044 0.2212 0.1709 0.2112 0.1849 0.1946
22338.62 17172.89 18652.85 14604.86 13855.66 11264.92
0.4994 0.8500 1.479 3.063 2.371 4.126
0.1274 0.1626 0.1550 0.1578 0.1534 0.1618
37304.44 22391.25 21019.28 18332.88 16249.91 13444.61
0.2419 1.531 2.755 2.507 2.394 4.528
The relative error (RD) of the experimental and calculated solubility values of florfenicol form A (PDF)
AUTHOR INFORMATION
Corresponding Authors
*E-mail:
[email protected]; Tel.: +86-371-67781267; Fax: +86-371-67781267. *E-mail:
[email protected]; Tel.: +86-371-67781267; Fax: +86-371-67781267. ORCID
Tao Li: 0000-0003-1780-8009 Funding
This study was financially supported by the National Science
ASSOCIATED CONTENT
Foundation of China (Grant 21506197; Grant 21646011).
S Supporting Information *
Notes
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.8b00043.
The authors declare no competing financial interest. I
DOI: 10.1021/acs.jced.8b00043 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
■
Article
LIST OF SYMBOLS M1, the molar mass of florfenicol (g·mol−1); Mi, the molar mass of the solvent (g·mol−1); m1, the mass of florfenicol (g); mi, the mass of the solvent (g); x1, the mole fraction solubility of florfenicol (mol·mol−1); xi,cal, the calculated mole fraction solubility of florfenicol (mol·mol−1); xi,exp, the experimental mole fraction solubility of florfenicol (mol·mol−1); T, absolute temperature (K); Tm, the melting point of florfenicol (K); A,B,C, empirical constant for the modified Apelblat model equation; λ,h, empirical constant for the λh model equation; Δλ12, empirical constant for the Wilson model equation; Δλ21, empirical constant for the Wilson model equation; Δg12, empirical constant for the NRTL model equation; Δg21, empirical constant for the NRTL model equation; γ1, the activity coefficient of the solute; RD, the relative error; RAD, the average relation deviation; RMSD, the root-mean-square-deviations
■
REFERENCES
(1) Anadón, A.; Martínez, M. A.; Martínez, M.; Ríos, A.; Caballero, V.; Ares, I.; Martínez-Larrañaga, M. R. Plasma and tissue depletion of florfenicol and florfenicol-amine in chickens. J. Agric. Food Chem. 2008, 56, 11049−11056. (2) Lim, J. H.; Kim, M. S.; Hwang, Y. H.; Song, I. B.; Park, B. K.; Yun, H. I. Plasma and tissue depletion of florfenicol in olive flounder (Paralichthys olivaceus) after oral administration. Aquaculture 2010, 307, 71−74. (3) Domanska, U.; Pobudkowska, A.; Rogalski, M. Solubility of Imidazoles, Benzimidazoles, and Phenylimidazoles in Dichloromethane, 1-Chlorobutane, Toluene, and 2-Nitrotoluene. J. Chem. Eng. Data 2004, 49, 1082−1090. (4) Gao, L.; Wang, J.; Hao, H. Solubility of Acesulfame Potassium in Ethanol + Water and Methanol + Water Systems from (275.84 to 322.90) K. J. Chem. Eng. Data 2008, 53, 854−856. (5) Krivankova, I.; Marcisinova, M.; Sohnel, O. Solubility of itaconic and kojic acids. J. Chem. Eng. Data 1992, 37, 23−24. (6) Li, T.; Jiang, Z. X.; Chen, F. X.; Ren, B. Z. Solubilities of d -xylose in water + (acetic acid or propionic acid) mixtures at atmospheric pressure and different temperatures. Fluid Phase Equilib. 2012, 333, 13−17. (7) Sun, Z.; Hao, H.; Xie, C.; Xu, Z.; Yin, Q.; Bao, Y.; Hou, B.; Wang, Y. Thermodynamic Properties of Form A and Form B of Florfenicol. Ind. Eng. Chem. Res. 2014, 53, 13506. (8) Apelblat, A.; Manzurola, E. Solubilities of L-aspartic, DL-aspartic, DL-glutamic, p-hydroxybenzoic, o-anisic, p-anisic, and itaconic acids in water from T = 278 K to T = 345 K. J. Chem. Thermodyn. 1997, 29, 1527−1533. (9) Gong, H.; Nakamura, T.; Hattori, K.; Ohnuki, T.; Rashid, M.; Nakazawa, M.; Watanabe, K.; Nagatomo, T. A Novel 5-HT2 Antagonist, Sarpogrelate Hydrochloride, Shows Inhibitory Effects on Both Contraction and Relaxation Mediated by 5-HT Receptor Subtypes in Porcine Coronary Arteries. Pharmacology 2000, 61, 263−8. (10) Buchowski, H.; Ksiazczak, A.; Pietrzyk, S. Solvent activity along a saturation line and solubility of hydrogen-bonding solids. J. Phys. Chem. 1980, 84, 975−979. (11) Shi, H.; Xie, Y.; Du, C.; Cong, Y.; Wang, J.; Zhao, H. Thermodynamic study of the solubility of 2,4′-dihydroxydiphenyl sulfone in nine organic solvents from T = (278.15 to 313.15) K and thermodynamic properties of dissolution. J. Chem. Thermodyn. 2016, 102, 79−88. (12) Renon, H.; Prausnitz, J. M. Estimation of Parameters for the NRTL Equation for Excess Gibbs Energies of Strongly Nonideal Liquid Mixtures. Ind. Eng. Chem. Process Des. Dev. 1969, 8, 413−419. (13) Renon, H.; Prausnitz, J. M. Local compositions in thermodynamic excess functions for liquid mixtures. AIChE J. 1968, 14, 135−144.
J
DOI: 10.1021/acs.jced.8b00043 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
