Measurement and Correlation of the Solubility of Mifepristone in Eight

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Measurement and Correlation of the Solubility of Mifepristone in Eight Pure and Water + Methanol Mixed Solvents at Temperatures from 273.15 to 318.15 K Juan Xu, Peng Li, Xiaofeng Chen, Huiping Wang, and Lifeng Ning*

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National Research Institute for Family Planning, Beijing 100081, People’s Republic of China ABSTRACT: The solubility of Mifepristone in eight pure organic solvents, including methanol, ethanol, n-propanol, isopropanol, n-butanol, propanone, ethyl acetate, tetrahydrofuran, and mixed solvents of water + methanol have been experimented at 273.15−318.15 K by using an experimental method of high-performance liquid chromatography. The solubility data in eight pure solvents was correlated by the modified Apelblat equation, Van’t Hoff equation, λh equation, NRTL equation, UNIQUAC equation, and Wilson equation. The solubility data in the mixed solvents of water + methanol was correlated by the modified Apelblat equation, Van’t Hoff equation, λh equation, NRTL equation, UNIQUAC equation, Jouyban−Van’t Hoff equation, and Jouyban−Apelblat equation. The solubility of the Mifepristone in eight pure solvents and mixed solvents increased as the temperature increased. The calculated values by using the modified Apelblat equation, Van’t Hoff equation, λh equation, NRTL equation, UNIQUAC equation, Jouyban−Van’t Hoff equation and Jouyban−Apelblat equation is consistent with the experimental values. The experimental results and calculated values would be very useful in the purification and the synthesis process of Mifepristone.

1. INTRODUCTION Mifepristone (11β-[p-(dimethylamino)phenyl]-17β-hydroxy17-(1-propynyl)estra-4,9-dien-3-one, is also called as RU-486; formula, C29H35NO2; molecular weight, 429.59 g·mol−1; CAS Registry No. 84371-65-3) is a pale-yellow solid. The structure of Mifepristone is shown in Figure 1. Mifepristone is a potent oral

necessary to measure the solubility of Mifepristone in common solvents.4 In this study, the solubility of Mifepristone in eight pure organic solvents, including methanol, ethanol, n-propanol, isopropanol, n-butanol, propanone, ethyl acetate, tetrahydrofuran, and mixed solvents of water + methanol have been experimented at 273.15−318.15 K by using an experimental method of high-performance liquid chromatography (HPLC). Moreover, the solubility data in eight pure solvents was correlated by the modified Apelblat equation, Van’t Hoff equation, λh equation, NRTL equation, UNIQUAC equation, and Wilson equation. The solubility data in the mixed solvents of water + methanol was correlated by the modified Apelblat equation, Van’t Hoff equation, λh equation, NRTL equation, UNIQUAC equation, Jouyban−Van’t Hoff equation and Jouyban−Apelblat equation. In addition, the experimental results and calculated values would be very useful in further thermodynamic research.

Figure 1. Molecular structure of Mifepristone.

antiprogestogen.1 Because Mifepristone has a high adhesion for the progesterone receptor, it could act at the level of the receptor.2 Mifepristone can be used in diseases related to progesterone receptors, such as hysteromyoma, endometriosis, ovarian epithelial cancer, cervical cancer, and endometrial cancer.2,3 Mifepristone is a synthetic antiprogestin drug. Mifepristone is exposed to tetrahydrofuran and methanol during the process of production, thus the solubility data of Mifepristone in the solvents is very helpful in production process. However, we did not found the solubility data of Mifepristone in tetrahydrofuran and methanol from published literature. Therefore, it is © XXXX American Chemical Society

2. EXPERIMENTAL SECTION 2.1. Materials. The Mifepristone was purchased in China Resources Zizhu Pharmaceutical Co., Ltd. (Beijing, China), the mass fraction of Mifepristone is higher than 0.99. The solvents of methanol, ethanol, n-propanol, isopropanol, n-butanol, propanone, ethyl acetate, and tetrahydrofuran were supplied by J&K Received: November 12, 2018 Accepted: March 5, 2019

A

DOI: 10.1021/acs.jced.8b01062 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Sources and Purity of Chemicals chemical Mifepristone methanol (AR)b ethanol n-propanol isopropanol n-butanol propanone ethyl acetate tetrahydrofuran water

purity (mass fraction) ≥0.990 ≥0.995 ≥0.995 ≥0.995 ≥0.995 ≥0.995 ≥0.995 ≥0.995 ≥0.995 laboratory distilled water

source

analysis method

China Resources Zizhu Pharmaceutical Co., Ltd. (Beijing, China) J&K Scientific Ltd. (Beijing, China) J&K Scientific Ltd. (Beijing, China) J&K Scientific Ltd. (Beijing, China) J&K Scientific Ltd. (Beijing, China) J&K Scientific Ltd. (Beijing, China) J&K Scientific Ltd. (Beijing, China) J&K Scientific Ltd. (Beijing, China) J&K Scientific Ltd. (Beijing, China)

HPLCa GCc GC GC GC GC GC GC GC

a

HPLC means high-performance liquid chromatography. bAR means analytical reagent. cGC means gas chromatography.

Figure 2. Powder X-ray diffraction patterns of form M in patent and commercial Mifepristone.

water (70:30, v/v with 1.0 mL/min flow rate and 20 μL sample size.6 The solubility of Mifepristone in eight pure organic solvents, including methanol, ethanol, n-propanol, isopropanol, nbutanol, propanone, ethyl acetate, tetrahydrofuran, and mixed solvents of water + methanol were measured by HPLC method from 273.15 to 318.15 K. An excessive amount of Mifepristone powder was added to a glassware containing 10 mL of solvent. The glassware was placed in a constant temperature water bath shaker. The glassware was shaken for 24 h in the constant temperature water bath shaker. After standing in the constant temperature for another 24 h, the supernatant in the glassware was a saturated solution. Part of the supernatant was filtered by a syringe with a 0.25 μm membrane, and then an appropriate amount of the solution was taken out and placed in a clean tube. Evaporation of the solvent in the tube was performed at room temperature and atmospheric pressure until the mass of the tube was constant.7 Finally, 5 mL of methanol was added to the tube as a solvent. When all the solid Mifepristone were dissolved in methanol, the solution can be used as a test sample and the concentration of Mifepristone can be determined by HPLC analysis. To reduce experimental error, all experiments were performed three times at each temperature and the results were taken from the average of three experiments. The mole fraction solubility of Mifepristone (x1) in pure organic solvents was computed by eq 18

Scientific Ltd.; the mass fraction of the solvents is higher than 0.995. The details of the solute and solvents are listed in Table 1. This commercial Mifepristone was polymorph form M because it had the same PXRD patterns as M (US 20070105828A1, Figure 2). The characteristic peaks of both form M in patent and the commercial Mifepristone we used appeared at 2θ = 10.6, 11.8, 16.5, 17.3, 18.6, 19.5, and 22.2°. 2.2. Differential Scanning Calorimetry. In this experiment, the physical properties of Mifepristone were analyzed by differential scanning calorimeter (DSC) (TGA/DSC1/1600LF, Mettler Toledo Co., Switzerland). The standard uncertainty of Tm (measurement of the instrument) is 0.2 K. The relative standard uncertainty of ΔfusH (measurement of the instrument) is 0.02. The solute powder of Mifepristone was about 5 mg, the heating rate of the instrument was 10 K/min, and the detection temperature range was 40−400 °C, the whole experimental operation was carried out under a nitrogen atmosphere, the melting point (Tm) and melting enthalpy of the solute (ΔfusH) can be obtained from the peak of the curve and the area enclosed by the curve and the x-axis, respectively.5 2.3. Solubility Measurement. We added certain amount of solvent and excessive amount of solute in the conical flask under the experimental temperature. The conical flask shaked for 72 h and then standed for 24 h under the constant temperature. We measured the concentration of the supernatant by using the method of HPLC. Dissolution tests of Mifepristone in the solution were measured using LC-20A (HPLC, Japanese Shimadzu Corporation) coupled with diode array detector. The wavelength was at 303 nm and chromatographic column was Inertsil ODS-3 C18 (5 μm × 4.6 mm × 150 mm). Mobile phase was acetonitrile:

x1 = B

m1 M1 m1 M1

+

m2 M2

(1) DOI: 10.1021/acs.jced.8b01062 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

In the above equation, m1 and m2 are the mass of Mifepristone and the solvent; M1 and M2 are the molar mass of Mifepristone and the solvent. The mass fraction of water (w2) in mixed solvents of water + methanol varied from 0.1 to 0.9, the mass fraction of water (w2) in water + methanol mixed solvents was computed by eq 2 m3 w2 = m 2 + m3 (2) In the above equation, m2 and m3 are the mass of the methanol and water. The mole fraction solubility of Mifepristone (x1) in water + methanol solvents was computed by eq 3 x1 =

m1 M1

+

m1 M1 m2 M2

+

m3 M3

Figure 3. DCS analysis result of Mifepristone.

(3)

In the above equation, m1, m2, and m3 represent the mass of Mifepristone, methanol, and water; M1, M2, and M3 are the molar mass of Mifepristone, methanol, and water. 2.4. Method Verification. To verify the reliability of the experimental method, we measured the mole fraction solubility of Glibenclamide (GCM) in methanol from 283.15 to 323.15K. The measurement results were compared with the literature results,9 which is presented in Table 2. The relative deviations (RD) between the measurement results and the literature results were less than 4%. This indicates that the experimental method is reliable.

equation, λh equation, NRTL equation, UNIQUAC equation, and Wilson equation, and the corresponding graphs are shown in Figure 4 and Figure 5. It could be seen from the figure that the solubility of Mifepristone in eight pure solvents increases with the temperature increasing. Mifepristone has the highest solubility in methanol and the lowest in tetrahydrofuran. The solubility order of Mifepristone in eight pure solvents is methanol > isopropanol > n-butanol > propanone > n-propanol > ethanol > ethyl acetate > tetrahydrofuran, the polarity order of eight pure solvents is methanol (76.2) > ethanol (65.4) > n-propanol (61.7) > nbutanol (60.2) > isopropanol (54.6) > propanone (35.5) > ethyl acetate (23) > tetrahydrofuran (21). We can see that the solubility of Mifepristone in solvents has a great relationship with the polarity of the solvent. The result is also corresponded with the rule of “like dissolves like”. The structure of Mifepristone is complicated and the interaction of the functional groups between solute and solvents is complex, so the solubility of Mifepristone in the solvent and the polarity of the solvent is not fully consistent. The experimental solubility data of Mifepristone in mixed solvents at the temperature range from 273.15 to 318.15 K are listed in Table 4, which were correlated by the modified Apelblat equation, Van’t Hoff equation, λh equation, NRTL equation, UNIQUAC equation, Jouyban−Van’t Hoff equation, and Jouyban−Apelblat equation, and the related graph is showed in Figure 6 and Figure 7. These results indicate that the solubility of Mifepristone in mixed solvents increases with the temperature increasing. The solubility of Mifepristone in the mixed solvents increases with the increasing of the mass fraction of methanol, because Mifepristone is much more soluble in methanol than in water.

Table 2. Comparison of Experimental Solubility and Literature Solubility of GCM in Methanol at 283.15−323.15 K and p = 0.1 MPaa .

104x1exp

104x1lit

100RD

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

1.2587 1.6372 2.1356 2.8988 3.6628 4.7053 7.1458 10.7156 14.2187

1.2379 1.6469 2.0986 2.8379 3.5515 4.8798 6.9545 10.4967 14.3187

1.65 −0.59 1.73 2.10 3.04 −3.71 2.68 2.04 −0.70

a

x1exp is the experimental solubility of GCM in methanol, x1lit is the solubility of GCM in methanol published in literature. RD is the relative deviation between the experimental data and the literature data. The standard uncertainties of temperature and pressure are respectively u(T) = 0.1 K andu(p) = 1 kPa. The relative standard uncertainty of mole fraction solubility is ur(x1) = 0.01. Standard uncertainty u are u(T) = 0.1 K; the relative standard uncertainty u are ur(p) = 0.05, ur(x1) = 0.30.

4. THEORETICAL BASIS 4.1. Van’t Hoff Equation. The Van’t Hoff equation is a simplified form of the activity coefficient equation in the solid− liquid equilibrium. In an ideal solution, the logarithm of solubility and the reciprocal of system temperature are linearly related. In the actual solution, the nonideality of the solute and solvent molecules needs to be considered, so the Van’ t Hoff equation is a semiempirical equation. Its expression is as follows10 b ln x = a + (4) T

3. RESULTS AND DISCUSSION 3.1. Thermodynamic Properties. The melting temperature Tm of Mifepristone is 465.45 K (192.30 °C), the fusion enthalpy is 45.20 J/g. The Tm of Mifepristone is 465.45 K, the ΔfusH of Mifepristone is 19417.468 J/mol. The DCS analysis result of Mifepristone is shown in Figure 3. 3.2. Solubility Data. The experimental solubility data of Mifepristone in eight pure organic solvents at the temperature range from 273.15 to 318.15 K are shown in Table 3, which were correlated by the modified Apelblat equation, Van’t Hoff C



Article

Table 3. Experimental Mole Fraction Solubility (x1) and Relative Deviations, RD, of Mifepristone in Eight Pure Organic Solvents at Temperature T and Pressure p = 0.1 MPaa 100RD T/K

1000x1exp

Apelblat

Van’t Hoff

λh

NRTL

UNIQUAC

Wilson

2.96 0.72 −0.50 −1.06 −0.52 −0.28 0.20 0.22 0.19 −0.14

−21.43 −17.11 −12.07 −6.86 −1.10 3.79 8.38 12.10 15.34 17.99

−1.62 −1.63 −0.98 −0.11 1.31 1.93 2.20 1.45 −0.02 −2.47

−9.47 −8.40 −6.42 −4.01 −0.79 1.84 4.44 6.38 8.05 9.27

3.43 2.09 0.76 −0.19 −0.78 −0.86 −0.87 −0.53 0.00 0.65

6.25 3.76 1.37 −0.66 −2.24 −3.20 −4.08 −4.48 −4.62 −4.54

0.55 0.30 −0.13 −0.45 −0.59 −0.37 −0.32 −0.05 0.25 0.54

28.90 21.72 14.14 6.44 −1.26 −8.71 −16.36 −23.80 −31.11 −38.34

3.99 2.33 0.85 −0.08 −0.43 −1.42 −1.68 −0.37 0.07 0.85

9.09 5.71 2.53 −0.06 −2.03 −4.59 −6.29 −6.29 −7.07 −7.37

0.93 0.34 −0.24 −0.47 −0.33 −1.00 −1.08 0.22 0.55 1.10

29.72 22.19 14.34 6.53 −1.13 −9.76 −17.91 −24.49 −32.13 −39.41

0.01 0.03 −0.17 −0.04 0.01 0.00 0.01 −0.05 0.06 −0.02

−94.40 −63.27 −38.40 −17.72 −0.90 12.91 24.29 33.67 41.54 47.96

−71.14 −47.81 −28.80 −12.61 0.79 11.93 21.18 28.80 35.15 40.17

−2.62 0.23 1.94 2.77 2.87 2.37 1.37 −0.06 −1.87 −3.99

−1.42 −2.56 −2.84 −0.80 0.54 0.51 1.25 0.74 0.56 −1.00

0.39 −0.93 −1.44 0.31 1.35 1.05 1.48 0.71 0.25 −1.57

−0.75 −1.48 −1.55 0.50 1.72 1.46 1.84 0.89 0.15 −2.05

12.12 8.14 4.84 3.67 1.94 −1.04 −3.26 −6.69 −9.79 −14.33

4.79 2.79

1.65 0.26

0.80 0.09

13.64 9.28

Methanol 273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

4.45 5.80 7.56 9.82 1.28 1.64 2.10 2.66 3.33 4.14

× × × ×

10−1 10−1 10−1 10−1

−2.76 −2.87 −2.37 −1.65 −0.24 0.48 1.10 0.93 0.40 −0.70

2.11 −0.01 −1.08 −1.50 −0.81 −0.42 0.23 0.42 0.56 0.44

273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

1.22 1.46 1.74 2.06 2.44 2.89 3.41 4.01 4.72 5.52

× × × × × × × × × ×

10−1 10−1 10−1 10−1 10−1 10−1 10−1 10−1 10−1 10−1

−0.70 −0.20 −0.09 −0.05 −0.01 0.21 0.14 0.13 0.04 −0.15

1.98 0.72 −0.43 −1.21 −1.54 −1.28 −0.95 −0.19 0.82 2.00

273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

1.38 1.63 1.92 2.26 2.66 3.10 3.62 4.28 4.99 5.82

× × × × × × × × × ×

10−1 10−1 10−1 10−1 10−1 10−1 10−1 10−1 10−1 10−1

0.00 0.16 0.08 0.16 0.41 −0.33 −0.64 0.28 0.09 0.00

2.29 0.76 −0.53 −1.20 −1.26 −1.91 −1.73 0.05 1.03 2.41

273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

7.13 1.09 1.64 2.44 3.58 5.18 7.40 1.05 1.46 2.02

× × × × × × ×

10−2 10−1 10−1 10−1 10−1 10−1 10−1

−2.04 −1.41 −1.14 −0.64 −0.33 −0.14 −0.03 −0.08 −0.03 −0.25

0.01 0.06 −0.13 −0.01 0.04 0.04 0.04 −0.04 0.05 −0.06

273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

1.72 2.13 2.64 3.32 4.12 5.02 6.12 7.33 8.75 1.03

× × × × × × × × ×

10−1 10−1 10−1 10−1 10−1 10−1 10−1 10−1 10−1

−2.98 −3.39 −3.12 −0.70 0.87 0.95 1.67 1.07 0.70 −1.12

0.74 −0.86 −1.60 0.00 0.97 0.64 1.11 0.41 0.09 −1.55

273.15 278.15

1.49 × 10−1 1.84 × 10−1

−0.02 −0.02

2.26 0.62

Ethanol

n-Propanol

Isopropanol

n-Butanol

Propanone

D



Article

Table 3. continued 100RD T/K

1000x1exp

Apelblat

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

2.28 2.81 3.45 4.22 5.16 6.28 7.62 9.22

× × × × × × × ×

10−1 10−1 10−1 10−1 10−1 10−1 10−1 10−1

0.00 0.03 0.10 0.02 0.05 0.04 0.01 0.03

273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

1.03 1.25 1.52 1.84 2.23 2.70 3.25 3.92 4.71 5.65

× × × × × × × × × ×

10−1 10−1 10−1 10−1 10−1 10−1 10−1 10−1 10−1 10−1

0.96 0.74 0.25 −0.08 −0.14 −0.18 −0.21 −0.24 0.01 0.16

273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

5.16 6.00 6.95 8.05 9.30 1.07 1.23 1.42 1.63 1.88

× × × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−1 10−1 10−1 10−1 10−1

−1.05 −0.40 −0.09 0.29 0.44 0.28 −0.04 0.16 −0.21 −0.04

λh

Van’t Hoff

Propanone −0.54 1.28 −1.24 0.19 −1.49 −0.50 −1.50 −0.97 −1.02 −0.96 −0.24 −0.69 0.83 −0.16 2.23 0.68 Ethyl Acetate 2.67 5.48 0.93 3.37 −0.65 1.40 −1.62 −0.04 −1.90 −0.82 −1.75 −1.18 −1.23 −1.22 −0.37 −0.92 1.08 −0.09 2.71 0.91 Tetrahydrofuran 2.02 3.12 0.67 1.80 −0.47 0.66 −1.03 −0.03 −1.31 −0.54 −1.45 −0.93 −1.30 −1.21 −0.23 −0.51 0.63 −0.20 2.38 0.96

NRTL

UNIQUAC

Wilson

−0.70 −1.28 −1.46 −1.46 −1.05 −0.38 0.52 1.70

−0.38 −0.64 −0.68 −0.70 −0.46 −0.14 0.27 0.80

5.23 1.53 −1.80 −4.93 −7.60 −9.98 −12.06 −13.77

2.11 0.59 −0.81 −1.67 −1.90 −1.76 −1.31 −0.57 0.68 2.07

1.42 0.45 −0.57 −1.17 −1.29 −1.18 −0.88 −0.39 0.50 1.45

19.62 13.90 8.11 2.66 −2.29 −6.93 −11.25 −15.24 −18.59 −21.69

21.76 15.79 9.76 4.07 −1.51 −7.07 −12.44 −16.81 −21.42 −24.90

0.73 0.28 −0.21 −0.37 −0.49 −0.70 −0.84 −0.25 −0.04 0.88

39.11 30.18 20.47 10.29 −0.54 −12.10 −24.21 −35.97 −48.65 −60.63

a

Standard uncertainty u is u(T) = 0.1 K; the relative standard uncertainty u are ur(p) = 0.05, ur(x1) = 0.30.

Figure 4. Mole fraction solubility of Mifepristone (x1) in eight pure solvents: □, methanol; ■, ethanol; ▲, n-propanol; △, isopropanol; ○, n-butanol; ●, propanone; ★, ethyl acetate; ☆, tetrahydrofuran.

Figure 5. Van’t Hoff plot of the mole fraction solubility (ln x1) versus reciprocal of the temperature (1/T − 1/Tm) for Mifepristone in eight pure solvents: □, methanol; ■, ethanol; ▲, n-propanol; △, isopropanol; ○, n-butanol; ●, propanone; ★, ethyl acetate; ☆, tetrahydrofuran.

ij ij 1 1 − x1 yzz 1 yzz lnjjj1 + λ zzz = λhjjjj − z j x1 { Tm zz{ k kT

a and b are two parameters of the equation. 4.2. λh Equation. Buchowski first proposed the λh Equation with certain physical and chemical significance,11 which is expressed as follows E

(5)



Article

Table 4. Experimental Mole Fraction Solubility (x1) and Relative Deviations (RD) of Mifepristone in Mixed Solvents of Water + Methanol at Temperature T and Pressure p = 0.1 MPaa 100RD T/K

100x1exp

Apelblat

Van’t Hoff

λh

273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

5.05 5.46 6.06 6.57 7.27 7.87 8.68 9.40 1.02 1.11

× × × × × × × ×

10−1 10−1 10−1 10−1 10−1 10−1 10−1 10−1

0.79 −0.93 0.38 −0.71 0.47 −0.39 0.59 −0.02 −0.17 0.01

1.77 −0.66 0.13 −1.28 −0.22 −1.05 0.14 −0.11 0.23 1.03

1.11 −0.83 0.35 −0.82 0.34 −0.51 0.51 −0.04 −0.13 0.10

273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

3.13 3.43 3.74 4.04 4.35 4.65 4.95 5.26 5.56 5.86

× × × × × × × × × ×

10−1 10−1 10−1 10−1 10−1 10−1 10−1 10−1 10−1 10−1

−0.18 0.01 0.07 0.12 0.20 −0.06 −0.15 −0.07 −0.04 0.10

−1.65 −0.39 0.41 0.92 1.19 0.87 0.50 0.07 −0.60 −1.37

−3.56 −1.41 0.09 1.10 1.70 1.54 1.16 0.57 −0.45 −1.73

273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

1.72 1.82 1.95 2.10 2.22 2.37 2.52 2.73 2.93 3.09

× × × × × × × × × ×

10−1 10−1 10−1 10−1 10−1 10−1 10−1 10−1 10−1 10−1

0.26 −0.53 −0.05 0.84 −0.18 −0.28 −0.75 0.33 0.82 −0.47

1.76 −0.11 −0.40 0.02 −1.22 −1.26 −1.43 0.17 1.39 1.02

0.97 −0.27 −0.10 0.60 −0.51 −0.60 −0.99 0.23 0.92 −0.15

273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

6.24 6.95 7.68 8.45 9.24 1.00 1.07 1.17 1.26 1.35

× × × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−1 10−1 10−1 10−1 10−1

−1.66 −0.58 0.16 0.74 1.04 0.63 −0.74 0.32 0.10 −0.41

−1.17 −0.23 0.38 0.85 1.05 0.57 −0.86 0.15 −0.11 −0.65

−2.86 −1.13 0.09 1.01 1.50 1.16 −0.27 0.56 −0.02 −1.03

273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

1.32 1.58 1.83 2.16 2.55 3.03 3.53 4.15 4.85 5.66

× × × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

−0.18 1.08 −0.72 −0.59 −0.27 0.57 −0.02 0.10 0.04 −0.10

2.15 1.74 −1.26 −1.88 −1.87 −0.93 −1.07 −0.14 0.93 2.21

3.85 3.23 0.09 −0.78 −1.09 −0.49 −1.03 −0.54 0.01 0.73

273.15 278.15

7.68 × 10−3 7.88 × 10−3

−0.05 0.08

−0.61 −0.08

−1.73 −0.54

NRTL w2b = 0.1 −54.75 −38.74 −21.60 −9.48 2.83 11.73 20.60 27.42 33.37 38.79 w2 = 0.2 −45.36 −42.16 −39.55 −37.39 −35.47 −34.09 −32.85 −31.82 −30.98 −30.32 w2 = 0.3 19.64 17.37 15.54 13.89 11.34 9.20 6.88 5.30 3.47 0.81 w2 = 0.4 34.67 34.44 33.77 32.84 31.56 29.75 27.28 25.89 23.70 21.20 w2 = 0.5 −9.34 −1.99 1.74 6.74 11.38 15.95 19.03 22.30 25.18 27.73 w2 = 0.6 21.02 14.63

F

UNIQUAC

Jouyban−Van’t Hoff

Jouyban−Apelblat

−23.38 −23.98 −21.19 −21.53 −19.40 −19.89 −18.52 −19.35 −19.75 −20.16

−2.86 −3.77 −1.42 −1.37 1.09 1.62 4.05 5.02 6.51 8.36

−2.62 −3.71 −1.47 −1.49 0.94 1.48 3.95 5.00 6.59 8.56

10.23 11.29 11.66 11.45 10.83 9.45 7.80 5.78 3.38 0.62

−5.97 −5.17 −4.81 −4.74 −4.90 −5.68 −6.50 −7.37 −8.50 −9.73

−6.04 −5.19 −4.79 −4.70 −4.86 −5.63 −6.47 −7.36 −8.52 −9.79

27.03 25.60 25.06 24.83 23.23 22.28 21.04 20.87 20.26 18.34

10.24 7.41 6.03 5.33 3.09 2.00 0.81 1.40 1.65 0.35

9.93 7.32 6.10 5.51 3.32 2.22 0.97 1.43 1.52 0.00

15.32 17.85 19.74 21.25 22.24 22.47 21.79 22.70 22.47 21.85

7.16 8.16 8.86 9.42 9.73 9.40 8.22 9.25 9.12 8.74

6.57 8.00 8.99 9.73 10.11 9.77 8.48 9.31 8.90 8.16

−57.23 −41.94 −32.33 −21.23 −11.05 −1.40 5.92 13.12 19.50 25.19

−47.09 −36.45 −30.25 −21.72 −13.34 −4.81 1.81 8.80 15.23 21.23

−48.46 −36.80 −29.98 −21.11 −12.63 −4.20 2.22 8.88 14.93 20.51

4.33 −1.56

19.29 11.60

18.31 11.30



Article

Table 4. continued 100RD 100x1exp

T/K

Apelblat

Van’t Hoff

λh 0.14 0.71 0.99 0.81 1.00 0.19 −0.46 −1.23

NRTL

UNIQUAC

Jouyban−Van’t Hoff

Jouyban−Apelblat

−8.19 −15.38 −23.08 −31.77 −40.53 −51.04 −61.92 −73.60

3.19 −5.74 −15.15 −25.42 −35.68 −47.50 −59.50 −72.03

3.45 −5.05 −14.21 −24.45 −34.95 −47.31 −60.22 −74.10

30.10 29.32 29.03 28.22 25.99 24.99 22.89 20.76 18.35 15.77

37.39 34.95 33.17 31.11 27.86 26.01 23.29 20.75 18.14 15.62

36.44 34.67 33.40 31.66 28.59 26.72 23.81 20.87 17.68 14.37

−9.79 −9.90 −9.78 −9.11 −8.34 −8.46 −6.06 −3.37 0.29 2.77

−27.09 −28.35 −28.78 −28.02 −26.62 −25.77 −21.58 −16.73 −10.53 −5.47

−29.38 −29.00 −28.26 −26.79 −25.10 −24.34 −20.61 −16.51 −11.27 −7.35

21.37 17.18 13.75 12.11 7.74 4.11 −0.64 −6.26 −12.37 −20.63

−6.26 −6.07 −4.08 0.57 2.64 6.05 8.85 11.39 14.05 15.67

−8.49 −6.69 −3.59 1.69 4.00 7.29 9.69 11.58 13.38 13.92

w2 = 0.6

283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

8.05 8.22 8.38 8.52 8.69 8.79 8.91 9.03

× × × × × × × ×

10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

0.00 −0.04 0.03 −0.12 0.22 −0.10 −0.07 0.06

0.12 0.27 0.41 0.24 0.47 −0.05 −0.28 −0.50

273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

3.23 3.53 3.89 4.25 4.55 4.95 5.32 5.71 6.11 6.53

× × × × × × × × × ×

10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

−0.42 −0.59 0.29 0.73 −0.45 0.36 0.03 −0.03 −0.12 −0.07

−0.54 −0.55 0.43 0.93 −0.24 0.54 0.13 −0.04 −0.27 −0.40

273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

5.56 6.31 7.17 8.19 9.36 1.06 1.23 1.43 1.68 1.96

× × × × × × × × × ×

10−4 10−4 10−4 10−4 10−4 10−3 10−3 10−3 10−3 10−3

−1.05 −0.03 0.48 0.84 0.70 −0.81 −0.47 −0.27 0.55 −0.12

4.89 1.72 −0.81 −2.37 −3.35 −4.72 −3.20 −0.94 2.69 5.50

273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

2.55 2.96 3.46 4.14 4.82 5.66 6.58 7.61 8.79 1.00

× × × × × × × × × ×

10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−3

0.05 −1.57 −1.73 0.58 0.19 1.04 1.18 0.95 0.77 −0.70

2.43 −0.58 −1.81 −0.22 −1.01 −0.25 0.07 0.28 0.79 0.24

7.18 −1.19 −10.51 −21.22 −32.59 −46.21 −60.85 −77.00 w2 = 0.7 −2.10 26.65 −1.33 25.01 0.22 23.67 1.09 21.56 0.37 17.74 1.24 15.03 0.66 10.95 0.27 6.61 −0.23 1.75 −0.97 −3.47 w2 = 0.8 8.21 −41.11 4.85 −40.76 2.36 −40.51 −0.14 −39.88 −1.48 −39.35 −3.66 −40.16 −3.16 −37.86 −1.89 −35.26 0.30 −31.43 2.52 −29.14 w2 = 0.9 2.12 24.87 −1.51 24.07 −1.14 24.01 1.02 25.49 0.32 24.69 −0.79 24.59 −0.32 23.74 0.11 22.40 0.97 20.93 −0.07 18.21

a

Standard uncertainty u is u(T) = 0.1 K; the relative standard uncertainty u are ur(p) = 0.05, ur(x1) = 0.30; bw2 is the mass fraction of water in mixed solvents of water + methanol; the relative standard uncertainties u are ur(w2) = 0.05.

The form of the equation is simple. Tm is the melting point of the solute, and λ and h are the two parameters of the equation, which can be obtained by fitting the solubility data. 4.3. Apelblat Equation. Apelblat equation first proposed a simplified equation with three parameters. It is a semiempirical correlation equation. Because of the simplicity of the Apelblat equation, it is broadly applied in the correlation of solubility. Its expression is as follows12 ln x1 = a +

b T + c ln T /K K

solvent is related to its activity coefficient. Therefore, it is necessary to study the relationship between the activity coefficient and the solubility and temperature, which is called the activity coefficient equation.13 ij 1 yz ΔfusH i T zz = jj m − 1yzz lnjjjj zz z j RTm k T { k γ1x1 {

(7)

In this paper, we use three commonly used activity coefficient equations (NRTL Equation, UNIQUAC Equation, and Wilson Equation). 4.5. NRTL Equation. On the basis of local composition theory and nonrandom two-fluid model, Renon proposed NRTL equation for partially miscible system and completely

(6)

a, b, c are the three associated parameters of the model. 4.4. Local Composition Model. According to the basic principles of thermodynamics, the solubility of a solute in G



Article

adjustable parameter, and the value of α12 is about 0.20∼0.47; the value is 0.30 in most cases. 4.6. UNIQUAC Equation. The UNIQUAC equation is a semitheoretical model proposed by Abrams and Maurer in which the excess free energy gE can be further divided into a combination term and a residual term; the combination term depends on the entropy contribution of the solution, and the remainder depends on the intermolecular force of the solution. The expression of the model is16,17 g E = gC E + gR E

gC E RT

N

=

∑ xi ln i=1

(13)

ϕi xi

+

z 2

N

∑ qixi ln i=1

N ij N yz j zz zz = −∑ qixi lnjjj∑ θτ j ji j zz RT j j=1 i=1 k {

θi ϕi

(14)

gR E Figure 6. Mole fraction solubility of Mifepristone (x1) in mixed solvents of water + methanol: □, w2 = 0.1; ■, w2 = 0.2; ▲, w2 = 0.3; △, w2 = 0.4; ○, w2 = 0.5; ●, w2 = 0.6; ★, w2 = 0.7; ☆, w2 = 0.8; ◇, w2 = 0.900.

(15)

thus ln γic = ln

ϕi xi

+

ϕ θ z qi ln i + li − i xi 2 ϕi

N

∑ xjlj

yz zz zz N ∑k = 1 θkτkj zzz {

(16)

i uji − uii yz zz τij = expjjj− RT { k

(18)

ij ij N yz j j zz ln γi R = qijjjj1 − lnjjj∑ θτ zz − j ji z jj jj z j 1 = k { k

N

∑ j=1

j=1

θτ j ij

(17)

with θi =

qx

i i N ∑ j = 1 qjxj

;

ϕi =

i uij − ujj yz zz; τij = expjjj− RT { k li =

Figure 7. Van’t Hoff plot of the mole fraction solubility (lnx1) versus reciprocal of the temperature (1/T − 1/Tm) for Mifepristone in mixed solvents of water + methanol: □, w2 = 0.1; ■, w2 = 0.2; ▲, w2 = 0.3; △, w2 = 0.4; ○, w2 = 0.5; ●, w2 = 0.6; ★, w2 = 0.7; ☆, w2 = 0.8; ◇, w2 = 0.900.

G12 = exp( −α12τ12)

τ12 =

g12 − g22 RT

α12 = α21

τ21 =

G21 = exp( −α12τ21)

(8)

(9) (10)

g21 − g11 RT

z (ri − qi) − (ri − 1) 2

(19)

(20)

z is the number of central atomic coordination number, and it is usually equal to 10; ri and qi are the volume and surface area parameters of each component i; Rj and Qj represent the volume and surface area of the molecule. Δu12 (= u12 − u22) and Δu21 (= u21 − u11) is an adjustable parameter of the equation; generally it does not vary with temperature and composition. 4.7. Wilson Equation. The solute’s activity coefficient of this equation is given according to the local composition theory. The interaction force between the molecular pairs is different in the binary mixture, resulting in different types of molecules around the molecules, and thus the local composition is different. On the basis of this theory, Wilson put forward the Wilson equation which has great significance18 ÄÅ ÉÑ Λ12 Λ 21 ÅÅÅ ÑÑÑ ÑÑ ln γ1 = −ln(x1 + Λ12x 2) + x 2ÅÅÅ − ÅÅÇ x1 + Λ12x 2 x 2 + Λ 21x1 ÑÑÑÖ

miscible system.14,15 It takes the following form in binary systems ij τ21G212 yz τ12G12 zz ln γ1 = x 2 2jjj + z 2 2 j (x + G x ) (G12x1 + x 2) z{ 21 2 k 1 ÄÅ ÉÑ Å τ G 2 ÑÑ τ21G21 2Å 12 12 Å ÑÑ ln γ2 = x1 ÅÅÅ + Ñ ÅÅÇ (x 2 + x1G12)2 (x1 + x 2G21)2 ÑÑÑÖ

rx i i N ∑ j = 1 qjxj

(11)

ÄÅ ÉÑ ÅÅ ÑÑ Λ12 Λ 21 Å ÑÑ ln γ2 = −ln(x 2 + Λ 21x1) + x1ÅÅÅ − Ñ ÅÅÇ x1 + Λ12x 2 x 2 + Λ 21x1 ÑÑÑÖ

(12)

(21)

x1 is the mole fraction of the solute, x2 is the mole fraction of the solvent; Δg12 (= g12 − g22) and Δg21 (= g21 − g11) is an interaction parameter. Δg12 and Δg21 have no relationship with the temperature and composition. The parameter α12 is an

(22) H



Article

Table 5. Parameters of the Modified Apelblat Equation, Van’t Hoff Equation, λh Equation, NRTL Equation, UNIQUAC Equation, and Wilson Equation for Mifepristone in Eight Pure Solvents Apelblat

λh

Van’t Hoff

b

c

b

λ

−4336.417 −2913.263 −2775.574 −6457.991 −3494.670 −3527.204 −3293.953 −2491.633

0.4569 0.0121 0.0109 2.1753 0.0400 0.0428 0.0202 0.0024

solvent

a

methanol ethanol n-propanol isopropanol n-butanol propanone ethyl acetate tetrahydrofuran

−75.859 −89.931 −92.197 −4.067 −33.011 −84.644 −86.894 −105.285

−575.325 1128.281 1338.383 −5627.722 −1791.546 381.702 644.896 2122.428 NRTL J·mol−1

a

solvent

Δg12

Δg21

Δu12

Δu21

Δλ12

Δλ21

methanol ethanol n-propanol isopropanol n-butanol propanone ethyl acetate tetrahydrofuran

−902 24184 24224 −773 7395.9 7494.1 15067 24406

10083 9717 9516 13002 7823.5 8165.8 8891 12113

92.3587 4561.6 4001.5 −140 2212.5 2861.2 2694.2 4870.0

292.8147 −373.0 −527.1 1277.5 −231.9 −197.3 −329.5 −573.6

12405 15132 14323 28509 12854 13687 14089 16800

−1240 62656 66871 −6417 68424 58170 80288 2679200

12.527 8.138 13.689 1.636 13.977 1.250 2.699 14.094 5.513 4.118 13.268 4.075 13.429 2.848 15.624 −0.770 UNIQUAC J·mol−1

h 9533.477 239745.513 254295.456 2969.054 85013.414 83553.157 165270.567 1011822.745 Wilson J·mol−1

Table 6. Parameters of the Modified Apelblat Equation, Van’t Hoff Equation, λh Equation, NRTL Equation, and UNIQUAC Equation for Mifepristone in Mixed Solvents of Water + Methanola Apelblat w2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

a −39.050 55.168 −60.560 −4.708 −89.318 13.420 4.561 −232.575 −70.037 NRTL

λh

Van’t Hoff

b

c

a

196.158 −3691.919 1421.525 −1347.529 1178.318 −1269.210 −1788.782 7682.141 295.183

5.889 −8.452 8.732 0.406 13.560 −3.253 −1.488 34.289 9.996

0.323 −1.346 −2.173 −1.945 1.350 −8.330 −5.375 −3.286 −3.101

b −1537.527 −1202.911 −1150.229 −1481.116 −2815.612 −311.162 −1354.583 −2421.458 −2677.171 UNIQUAC

λ

.

0.0345 0.00768 0.00376 0.00347 0.0119 −0.0000665 0.000127 0.000273 0.000168

36858.993 97294.084 191030.025 330089.085 235579.133 17691988.340 7655442.846 9045882.006 15533187.935

parameter

J·mol−1

parameter

J·mol−1

Δg12 Δg21 Δg13 Δg31 Δg23 Δg32

−8811 44343 33947 29167 61127 31635

Δλ12 Δλ21 Δλ13 Δλ31 Δλ23 Δλ32

−3330 −517 4157 −1392 −3109 −12253

a

ÄÅ É ÅÅ (λ12 − λ11) ÑÑÑ Å ÑÑ expÅÅ− ÑÑ ÅÅÅ RT ÑÑÖ Ç

w2 is the mass fraction of water in the mixed solvents.

Λ12 =

Λ 21 =

V2, m V1, m V1, m V2, m

ÅÄÅ (λ − λ ) ÑÉÑ Å 22 Ñ ÑÑ expÅÅÅ− 21 ÑÑ ÅÅÅ RT ÑÑÖ Ç

4.8. Jouyban−Van’t Hoff Model. The Van’t Hoff model is combined with the Jouyban−Acree equation and the Jouyban− Van’t Hoff equation is obtained19,20

(23)

ln x1 = C1 + C2ω2 +

(24)

C3 ω ω2 ω3 ω4 + C4 2 + C5 2 + C6 2 + C7 2 T T T T T

(25)

The Jouyban−Van’t Hoff equation in the above equation has seven parameters and three variables, which can be correlated to fit the solubility of the solute in the mixed solvents. 4.9. Jouyban−Apelblat Model. The semiempirical Apelblat equation is combined with the Jouyban−Acree equation and the Jouyban−Apelblat equation is obtained.21

In which V1,m and V2,m are the molar volumes of solute and solvent; λ11, λ12, λ21, and λ22 represent the intermolecular interaction energy; Δλ12 (= λ12 − λ21) and Δλ21 (= λ21 − λ12) are the two interactions of the equation the parameters, Λ12 and Λ21 are two adjustable parameters of the equation. I



Article

Table 7. Parameters of the Jouyban−Van’t Hoff Equation for Mifepristone in Mixed Solvents of Water + Methanol parameters

C1

C2

C3

C4

C5

C6

C7

Jouyban−Acree

0.0381

−5.383

−1445.384

2179.988

−7911.455

6655.834

−1750.421

Table 8. Parameters of the Jouyban−Apelblat Equation for Mifepristone in Mixed Solvents of Water + Methanol parameters

C1

C2

C3

C4

C5

C6

C7

C8

C9

Jouyban−Acree

19.850

−116.220

−2318.101

7062.460

−7911.455

6655.8344

−1750.421

−2.963

16.576

Table 9. RAD of the Modified Apelblat Equation, Van’t Hoff Equation, λh Equation, NRTL Equation, UNIQUAC Equation, and Wilson Equation for Mifepristone in Eight Pure Solvents 100RAD solvent

Apelblat

Van’t Hoff

λh

NRTL

UNIQUAC

Wilson

methanol ethanol n-propanol isopropanol n-butanol propanone ethyl acetate tetrahydrofuran (1/8)∑81RAD

1.35 0.17 0.22 0.61 1.66 0.03 0.30 0.30 0.58

0.76 1.11 1.32 0.05 0.80 1.20 1.49 1.15 0.99

0.68 1.02 1.21 0.04 1.22 1.30 1.54 1.00 1.00

11.62 3.52 5.10 37.51 0.95 1.05 1.35 13.55 9.33

1.37 0.36 0.63 29.84 1.24 0.49 0.93 0.48 4.42

5.91 19.08 19.76 2.01 6.58 7.98 12.03 28.21 12.70

Table 10. RAD of the Modified Apelblat Equation, Van’t Hoff Equation, λh Equation, NRTL Equation, UNIQUAC Equation, Jouyban−Van’t Hoff Equation, and Jouyban−Apelblat Equation for Mifepristone in Mixed Solvents of Water + Methanol 100RAD w2

Apelblat

Van’t Hoff

λh

NRTL

UNIQUAC

Jouyban−Van’t Hoff

Jouyban−Apelblat

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 (1/9)∑91RAD

0.45 0.10 0.45 0.64 0.37 0.08 0.31 0.53 0.88 0.42

0.66 0.80 0.88 0.60 1.42 0.30 0.41 3.02 0.77 0.98

0.47 1.33 0.54 0.96 1.18 0.78 0.85 2.86 0.84 1.09

25.93 36.00 10.34 29.51 14.14 29.24 15.24 37.55 23.30 24.58

20.71 8.25 22.85 20.77 22.89 31.14 24.54 6.79 11.61 18.84

3.61 6.34 3.83 8.81 20.07 29.51 26.83 21.89 7.56 14.27

3.58 6.34 3.83 8.80 19.97 29.33 26.82 21.86 8.03 14.28

ln x1 = c1 + c 2ω2 + + c 9ω2 ln T

c3 ω ω2 ω3 ω4 + c4 2 + c5 2 + c6 2 + c 7 2 + c8 ln T T T T T T

RAD =

(26)

5. CORRELATION RESULT The parameters of the associated equation are showed in Table 5−Table 8. The relative deviation (RD) between the experimental value of the solubility and the correlated value of the solubility is shown as x1 − x1cal x1

N

∑ i=1

x1, i − x1, i cal x1, i

(28)

In which, N represents the number of the experimental solubility data, x1,i is the experimental solubility value, and x1,ical is the correlated solubility value. The values of RAD are shown in Table 9 and Table 10. The mean values of RAD in eight pure solvents of several equations are 0.58%, 0.99%, 1.00%, 9.33%, 4.42%, and 12.70%, respectively. The mean values of RAD in mixed solvents of several equation are 0.42%, 0.98%, 1.09%, 24.58%, 18.84%, 14.27%, and 14.28%, respectively. They show good correction result with the solubility data of Mifepristone in eight pure solvents and water + methanol mixed solvents. The Apelblat equation shows the best correlation effect.

The Jouyban−Apelblat equation in the above equation has nine parameters and three variables, which can be correlated to match the solubility of the solute in the mixed solvents.

RD =

1 N

6. CONCLUSIONS The experimental solubility data of Mifepristone in eight pure solvents and mixed solvents of water + methanol were measured by an HPLC method from 273.15 to 318.15 K. The solubility data of Mifepristone in eight pure solvents can be well-correlated by the modified Apelblat equation, Van’t Hoff equation, λh

(27)

In which, x1cal is the correlated value of the solubility. The average relative deviation (RAD) between the experimental value of the solubility and the correlated value of the solubility is shown as J



Article

(14) Zhang, Q.; Yang, Y.; Cao, C.; Cheng, L.; Shi, Y.; Yang, W.; Hu, Y. Thermodynamic models for determination of the solubility of dibenzothiophene in (methanol + acetonitrile) binary solvent mixtures. J. Chem. Thermodyn. 2015, 80, 7−12. (15) Patel, A.; Vaghasiya, A.; Gajera, R.; Baluja, S. Solubility of 5amino salicylic acid in different solvents at various temperatures. J. Chem. Eng. Data 2010, 55, 1453−1455. (16) Sander, B.; Fredenslund, A.; Rasmussen, P. Calculation of vapour-liquid equilibria in mixed solvent/salt systems using an extended UNIQUAC equation. Chem. Eng. Sci. 1986, 41, 1171−1183. (17) Anderson, T. F.; Prausnitz, J. M. Application of the UNIQUAC equation to calculation of multicomponent phase equilibria. 1. Vaporliquid equilibria. Ind. Eng. Chem. Process Des. Dev. 1978, 17, 552−561. (18) de Mateo, A.; Kurata, F. Correlation and rediction of solubilities of solid hydrocarbons in liquid methane using the Redlich-Kwong equation of state. Ind. Eng. Chem. Process Des. Dev. 1975, 14, 137−140. (19) Jouyban, A. Review of the cosolvency models for predicting solubility of drugs in water-cosolvent mixtures. J. Pharm. Pharm. Sci. 2008, 11, 32−58. (20) Liu, B. S.; Sun, H.; Wang, J. K.; Yin, Q. X. Solubility of disodium 5′-guanylate heptahydrate in aqueous methanol mixtures. Food Chem. 2011, 128, 218−221. (21) Cristancho, D. M.; Delgado, D. R.; Martínez, F.; Abolghassemi, F.; Mohammad, A.; Jouyban, A. Volumetric properties of glycerol + water mixtures at several temperatures and correlation with the ́ Farm 2011, 40, 92− Jouyban−Acree model. Rev. Colomb. Cienc. Quim. 115. (22) Li, Q.; Xing, F.; Lei, Z.; Wang, B.; Chang, Q. Isobaric vapor− liquid equilibrium for isopropanol + water + 1-ethyl-3-methylimidazolium tetrafluoroborate. J. Chem. Eng. Data 2008, 53, 275−279. (23) Suren, S.; Sunsandee, N.; Stolcova, M.; Hronec, M.; Leepipatpiboon, N.; Pancharoen, U.; Kheawhom, S. Measurement on the solubility of adipic acid in various solvents at high temperature and its thermodynamics parameters. Fluid Phase Equilib. 2013, 360, 332− 337. (24) Lim, J.; Jang, S.; Cho, H. K.; Shin, M. S.; Kim, H. Solubility of salicylic acid in pure alcohols at different temperatures. J. Chem. Thermodyn. 2013, 57, 295−300.

equation, NRTL equation, UNIQUAC equation, and the Wilson equation.22 The solubility data of Mifepristone in the mixed solvents can be well-correlated by the modified Apelblat equation, Van’t Hoff equation, λh equation, NRTL equation, UNIQUAC equation, Jouyban−Van’t Hoff equation, and Jouyban−Apelblat equation. It was shown that the modified Apelblat equation showed the best correlated results in pure solvents and mixed solvents. Furthermore, the experimental solubility and the correlation equation could be used for the purification of the Mifepristone and further thermodynamic research.23,24

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AUTHOR INFORMATION

Corresponding Author

*Tel: +86-010-62179135. E-mail: [email protected]. ORCID

Lifeng Ning: 0000-0002-1686-0668 Funding

We are thankful for financial support from the National Key R&D Program of China (No. 2016YFC1000901). Notes

The authors declare no competing financial interest.

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REFERENCES

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Measurement and Correlation of the Solubility of Mifepristone in Eight

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