Thermodynamic Models for Determination of the Solubility of Boc-(R

Article pubs.acs.org/jced

Thermodynamic Models for Determination of the Solubility of Boc(R)-3-Amino-4-(2, 4, 5‑trifluorophenyl)butanoic acid in Different Pure Solvents and (Tetrahydrofuran + n‑Butanol) Binary Mixtures with Temperatures from 280.15 to 330.15 K Shimin Fan,† Wenge Yang,*,† Qirun Guo,† Jianfeng Hao,† Hongjie Li,† Shouhai Yang,† and Yonghong Hu‡ †

School of Pharmaceutical Sciences, Nanjing Tech University, No. 30, South Puzhu Road, Nanjing 211816, China State Key Laboratory of Materials-Oriented Chemical Engineering, Nanjing Tech University, No. 200, North Zhongshan Road, Nanjing 210009, China

‡

ABSTRACT: A gravimetric method was taken to measure the solubility of the Boc-(R)-3-amino-4-(2,4,5-trifluorophenyl)butanoic acid under atmospheric pressure in methanol, ethanol, propanol, n-butanol, ethyl acetate, and tetrahydrofuran as well as in the (tetrahydrofuran + n-butanol) mixtures from 280.15 to 330.15 K.The experiment results have proved that the rising temperature leads to increased solubility of the Boc-(R)-3-amino-4- (2,4,5-trifluorophenyl)butanoic acid in all selected solvents. The solid−liquid equilibrium data in pure and mixed solvents is correlated with a series of equations, including the modified Apelblat equation, the Buchowski−Ksiazaczak λh equation, CNIBS/R−K equation and the Jouyban−Acree equation. During the study, the computational values were in good agreement with the experimental results according to the calculations based on all selected equations, however, the modified Apelblat equation stood out to be the higher suitable with the higher accuracy. The thermodynamic properties of the solution process, including the Gibbs energy, enthalpy, and entropy were calculated by the van’t Hoff equation. The calculated thermodynamic parameters indicated that in each studied solvent the dissolution process of Boc(R)-3-amino-4-(2,4,5-trifluorophenyl)butanoic acid is endothermic.

1. INTRODUCTION As we know, diabetes is one kind of metabolic disease; the reason for this disease is that the insulin production is inadequate, either because the person has high blood glucose, because the cells of the body do not respond properly to insulin, or both.1 Sitagliptin is the first approved drug for the treatment of type 2 diabetes DPP-4 inhibitors.2,3 To reduce the clinical effects of blood glucose concentration, it triggers the pancreas to improve insulin production and stops glucose product in the liver by inhibiting the enzyme activity and increasing incretin relatively.4 Boc-(R)-3-amino-4-(2,4,5-trifluorophenyl)butanoic acid (C15H18F3NO4, FW333.30, Tm 388.15K CASRN: 486460-008, Figure 1) or BAFBA for short is a kind of significant pharmaceutical intermediate that is used to synthesize Sitagliptin.5 The solubility of organic compounds in different solvents is important to understand the solid−liquid equilibria © XXXX American Chemical Society

Figure 1. Chemical Structure of Boc-(R)-3-amino-4-(2,4,5trifluorophenyl)butanoic acid.

(SLE) or phase equilibria in the development of a crystallization process. The solubility of BAFBA can also provide industrial production with experimental data. In order to determine appropriate solvents and to design an optimized Received: September 6, 2015 Accepted: January 20, 2016

A

DOI: 10.1021/acs.jced.5b00758 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

2.2. Methods. The method used to measure the solubility was similar to that described in the literature.7,8 Excess BAFBA and 8 mL of organic solvent were added into a 10 mL glass test tube with a stopper. The glass test tubes were maintained in a required temperatures thermostatic bath (280.15−330.15 K) that was on a magnetic stirrer and stirred continuously. It required 24 h to ensure the solution reached the solid−liquid equilibrium. The stirrer was turned off after 6 h at constant temperature to settle the undissolved solid. A pipet gun was used to remove 1 mL of the clear portion at the top of the saturated solution, and then this 1 mL sample was transferred into a 5 mL beaker and covered immediately; it was necessary to have been weighed beforehand. Next, we measured the total weight immediately, put the beaker into a dryer, and then recorded the sample repeatedly until the weight remained constant. In order to check the repeatability of the solubility determination, each experiment was repeated at least three times. Then three samples were taken at each temperature from every solvent and the mean value was used to calculate the mole fraction solubility. The saturated mole fraction solubility of BAFBA in pure solvents was calculated by eq 1

production process, it is necessary to know the solubility of BAFBA in different solvents. Solubility data for BAFBA in solo and mixed organic solvents have not been recorded in literature yet, therefore, it is necessary to study the experimental data of solubility of BAFBA in pure solvents and binary mixtures. In this study, gravimetric method is used to measure the solubility of BAFBA in six organic pure solvents, including methanol, ethanol, propanol, n-butanol, ethyl acetate (EA), tetrahydrofuran (THF), and binary mixtures of (tetrahydrofuran + n-butanol) in the temperature range from 280.15 to 330.15 K at atmospheric pressure. Tetrahydrofuran is a typical solvent and it has good solubility, while n-butanol has poor solubility; we choose this binary mixture because it may has a better crystallization process. The modified Apelblat equation and the Buchowski−Ksiazaczak λh equation were used to correlate and predict the solubility of BAFBA in pure solvents, as well as modified Apelblat equation; Redlich−Kister (CNIBS/R−K) equation and the Jouyban−Acree equation were also applied to correlate the experimental data in (tetrahydrofuran + n-butanol) mixed solvents, which give good agreement with experimental data. Thermodynamic models of BAFBA solubility corresponding to mathematic expressions were developed and employed to correlate and predict the measured solubility data. For the thermodynamic parameters of dissolution, the standard enthalpy (ΔH0Diss), standard entropy (ΔS0Diss), and Gibbs free energy (ΔG0Diss) of solution of BAFBA were determined from the solubility data by the Van’t Hoff equation.6

x=

xi =

solvent BAFBA

methanol ethanol propanol n-butanol ethyl acetate tetrahydrofuran

source Nanjing Chemlin Chemical Industrial Shenbo Chemicals Shenbo Chemicals Shenbo Chemicals Shenbo Chemicals Shenbo Chemicals Shenbo Chemicals

≥ 0.980

333.3

CASRN

32.04

67-56-1

≥ 0.990

46.07

64-17-5

≥ 0.995

60.1

71-23-8

≥ 0.995

74.12

71-36-3

≥ 0.995

88.11

141-78-6

≥ 0.990

72.11

m2 M2

(1)

m1 M1

+

m1 M1 m2 M2

+

m3 M3

(2)

3. RESULTS AND DISCUSSION 3.1. Solubility Data and Correlation Models. 3.1.1. In Pure Solvents. 3.1.1.1. Modified Apelblat Equation. The saturated mole fraction solubility (x) in methanol, ethanol, propanol, n-butanol, ethyl acetate, and tetrahydrofuran over the temperature from 280.15 to 330.15 K are presented in Table 2. The effect of temperatures on the solubility of BAFBA has been represented by the following modified Apelblat model. It was first used by Apelblat,9,10 which can give a relatively accurate correlation with three parameters

486460-00-8

≥ 0.997

+

where m1, m2, and 3 represent the mass of the solute, n-butanol, and tetrahydrofuran, respectively, and M 1, M 2, and M3 represent the molecular weight of the solute, n-butanol, and tetrahydrofuran, respectively.

Table 1. Provenance and Purity of the Materials Used molar mass (g mol−1)

m1 M1

where m1 and m2 represent the mass of solute and solvent, respectively; M1 and M2 represent the molecular mass of solute and solvent, respectively. All molar quantities are based on the IUPAC relative atomic mass table. The saturated mole fraction solubility of BAFBA in different compositions of the binary mixtures at various temperatures was obtained by eq 2

2. EXPERIMENTAL SECTION 2.1. Materials and Apparatus. Boc-(R)-3-amino-4-(2,4,5trifluorophenyl)butanoic acid with a mass fraction purity >98 was purchased from Nanjing Chemlin Chemical Industrial Co., Ltd. High-performance liquid chromatography (HPLC type Agilent 1260 Infinity LC, Agilent Technologies) was used to measure its purity. Meanwhile, all solvents used for experiments are analytical reagent grade and their mass fraction purities are higher than 99. Also, more details about the purity of solvents were listed in Table 1. All the solvents were used without further purification.

mass fraction purity

m1 M1

ln x = A +

B + C ln(T /K ) T /K

(3)

where x represents solubility mole fraction of BAFBA, T represents the experimental temperature, and A, B, and C are the model parameters determined by the experimental solubility data. 3.1.1.2. Buchowski−Ksiazaczak λh Equation. The Buchowski−Ksiazaczak λh equation is an alternate way that was first proposed by Buchowski et al. was used to describe solid−liquid

109-99−9

a The sample purities were stated by the suppliers and no purification was applied to the chemicals. b BAFBA is the short of tbutyloxycarbonyl-(R)-3-amino-4-(2,4,5-trifluorophenyl) butanoic acid.

B



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Table 4. Parameters of Buchowski−Ksiazaczak λh Equation for Mole Fraction Solubility of BAFBA in Different Pure Solvents

Table 2. Saturated Mole Fraction Solubility (x) of BAFBA in Different Solvents over the Temperature Range of 280.15− 320.15 K under 100 ± 2 kPaa 100RD T/K

100X

280.15 285.15 290.15 295.15 300.15 305.15 310.15 315.15 320.15 325.15 330.15

9.33 10.47 11.64 12.91 14.45 16.33 18.69 21.47 24.45 27.92 32.20

280.15 285.15 290.15 295.15 300.15 305.15 310.15 315.15 320.15 325.15 330.15

5.30 5.82 6.69 7.51 8.50 9.70 11.09 12.90 15.11 17.82 21.15

280.15 285.15 290.15 295.15 300.15 305.15 310.15 315.15 320.15 325.15 330.15

4.09 4.77 5.56 6.52 7.73 8.90 10.40 12.12 14.03 16.36 18.79

eq 2

100RD

eq 3

100X

THF 0.50 −9.41 −0.86 −6.29 −0.76 −2.69 0.23 0.94 0.78 3.29 0.84 4.27 0.03 3.52 −0.76 2.01 −0.29 1.10 0.23 −0.41 0.05 −3.16 Methanol 1.07 −12.98 1.59 −6.59 −1.36 −4.56 −1.09 −0.66 −0.76 2.15 −0.38 3.88 0.50 5.03 0.42 4.15 0.30 2.32 0.06 −0.43 −0.21 −3.83 EA −0.89 −3.19 0.02 −1.22 0.61 0.16 0.53 0.63 −0.88 −0.46 0.45 1.03 0.16 0.72 −0.08 0.34 0.14 0.33 −0.47 −0.56 0.23 −0.18

3.60 4.20 4.83 5.59 6.59 7.54 8.94 10.28 12.49 14.69 17.33 3.12 3.74 4.49 5.22 6.19 7.18 8.47 9.85 11.64 13.86 16.24 2.74 3.06 3.53 4.26 5.14 6.19 7.35 8.68 10.34 12.58 15.41

eq 2 Ethanol 1.11 −0.52 −0.21 −0.06 −1.31 0.66 −0.38 1.96 −0.98 −0.35 0.22 Propanol 2.78 0.52 −1.54 −0.45 −1.34 0.07 −0.27 0.94 0.62 −0.50 −0.03 n-butanol −2.58 1.91 3.25 1.04 −0.91 −2.14 −1.38 0.17 1.22 0.58 −0.51

eq 3 −9.53 −6.73 −2.98 −0.22 0.31 3.31 2.48 4.44 0.39 −0.54 −1.98

λ

h

100RMSD

100RAD

tetrahydrofuran methanol ethyl acetate ethanol propanol n-butanol

0.86 0.54 0.54 0.54 0.51 0.61

2735.22 4632.45 4930.30 5284.95 5607.92 5402.14

0.59 0.45 0.07 0.25 0.13 0.24

3.37 4.23 0.80 2.99 1.67 3.34

nonideality of the solution system, where λh estimates the enthalpy of solution. According to the data of Table 2, the parameters of A, B, and C were calculated and presented in Table 3, and the parameters of λ and h were presented in Table 4 with the root-mean-square deviations (RMSDs) and the relative average deviation (RAD).

−3.42 −2.99 −3.02 −0.50 −0.44 1.49 1.25 2.21 1.32 −0.62 −1.16

N

RMSD =

RAD =

1 N

∑i = 1 (x − x c)2 N

∑ i=1

N

(5)

x − xc x

(6)

The relative deviations (RDs) between the calculated values and the experimental values are listed in Table 2 and Table 5. The value of RD is defined as follows x − xc x

RD =

−15.98 −6.81 −1.14 0.12 0.54 0.66 1.91 3.13 3.05 0.56 −2.89

(7)

c

where x represents the calculated solubility values. N represents the number of experimental data points. According to the data in Tables 3 and 4, the small RMSDs show that the calculated data of BAFBA in six pure solvents were in good agreement with the experimental values. The relative average deviations calculated by eq 2 are 0.48, 0.70, 0.41, 0.71, 0.82, and 1.42% respectively. Any absolute value of relative deviations does not exceed 3.25%, which indicates that the modified Apelblat equation is suitable for the solubility data of BAFBA in the six pure solvents. Also, the relative average deviations from eq 3 are 3.37, 4.23, 0.80, 2.99, 1.67, and 3.34% respectively. From Tables 2 and 3 for the modified Apelblat equation and the λh equation, the average RMSDs are 0.07 and 1.73%, respectively. As was previously stated, the solubility can be calculated by both the Apelblat equation and the λh equation, but the Apelblat equation is more accurate than the λh equation in this research. The X/T-curves of BAFBA in the six pure solvents are shown in Figure 2. It describes the temperature dependence of the BAFBA solubility in the six pure solvents clearly. The solubility increases with the increasing temperature and the solubility is

a The standard uncertainty u(T) = 0.1 K; u(p) = 2 kPa. The relative standard uncertainty ur(x) = 0.01

equilibrium. In this research, the solubility data was correlated with the λh equation11 ⎡ 1 ⎛ λ(1 − x) ⎞ 1 ⎤ ln⎜1 + ⎟ = λh⎢ − ⎥ ⎝ ⎠ x (Tm/K ) ⎦ ⎣ (T / K )

solvent

(4)

where λ and h are two equation constants, and Tm is the melting temperature of the solute. The value of λ reflects the

Table 3. Parameters of Modified Apelblat Equation for Mole Fraction Solubility of BAFBA in Different Pure Solvents solvent

A

B

C

100RMSD

100RAD


−203.38 −297.85 −73.62 −213.80 −135.84 −243.99

7171.92 11206.05 800.65 7093.41 3470.03 8157.27

31.13 45.24 11.99 32.86 21.30 37.49

0.09 0.06 0.04 0.08 0.06 0.09

0.48 0.70 0.41 0.71 0.82 1.42

C



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Table 5. Saturated Mole Fraction Solubility (x) of BAFBA in (Tetrahydrofuran + n-Butanol) Binary Solvent Mixtures over the Temperature Range of 280.15−320.15 K under 100 ± 2 kPaa 100RD xA

100X

eq 3

eq 11

100RD eq 14

100X

T = 280.15 K 0.0000 0.1535 0.3058 0.4568 0.6066 0.7551 0.9024 1.0000

2.74 3.32 4.03 4.83 5.85 6.93 8.01 9.33

0.0000 0.1535 0.3058 0.4568 0.6066 0.7551 0.9024 1.0000

3.53 4.33 5.31 6.26 7.31 8.57 9.92 11.64

0.0000 0.1535 0.3058 0.4568 0.6066 0.7551 0.9024 1.0000

5.14 6.00 7.11 8.22 9.46 10.91 12.62 14.45

0.0000 0.1535 0.3058 0.4568 0.6066 0.7551 0.9024 1.0000

7.35 8.35 9.48 10.99 12.63 14.41 16.42 18.69

0.0000 0.1535 0.3058 0.4568 0.6066 0.7551 0.9024 1.0000

10.34 11.63 13.09 14.82 16.91 19.11 21.59 24.45

0.0000 0.1535 0.3058 0.4568 0.6066 0.7551 0.9024 1.0000

15.41 16.65 18.25 20.15 22.67 25.55 28.75 32.20

−2.58 0.29 −1.22 −0.87 0.89 0.45 0.65 0.50 T 3.25 −1.54 0.13 −0.23 −0.77 −0.47 −0.04 −0.76 T −0.91 0.45 0.90 −0.09 −0.90 −0.84 −0.15 0.78 T −1.38 0.96 −0.58 0.32 0.43 0.49 0.19 0.03 T 1.22 −0.05 −0.11 0.32 0.63 0.53 0.08 −0.29 T −0.51 0.34 0.02 0.06 −0.21 −0.06 −0.05 0.05

= 290.15

= 300.15

= 310.15

= 320.15

= 330.15

0.00 1.52 0.21 −1.55 0.15 1.30 −1.10 0.00 K 0.00 0.33 0.57 −0.79 −0.44 1.26 −0.88 0.00 K 0.00 −0.10 0.45 −0.39 −0.22 0.55 −0.37 0.00 K 0.00 1.24 −0.68 −0.44 0.16 0.65 −0.64 0.00 K 0.00 0.98 −0.26 −0.83 0.31 0.71 −0.74 0.00 K 0.00 0.56 −0.01 −0.74 0.17 0.69 −0.67 0.00

eq 3

eq 11

eq 14

T = 285.15 K 10.37 13.56 14.40 14.00 15.21 14.72 10.42 10.02

3.06 3.84 4.63 5.57 6.52 7.71 8.81 10.47

−4.37 2.11 5.59 5.12 4.51 4.47 1.42 2.93

4.26 5.06 6.13 7.19 8.43 9.71 11.21 12.91

−4.76 −1.67 0.06 −0.88 −1.50 −1.72 −3.45 −3.30

6.19 7.03 8.24 9.45 10.88 12.54 14.27 16.33

−4.44 −2.70 −3.88 −3.10 −2.45 −2.36 −4.19 −3.59

8.68 9.79 11.08 12.66 14.46 16.41 18.82 21.47

−3.38 −1.47 −2.16 −2.45 −1.21 −0.79 −2.10 −1.05

12.58 13.77 15.48 17.19 19.53 21.98 24.87 27.92

1.91 0.95 −0.16 0.99 0.03 0.36 −0.58 −0.86 T 1.04 −1.02 0.53 0.28 0.75 0.04 0.33 0.23 T −2.14 0.24 0.73 −0.29 −0.51 0.07 −0.65 0.84 T 0.17 −0.01 −0.71 −0.34 −0.37 −0.41 0.26 −0.76 T 0.58 −0.75 0.25 −0.21 0.10 −0.13 −0.02 0.23

= 295.15

= 305.15

= 315.15

= 325.15

0.00 2.11 −0.54 −0.82 −0.60 2.00 −1.52 0.00 K 0.00 0.19 0.53 −0.88 0.11 0.59 −0.50 0.00 K 0.00 0.11 0.60 −0.76 −0.28 1.01 −0.74 0.00 K 0.00 0.84 −0.37 −0.50 0.24 0.45 −0.48 0.00 K 0.00 0.18 0.45 −0.94 0.30 0.48 −0.49 0.00

1.07 8.86 9.89 10.54 9.48 9.53 4.66 6.70 −5.05 −0.81 2.35 2.12 2.62 1.58 −1.04 −0.85 −4.07 −3.17 −1.79 −2.83 −2.70 −2.27 −4.97 −4.35 −4.64 −3.02 −3.83 −3.84 −3.15 −2.93 −3.40 −2.05 0.40 0.20 0.04 −1.55 −0.14 0.48 −0.03 0.58

5.20 4.33 2.32 0.81 1.82 3.14 2.71 3.52

a

The standard uncertainty u(T) = 0.1 K; u(p) = 2 kPa; u(xA) = 0.0001. The relative standard uncertainty ur(x) = 0.01 bxA represents the initial mole fraction composition of the tetrahydrofuran in the binary solvent mixtures D



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Table 7. Parameters of the CNIBS/R−K Model for BAFBA in (Tetrahydrofuran + n-Butanol) Binary Solvent Mixtures T/K 280.15 285.15 290.15 295.15 300.15 305.15 310.15 315.15 320.15 325.15 330.15 Ave(100RAD)

Figure 2. Mole fraction solubility (x) of BAFBA versus temperature (T) in pure solvents at atmospheric pressure: (black square), tetrahydrofuran; (red circle), methanol; (blue triangle), ethyl acetate; (green triangle), ethanol; (magenta triangle), propanol; (olive triangle), n-butanol.

S0

S1

S2

100RAD

0.09 0.16 0.12 0.09 −0.01 −0.06 −0.08 −0.13 −0.11 −0.17 −0.25 = 0.48

−0.05 −0.32 −0.31 −0.17 −0.18 −0.09 −0.06 −0.12 −0.09 −0.05 −0.03

−0.46 −0.51 −0.42 −0.43 −0.30 −0.38 −0.36 −0.33 −0.30 −0.25 −0.19

0.73 0.95 0.54 0.35 0.26 0.44 0.48 0.36 0.48 0.35 0.35

Table 8. Parameters of the Jouyban−Acree Model for BAFBA in (Tetrahydrofuran + n-Butanol) Binary Solvent Mixtures T/K

100RAD

280.15 12.84 285.15 7.59 290.15 3.82 295.15 2.05 300.15 2.17 305.15 3.27 310.15 3.34 315.15 3.36 320.15 1.83 325.15 0.43 330.15 2.98 Ave(100RAD) = 3.94

parameters

parameters

A0 A1 A2 A3 A4 A5 A6

−3295.18 8.06 −1.89 757.96 449.18 −703.99 370.84

Figure 3. Mole fraction solubility (x) of BAFBA versus temperature (T) in (tetrahydrofuran + n-butanol) binary solvent mixtures at atmospheric pressure: (black square) w = 0; (red circle) w = 0.1535; (blue triangle) w = 0.3058; (green triangle) w = 0.4568; (magenta triangle) w = 0.6066; (olive triangle) w = 0.7551; (navy diamond) w = 0.9024; (maroon pentagon) w = 1.

Table 6. Parameters of the Modified Apelblat Equation for BAFBA in (Tetrahydrofuran + n-Butanol) Binary Solvent Mixtures xA 0.0000 0.1535 0.3058 0.4568 0.6066 0.7551 0.9024 1.0000 Ave(100RAD)

A

B

C

100RAD

−243.99 −235.33 −222.63 −198.20 −202.33 −217.50 −203.37 −203.38 = 0.56

8157.27 7983.98 7595.87 6622.14 6899.63 7679.52 7086.18 7171.92

37.49 36.10 34.13 30.44 31.03 33.26 31.15 31.13

1.42 0.60 0.49 0.36 0.51 0.35 0.27 0.48

Figure 4. ln x of BAFBA in pure solvents against 1/T − 1/Tmean with a straight line to correlate the data: (black square), tetrahydrofuran; (red circle), methanol; (blue triangle), ethyl acetate; (green triangle), ethanol; (magenta triangle), propanol; (olive triangle), n-butanol.

in the following order: methanol > EA > THF > ethanol > propanol > n-butanol. As seen from Figure 2, the solubility depends on the structure and the polarity of the solvents and is in the following order: THF > methanol > EA > ethanol > propanol > n-butanol. Oxygen atoms of tetrahydrofuran can provide a lone pair of electrons to combine with carboxyl proton of BAFBA so it can dissolve the largest amount of

relatively high in THF but low in n-butanol. In addition, the solubility of BAFBA depends not only on the temperature but also on the structure of the solvents. The polarity of solvents is E



Article

the model parameters determined by the experimental solubility data and listed in Table 6. 3.1.2.2. CNIBS/R−K Model. The changing trends of solubility against different ratios of tetrahydrofuran under isothermal conditions are described by the CNIBS/R−K model,14,15 which is one of the theoretical models to calculate the solute solubility in binary solvent mixtures and represented in eq 8 N

ln x = xA ln XA + x B ln XB + xAx B ∑ Si(xA − x B)i

(8)

i=0

where xA and xB represent the initial mole fraction composition of the binary solvent mixtures when the BAFBA was not added. XA and XB represent the saturated mole solubility of BAFBA in pure tetrahydrofuran and n-butanol, respectively. Si is the model constant and N can be equal to 0, 1, 2, and 3. (x)i is the saturated mole fraction solubility of the solute in pure solvent i. When N = 2 and substitution of (1 − xA) for xB, eq 8 can be written as eq 9

Figure 5. ln x of BAFBA in (tetrahydrofuran + n-butanol) binary mixtures against 1/T −1/Tmean with a straight line to correlate the data: (black square) w = 0; (red circle) w = 0.1535; (blue triangle) w = 0.3058; (green triangle) w = 0.4568; (magenta triangle) w = 0.6066; (olive right-pointing triangle) w = 0.7551; (navy diamond) w = 0.9024; (maroon pentagon) w = 1.

ln x − (1 − xA )ln XB − xA ln XA = (1 − xA)xA[S0 + S1(2xA − 1) + S2(2xA − 1)2 ]

(9)

It is a variant of CNIBS/R−K model. The parameters Si would be obtained by regressing

solute. The solubility of the remaining five solvents approximately abide by the empirical rule “like dissolves like”.12,13 The solubility of BAFBA increases with the increasing polarity of the solvents. 3.1.2. In Binary Solvent Mixtures. The solubility data of BAFBA in (tetrahydrofuran + n-butanol) binary solvent mixtures with the temperature range from 280.15 to 330.15 K is presented in Table 5. To compare with each of the experimental data, experimental solubility data of BAFBA in (tetrahydrofuran + n-butanol) binary solvent mixtures in the temperature range from 280.15 to 330.15 K is presented in Figure 3. From Table 5 and Figure 3, we can see that the solubility of BAFBA in (tetrahydrofuran + n-butanol) binary solvent mixtures is a function of solvent composition and temperature. More specifically, we could observe that the solubility of BAFBA in solvents increases with the increasing fraction of tetrahydrofuran in (tetrahydrofuran + n-butanol) binary solvent mixtures and the increasing temperature. 3.1.2.1. Modified Apelblat Equation. The changing trends of solubility against temperature in the solvents with same ratio of tetrahydrofuran to n-butanol are described by the modified Apelblat equation. It was first used by Apelblat9,10 and can give a relatively accurate correlation with three parameters B ln x = A + + C ln(T /K ) T /K

{ln x − (1 − xA)ln XB − xA ln XA}versus

{(1 − xA)xA[S0 + S1(2xA − 1) + S2(2xA − 1)2 ]}

The values of the parameters are listed in Table 7. However, the CNIBS/R−K model can only be used for describing and predicting solubility data for different concentrations of a mixed solvent at a fixed temperature. In order to describe the influence of both temperature and solvent compositions on the solubility of BAFBA, we select another equation. 3.1.2.3. Jouyban-Acree Model. It is a relatively more universal model16−18 to describe the solubility of a solute with the variation of both initial composition of binary solvent mixtures and temperature N

ln x = xA ln XA + x B ln XB + xAx B ∑ i=0

Ji (xA − x B)i T

(10)

where T is the absolute temperature, Ji is the model constant, and the other symbols have the same meaning as eq 8. When N = 2 and replacement of (1 − xA) for xB in eq 10 subsequent rearrangements result in eq 11 ln x = ln XB + (ln XA − ln XB)xA + +

where x represents solubility mole fraction of BAFBA, T represents the experimental temperature, and A, B, and C are

(− J0 + 3J1 − 5J2 )xA2 T

+

(J0 − J1 + J2 )xA

T (− 2J1 + 8J2 )xA3 T

+

(− 4J2 )xA4 T (11)

Table 9. Thermodynamic Functions Relative to Solution Process of BAFBA in Pure Solvents at Mean Temperature solvent

ΔH0soln/KJ·mol−1

ΔG0soln/KJ·mol−1

ΔS0soln /KJ·mol−1

%ξH

%ξTS


19.00 27.91 25.50 29.03 25.63 23.64

4.47 10.38 9.81 10.44 8.79 9.01

0.05 0.06 0.05 0.06 0.06 0.05

56.67 61.43 61.91 60.96 60.34 61.78

43.33 42.10 42.60 42.29 42.41 42.55

F



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Table 10. Thermodynamic Functions Relative to Solution Process of BAFBA in (Tetrahydrofuran + n-Butanol) Binary Solution Mixtures at Mean Temperature xA

ΔH0soln/KJ·mol−1

ΔG0soln/KJ·mol−1

ΔS0soln/KJ·mol−1

%ξH

%ξTS

0.0000 0.1535 0.3058 0.4568 0.6066 0.7551 0.9024 1.0000

26.92 24.82 23.11 21.85 20.99 20.15 19.77 19.00

6.99 6.62 6.24 5.87 5.51 5.16 4.82 4.47

0.07 0.06 0.06 0.05 0.05 0.05 0.05 0.05

57.45 57.69 57.80 57.76 57.55 57.34 56.94 56.67

42.55 42.31 42.20 42.24 42.25 42.66 43.06 43.33

The standard molar Gibbs energy of solution ΔG0soln21 can be calculated by

Equation 11 can be further simplified as T ln x = A 0 + A1T + A 2 TxA + A3xA + A4 xA2 + A5xA3 + A 6xA4

0 ΔGsoln = −RTmean × intercept

(12)

where the intercept can be obtained by plotting ln x1 versus (1/ T − 1/Tmean) . 0 22 The standard molar entropy of dissolution ΔSsoln is obtained by

where A0, A1, A2, A3, A4, A5, and A6 are parameters of the model and could be calculated by regressing T ln x against T, TxA, xA, x2A, x3A, and x4A by least-squares analysis. The parameter values of eqs 3, 9, and 12 are listed in Tables 6−8 together with the values of 100RAD. From the data listed in Tables 6−8, it can be found that the relative average deviations of the modified Apelblat equation, CNIBS/R−K model and Jouyban−Acree model are 0.56, 0.48, and 3.94%, respectively. From the result, we can see that the modified Apelblat equation is the best, while the CNIBS/R−K model and Jouyban−Acree cause high deviations. In fact, the Jouyban−Acree model leads to a higher deviation only at low temperatures. Therefore, the modified Apelblat equation can be used for describing and predicting the solubility at different temperatures. Nevertheless, when both composition and temperature need to be considered, the Jouyban−Acree model can be applied. 3.2. Thermodynamic Properties of Solutions. Thermodynamic parameters of BAFBA solute relating to the mole fraction of solubility at the corresponding temperatures were estimated. The obvious enthalpy change of solution can be related to the temperature and the solubility as the following equation19 ⎛ ⎞ ⎜ ∂ ln x ⎟ 0 ΔHsoln = −R × ⎜ 1 ⎟ ⎝∂ T ⎠

()

0 ΔSsoln =

%ξH =

%ξTS =

0 ΔHsoln

(

1 T

−

1 Tmean

)

⎞ ⎟ ⎟ ⎟ ⎠

(16)

0 |ΔHsoln | 0 |ΔHsoln |

0 + |T ΔSsoln |

0 |T ΔSsoln | 0 0 |ΔHsoln | + |T ΔSsoln |

× 100 (17)

× 100 (18)

The calculated values of ξH and ξTS were listed in Tables 9 and 10. From the tables, we can see that the enthalpy and the standard Gibbs free energy of BAFBA are positive in the pure solvents and in the studied binary solvent mixtures, which indicates that the solution process of BAFBA in (tetrahydrofuran + n-butanol) binary solvent mixtures is endothermic. What’s more, the enthalpy during the dissolution is the main contributor to the standard molar Gibbs free energy of solution because all values of %ξH are ≥56.67%.

(13)

∂ ln x

0 0 ΔHsoln − ΔGsoln Tmean

The relative contributions of the enthalpy ξH and ξTS to the standard free energy of solution were calculated23 by eqs 17 and 18

where x represents the mole fraction solubility, T represents the absolute temperature, R represents the universal gas constant (8.314 J K−1 mol−1). The obvious enthalpy change of solution in a limited range of temperature may be assumed to be constant, therefore, the values of ΔH0soln would be valid for the mean temperature. The ΔH0soln can be calculated by the van’t Hoff analysis20 ⎛ ⎜ = −R × ⎜ ⎜∂ ⎝

(15)

4. CONCLUSIONS In our research, the solubility of BAFBA in selected organic solvents of methanol, ethanol, propanol, n-butanol, ethyl acetate, and tetrahydrofuran as well as in the (tetrahydrofuran + n-butanol) mixtures from 280.15 to 330.15 K was measured by the gravimetric method. The solubility of BAFBA increased with the mole fraction of tetrahydrofuran in the binary system and the temperature. The experiment solubility values of BAFBA were correlated with the modified Apelblat equation, Buchowski− Ksiazaczak λh equation, the CNIBS/R−K equation, and the modified Jouyban−Acree model with good agreement. We achieved the thermodynamic properties of the dissolution process through van’t Hoff equation analysis. The dissolution process was endothermic and entropy-driving. The experiment data in this research could be used to choose a suitable solvent and to purify BAFBA in industry.

(14)

where Tmean represents the mean temperature of the temperature range. The ln x versus (1/T − 1/Tmean) curves of BAFBA in different pure solvents and in (tetrahydrofuran + n-butanol) binary solvent mixtures are shown in Figures 4 and 5. G



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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Funding

This research work was financially supported by Key topics for State Key Laboratory of Materials-Oriented Chemical Engineering (Grant ZK201304) and Jiangsu Province agricultural science and technology innovation fund projects (CX(14)2057). We thank the Editors and the anonymous reviewers. Notes

The authors declare no competing financial interest.

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