Measurement and Correlation of Solubility of γ-Aminobutyric Acid in

Feb 26, 2016 - The solubility data have been correlated with the modified Apelblat equation, the CNIBS/R-K equation, two modified versions of Jouyban-...
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Measurement and Correlation of Solubility of γ‑Aminobutyric Acid in Different Binary Solvents Kaifei Zhao,†,‡ Lanlan Lin,†,‡ Cong Li,† Shichao Du,†,‡ Cui Huang,†,‡ Yujia Qin,†,‡ Peng Yang,†,‡ Kangli Li,†,‡ and Junbo Gong*,†,‡ †

School of Chemical Engineering and Technology, State Key Laboratory of Chemical Engineering, Tianjin University, Tianjin 300072, China ‡ The Co-Innovation Center of Chemistry and Chemical Engineering of Tianjin, Tianjin 300072, China S Supporting Information *

ABSTRACT: The solubility of γ-aminobutyric acid (GABA) in binary solvent mixtures of ethanol + methanol, 1-propanol + methanol and 2-propanol + methanol was measured over the temperature ranging from(283.15 to 323.15 K with the gravimetric method. It is found that the solubility of GABA increases with increasing temperature, whereas it decreases with the increase of the GABA free-base mole fraction of ethanol, 1-propanol, or 2-propanol. The solubility data have been correlated with the modified Apelblat equation, the CNIBS/R-K equation, two modified versions of JouybanAcree models (the Van’t-JA equation and the Apel-JA equation) and NRTL model, respectively. The results show that the CNIBS/R-K equation gives the best correlation results in these three binary mixed solvents. Also, the mixing thermodynamic properties of enthalpy, entropy, and Gibbs energy change of GABA in these solvent mixtures have also been calculated and discussed.

1. INTRODUCTION γ-aminobutyric acid (GABA; CAS Registry No. 56-12-2; Figure 1), a nonproteinaceous amino acid widely distributed in various

of crystallization method and crystallization solvents, the calculation of yield, and annual output. From literature review, Yang et al.3 investigated the thermal property of GABA in aqueous ethanol solution from 288.2 to 313.2 K. However, there is no more systematic research focused on the thermodynamic data of GABA in organic solvents. In this paper, the solubility of GABA in binary solvent mixtures of ethanol + methanol, 1-propanol + methanol, and 2-propanol + methanol was experimentally determined at temperatures ranging from 283.15 to 323.15 K by gravimetric method. The solubility data have been correlated by the modified Apelblat equation, the CNIBS/R-K equation, two modified versions of Jouyban-Acree models (the Van’t-JA equation and the Apel-JA equation), and NRTL model. Furthermore, the mixing thermodynamic properties in these solvent mixtures, such as the enthalpy, entropy, and Gibbs energy change, have also been calculated and discussed.

Figure 1. Chemical Structure of GABA.

organisms, has been widely applied in foods and pharmaceuticals as a bioactive compound. As is well-known, GABA is the major inhibitory neurotransmitter in the mammalian central nervous system, which plays a significant role in regulating neuronal excitability throughout the nervous system. Because of its physiological functions, such as inhibition of neurotransmission, tranquilization, and antihypotensive and diuretic effects, increasing attention has been focused on the benefits of GABA for human health.1−3 During the manufacturing process of GABA, crystallization is the key step. The quality of product, such as purity, size distribution, and mobility, will be directly determined by the design and operation of crystallization process.4 To make a reliable and robust crystallization process, it is crucial to know the thermodynamic data, such as solubility and dissolution enthalpy. These data are valuable in theoretical study, such as the selection © 2016 American Chemical Society

2. EXPERIMENTAL SECTION 2.1. Materials. A detailed description of chemicals used in this paper is given in Table 1. GABA was purchased from Beijing HWRK Chem Co.,Ltd. (Beijing, China). All organic solvents, including methanol, ethanol, 1-propanol, and 2-propanol, were analytical grade and purchased from Tianjin Jiangtian Chemical Received: September 26, 2015 Accepted: February 19, 2016 Published: February 26, 2016 1210

DOI: 10.1021/acs.jced.5b00829 J. Chem. Eng. Data 2016, 61, 1210−1220

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Table 1. Description of Materials Used in This Paper IUPAC name

CASRN

source

mass fraction purity

purification method

analysis method

γ-aminobutyric acid methanol ethanol 1-propanol 2-propanol

56-12-2 67-56-1 64-17-5 71-23-8 67-63-0

Beijing HWRK Chem Co.,Ltd. Tianjin Jiangtian Chemical Co., Ltd. Tianjin Jiangtian Chemical Co., Ltd. Tianjin Jiangtian Chemical Co., Ltd. Tianjin Jiangtian Chemical Co., Ltd.

≥ 0.990 > 0.995 > 0.995 > 0.995 > 0.995

none none none none none

HPLCa GCb GCb GCb GCb

a

High-performance liquid chromatography. bGas liquid chromatography. Both the analysis method and the mass fraction purity were provided by the suppliers.

respectively, and MA, MB, and MC represent their corresponding molecular mass.

Co., Ltd. (Tianjin, China). All chemicals were employed without further purification. 2.2. Melting Properties Measurements. Thermogravimetry (Mettler Toledo TGA/DSC1/SF, Greifensee, Switzerland) measurements were used to determine whether GABA will decompose at the melting point. Approximately 5−10 mg of sample was used and the thermal analyses were performed at a heating rate of 10 K/min within the temperature range from 303.15 to 573.15 K under a dynamic nitrogen atmosphere. 2.3. Solubility Measurements. The solubility of GABA in binary solvent mixtures of ethanol + methanol, 1-propanol + methanol, and 2-propanol + methanol was measured by gravimetric method.5 The environmental temperature was controlled by using a shaker (Tianjin Ounuo Instrument Co., Ltd., China) with a temperature-controlled system, which showed standard uncertainty of 0.1 K. Excess amount of GABA was added to the binary solvent mixtures and kept at the given temperature. The solution was allowed for 8 h to reach equilibrium. Concentration analyses were undertaken at an interval of 1 h until the results were constant.6 In order to obtain the clear saturated supernatant, the solution was allowed to sit for another 4 h without stirring. After that, 5 mL of the supernatant was filtered into a preweighed beaker by a preheated (or precooled) injector with an organic membrane (0.45 μm, Tianjin legg technology Co., Ltd., Tianjin, China).7 The total weight of the beaker and solution was recorded immediately. Then beakers were placed into a vacuum oven at a temperature of 323.15 K for 12 h. The dried samples were weighed every 2 h until the weight of the beaker was constant. Then the final weights of the beakers were obtained. The same experiment was conducted three times, and the arithmetic average value was used as the final result. All of the masses were measured by an electric balance (Type AB204, Mettler Toledo, Switzerland) with a standard uncertainty of 0.0001 g. The X-ray diffraction (XRD) analysis was performed to determine the crystalline structure of the sample during the measurement. The consistent PXRD patterns indicated that there was no phase transition during the experiment.8 The GABA free-base mole fraction (x0B) of ethanol, 1propanol, or 2-propanol in the solvent mixtures and the mole fraction solubility (xA) of the solute in the binary solvent mixtures are defined by eqs 1 and 2, respectively

x B0

=

xA =

3. RESULTS AND DISCUSSION 3.1. Solubility Data. The solubility data of GABA in binary solvent mixtures of ethanol + methanol, 1-propanol + methanol, and 2-propanol + methanol are listed in Tables 2, 3, and 4 and graphically plotted in Figures 2, 3, and 4. As shown in Tables 2, 3, and 4, it can be seen that the solubility of GABA increased with the increasing temperature in these three binary solvent mixtures at a given solvent composition. In addition, it can also be seen that the solubility of GABA increased with the increase of the GABA free-base mole fraction of methanol at a given temperature. GABA is a polar compound. According to the principle of “like dissolves like”,9 GABA should be more soluble in strongly polar solvent (methanol) than in the moderate and weak polar solvents (ethanol, 1-propanol, and 2propanol).10 Thus, it can be concluded that the polarity of solvents is one of the key factors to determine the solubility. At a given temperature, the decreasing solubility of GABA is mainly caused by the decreasing polarity (dielectric constant) of the mixed solvents. Actually, the mutual competition of the interaction between the solute−solvent and solvent−solvent finally determine the solubility. As shown in Figure 1, the solute molecule contains both hydrogen donor and hydrogen acceptor groups, which could form hydrogen bonding with solvent molecules.11 With the composition of methanol increasing in the solvent mixtures, the intermolecular force between solute− solvent are enhanced and the intermolecular force between solvent−solvent are weakened, so the solubility of GABA increases significantly. Thus, in this system both the van de Waals interaction (represented by polarity) and hydrogen bonding (represented by hydrogen bond donor/acceptor groups) contribute to the solute−solvent interaction. 3.2. Data Correlation. There are various models for correlating solubility. One main purpose of this paper is to provide necessary data for industrial application, and simplicity of the models are of great importance for the correlation or calculation of solid−liquid equilibrium data in industry. In order to describe solid−liquid equilibrium quantitatively and extend the application range of the solubility data, five thermodynamic models, including the modified Apelblat equation, the CNIBS/ R-K equation, two modified versions of Jouyban-Acree models12 (the Van’t-JA equation and the Apel-JA equation) and NRTL model, were applied to correlate the solubility of GABA in these three binary solvent mixtures of ethanol + methanol, 1-propanol + methanol and 2-propanol + methanol. 3.2.1. Modified Apelblat Equation. The modified Apelblat equation is a widely used semiempirical model based on the solid−liquid equilibrium theory, which correlates the mole fraction solubility and the absolute temperature T, as is shown in eq 3

mB MB mB MB

mA MA

+

+

mC MC mA MA mB MB

(1)

+

mC MC

(2)

where mA, mB, and mC are the masses of GABA, solvent B (ethanol, 1-propanol, or 2-propanol) and solvent C (methanol), 1211

DOI: 10.1021/acs.jced.5b00829 J. Chem. Eng. Data 2016, 61, 1210−1220

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Table 2. Experimental (xexp) and Correlated (xcal) Mole Fraction Solubility Data of GABA in Binary Solvent Mixtures of Ethanol + Methanol (p = 0.1 MPa)a,b x0B

103xexp A

103xcal A (eq 3)

0.10 0.15 0.20 0.25 0.30 0.40 0.50 0.60 0.70

1.7221 1.5323 1.3511 1.1927 1.0853 0.8316 0.6020 0.4455 0.3834

1.7514 1.5430 1.3550 1.1803 1.0885 0.8220 0.6091 0.4396 0.3808

0.10 0.15 0.20 0.25 0.30 0.40 0.50 0.60 0.70

1.9406 1.7176 1.4821 1.2970 1.1755 0.8795 0.6746 0.4912 0.4200

1.9241 1.7034 1.4875 1.3084 1.1867 0.9006 0.6730 0.5044 0.4278

0.10 0.15 0.20 0.25 0.30 0.40 0.50 0.60 0.70

2.1534 1.8905 1.6513 1.4463 1.3183 0.9913 0.7723 0.5769 0.4972

2.1052 1.8671 1.6271 1.4407 1.2912 0.9862 0.7435 0.5745 0.4808

0.10 0.15 0.20 0.25 0.30 0.40 0.50 0.60 0.70

2.2855 1.9957 1.7416 1.5301 1.4014 1.0828 0.8068 0.6511 0.5254

2.2947 2.0331 1.7735 1.5763 1.4023 1.0793 0.8211 0.6499 0.5405

0.10 0.15 0.20 0.25 0.30 0.40 0.50 0.60 0.70

2.5294 2.2125 1.9726 1.7409 1.5176 1.2078 0.8963 0.7435 0.6046

2.4921 2.1999 1.9267 1.7144 1.5203 1.1804 0.9064 0.7304 0.6077

ln xA = A +

103xcal A (eq 6)

103xcal A (eq 11)

T = 283.15 1.7319 1.5126 1.3495 1.2109 1.0807 0.8272 0.6028 0.4461 0.3832 T = 288.15 1.9555 1.6881 1.4850 1.3157 1.1639 0.8902 0.6607 0.4977 0.4186 T = 293.15 2.1626 1.8729 1.6509 1.4656 1.3004 1.0052 0.7589 0.5827 0.4960 T = 298.15 2.2839 1.9879 1.7514 1.5518 1.3761 1.0727 0.8254 0.6409 0.5273 T = 303.15 2.5197 2.2289 1.9687 1.7358 1.5282 1.1823 0.9201 0.7314 0.6067

K 1.8180 1.5643 1.3638 1.1954 1.0477 0.7952 0.5954 0.4545 0.3781 K 1.9736 1.7053 1.4926 1.3134 1.1556 0.8841 0.6674 0.5135 0.4299 K 2.1364 1.8535 1.6286 1.4384 1.2703 0.9794 0.7452 0.5777 0.4867 K 2.3066 2.0090 1.7717 1.5705 1.3920 1.0812 0.8290 0.6474 0.5487 K 2.4840 2.1717 1.9221 1.7098 1.5207 1.1897 0.9190 0.7227 0.6161

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

103xcal A (eq 15)

103xcal A (eq 16)

x0B

103xexp A

103xcal A (eq 3)

1.8022 1.5534 1.3566 1.1911 1.0457 0.7964 0.5984 0.4583 0.3826

1.7659 1.5561 1.3673 1.1984 1.0482 0.7995 0.6111 0.4730 0.3768

0.10 0.15 0.20 0.25 0.30 0.40 0.50 0.60 0.70

2.6792 2.3766 2.0958 1.8951 1.6577 1.2727 0.9988 0.8295 0.6954

2.6973 2.3663 2.0867 1.8540 1.6454 1.2903 1.0003 0.8158 0.6834

1.9701 1.7029 1.4910 1.3125 1.1551 0.8844 0.6681 0.5143 0.4310

1.9347 1.7058 1.5002 1.3166 1.1534 0.8838 0.6798 0.5308 0.4275

0.10 0.15 0.20 0.25 0.30 0.40 0.50 0.60 0.70

2.8289 2.5031 2.2230 1.9768 1.7545 1.4068 1.1120 0.8916 0.7734

2.9098 2.5313 2.2531 1.9944 1.7779 1.4094 1.1035 0.9060 0.7686

2.1428 1.8579 1.6315 1.4402 1.2711 0.9789 0.7440 0.5760 0.4847

2.1106 1.8622 1.6394 1.4407 1.2644 0.9736 0.7539 0.5938 0.4834

0.10 0.15 0.20 0.25 0.30 0.40 0.50 0.60 0.70

3.0964 2.7163 2.3775 2.1506 1.8911 1.5255 1.2035 0.9717 0.8588

3.1295 2.6935 2.4260 2.1346 1.9181 1.5386 1.2169 1.0005 0.8645

2.3194 2.0180 1.7777 1.5741 1.3937 1.0801 0.8264 0.6439 0.5445

2.2938 2.0256 1.7854 1.5714 1.3818 1.0694 0.8339 0.6625 0.5452

0.10 0.15 0.20 0.25 0.30 0.40 0.50 0.60 0.70

3.4385 2.8484 2.6547 2.2545 2.0993 1.6910 1.3526 1.1243 0.9709

3.3558 2.8519 2.6051 2.2738 2.0662 1.6786 1.3413 1.0991 0.9722

2.4994 2.1826 1.9294 1.7142 1.5228 1.1884 0.9158 0.7185 0.6109

2.4829 2.1950 1.9372 1.7080 1.5053 1.1711 0.9197 0.7373 0.6132

103xcal A (eq 6)

103xcal A (eq 11)

T = 308.15 2.6656 2.3898 2.1216 1.8717 1.6464 1.2767 1.0082 0.8219 0.6971 T = 313.15 2.8354 2.4951 2.2167 1.9780 1.7665 1.4020 1.1087 0.8947 0.7726 T = 318.15 3.1028 2.7017 2.3907 2.1331 1.9082 1.5196 1.2024 0.9734 0.8583 T = 323.15 3.4085 2.9224 2.5725 2.3007 2.0739 1.6896 1.3656 1.1154 0.9728

K 2.6686 2.3417 2.0797 1.8563 1.6566 1.3050 1.0153 0.8040 0.6891 K 2.8604 2.5189 2.2446 2.0100 1.7997 1.4274 1.1182 0.8914 0.7682 K 3.0593 2.7033 2.4168 2.1711 1.9501 1.5567 1.2278 0.9850 0.8533 K 3.2652 2.8949 2.5963 2.3395 2.1078 1.6933 1.3442 1.0851 0.9448

103xcal A (eq 15)

103xcal A (eq 16)

2.6819 2.3511 2.0860 1.8601 1.6584 1.3039 1.0125 0.8002 0.6845

2.6792 2.3711 2.0959 1.8511 1.6350 1.2793 1.0119 0.8185 0.6880

2.8662 2.5230 2.2474 2.0117 1.8005 1.4269 1.1169 0.8896 0.7661

2.8820 2.5540 2.2611 2.0011 1.7715 1.3939 1.1107 0.9066 0.7702

3.0514 2.6977 2.4130 2.1688 1.9490 1.5574 1.2296 0.9874 0.8563

3.0902 2.7427 2.4327 2.1573 1.9145 1.5154 1.2166 1.0020 0.8602

3.2370 2.8748 2.5826 2.3311 2.1038 1.6959 1.3508 1.0942 0.9559

3.3041 2.9384 2.6103 2.3206 2.0641 1.6439 1.3298 1.1052 0.9587

a 0 xB is the GABA free-base mole fraction of ethanol in the binary cal solvent mixture; xexp A is the experimentally determined solubility; xA cal cal cal (eq 3), xcal A (eq 6), xA (eq 11), xA (eq 15), and xA (eq 16) are the calculated solubility according to eqs 3, 6, 11, 15, and 16, respectively. b The standard uncertainty of T is u(T) = 0.1 K. The relative standard uncertainty of pressure is ur(P) = 0.05. The relative standard uncertainty of the solvent composition is ur(x0B) = 0.0050. The relative standard uncertainty of the solubility measurement is ur(x) = 0.03.

3.2.2. CNIBS/R-K Equation. To describe the solubility of the (3)

solute in the binary solvent system, the combined nearly ideal

where xA is the mole fraction solubility, A and B reflect the nonidealities of the real solution in term of the variation of activity coefficient in the solution, and C represents the effect of temperature on the fusion enthalpy.13

binary solvent/Redlich−Kister (CNIBS/R-K) equation was proposed,14 which relies on the solvent composition, as is presented in eq 4 1212

DOI: 10.1021/acs.jced.5b00829 J. Chem. Eng. Data 2016, 61, 1210−1220

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Table 3. Experimental (xexp) and Correlated (xcal) Mole Fraction Solubility Data of GABA in Binary Solvent Mixtures of 1Propanol + Methanol (p = 0.1 MPa)a,b x0B

103xexp A

103xcal A (eq 3)

0.10 0.15 0.20 0.25 0.30 0.40 0.50

1.7266 1.4251 1.1440 0.9644 0.8515 0.6311 0.5072

1.7266 1.4319 1.1720 0.9750 0.8667 0.6349 0.5194

0.10 0.15 0.20 0.25 0.30 0.40 0.50

1.8461 1.5330 1.3069 1.0681 0.9554 0.6962 0.5768

1.8552 1.5430 1.2770 1.0649 0.9468 0.6866 0.5628

0.10 0.15 0.20 0.25 0.30 0.40 0.50

2.0108 1.7026 1.4453 1.1926 1.0560 0.7406 0.6244

2.0009 1.6695 1.3933 1.1647 1.0345 0.7458 0.6091

0.10 0.15 0.20 0.25 0.30 0.40 0.50

2.1754 1.8264 1.5014 1.2774 1.1465 0.8109 0.6553

2.1657 1.8133 1.5218 1.2751 1.1305 0.8132 0.6585

0.10 0.15 0.20 0.25 0.30 0.40 0.50

2.3492 1.9578 1.6327 1.3893 1.2314 0.8987 0.7009

2.3517 1.9763 1.6639 1.3973 1.2355 0.8900 0.7111

103xcal A (eq 6)

103xcal A (eq 11)

T = 283.15 1.7354 1.4004 1.1583 0.9765 0.8357 0.6347 0.5067 T = 288.15 1.8485 1.5320 1.2909 1.0967 0.9362 0.6992 0.5764 T = 293.15 2.0163 1.6914 1.4383 1.2223 1.0328 0.7446 0.6238 T = 298.15 2.1885 1.7907 1.5183 1.3031 1.1172 0.8169 0.6545 T = 303.15 2.3569 1.9380 1.6404 1.4076 1.2129 0.9026 0.7004

K 1.6516 1.3734 1.1608 0.9898 0.8482 0.6333 0.5016 K 1.8236 1.5163 1.2810 1.0918 0.9350 0.6971 0.5507 K 2.0068 1.6684 1.4090 1.2002 1.0273 0.7647 0.6026 K 2.2012 1.8299 1.5448 1.3153 1.1251 0.8363 0.6575 K 2.4071 2.0009 1.6886 1.4370 1.2285 0.9119 0.7153

103xcal A (eq 15)

103xcal A (eq 16)

x0B

103xexp A

103xcal A (eq 3)

1.6952 1.4073 1.1874 1.0108 0.8648 0.6436 0.5080

1.6613 1.3846 1.1635 0.9860 0.8423 0.6281 0.4782

0.10 0.15 0.20 0.25 0.30 0.40 0.50

2.5764 2.1484 1.8093 1.5025 1.3297 0.9640 0.7637

2.5614 2.1608 1.8208 1.5326 1.3503 0.9773 0.7670

1.8332 1.5237 1.2869 1.0964 0.9387 0.6993 0.5521

1.8232 1.5211 1.2789 1.0845 0.9268 0.6918 0.5275

0.10 0.15 0.20 0.25 0.30 0.40 0.50

2.7410 2.3550 1.9881 1.6658 1.4309 1.0789 0.8239

2.7974 2.3696 1.9942 1.6822 1.4757 1.0764 0.8264

1.9891 1.6546 1.3982 1.1917 1.0205 0.7606 0.6000

1.9971 1.6679 1.4035 1.1907 1.0181 0.7606 0.5807

0.10 0.15 0.20 0.25 0.30 0.40 0.50

3.1018 2.6093 2.2020 1.8986 1.6450 1.1988 0.8807

3.0629 2.6057 2.1855 1.8476 1.6126 1.1891 0.8894

2.1649 1.8017 1.5226 1.2977 1.1113 0.8278 0.6522

2.1841 1.8262 1.5380 1.3054 1.1165 0.8347 0.6381

0.10 0.15 0.20 0.25 0.30 0.40 0.50

3.3601 2.8876 2.4045 2.0176 1.7756 1.3121 0.9701

3.3615 2.8725 2.3967 2.0305 1.7621 1.3170 0.9563

2.3631 1.9666 1.6616 1.4157 1.2118 0.9016 0.7089

2.3850 1.9965 1.6826 1.4288 1.2225 0.9145 0.6998

103xcal A (eq 6)

103xcal A (eq 11)

T = 308.15 2.5817 2.1384 1.8017 1.5315 1.3075 0.9679 0.7632 T = 313.15 2.7419 2.3538 1.9850 1.6734 1.4258 1.0798 0.8238 T = 318.15 3.1065 2.5953 2.2125 1.9027 1.6377 1.2006 0.8804 T = 323.15 3.3701 2.8613 2.4131 2.0443 1.7498 1.3174 0.9695

K 2.6247 2.1816 1.8405 1.5655 1.3377 0.9916 0.7760 K 2.8540 2.3720 2.0005 1.7008 1.4525 1.0754 0.8397 K 3.0952 2.5722 2.1687 1.8430 1.5731 1.1632 0.9065 K 3.3484 2.7824 2.3452 1.9921 1.6996 1.2552 0.9761

103xcal A (eq 15)

103xcal A (eq 16)

2.5861 2.1515 1.8168 1.5468 1.3230 0.9826 0.7704

2.6003 2.1791 1.8378 1.5616 1.3367 1.0004 0.7662

2.8370 2.3587 1.9900 1.6925 1.4460 1.0714 0.8373

2.8318 2.3752 2.0048 1.7043 1.4594 1.0928 0.8376

3.1191 2.5907 2.1832 1.8544 1.5821 1.1687 0.9099

3.0783 2.5853 2.1839 1.8573 1.5910 1.1920 0.9143

3.4362 2.8506 2.3987 2.0342 1.7326 1.2754 0.9885

3.3433 2.8106 2.3762 2.0221 1.7326 1.2986 0.9966

a 0 xB

is the GABA free-base mole fraction of 1-propanol in the binary cal solvent mixture; xexp A is the experimentally determined solubility; xA cal cal cal (eq 3), xcal (eq 6), x (eq 11), x (eq 15), and x (eq 16) are the A A A A calculated solubility according to eqs 3, 6, 11, 15, and 16, respectively. b The standard uncertainty of T is u(T) = 0.1 K. The relative standard uncertainty of pressure is ur(P) = 0.05. The relative standard uncertainty of the solvent composition is ur(x0B) = 0.0050. The relative standard uncertainty of the solubility measurement is ur(x) = 0.03.

N

ln xA = ln(xA )C + (ln(xA )B − ln(xA )C + S0 − S1 + S2)x B0

ln xA = x B0 ln(xA )B + xC0 ln(xA )C + x B0xC0 ∑ Si(x B0 − xC0)i

+ (− S0 + 3S1 − 5S2)(x B0)2 + (− 2S1 + 8S2)(x B0)3

i=0

(4)

+ (− 4S2)(x B0)4

where x0B is the GABA free-base mole fraction composition of

(5)

Introducing a constant term to eq 5, it can be further simplified as

ethanol, 1-propanol, or 2-propanol in the solvent mixture, and x0C is the GABA free-base mole fraction composition of methanol in

ln xA = B0 + B1x B0 + B2 (x B0)2 + B3(x B0)3 + B4 (x B0)4

the solvent mixture. xA is the mole fraction solubility of the solute

(6)

where B0, B1, B2, B3, and B4 are model constants. 3.2.3. Jouyban-Acree Models. Jouyban-Gharamaleki and his co-workers15 proposed the Jouyban-Acree model, which correlates the effect of both temperature and solvent composition on the solubility data. With acceptable deviation, it is perhaps one of the more versatile models. The model for representing the solubility of a drug in a binary mixture is

GABA. Si is the model constant and N refers to the number of “curve-fit” parameters. (xA)i is the saturated mole fraction solubility of the solute in monosolvent i. For binary solvent systems, the value of N is 2 and x0C = 1 − x0B. Substituting them into eq 4, a new equation can be obtained 1213

DOI: 10.1021/acs.jced.5b00829 J. Chem. Eng. Data 2016, 61, 1210−1220

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Table 4. Experimental (xexp) and Correlated (xcal) Mole Fraction Solubility Data of GABA in Binary Solvent Mixtures of 2Propanol + Methanol (p = 0.1 MPa)a,b x0B

103xexp A

103xcal A (eq 3)

0.10 0.15 0.20 0.25 0.30 0.40 0.50

1.4699 1.0989 0.8540 0.7013 0.5133 0.3599 0.2636

1.4438 1.0891 0.8568 0.6954 0.5108 0.3671 0.2619

0.10 0.15 0.20 0.25 0.30 0.40 0.50

1.5051 1.1729 0.9297 0.7428 0.5624 0.4131 0.2915

1.5495 1.1735 0.9235 0.7483 0.5599 0.4017 0.2928

0.10 0.15 0.20 0.25 0.30 0.40 0.50

1.6615 1.2462 0.9925 0.8071 0.6039 0.4508 0.3254

1.6653 1.2673 0.9999 0.8079 0.6158 0.4410 0.3264

0.10 0.15 0.20 0.25 0.30 0.40 0.50

1.8077 1.3654 1.0957 0.8680 0.6789 0.4736 0.3594

1.7919 1.3714 1.0870 0.8747 0.6794 0.4855 0.3628

0.10 0.15 0.20 0.25 0.30 0.40 0.50

1.9760 1.5004 1.1894 0.9500 0.7673 0.5339 0.4026

1.9303 1.4870 1.1861 0.9496 0.7518 0.5359 0.4021

103xcal A (eq 6)

103xcal A (eq 11)

T = 283.15 1.4618 1.1139 0.8580 0.6700 0.5319 0.3564 0.2640 T = 288.15 1.4962 1.1929 0.9244 0.7212 0.5785 0.4096 0.2919 T = 293.15 1.6483 1.2745 0.9850 0.7750 0.6269 0.4457 0.3260 T = 298.15 1.7994 1.3859 1.0831 0.8581 0.6898 0.4712 0.3597 T = 303.15 1.9730 1.5081 1.1839 0.9478 0.7707 0.5331 0.4027

K 1.4012 1.0797 0.8346 0.6538 0.5223 0.3562 0.2584 K 1.5279 1.1828 0.9186 0.7227 0.5798 0.3982 0.2905 K 1.6612 1.2918 1.0077 0.7963 0.6413 0.4434 0.3254 K 1.8010 1.4067 1.1021 0.8744 0.7070 0.4920 0.3630 K 1.9474 1.5275 1.2017 0.9573 0.7768 0.5440 0.4036

103xcal A (eq 15)

103xcal A (eq 16)

x0B

103xexp A

103xcal A (eq 3)

1.4379 1.1065 0.8542 0.6683 0.5333 0.3627 0.2624

1.4012 1.0785 0.8385 0.6595 0.5258 0.3501 0.2516

0.10 0.15 0.20 0.25 0.30 0.40 0.50

2.0620 1.6195 1.2804 1.0269 0.8154 0.5882 0.4500

2.0814 1.6152 1.2988 1.0335 0.8342 0.5929 0.4445

1.5359 1.1887 0.9228 0.7259 0.5822 0.3996 0.2914

1.5246 1.1776 0.9190 0.7258 0.5809 0.3900 0.2829

0.10 0.15 0.20 0.25 0.30 0.40 0.50

2.2166 1.7510 1.4504 1.1585 0.9466 0.6626 0.4958

2.2464 1.7572 1.4267 1.1274 0.9278 0.6574 0.4900

1.6467 1.2811 0.9998 0.7903 0.6368 0.4407 0.3237

1.6548 1.2834 1.0055 0.7972 0.6408 0.4339 0.3175

0.10 0.15 0.20 0.25 0.30 0.40 0.50

2.4477 1.9600 1.5504 1.2274 1.0400 0.7324 0.5302

2.4263 1.9145 1.5719 1.2324 1.0343 0.7305 0.5389

1.7715 1.3848 1.0858 0.8623 0.6977 0.4863 0.3595

1.7929 1.3960 1.0982 0.8743 0.7056 0.4820 0.3559

0.10 0.15 0.20 0.25 0.30 0.40 0.50

2.6182 2.0539 1.7473 1.3389 1.1444 0.8129 0.5929

2.6226 2.0887 1.7366 1.3498 1.1554 0.8131 0.5913

1.9120 1.5011 1.1821 0.9425 0.7655 0.5371 0.3992

1.9391 1.5160 1.1975 0.9574 0.7759 0.5346 0.3983

ln xA =

ln(xA )B +

xC0

ln(xA )C +

x B0xC0

∑ i=0

K 2.1003 1.6542 1.3067 1.0450 0.8510 0.5996 0.4471 K 2.2598 1.7869 1.4171 1.1375 0.9295 0.6588 0.4937 K 2.4258 1.9256 1.5329 1.2349 1.0124 0.7217 0.5435 K 2.5983 2.0702 1.6541 1.3372 1.0998 0.7884 0.5965

103xcal A (eq 16)

2.0696 1.6313 1.2895 1.0320 0.8410 0.5934 0.4432

2.0946 1.6440 1.3040 1.0469 0.8521 0.5922 0.4452

2.2464 1.7768 1.4095 1.1317 0.9250 0.6560 0.4920

2.2588 1.7802 1.4178 1.1431 0.9344 0.6552 0.4969

2.4443 1.9395 1.5434 1.2429 1.0186 0.7255 0.5460

2.4322 1.9249 1.5399 1.2469 1.0235 0.7239 0.5538

2.6658 2.1213 1.6927 1.3667 1.1227 0.8027 0.6058

2.6161 2.0795 1.6701 1.3584 1.1198 0.7990 0.6165

Substituting them into eq 7 and substituting x0C with (1 − x0B), a new equation (called the Van’t-JA equation) can be obtained

Ji (x B0 − xC0)i T

x0 B2 + (A1 − A 2 )x B0 + (B1 − B2 + J0 − J1 + J2 ) B T T (x B0)2 (x B0)3 + (− J0 + 3J1 − 5J2 ) + (− 2J1 + 8J2 ) T T 0 4 (x B) + (− 4J2 ) (10) T

ln xA = A 2 +

where Ji is the model constant and the other symbols represent the same meanings as eq 4. 3.2.3a. Van’t-JA Equation. When combining the van’t Hoff equation with the Jouyban-Acree model,16 (xA)B and (xA)C, the solubility of the solute in monosolvent, can be obtained from the former

ln(xA )C = A 2 +

T = 308.15 2.0582 1.6280 1.2794 1.0158 0.8238 0.5865 0.4502 T = 313.15 2.2096 1.7717 1.4296 1.1613 0.9511 0.6611 0.4960 T = 318.15 2.4529 1.9491 1.5482 1.2466 1.0250 0.7351 0.5298 T = 323.15 2.6068 2.0936 1.6861 1.3730 1.1356 0.8127 0.5930

103xcal A (eq 15)

is the GABA free-base mole fraction of 2-propanol in the binary cal solvent mixture; xexp A is the experimentally determined solubility; xA cal cal cal (eq 3), xcal (eq 6), x (eq 11), x (eq 15), and x (eq 16) are the A A A A calculated solubility according to eqs 3, 6, 11, 15, and 16, respectively. b The standard uncertainty of T is u(T) = 0.1 K. The relative standard uncertainty of pressure is ur(P) = 0.05. The relative standard uncertainty of the solvent composition is ur(x0B) = 0.0050. The relative standard uncertainty of the solubility measurement is ur(x) = 0.03.

(7)

ln(xA )B = A1 +

103xcal A (eq 11)

a 0 xB

2

x B0

103xcal A (eq 6)

B1 T

(8)

B2 T

(9)

Introducing a constant term to eq 10, it can be further simplified as x0 (x 0)2 (x 0)3 V2 + V3x B0 + V4 B + V5 B + V6 B T T T T (x B0)4 + V7 (11) T

ln xA = V1 +

1214

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Figure 4. Mole fraction solubility data of GABA in binary solvent of 2propanol + methanol at different temperatures: ■, 283.15 K; □, 288.15 K; ●, 293.15 K; ○, 298.15 K; ▲, 303.15 K; ▼, 308.15 K; ◆, 313.15 K; ◀, 318.15 K; ▶, 323.15 K; solid line, calculated data by the CNIBS/RK equation.

Figure 2. Mole fraction solubility data of GABA in binary solvent of ethanol + methanol at different temperatures: ■, 283.15 K; □, 288.15 K; ●, 293.15 K; ○, 298.15 K; ▲, 303.15 K; ▼, 308.15 K; ◆, 313.15 K; ◀, 318.15 K; ▶, 323.15 K; solid line, calculated data by the CNIBS/R-K equation.

Figure 5. Thermal analysis (TGA/DSC) of GABA.

b2 + c 2 ln T + (a1 − a 2)x B0 T x0 + (b1 − b2 + J0 − J1 + J2 ) B + ( − J0 + 3J1 − 5J2 ) T (x B0)2 T (x 0)3 (x 0)4 + ( − 2J1 + 8J2 ) B + ( − 4J2 ) B T T

ln xA = a 2 +

Figure 3. Mole fraction solubility data of GABA in binary solvent of 1propanol + methanol at different temperatures: ■, 283.15 K; □, 288.15 K; ●, 293.15 K; ○, 298.15 K; ▲, 303.15 K; ▼, 308.15 K; ◆, 313.15 K; ◀, 318.15 K; ▶, 323.15 K; solid line, calculated data by the CNIBS/RK equation.

where V1, V2, V3, V4, V5, V6, and V7 are model constants. 3.2.3b. Apel-JA Equation. For wider temperature ranges where nonlinear solubility behavior is observed, according to the modified Apelblat equation (xA)B and (xA)C can be expressed by ln(xA )B =

a1 + b1 + c1 ln T T

+ (c1 − c 2)x B0 ln T

(14)

This equation is also referred as a hybrid model.17,18 Introducing a constant term to eq 14, it can be further simplified as

(12) b2 + c 2 ln T + (a1 − a 2)x B0 T (x 0)2 x0 + (b1 − b2 + J0 − J1 + J2 ) B + (− J0 + 3J1 − 5J2 ) B T T (x B0)3 (x B0)4 0 + (− 2J1 + 8J2 ) + (− 4J2 ) + (c1 − c 2)x B ln T T T

ln xA = a 2 +

ln(xA )C =

a 2 + b2 + c 2 ln T T

(13)

Substituting them into eq 7 and substituting xC0 with (1-xB0), a new equation (called the Apel-JA equation) can be obtained:

(15) 1215

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Table 5. Mixing Thermodynamic Properties of GABA in Binary Solvent Mixtures of Ethanol + Methanol (p = 0.1 MPa)a,b x0B

ΔmixG kJ·mol−1

0.10 0.15 0.20 0.25 0.30 0.40 0.50 0.60 0.70

−1.5983 −2.1753 −2.6664 −3.0796 −3.4183 −3.8741 −4.0310 −3.8781 −3.4038

0.10 0.15 0.20 0.25 0.30 0.40 0.50 0.60 0.70

−1.5930 −2.1634 −2.6476 −3.0539 −3.3859 −3.8293 −3.9771 −3.8192 −3.3466

0.10 0.15 0.20 0.25 0.30 0.40 0.50 0.60 0.70

−1.5878 −2.1520 −2.6299 −3.0296 −3.3553 −3.7869 −3.9257 −3.7633 −3.2925

0.10 0.15 0.20 0.25 0.30 0.40 0.50 0.60 0.70

−1.5822 −2.1406 −2.6123 −3.0059 −3.3255 −3.7461 −3.8761 −3.7098 −3.2407

0.10 0.15 0.20 0.25 0.30 0.40 0.50

−1.5780 −2.1306 −2.5967 −2.9841 −3.2972 −3.7073 −3.8290

ΔmixH kJ·mol−1 T = 283.15 K 2.0078 2.8989 3.7175 4.4582 5.1146 6.1435 6.7366 6.8105 6.2641 T = 288.15 K 1.9877 2.8650 3.6687 4.3940 5.0348 6.0317 6.5960 6.6478 6.0942 T = 293.15 K 1.9678 2.8314 3.6210 4.3313 4.9567 5.9228 6.4588 6.4900 5.9303 T = 298.15 K 1.9472 2.7975 3.5731 4.2689 4.8794 5.8157 6.3243 6.3364 5.7711 T = 303.15 K 1.9281 2.7653 3.5274 4.2087 4.8037 5.7112 6.1934

ΔmixS J·mol−1·K−1

x0B

ΔmixG kJ·mol−1

12.7357 17.9202 22.5461 26.6210 30.1356 35.3791 38.0278 37.7490 34.1441

0.60 0.70

−3.6589 −3.1918

0.10 0.15 0.20 0.25 0.30 0.40 0.50 0.60 0.70

−1.5732 −2.1208 −2.5809 −2.9629 −3.2703 −3.6697 −3.7840 −3.6103 −3.1455

0.10 0.15 0.20 0.25 0.30 0.40 0.50 0.60 0.70

−1.5687 −2.1111 −2.5658 −2.9420 −3.2442 −3.6342 −3.7411 −3.5638 −3.1014

0.10 0.15 0.20 0.25 0.30 0.40 0.50 0.60 0.70

−1.5656 −2.1026 −2.5517 −2.9228 −3.2195 −3.6000 −3.7000 −3.5196 −3.0596

0.10 0.15 0.20 0.25 0.30 0.40 0.50 0.60 0.70

−1.5632 −2.0939 −2.5391 −2.9039 −3.1964 −3.5677 −3.6611 −3.4779 −3.0200

12.4264 17.4507 21.9202 25.8474 29.2233 34.2220 36.6929 36.3249 32.7635 12.1290 16.9996 21.3233 25.1099 28.3543 33.1219 35.4239 34.9762 31.4608 11.8376 16.5623 20.7460 24.3996 27.5194 32.0707 34.2121 33.6952 30.2255 11.5658 16.1502 20.2015 23.7271 26.7224 31.0687 33.0608

T = 303.15 K 6.1872 5.6174 T = 308.15 K 1.9082 2.7329 3.4812 4.1490 4.7296 5.6081 6.0657 6.0419 5.4687 T = 313.15 K 1.8886 2.7006 3.4358 4.0894 4.6563 5.5078 5.9411 5.9004 5.3245 T = 318.15 K 1.8707 2.6697 3.3913 4.0318 4.5846 5.4094 5.8192 5.7628 5.1848 T = 323.15 K 1.8540 2.6384 3.3490 3.9744 4.5150 5.3134 5.7006 5.6296 5.0497

ΔmixS J·mol−1·K−1 32.4793 29.0590 11.2979 15.7510 19.6726 23.0792 25.9608 30.1081 31.9641 31.3233 27.9546 11.0405 15.3653 19.1653 22.4539 25.2289 29.1935 30.9188 30.2227 26.9070 10.8006 15.0002 18.6799 21.8593 24.5297 28.3181 29.9204 29.1763 25.9136 10.5745 14.6442 18.2208 21.2851 23.8632 27.4829 28.9701 28.1836 24.9720

a 0 xB

is the GABA free-base mole fraction of ethanol in the binary solvent mixture; Δ mix G, Δ mix H, and Δ mix S are the mixing thermodynamic properties according to eqs 22, 23, and 24. bThe expanded uncertainties are U(ΔmixG) = 0.050ΔmixG, U(ΔmixH) = 0.060ΔmixH, and U(ΔmixS) = 0.065ΔmixS (0.95 level of confidence).

where A1, A2, A3, A4, A5, A6, A7, A8, and A9 are model constants. 3.2.4. NRTL Model. According to the solid−liquid phase equilibrium theory and the solute−solvent interactions, the local composition equation19 can be simplified and expressed by eq 16 Δ H⎛ 1 1⎞ ln xi = fus ⎜ − ⎟ − ln γi R ⎝ Tm T⎠

ΔmixH kJ·mol−1

ln γi =

(Gjixj + Gkjxk)(τjiGjixj + τkiGkixk) (xi + xjGj + xkGki)2 +

+

(16)

where ΔfusH and Tm stand for the enthalpy of fusion and melting temperature of solute. γi is the activity coefficient of solute in the saturated solution, which can be calculated by NRTL model

[τijGijx j2 + GijGkjxjxk(τij − τkj)] (xj + xiGij + xkGkj)2 [τikGijx j2 + GijGkjxjxk(τik − τjk)] (xk + xiGik + xjGjk )2

(17)

where Gij, Gik, Gji, Gjk, Gki, Gkj, τij,τik, τji, τjk, τki, and τkj are parameters of this model. The definition of these terms can be expressed as 1216

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Table 6. Mixing Thermodynamic Properties of GABA in Binary Solvent Mixtures of 1-Propanol + Methanol (p = 0.1 MPa)a,b x0B

ΔmixG kJ·mol−1

0.10 0.15 0.20 0.25 0.30 0.40 0.50

−0.9624 −1.2662 −1.4470 −1.5274 −1.5286 −1.3629 −1.0585

0.10 −0.9578 0.15 −1.2654 0.20 −1.4503 0.25 −1.5364 0.30 −1.5420 0.40 −1.3834 0.50 −1.0818 T = 293.15 K 0.10 −0.9521 0.15 −1.2632 0.20 −1.4530 0.25 −1.5439 0.30 −1.5541 0.40 −1.4027 0.50 −1.1039 0.10 0.15 0.20 0.25 0.30 0.40 0.50

−0.9461 −1.2610 −1.4558 −1.5508 −1.5651 −1.4202 −1.1248

0.10 0.15 0.20 0.25 0.30 0.40

−0.9397 −1.2580 −1.4569 −1.5563 −1.5750 −1.4362

ΔmixH kJ·mol−1 T = 283.15 K 1.2412 1.3407 1.2507 1.0466 0.7820 0.2103 0.2864 T = 288.15 K 1.2648 1.3809 1.3046 1.1133 0.8574 0.2946 0.2040 1.2866 1.4183 1.3567 1.1773 0.9304 0.3770 0.1232 T = 298.15 K 1.3074 1.4550 1.4083 1.2397 1.0011 0.4565 0.0441 T = 303.15 K 1.3271 1.4900 1.4566 1.2994 1.0696 0.5336

Gij = exp( −αijτij)

τij =

(gij − gjj) RT

=

ΔmixS J·mol−1·K−1

x0B

ΔmixG kJ·mol−1

7.7826 9.2067 9.5274 9.0905 8.1601 5.5560 4.7496

0.50

−1.1441

0.10 0.15 0.20 0.25 0.30 0.40 0.50

−0.9324 −1.2538 −1.4566 −1.5608 −1.5835 −1.4511 −1.1620

0.10 0.15 0.20 0.25 0.30 0.40 0.50

−0.9255 −1.2489 −1.4555 −1.5638 −1.5909 −1.4641 −1.1786

0.10 0.15 0.20 0.25 0.30 0.40 0.50

−0.9162 −1.2430 −1.4534 −1.5651 −1.5960 −1.4760 −1.1940

0.10 0.15 0.20 0.25 0.30 0.40 0.50

−0.9079 −1.2364 −1.4507 −1.5669 −1.6011 −1.4867 −1.2079

7.7132 9.1838 9.5605 9.1954 8.3268 5.8236 4.4621 7.6368 9.1474 9.5846 9.2825 8.4751 6.0709 4.1858 7.5584 9.1092 9.6062 9.3592 8.6071 6.2948 3.9203 7.4776 9.0647 9.6107 9.4201 8.7237 6.4977

T = 303.15 K 0.0330 T = 308.15 K 1.3451 1.5226 1.5024 1.3570 1.1357 0.6089 0.1079 T = 313.15 K 1.3633 1.5536 1.5464 1.4118 1.1996 0.6813 0.1810 T = 318.15 K 1.3776 1.5827 1.5883 1.4636 1.2596 0.7516 0.2525 T = 323.15 K 1.3929 1.6102 1.6288 1.5154 1.3191 0.8201 0.3218

ΔmixS J·mol−1·K−1 3.8828 7.3909 9.0098 9.6024 9.4688 8.8243 6.6850 4.1208 7.3090 8.9495 9.5864 9.5022 8.9112 6.8511 4.3417 7.2100 8.8815 9.5605 9.5197 8.9758 7.0016 4.5466 7.1198 8.8089 9.5298 9.5384 9.0367 7.1385 4.7337

a 0 xB is the GABA free-base mole fraction of 1-propanol in the binary solvent mixture; Δ mix G, Δ mix H, and Δ mix S are the mixing thermodynamic properties according to eqs 22, 23, and 24. bThe expanded uncertainties are U(ΔmixG) = 0.050ΔmixG, U(ΔmixH) = 0.060ΔmixH, and U(ΔmixS) = 0.065ΔmixS (0.95 level of confidence).

To test the applicability and accuracy of the models used in this paper, the relative deviation (RD) and the average relative deviation (ARD) are introduced by the following definitions

(18)

Δgij RT

ΔmixH kJ·mol−1

(19)

RD =

where Δgij represents the Gibbs energy of intermolecular interaction which are independent of the composition and temperature. αij is an adjustable empirical constant between 0 and 1 and is a criterion of the nonrandomness of the solution. These five models were employed to correlate the solubility data by matlab program that gave both the parameters in each model and the calculated solubility. To minimize the objective N cal exp function f = ∑i = 1|xexp A,i − xA,i| /xA,i , we used the optimization method, “nlinfit”, a nonlinear nonweighted least-squares regression in this paper. The calculated mole fraction solubility data xcal A of these five models are also listed in Tables 2, 3, and 4. The model parameters of eqs 3, 6, 11, 15, and 16 are listed in the Supporting Information, Tables S1, S2, S3, S4, and S5.

exp cal xA, i − xA , i

ARD =

exp xA, i

1 N

N

∑ i=1

(20) exp cal xA, i − xA, i exp xA, i

(21)

cal where xexp A,i and xA,i are the experimental solubility values and calculated solubility values respectively and N refers to the numbers of experimental points. The obtained ARD values for all models are also showed in the Supporting Information, Tables S1, S2, S3, S4, and S5. As shown in Tables S1, S2, S3, S4, and S5, it can be seen that the overall ARD% for the modified Apelblat equation, the CNIBS/R-K equation, two modified versions of Jouyban-Acree models (the van’t-JA equation and the Apel-JA equation), and

1217

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Table 7. Mixing Thermodynamic Properties of GABA in Binary Solvent Mixtures of 2-Propanol + Methanol (p = 0.1 MPa)a,b x0B

ΔmixG kJ·mol−1

0.10 0.15 0.20 0.25 0.30 0.40 0.50

−1.1657 −1.8006 −2.4048 −2.9695 −3.4912 −4.3837 −5.0497

0.10 0.15 0.20 0.25 0.30 0.40 0.50

−1.1821 −1.8267 −2.4413 −3.0167 −3.5480 −4.4573 −5.1355

0.10 0.15 0.20 0.25 0.30 0.40 0.50

−1.1967 −1.8525 −2.4774 −3.0628 −3.6039 −4.5297 −5.2193

0.10 0.15 0.20 0.25 0.30 0.40 0.50

−1.2112 −1.8772 −2.5123 −3.1081 −3.6583 −4.6009 −5.3011

0.10 0.15 0.20 0.25 0.30 0.40

−1.2252 −1.9013 −2.5468 −3.1524 −3.7114 −4.6700

ΔmixH kJ·mol−1 T = 283.15 K 0.2754 0.3438 0.3687 0.3631 0.3405 0.2825 0.2823 T = 288.15 K 0.2898 0.3666 0.4016 0.4073 0.3961 0.3630 0.3896 T = 293.15 K 0.3027 0.3902 0.4354 0.4521 0.4529 0.4449 0.4976 T = 298.15 K 0.3163 0.4136 0.4694 0.4979 0.5101 0.5279 0.6061 T = 303.15 K 0.3300 0.4374 0.5043 0.5440 0.5680 0.6110

ΔmixS J·mol−1·K−1

x0B

ΔmixG kJ·mol−1

5.0895 7.5732 9.7953 11.7700 13.5324 16.4794 18.8312

0.50

−5.3809

0.10 0.15 0.20 0.25 0.30 0.40 0.50

−1.2400 −1.9252 −2.5808 −3.1959 −3.7642 −4.7378 −5.4587

0.10 0.15 0.20 0.25 0.30 0.40 0.50

−1.2537 −1.9486 −2.6131 −3.2378 −3.8148 −4.8038 −5.5346

0.10 0.15 0.20 0.25 0.30 0.40 0.50

−1.2664 −1.9707 −2.6457 −3.2799 −3.8649 −4.8685 −5.6089

0.10 0.15 0.20 0.25 0.30 0.40 0.50

−1.2795 −1.9937 −2.6765 −3.3205 −3.9139 −4.9316 −5.6810

5.1082 7.6118 9.8659 11.8830 13.6877 16.7285 19.1745 5.1149 7.6501 9.9363 11.9902 13.8387 16.9694 19.5014 5.1233 7.6834 10.0009 12.0946 13.9809 17.2018 19.8128 5.1301 7.7147 10.0647 12.1933 14.1165 17.4204

ΔmixH kJ·mol−1 T = 303.15 K 0.7149 T = 308.15 K 0.3454 0.4620 0.5398 0.5910 0.6271 0.6948 0.8238 T = 313.15 K 0.3601 0.4869 0.5747 0.6377 0.6856 0.7788 0.9329 T = 318.15 K 0.3739 0.5110 0.6111 0.6859 0.7452 0.8633 1.0420 T = 323.15 K 0.3891 0.5373 0.6466 0.7339 0.8051 0.9478 1.1506

ΔmixS J·mol−1·K−1 20.1080 5.1450 7.7470 10.1269 12.2889 14.2506 17.6297 20.3878 5.1536 7.7774 10.1797 12.3759 14.3714 17.8274 20.6530 5.1557 7.8002 10.2368 12.4649 14.4904 18.0159 20.9050 5.1634 7.8322 10.2835 12.5464 14.6030 18.1940 21.1405

a 0 xB is the GABA free-base mole fraction of 2-propanol in the binary solvent mixture; Δ mix G, Δ mix H, and Δ mix S are the mixing thermodynamic properties according to eq 22, 23 and 24. bThe expanded uncertainties are U(ΔmixG) = 0.050ΔmixG, U(ΔmixH) = 0.060ΔmixH, and U(ΔmixS) = 0.065ΔmixS (0.95 level of confidence).

NRTL model are 1.25, 0.82, 1.71, 1.64, and 1.74, respectively, for binary ethanol + methanol solvent mixtures. For binary 1propanol + methanol solvent mixtures, the overall ARD% for corresponding equation are 1.10, 0.76, 2.05, 1.66, and 2.03, respectively. Also, for binary 2-propanol + methanol solvent mixtures the overall ARD% for the corresponding equation are 1.02, 1.00, 1.93, 1.62 and 2.01, respectively. These results indicate that solubility data of GABA in binary solvent mixtures were well correlated by these five models and the CNIBS/R-K model showed the best correlation results for these three binary solvent mixtures. The Apelblat equation represented temperature effect, and the CNIBS/R-K equation expressed the change of the solubility with the changing of solvent composition. As a function of both temperature and solvent composition, the two modified versions of Jouyban-Acree models still showed good correlation results with satisfactory accuracy. 3.3. Solution Mixing Thermodynamics. 3.3.1. Evaluation of Melting Point and Enthalpy of Fusion. The thermal analysis (TGA/DSC) of GABA is presented in Figure 5. It can be seen that the samples decompose before showing a melting

characteristic. Therefore, the melting temperature of GABA cannot be obtained by this conventional calorimetric method. But as fundamental and basic data, melting temperature and enthalpy of fusion are necessary for several thermodynamic models. So we used the group contribution method20 to estimate the melting temperature Tm and the enthalpy of fusion ΔfusH. The estimation method we used is performed at three levels. The primary level used contributions from simple groups that allowed describing a wide variety of organic compounds, while the higher levels involved polyfunctional and structural groups that provide more information about molecular fragments whose description through first-order groups was not possible. In this study, the melting temperature and enthalpy of fusion of GABA estimated by this method were 478.49 K (the expanded uncertainty is U = 0.5 K with 0.95 level of confidence) and 29.45 kJ·mol−1 (the expanded uncertainty is U = 1.55 kJ·mol−1 with 0.95 level of confidence), respectively. It is worthwhile to mention that the results were only used for prediction but not as a result of the real physical properties of GABA. Therefore, 1218

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spontaneous. Also, the positive values of mixing enthalpy demonstrate an endothermic process. On the basis of the above results, the experimental solubility data and equations presented in this study can be used to optimize the practical crystallization conditions of GABA.

different results could be obtained in other experimental observations. 3.3.2. Solution Mixing Thermodynamics. For a nonideal solution, it is necessary to study the mixing thermodynamic properties of the solute in different binary solvent mixtures, such as the mixing enthalpy (ΔmixH), the mixing Gibbs energy (ΔmixG), and the mixing entropy(ΔmixS). On the basis of per mole solution, the mixing properties can be calculated by the following equations21 Δmix M = Δmix M id + ME

■

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.5b00829.

(22)

where M can be replaced by G, H, and S. ΔmixMid is the mixing properties of ideal systems and ME is the excess properties. For the ideal solution, ΔmixHid = 0. The mixing thermodynamic properties of this nonideal solution can be calculated by the following equations21,22 i

■

n

(23)

⎛ ∂ ln γi ⎞ Δmix H = −RT 2 ∑ xi⎜ ⎟ ⎝ ∂T ⎠ p, x n

(24)

n

Calculated parameters for different models. (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: 86-22-27405754. Fax: +86-22-27374971.

i

Δmix G = RT ∑ xi ln xi + RT ∑ xi ln γi

ASSOCIATED CONTENT

Funding

We are grateful for the financial support of the National Natural Science Foundation of China (No. NNSFC 21176173), and the National High Technology Research and Development Program (863 Program No.2012AA021202).

i

Notes

Δ H − Δmix G Δmix S = mix T

The authors declare no competing financial interest.

■

(25)

where xi and γi are the mole fraction and activity coefficient of component i in real solution, respectively. γi is calculated by the given NRTL model. The calculated mixing thermodynamic properties in the three binary mixtures are given in Tables 5, 6, and 7. As shown in these tables, it can be found that the values of ΔmixG are all negative, which indicates that the mixing of GABA in all investigated solvents is a spontaneous and favorable process. The positive ΔmixH illustrates that the mixing processes is endothermic, which can explain the reason why the solubility increase with the increasing temperature in the binary solvent mixture with a confirmed solvent composition.23 Briefly, these results are helpful for the optimization of the mixing and crystallization processes of GABA.

REFERENCES

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