Measurement and Correlation of the Solubility of Tetramethylpyrazine

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

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Measurement and Correlation of the Solubility of Tetramethylpyrazine in Nine Monosolvents and Two Binary Solvent Systems Nuoyang Zhang,†,‡,§ Si Li,†,‡,§ Haiyan Yang,†,‡,§ Mengya Li,†,‡,§ Yang Yang,†,‡,§ and Weiwei Tang*,†,‡,§

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†

School of Chemical Engineering and Technology, State Key Laboratory of Chemical Engineering, Tianjin University, Tianjin 300072, China ‡ Collaborative Innovation Center of Chemistry Science and Engineering, Tianjin 300072, China § Key Laboratory for Modern Drug Delivery and High Efficiency, Tianjin University, Tianjin, China S Supporting Information *

ABSTRACT: The solubility of tetramethylpyrazine (TMP) in nine monosolvents (methanol, ethanol, n-propanol, isopropanol, n-butanol, acetone, acetonitrile, methyl acetate, and ethyl acetate) and two binary solvent mixtures of (methanol + acetonitrile) and (n-butanol + acetonitrile) was determined by a static method using UV−vis spectroscopy at temperatures ranging from 273.15 to 313.15 K. Expectedly, the solubility displays monotonously rising temperature dependence, and the most remarkable change was found in acetonitrile. In binary solvent mixtures, TMP solubility bears a maximum value at 0.8 mole fraction of alcohols independent of both temperature and solvent nature. The statistical correlations were well performed by the λh equation, Apelblat equation, and NRTL model, and the NRTL model achieves the best fitting results. The mixing enthalpy, entropy, and Gibbs free energy were derived on the basis of thermodynamic relations and the NRTL model. The results suggest a spontaneous and entropy-driven mixing process of TMP in studied solvent systems. The solubility data, correlated models, and derived thermodynamic functions provide thermodynamic fundamentals for the separation and purification of TMP crystallization in industrial production.

1. INTRODUCTION Tetramethylpyrazine (TMP, C8H12N2, CAS Registration No. 1124-11-4, Figure 1) is a biologically active alkaloid, which was isolated from the traditional Chinese herb called Ligusticum wallichii.1,2 TMP has a pleasant flavor of roasting, peanuts, and cocoa.1,3,4 It was found in lots of natural and fermentation products such as potato, wheaten bread, beef, cheese, whiskey, and Chinese liquor.5−7 TMP has long been a favorite as a widely used food additive;8,9 nevertheless, it gathered more focus on healing power. TMP has been identified to have significant physiological activity on cardiovascular and cerebrovascular diseases by enhancing the microcirculation of the brain, restraining the formation of thrombus and reducing the aggregation of platelets.10−13 Recently, TMP was also reported to have a positive influence on kidney injury.14,15 Additionally, TMP as precursors could be used to synthesize several other © XXXX American Chemical Society

Figure 1. Chemical structure of tetramethylpyrazine (TMP).

valuable biological materials.16 In spite of more and more attention being paid on the physical and chemical properties of Received: October 4, 2018 Accepted: February 1, 2019

A

DOI: 10.1021/acs.jced.8b00888 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Detailed Information of the Chemicals Used in This Work chemical name

CAS

source

mass fraction purity

analysis method

tetramethylpyrazine benzoic acid methanol ethanol n-propanol isopropanol n-butanol methyl acetate ethyl acetate acetonitrile acetone

1124-11-4 65-85-0 67-56-1 64-17-5 71-23-8 67-63-0 71-36-3 79-20-9 141-78-6 75-05-8 67-64-1

Shanghai Titan Technology Co., Ltd. TCI (Shanghai) Development Co., Ltd. Tianjin Kemiou Chemical Reagent Co., Ltd. Tianjin Kemiou Chemical Reagent Co., Ltd. Tianjin Kemiou Chemical Reagent Co., Ltd. Tianjin Kemiou Chemical Reagent Co., Ltd. Tianjin Kemiou Chemical Reagent Co., Ltd. Tianjin Kemiou Chemical Reagent Co., Ltd. Tianjin Kemiou Chemical Reagent Co., Ltd. Tianjin Kemiou Chemical Reagent Co., Ltd. Tianjin Kemiou Chemical Reagent Co., Ltd.

≥0.990 ≥0.990 ≥0.995 ≥0.995 ≥0.995 ≥0.995 ≥0.995 ≥0.995 ≥0.995 ≥0.995 ≥0.995

HPLCa GCb GCb GCb GCb GCb GCb GCb GCb GCb GCb

a

High performance liquid chromatograph. bGas chromatograph.

Figure 2. Typical standard curve of absorbance versus solution concentration (mg·mL−1) for concentration determination at 210 nm by UV−vis spectroscopy.

Figure 3. PXRD patterns of TMP raw material and excess slurry crystals.

TMP, some problems such as low purity and low yield in industrial production are urgently needed to be resolved.1,17 Solution crystallization is one of the most effective ways to acquire high-quality APIs (active pharmaceutical ingredients), but the critical quality attributes such as crystal structure, size, and size distribution of harvested crystals are mainly affected by the operation parameters of the crystallization process. Better control and optimization of the crystallization process need a fundamental understanding of the solution thermodynamics and solid−liquid phase equilibrium of TMP in a selected solvent system.18 Solvent selection based on the equilibrium solubility data of TMP is also an essential step for the design of appropriate crystallization pathways from solution. Design, control, and optimization of the crystallization process are dependent on solubility data and related solution thermodynamic properties of TMP. Few available literature reported the solubility of TMP in buffer solution and supercritical carbon dioxide at several temperatures or pressure points.13,19 However, these limited data could not meet the requirements of solvent selection for crystallization and the development of the crystallization technique. Therefore, a thorough investigation of the solubility of TMP in different solvent systems is desirable and important. Here, the solubility of TMP was determined in nine solvents (methanol, ethanol, propanol, isopropanol, n-butanol, acetone, acetonitrile, methyl acetate, and ethyl acetate) and two binary solvent mixtures (methanol + acetonitrile, n-butanol + acetonitrile) at temperatures ranging from 273.15 to 313.15 K using the UV-spectroscopic method.20−23 The solubility behaviors of TMP in both pure and binary mixed solvents were investigated. The solubility profile was then correlated by the λh equation,

Figure 4. DSC curve of TMP.

Apelblat equation, and NRTL model. Finally, thermodynamic functions (enthalpy, entropy, and Gibbs free energy change) of the mixing process were derived and discussed.

2. MATERIALS AND METHODS 2.1. Material. Tetramethylpyrazine and benzoic acid were respectively purchased from ShangHai Titan Technology Co., Ltd., and TCI (Shanghai) Development Co., Ltd., both with a purity of ≥99.0% (mass percentage). All solvents including methanol, ethanol, propanol, isopropanol, n-butanol, acetone, acetonitrile, methyl acetate, and ethyl acetate are of analytical grade (≥99.5%) purchased from Tianjin Kemiou Chemical Reagent Co., Ltd. All chemicals were used as received without further purifications. Detailed information about the utilized materials was tabulated and presented in Table 1. B



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cal Table 2. Experimental (xexp 1 ) and Calculated (x1 ) Mole Fraction Solubility of TMP in Nine Monosolvents at Temperatures Ranging from 273.15 to 313.15 K (P = 0.1 MPa)a

solvent

10xexp 1

methanol ethanol n-propanol isopropanol n-butanol methyl acetate ethyl acetate acetonitrile acetone

1.1060 0.6442 1.0232 0.5336 1.0560 0.7577 0.9584 0.2792 0.4589


1.1922 0.7746 1.1411 0.7020 1.2621 0.9396 1.1340 0.3399 0.5918


1.4257 0.9112 1.3787 0.8138 1.5206 1.1179 1.3560 0.4046 0.7123


1.6166 1.0979 1.5812 0.9975 1.7481 1.3327 1.5950 0.5034 0.8695

methanol ethanol n-propanol isopropanol n-butanol

1.9381 1.2844 1.8534 1.1513 2.0544

Apelblat, 10xcal 1 T = 273.15 K 1.0730 0.6409 1.0155 0.5522 1.0630 0.7632 0.9672 0.2834 0.4600 T = 278.15 K 1.2352 0.7704 1.1701 0.6700 1.2665 0.9273 1.1376 0.3362 0.5792 T = 283.15 K 1.4248 0.9231 1.3538 0.8106 1.4955 1.1171 1.3349 0.4033 0.7203 T = 288.15 K 1.6465 1.1025 1.5721 0.9779 1.7510 1.3346 1.5629 0.4886 0.8855 T = 293.15 K 1.9057 1.3130 1.8318 1.1766 2.0339

λh, 10xcal 1

NRTL, 10xcal 1

solvent

10xexp 1

1.0459 0.6360 0.9817 0.5469 1.0755 0.7701 0.9564 0.2681 0.4704

1.0591 0.6477 0.9959 0.5551 1.0814 0.7792 0.9666 0.2769 0.4784

methyl acetate ethyl acetate acetonitrile acetone

1.5561 1.8080 0.5875 1.0589

1.2296 0.7696 1.1640 0.6695 1.2685 0.9287 1.1361 0.3333 0.5814

1.2256 0.7731 1.1617 0.6784 1.2685 0.9326 1.1375 0.3369 0.5855


2.2208 1.6160 2.1261 1.4234 2.3543 1.8947 2.1210 0.7429 1.3234

1.4382 0.9260 1.3723 0.8145 1.4877 1.1129 1.3417 0.4120 0.7140

1.4313 0.9176 1.3674 0.8081 1.4868 1.1071 1.3384 0.4076 0.7066


2.6223 1.8640 2.4466 1.6554 2.6180 2.1592 2.4400 0.8882 1.5632

1.6741 1.1083 1.6092 0.9851 1.7357 1.3260 1.5760 0.5069 0.8715

1.6559 1.0939 1.5928 0.9751 1.7271 1.3137 1.5681 0.4986 0.8565


2.9622 2.1625 2.9971 1.9630 3.0180 2.5429 2.8420 1.1450 1.8513

1.9400 1.3198 1.8776 1.1851 2.0149

1.9286 1.2947 1.8592 1.1577 2.0095


3.4215 2.5530 3.4745 2.4890 3.5143 2.9107 3.3980 1.4740 2.0924

Apelblat, 10xcal 1 T = 293.15 K 1.5823 1.8260 0.5976 1.0766 T = 298.15 K 2.2087 1.5590 2.1409 1.4119 2.3447 1.8623 2.1289 0.7371 1.2955 T = 303.15 K 2.5631 1.8460 2.5091 1.6898 2.6839 2.1768 2.4769 0.9165 1.5437 T = 308.15 K 2.9776 2.1799 2.9480 2.0174 3.0514 2.5277 2.8761 1.1478 1.8226 T = 313.15 K 3.4622 2.5675 3.4715 2.4027 3.4473 2.9171 3.3332 1.4472 2.1330

λh, 10xcal 1

NRTL, 10xcal 1

1.5711 1.8418 0.6208 1.0577

1.5498 1.8205 0.5998 1.0394

2.2388 1.5648 2.1804 1.4189 2.3280 1.8521 2.1423 0.7578 1.2773

2.2264 1.5655 2.1572 1.4045 2.3231 1.8491 2.1251 0.7416 1.2770

2.5736 1.8476 2.5207 1.6911 2.6779 2.1727 2.4806 0.9224 1.5352

2.5826 1.8468 2.5004 1.6717 2.6627 2.1633 2.4664 0.9024 1.5400

2.9478 2.1735 2.9020 2.0075 3.0675 2.5373 2.8602 1.1205 1.8376

2.9643 2.1818 2.9424 2.0050 3.0690 2.5550 2.8682 1.1396 1.8608

3.3652 2.5484 3.3279 2.3745 3.4999 2.9506 3.2848 1.3597 2.1913

3.4157 2.5952 3.4115 2.4804 3.5406 2.9858 3.3581 1.4545 2.2009

a exp x1 is the experimental solubility; xcal 1 is the calculated solubility by the Apelblat model, the λh model, and the NRTL model. The standard uncertainty of T is u(T) = 0.1 K. The relative standard uncertainty of the solubility is ur(x) = 0.05. The relative uncertainty of pressure is ur(P) = 0.05.

2.2. Solid-State Characterization Methods. The X-ray powder diffractometer (XRPD) was applied to analyze the solidstate structure of tetramethylpyrazine. The structural characterization of raw material and excess slurry solid of the solid−liquid equilibrium in the solvent was carried out on a Rigaku D/max2500 instrument (Rigaku, Japan) in the 2θ range of 2−40° with a scanning rate of 8°/min using Cu Kα radiation (0.15405 nm). A differential scanning calorimeter (DSC 1/500, Mettler Toledo, Switzerland) with zinc and indium as the calibration

substances was used to measure the melting temperature (Tm) and enthalpy of fusion (ΔfusH) of TMP under a nitrogen atmosphere. A 5−10 mg portion of TMP sample was heated from 298.15 to 373.15 K with a heating rate of 10 K/min. 2.3. Solubility Measurements. The solubility of TMP in nine monosolvents and two binary mixed solvents was measured at temperatures ranging from 278.15 to 318.15 K using the UV-spectroscopic method. Excess TMP was added into 30 mL screw capped vials containing 5 mL solvents being magnetically C



Article

stirred (1000 rpm) for more than 12 h to reach the equilibrium state. The samples were kept at the desired temperature controlled by an external water circulator (CF41, Julabo Technology Co., LTD) for more than 12 h to reach the solid−liquid equilibrium. Then, the suspension was standing still for at least 2 h to get the upper clear saturated solution. Then, the supernatant filtered by an organic membrane (pore size 0.45 μm) was transferred into a volumetric flask. The solution was further diluted into proper concentration for concentration measurements by UV−vis spectroscopy (UV-3010 spectrophotometer, HITACHI, Japan). The absorbance of TMP solution was recorded at 210 nm. Before solubility measurements, six samples at known concentrations were prepared to obtain a set of standards for constructing a standard curve for quantitative concentration analysis. The following equations were used to determine the mole fraction solubility of TMP m=

x=

A−b ×V k m M m M

+

ms Ms

Figure 5. Experimental solubility data of TMP in monosolvents at different temperatures from 273.15 to 313.15 K (p = 0.1 MPa). 1 − xc zyz 1 zyz ji ji 1 zz = λhjjj − lnjjj1 + λ zz j z j z x T T c m{ k k {

(1)

in which Tm is the melting temperature and λ and h are constants of the equation. 3.3. The Nonrandom Two-Liquid (NRTL) Model. The equilibrium solubility on the basis of thermodynamic relations of solid−liquid equilibrium can be expressed by the following simplified equation27−29

(2)

where A is the absorbance of the diluent, V refers to the volume of the diluent, and k and b are the slope and the intercept of the calibration curve, respectively. m and ms stand for the mass of TMP and solvent, respectively. M and Ms are the m of TMP and solvent, respectively. Ms, when it is applied for a binary solvent mixture, represents the molecular weight of mixed solvent and is computed by Ms = MA xA + MBx B

(5)

ln xc =

ΔfusH jij 1 1 zy − zzz − ln γc jj R jk Tm T z{

(6)

where R is the gas constant, ΔfusH denotes the enthalpy of fusion, and γc is the activity coefficient of the solute in the saturated solution which could be derived from activity coefficient models, for example, the NRTL model. The NRTL model was commonly applied to determine thermodynamic activities and solubility. Here, for a binary solvent mixture system, a simplified form by Renon and Prausnitz was given as follows

(3)

in which xA and MA represent the mole fraction and molar mass of solvent A and xB and MB, for solvent B. The typical calibration curve for quantitative concentration analysis was illustrated in Figure 2 for TMP solution in ethanol. The linear calibration curve of absorbance as a function of concentration was obtained with correlation coefficient R2 = 0.9991.

ln γi = (Gjixj + τjiGijxj − τkiGkixk)/(xi + xjGij + xkGik)2 + [τjiGijxj 2 + GijGkjxjxk(τij − τkj)] /(xj + xiGij + xkGkj)2

3. THERMODYNAMIC MODELS Solubility profiles, as necessary and fundamental data, are important in the design, optimization, and control of the crystallization process. To extend the application of the determined solubility data, the experimental data were correlated by the λh equation, Apelblat equation, and NRTL model. Further, thermodynamic functions of the mixing process were derived to understand thermodynamic behaviors of solution. 3.1. Apelblat Equation. Deriving from the Clausius− Clapeyron equation, the Apelblat equation was widely used to describe the effect of temperature on the solubility in monosolvents and binary mixed solvents.24,25 The equation is expressed by B ln xc = A + + C ln T (4) T where xc stands for the mole fraction solubility of TMP and T refers to the corresponding temperature. As the equation constants, A and B indicate the nonidealities of the real solution by the variation of the activity coefficient in the solution and C reflects how the fusion enthalpy was affected by the temperature. 3.2. λh Model. The λh model, a semiempirical equation, relates the mole fraction solubility with temperature by26

+ [τikGik xk 2 + Gik Gjkxjxk(τik − τjk)] /(xk + xiGik + xjGjk)2 (7)

where Gji, Gij, Gkj, Gjk, Gki, Gik, τji, τij, τik, τki, τjk, and τkj are the parameters of the NRTL model and are defined as Gij = exp(− αijτij)

(8)

τij = (gij − gjj)/RT = Δgij /RT

(9)

i , j = 1, 2, 3

αij = αji ,

(10)

in which Δgij stands for the Gibbs free energy of intermolecular interactions, αij represents an empirical constant between 0 and 1, and τ indicates the nonrandomness of the mixture. To assess the applicability of thermodynamic models, the average relative deviation (ARD) and the root-mean-square deviation (RMSD) are calculated as follows. ARD =

1 N

N

xiexp − xical

∑

xical

i=1

(11)

N

RMSD = D

∑i = 1 (xical − xiexp)2 N

(12) DOI: 10.1021/acs.jced.8b00888 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


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cal Table 3. Experimental (xexp 1 ) and Calculated (x1 ) Mole Fraction Solubility of TMP in Methanol (x2) + Acetonitrile (1 − x2) at Temperatures Ranging from 273.15 to 313.15 K (p = 0.1 MPa)a

x2

10xexp 1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.4128 0.5697 0.7063 0.8658 0.9708 1.0640 1.1450 1.1610 1.1500

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.4952 0.6902 0.8388 1.0052 1.1232 1.2129 1.2590 1.2895 1.2726

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.6110 0.8079 0.9976 1.1702 1.3407 1.4415 1.4937 1.5371 1.5286

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.7438 0.9500 1.1607 1.3600 1.5142 1.6330 1.7037 1.7304 1.6864

0.1 0.2 0.3 0.4 0.5

0.8982 1.1360 1.3934 1.6042 1.8056

Apelblat, 10xcal 1 T = 273.15 0.4117 0.5749 0.7080 0.8690 0.9746 1.0664 1.1323 1.1509 1.1370 T = 278.15 0.5010 0.6810 0.8389 1.0062 1.1327 1.2275 1.2904 1.3157 1.3000 T = 283.15 0.6084 0.8068 0.9914 1.1668 1.3147 1.4155 1.4787 1.5116 1.4933 T = 288.15 0.7374 0.9560 1.1689 1.3549 1.5237 1.6347 1.7029 1.7447 1.7227 T = 293.15 0.8920 1.1326 1.3750 1.5750 1.7635

λh, 10xcal 1

NRTL, 10xcal 1

x2

10xexp 1

0.4078 0.5669 0.7039 0.8532 0.9661 1.0434 1.0899 1.1073 1.0959

0.4193 0.5699 0.7108 0.8442 0.9560 1.0488 1.1179 1.1534 1.1527

0.6 0.7 0.8 0.9

1.9228 1.9933 2.0398 2.0088

0.5006 0.6800 0.8386 1.0039 1.1318 1.2240 1.2825 1.3073 1.2918

0.5027 0.6798 0.8397 0.9898 1.1160 1.2182 1.2905 1.3308 1.3291

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1.0715 1.3398 1.5895 1.7947 1.9989 2.1765 2.2930 2.3178 2.2772

0.6111 0.8118 0.9942 1.1761 1.3200 1.4288 1.5010 1.5344 1.5143

0.6064 0.8051 0.9915 1.1590 1.3061 1.4188 1.4973 1.5415 1.5396

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1.3105 1.6159 1.9328 2.1552 2.3548 2.5139 2.6812 2.8279 2.8191

0.7423 0.9653 1.1737 1.3725 1.5335 1.6603 1.7478 1.7910 1.7656

0.7305 0.9538 1.1650 1.3548 1.5130 1.6385 1.7256 1.7705 1.7634

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1.5063 1.8178 2.1454 2.4270 2.6491 2.8572 3.0375 3.1495 3.1315

0.8976 1.1435 1.3802 1.5960 1.7748

0.8799 1.1354 1.3789 1.5878 1.7677

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1.9158 2.2699 2.6133 2.9522 3.1877 3.5072 3.7332 3.8041 3.6821

K

K

K

K

K

Apelblat, 10xcal 1 T = 293.15 1.8903 1.9703 2.0223 1.9952 T = 298.15 1.0768 1.3416 1.6137 1.8326 2.0383 2.1884 2.2892 2.3531 2.3189 T = 303.15 1.2974 1.5889 1.8898 2.1341 2.3526 2.5361 2.6701 2.7476 2.7039 T = 308.15 1.5602 1.8811 2.2083 2.4869 2.7118 2.9415 3.1252 3.2186 3.1622 T = 313.15 1.8727 2.2262 2.5751 2.8997 3.1215 3.4141 3.6698 3.7812 3.7081

λh, 10xcal 1

NRTL, 10xcal 1

1.9212 2.0254 2.0795 2.0483

1.9006 1.9922 2.0413 2.0340

1.0811 1.3505 1.6176 1.8502 2.0473 2.2145 2.3365 2.4024 2.3649

1.0579 1.3480 1.6115 1.8370 2.0323 2.1869 2.2912 2.3380 2.3274

1.2979 1.5908 1.8900 2.1388 2.3546 2.5433 2.6839 2.7622 2.7182

1.2872 1.6153 1.9199 2.1630 2.3665 2.5232 2.6406 2.7087 2.7009

1.5540 1.8699 2.2027 2.4666 2.7006 2.9111 3.0707 3.1617 3.1111

1.5320 1.8906 2.2236 2.5025 2.7233 2.8984 3.0220 3.0847 3.0734

1.8568 2.1946 2.5615 2.8389 3.0903 3.3220 3.4999 3.6033 3.5463

1.9127 2.3091 2.6617 2.9674 3.1924 3.3950 3.5238 3.5725 3.5357

K

K

K

K

K

a exp x1 is the experimental solubility in the binary solvent (methanol + acetonitrile); xcal 1 is the calculated solubility by the Apelblat model, the λh model, and the NRTL model. The standard uncertainty of T is u(T) = 0.1 K. The relative standard uncertainty of the solubility is ur(x) = 0.05. The relative uncertainty of pressure is ur(P) = 0.05. The relative standard uncertainty of methanol + acetonitrile solvents is ur(x) = 0.01.

3.4. Mixing Thermodynamic Functions. The overall dissolution process could be divided into two hypothetical stages, melting of pure component and subsequent mixing of the solute with solvent.30 According to this thermodynamic cycle, thermodynamic functions of mixing determine the solubility behavior of a solute in different solvent systems. Thus, mixing functions (mixing enthalpy ΔmixH, mixing entropy ΔmixS, and mixing Gibbs free energy ΔmixG) were derived to understand the solubility behavior of TMP in different solvent systems and can be calculated by31

Δmix G = Δmix Gid + ΔGE

(13)

Δmix H = Δmix H id + ΔHE

(14)

Δmix S = Δmix S id + ΔS E

(15)

where ΔME and ΔmixMid refer to the excess thermodynamic property and the ideal mixing property, respectively. E



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cal Table 4. Experimental (xexp 1 ) and Calculated (x1 ) Mole Fraction Solubility of TMP in n-Butanol (x2) + Acetonitrile(1 − x2) at Temperatures Ranging from 273.15 to 313.15 K (p = 0.1 MPa)a

x2

10xexp 1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.5047 0.7283 0.9175 1.0529 1.1614 1.2659 1.3145 1.3219 1.2660

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.6008 0.8531 1.0912 1.2207 1.3280 1.3659 1.4039 1.4114 1.3865

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.7274 0.9654 1.2116 1.3848 1.5609 1.6458 1.6849 1.7093 1.6754

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.8197 1.1513 1.4329 1.6398 1.7863 1.8860 1.9291 1.9657 1.8659

0.1 0.2 0.3 0.4 0.5

1.0815 1.3915 1.6941 1.9521 2.1429

Apelblat, 10xcal 1 T = 273.15 0.5003 0.7219 0.9172 1.0434 1.1492 1.2271 1.2681 1.2743 1.2359 T = 278.15 0.6013 0.8473 1.0718 1.2219 1.3479 1.4274 1.4713 1.4843 1.4371 T = 283.15 0.7215 0.9929 1.2457 1.4207 1.5663 1.6487 1.6962 1.7164 1.6612 T = 288.15 0.8643 1.1614 1.4404 1.6406 1.8043 1.8915 1.9436 1.9712 1.9095 T = 293.15 1.0338 1.3564 1.6574 1.8824 2.0616

λh, 10xcal 1

NRTL, 10xcal 1

x2

10xexp 1

0.4953 0.7181 0.9268 1.0588 1.1738 1.2435 1.2811 1.2894 1.2443

0.5042 0.7258 0.9111 1.0584 1.1721 1.2539 1.3005 1.3116 1.2832

0.6 0.7 0.8 0.9

2.2519 2.3362 2.3600 2.2859

0.6006 0.8470 1.0742 1.2251 1.3524 1.4307 1.4740 1.4872 1.4389

0.6000 0.8499 1.0600 1.2200 1.3444 1.4302 1.4815 1.4940 1.4650

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1.2006 1.5631 1.8804 2.1180 2.3090 2.4169 2.5050 2.5644 2.5086

0.7245 0.9953 1.2411 1.4125 1.5525 1.6400 1.6895 1.7083 1.6568

0.7170 0.9883 1.2203 1.4006 1.5421 1.6378 1.6931 1.7083 1.6778

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1.5532 1.8794 2.1843 2.4420 2.6254 2.7347 2.7653 2.7855 2.7183

0.8700 1.1654 1.4298 1.6234 1.7765 1.8736 1.9296 1.9548 1.9003

0.8420 1.1600 1.4165 1.6141 1.7624 1.8663 1.9260 1.9439 1.9069

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1.7433 2.1401 2.4633 2.7303 2.9134 3.0914 3.2121 3.2785 3.2354

1.0404 1.3605 1.6432 1.8604 2.0268

1.0351 1.3682 1.6456 1.8629 2.0239

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

2.0496 2.4568 2.7630 3.0821 3.2864 3.4330 3.5227 3.5823 3.5359

Apelblat, 10xcal 1

K

K

K

K

K

T = 293.15 2.1563 2.2143 2.2494 2.1834 T = 298.15 1.2345 1.5814 1.8983 2.1468 2.3375 2.4436 2.5091 2.5512 2.4840 T = 303.15 1.4718 1.8408 2.1646 2.4342 2.6309 2.7534 2.8285 2.8769 2.8126 T = 308.15 1.7520 2.1394 2.4579 2.7451 2.9410 3.0859 3.1732 3.2264 3.1702 T = 313.15 2.0823 2.4824 2.7799 3.0797 3.2662 3.4410 3.5433 3.5998 3.5580

λh, 10xcal 1

NRTL, 10xcal 1

2.1337 2.1966 2.2287 2.1716

2.1330 2.1990 2.2176 2.1825

1.2398 1.5842 1.8846 2.1265 2.3063 2.4232 2.4930 2.5328 2.4732

1.2100 1.5861 1.8875 2.1168 2.2898 2.4068 2.4784 2.5026 2.4678

1.4729 1.8406 2.1579 2.4254 2.6182 2.7449 2.8219 2.8695 2.8081

1.4968 1.8755 2.1864 2.4291 2.6072 2.7284 2.7957 2.8173 2.7797

1.7456 2.1350 2.4677 2.7610 2.9662 3.1024 3.1862 3.2419 3.1792

1.7577 2.1844 2.5149 2.7698 2.9543 3.0906 3.1720 3.2012 3.1685

2.0648 2.4737 2.8195 3.1383 3.3547 3.4994 3.5896 3.6534 3.5900

2.1064 2.5525 2.8876 3.1641 3.3558 3.4885 3.5669 3.5968 3.5635

K

K

K

K

K

a exp x1 is the experimental solubility in the binary solvent (n-butanol + acetonitrile); xcal 1 is the calculated solubility by the Apelblat model, the λh model, and the NRTL model. The standard uncertainty of T is u(T) = 0.1 K. The relative standard uncertainty of the solubility is ur(x) = 0.05. The relative uncertainty of pressure is ur(P) = 0.05. The relative standard uncertainty of n-butanol + acetonitrile solvents is ur(x) = 0.01.

Δmix H id = 0

For an ideal solution, the thermodynamic functions can be calculated by the following equations on the basis of the Lewis− Randall rule.

And the excess mixing properties can be calculated by n

n

Δmix Gid = RT ∑ xi ln xi i=1

GE = RT ∑ xi ln γi

ÄÅ É Å ∂(GE /T ) ÑÑÑ E 2Å Å ÑÑ Å H = −T ÅÅ Ñ ÅÅÇ ∂T ÑÑÑÖ

(16)

i=1

n

Δmix Sid = − R ∑ xi ln xi i=1

(18)

(17) F

(19)

(20) DOI: 10.1021/acs.jced.8b00888 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data SE =

HE − GE T

Article

(21)

where xi is the mole fraction; γi refers to the activity coefficient which can be computed from the NRTL model.

4. RESULTS AND DISCUSSION 4.1. X-ray Powder Diffraction (XRPD) Analysis. XRPD patterns of excess slurry solids and raw material were illustrated in Figure 3. It is evident that the slurry TMP crystals bear the same crystal forms as that of the raw material, indicating the absence of polymorphic transformation or formation of solvates during solubility measurements. 4.2. Melting Properties. As presented in Figure 4, the melting temperature defined as the onset temperature of TMP was determined to be 358.5 ± 0.5 K, which is in good agreement with the reported value of 358.15−359.15 K.32 The enthalpy of fusion was estimated to be 16.41 ± 0.82 kJ·mol−1 (calculated by Mettler Stare software v10.00). Note the expanded uncertainties are given for the 0.95 level of confidence. 4.3. Solubility Data of TMP. The solubility data of TMP in nine monosolvents at temperatures ranging from 273.15 to 313.15 K are depicted in Table 2 and Figure 5. It can be seen that the solubility increases monotonously as the temperature rises in all studied monosolvent systems. Further, the solubility of TMP at high temperature was found to be 3 or 4 times larger than that at low temperature, suggesting that cooling crystallization can be an appropriate way to separate and purify TMP products in industrial production. At a given temperature, the solubility values of TMP in monosolvents rank as follows: n-butanol > methanol > n-propanol > ethyl acetate > methyl acetate > ethanol > isopropanol > acetone > acetonitrile. Given the symmetric and nonpolar nature of TMP (Figure 1), the solubility of TMP may rise with a decrease in the polarity of solvents if the principle of “like dissolves like” applies.33 The polarity index followed by dielectric constant as acetonitrile > methanol > ethanol > acetone > n-propanol > isopropanol > n-butanol > methyl acetate > ethyl acetate. Nevertheless, the solvent polarity does not follow the same trend as the solubility rank, indicating other factors including functional groups and steric effects are involved.34,35 TMP has good hydrogen-bonding acceptors, and thus, in alcohols, the hydrogen-bonding interactions between the nitrogen atom of the solute molecule and the hydroxyl group of the solvent molecule could be formed, which promotes the dissolution of TMP. Additionally, the branched chain being a steric hindrance to solvent molecules could lead to the weak solvation of the solute and decrease intermolecular interactions between solute and solvent molecules and hence TMP solubility. The solubility data of TMP in two binary solvent mixtures are summarized in Tables 3 and 4 and were demonstrated in Figures 6 and 7. On the basis of solubility data in monosolvents, n-butanol or methanol seen as good solvents and acetonitrile chosen as a poor solvent can be combined to regulate TMP solubility in binary solvent mixtures of methanol + acetonitrile or n-butanol + acetonitrile. Expectedly, TMP solubility increases when the temperature elevates in both mixed solvents. Further, as displayed in Figures 6 and 7, TMP solubility curves at a given temperature all display a maximum value at 0.8 solute-free mole fraction of alcohols in binary solvent mixtures of methanol + acetonitrile and n-butanol + acetonitrile. The phenomenon is referred to as cosolvency and was reported in many other systems,36,37 likely due to complex intermolecular interactions

Figure 6. Experimental solubility of TMP (x1) in a binary solvent mixture of methanol + acetonitrile at different temperatures from 273.15 to 313.15 K (p = 0.1 MPa).

Figure 7. Experimental solubility of TMP (x1) in a binary solvent mixture of n-butanol + acetonitrile at different temperatures from 273.15 to 313.15 K (p = 0.1 MPa).

among solute, solvent, and antisolvent molecules.38 Interestingly, the solvent composition corresponding to maximum solubility values was found to be independent of both temperature and solvent nature. 4.4. Data Correlations. The λh equation, Apelblat equation, and NRTL model were applied here to correlate experimental solubility profiles in nine monosolvents and two binary solvent mixtures. The optimized model parameters along with the average relative deviation (ARD) and the root-mean square deviation (RMSD) are presented in Tables 5−8. It is evident that ARDs of all correlations are less than 3%, suggesting well fitted solubility data profiles by three models. The maximum value of ARD for the λh equation was found to be 2.42%, and it was 2.84 and 2.24%, respectively, for the Apelblat equation and the NRTL model. Moreover, the overall fitting ARDs for the λh equation, Apelblat equation, and NRTL model are 1.85, 1.48, and 1.46%, respectively. Therefore, the NRTL model achieves the best fitting performance among three models. 4.5. Mixing Thermodynamic Functions of Solution. The mixing thermodynamic properties of TMP in two binary solvent mixtures from 273.15 to 313.15 K calculated by the NRTL model were presented in Tables 9 and 10. A negative value of mixed Gibbs free energy ΔmixG was found in all cases, indicating a spontaneous and favorable mixing process of TMP with a binary solvent mixture. Meanwhile, it is obvious that at a certain solvent composition the higher the temperature, the smaller the ΔmixG value. With ΔmixG decreasing, the interactions G



Article

Table 5. Model Parameters of the Apelblat Model for TMP in Nine Monosolvents and Two Binary Solvent Mixtures 10−2A

10−3B

monosolvents 3.9385 22.0484 0.0551 10.3433 5.7291 28.5984 0.4843 12.4172 −5.0848 −8.7906 −4.4934 −5.5648 0.5353 10.8851 12.1825 53.6177 −7.1719 −13.3151 methanol + acetonitrile 1.2735 15.4419 2.7545 19.3324 0.4895 11.1227 3.5646 21.0151 1.1080 12.3092 3.6670 21.0630 6.7876 31.8306 6.4445 30.7559 6.1385 29.6547 n-butanol + acetonitrile 1.4581 15.4236 0.9976 12.4513 −2.3027 0.2341 −3.8205 −5.1529 −5.5602 −11.3830 −3.8369 −5.5844 −3.2720 −3.6778 −3.9241 −5.8289 −2.8007 −1.8466

−1.4034 −0.6098 −1.8370 −0.7433 0.6569 0.4510 −0.6536 −3.4896 0.9787

methanol ethanol n-propanol isopropanol n-butanol methyl acetate ethyl acetate acetonitrile acetone x2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 x2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

C

−0.9448 −1.2140 −0.6684 −1.3339 −0.7544 −1.3383 −2.0560 −1.9830 −1.9101 −0.9486 −0.7613 0.0473 0.4063 0.8205 0.4328 0.3055 0.4501 0.1852

Table 6. Model Parameters of the λh Model for TMP in Nine Monosolvents and Two Binary Solvent Mixtures λ methanol ethanol n-propanol isopropanol n-butanol methyl acetate ethyl acetate acetonitrile acetone x2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 x2 0.1 0.2 0.3 0.4 0.5

0.8335 0.7299 0.9050 0.7398 0.9332 0.8878 0.9026 0.4098 0.7255 0.5387 0.5294 0.6164 0.6254 0.6837 0.7918 0.9080 0.9988 0.9512 0.5477 0.5181 0.5041 0.5932 0.6302

10−3h

102ARD

monosolvents 2.8842 1.9879 3.8707 1.3326 2.8278 2.5091 4.0672 2.3025 2.6646 1.4003 3.1706 1.0203 2.8650 1.2381 7.7371 3.317 4.3526 1.7313 methanol + acetonitrile 5.5673 1.1885 4.9461 1.4729 4.1167 1.2667 3.7443 1.4270 3.3558 1.4674 2.9745 1.7302 2.6916 2.3012 2.5255 2.5849 2.6122 2.8428 n-butanol + acetonitrile 5.1160 2.3928 4.5177 1.4440 4.0517 1.3206 3.4669 1.4063 3.1795 1.5197

102ARD

103RMSD

1.6321 1.2080 1.3124 2.4139 1.0846 0.8089 1.1984 1.5105 1.5392

3.6118 2.5221 3.2831 4.2018 3.7354 1.7676 3.2885 1.5462 2.3528

1.1903 1.1691 1.2265 1.1435 1.4052 1.3404 1.2194 1.4893 1.7802

2.5212 2.9164 3.2203 3.3795 3.9540 4.7899 4.1463 4.3218 5.0351

2.4192 1.3449 1.1105 1.0566 1.1889 1.6082 2.1343 2.2238 2.3099

4.0682 2.4108 2.2257 3.0315 3.4498 4.4199 5.9002 6.2677 6.1561

Table 6. continued λ

103RMSD

102ARD

103RMSD

n-butanol + acetonitrile

x2

4.2634 2.4269 7.2998 4.8629 3.5627 2.2878 4.6044 4.5262 4.0525

10−3h

0.6

0.6700

2.9845

1.7446

5.4258

0.7

0.7053

2.8583

2.1149

6.5233

0.8

0.7577

2.7417

2.3723

6.9461

0.9

0.7584

2.7919

2.3811

6.4441

Table 7. Model Parameters of the NRTL Model for TMP in Nine Monosolvents methanol ethanol n-propanol isopropanol n-butanol methyl acetate ethyl acetate acetonitrile acetone

2.7532 3.4524 3.3416 4.7664 4.5180 7.1586 8.9474 8.6874 7.7510

10−3Δg12

10−3Δg21

a

102ARD

103RMSD

1.3873 1.3727 1.0237 1.1955 0.9618 0.9687 1.0438 1.7630 1.1205

0.4306 1.6795 0.8327 2.1575 0.6389 1.4877 0.8828 3.4799 2.5673

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

1.3740 1.0223 1.5175 1.7422 1.5536 1.3366 0.9129 1.0021 2.2401

0.2878 0.2544 0.3921 0.2251 0.3630 0.3336 0.2310 0.1004 0.4412

between the solvent and the solute become stronger, which interprets the monotonous rise of the temperature dependence of TMP solubility. In addition, the mixed enthalpy ΔmixH is positive, suggesting the endothermic process of mixing of TMP with various binary mixed solvents.39 The positive values of mixing entropy ΔmixS demonstrate the entropy-driven process of mixing of TMP with various solvent mixtures.

3.9582 2.3598 3.1163 4.1792 5.2327 H



Article

5. CONCLUSION The solubility of TMP was measured in nine monosolvents and two binary mixed solvents at temperatures ranging from 273.15 to 313.15 K using the UV-spectroscopic method under atmospheric pressure. The solubility was found to increase as the temperature elevates. The solubility rank in nine monosolvents at a given temperature follows the order of n-butanol > methanol > n-propanol > ethyl acetate > methyl acetate > ethanol > isopropanol > acetone > acetonitrile. Surprisingly, TMP solubility in binary solvent mixtures bears a maximum value at 0.8 mole fraction of alcohols independent of both temperature and solvent nature. Further, the solubility data in all studied solvent systems were well correlated by the

Table 8. Model Parameters of the NRTL Model for TMP in Two Binary Solvent Mixtures parameters

methanol + acetonitrile

n-butanol + acetonitrile

a1 a2 a3 10−3Δg12 10−3g13 10−3Δg21 10−3Δg23 10−3Δg31 10−3Δg32 102ARD 103RMSD

0.2 0.4 0.7 3.2082 2.2729 −1.1327 2.7802 2.8499 0.7666 1.5335 5.3370

0.2 0.4 0.7 4.8859 1.9693 −2.1533 2.3721 3.1840 0.5576 1.8064 5.0604

Table 9. Mixing Thermodynamic Functions of TMP in Methanol + Acetonitrile Binary Mixed Solvent at Temperatures Ranging from 288.15 to 328.15 K (P = 0.1 MPa)a,b x2

ΔmixG (kJ mol−1)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

−0.737 −1.021 −1.194 −1.310 −1.364 −1.376 −1.348 −1.255 −1.081

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

−0.782 −1.082 −1.262 −1.381 −1.440 −1.452 −1.413 −1.323 −1.145

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

−0.835 −1.139 −1.333 −1.455 −1.527 −1.542 −1.506 −1.420 −1.243

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

−0.890 −1.201 −1.401 −1.530 −1.599 −1.619 −1.588 −1.497 −1.311

0.1 0.2 0.3 0.4 0.5

−0.948 −1.268 −1.479 −1.610 −1.688

ΔmixH (kJ mol−1) 273.15 K 0.202 0.298 0.382 0.454 0.502 0.523 0.504 0.432 0.291 278.15 K 0.221 0.319 0.401 0.471 0.518 0.535 0.512 0.439 0.297 283.15 K 0.246 0.340 0.424 0.491 0.537 0.550 0.523 0.447 0.308 288.15 K 0.273 0.364 0.446 0.512 0.553 0.562 0.533 0.455 0.315 293.15 K 0.304 0.394 0.475 0.536 0.573

ΔmixS (J mol−1 K−1)

x2

3.436 4.829 5.769 6.457 6.832 6.951 6.778 6.175 5.024 3.603 5.037 5.978 6.659 7.038 7.142 6.922 6.334 5.185 3.816 5.225 6.203 6.871 7.287 7.388 7.168 6.594 5.477 4.037 5.431 6.411 7.086 7.467 7.571 7.360 6.774 5.643 4.270 5.669 6.665 7.320 7.711

ΔmixG (kJ mol−1)

0.6 0.7 0.8 0.9

−1.708 −1.678 −1.592 −1.411

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

−1.006 −1.335 −1.545 −1.677 −1.754 −1.783 −1.760 −1.672 −1.492

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

−1.073 −1.408 −1.625 −1.758 −1.834 −1.860 −1.842 −1.768 −1.600

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

−1.129 −1.465 −1.684 −1.821 −1.898 −1.927 −1.907 −1.830 −1.664

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

−1.207 −1.541 −1.754 −1.888 −1.962 −1.987 −1.964 −1.889 −1.732

ΔmixH (kJ mol−1) 293.15 K 0.577 0.543 0.464 0.327 298.15 K 0.337 0.424 0.500 0.555 0.588 0.589 0.552 0.471 0.337 303.15 K 0.379 0.462 0.535 0.583 0.607 0.601 0.560 0.479 0.353 308.15 K 0.412 0.490 0.558 0.604 0.622 0.610 0.565 0.484 0.363 313.15 K 0.471 0.540 0.596 0.630 0.636 0.614 0.562 0.484 0.375

ΔmixS (J mol−1 K−1) 7.795 7.577 7.012 5.930 4.506 5.901 6.858 7.486 7.856 7.957 7.755 7.188 6.134 4.789 6.168 7.127 7.723 8.053 8.119 7.922 7.412 6.444 5.000 6.346 7.276 7.870 8.178 8.232 8.022 7.509 6.578 5.357 6.645 7.503 8.042 8.296 8.305 8.067 7.578 6.725

ΔmixH, ΔmixG, and ΔmixS stand for mixing enthalpy, mixing Gibbs energy, and mixing entropy. bThe expanded uncertainties are U(ΔmixH) = 0.06ΔmixH, U(ΔmixS) = 0.05ΔmixS, U(ΔmixG) = 0.05ΔmixG (0.95 level of confidence). a

I



Article

Table 10. Mixing Thermodynamic Functions of TMP in n-Butanol + Acetonitrile Binary Mixed Solvent at Temperatures Ranging from 288.15 to 328.15 K (P = 0.1 MPa)a,b x2

ΔmixG (kJ mol−1)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

−0.814 −1.157 −1.372 −1.497 −1.559 −1.572 −1.523 −1.408 −1.190

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

−0.863 −1.218 −1.448 −1.574 −1.637 −1.633 −1.581 −1.464 −1.252

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

−0.919 −1.274 −1.508 −1.646 −1.724 −1.733 −1.682 −1.570 −1.357

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

−0.964 −1.345 −1.586 −1.731 −1.803 −1.815 −1.766 −1.656 −1.429

0.1 0.2 0.3 0.4 0.5

−1.046 −1.421 −1.664 −1.815 −1.893

ΔmixH (kJ mol−1) 273.15 K 0.154 0.204 0.255 0.302 0.336 0.347 0.326 0.264 0.149 278.15 K 0.169 0.215 0.262 0.306 0.337 0.349 0.328 0.265 0.149 283.15 K 0.187 0.226 0.271 0.311 0.337 0.342 0.319 0.254 0.142 288.15 K 0.202 0.241 0.281 0.316 0.338 0.340 0.313 0.248 0.140 293.15 K 0.235 0.260 0.294 0.322 0.337

ΔmixS (J mol−1 K−1)

x2

ΔmixG (kJ mol−1)

3.546 4.982 5.957 6.588 6.939 7.024 6.771 6.123 4.905

0.6 0.7 0.8 0.9

−1.906 −1.865 −1.755 −1.541

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

−1.093 −1.480 −1.725 −1.873 −1.950 −1.963 −1.922 −1.815 −1.606

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

−1.177 −1.554 −1.794 −1.941 −2.016 −2.030 −1.983 −1.874 −1.664

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

−1.229 −1.614 −1.853 −1.997 −2.070 −2.086 −2.046 −1.943 −1.746

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

−1.293 −1.672 −1.905 −2.046 −2.117 −2.131 −2.090 −1.987 −1.795

3.709 5.151 6.150 6.760 7.097 7.126 6.862 6.215 5.035 3.905 5.297 6.284 6.913 7.280 7.330 7.066 6.442 5.292 4.045 5.503 6.481 7.104 7.432 7.477 7.214 6.606 5.447 4.367 5.733 6.679 7.291 7.607

ΔmixH (kJ mol−1) 293.15 K 0.333 0.301 0.237 0.134 298.15 K 0.253 0.277 0.306 0.331 0.343 0.336 0.302 0.236 0.135 303.15 K 0.294 0.302 0.322 0.340 0.345 0.333 0.300 0.236 0.138 308.15 K 0.320 0.324 0.339 0.350 0.349 0.331 0.291 0.227 0.137 313.15 K 0.354 0.350 0.356 0.360 0.352 0.330 0.289 0.227 0.141

ΔmixS (J mol−1 K−1) 7.638 7.388 6.794 5.712 4.514 5.891 6.813 7.391 7.689 7.711 7.458 6.881 5.838 4.853 6.121 6.982 7.524 7.788 7.794 7.531 6.958 5.944 5.026 6.290 7.111 7.616 7.851 7.844 7.585 7.043 6.111 5.259 6.457 7.219 7.684 7.885 7.856 7.597 7.071 6.184

a ΔmixH, ΔmixG, and ΔmixS stand for mixing enthalpy, mixing Gibbs energy, and mixing entropy. bThe expanded uncertainties are U(ΔmixH) = 0.06ΔmixH, U(ΔmixS) = 0.05ΔmixS, and U(ΔmixG) = 0.05ΔmixG (0.95 level of confidence).

■

Apelblat equation, λh equation, and NRTL model, and the NRTL model fits the best. In addition, mixing thermodynamic functions including enthalpy, entropy, and Gibbs free energy are derived, and the data suggest a spontaneous and entropy-driven mixing process of TMP in both pure and binary mixed solvent systems. The determined solubility data, correlated equations, and derived thermodynamic functions presented in this paper could be of great importance in the design, control, and optimization of the TMP crystallization process in industry.

ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.8b00888. UV−vis spectroscopy method verification (PDF)

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: 86-22-27405754. Fax: 8622-27374971. J



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Weiwei Tang: 0000-0002-7998-4350 Funding

The authors are grateful for the financial support of the open foundation of State Key Laboratory of Chemical Engineering (No. SKL-ChE-18B04), National Natural Science Foundation of China (NNSFC 21808159, NNSFC 21676179, and NNSFC 91634117), and Innovative Group Project 21621004. Notes

The authors declare no competing financial interest.

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Measurement and Correlation of the Solubility of Tetramethylpyrazine

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