Thermodynamic properties of betulinic acid in THF + water mixed solvents at different temperatures

Accepted Manuscript Title: Thermodynamic properties of betulinic acid in THF + water mixed solvents at different temperatures Author: Wei Shi Yong Cheng Yundong Shao Weidong Yan PII: DOI: Reference:

S0040-6031(14)00490-0 http://dx.doi.org/doi:10.1016/j.tca.2014.10.026 TCA 77056

To appear in:

Thermochimica Acta

Received date: Revised date: Accepted date:

14-8-2014 28-10-2014 29-10-2014

Please cite this article as: Wei Shi, Yong Cheng, Yundong Shao, Weidong Yan, Thermodynamic properties of betulinic acid in THF+water mixed solvents at different temperatures, Thermochimica Acta http://dx.doi.org/10.1016/j.tca.2014.10.026 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Thermodynamic Properties of Betulinic Acid in THF + Water Mixed Solvents at Different Temperatures Wei Shia, Yong Chenga,b, Yundong Shaob, and Weidong Yana,*

b

Department of Chemistry, Zhejiang University, Hangzhou 310027, China and Skyherb Ingredients, Anji 313300, China

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a

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Highlights

The solubilities of betulinic acid in the THF + water were determined at different temperatures. The highest solubility value is obtained in the pure THF. The thermodynamic properties of the solution process and the crystal habit of betulinic acid were discussed.

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 

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Abstract

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The solubilities of betulinic acid in binary solvent mixtures of THF + water in the

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temperature range of (278.2 to 318.2) K were determined by an analytical method.

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The solubility of betulinic acid in a binary solvent mixture increased with the increase of molar fraction of THF and the temperature. The solubilities data were correlated

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with a semi-empirical equation. The calculated solubilities showed good agreement with the experimental data. According to the van’t Hoff equation and the Gibbs

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equation, the thermodynamic properties for the solution process including Gibbs energy, enthalpy, and entropy were obtained. The crystal habit of betulinic acid

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changes in morphology at different solvent mixtures was observed using SEM.

Keywords: Solubility; Betulinic acid; Tetrahydrofuran; Water; Correlation

*

Corresponding author. Tel.: +86 571 87951430; fax: +86 571 87951895. E-mail address: [email protected] (W.D. Yan).

1. Introduction Betulinic acid (Fig. 1) is a naturally occurring pentacyclic triterpenoid which has anti-bacterial, anti-melanoma [1], anti-malarial [2], and anti-inflammatory [3] properties, as well as a more recently discovered potential as an anticancer agent, by inhibition of topoisomerase [4]. It is discovered in the bark of several species of plants, principally the white birch (Betula pubescens), but also the Ziziphus spp. [5], Syzygium spp. [6] and Doliocarpus spp. [7].

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It is difficult to obtain a commercial quantity (i.e., kgs) of betulinic acid from nature because of the very low content of betulinic acid in the plants. Betulin (Fig. 1),

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a naturally occurring triterpene seems to be an ideal starting material for the synthesis

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of betulinic acid using two-step reactions: oxidation and reduction. In order to effectively separate the betulin and betulinic acid from reactive mixture or plant

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extracts by recrystallization or anti-solvent crystallization, it is necessary to determine

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the solubilities of betulin and betulinic acid in different solvents. The solubilities of

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betulin have been measured in the pure solvents [8] and mixed solvents [9]. The

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solubilities of betulinic acid have also been measured in the different pure solvents [10]. However, the solubilities of betulinic acid in the mixed solvents have not been

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found in the literature. As a continuation of our previous work, we measured the

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solubilities of betulinic acid (1) in THF (2) + water (3) solvents by an analytical

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method [11] at T = (278.2 to 318.2) K and at different mole fractions, x 2' of THF on a solute-free basis. The semi-empirical equation model was used to correlate the

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solubility data. In addition, the thermodynamic properties of the solution process and

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crystal appearances of betulinic acid were discussed.

2. Experimental

2.1 Materials The white powder of betulinic acid with Chemical Abstract Service No. of

472-15-1 (purity > 0.98 in mass fraction) was supplied by Skyherb Ingredients (China). A total of 100 g of betulinic acid was dissolved in about 5 L of methanol, refluxed for about 2 h, filtered, and crystallized at 5 oC. About 20 g of white needle-like betulinic acid was obtained after recrystallization three times. It was dried in a vacuum oven at T = 348.2 K for 24 h and stored in a desiccator to avoid moisture absorption. The purity of betulinic acid was higher than 0.995 in mass fraction, determined by HPLC (Shimadzu LC-10AT). The reference standard of betulinic acid, with a purity of higher than 0.98 mass fractions, was purchased from Sigma-Aldrich

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Chemical Corporation. Tetrahydrofuran, THF (0.995 in mass fraction) obtained from Sinopharm Chemical Reagent Co., Ltd. (China) was of analytical grade. The solvent

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were dehydrated with molecular sieves (3 to 4) Å before use. Distilled deionized

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water was obtained from the distilled water generator (SZ-97, Shanghai Yarong

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Biochemical Instrument Co. Ltd., China).

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2.2 Sample preparation

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Glass-stoppered test tubes (10 mL) were used to prepare saturated solutions (about 8.0

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mL) of betulinic acid (1) with excess solid solute in THF (2) + water (3) mixed

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solvents at different mole fractions, x 2' of THF on a solute-free basis. The test tubes

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were stoppered and sealed with Parafilm and Teflon tape to prevent evaporation of solvents. Then the tubes were directly placed in a constant temperature thermostatic

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bath (THID-0510W, China) with periodic agitation for several times. The thermostatic bath is a temperature fluctuation of ± 0.01 K and a temperature uncertainty of ± 0.1 K.

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After agitation, the tubes were allowed to settle about 36 to 48 h to ensure equilibrium. For each tube, three samples were withdrawn from the clear saturated solution using

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preheated glass syringes. The glass syringe with a saturated solution was weighted using a Sartorius Type CPA225D analytical balance with an uncertainty of ± 0.01 mg. The needle was closed with silicon rubber to prevent evaporation of solvents during the weighing procedure. To prevent precipitation, the saturated solution was injected into the volumetric flask immediately. Subsequently, the mass of the glass syringe

with the remaining solution was weighed. Then the mass of saturated solution which was put into 10-mL flask was calculated. The samples used for HPLC analysis were diluted with methanol to 10.0 ml.

2.3 Chromatographic conditions The solubility was determined using HPLC (Shimadzu Corporation, Kyoto, Japan) consisting of a degasser (DGU-4A), a solvent delivery module (LC-10AT), and UV detector (SPD-10A). The data were acquired using the N2000 Chromatographic Data

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System (Zheda information and Technologies Ltd., Hangzhou, China). The analysis was performed on a Diamonsil C18 column (250 mm × 4.6 mm, 5 m).

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The optimum separation of HPLC was carried out with a mobile phase composed of

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acetonitrile and water in a volume ratio of 92: 8 at a flow rate of 1.0 mL·min-1. The injected volumes of sample and reference standard solutions were 20 L. The

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2.4 Scanning electron microscope

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performed at room temperature [11].

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detection wavelength was set at 210 nm. All chromatograph procedures were

The hot solutions of binary solvent mixtures that were saturated by betulinic acid

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were slowly cooled and crystallized at 0 oC about 48 h. Then, the crystals of betulinic

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acid were dried in a vacuum oven for 24 h and observed by SEM (FEI Sirion,

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Holland). These images of samples were received at 25.0 kV accelerating voltage.

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3. Results and discussion

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3.1 Solubility in selected mixed solvents The solubilities, molality (m1) and mole fraction (x1) of betulinic acid (1) in THF

(2) + water (3) mixture at different mole fractions, x 2' of THF on a solute-free basis are listed in Table 1. Fig. 2 and Fig. 3 give the plots of the solubility of betulinic acid in mixed solvents at a temperature range of about (278.2 to 318.2) K. It may be

observed that the highest solubility value in mole fraction is obtained in the pure THF, and the lowest values were found in pure water at every temperature. According to the theory of solid-liquid phase equilibrium [12] and some reasonable assumptions, the solubility in mole fraction of betulinic acid (1) in THF (2) + water (3) mixture can be expressed by Eq. 1, that is only valid for simple eutectic systems [13]:

 1  fusH  Tt  Cp  Tt  Cp Tt   ln  ln   1    1  RTt  T R T R T    γxx1 

(1)

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where γx is the activity coefficient of betulinic acid on a mole fraction basis, x1 is the mole fraction solubility of betulinic acid, fusH is the enthalpy of fusion of betulinic

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acid, Cp is the difference of the heat capacities of liquid and solid betulinic acid, T is

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the absolute temperature, Tt is the tripe-point temperature of betulinic acid and R is the gas constant.

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For regular solution, the activity coefficient is given by [14]

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Β T/K

(2)

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ln γx  Α 

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rearrangement results in

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where A and B are constants. Introducing γx from Eq. (2) into Eq. (1) and subsequent

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    H Cp ln x1   fus  1  ln Tt   A   B    fus H  Cp Tt  1  Cp ln T R R  T R  RTt    RTt (3)

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The Eq. (3) could be expressed as

ln x1  a 

b T  c ln T /K K

(4)

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where a, b, and c are empirical parameters. The values of the three parameters a, b, and c were obtained by nonlinear least-squares fitting using the experimental data and listed in Table 2 together with the root mean square deviation (rmsd). The rsmd are defined as 1 n  rmsd    ( xi , calcd  xi , exptl ) 2   n i 1 

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(5)

where xi,calcd is mole fraction solubility calculated by Eq. (4) using the parameters in Table 2; xi,exptl is the experimental values of mole fraction solubility of betulinic acid; and n is the number of experimental points. As can be seen from Tables 1 to 2 and Fig. 2 and Fig. 3, the results correlated by semi-empirical equations are satisfactory. The following conclusions can be draw: (1) The solubilities of betulinic acid in THF + water mixtures increase with the increase of temperature and the mole fraction of tetrahydrofuran in mixed solvents. The highest solubility value is obtained in the pure THF.

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(2) The calculated solubilities of betulinic acid sets a good coherence with the experimental values, and the experimental solubilities and correlation equation in this

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work can be used for model research of the crystallization process of betulinic acid.

3.2 Thermodynamic properties of solutions

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According to van’t Hoff equation, the standard molar enthalpy change, H so

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of solution could be related to the temperature and the solubility [15]. (6)

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H so  ln x1  R 1 T 

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As the mole fraction solubility is temperature dependent, Eq. (4) could be put

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into Eq. (6). In a limited temperature interval ((278.2 - 318.2) K in the present case), the heat capacity change of solution could be assumed to be constant, so that the

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Thus:

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derived values of H So would be valid for the mean temperature, Tmean = 298.15 K.

  ln x1     R(b  cTmean ) H so   R  1 T  

(7)

The standard molar Gibbs energy change, Gso and standard molar entropic

change, S so for the solution process could be calculated by the following equation [16].

G oS   RTmean  intercept  H So  Tmean S So

(8)

where the intercept could be obtained from the line of ln x1 vs. (1/T - 1/Tmean) (shown in Fig. 4). These standard thermodynamic parameters for the solution process for different mixture have been calculated and presented in Table 3. The standard Gibbs free energy of solution was positive in all cases, which indicates the process was endothermic. The value of standard molar enthalpy increased with the increase in the molar fraction of THF on a solute-free basis and obtained a maximum at x 2' = 0.2002, which implied that the dissolution at x 2' = 0.2002 is more difficult than at the other mixtures.

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The values of the standard molar Gibbs free energy change of solution were

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positive for all cases. The entropy of solution is negative only when pure water is the solvent, whereas it is positive in all other mixtures, which demonstrated that the

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entropy was driving the solution process [17]. Eqs. (9) and (10) were employed to compare the percent relative contributions of enthalpy (%H) and entropy (%TS) to

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the solution process, respectively.

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H So

H So  TS So

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A

% H  100

H So  TS So

(10)

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% TS  100

TS So

(9)

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The values of % H and % TS were calculated and listed in Table 3. The values of % TS were greater than 59 %, which implied that the main contributing force to

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 G so was the enthalpy during the dissolution of betulinic acid in all the mixtures

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selected.

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3.3 Crystals of betulinic acid The crystal habit of betulinic acid changes in morphology at different solvent

mixtures was characterized using SEM. It is apparent from Fig. 5 that the betulinic acid crystals obtained in all mixtures show a regular rod-like shape, but glassy appearance in THF [10]. Moreover, the crystals of betulinic acid got bigger with the molar fraction of THF.

4. Conclusions

The solubilities of betulinic acid in binary solvent mixtures of THF + water were investigated and correlated by empirical equation. As illustrated from Fig. 2, Fig. 3, and Table 1, the solubility of betulinic acid increased with increases of the molar fraction of THF and the temperature. The correlated result indicated that the experimental data agreed well with the calculated results from the selected model.

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According to the van’t Hoff equation and the Gibbs equation, the thermodynamic properties for the solution process including Gibbs energy, enthalpy, and entropy were

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obtained. Endothermic, not spontaneous, and entropy-driving were found overall to be

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the solution process for all the mixture selected.

The changes of morphology of the betulinic acid in binary solvent mixtures

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indicated that water could be used as an effective anti-solvent in the crystallization

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A

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process.

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References

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[1] W.-K. Liu, J.C.K. Ho, F.W.K. Cheung, B.P.L. Liu, W.-C. Ye, C.-T. Che, Apoptotic activity of betulinic acid derivatives on murine melanoma B16 cell line. Eur. J. Pharmacol. 498 (2004) 71-78. [2] P. Yogeeswari, D. Sriram, Betulinic acid and its derivatives: a review on their biological properties, Curr. Med. Chem. 12 (2005) 657-666. [3] T. Honda, K.T. Liby, X. Su, C. Sundararajan, Y. Honda, N. Suh, R. Risingsong, C.R. Williams, D.B. Royce, M.B. Sporn, G.W. Gribble, Design, synthesis, and anti-inflammatory activity both in vitro and in vivo of new betulinic acid analogues having an enone functionality in ring A, Bioorg. Med. Chem. Lett. 16 (2006) 6306-6309. [4] A.R. Chowdhury, S. Mandal, B. Mittra, S. Sharma, S. Mukhopadhyay, H. Majumder, Betulinic acid, a potent inhibitor of eukaryotic topoisomerase I: identification of the inhibitory step, the major functional group responsible and development of more potent derivatives, Medical science monitor, Int. Med. J. Exp. Clin. Res. 8 (2002) BR254. [5] B. Su, M. Cuendet, N. Farnsworth, H. Fong, J. Pezzuto, A. Kinghorn, Activity-guided fractionation of the seeds of Ziziphus jujuba using a cyclooxygenase-2 inhibitory assay,

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Planta Med. 68 (2002) 1125-1127. [6] C. Chang, T. Wu, Y. Hsieh, S. Kuo, P. Chao, Terpenoids of Syzygium formosanum, J. Nat. Prod. 62 (1999) 327-328. [7] B. de Oliveira, C. Santos, A. Espindola, Determination of the triterpenoid, betulinic acid, in Doliocarpus schottianus by HPLC, Phytochem. Anal. 13 (2002) 95-98. [8] D. Cao, G. Zhao, W. Yan, Solubilities of betulin in fourteen organic solvents at different temperatures, J. Chem. Eng. Data 52 (2007) 1366-1368. [9] G. Zhao, W. Yan, Solubilities of betulin in chloroform+methanol mixed solvents at T=(278.2, 288.2, 293.2, 298.2, 308.2 and 313.2) K, Fluid Phase Equilib. 267 (2008) 79-82. [10) Y. Cheng, Y. Shao, W.D. Yan, Solubilities of Betulinic Acid in Thirteen Organic Solvents at Different Temperatures J. Chem. Eng. Data 56 (2011) 4587-4591. [11] G. Zhao, W.D. Yan, D. Cao, Simultaneous determination of betulin and betulinic acid in white birch bark using RP-HPLC, J. Pharm. Biomed. Anal. 43 (2007) 959-962. [12] J.M. Prausnitz, R.N. Lichtenthaler, E.G. de Azevedo, Molecular thermodynamics of fluid-phase equilibria, 3rd ed., Prentice-Hall Inc. 1999. [13] J. Gmehling, B. Kolbe, M. Kleiber, J. Rarey, Chemical thermodynamics: for Process Simulation, , Wiley-VCH, Weinheim, 2012. [14] D. Kondepudi, I. Prigogine, Modern Thermodynamics: From Heat Engines to Dissipative Structures, John Wiley and Sons Ltd., Chichester, England, 1998. [15] P. Bustamante, S. Romero, A. Reillo, Thermodynamics of Paracetamol in Amphiprotic and Amphiprotic—aprotic Solvent Mixtures, J. Pharm. Pharmacol. 1 (1995) 505-507. [16] M.A. Ruidiaz, D.R. Delgado, F. Martínez, Y. Marcus, Solubility and preferential solvation of indomethacin in 1,4-dioxane + water solvent mixtures, Fluid Phase Equilib. 299 (2010) 259-265. [17] Y. Manrique, D. Pacheco, F. Martínez, Thermodynamics of Mixing and Solvation of Ibuprofen and Naproxen in Propylene Glycol + Water Cosolvent Mixtures, J. Solution Chem. 37 (2008) 165-181.

FIGURE 1. Molecule structure of betulinic acid and betulin.

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FIGURE 2. Mole fraction solubilities of betulinic acid (1) in: , x 2' = 1.0000; , x 2' = 0.9000; ●, x 2' = 0.8001; ○, x 2' = 0.7001; , x 2' = 0.6002; , x 2' = 0.4999; ▼, x 2' = 0.4002; , x 2' = 0.3000; , x 2' = 0.2002; , x 2' = 0.1001; ★, x 2' = 0; solid line, calculated by Eq. (4) using parameters in Table 2. FIGURE 3. Mole fraction solubilities of betulinic acid (1) vs the mole fraction of THF on a solute-free basis in THF (2) + water (3) mixtures at: , 278.15; , 288.15; 298.15; , 308.15; , 318.15; solid line, calculated by Eq. (4) using parameters in Table2.

FIGURE 4. Temperature dependence of solubility of betulinic acid (1) in THF (2) + water (3) mixtures. , x 2' = 1.0000; , x 2' = 0.9000; ●, x 2' = 0.8001; ○, x 2' = 0.7001; , x 2' = 0.6002; , x 2' = 0.4999; ▼, x 2' = 0.4002; , x 2' = 0.3000; , x 2' = 0.2002; , x 2' = 0.1001; ★, x 2' = 0. The points represent the experimental data, and the curves represent the results based on linear fitting. FIGURE 5. SEM images of the betulinic acid crystals crystallized in binary THF (2) + water (3) mixtures. (a) x 2' = 0.2002; (b) x 2' = 0.4002; (c) x 2' = 0.6002; (d) x 2' = 0.8001. Table 1 Experimental data of solubilities for betulinic acid (1) in THF (2) + water (3) mixture at T = x1 ( × 103 )

278.2

(2.63±0.02)×10-3

(4.63±0.05)×10-4

288.2

(3.90±0.06)×10-3

(7.13±0.14)×10-4

298.2

(5.71±0.08)×10-3

(1.03±0.02)×10-3

308.2

(8.77±0.05)×10-3

(1.58±0.01)×10-3

318.2 ' x 2 = 0.1001

(1.29±0.03)×10-2

278.2

(3.32±0.04)×10-2

288.2

(5.45±0.05)×10-2

298.2

(1.04±0.03)×10

-1

(2.43±0.07)×10-2

308.2

(2.46±0.03)×10-1

(5.75±0.06)×10-2

318.2 ' x 2 = 0.2002

(5.70±0.06)×10-1

(1.30±0.01)×10-1

278.2

(2.87±0.02)×10-1

(8.28±0.18)×10-2

288.2

(7.22±0.08)×10-1

(2.08±0.07)×10-1

1.55±0.03

(4.47±0.07)×10-1

3.11±0.01

(8.95±0.02)×10-1

7.29±0.10

2.08±0.02

278.2

1.22±0.05

(4.18±0.10)×10-1

288.2

2.07±0.04

(7.07±0.09)×10-1

298.2

3.85±0.03

1.30±0.01

308.2

6.30±0.08

2.19±0.02

318.2 = 0.4002 x

11.15±0.02

3.80±0.05

278.2

2.01±0.04

(7.96±0.09)×10-1

288.2

3.28±0.06

1.30±0.01

298.2

5.93±0.07

2.34±0.02

308.2

9.18±0.10

3.62±0.03

318.2 x = 0.4999

15.50±0.02

6.11±0.05

308.2

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D

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318.2 x = 0.3000 ' 2

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298.2

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SC U

(2.32±0.07)×10-3

N

A

T/K ' b = 0.0000 x2

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m1 ( × 102 mol·kg-1 )

M

(278.2, 288.2, 298.2, 308.2 and 318.2) Ka

(7.91±0.09)×10-3 (1.28±0.10)×10-2

' 2

' 2

278.2

2.94±0.08

1.32±0.02

288.2

4.54±0.10

2.04±0.06

298.2

7.59±0.10

3.41±0.06

308.2

11.58±0.03

5.19±0.11

318.2 x = 0.6002

18.70±0.01

8.36±0.04

278.2

4.13±0.03

2.08±0.01

288.2

6.01±0.20

3.03±0.10

298.2

9.84±0.05

4.85±0.23

308.2

14.41±0.02

7.22±0.10

318.2 x = 0.7001

21.43±0.05

10.70±0.25

278.2

5.37±0.10

2.99±0.05

288.2

7.68±0.15

4.27±0.08

298.2

12.04±0.03

6.68±0.16

308.2

18.13±0.03

10.03±0.14

318.2 = 0.8001 x

26.45±0.06

14.56±0.31

278.2

6.74±0.02

288.2

9.95±0.03

298.2

14.88±0.02

308.2

21.39±0.01

318.2 x = 0.9000

30.98±0.03

278.2

9.75±0.03

288.2

14.32±0.03

9.46±0.16

298.2

20.24±0.04

13.32±0.26

308.2

28.84±0.04

18.84±0.24

40.59±0.10

26.58±0.60

' 2

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' 2

278.2

N

U

6.10±0.19

M

D

9.04±0.11

12.92±0.07 18.63±0.18 6.46±0.21

13.65±0.01

9.75±0.01

19.06±0.02

13.56±0.03

298.2

29.11±0.02

20.56±0.10

308.2

39.32±0.01

27.57±0.01

CC

c

TE

318.2 x 2' = 1.0000

4.15±0.10

A

' 2

SC

' 2

55.91±0.02

38.75±0.14

EP

288.2

A

318.2

a

Expanded uncertainties (±) were calculated using standard deviation, SDcoverage factor k; k=2. b Mole

fraction of THF on a solute-free basis. c values taken from reference [10] . u(T) = ± 0.1; u( x 2' ) = 0.0001; u(x1)

= 0.0110-3

Table 2 Parameters of Eq. (4) for betulinic acid (1) in THF (2) + water (3) mixture.

x 2'

104 rmsd

b/K

c

0.0000

-122.361

1794.317

18.004

0.03·10-3

0.1001

-1082.117

42207.839

163.217

0.17·10-2

0.2002

-77.216

-2881.364

13.893

0.04

0.3000

-182.150

3615.700

28.670

0.02

0.4002

-117.624

1109.149

18.921

0.06

0.4999

-168.519

3748.840

26.368

0.06

0.6002

-133.774

2580.527

21.020

0.08

0.7001

-125.937

2357.757

19.826

0.08

0.8001

-82.270

611.899

13.242

0.04

0.9000

-75.052

486.571

12.119

0.07

1.0000b

-47.714

-669.958

8.081

0.38

PT

a

Mole fraction of THF on a solute-free basis. b [10].

RI

a

a

%-H

%-TS

-14.62

U

87.20

12.80

93.36

65.85

34.15

131.74

59.78

40.22

82.32

62.56

37.44

29.71

34.07

0.1001

53.67

25.83

0.2002

58.39

19.11

0.3000

41.01

16.46

0.4002

37.68

15.07

75.82

62.50

37.50

0.4999

34.19

14.08

67.45

62.97

37.03

0.6002

30.65

13.21

58.49

63.74

36.26

0.7001

29.54

12.50

57.15

63.42

36.58

0.8001

27.74

11.78

53.51

63.49

36.51

26.00

10.80

50.96

63.12

36.88

25.60

9.69

53.36

61.68

38.32

CC

A

D

EP

1.0000

TE

b

N

0.0000

0.9000

a

A

So (J/mol)

M

of THF (x2’) on a solute-free basis at 298.15K a x 2' (mole fraction) Ho (kJ/mol) Go (kJ/mol)

SC

Table 3 Thermodynamic functions related to solution process of betulinic acid in various contents

Mole fraction of THF on a solute-free basis. b [10].

U

SC

RI

PT

FIGURE 1

D

0.02

EP

TE

x1

M

A

N

0.04

A

CC

0.00

FIGURE 2

280

285

290

295

300 T/K

305

310

315

320

0.04

x1

0.03

0.02

0.2

0.4

RI

0.00 0.0

PT

0.01

0.6

0.8

'

SC

x2

1.0

D

M

A

N

U

FIGURE 3

EP

TE

-4

-12

A

CC

lnx1

-8

-0.0002

-0.0001

0.0000 1/T-1/Tmean

FIGURE 4

0.0001

0.0002

TE

EP

CC

A D

PT

RI

SC

U

N

A

M

TE

EP

CC

A D

PT

RI

SC

U

N

A

M

FIGURE 5