Article pubs.acs.org/jced
Experimental Measurement and Modeling of the Solubility of Biotin in Six Pure Solvents at Temperatures from 298.15 K to 333.85 K Jiahui Su,† Chao Qian,† Nengzhen Luo,‡ Xiangao Xiang,‡ Yiming Xu,‡ and Xinzhi Chen*,† †
Key Laboratory of Biomass Chemical Engineering of Ministry of Education, Department of Chemical and Biological Engineering, Zhejiang University, Hangzhou, 310027, P. R. China ‡ China Construction Industrial Equipment Installation Company Limited, Nanjing, 210046, P. R. China ABSTRACT: The solubilities of biotin in water, methanol, ethanol, acetic acid, dimethylformamide (DMF), and dimethyl sulfoxide (DMSO) were measured at temperatures ranging from 298.15 K to 333.85 K (p = 0.1 MPa) by the synthetic method with a laser monitoring dynamic technique. The mole fraction solubilities of biotin were observed to be highest in DMSO, and be lowest in water. The experimental data were well-correlated with the modified Apelblat equation, van’t Hoff equation, and λh equation, in which the correlation coefficients (R2) were noted in the range of 0.997 to 1.000 and the root-mean-square deviations (rmsd) were less than 2.82 %. Thermodynamic studies showed that dissolution of biotin was an endothermic and spontaneous process in all selected solvents.
1. INTRODUCTION Biotin (IUPAC name 5-[(3aS,4S,6aR)-2-oxohexahydro-1Hthieno[3,4-d]imidazol-4-yl]pentanoic acid; CAS Registry no. 58-85-5), also known as vitamin H, is an indispensible growth promoter for animals and human beings,1 and it plays an important role in cell proliferation and biotinylation of carboxylases and histones.2 Biotin deficiency may lead to dermatitis, baldness, and other degenerative effects, even fetal malformations.2,3 The molecular structure of biotin is illustrated in Figure 1.
results were regressed by the modified Apelblat equation, van’t Hoff equation, and λh equation.
2. EXPERIMENTAL SECTION 2.1. Materials. Biotin was kindly supplied by Xinchang Pharmaceuticals Factory, Zhejiang Medicine Co., Ltd. of China. Its mass fraction purity is higher than 0.997, which was confirmed by high-performance liquid chromatography (HPLC). The distilled water used in the experiment was purchased from market. The organic solvents of methanol, ethanol, acetic acid, DMF, and DMSO were purchased from Sinopharm Chemical Reagent Co., Ltd., which are analytical reagents. These organic solvents were dried by the molecular sieves of 0.4 nm aperture before use, and their purities were confirmed by gas chromatography (GC). Details of the solvents are shown in Table 1. 2.2. Apparatus and Procedure. The solubilities of biotin were measured following the synthetic method6 with laser monitoring dynamic technique. According to the literature,8,11 the solubility apparatus was set, and is shown in Figure 2. A 200 mL jacketed glass vessel was used to dissolve the biotin in this experiment and its temperature was maintained by continuous circulating water from a thermostat (type CH1015, Selon, Shanghai, China, uncertainty of ± 0.1 K). The mixture was kept constant stirring by a magnetic stirrer. A microthermometer (uncertainty of ± 0.01 K) was used to measure the real temperature of mixture in the vessel and a condenser was introduced to prevent evaporation of the solvents. Besides, the dissolution of the liquid−solid mixture was observed by a solubility measurement system with a laser beam. A light signal that passed through the vessel was collected by a detector, then
Figure 1. Molecular structure of biotin.
Researchers have shown great interest in the synthesis and extraction of biotin since it was discovered.3,4 The purity of obtained biotin is an important indicator of its quality and to get high quality biotin, chemical workers usually need do some purification processes, such as crystallization and recrystallization, a useful and convenient method in purification, in which the solubility data in appropriate solvents are imperative.5−7 In addition, solubility data are always taken into consideration when choosing solvents for reaction, extraction, or absorption.8,9 However, the solubility data of biotin have not been reported previously. Therefore, it is necessary to obtain the solubility data of biotin in different solvents. In this work, a synthetic method with laser monitoring dynamic technique was used to measure the solubility data of biotin in water, methanol, ethanol, acetic acid, dimethylformamide (DMF), and dimethyl sulfoxide (DMSO) at temperatures ranging from 298.15 K to 333.85 K (p = 0.1 MPa), and the © 2014 American Chemical Society
Received: August 25, 2014 Accepted: October 16, 2014 Published: October 27, 2014 3894
dx.doi.org/10.1021/je500787x | J. Chem. Eng. Data 2014, 59, 3894−3899
Journal of Chemical & Engineering Data
Article
Table 1. Details of the Biotin and Solvents Used in the Experimenta chemical name
source
biotin methanol ethanol acetic acid DMF DMSO water
XCPFb Sinopharmc Sinopharm Sinopharm Sinopharm Sinopharm HZWGd
initial mass fraction purity ≥ ≥ ≥ ≥ ≥ ≥
0.997 0.995 0.997 0.995 0.995 0.990
purification method none none none none none none distillation
final mass fraction purity ≥ ≥ ≥ ≥ ≥ ≥
analysis method HPLCe GCf GC GC GC GC
0.997 0.995 0.997 0.995 0.995 0.990
dielectric constant (20 °C)
dipole moment (10−30 C·m)
boiling point (°C)
31.2 25.7 6.15 36.71(25 °C) 48.9 80.103
5.55 5.60 5.60 12.88 13.34 6.47
64.51 78.32 118.1 153 189 100
a
Data of dielectric constant, dipole moment, and boiling point derived from solvent handbook.10 bXinchang Pharmaceuticals Factory, Zhejiang Medicine Co., Ltd. cSinopharm Chemical Reagent Co., Ltd. dHangzhou Wahaha Group Co., Ltd. eHigh performance liquid chromatography. fGas chromatography.
Figure 2. Solubility apparatus. (1) signal display; (2) laser acceptor; (3) jacked dissolution vessel; (4) condenser; (5) precise mercurial thermometer; (6) titration funnel; (7) feed inlet; (8) magnetic stirrer; (9) laser generator; (10) thermostat.
dure may cause the uncertainty of solubility measurement of biotin, and the value is no more than 1.0%.
equilibrium point of the given system could be judged depending on the signal change. An electronic analytical balance (type BS210S, Napco, Guangdong, China, uncertainty of ± 0.0001 g) was used to determine the masses of solutes and solvents. The procedure and method to measure the solubility data of biotin had been explained in detail by our co-workers in the literature.6,8,11,12 The laser method used has a definite close relation to some form of perhaps more frequently used turbidimetry. At first, a known mass of biotin was added into the vessel with a known mass of solvent at the desired temperature. When the solid particles were still undissolved after stirring for 30 min, additional quantitative solvent was put into the vessel with a buret. With the solid dissolving, the intensity of laser signal increased gradually, and when the last portion of solid particles were just dissolved, the intensity of laser signal arrived at its maximum. At the same time, the masses of the solute and the entire solvent were recorded. The mole fraction solubility of biotin (x1) could be obtained in accordance with the following equation: x1 =
m1/M1 m1/M1 + m2 /M 2
3. RESULTS AND DISCUSSION 3.1. Solubility Data of Biotin. The solubilities of biotin in the selected solvents (water, methanol, ethanol, acetic acid, DMF, and DMSO) were determined at temperatures ranging from 298.15 K to 333.85 K and the mole fraction solubilities are presented in Table 2 and plotted in Figure 3 (panels a and b). According to Table 2, we can see that the solubilities of biotin in acetic acid, DMF, and DMSO are especially higher than that in water, methanol, and ethanol. They are in different orders of magnitude. As shown in Figure 3 (panels a and b), the solubilities of biotin in the selected solvents increase with the rising temperature of the solvents. Additionally, the solubility of biotin is much higher in DMSO than in the other five solvents, while it is the lowest in water. At the same temperature and pressure, the solubility ordering in the selected solvents is DMSO > DMF > acetic acid > methanol > ethanol > water. As the solubility and structure of biotin was analyzed, we speculated that a solvent with similar structure and high polarity is beneficial to dissolve the biotin. 3.2. Correlation of Solubility Data. In this work, the relationship of the absolute temperature (T/K) and experimental mole fraction solubility data (x1) of biotin were correlated by the modified Apelblat equation, van’t Hoff equation, and λh equation. 3.2.1. Modified Apelblat Equation. The modified Apelblat equation was widely used in relating solubility data of a solute in various pure solvents, and it is a semiempirical equation,
(1)
where m1 and m2 stand for the masses of biotin and solvent, and M1 and M2 represent the homologous molecular weight, respectively. Each experiment in different solvents was repeated at least three times. The uncertainties of temperature fluctuation of the water bath, temperature measurements, and weighing proce3895
dx.doi.org/10.1021/je500787x | J. Chem. Eng. Data 2014, 59, 3894−3899
Journal of Chemical & Engineering Data
Article
Table 2. Experimental Mole Fraction Solubilities x1 along with Relative Deviations RD of Biotin in Different Pure Solvents at Temperature T and Pressure p = 0.1 MPaa 102 RD T/K
4
10 x1
298.15 303.15 308.05 312.75 318.55 323.15 328.95 332.95
0.0497 0.0818 0.1277 0.2055 0.3523 0.5425 0.9122 1.2853
298.15 302.75 308.05 313.25 317.85 323.55 327.65 332.95
0.6919 0.9372 1.4306 2.0824 2.9820 4.5967 6.0056 8.6205
298.15 302.95 308.85 313.95 318.45 323.55 329.35 333.85
0.6350 0.8687 1.3268 1.7563 2.2999 3.0935 4.4194 5.8170
298.15 303.15 308.15 313.25 317.95 323.45 327.85 333.25
22.568 28.349 35.003 42.430 50.934 64.613 76.614 92.241
298.65 303.25 308.15 313.15 318.15 323.25 328.15 333.15
35.632 41.288 49.686 60.287 74.996 90.235 106.83 127.73
298.15 303.15 308.15 313.15 318.05 322.75 327.65 332.85
377.84 424.81 478.55 529.59 581.92 633.29 687.35 747.62
modified Apelblat Water 1.75 1.09 −2.64 −0.28 −0.77 0.31 0.45 −0.21 Methanol 0.22 −4.55 −1.90 −2.71 −0.17 2.33 0.20 −0.48 Ethanol −3.39 −2.40 3.10 −0.20 −0.61 −1.64 −0.36 0.75 Acetic Acid −2.08 0.04 0.69 −0.61 −1.03 1.18 1.19 −0.88 DMF 2.14 −1.23 −1.75 −1.54 1.42 0.96 −0.13 −0.36 DMSO −1.30 −0.71 0.60 0.61 0.57 0.34 −0.12 −0.49
van’t Hoff
λh
6.39 3.95 −1.09 0.27 −0.94 −0.07 0.23 −0.06
6.40 3.96 −1.08 0.28 −0.93 −0.07 0.23 −0.05
6.61 −0.49 −0.21 −2.53 −0.75 1.54 −0.31 −0.08
6.63 −0.47 −0.20 −2.53 −0.75 1.54 −0.30 −0.07
4.59 2.62 5.26 0.41 −0.89 −2.36 −0.85 0.92
4.55 2.59 5.25 0.41 −0.88 −2.35 −0.84 0.92
0.58 1.19 0.81 −1.15 −1.82 0.53 0.92 −0.34
0.47 1.14 0.80 −1.13 −1.78 0.57 0.94 −0.37
4.30 −0.19 −1.64 −2.01 0.75 0.39 −0.30 0.17
4.19 −0.25 −1.65 −1.99 0.78 0.42 −0.28 0.15
−2.04 −0.91 0.74 0.93 0.92 0.60 −0.09 −0.83
−2.30 −0.97 0.81 1.08 1.08 0.71 −0.09 −1.02
Figure 3. Solubilities of biotin in six selected solvents: ■, water; ●, methanol; ▲, ethanol; ▼, acetic acid; ○, DMF; □, DMSO. Solid lines are calculated values based on the modified Apelblat equation.
which was originated from the Williamson equation,13 and is expressed as follows: ln x1 = A +
B + C ln T T
(2)
where A, B, and C are model parameters. The values of A and B stand for the variation in the solution activity coefficient and give an indication of the effect of solution nonidealities on the solubility of solute, while the value of C represents the effect of temperature on the fusion enthalpy. 3.2.2. van’t Hoff Equation. For an ideal solution, the logarithm of mole fraction solubility data of a solute and the reciprocal of the absolute temperature are in a good linear relationship, which could be reflected by the van’t Hoff equation:14 ln x1 = −
ΔHd ΔSd + RT R
(3)
where R is the gas constant, and ΔHd and ΔSd represent the enthalpy and entropy of dissolution, respectively.
Standard uncertainties are u(T) = ± 0.01 K, ur(p) = 0.05, and ur(x1) = 0.01.
a
3896
dx.doi.org/10.1021/je500787x | J. Chem. Eng. Data 2014, 59, 3894−3899
Journal of Chemical & Engineering Data
Article
Table 3. Model Parameters in Different Pure Solvents modified Apelblat
λh
van’t Hoff
solvent
A
B
C
ΔHd/(KJ·mol−1)
ΔSd/(J·mol−1·K−1)
λ
h
water methanol ethanol acetic acid DMF DMSO
−79.7373 −145.689 −147.638 −90.1909 −81.7685 42.3641
−4726.42 259.026 1329.53 589.987 384.497 −3754.17
14.6308 23.7362 23.4393 14.4164 13.1284 −5.79814
78.7174 61.4668 52.2201 33.3535 31.6247 15.9435
161.937 125.951 94.4022 61.1531 58.6577 26.4056
2.12441 1.69876 0.34225 0.54598 0.60938 0.42887
4456.75 4352.73 18339.2 7312.60 6209.42 4161.89
Table 4. Correlation Coefficients (R2), Average Absolute Deviations (AAD), and Root-Mean-Square Deviations (rmsd) for the Selected Models in Different Pure Solvents modified Apelblat
λh
van’t Hoff
solvent
102 AAD
102 rmsd
R2
102 AAD
102 rmsd
R2
102 AAD
102 rmsd
R2
water methanol ethanol acetic acid DMF DMSO
0.94 1.57 1.56 0.96 1.19 0.59
1.24 2.16 1.96 1.11 1.35 0.67
0.99995 0.99951 0.99955 0.99910 0.99915 0.99902
1.62 1.56 2.24 0.92 1.22 0.88
2.71 2.58 2.82 1.02 1.81 1.02
0.99997 0.99977 0.99918 0.99944 0.99922 0.99806
1.63 1.56 2.23 0.90 1.22 1.01
2.71 2.59 2.81 0.99 1.78 1.16
0.99997 0.99977 0.99918 0.99944 0.99923 0.99741
3.2.3. λh Equation. The λh equation, which was initially proposed by Buchowski et al.,15 is also a common model for associating the solubility data: ⎛1 ⎛ 1 − x1 ⎞ 1 ⎞ ln⎜1 + λ ⎟ ⎟ = λh⎜ − x1 ⎠ Tm ⎠ ⎝T ⎝
equation gives the best correlation result where the AADs are less than 1.57 % and values of rmsd are less than 2.16 %. 3.3. Thermodynamic Parameters for Dissolution of Biotin. Thermodynamic parameters for dissolution of biotin containing of molar enthalpy change (ΔH0), molar entropy change (ΔS0), and Gibbs function (ΔG0) were determined. According to the van’t Hoff analysis,16 the values of ΔH0 at mean harmonic temperature in selected solvents could be calculated on the basis of eq 8.
(4)
where λ and h are model parameters and Tm is the melting temperature of solute. The value of λ denotes the nonideality of solution, and h reflects the enthalpy of the solution. The parameters of the aforementioned models were determined by nonlinear multivariate regression analysis and listed in Table 3. The relative deviations (RD), average absolute deviations (AAD), and root-mean-square deviations (rmsd) were determined to identify the differences between the experimental and calculated results, and they are defined as the following formulas: RD =
xi − xi calcd xi
AAD =
1 N
⎡ 1 rmsd = ⎢ ⎢N ⎣
N
∑ i=1
xi − xicalcd xi
1/2 ⎛ x calcd − x ⎞2 ⎤ i ⎥ ∑ ⎜⎜ i ⎟⎟ ⎥ x ⎝ ⎠⎦ i i=1
⎛ ⎜ ∂ ln x1 ⎜ ⎜∂ 1 − 1 Thm ⎝ T
(
)
⎞ ⎟ ΔH ° ⎟ =− R ⎟ ⎠p
(8)
Here, Thm is the mean harmonic temperature and its value is 315.55 K in the current study. R is the universal gas constant equal to 8.314 J·mol−1·K−1. When plotting ln x1 versus (1/T − 1/Thm), the slope is the value of (−ΔH0/R), then the value of molar enthalpy change (ΔH0) for dissolution of biotin was obtained. The van’t Hoff plots for biotin in different pure solvents are presented in Figure 4. These plots for solubilities of biotin in selected solvents were deemed to be linear with correlation coefficients (R2) in the range of 0.997 to 1.000 (as shown in Table 5). The Gibbs function (ΔG0) for dissolution of biotin was calculated using the following equation:17
(5)
(6)
N
(7)
ΔG° = − RThm × intercept
xicalcd
where and xi stand for the calculated solubility and the experimental solubility, respectively, and N represents the number of experimental points. The RD values for each model are listed in Table 2 with the solubility data, whereas AAD and rmsd are shown in Table 4 with correlation coefficients (R2). From Table 2 and Table 4, we can find that all the absolute values of RDs are less than 6.63 %, and all the AAD and rmsd values are no more than 2.24 % and 2.82 %, respectively. There is no doubt that the solubilities of biotin calculated by the selected models are all in good agreement with the experimental solubilities in each solvent with the R2 values in the range of 0.997 to 1.000. Meanwhile, the modified Apelblat
(9)
in which the intercept can also be obtained by plotting ln x1 against (1/T − 1/Thm), which are presented in Figure 4. With the values of molar enthalpy change (ΔH0) and Gibbs function (ΔG0) being obtained, the molar entropy change (ΔS0) could be calculated using eq 10. ΔS ° =
ΔH ° − ΔG° Thm
(10)
The values of ΔH , ΔG , and ΔS together with R values for the dissolution of biotin in water, methanol, ethanol, acetic acid, DMF, and DMSO are listed in Table 5. From the table, we can 0
3897
0
0
2
dx.doi.org/10.1021/je500787x | J. Chem. Eng. Data 2014, 59, 3894−3899
Journal of Chemical & Engineering Data
Article
different. For instance, solubilities in acetic acid and DMF are more sensitive than that in DMSO. Besides, the solubilities of biotin are different in the selected solvents, and the solubility ordering is water < ethanol < methanol < acetic acid < DMF < DMSO. According to the van’t Hoff analysis, thermodynamic parameters for dissolution of biotin were determined in terms of molar enthalpy change (ΔH0), molar entropy change (ΔS0), and Gibbs function (ΔG0). Thermodynamic studies demonstrated that dissolution of biotin was an endothermic and spontaneous process in selected solvents. Basic data and models are essential in the fabrication and purification processes of biotin, and the experimental solubility data and regression equations obtained in our work can provide some help.
■
AUTHOR INFORMATION
Corresponding Author
*Tel: +86-571-87951615. Fax: +86-571-87951742. E-mail:
[email protected].
Figure 4. Van’t Hoff plots for experimental solubilities of biotin in ■, water; ●, methanol; ○, ethanol; ▼, acetic acid; △, DMF; □, DMSO.
Funding
The authors are grateful for the financial support from the Natural Science Foundation of China (21376213), the Research Fund for the Doctoral Program of Higher Education of China (20120101110062), and the Low Carbon Fatty Amine Engineering Research Center of Zhejiang Province (2012E10033).
see that the ΔH0 and ΔG0 values are observed as positive values in the investigated solvents, indicating that the dissolution of biotin in selected solvents was endothermic and spontaneous, respectively. These positive values also mean that the interactions between the biotin molecules and solvent molecules are much stronger than those between the biotin− biotin molecules and solvent−solvent molecules. The values of ΔS0 for the dissolution of biotin in investigated solvents are also positive values, indicating the entropy-driven dissolution of biotin. According to Table 5, the values of ΔH0 and ΔG0 for the dissolution of biotin in acetic acid, DMF, and DMSO are lower than that in water, methanol, and ethanol, which indicated that energy for the solubilization of biotin in acetic acid, DMF, and DMSO is low as compared to water, methanol, or ethanol.
Notes
The authors declare no competing financial interest.
■
REFERENCES
(1) Na, K.; Bum Lee, T.; Park, K. H.; Shin, E. K.; Lee, Y. B.; Choi, H. K. Self-assembled nanoparticles of hydrophobically-modified polysaccharide bearing vitamin H as a targeted anti-cancer drug delivery system. Eur. J. Pharm. Sci. 2003, 18, 165−173. (2) Crisp, S. E.; Griffin, J. B.; White, B. R.; Toombs, C. F.; Camporeale, G.; Said, H. M.; Zempleni, J. Biotin supply affects rates of cell proliferation, biotinylation of carboxylases and histones, and expression of the gene encoding the sodium-dependent multivitamin transporter in JAr choriocarcinoma cells. Eur. J. Nutr. 2004, 43, 23−31. (3) Confalone, P. N.; Pizzolato, G.; Uskokovic, M. R. A stereospcific synthesis of biotin via thiophene intermediates. J. Org. Chem. 1977, 42, 135−139. (4) Whitney, R. A. A total synthesis of (±)-biotin. Can. J. Chem. 1983, 61, 1158−1160. (5) Wang, P.; Wang, J. K.; Gong, J. B.; Zhang, M. J. Determination of the solubility, dissolution enthalpy and entropy of Deflazacort in different solvents. Fluid Phase Equilib. 2011, 306, 171−174. (6) Wang, Y. N.; Jia, Y. X.; Qian, C.; Tao, M.; Lv, X. H.; Chen, X. Z. Solubilities of 4,4′-dichlorodiphenyl disulfide in six organic solvents between (303.15 and 333.15) K. J. Chem. Eng. Data 2013, 58, 660− 662. (7) Wu, J. G.; Ge, J.; Zhang, Y. P.; Yu, Y.; Zhang, X. Y. Solubility of genistein in water, methanol, ethanol, propan-2-ol, 1-butanol, and ethyl acetate from (280 to 333) K. J. Chem. Eng. Data 2010, 55, 5286− 5288.
4. CONCLUSIONS Solubilities of biotin in methanol, ethanol, water, acetic acid, DMF, and DMSO were measured at temperatures ranging from (298.15 to 333.85) K using the synthetic method with laser monitoring dynamic technique. The experimental solubility data were correlated by the modified Apelblat equation, van’t Hoff equation, and λh equation with good consequences, in which the three models of R2 values are more than 0.997, the absolute values of relative deviations are no more than 6.63%, the average absolute deviations are less than 2.24%, and the root-mean-square deviations are less than 2.82%. And more specifically, the modified Apelblat model gives the best fitting result, where the 102 AAD of the modified Apelblat equation in each solvent are as follows: 0.94 (water), 1.57 (methanol), 1.56 (ethanol), 0.96 (acetic acid), 1.19 (DMF), and 0.59 (DMSO). The solubilities of biotin increase with the temperature of solvents rising, and their sensitivities to temperature are
Table 5. Thermodynamic Parameters for Dissolution of Biotin in Different Pure Solvents parameters −1
ΔH /(KJ·mol ) ΔG0/(KJ·mol−1) ΔS0/(J·mol−1·K−1) R2 0
water
methanol
ethanol
acetic acid
DMF
DMSO
77.44 27.59 158.0 0.99967
60.64 21.71 123.4 0.99910
50.89 22.40 90.31 0.99929
33.16 14.05 60.55 0.99948
31.19 13.11 57.29 0.99813
16.21 7.612 27.23 0.99789
3898
dx.doi.org/10.1021/je500787x | J. Chem. Eng. Data 2014, 59, 3894−3899
Journal of Chemical & Engineering Data
Article
(8) Jia, Y. X.; Qian, C.; Chen, X. Z.; He, C. H. Solubilities of 3methoxy-N-phenylaniline and 3-(methylthio)-N-phenylaniline in five organic solvents (285 to 333.75 K). J. Chem. Eng. Data 2012, 57, 1581−1585. (9) Zhang, H. T.; Wang, J. K.; Chen, Y.; Zhang, M. J. Solubility of sodium cefotaxime in different solvents. J. Chem. Eng. Data 2007, 52, 982−985. (10) Cheng, N. L. Solvent Handbook, 4th ed.; Chemistry Industrial Press: Beijing, China, 2007. (11) Fu, S. X.; Wang, Y. N.; Jia, Y. X.; Qian, C.; Tao, M.; Lv, X. H.; Chen, X. Z. Solubilities of 4-amino-4′-nitrodiphenyl sulfide in six organic solvents from 287.45 to 365.55 K. J. Chem. Eng. Data 2013, 58, 1675−1678. (12) Qian, C.; Zhang, T.; Pi, S. Q.; Chen, X. Z. Solubility of canthaxanthin in pure solvents from (293.15 to 343.15) K. J. Chem. Eng. Data 2009, 54, 1115−1116. (13) Manzurola, E.; Apelblat, A. Solubilities of L-glutamic acid, 3nitrobenzoic acid, p-toluic acid, calcium-L-lactate, calcium gluconate, magnesium-DL-aspartate, and magnesium-L-lactate in water. J. Chem. Thermodyn. 2002, 34, 1127−1136. (14) Grant, D. J. W.; Mehdizadeh, M.; Chow, A. H. L.; Fairbrother, J. E. Non-linear van’t Hoff solubility-temperature plots and their pharmaceutical interpretation. Int. J. Pharm. 1984, 18, 25−38. (15) Buchowski, H.; Ksiazczak, A.; Pietrzyk, S. Solvent activity along a saturation line and solubility of hydrogen-bonding solids. J. Phys. Chem. 1980, 84, 975−979. (16) Holguín, A. R.; Rodríguez, G. A.; Cristancho, D. M.; Delgado, D. R.; Martínez, F. Solution thermodynamics of indomethacin in propylene glycol + water mixtures. Fluid Phase Equilib. 2012, 314, 134−139. (17) Krug, R. R.; Hunter, W. G.; Grieger, R. A. Enthalpy-entropy compensation. 2. Separation of the chemical from the statistical effect. J. Phys. Chem. 1976, 80, 2341−2351.
3899
dx.doi.org/10.1021/je500787x | J. Chem. Eng. Data 2014, 59, 3894−3899
