Equilibrium Solubility, Model Correlation, and Solvent Effect of Indole

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

Equilibrium Solubility, Model Correlation, and Solvent Effect of Indole-3-acetic Acid in Twelve Pure Solvents Rongrong Li,*,† Shiyun Zhan,† Gang Chen,† Yanxian Jin,† Binbin Yu,† Jia Zhao,‡ Deman Han,*,† and Huajun Fan*,§ †

School of Pharmaceutical and Materials Engineering, TaiZhou University, Taizhou, Zhejiang 318000, PR China Industrial Catalysis Institute, Zhejiang University of Technology, Hangzhou 310014, PR China § Department of Chemistry, Prairie View A&M University, Prairie View, Texas 77446, United States Downloaded via UNIV OF ALABAMA BIRMINGHAM on March 17, 2019 at 01:10:40 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

‡

ABSTRACT: The solid−liquid solubility of indole-3-acetic acid in pure methanol, ethanol, n-propanol, isopropanol, acetone, n-butanol, acetonitrile, chloroform, ethyl acetate, 1,4-dioxane, N,N-dimethylformamide (DMF), and dimethyl sulfoxide (DMSO) was measured by using a isothermal saturation method. The determination temperature range is from 278.15 to 323.15 K. The order of solubility data from high to low was ethyl acetate > DMSO > DMF > n-butanol > acetone > isopropanol > 1,4dioxane > n-propanol > ethanol > methanol > acetonitrile > chloroform. Two thermodynamic models (modified Apelblat equation and λh equation) were used to correlate the solubility values of indole-3-acetic acid in different monosolvents, and the two equations can correlate the experimental values very well. The values of root-meansquare deviations (RMSDs) and relative average deviations (RADs) between the experimental and calculated solubility values were not exceeding 0.27 × 10−6 and 0.75 × 10−2, respectively. In order to study the effect of solvation interaction on solubility, the solute−solvent and solvent−solvent interactions were discussed.

1. INTRODUCTION Indole-3-acetic acid (CAS Reg. No. 87-51-4, shown in Figure 1) was the first natural auxin identified, and today it is widely

acid is necessary to determine. However, the solubility data of indole-3-acetic acid in water were reported from the Human Metabolome Database (HMDB), and the solubility data in water are 1.5 mg·mL−1. Solubility in aqueous solubility in buffer is more than 26.3 μg·mL−1 and is from the Burnham Center for Chemical Genomics. For selection of solvents, solvent selection is a pivotal procedure. Practicable solvents should be thermally stable, nontoxic (environmentally safe), noncorrosive, and commercially available. The frequently used solvents in the pharmaceutical and agriculture fields are methanol, ethanol, propanol, butanol, and N,N-dimethylformamide (DMF) and so forth.8,9 Ethanol and isopropanol are safe and common solvents to be used in the pharmaceutical industry due to its high solubilization capacity.10 DMSO is an important polar aprotic solvent with very low toxicity and immense biological importance.11 Chloroform, acetone, ethyl acetate, and 1,4dioxane are used as extractant in the pharmaceutical and agriculture fields. Chloroform and 1,4-dioxane can be used as extractants of cosmetics, antibiotics, and auxins. In addition, acetone and acetonitrile possess high solubilization capacity and are usually used as reaction media for recrystallization. On the basis of the considerations mentioned above, in this research, the solubility of indole-3-acetic acid in methanol, ethanol, n-propanol, isopropanol, acetone, n-butanol, acetoni-

Figure 1. Chemical structure of indole-3-acetic acid.

considered to be the main auxin in plants.1 It is the major form of natural auxin in higher plants and the most studied form of auxin.2 Indole-3-acetic acid may play an important role in plant water relations.3 Indole-3-acetic acid stimulates stomatal opening and water movement in roots and is thought to act with abscisic acid in responding to the types of stress that affect turgor (e.g., drought and salinity).1 It has an inhibitory effect on S-37, and its downstream product methylindole acetate has an inhibitory effect on Ehrlich’s carcinoma. Among phytohormones, indole-3-acetic acid is the most stimulatory to the plant growth process.4 According to some research, the content of indole-3-acetic acid has a great effect on the growth of plant fruit as well as plant apical dominance, shoot growth, cell division, and root germination.5−7 Therefore, in order to control the plant growth well, the solubility of indole-3-acetic © XXXX American Chemical Society

Received: December 31, 2018 Accepted: March 5, 2019

A

DOI: 10.1021/acs.jced.8b01265 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 1. Source and Purity of the Materials Used in the Work chemicals

molar mass (g·mol−1)

CAS no.

melting point (K)

indole-3-acetic acid

175.18

87-51-4

437.15a

methanol n-propanol isopropanol ethanol n-butanol DMF ethyl acetate acetonitrile 1,4-dioxane DMSO chloroform acetone

32.04 60.06 60.06 46.07 74.12 73.09 88.11 41.05 88.11 78.13 119.38 58.05

67-56-1 71-23-8 67-63-0 64-17-5 71-36-3 68-12-2 141-78-6 75-05-8 123-91-1 67-68-5 67-66-3 67-64-1

source Shanghai Aladdin Bio-Chem Technology Co., Ltd. Sinopharm Chemical Reagent Co., Ltd., China

mass fraction purity

analysis method

0.996

HPLCb

0.997 0.994 0.995 0.995 0.995 0.996 0.995 0.994 0.996 0.994 0.994 0.995

GCc GC GC GC GC GC GC GC GC GC GC GC

a

Take from ref 28. bHigh-performance liquid-phase chromatograph. cGas chromatography.

experimental temperature was displayed by a mercury glass microthermometer (standard uncertainty: 0.02 K). The solution was kept stirring for 24 h. Then, stirring was stopped, and the sample was let to precipitate for about 1 h. Upper equilibrium liquor was withdrawn by a 5 mL preheated syringe and transferred into a 25 mL preweighed volumetric flask covered with a rubber stopper. The total amount of the sample and flask was weighed by an analytical balance. It was diluted to 25 mL with the corresponding solvent and tested by the HPLC. The mole fraction solubility of indole-3-acetic acid (xw,T) in pure solvents was obtained by eq 1.

trile, chloroform, ethyl acetate, 1,4-dioxane, DMF, and DMSO was determined. To extend the applicability of the solubility, the modified Apelblat equation and λh equation were used to correlate to the experimental values. Moreover, in order to study the effect of solvation interaction on solubility, solute− solvent and solvent−solvent interactions were discussed.

2. EXPERIMENTAL SECTION 2.1. Materials. Indole-3-acetic acid was purchased by Shanghai Aladdin Bio-Chem Technology Co., Ltd., China. The mass fraction of the sample was 0.996, which was confirmed by a high-performance liquid-phase chromatograph (HPLC). The solvents were purchased from Sinopharm Chemical Reagent Co., Ltd., China. They were analytical grade, and the mass fraction of these was all greater than 0.994, which was determined by gas chromatography (GC). The detailed information on the chemicals was listed in Table 1. 2.2. Solubility Determination. The solid−liquid equilibrium solubility in this work was measured by the isothermal saturation method12,13 in the temperature range from T = 283.15 to 323.15 K under atmospheric pressure. The reliability of verification of the experimental apparatus was verified by determining the solubility of benzoic acid in toluene, and the results are presented in Table 2.14 The solubility of indole-3acetic acid in different solvents was analyzed by HPLC. First of all, excessive solid indole-3-acetic acid and 25 mL of solvents were added to the jacketed glass vessel. The temperature was kept by a thermostatic circulator bath. The

x w,T =

xexp

xref

100RD

278.15 283.15 293.15 303.15 313.15

0.129 0.141 0.165 0.196 0.232

0.128 0.139 0.166 0.196 0.234

0.77 1.42 −0.61 0 −0.86

(1)

where m1 and m2 stand for the mass of indole-3-acetic acid and solvents. M1 and M2 refer to the molar mass of indole-3-acetic acid and the solvents. 2.3. Analysis Method. The sample was analyzed by highperformance liquid chromatography (HPLC). The type of reverse-phase column was Agilent Eclipse XDB-C18 (250 mm × 4.6 mm). The column temperature was kept at 303 K. The ultraviolet wavelength was set at 215 nm. The mobile phase was pure acetonitrile, and the flow rate was 1 mL·min−1. Furthermore, each experiment was carried out three times, and the average value was employed to calculate the mole fraction solubility.

3. RESULTS AND DISCUSSION 3.1. Solubility Data. The measured and calculated mole fraction solubility of indole-3-acetic acid in monosolvents was presented in Table 3 and graphically shown in Figure 2. In addition, the van’t Hoff plots of ln(x) versus 1/T in 12 solvents are plotted in Figure 3, and the correlation coefficient was listed in Table 4. It can be seen from Table 3 and Figure 2 that the solubility of indole-3-acetic acid increases with increasing temperature at a certain solvent. At a certain temperature, the solubility values of indole-3-acetic acid in mole fraction in monosolvents can be ranked as ethyl acetate > DMSO > DMF > n-butanol > acetone > isopropanol > 1,4-dioxane > npropanol > ethanol > methanol > acetonitrile > chloroform. Table 4 presents the polarity of the solvents.15 It can be found from Figure 2 and Tables 3 and 5 that, for the systems of

Table 2. Solubility (x) of Benzoic Acid in Ethanol with the Relative Deviation at the Temperature Range from T = 278.15 to 313.15 K under 101.2 kPaa T/K

m1/M1 m1/M1 + m2 /M 2

a

Standard uncertainties u are u(T) = 0.02 K and u(p) = 400 Pa. Relative standard uncertainty ur is ur(x) = 0.0101. xexp, experimental data. xref, taken from ref 14. RD is the relative deviations of experiment value with the reference data. B

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Table 3. Experimental Solubility (x) of Indole-3-acetic Acid in Mole Fraction in Studied Monosolvents at the Temperature Range from T = (278.15 To 323.15) K under 101.2 kPaa,b solvents T/K

1000xexp

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 100RAD

0.008954 0.009757 0.01053 0.01172 0.01267 0.01383 0.01528 0.01667 0.01832 0.01991

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 100RAD

0.01445 0.01539 0.01654 0.01802 0.01930 0.02082 0.02238 0.02422 0.02623 0.02847

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 100RAD

0.02775 0.02898 0.03038 0.03201 0.03391 0.03600 0.03832 0.04086 0.04344 0.04648

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 100RAD

0.02059 0.02198 0.02346 0.02506 0.02691 0.02891 0.03123 0.03382

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 100RAD

0.02984 0.03117 0.03287 0.03470 0.03667 0.03903 0.04158 0.04448 0.04742 0.05068

1000xapelblat methanol 0.008920 0.009737 0.01064 0.01163 0.01271 0.01391 0.01522 0.01666 0.01824 0.01997 0.45 n-propanol 0.01447 0.01552 0.01668 0.01796 0.01935 0.02089 0.02257 0.02442 0.02644 0.02865 0.25 n-butanol 0.02767 0.02898 0.03045 0.03210 0.03394 0.03598 0.03824 0.04074 0.04349 0.04652 0.17 1,4-dioxane 0.02064 0.02194 0.02342 0.02506 0.02690 0.02896 0.03125 0.03379 0.11 DMF 0.02976 0.03123 0.03287 0.03472 0.03677 0.03904 0.04156 0.04434 0.04740 0.05077 0.14

1000xλh

1000xexp

0.008869 0.009727 0.01066 0.01166 0.01276 0.01395 0.01524 0.01666 0.01820 0.01990 0.55

0.01171 0.01250 0.01354 0.01467 0.01598 0.01726 0.01862 0.02035 0.02216 0.02413

0.01437 0.01550 0.01672 0.01803 0.01944 0.02097 0.02262 0.02441 0.02636 0.02849 0.42

0.02154 0.02274 0.02406 0.02557 0.02715 0.02885 0.03101 0.03338 0.03583 0.03877

0.02737 0.02891 0.03055 0.03230 0.03418 0.03621 0.03839 0.04074 0.04330 0.04607 0.61

0.03442 0.03635 0.03851 0.04093 0.04322 0.04581 0.04848 0.05131 0.05430 0.05760

0.02047 0.02193 0.02351 0.02521 0.02704 0.02903 0.03119 0.03354 0.43

 0.03731 0.03952 0.04199 0.04453 0.04769 0.05117 0.05485

0.02944 0.03115 0.03298 0.03493 0.03703 0.03928 0.04171 0.04434 0.04718 0.05028 0.59

0.02492 0.02599 0.02730 0.02889 0.03069 0.03258 0.03490 0.03734 0.03980 0.04251

C

1000xapelblat ethanol 0.01167 0.01257 0.01357 0.01467 0.01589 0.01723 0.01871 0.02035 0.02215 0.02413 0.25 isopropanol 0.02160 0.02273 0.02402 0.02548 0.02713 0.02897 0.03103 0.03333 0.03589 0.03873 0.18 ethyl acetate 0.03439 0.03641 0.03855 0.04083 0.04323 0.04578 0.04848 0.05134 0.05436 0.05755 0.10 DMSO  0.03733 0.03949 0.04192 0.04465 0.04769 0.05109 0.05488 0.11 acetone 0.02478 0.02602 0.02742 0.02898 0.03072 0.03265 0.03479 0.03716 0.03977 0.04264 0.29

1000xλh 0.01155 0.01254 0.01360 0.01474 0.01598 0.01732 0.01877 0.02035 0.02207 0.02395 0.49 0.02126 0.02264 0.02412 0.02570 0.02740 0.02923 0.03121 0.03335 0.03567 0.03819 0.75 0.03454 0.03647 0.03852 0.04072 0.04308 0.04561 0.04834 0.05129 0.05449 0.05797 0.33  0.03713 0.03951 0.04207 0.04483 0.04782 0.05106 0.05459 0.33 0.02450 0.02595 0.02750 0.02916 0.03095 0.03286 0.03493 0.03716 0.03958 0.04222 0.70

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Table 3. continued solvents T/K 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 100RAD

1000x

1000x

1000x

1000xexp

1000xapelblat

1000xλh

0.006506 0.006977 0.007475 0.008029 0.008678 0.009364 0.01015 0.01102 0.01197 0.01301

acetonitrile 0.006509 0.006966 0.007475 0.008042 0.008673 0.009373 0.01015 0.01101 0.01196 0.01302 0.07

0.006427 0.006944 0.007499 0.008098 0.008743 0.009440 0.01020 0.01102 0.01191 0.01288 0.64

0.002878 0.002987 0.003111 0.003295 0.003484 0.003624 0.003876 0.004073 0.004341 0.004612

chloroform 0.002869 0.002993 0.003132 0.003287 0.003459 0.003649 0.003857 0.004086 0.004337 0.004612 0.37

0.002845 0.002988 0.003140 0.003303 0.003477 0.003665 0.003867 0.004086 0.004322 0.004580 0.53

exp

λh

apelblat

a

x denotes the experimental mole fraction solubility of indole-3-acetic acid at the studied temperature T; RAD denotes the relative average deviation, respectively. bStandard uncertainties u are u(T) = 0.02 K and u(p) = 400 Pa. Relative standard uncertainty ur is ur(x) = 0.0128. xexp, experimental data; xapelblat, calculated by the apelblat model; xλh, calculated by the λh model.

Table 4. Correlation Coefficient from Experimental Data and the van’t Hoff equation solvents

R2

solvents

R2

solvents

R2

methanol isopropanol acetonitrile DMF

0.99 0.98 0.99 0.98

ethanol n-butanol ethyl acetate DMSO

0.99 0.98 0.99 0.99

n-propanol acetone 1,4-dioxane chloroform

0.99 0.98 0.99 0.98

Table 5. Physical Properties for the Selected Solventsa

Figure 2. Mole fraction solubility x of indole-3-acetic acid in 12 monosolvents at different temperature: □, ethyl acetate; ★, DMSO; ◀, DMF; ◆, n-butanol; △, acetone; ▼, isopropanol; ◇, 1,4dioxane; ▲, n-propanol; ●, ethanol; ■, methanol; ☆, acetonitrile; ○, chloroform.

solvent

polarity (water 100)

α

β

π*

δ2/1000 (J/cm3)

methanol isopropanol acetonitrile ethyl acetate ethanol n-butanol chloroform acetone n-propanol 1,4-dioxane DMF DMSO

76.2 54.6 46.0 23.0 65.4 60.2 25.9 35.5 61.7 16.4 40.4 44.4

0.98 0.76 0.19 0 0.86 0.84 0.44 0.08 0.84 0 0 0

0.66 0.84 0.40 0.45 0.75 0.84 0 0.43 0.90 0.37 0.69 0.76

0.60 0.48 0.75 0.55 0.54 0.47 0.58 0.71 0.52 0.55 0.88 1

0.8797 0.5630 0.5806 0.3310 0.5630 0.5333 0.3769 0.3994 0.6025 0.4194 0.6126 0.6027

a

Taken from refs 15 and 19−21.

butanol > isopropanol > n-propanol > ethanol > methanol. The molecule of indole-3-acetic acid is large, and when solute dissolves in solvents, solvents are more easily to self-cohesive. Because the methanol molecule is smallest in alcohol, methanol−methanol interaction is the strongest. As a result, the solubility of indole-3-acetic acid in methanol is the lowest and in n-butanol is largest. For the other solvents, the order of them high to low is in accordance with the polarities expect for ethyl acetate, 1,4-dioxane, and acetonitrile. It seems that polarities are a significant factor to affect the solubility behavior, but the polarities are not the only factor on solubility of indole-3-acetic acid. Both the indole-3-acetic acid molecule and ethyl acetate molecule have a carbon oxygen double bond. Besides, the 1,4-dioxane molecule has a ring structure similar to the indole-3-acetic acid molecule. Based on the principle that a similar structure is more likely to be dissolved by each other, the structural similarity between indole-3-acetic acid and

Figure 3. Van’t Hoff plots of ln(x) versus 1/T in 12 solvents: □, ethyl acetate; ★, DMSO; ◀, DMF; ◆, n-butanol; △, acetone; ▼, isopropanol; ◇, 1,4-dioxane; ▲, n-propanol; ●, ethanol; ■, methanol; ☆, acetonitrile; ○, chloroform.

indole-3-acetic acid + alcohol, the sequence of the solubility in mole fraction is in accordance with the polarities. The order of solubility data in alcohol from high to low is ranked as nD

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Table 6. Parameters of the Equations and RMSD Values for Indole-3-acetic Acid in Different Monosolvents λh equation

modified Apelblat equation solvent

A

B

C

106 RMSD

R2

104λ

10−4h

106 RMSD

R2

ethanol n-propanol 1,4-dioxane acetonitrile ethyl acetate isopropanol DMSO methanol DMF n-butanol chloroform acetone

−104.746 −98.233 −134.267 −119.203 −52.518 −134.414 −137.370 −86.906 −116.302 −116.977 −109.071 −118.352

2953.355 2745.515 4496.971 3629.342 1023.727 4545.131 4786.818 2011.268 3834.388 3885.615 3506.160 3903.059

14.706 13.720 19.047 16.740 6.851 19.070 19.513 12.091 16.363 16.437 14.872 16.651

0.05 0.06 0.03 0.008 0.05 0.06 0.06 0.07 0.07 0.07 0.02 0.11

0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99

0.2386 0.2236 0.1849 0.1074 0.6785 0.1397 0.1646 0.2823 0.08953 0.05864 −0.000944 0.08888

3589.72 3209.99 2942.23 6996.34 2021.36 2765.13 1983.81 3876.96 2267.97 2531.54 27337.9 2663.50

0.10 0.10 0.14 0.07 0.18 0.27 0.18 0.08 0.26 0.24 0.02 0.24

0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99

n = 12, R = 0.93, RSS = 0.81, F = 63.93

ethyl acetate/1,4-dioxane enhances the solubility; thus, the solubility of indole-3-acetic acid in ethyl acetate/1,4-dioxane appears to be an abnormal phenomenon which is inconsistent with the law of polarity. However, one factor cannot fully account for the solubility results, and many factors should be considered, such as the rule of “like dissolves like”, hydrogen bond, van der Waals force, polarity, dielectric constant, dipole moment and so on. 3.2. Solvent Effect. In order to study the effect of solvation interaction on solubility, a multiple linear regression analysis (MLRA) involving various solvent parameters has been sought. Generally, several independent modes of solute− solvent interaction have been proposed. It is customary to describe any property linearly related to the Gibbs energy (XYZ) of a solute−solvent system in terms of linear solvation energy relationship (LSER) by the following equation.16,17

From eq 4, the regression coefficient of β is positive, which indicates that solubility increases with an increase in the value of this parameters. Therefore, HBA interaction of the solvent with the solute favors the increase of solubility. Otherwise, the 2

coefficients of α, π*, and Vsδ H are negative, which indicates 100RT that HBD interaction of the solvent with the solute, nonspecific dipolarity/polarizability interactions, and the cavity term, accounted for by the Hildebrand solubility parameter, is unfavorable. 3.3. Solubility Model and Correlation. In this research, the solubility of indole-3-acetic acid in monosolvents is correlated by the modified Apelblat equation and λh equation. 3.3.1. Modified Apelblat equation. The modified Apelblat equation22−24 has been widely used in describing the solid− liquid phase equilibrium. It is a semiempirical model with three parameters, and the equation is expressed as eq 5.

XYZ = XYZ0 + cavity formation energy + Σsolute − solvent interaction energy

(2)

ln x = A + B /(T /K) + C ln(T /K)

The term XYZ0 depends only on the solute. The summation in the above equation extends over all the modes of solute− solvent interaction. The Kamlet and Taft linear solvation energy relationship model, KAT-LSER, has been developed to relate the Gibbs free energy change of solvent-dependent reactions, which is described as eq 3.18 ln(x) = c0 + c1α + c 2β + c3π * + c4

Vsδ H2 100RT

In eq 5, x donates the solubility of indole-3-acetic acid in mole fraction, and parameters A and B reveal the influence of solution nonideality upon the solute solubility and the variation of solute activity coefficient, respectively. The parameter C represents the influence of temperature upon the fusion enthalpy of a solute. 3.3.2. λh Equation. The λh equation is also a semiempirical model proposed by Buchowski first.25,26 This equation can be used to correlate the solubility data for solid−liquid equilibrium systems. λ and h are two parameters in λh equation. This equation is expressed as eq 6. ÄÅ É ÅÅ λ(1 − x) ÑÑÑÑ 1 zyz ji 1 Å lnÅÅ1 + − Ñ = λhjjj z Ñ j ÅÅÇ Ñ x Tm/K zz{ ÑÖ (6) k T /K

(3)

In this equation, α, β, and π* represent the hydrogen bond acidity, hydrogen bond basicity, and dipolarity/polarizability of the solvent, respectively. The variable δH stands for Hildebrand solubility parameter of the solute. Vs stands for molar volume of solute. The solubility of indole-3-acetic acid in monosolvents was examined by the KAT-LSER model at 298.15 K. Table 3 lists α, β, π*, and δ2H values for these solvents, which are taken from the literature.19−21 The results of multiple regression analysis on solubility can be represented by the following equation for all studied monosolvents.

where λ and h are two adjustable parameters, and Tm donates the melting temperature of indole-3-acetic acid in Kelvin. The value of parameter λ is considered as the association number of solute molecules in the associating system, and h represents excess enthalpy of solution. 3.3.3. Solubility Calculation. The experimental solubility of indole-3-acetic acid in the selected pure solvents is correlated and calculated by using the method of nonlinear regression.27 During the regression process, the objective function is defined as

ln(x) = −10.574 − 1.851α + 3.017β − 1.809π * − 0.384

Vsδ H2 100RT

(5)

(4) E

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Figure 4. Experimental and calculated mole fraction solubility of indole-3-acetic acid in 12 pure solvents: □, ethyl acetate; ★, DMSO; ◀, DMF; ◆, n-butanol; △, acetone; ▼, isopropanol; ◇, 1,4-dioxane; ▲, n-propanol; ●, ethanol; ■, methanol; ☆, acetonitrile; ○, chloroform. (a) Solid line represents calculated data via the modified Apelblat equation. (b) Dotted line represents calculated data via the λh equation.

Figure 5. Calculated solubility values using two equations as a function of the corresponding experimental solubility values for indole-3-acetic acid in 12 solvents.

F=

∑ (ln xie − ln xic)2 i=1

3-acetic acid + isopropanol correlated by the λh equation (0.27 × 10−6). However, the RAD values are not exceeding 0.75 × 10 −2 , which is obtained from indole-3-acetic acid + isopropanol with the λh equation. Figure 5 highlights the fit quality of four models by comparing the calculated values (yaxis) and the measured values (x-axis) for indole-3-acetic acid in the analyzed solvents. All in all, the two thermodynamic models can correlate the experimental data very well. The model parameters of the correlation were important for industrial design and operation.

(7)

Here ln xei and ln xci donate the logarithm of experimental solubility data and logarithm of calculated solubility using the model in mole fraction, respectively. In addition, the relative average deviation (RAD) and rootmean-square deviation (RMSD) were used to evaluate the selected solubility models. RAD =

1 N

RMSD =

c e ji |x w,T − x w,T| zyz zz e z x w,T k {

∑ jjjj N

i=1

N c ∑i = 1 (x w,T

N

(8)

4. CONCLUSION The solubility of indole-3-acetic acid in pure methanol, ethanol, n-propanol, isopropanol, acetone, n-butanol, acetonitrile, chloroform, ethyl acetate, 1,4-dioxane, DMF, and DMSO was measured by using an isothermal saturation method from 278.15 to 323.15 K. The solubility data from high to low are ranked as ethyl acetate > DMSO > DMF > n-butanol > acetone > isopropanol >1,4-dioxane > n-propanol > ethanol > methanol > acetonitrile > chloroform. The dependence of indole-3-acetic acid solubility upon temperature was correlated by the modified Apelblat equation and λh equation. The RADs are not exceeding 0.75 × 10−2, and the RMSDs are not lager than 0.27 × 10−6. On the whole, the two thermodynamic

e )2 − x w,T

(9)

Here N is the number of experimental data points. During the regression process, the Tm of the indole-3-acetic acid is taken from the ref 28. The values of parameters in each model, along with the RMSD values, are presented in Table 6. The solubility of indole-3-acetic acid in monosolvents is correlated in terms of the regressed model parameters. The calculated values of the two models are graphed by a solid and dotted line in Figure 4. From Table 6, the RMSD between the calculated and experimental values value is highest for the system of indoleF

DOI: 10.1021/acs.jced.8b01265 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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models can all be employed to correlate the solubility of indole-3-acetic acid in monosolvents. In addition, solute− solvent and solvent−solvent interactions were discussed, and from solvent effect, the HBA interaction of the solvent with the solute was in favor of the increase of solubility. Otherwise, HBD interaction of the solvent with the solute, nonspecific dipolarity/polarizability interactions, and the cavity term, accounted for by the Hildebrand solubility parameter, are unfavorable. This research will provide important insight into the dissolution process of indole-3-acetic acid.

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AUTHOR INFORMATION

Corresponding Authors

*Tel.: +86 576 88660353. E-mail: [email protected] (Rongrong Li) *Tel.: +86 576 88660177. E-mail: [email protected] (Deman Han). *Tel.: (936) 261-3111. E-mail: [email protected] (Huajun Fan). ORCID

Rongrong Li: 0000-0001-6112-6203 Funding

The project was supported by the National Science Foundation, China (21506138, 21375092, 21575097and 21606199), Science and Technology Plan Project of TaiZhou. HJ Fan gratefully acknowledges the partial financial support by the U.S. Department of Energy, National Nuclear Security Administration grant (DE-NA 0001861 & DE-NA 0002630), and the Welch Foundation Grant (#L0002). Notes

The authors declare no competing financial interest.

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REFERENCES

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DOI: 10.1021/acs.jced.8b01265 J. Chem. Eng. Data XXXX, XXX, XXX−XXX