Solubility Measurement and the Correlation of 1-Naphthaleneacetic

Mar 3, 2017 - The solubilities of 1-naphthaleneacetic acid (NAA) have been measured by the synthetic method in 10 pure organic solvents including meth...
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Solubility Measurement and the Correlation of 1‑Naphthaleneacetic Acid in Pure and Methanol + Water Binary Solvents from T = (278.25 to 323.55) K Yu Zhang, Song Wei, Hui-Hui Wang, Jin-Qiang Liu,* and Weizhou Wang College of Chemistry and Chemical Engineering and Henan Key Laboratory of Function-Oriented Porous Materials, Luoyang Normal University, Luoyang 471934, China ABSTRACT: The solubilities of 1-naphthaleneacetic acid (NAA) have been measured by the synthetic method in 10 pure organic solvents including methanol, ethanol, 2-propanol, toluene, acetone, acetonitrile, 1,4-dioxane, 1,2dichloroethane, ethyl acetate, and tetrahydrofuran and binary methanol + water mixtures from (278.25 to 323.55) K under atmospheric pressure. The modified Apelblat equation, λh equation, and Wilson equation were employed to correlate the solubility data. Furthermore, the solubility of NAA in a binary solvent mixture was regressed with a combined nearly ideal binary solvent/ Redlich−Kister (CNIBS/R−K) equation and the hybrid equation. According to the calculations based on these equations, the modified Apelblat equation gave the best correlation results with the experimental data in all selected solvents.

a moderately lipophilic weak acid (log P = 2.24),11 and its solubility was measured in several pure solvents at different temperatures including water, 1,1,1,2-tetrafluoroethane, carbon tetrachloride, and xylene.12−14 In mixed solvents, the solubility data of NAA in 1,1,1,2-tetrafluoroethane/ethanol systems at 298.15 K is available.13 Another literature reported the solubility of NAA in supercritical CO2 with ethanol, acetone, and cyclohexane as cosolvents in the pressure range of 10.0 to 30.0 MPa at 308.15 and 328.15 K, respectively.15 These studies indicated that the solubility of NAA increases not only with increasing temperature and pressure but also with increasing polarity of cosolvents. It is well known that the solubility of NAA in water is too low (420 mg·L−1 at 293.15 K).12 To optimize biological activity, NAA must be applied in combination with other chemicals to aid solubility, wetting, and handling in the spraying solution.16 Therefore, to give a clear view of the solubility varying with some cosolvents containing water, it is necessary to obtain the experimental solubility data of NAA in widely used pure organic solvents in a certain temperature range. The objective of this study was to determine the solubility of NAA in various pure organic solvents and in binary solvents using the synthetic method at atmospheric pressure. First, the solubility of NAA was measured in methanol, ethanol, 2propanol, toluene, acetone, acetonitrile, 1,4-dioxane, 1,2dichloroethane, ethyl acetate, and tetrahydrofuran within the temperature range of 278.25−323.55 K at atmosphere pressure. On the basis of the above experimental results, an effective

1. INTRODUCTION Auxins are plant hormones that function as key regulators in a number of plant development processes including apical dominance, abscission, root formation, tropistic curvature, leaf senescence, and fruit ripening.1 As a synthetic auxin, 1naphthaleneacetic acid (NAA, C12H10O2, molecular weight 186.21 g·mol−1, CAS registry no. 86-87-3, shown in Figure 1) is

Figure 1. Molecular structure of NAA.

a naphthalene derivative that is widely used as a plant growth regulator in agriculture to the prevent premature dropping of fruit.2,3 It is also applied in combination with other chemicals as a thinning fruit agent. In addition, NAA is used as a fungicide on fruit and as a rooting promoter on germination;4 nevertheless, chemically pure NAA is an important intermediate in medicinal synthesis.5,6 In industry, NAA is mainly obtained by crystallization from a suitable solution, which not only can affect the final yield but also can affect the quality of the final product.7 On the other hand, trace amounts of NAA in soil, fruits, and underground water may be expected to arise from farming operations. The potential toxicity of NAA in mammals and birds has raised the need for effective solvents to help its determination in varied analytical methods for real samples.8−10 Therefore, the reliable solubility of NAA in pure solvent and in mixed solvents is needed for the crystallization and separation processes. NAA is © XXXX American Chemical Society

Received: September 20, 2016 Accepted: February 22, 2017

A

DOI: 10.1021/acs.jced.6b00816 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Figure 2. Differential scanning calorimetry of NAA. The uncertainty in the temperature of fusion is u(T) = 0.5 K. The uncertainty in the enthalpy of fusion is ur(ΔH) = 0.005.

Table 1. Provenance and Purity of the Materials

a

chemical name

source

CAS no.

mass fraction purity (mass %)

purification method

analysis method

1-naphthalene acetic acid (NAA) methanol ethanol 2-propanol toluene acetone acetonitrile 1,4-dioxane 1,2-dichloroethane ethyl acetate tetrahydrofuran water

Sinopharm Chemical Reagent Co. Ltd. of China Tianjin Wind Ship Chemical Co. Ltd. of China Tianjin Wind Ship Chemical Co. Ltd. of China Tianjin Wind Ship Chemical Co. Ltd. of China Tianjin Wind Ship Chemical Co. Ltd. of China Tianjin Wind Ship Chemical Co. Ltd. of China Tianjin Wind Ship Chemical Co. Ltd. of China Tianjin Wind Ship Chemical Co. Ltd. of China Tianjin Wind Ship Chemical Co. Ltd. of China Tianjin Wind Ship Chemical Co. Ltd. of China Tianjin Wind Ship Chemical Co. Ltd. of China our laboratory

86-87-3

>0.99

none

HPLCa

67-56-1 64-17-5 67-63-0 108-88-3 67-64-1 75-05-8 123-91-1 107-06-2 141-78-6 109-99-9 7732-18-5

>0.995 >0.995 >0.995 >0.995 >0.995 >0.995 >0.995 >0.995 >0.995 >0.995 >0.995

none none none none none none none none none none none

GCb GCb GCb GCb GCb GCb GCb GCb GCb GCb none

High-performance liquid chromatography. bGas−liquid chromatography.

applied without further treatment. All of the information about the materials used in this article is collected in Table 1. 2.2. Apparatus and Procedure. The solubility of NAA was measured by the synthetic method with a laser monitoring observation system described in the literature.17−20 The experiment was carried out in a 100 mL jacketed, magnetically stirred vessel using a mercury-in-glass thermometer (type WLB, China) with an uncertainty of ±0.01 K to monitor the temperature. The circulating water from a water bath (type CS501, China) was applied to maintain a constant temperature (±0.05 K), and a condenser was used to keep the solvents from evaporating. The mass of the solute and solvents was weighed with an analytical balance (type Sartorius BS210S, Germany) with an uncertainty of ±0.0001 g. During the experiments, the dissolution of the solute was examined by the laser beam penetrating the glass vessel. At the beginning, a certain amount of solvent was added to the vessel. Then, 3 to 5 mg of solute was added to the vessel at a constant temperature. The addition of solute was repeated until the last addition was not totally dissolved in 5 h. The strength of the laser beam penetrating the vessel was lower than the highest value. The amount of solvent and every addition of solute were recorded. Then, the

solvent of NAA as a cosolvent is determined. Second, the solubility of measurements of NAA in water + cosolvent mixtures were performed at temperature ranging from (298.15 to 319.15) K. The effects of the mass fraction of cosolvent in binary solvent mixtures at (0.5 to 1.00) on the solubilities were investigated. The modified Apelblat equation, λh equation, Wilson equation, and CNIBS/R-K equation and the hybrid model were applied to correlate the resultant data.

2. EXPERIMENTAL SECTION 2.1. Materials. NAA was supplied by Sinopharm Chemical Reagent Co. Ltd. of China with purity greater than 0.99 mass faction, which was determined with HPLC. The melting point and the enthalpy of fusion were obtained using a differential scanning calorimeter (DSC Q2000, TA) at a heating rate of 10 K·min−1 from 313.15 to 453.15 K. Standard indium was used to calibrate the DSC instrument before the measurement. The melting temperature of indium was 429.7 K (as determined by at least 10 measurements). The thermal analysis results are shown in Figure 2. All of the organic solvents were purchased from Tianjin Wind Ship Chemical Co. Ltd. of China. The mass fractions of the solvents were all higher than 0.995 and were B

DOI: 10.1021/acs.jced.6b00816 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 2. Solubility Data of NAA in Different Pure Solvents from 278.25 to 321.45 K at 0.1 MPa T/K 278.25 283.15 289.65 298.35 301.15 304.15 307.15 310.15 313.15 316.15 319.15 321.45 278.25 283.15 289.65 297.95 300.15 303.15 306.15 309.15 312.15 316.15 319.15 321.45 278.25 283.15 289.65 295.95 301.85 304.55 308.15 311.15 314.15 317.15 319.95 321.45 278.25 283.15 289.65 295.95 298.95 301.95 304.95 307.85 310.85 313.85 316.55 321.45 278.25 283.15 289.65 295.95 298.95 301.95 304.95 307.85

102x1 Methanol 8.16 9.24 10.8 13.0 14.0 15.1 16.2 17.3 18.3 19.2 20.0 21.3 Ethanol 1.56 2.09 3.03 4.70 5.37 6.28 7.31 8.41 9.79 11.8 13.4 15.0 2-Propanol 0.106 0.159 0.262 0.419 0.636 0.760 0.987 1.21 1.48 1.76 2.08 2.31 Toluene 0.918 1.21 1.71 2.35 2.71 3.17 3.74 4.20 4.86 5.50 6.25 7.73 Acetone 16.2 18.0 20.5 23.2 24.3 25.8 27.3 28.6

a

102x1cal‑Apel

102RDApel

102x1cal‑λh

102RDλh

102x1cal‑Wil

102RDWil

8.14 9.23 10.8 13.2 14.1 15.0 16.0 17.0 18.1 19.2 20.4 21.3

0.30 0.09 −0.11 −1.72 −0.71 0.34 1.30 1.24 0.82 −0.24 −1.66 0.27

8.18 9.23 10.8 13.2 14.0 15.0 16.0 17.0 18.1 19.3 20.5 21.5

−0.21 0.09 0.33 −1.10 −0.15 0.79 1.60 1.33 0.64 −0.75 −2.57 −0.94

8.16 9.23 10.8 13.0 14.0 15.1 16.2 17.3 18.3 19.7 20.0 21.3

−0.07 −0.02 0.02 −0.09 −0.01 0.06 0.11 0.09 0.05 −0.03 −0.12 −0.03

1.56 2.09 3.03 4.76 5.35 6.24 7.26 8.42 9.74 11.8 13.5 15.0

0.15 0.04 −0.05 −1.45 0.18 0.57 0.68 −0.19 0.52 0.09 −0.77 0.13

1.56 2.10 3.05 4.79 5.37 6.25 7.25 8.38 9.64 11.6 13.2 14.5

0.26 −0.18 −0.55 −1.93 −0.19 0.41 0.82 0.34 1.55 1.98 1.92 3.50

1.54 2.09 3.05 4.70 5.37 6.29 7.32 8.40 9.79 11.8 13.4 15.0

−1.53 0.08 0.60 0.16 0.27 0.18 0.07 −0.07 −0.06 −0.09 −0.11 −0.03

0.107 0.158 0.262 0.419 0.638 0.770 0.982 1.20 1.46 1.76 2.10 2.31

−0.12 0.46 −0.24 0.06 −0.35 −1.20 0.53 0.55 1.68 −0.50 −1.00 0.15

0.107 0.158 0.263 0.419 0.639 0.770 0.983 1.20 1.46 1.77 2.10 2.31

−0.13 0.45 −0.27 0.00 −0.43 −1.29 0.43 0.46 1.59 −0.56 −1.04 0.14

0.024 0.124 0.307 0.508 0.725 0.835 1.05 1.24 1.48 1.71 2.00 2.21

−77.05 −21.98 17.27 21.18 13.95 9.83 5.93 2.57 0.07 −2.50 −4.04 −4.46

0.918 1.21 1.71 2.36 2.74 3.18 3.67 4.21 4.83 5.54 6.25 7.74

−0.04 0.21 0.18 −0.39 −1.22 −0.23 1.87 −0.17 0.46 −0.72 0.06 −0.09

0.918 1.21 1.71 2.37 2.75 3.18 3.67 4.20 4.82 5.51 6.20 7.65

0.03 0.11 −0.03 −0.58 −1.37 −0.29 1.91 0.00 0.81 −0.17 0.82 1.13

0.873 1.20 1.73 2.38 2.73 3.19 3.77 4.21 4.86 5.49 6.23 7.69

−4.90 −0.97 0.91 1.00 0.69 0.74 0.85 0.28 0.11 −0.23 −0.33 −0.58

16.3 18.0 20.5 23.1 24.4 25.8 27.2 28.6

−0.01 −0.05 0.11 0.41 −0.69 0.09 0.31 −0.21 C

16.2 18.0 20.5 23.1 24.5 25.8 27.2 28.7

0.00 −0.05 0.10 0.40 −0.71 0.08 0.30 −0.21

16.3 18.0 20.5 23.2 24.3 25.8 27.3 28.6

0.09 0.02 −0.01 −0.01 −0.07 −0.02 −0.01 −0.03

DOI: 10.1021/acs.jced.6b00816 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 2. continued T/K 310.85 313.85 316.55 321.45 278.25 283.15 289.65 295.95 298.95 301.95 304.95 307.85 310.85 313.85 316.55 321.45 278.25 283.15 289.65 295.95 298.95 301.95 304.95 307.85 310.85 313.85 316.55 321.45 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.35 323.35 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.75 323.55 278.15 283.15 288.15 293.95 298.15 303.75 308.45

102x1 Acetone 30.1 31.7 33.2 35.8 Acetonitrile 1.80 2.41 3.48 4.91 5.82 6.67 7.86 9.09 10.6 12.1 13.8 17.3 1,4-Dioxane 25.6 27.3 29.6 32.0 33.2 34.6 35.7 36.7 37.9 39.1 40.3 42.4 1,2-Dichloroethane 3.97 4.73 5.61 6.54 7.72 9.14 10.5 12.2 14.1 16.0 Ethyl Acetate 8.05 9.09 10.1 11.2 12.5 14.0 15.4 17.0 18.6 20.3 Tetrahydrofuran 31.1 32.0 33.3 34.6 35.7 37.0 38.2

102x1cal‑Apel

102RDApel

102x1cal‑λh

102RDλh

102x1cal‑Wil

102RDWil

30.2 31.7 33.1 35.9

−0.03 −0.02 0.14 −0.04

30.2 31.7 33.1 35.8

−0.03 −0.01 0.16 −0.00

30.1 31.7 33.2 35.9

−0.01 0.00 0.02 0.03

1.80 2.40 3.49 4.92 5.77 6.74 7.86 9.08 10.5 12.1 13.8 17.3

−0.07 0.15 −0.07 −0.18 0.89 −1.04 0.04 0.10 0.72 −0.76 0.30 −0.03

1.79 2.41 3.51 4.96 5.80 6.77 7.86 9.04 10.4 11.9 13.4 16.5

0.22 −0.07 −0.72 −0.89 0.31 −1.41 0.02 0.53 1.73 1.02 2.86 4.31

1.78 2.42 3.50 4.92 5.83 6.66 7.85 9.08 10.6 12.0 13.8 17.3

−0.72 0.27 0.36 0.14 0.15 −0.13 −0.08 −0.10 −0.05 −0.10 0.01 0.12

25.6 27.3 29.7 32.1 33.2 34.4 35.6 36.7 37.9 39.2 40.3 42.3

0.11 −0.05 −0.20 −0.18 −0.12 0.46 0.26 −0.07 −0.04 −0.27 −0.07 0.10

25.7 27.3 29.6 31.9 33.1 34.3 35.5 36.7 38.0 39.3 40.5 42.7

−0.33 −0.09 0.09 0.24 0.29 0.82 0.52 0.07 −0.08 −0.52 −0.55 −0.86

25.6 27.3 29.6 32.0 33.2 34.6 35.7 36.7 37.9 39.1 40.2 42.3

0.00 −0.01 −0.01 0.00 0.00 0.04 0.02 0.00 0.00 −0.02 −0.01 −0.01

3.96 4.73 5.61 6.62 7.76 9.05 10.5 12.1 14.0 16.0

0.26 0.15 0.05 −1.11 −0.47 0.94 0.11 0.39 0.29 −0.61

3.97 4.73 5.60 6.60 7.74 9.03 10.5 12.1 14.0 16.1

0.03 0.10 0.13 −0.94 −0.26 1.13 0.24 0.40 0.12 −1.02

3.96 4.73 5.61 6.54 7.72 9.15 10.5 12.2 14.1 15.9

−0.13 −0.02 0.04 −0.10 0.01 0.16 0.05 0.04 −0.01 −0.09

8.04 9.04 10.1 11.3 12.6 13.9 15.3 16.9 18.7 20.4

0.16 0.48 −0.70 −0.45 −0.24 0.49 0.25 0.54 −0.26 −0.25

8.09 9.05 10.1 11.2 12.5 13.8 15.3 16.9 18.9 20.7

−0.44 0.45 −0.33 0.14 0.41 1.02 0.50 0.33 −1.21 −2.02

8.08 9.11 10.1 11.2 12.5 14.0 15.4 17.0 18.6 20.3

0.32 0.26 0.06 0.02 −0.01 0.01 −0.04 −0.06 −0.13 −0.15

31.0 32.1 33.3 34.7 35.7 37.0 38.1

0.34 −0.40 −0.07 −0.08 0.03 0.01 0.17

31.2 32.2 33.2 34.4 35.4 36.8 38.0

−0.37 −0.47 0.33 0.61 0.77 0.63 0.49

31.2 32.1 33.3 34.7 35.7 37.0 38.1

0.26 0.14 0.14 0.07 0.04 −0.03 −0.08

D

DOI: 10.1021/acs.jced.6b00816 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 2. continued T/K

102x1

102x1cal‑Apel

313.15 318.15 323.15

Tetrahydrofuran 39.3 40.3 41.6

102RDApel

39.2 40.4 41.6

102x1cal‑λh

0.32 −0.29 −0.04

39.3 40.7 42.3

102RDλh 0.19 −1.10 −1.72

102x1cal‑Wil

102RDWil −0.13 −0.25 −0.29

39.3 40.2 41.5

a

Standard uncertainties u are for temperature u(T) = 0.05 K. The relative standard uncertainty for pressure is ur(p) = 0.05; for the mole fraction solubility, it is ur(x1) = 0.05.

Table 3. Solubility Data of NAA in Different Methanol + Water Mixture Solvents from 298.15 to 319.95 K at 0.1 MPaa 102x1

x1cal‑Apel

298.15 301.15 304.15 307.15 310.15 313.15 316.15 319.15

12.8 13.7 14.8 15.8 16.8 17.9 19.1 20.0

12.8 13.8 14.8 15.8 16.8 17.9 19.0 20.1

298.15 301.15 304.15 307.15 310.15 313.15 316.15 319.15

8.99 9.93 10.7 11.7 12.5 13.6 14.7 15.8

298.15 301.15 304.15 307.15 310.15 313.15 316.15 319.15

6.36 7.28 8.24 9.32 10.4 11.6 13.0 14.5

298.15 301.15 304.15 307.15 310.15 313.15 316.15 319.15

4.50 5.32 6.15 7.02 8.12 9.30 10.5 11.9

298.15 301.15 304.15 307.15 310.15 313.15 316.15 319.15

3.24 3.84 4.57 5.44 6.41 7.40 8.59 10.1

298.15 301.15

2.22 2.69

T/K

102RDApel

102RDλh

T/K

102x1

12.9 13.8 14.7 15.7 16.8 17.9 19.0 20.3

−0.16 −0.45 0.30 0.64 0.34 0.28 0.07 −1.18

304.15 307.15 310.15 313.15 316.15 319.15

3.18 3.85 4.72 5.66 6.73 8.00

9.05 9.84 10.7 11.6 12.6 13.6 14.7 15.8

−0.66 0.84 −0.00 0.63 −0.57 −0.15 −0.03 −0.17

298.15 301.15 304.15 307.15 310.15 313.15 316.15 319.15

1.51 1.83 2.16 2.60 3.13 3.72 4.39 5.19

6.40 7.26 8.21 9.26 10.4 11.7 13.0 14.5

−0.54 0.37 0.35 0.69 0.28 −0.47 −0.65 −0.49

298.15 301.15 304.15 307.15 310.15 313.15 316.15 319.15

0.811 0.964 1.14 1.34 1.54 1.78 2.06 2.39

4.53 5.27 6.11 7.05 8.10 9.28 10.6 12.0

−0.82 0.99 0.68 −0.34 0.20 0.23 −0.81 −0.92

298.15 301.15 304.15 307.15 310.15 313.15 316.15 319.15

0.428 0.535 0.641 0.790 0.926 1.13 1.33 1.62

3.24 3.86 4.58 5.41 6.36 7.45 8.68 10.1

0.12 −0.41 −0.06 0.64 0.72 −0.57 −1.08 0.46

298.15 301.15 304.15 307.15 310.15 313.15 316.15 319.15

0.286 0.327 0.387 0.452 0.517 0.591 0.693 0.801

2.20 2.68

0.61 0.29

x1cal‑λh

ω2 = 0.95 0.32 −0.50 −0.09 0.13 −0.11 0.09 0.32 −0.31 ω2 = 0.9 9.04 −0.54 9.85 0.81 10.7 −0.13 11.6 0.48 12.6 −0.69 13.6 −0.17 14.7 0.09 15.8 0.16 ω2 = 0.85 6.38 −0.32 7.27 0.21 8.24 −0.01 9.30 0.29 10.4 −0.02 11.8 −0.52 13.0 −0.32 14.4 0.33 ω2 = 0.8 4.52 −0.47 5.28 0.90 6.13 0.37 7.07 −0.68 8.12 0.01 9.27 0.36 10.5 −0.23 11.9 0.24 ω2 = 0.75 3.24 0.19 3.86 −0.45 4.58 −0.15 5.41 0.57 6.36 0.71 7.44 −0.50 8.67 −0.94 10.1 0.67 ω2 = 0.7 2.21 0.36 2.67 0.61

x1cal‑Apel

102RDApel

ω2 = 0.7 −1.48 −0.78 1.09 0.90 0.08 −0.55 ω2 = 0.65 1.51 −0.11 1.82 −0.45 2.18 1.08 2.61 0.44 3.11 −0.67 3.70 −0.43 4.40 0.09 5.21 0.31 ω2 = 0.6 0.814 −0.45 0.963 0.13 1.13 0.20 1.33 0.75 1.55 −0.37 1.79 −0.84 2.07 −0.44 2.38 0.55 ω2 = 0.55 0.432 −0.92 0.528 1.19 0.643 −0.27 0.779 1.43 0.939 −1.41 1.13 0.15 1.35 −1.13 1.60 0.96 ω2 = 0.5 0.285 0.50 0.331 −1.36 0.384 0.61 0.446 1.27 0.517 0.00 0.598 −1.18 0.691 0.20 0.798 0.35 3.22 3.88 4.67 5.61 6.72 8.04

x1cal‑λh

102RDλh

3.24 3.91 4.69 5.59 6.65 7.86

−2.10 −1.40 0.75 1.14 1.18 1.73

1.51 1.82 2.19 2.61 3.11 3.70 4.37 5.15

−0.30 −0.34 1.35 0.72 −0.53 −0.58 −0.51 −0.88

0.816 0.961 1.13 1.32 1.54 1.79 2.08 2.41

−0.65 0.37 0.66 1.23 −0.04 −0.87 −1.02 −0.76

0.432 0.527 0.641 0.777 0.939 1.13 1.35 1.62

−0.89 1.38 −0.04 1.60 −1.41 −0.13 −1.79 −0.16

0.284 0.332 0.386 0.447 0.518 0.598 0.689 0.793

0.71 −1.50 0.30 0.92 −0.26 −1.23 0.48 1.04

a

Standard uncertainties u are u(T) = 0.05 K for temperature. The relative standard uncertainty for pressure is ur(p) = 0.05; for the mole fraction solubility, it ur(x1) = 0.05, and for the mass fraction of methanol it is ur(ω2) = 0.01. ω2 is the mass fraction of methanol in the mixed solvents in the absence of the solute.

temperature was increased to the next experimental point and the above process was repeated until the last experimental point

was achieved. The same solubility experiment was conducted three times by employing different amounts of solvent to E

DOI: 10.1021/acs.jced.6b00816 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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represent the temperature and pressure of the triple point; P is the absolute pressure; and R is the universal gas constant. Generally, the negligible difference between the triple point and normal melting point makes it suitable to replace ΔfusHtp and Ttp by the enthalpy of melting ΔfusHm and the melting point Tm. Furthermore, the last two terms containing ΔCp and ΔV are the correction of the heat capacity and the pressure difference, which are often minor and also negligible. Therefore, eq 6 can be simplified as

ensure that the estimated uncertainty of the solubility values was less than 2%. The mole fraction solubility of NAA in different pure organic solvents was calculated using eq 1, whereas that in water + methanol mixtures over a certain temperatures range at atmospheric pressure was computed on the basis of eq 2. The results are listed in Tables 2 and 3, respectively. The composition of the binary solvent mixtures is expressed as eq 3 x1 = x1 = ω2 =

m1/M1 m1/M1 + m2/M 2 m1/M1 m1/M1 + m2 /M 2 + m3 /M3 m2/M 2 m2/M 2 + m3/M3

(1)

ln x1γ1 =

(3)

⎛ ⎞ Λ12 Λ 21 ln γ1 = −ln(x1 + Λ12x 2) + x 2⎜ − ⎟ x 2 + Λ 21x1 ⎠ ⎝ x1 + Λ12x 2 (8)

where Λ12 =

3. THERMODYNAMIC MODELS 3.1. Modified Apelblat Equation. The modified Apelblat model, expressed as eq 4, is a semiempirical model deduced from the solid−liquid phase equilibrium21,22 B ln x1 = A + + C ln T (4) T where A, B, and C are the parameters; x1 is the mole fraction equilibrium solubility of NAA in a selected pure solvent or mixed solvents; and T is the solid−liquid equilibrium temperature. 3.2. λh Equation. The λh equation is another semiempirical model to describe the solid−liquid equilibrium, which is shown as follows23,24

−

Λ 21 =

⎛ λ − λ 22 ⎞ ⎛ Δλ ⎞ ν1 ν ⎟ = 2 exp⎜ − 21 ⎟ exp⎜ − 21 ⎝ ⎝ RT ⎠ RT ⎠ ν2 ν1

(9)

In eq 8, x2 is the mole fraction of the selected solvent. In eq 9, Δλ12 (= λ12 − λ11) and Δλ21 (= λ21 − λ22) are two binary cross-interaction parameters that are independent of composition and temperature and v1 and v2 represent the molar volumes of solute and pure solvent, respectively. The values of v2 are obtained from the literature. 3.4. Combined Nearly Ideal Binary Solvent/Redlich− Kister (CNIBS/R−K) Model. The CNIBS/R−K model was also employed to fit the experimental data and describe the influence of binary solvent compositions on NAA solubility. The model that relies on the solvent composition is defined as follows:26

(5)

N

ln x1 = x 2 ln(x1)2 + x3 ln(x1)3 + x 2x3 ∑ Si(x 2 − x3)i i=0

(10)

In eq 10, variables x2 and x3 denote the initial mole fraction composition of the binary methanol + water solvent mixtures when there is no solute added. x1 is the mole fraction solubility of NAA, which is the same as the one in eq 4. Si is the model constant and N is the number of solvents, which equals 2 in this work. Substituting (1 − x2) for x3, eq 10 can be simplified as

⎞ ΔfusHtp ⎛ 1 Ttp 1 ⎞ ΔCp ⎛ Ttp ⎜⎜ − ⎟⎟ − − + 1⎟ ⎜ln R ⎝ Ttp T⎠ R ⎝ T T ⎠

ΔV (P − Ptp) RT

⎛ λ − λ11 ⎞ ⎛ Δλ ⎞ ν2 ν ⎟ = 2 exp⎜ − 12 ⎟ exp⎜ − 12 ⎝ ⎝ RT ⎠ RT ⎠ ν1 ν1

and

where λ and h are the model parameters; Tm is the normal melting temperature of NAA, which is 403.06 K; and x1 and T in eq 5 are the same as those in eq 4. 3.3. Wilson Model. On the basis of the solid−liquid equilibrium criteria, the solubility of a solute in liquid solvents can be regressed by the frequently used thermodynamic equation expressed below25 ln x1γ1 =

(7)

To use eq 7, a thermodynamic model is demanded to represent the activity coefficients as a function of temperature and composition at constant pressure. In this article, the Wilson equation, a local composition model initially proposed by Wilson, was used to derive γ1, which can be expressed as eq 8 in a binary system

(2)

where x1 represents the solubility (solid−liquid equilibrium) of NAA in mole fraction in pure organic solvents and in binary water + methanol mixture systems; ω2 denotes the solute-free mole fraction of cosolvent in the binary mixed solvents; m1, m2, and m3 refer to the masses of NAA, selected pure organic solvent, and water in different solvent systems; M1, M2, and M3 represent the molecular weights of the solute and relevant solvents, respectively.

⎛1 ⎛ 1 − x1 ⎞ 1 ⎞ ln⎜1 + λ ⎟ ⎟ = λh⎜ − x1 ⎠ Tm ⎠ ⎝T ⎝

ΔfusHm ⎛ 1 1⎞ − ⎟ ⎜ R ⎝ Tm T⎠

ln x1 = B0 + B1x 2 + B2 x 2 2 + B3x 2 3 + B4 x 2 4

(6)

where γ1 is the liquid-phase activity coefficient of the solute; ΔfusHtp is the molar enthalpy of fusion at the triple point; ΔCp denotes the molar heat capacity difference of the solute between the solid and the liquid; ΔV represents the volume difference between the solid and liquid phases; Ttp and Ptp

(11)

where B0, B1, B2, B3, and B4 are model parameters. 3.5. Hybrid Model. In addition, to describe the effects of both solvent composition and temperature on the solubility of NAA, the hybrid model was also applied to represent the experiment data, which was written as eq 1227 F

DOI: 10.1021/acs.jced.6b00816 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

and 15.041 × 10−2 at 321.45 K) varies more obviously than that in others organic solvents, which shows its potential advantages in the recrystallization of NAA. In addition, according to the experimental data, tetrahydronfuran, 1,4-dioxane, acetone, methanol, and ethyl acetate are good solvents for NAA. Considering the miscibility of an organic solvent with water, tetrahydrofuran, 1,4-dioxane, acetone, and methanol are potential cosolvents for NAA. As we know, methanol is the cheapest one among these solvents. In the next section, we reported the solubility data of NAA in a methanol + water mixture. The measurement of the solubility of NAA in tetrahydrofuran, 1,4-dioxane, and acetone with water is still going on in our laboratory, and the data will be published in due time. 4.2.2. Solubility of NAA in Methanol + Water Mixtures. The solubility data of NAA in different methanol + water mixed solvents at temperature ranging from 298.15 to 319.15 K are listed in Table 3 and graphically in Figure 4, corresponding to the mass fraction of methanol (ω2) in mixtures prepared in varying intervals of 0.05 from 0.5 to 0.95.

A2 x (x )2 + A3 ln T + A4 x 2 + A5 2 + A 6 2 T T T 3 4 (x ) (x ) + A 7 2 + A8 2 + A 9x 2 ln T (12) T T where T denotes the absolute temperature in Kelvin and x2 denotes the same meanings as in eq 10. A1 to A9 represent the model parameters. ln x1 = A1 +

4. RESULTS AND DISSCUSSION 4.1. Melting Point and Enthalpy of Fusion. As shown in Figure 2, the melting point of NAA is 403.06 K, and the enthalpy of fusion of NAA is 21.47 kJ·mol−1, which is in agreement with the literature.12 The melting point measured was a little lower than the literature value,12 which might be due to the purity and the measurement apparatus. 4.2. Experimental Solubility Data. 4.2.1. Solubilities of NAA in Pure Solvents. Using the synthetic method, the solubilities of NAA in 10 pure organic solvents including methanol, ethanol, 2-propanol, toluene, acetone, acetonitrile, 1,4-dioxane, 1,2-dichloroethane, ethyl acetate, and tetrahydrofuran were measured within the temperature range of (278.25 to 323.55) K, and the experimental solubility data are presented in Table 2. Figure 3 is plotted to show the results. From Table

Figure 4. Solubility of NAA in binary methanol + water solvent mixtures: ■, ω2 = 95%; ●, ω2 = 90%; ▲, ω2 = 85%; ▼, ω2 = 80%; ◆, ω2 = 75%; ◀, ω2 = 70%; ▶, ω2 = 65%; ★, ω2 = 60%; +, ω2 = 55%; and ×, ω2 = 50%; Lines are drawn according to calculated values with the modified Apelblat equation. Figure 3. Solubility of NAA in 10 selected pure organic solvents: ■, methanol; ●, ethanol; ▲, 2-propanol; ▼, toluene; ◆, acetone; ◀, acetonitrile; ▶, 1,4-dioxane; +, 1,2-dichloroethane; ×, ethyl acetate; and *, tetrahydrofuran. Lines are drawn according to calculated values with the modified Apelblat equation.

From Table 3 and Figure 4, the conclusion can be drawn that the solubility of NAA increases with increasing temperature and decreases with the mole fraction of water in the solvent mixtures at constant temperature. In addition, at the same temperature the solubility of NAA in the mixed solvents is lower than in pure methanol. As we know, the factors that influence solubility include intermolecular interactions of the solution molecules and the physicochemical properties of the solute and solvents. In the present study, the studied system is composed of water + methanol and NAA. NAA is a lipophilic compound, and methanol has a high polarity. Thus, on the basis of the general rule “like dissolves like”, the solubility behavior of NAA in mixed solvents can be explained by the fact that methanol can associate with water more strongly by forming hydrogen bonds than with NAA, which weakens the solubility of NAA in methanol. 4.3. Data Correlation. 4.3.1. Solubility Data in Pure Solvents. The modified Apelblat model, λh model, and Wilson equation were used to correct the experimental solubility values

2 and Figure 3, it can be seen that the solubility data of NAA in 10 selected organic solvents are increased with the increase in temperature, and at room temperature, the maximum was observed in tetrahydrofuran and the minimum was observed in 2-propanol. The solubility of NAA in 10 pure solvents follows the order 2-propanol < toluene < ethanol < acetonitrile