Thermodynamic Models for Determination of SolidâLiquid Equilibrium

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

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Thermodynamic Models for Determination of Solid−Liquid Equilibrium of the Buprofezin in Pure and Binary Organic Solvents Qiang Xu, Bin Heng, Yonghong Hu,* Xinxin Liu, Wenge Yang, Yuwen Fan, Wenjun Zhu, Chaoqiang Wu, and Yuanyun Gu

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College of Biotechnology and Pharmaceutical Engineering, State Key Laboratory of Materials-Oriented Chemical Engineering, Jiangsu National Synergetic Innovation Center for Advanced Materials, Nanjing Tech University, No. 30, South Puzhu Road, Nanjing 211816, China

ABSTRACT: Buprofezin is a kind of insecticide and an important chemical intermediate product. Data on solid−liquid equilibrium of buprofezin in different solvents is essential for the area of industrial applications. In this work, the solubility of buprofezin in methanol, ethanol, isopropanol, n-butanol, acetonitrile, n-hexane, ethyl acetate, N,N-dimethylformamide, and two binary solvent mixtures (methanol + ethyl acetate and acetonitrile + ethyl acetate) was measured at the temperature range of 278.15−328.15 K at atmospheric pressure by the gravimetric method. The experimental values showed that elevated temperatures increased the solubility of buprofezin in all selected solvents. The modified Apelblat model, the Buchowski− Ksiazaczak λh model, combined nearly ideal binary solvent/Redlich−Kister (CNIBS/R-K) model, Jouyban−Acree model, and an ideal model were used to describe and predict the diversification trend of solubility.

1. INTRODUCTION Buprofezin (Figure 1, C16H23N3OS, FW = 305.44, CAS reg. no. 69327-76-0), is a white crystalline, odorless powdered insecticide.1,2

Furthermore, the solubility data can provide the guidance of the separation such as easier crystallization process. As we all know, the choice of different solvents will have a significant impact on the results of the synthesis and purification of the drug. In this work, the solubility of buprofezin in methanol, ethanol, isopropanol, n-butanol, acetonitrile, n-hexane, ethyl acetate, N,N-dimethylformamide, and two solvent mixtures (methanol + ethyl acetate and acetonitrile + ethyl acetate) was measured in the temperature range of 278.15−328.15 K under atmospheric pressure by the common gravimetric method. We expected to find out the suitable pure solvent or mixture solvents in the crystallization process of buprofezin from the selected solvents according to the experimental data. Besides, the analysis of thermodynamic properties would help determine the best temperature interval, which showed a variation tendency toward solubility at different temperatures.

Figure 1. Chemical structure of buprofezin.

As an insecticide, buprofezin has a potent larvicide activity against coleopteran, part from homoptera, and acarina. In addition, it is widely applied to potatoes, citrus plants, cotton, and so on.3−5 Purity is an important part of the chemical. Considering the easy introduction to impurities in the actual industrial production of buprofezin, this work aims to provide some useful data to the industrial production of buprofezin to improve its purity. In order to improve purity, the solubility in the different organic solvents plays an important role in extraction process, especially the solid−liquid equilibria and the liquid−liquid equilibria.6 At the same time, we want to reduce the unnecessary loss in the process of industrial production of buprofezin by studying the solubility of buprofezin, such as the blockage caused by the precipitation of drugs during pipeline transportation. © XXXX American Chemical Society

2. EXPERIMENTAL SECTION 2.1. Materials and Apparatus. Buprofezin (99% mass fraction purity) was purchased from Jiangsu Dongbao Agrochemical Received: February 20, 2019 Accepted: July 10, 2019

A

DOI: 10.1021/acs.jced.9b00172 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. . Properties of the Compounds Evaluated compounds

CAS reg. no.

molar mass

mass fraction purity (%)

analysis method

source

buprofezin methanol ethanol n-butanol isopropanol N,N-dimethylformamide acetonitrile n-hexane ethyl acetate

69327-76-0 67-56-1 64-17-5 71-36-3 67-63-0 68-12-2 75-05-8 110-54-3 141-78-6

305.44 32.04 46.07 74.12 60.06 73.09 41.05 86.18 88.11

99.0 99.9 99.9 99.5 99.9 99.7 99.6 99.6 99.8

HPLCa GCb GC GC GC GC GC GC GC

Jiangsu Dongbao Agrochemical Co., Ltd. Shenbo Chemicals Shenbo Chemicals Shenbo Chemicals Shenbo Chemicals Shenbo Chemicals Shenbo Chemicals Shenbo Chemicals Shenbo Chemicals

a

High-performance liquid chromatography. bGas chromatography.

laboratory by gas chromatography (GC; Agilent 7820A), and their mass fraction purities were higher than 0.995. More details about the solvents are listed in Table 1. An analytical balance (model CPA225D) was provided by Satorius Scientific Instrument (Beijing) Co., Ltd. with an uncertainty of ±0.00001 g. A smart thermostatic bath (model DC-2016) was provided by Ningbo Scientz Biotechnology Co., Ltd. with an uncertainty of ±0.05 K. 2.2. Solubility Measurements. The solubility of buprofezin was determined by the analytical stirred-flask method, and the compositions of the saturated solutions were measured using the gravimetric method. The 8 mL solvent mixtures and some excess buprofezin were added into a 10 mL glass test tube with a stopper. The test tube was kept in a jacket glass vessel full of water, whose temperature was maintained at the desired value by circulating water through the outer jacket from a smart thermostatic water-circulator bath. Magnetic stirrers were used to mix the solid and solvent mixtures adequately. In order to ensure the solution reaching equilibrium, this stirring process would last at least 24 h. Then, magnetic stirring was stopped, and the solution was allowed to settle down, then the solution

Figure 2. X-ray power diffraction pattern of buprofezin.

Co., Ltd. (Yangzhou, China). Its purity was measured by highperformance liquid chromatography (HPLC; DIONEX P680, DIONEX Technologies). It was dried in a vacuum oven at 333 K for 12 h and stored in a desiccator. All of the organic solvents were supplied by Shanghai Shenbo Chemical Co., Ltd., China. The purities of the solvents were determined in our

Figure 3. HPLC pattern of buprofezin: (a) buprofezin before crystallization and (b) crystallized buprofezin. B



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Table 2. . Mole Fraction Solubility (x) of Buprofezin in Pure Organic Solvents with the Temperature Range of 278.15− 328.15) K under 0.1 MPaa 100RD T (K) Methanol 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 Ethanol 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 Isopropanol 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 n-Butanol 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15

100x

eq. 6

eq 7

100RD T (K)

eq 10

0.4821 0.5347 0.6815 0.7543 0.9297 1.1218 1.3560 1.6469 2.1259 2.8163 3.8301

−8.45 −7.02 5.42 1.15 4.89 4.33 1.86 −2.24 −2.09 −1.08 0.91

33.87 22.01 20.59 7.55 3.95 −1.35 −6.26 −10.46 −7.74 −2.23 5.55

40.31 27.88 24.94 10.90 5.89 −0.65 −6.57 −11.43 −8.80 −2.77 6.08

0.6481 0.7751 0.9475 1.1502 1.3623 1.6294 1.9666 2.4592 2.9998 3.9124 4.8732

−5.34 −2.24 1.67 3.62 2.11 0.54 −1.09 −0.03 −2.30 1.43 −0.15

16.29 11.29 8.62 5.75 0.87 −2.82 −5.31 −3.83 −4.78 1.17 2.33

23.46 16.91 12.56 8.13 1.87 −2.99 −6.33 −5.22 −6.02 0.72 3.25

0.7169 0.9273 1.0731 1.2875 1.6948 2.1923 2.7223 3.5115 4.5696 5.7944 6.9846

9.39 10.04 0.42 −6.05 −2.68 −0.92 −3.08 −1.12 1.92 2.59 −1.53

14.91 13.45 2.42 −5.29 −2.82 −1.52 −3.84 −1.75 1.57 2.59 −1.20

19.83 17.16 5.28 −3.47 −2.09 −1.62 −4.51 −2.67 0.77 2.27 −0.57

1.2826 1.5790 1.9304 2.3293 2.8448 3.3436 4.3761 5.3253 6.5222 7.8651 9.9537

−1.11 0.55 1.16 0.16 0.08 −4.16 2.27 1.19 0.56 −1.79 0.58

10.07 7.42 4.69 1.20 −0.61 −5.93 0.27 −0.61 −0.56 −1.85 1.82

15.38 11.40 7.40 2.77 −0.08 −6.23 −0.54 −1.64 −1.43 −2.16 2.52

100x

Acetonitrile 278.15 0.6186 283.15 0.6993 288.15 0.8190 293.15 0.9689 298.15 1.1763 303.15 1.4349 308.15 1.7676 313.15 2.1918 318.15 2.7112 323.15 3.4267 328.15 4.3539 n-Hexane 278.15 1.3411 283.15 1.4763 288.15 1.6442 293.15 1.8544 298.15 2.2212 303.15 2.4973 308.15 2.9563 313.15 3.5867 318.15 4.2884 323.15 5.3667 328.15 6.8905 Ethyl acetate 278.15 4.1630 283.15 5.3760 288.15 6.6240 293.15 7.8500 298.15 9.6680 303.15 11.5700 308.15 13.3600 313.15 15.6800 318.15 18.2600 323.15 20.9500 328.15 23.7800 N,N-Dimethylformamide 278.15 0.8686 283.15 1.0510 288.15 1.2440 293.15 1.5042 298.15 1.9065 303.15 2.3978 308.15 2.9844 313.15 3.8758 318.15 4.8603 323.15 6.1092 328.15 7.8242

eq. 6

eq 7

eq 10

1.90 −0.49 −0.71 −1.18 −0.21 0.15 0.49 0.58 −0.44 −0.09 0.06

22.97 13.51 6.89 1.32 −1.40 −3.26 −3.77 −3.33 −2.98 −0.39 2.57

29.74 19.15 11.03 3.90 −0.32 3.42 −4.78 −4.73 −4.22 −0.86 3.50

−3.25 −1.04 0.03 0.25 4.44 0.67 0.27 0.74 −1.73 −1.56 1.02

23.24 15.15 7.71 1.25 0.83 −5.84 −7.08 −5.59 −5.63 −1.60 5.64

30.27 20.79 11.77 3.65 1.62 −6.31 −8.41 −7.23 −7.01 −2.04 6.70

−2.19 1.20 1.15 −1.58 0.69 1.15 −0.93 −0.43 0.20 0.19 −0.07

−11.88 −4.37 −1.46 −2.01 1.79 3.14 1.40 1.62 1.42 0.05 −2.14

−10.33 −3.54 −1.17 −2.13 1.39 2.58 0.79 1.11 1.14 0.17 −1.45

3.66 2.89 −0.77 −3.01 −1.03 −0.39 −1.29 1.62 0.65 −0.46 −0.03

21.43 14.82 6.37 0.04 −1.10 −2.40 −4.21 −1.15 −1.27 −0.82 1.70

26.24 18.74 9.40 2.04 −0.14 −2.28 −4.71 −1.95 −2.04 −1.17 2.20

a

x is the mole fraction solubility of buprofezin at the corresponding temperature T. Standard uncertainties u are u(T) = 0.05 K, u(P) = 2 kPa. The relative standard uncertainties: ur(x) = 0.02.

was kept still for 6 h in order to allow the undissolved solid to settle to the lower portion of the equilibrium cell. Lastly, the beakers used were first weighed and then recorded. Then, 1 mL of solution supernatant was transferred into a 5 mL beaker with a cover and weighted immediately.7,8 All beakers were put into a dryer and weighted weekly until reaching constant weight. All operations and experiments were repeated three times to check the reproducibility, and then an average value was given.

The solid−liquid equilibrium data of buprofezin was represented in terms of mole fraction (x) in the corresponding solvent, and the formula is as follows: x=

m1/M1 m1/M1 + m2 /M 2

(1)

where m1 and M1 represent the mass and molar mass of the buprofezin, respectively, and m2 and M2 are the mass and molar mass of the pure solvents, respectively. C



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Figure 4. Mole fraction solubility (x) of buprofezin versus temperature (T) in the selected organic solvents: (a) ethanol; methanol; n-hexane; DMF. (b) isopropanol; acetonitrile; n-butanol. (c) ethyl acetate.

Table 3. Parameters of the Modified Apelblat Model for Buprofezin in Pure Organic Solvents at the Temperature Range of 278.15−328.15 K solvent

A

B

C

102RAD

methanol ethanol isopropanol n-butanol acetonitrile n-hexane ethyl acetate N,N-dimethylformamide

−689.80 −386.67 −123.73 −211.97 −400.73 −545.82 120.77 −292.51

27738.57 14147.44 1677.23 6223.28 14769.58 21903.58 −8205.86 9512.59

103.91 58.78 20.02 32.92 60.86 82.23 −16.78 45.05

3.59 1.86 3.61 1.24 0.57 1.36 0.89 1.44 ∑(102RAD) = 14.56

where m1, m2, and m3 represent the mass of buprofezin, ethyl acetate, and methanol or buprofezin, ethyl acetate, and acetonitrile, respectively, and M1, M2, and M3 represent the molar mass of buprofezin, ethyl acetate, and methanol or buprofezin, ethyl acetate, and acetonitrile, respectively.9 The relative standard uncertainties of the experimental solubility values are about 2%. The uncertainty of the solubility values can be due to the uncertainties of the weighing procedure, temperature measurements, excess addition of solute, and instabilities of the water bath.

The molar fraction solubility of the buprofezin (x) in two binary solvent mixtures (methanol + ethyl acetate and acetonitrile + ethyl acetate) was calculated by eq 2. The molar fraction of ethyl acetate (xA) in the binary solvent mixtures is defined using eq 3. x=

xA =

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

m2 /M 2 m2 /M 2 + m3 /M3

(2)

(3) D



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2.3. Analysis and Characterization. The crystal form of buprofezin used in this work was analyzed by X-ray powder diffraction (PXRD). In addition, in order to verify whether or not impurities were contained in the buprofezin after crystallization, HPLC were used to characterize the buprofezin before and after crystallization. PXRD was performed on an X-ray diffractometer (ARL XTRA, USA) with Cu Kα radiation at 40 mA and 40 kV, and samples were scanned from 5° to 40° (2θ) at a scanning rate of 0.02° s −1. The HPLC used in the experiment was the Diane U3000. The HPLC conditions were as follows: Thermo C8 column (4.6 mm × 250 mm, 5 μm); mobile phase = methanol/ water (volume ratio: 85:15); flow rate = 1 mL·min−1; detection wavelength = 240 nm; detection temperature = 40 °C; injection volume = 2 μL.

(ΔCp).11 The regression curve parameters of the modified Apelblat model are listed in Table 3. 3.2.3. Buchowski−Ksiazaczak λh Model. The Buchowski− Ksiazaczak λh model was first requested to describe the solution behavior by Buchowski and Khiat.12 The λh equation would fit the experimental data with two parameters, λ and h. The λh equation is defined as follows: ÄÅ É ÑÉ ÅÄÅ ÅÅ Å 1 λ(1 − x) ÑÑÑÑ 1 ÑÑÑ ÑÑ − lnÅÅÅ1 + ÑÑ = λhÅÅÅÅ ÅÅÇ (T /K ) x (Tm/K ) ÑÑÑÖ ÅÅÇ ÑÑÖ (7)

3. RESULTS AND DISCUSSION 3.1. Results of Analysis and Characterization. The PXRD patterns of all buprofezin were found to be similar. One of the typical results is shown in Figure 2. This can indicate that it has a high polymorphic purity of buprofezin. The HPLC patterns of buprofezin before and after crystallization are shown in Figure 3. In this, panel (a) is buprofezin before crystallization, and panel (b) is buprofezin after crystallization. By comparing the chromatograms before and after crystallization, the chromatogram after crystallization showed no other peaks, and the peak positions and retention times of the two spectra were consistent. This indicates that no impurities were introduced during the crystallization. 3.2. In Pure Solvents. 3.2.1. Solubility Data and Correlation Models. The solubility of buprofezin in methanol, ethanol, isopropanol, n-butanol, acetonitrile, n-hexane, ethyl acetate, and N,N-dimethylformamide in the temperature range of 278.15−328.15 K is presented in Table 2 and graphically showed in Figure 4. The relative deviations (RD) between the experimental values and the calculated values are also presented in Table 2. The relative average deviation (RAD) is also used to evaluate this thermodynamic model, and its related values are listed in Tables 3−5. The RD and RAD are defined as follows: x − xci RD = i xi (4)

Table 4. Parameters of the λh Model for Buprofezin in Pure Organic Solvents

RAD =

1 N

N

∑ i=1

xi − xci xi

where x is the mole fraction solubility of buprofezin, T is the experimental kelvin temperature, and Tm is the standard melting kelvin temperature.13,14 The parameters of λ and h are presented in Table 4.

100λ

h

102RAD


16.24 16.49 34.83 36.27 14.78 15.52 69.87 37.30

25560.96 21951.75 12248.11 10057.40 24631.94 18758.99 4106.85 11314.39

11.05 5.73 4.67 3.18 5.67 7.23 2.84 5.03 ∑(102RAD) = 45.40

3.2.4. Ideal Model. The ideal model is a universal equation for (solvent + solute) equilibrium, which is based on thermodynamic principles.15 The equation is defined as ln xγ =

ΔdissoH jij 1 1 zy − zzz jjj R k Tm T z{

(8)

where the solution is an ideal solution (γ = 1), and then we have some transformation as follows: def

A =

ΔdissoH 1 × R Tm

def

B = −

ΔdissoH R

(9)

We can get eq 10: B ln x = A + (10) T where x is the mole fraction solubility of buprofezin and T is the kelvin temperature. The parameters of A and B are recorded in Table 5.

(5)

where N represents the number of experimental points, xi stands for the experimental solubility values, and xci represents the calculated solubility values. 3.2.2. The Modified Apelblat Model. The solubility of buprofezin has been consistent with the following modified Apelblat model under temperature changes:10 B ln x = A + + C ln(T /K ) (T / K )

solvent

Table 5. Parameters of the Ideal Model for Buprofezin in Pure Organic Solvents at the Temperature Range of 278.15− 328.15 K

(6)

where T stands for the absolute kelvin temperature, A, B, and C represent the model parameters, and x represents the mole fraction solubility of buprofezin in the solvent. The factors A and B represent the variation in the solution activity coefficient and take an indication of the effect of non-ideal solution of solute solubility, and the factor C represents the temperature effect on the fusion enthalpy, which is a deviation from heat capacity E

solvents

A

B

102RAD


10.73 9.47 11.27 9.85 9.45 7.98 7.81 11.22

−4610.83 −4110.52 −4569.52 −3998.75 −4141.41 −3519.16 −3028.00 −4527.54

13.29 7.95 5.47 4.69 7.79 9.62 2.35 6.45 ∑(102RAD) = 57.61



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Table 6. Mole Fraction Solubility (x) of Buprofezin in a Binary Solution Mixture (Methanol + Ethyl Acetate) at the Temperature Range of 278.15−328.15 K under 0.1 MPaa xA

100x

T = 278.15 K 0.000 0.48 0.068 0.73 0.151 1.04 0.253 1.41 0.383 1.89 0.554 2.52 0.789 3.38 1.000 4.16 T = 283.15 K 0.000 0.53 0.068 0.86 0.151 1.26 0.253 1.76 0.383 2.39 0.554 3.22 0.789 4.35 1.000 5.38 T = 288.15 K 0.000 0.68 0.068 1.09 0.151 1.58 0.253 2.19 0.383 2.96 0.554 3.97 0.789 5.37 1.000 6.62 T = 293.15 K 0.000 0.75 0.068 1.24 0.151 1.82 0.253 2.55 0.383 3.47 0.554 4.69 0.789 6.35 1.000 7.85 T = 298.15 K 0.000 0.93 0.068 1.53 0.151 2.25 0.253 3.14 0.383 4.28 0.554 5.77 0.789 7.82 1.000 9.67 T = 303.15 K 0.000 1.12 0.068 1.83 0.151 2.70 0.253 3.77

100|x − xcal|/x (eq 6)

100|x − xcal|/x (eq 12)

100|x − xcal|/x (eq 15)

8.45 7.15 5.79 4.68 3.80 3.09 2.51 2.19

0.00 3.12 1.44 0.65 0.80 0.57 0.14 0.00

9.02 11.15 8.13 3.71 0.04 2.88 7.96 11.46

7.02 4.23 2.44 1.22 0.32 0.36 0.90 1.20

0.00 4.33 2.02 0.79 1.04 0.72 0.17 0.00

3.99 5.21 5.86 4.01 2.38 1.20 2.13 4.44

5.42 3.53 2.58 2.03 1.67 1.42 1.25 1.15

0.00 4.04 1.88 0.76 0.98 0.68 0.16 0.00

2.59 5.82 6.41 4.77 3.47 2.69 0.06 1.90

1.15 0.27 0.34 0.77 1.07 1.30 1.48 1.58

0.00 4.65 2.17 0.82 1.10 0.75 0.17 0.00

15.63 2.43 0.38 0.18 0.03 0.27 1.54 2.71

4.89 3.56 2.63 1.98 1.50 1.13 0.85 0.69

0.00 4.64 2.16 0.82 1.10 0.75 0.17 0.00

16.17 2.27 1.16 1.56 1.97 2.76 1.63 0.97

4.33 3.39 2.68 2.17

0.00 4.56 2.13 0.81

18.39 3.92 0.00 0.88

xA

100x

T = 303.15 K 0.383 5.13 0.554 6.91 0.789 9.36 1.000 11.57 T = 308.15 K 0.000 1.36 0.068 2.17 0.151 3.17 0.253 4.39 0.383 5.96 0.554 8.01 0.789 10.82 1.000 13.36 T = 313.15 K 0.000 1.65 0.068 2.60 0.151 3.76 0.253 5.20 0.383 7.03 0.554 9.42 0.789 12.71 1.000 15.68 T = 318.15 K 0.000 2.13 0.068 3.22 0.151 4.56 0.253 6.21 0.383 8.31 0.554 11.07 0.789 14.85 1.000 18.26 T = 323.15 K 0.000 2.82 0.068 4.05 0.151 5.55 0.253 7.41 0.383 9.77 0.554 12.86 0.789 17.11 1.000 20.95 T = 328.15 K 0.000 3.83 0.068 5.19 0.151 6.84 0.253 8.88 0.383 11.48 0.554 14.88 0.789 19.56 1.000 23.78

100|x − xcal|/x (eq 6)

100|x − xcal|/x (eq 12)

100|x − xcal|/x (eq 15)

1.80 1.51 1.28 1.15

1.08 0.74 0.17 0.00

1.79 3.07 2.51 2.29

1.86 0.86 0.24 0.17 0.46 0.68 0.84 0.93

0.00 4.16 1.93 0.77 1.01 0.70 0.16 0.00

19.63 6.41 2.80 1.92 0.85 0.71 0.53 0.62

2.24 1.65 1.27 1.00 0.79 0.63 0.50 0.43

0.00 3.87 1.79 0.74 0.95 0.66 0.16 0.00

19.54 7.21 3.74 2.76 1.46 0.40 0.64 1.06

2.09 1.60 1.11 0.72 0.39 0.14 0.08 0.20

0.00 3.08 1.42 0.64 0.79 0.56 0.14 0.00

11.71 3.78 2.12 2.05 1.24 0.42 0.67 1.22

1.08 0.95 0.68 0.43 0.22 0.04 0.11 0.19

0.00 2.18 1.00 0.51 0.59 0.44 0.11 0.00

1.13 1.48 0.52 0.96 1.13 0.08 0.13 0.36

0.91 0.89 0.73 0.53 0.34 0.17 0.02 0.07

0.00 1.34 0.60 0.36 0.39 0.31 0.08 0.00

11.31 8.76 4.72 1.14 0.56 0.59 1.33 1.14

a

xA is the mole fraction of ethyl acetate in the binary solvent mixture. x is the mole fraction solubility of buprofezin. Xcal is the calculated solubility. Standard uncertainties are u(T) = 0.05 K, u(P) = 2 kPa, u(xA) = 0.0001. The relative standard uncertainties: ur(x) =0.02.

3.3. In Binary Solvent Mixtures. 3.3.1. Solubility Data and Correlation Models. The saturated mole fraction solubility (x) of buprofezin in binary solvent mixtures (methanol + ethyl acetate and acetonitrile + ethyl acetate) was measured in the temperature range of 278.15−328.15 K. The values are listed in Tables 6 and 10 and Figures 5 and 6.

3.3.2. Modified Apelblat Model. The regression curve parameters of the modified Apelblat model are previously described in Section 3.2.2, and the relevant data and parameters are listed in Tables 7 and 11. 3.3.3. CNIBS/R-K Model. The changing trends of solubility against different ratios of isopropanol under isothermal conditions F



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the model constant, and N can be equal to 0, 1, 2, and 3. When N = 2 and substituting (1 − xA) for xB, Equation 12 can be deformed as

Table 7. Parameters of the Modified Apelblat Equation for Buprofezin in a Binary Solution Mixture (Methanol + Ethyl Acetate) xA

A

B/100

C

100MD

0.000 0.068 0.151 0.253 0.383 0.554 0.789 1.000

−689.80 −394.07 −217.51 −100.40 −16.94 45.47 94.00 120.77

277.39 146.21 67.86 15.90 −21.11 −48.76 −70.23 −82.06

103.91 59.82 33.51 16.08 3.66 −5.61 −12.81 −16.78

3.59 2.55 1.86 1.44 1.12 0.95 0.89 0.89 100MD = 1.66

ln x − (1 − xA )ln XB − xA ln XA = (1 − xA )xA[S0 + S1(2xA − 1) + S2(2xA − 1)2 ]

This is a variant of the CNIBS/R-K model. The parameter Si could be obtained by regressing {ln x − (1 − xA)ln XB − xA ln XA }

T

S0

S1

S2

100MD

1.97 2.21 2.16 2.27 2.27 2.25 2.18 2.12 1.96 1.74 1.47

−1.31 −1.55 −1.50 −1.61 −1.61 −1.59 −1.52 −1.46 −1.30 −1.08 −0.84

0.92 1.13 1.07 1.17 1.17 1.16 1.10 1.05 0.91 0.74 0.55

0.84 1.13 1.06 1.21 1.21 1.19 1.09 1.22 0.83 0.60 0.38 100MD = 0.98

The values of the parameters are listed in Tables 8 and 12. However, the CNIBS/R-K model can only be used to describe the solubility data and predict the solubility data for different concentrations of a mixed solvent at a fixed temperature. To describe the effect of both solvent compositions and temperature on the solubility of buprofezin, we adopt another equation. 3.3.4. Jouyban−Acree Model. This is a relatively more versatile model to describe the solubility of a solute with the variation in both the temperature and initial composition of binary solvent mixtures:18,19 N

ln x = xA ln XA + x B ln XB + xAx B∑ i=0

100MD

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15

6.79 3.65 3.46 2.90 3.56 4.11 4.18 4.60 2.90 0.72 3.69 100MD = 3.69

ln x = ln XB + (ln XA − ln XB)xA +

parameters A0 A1 A2 A3 A4 A5 A6

Ji (xA − x B)i T

(13)

where Ji is the parameter and T is the absolute temperature. Other symbols mean the same as eq 11. When N = 2 and substituting (1 − xA) for xB, Equation 13 can be rewritten as

Table 9. Parameters of the Jouyban−Acree Model for Buprofezin in a Binary Solution Mixture (Methanol + Ethyl Acetate) T

versus

{(1 − xA )xA[S0 + S1(2xA − 1) + S2(2xA − 1)2 ]}

Table 8. . Parameters of the CNIBS/R-K Model for Buprofezin in a Binary Solution Mixture (Methanol + Ethyl Acetate) 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15

(12)

−3736.86 8.01 −0.28 1863.71 −2710.50 2473.22 −893.38

+

( −J0 + 3J1 − 5J2 )xA 2

+

( −4J2 )xA 4

T T

+

(J0 − J1 + J2 )xA

T ( −2J1 + 8J2 )xA 3 T (14)

In this model, XA and XB represent the saturated molar solubility of buprofezin in pure ethyl acetate and methanol (or acetonitrile), respectively. As described above, the change in the mole fraction solubility of a solute in a single solvent can be described by the modified Apelblat equation. Thus, equation 14 can be simplified to a combination of the Jouyban−Acree model and the modified Apelblat model. The equation can be simplified as T ln x = A 0 + A1T + A 2 TxA + A3xA + A4 xA 2 + A5xA 3 + A 6xA 4

where A0, A1, A2, A3, A4, A5, and A6 are the parameters of this model and can be calculated by regressing T ln x against T, TxA, xA, xA2, xA3, xA4 by least-square analysis, which are listed in Tables 9 and 13. 3.3.5. Mean Deviation. The mean deviation (MD)20 is adopted to describe the deviation from the experimental data and calculated data.

are described by the combined nearly ideal binary solvent/ Redlich-Kister (CNIBS/R-K) model,11,16,17 which is one of the theoretical models for calculating the solute solubility in binary solvents and is represented in eq 11: N

ln x = xA ln XA + x B ln XB + xAx B∑ Si(xA − x B)2 i=0

(15)

(11)

where x represents the mole fraction solubility of buprofezin, xA and xB represent the initial mole fraction compositions of the binary solvents when the solute was not added, and XA and XB represent the saturated mole solubility of buprofezin in pure ethyl acetate and methanol (or acetonitrile), respectively. Si is

∑ MD =

|x − x cal| x

N

(16)

where N represents the number of experimental points, and x and xcal represent the experimental and calculated data, G



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Table 10. Mole Fraction Solubility (x) of Buprofezin in a Binary Solution Mixture (Acetonitrile + Ethyl Acetate) from 278.15 to 328.15 K under 0.1 MPaa xA

100x

T = 278.15 K 0.000 0.62 0.086 0.92 0.186 1.28 0.303 1.69 0.444 2.19 0.615 2.80 0.827 3.55 1.000 4.16 T = 283.15 K 0.000 0.70 0.086 1.10 0.186 1.57 0.303 2.12 0.444 2.77 0.615 3.57 0.827 4.57 1.000 5.38 T = 288.15 K 0.000 0.82 0.086 1.32 0.186 1.90 0.303 2.58 0.444 3.40 0.615 4.39 0.827 5.62 1.000 6.62 T = 293.15 K 0.000 0.97 0.086 1.56 0.186 2.25 0.303 3.06 0.444 4.02 0.615 5.20 0.827 6.66 1.000 7.85 T = 298.15 K 0.000 1.18 0.086 1.90 0.186 2.75 0.303 3.75 0.444 4.94 0.615 6.40 0.827 8.20 1.000 9.67 T = 303.15 K 0.000 1.43 0.086 2.30 0.186 3.31 0.303 4.51

100|x − xcal|/x (eq 6)

100|x − xcal|/x (eq 12)

100|x − xcal|/x (eq 15)

1.90 0.29 1.18 1.62 1.88 2.03 2.14 2.19

0.00 1.92 0.55 0.59 0.35 0.43 0.15 0.00

10.24 9.53 5.43 1.14 2.08 4.79 8.87 11.22

0.49 0.06 0.31 0.59 0.81 0.98 1.12 1.20

0.00 2.66 0.78 0.76 0.46 0.54 0.19 0.00

0.02 5.20 4.38 2.43 1.04 0.16 2.80 4.25

0.71 0.12 0.52 0.76 0.91 1.02 1.11 1.15

0.00 2.98 0.88 0.83 0.50 0.59 0.21 0.00

6.63 1.75 2.62 1.86 1.43 1.04 0.80 1.74

1.18 1.11 1.21 1.32 1.41 1.48 1.54 1.58

0.00 3.00 0.88 0.83 0.50 0.59 0.21 0.00

11.74 2.18 0.60 0.79 0.71 0.62 1.97 2.58

0.21 0.49 0.67 0.72 0.73 0.72 0.70 0.69

0.00 3.09 0.91 0.85 0.52 0.60 0.21 0.00

13.28 2.26 0.24 0.77 1.45 2.09 1.30 1.06

0.15 0.83 1.04 1.12

0.00 2.96 0.87 0.82

13.51 2.66 0.01 0.82

xA

100x

T = 303.15 K 0.444 5.93 0.615 7.67 0.827 9.82 1.000 11.57 T = 308.15 K 0.000 1.77 0.086 2.76 0.186 3.92 0.303 5.28 0.444 6.91 0.615 8.89 0.827 11.36 1.000 13.36 T = 313.15 K 0.000 2.19 0.086 3.35 0.186 4.70 0.303 6.28 0.444 8.18 0.615 10.48 0.827 13.35 1.000 15.68 T = 318.15 K 0.000 2.71 0.086 4.05 0.186 5.60 0.303 7.43 0.444 9.61 0.615 12.27 0.827 15.57 1.000 18.26 T = 323.15 K 0.000 3.43 0.086 4.93 0.186 6.68 0.303 8.74 0.444 11.20 0.615 14.20 0.827 17.92 1.000 20.95 T = 328.15 K 0.000 4.35 0.086 6.02 0.186 7.96 0.303 10.24 0.444 12.98 0.615 16.30 0.827 20.42 1.000 23.78

100|x − xcal|/x (eq 6)

100|x − xcal|/x (eq 12)

100|x − xcal|/x (eq 15)

1.15 1.16 1.16 1.15

0.50 0.59 0.20 0.00

1.80 2.75 2.34 2.36

0.50 0.01 0.31 0.52 0.68 0.79 0.88 0.93

0.00 2.55 0.74 0.74 0.44 0.53 0.19 0.00

11.91 3.37 1.53 1.06 0.19 0.80 0.52 0.66

0.58 0.10 0.12 0.25 0.32 0.38 0.41 0.43

0.00 2.24 0.64 0.67 0.39 0.48 0.17 0.00

8.92 2.29 1.11 0.91 0.10 0.94 0.80 1.08

0.44 0.38 0.24 0.12 0.01 0.08 0.15 0.20

0.00 1.92 0.55 0.59 0.35 0.43 0.16 0.00

5.65 1.01 0.64 0.80 0.15 0.87 0.83 1.21

0.09 0.14 0.08 0.01 0.06 0.11 0.16 0.19

0.00 1.49 0.41 0.49 0.28 0.36 0.13 0.00

0.27 1.67 0.45 0.62 0.52 0.17 0.02 0.33

0.06 0.14 0.12 0.08 0.04 0.00 0.04 0.07

0.00 1.08 0.29 0.38 0.21 0.28 0.11 0.00

6.85 4.97 1.90 0.36 1.07 0.90 1.41 1.19

a

xA is the mole fraction of ethyl acetate in the binary solvent mixture. x is the mole fraction solubility of buprofezin. Xcal is the calculated solubility. Standard uncertainties are u(T) = 0.05 K, u(P) = 2 kPa, u(xA) = 0.0001. The relative standard uncertainties: ur(x) = 0.02.

According to Tables 3−5, we can find that the sums of 100RAD values of the modified Apelblat equation, the λh model, and the ideal model are 14.56, 45.40, and 57.61, respectively. This result shows that the modified Apelblat equation is the best compared with the λh model and the ideal model.

respectively. The values of MD, together with the parameters, are listed in Tables 7−9 and Tables 11−13. 3.4. Chart Analysis. 3.4.1. In Pure Solvents. According to Table 2 and Figure 4, we determined that the solubility of buprofezin in different solvents is a function of temperature, where the solubility increases as the temperature increases. H



Article

3.4.2. In Binary Solvent Mixtures. In order to ensure that the data is more reliable and the experimental data of the binary solvent system are mutually comparable, our experimental design is carried out with the same two binary solvent volume fractions. According to Table 6 and Figure 5 and Table 10 and Figure 6, the solubility of buprofezin in binary solvent mixtures (ethyl acetate + methanol and acetonitrile + ethyl acetate) is a function of temperature, the solubility increases as temperature increases. Also, they also increase from the increase in the ratio of the ethyl acetate content of constant temperature. To clarify

Table 12. Parameters of the CNIBS/R-K Model for Buprofezin in a Binary Solution Mixture (Acetonitrile + Ethyl Acetate) T

S0

S1

S2

100MD

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15

1.60 1.80 1.87 1.88 1.90 1.87 1.77 1.69 1.60 1.46 1.30

−0.96 −1.14 −1.22 −1.22 −1.24 −1.21 −1.12 −1.04 −0.96 −0.84 −0.70

0.55 0.67 0.73 0.73 0.74 0.72 0.66 0.60 0.55 0.46 0.37

0.50 0.67 0.75 0.75 0.77 0.74 0.65 0.57 0.50 0.40 0.29 100MD = 0.60

Table 13. Parameters of the Jouyban−Acree Model for Buprofezin in a Binary Solution Mixture (Acetonitrile + Ethyl Acetate)

Figure 5. Mole fraction solubility (x) of buprofezin versus temperature (T) in a binary solvent mixture (ethanol + ethyl acetate).

T

100MD

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15

6.66 2.53 2.23 2.65 2.81 3.28 2.51 2.02 1.40 0.51 2.33 100MD = 2.63

Parameters A0 A1 A2 A3 A4 A5 A6

−3629.87 7.86 −0.11 1513.43 −2009.99 1694.23 −576.45

Table 14. . Physical Properties of the Selected Solvent in Mixed Solventsa solvent

polarity

dipole moment μ (D)

ethyl acetate methanol acetonitrile

23 76.2 46

1.7 1.7 3.2

b

dielectric constant ε (T = 293.15 K)

Hildebrand solubility parameter δH/(J·m−3)1/2

6.02 32.6 37.5

9.1 14.5 11.9

a

Taken from the literature.21 bValues of polarity are relative to water, with a polarity of 100.

this phenomenon of buprofezin in mixed solvents, consider the properties of each solvent in the mixed solvents, including polarities, dipole moments, dielectric constants, and Hildebrand solubility parameters. These data are listed in Table 14.21 From the data in Table 14, ethyl acetate, relative to methanol and acetonitrile, has a lower dielectric constant and Hildebrand solubility parameter as well as a smaller polarity. Combined with the previous blending data, it is not only a single factor that affects solubility but also the effects of interactions between different factors of the entire system, such as dielectric constants, hydrogen bonds, van der Waals forces, etc. From Tables 7−9, we can see that the averages of 100MD values of the modified Apelblat equation, the CNIBS/R-K model, and the Jouyban−Acree model are 1.66, 0.98, and 3.69, respectively. From Tables 11−13, these are 0.67, 0.60, and 2.63, respectively. So, the CNIBS/R-K model is the best compared with the modified Apelblat equation and the Jouyban−Acree model.

Figure 6. Mole fraction solubility (x) of buprofezin versus temperature (T) in a binary solvent mixture (acetonitrile + ethyl acetate).

Table 11. Parameters of the Modified Apelblat Equation for Buprofezin in a Binary Solution Mixture (Acetonitrile + Ethyl Acetate) xA

A

B/100

C

100MD

0.000 0.086 0.186 0.303 0.444 0.615 0.827 1.000

−400.69 −206.91 −93.09 −18.46 34.35 73.65 104.05 120.77

147.68 62.27 12.08 −20.82 −44.08 −61.37 −74.72 −82.06

60.85 31.95 15.00 3.89 −3.96 −9.80 −14.30 −16.78

0.57 0.33 0.53 0.65 0.73 0.80 0.86 0.89 100MD = 0.67 I



Article

Figure 7. Comparison of the molar fraction solubility of the buprofezin in the literature and the selected different organic solvents: (a) ethyl acetate. (b) DMF. (c) 1-butanol. (d) acetonitrile. (e) methanol. (f) ethanol. (g) isopropanol.

3.4.3. Comparison of Experimental Data. The experimental data in this work is compared with the literature,22 as shown in Figure 7. By comparison, among the seven solvents, the experimental data in the literature at the same temperature are higher than those in this work. In the literature, HPLC is used to measure the experimental data. In this work, the weight difference method is used. Because the amount of each extraction is small and different experimental methods, it causes a large error. In addition, the mass fraction purity of buprofezin in the literature is higher than this work, which may be another reason, although HPLC has been used to prove that no new impurities are introduced before and after crystallization in this work. In summary, these may be the cause of the error.

with increasing temperature in the temperature range of 278.15−328.15 K. For pure solvents, the solubility of buprofezin in ethyl acetate is the most pronounced. In addition, the experimental data also showed that the amount of buprofezin dissolved in the binary solvents increased as the content of ethyl acetate increased. Therefore, we consider ethyl acetate as an effective solvent for the crystallization of buprofezin. (ii) The experimental solubility data of buprofezin in a pure solvent is related to the ideal model, the modified Apelblat, and λh models, and the modified Apelblat model is more suitable than the other models. In the mixed solvent, the experimental solubility data of buprofezin is correlated with the CNIBS/R-K model and the Jouyban−Acree model, and the correlation is better because the CNIBS/R-K model has lower MD values. In general, the experimental solubility and correlation equation in this work can be used as essential data and models on the purification process of buprofezin, which can predict

4. CONCLUSIONS We can get conclusions from all tables and figures: (i) the solubility of buprofezin in pure and mixed solvents increases J



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unmeasured solubility and the optimum concentration of the solvent.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +86 25 58139208. Fax: +86 25 58139208. ORCID

Yonghong Hu: 0000-0002-8268-8763 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This research work was financially supported by the Jiangsu Science and Technology Support Program (BE2018396), the Jiangsu Province 2018 Provincial Fisheries Science and Technology Project (Y2018-21), and the Jiangsu Advanced Biomanufacturing Collaborative Innovation Center (XTB1805). We thank the editor and the anonymous reviewers.

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