Solubility Determination and Modeling for 4-Nitrobenzonitrile in Binary

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

Solubility Determination and Modeling for 4‑Nitrobenzonitrile in Binary Solvent Mixtures of Ethyl Acetate Plus (Methanol, Ethanol, n‑Propanol, and Isopropanol) Li Wanxin,† Mengyan Li,† Nan Wang,† Zhenghao Fei,† Jiao Chen,‡ and Hongkun Zhao*,‡ †

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School of Chemistry and Environmental Engineering, Yancheng Teachers University, Yancheng, Jiangsu 224002, People’s Republic of China ‡ College of Chemistry and Chemical Engineering, YangZhou University, YangZhou, Jiangsu 225002, People’s Republic of China ABSTRACT: The solubility of 4-nitrobenzonitrile in mixed solvents of (ethanol + ethyl acetate), (methanol + ethyl acetate), (isopropanol + ethyl acetate), and (npropanol + ethyl acetate) over temperatures ranging from 278.15 to 318.15 K was obtained experimentally. From analysis results in the present study, we found that the equilibrium 4-nitrobenzonitrile solubility in the ethyl acetate (1) + (ethanol, methanol, isopropanol, and n-propanol) (2) mixed solvents increased with the temperature and the ethyl acetate composition increasing. The largest 4nitrobenzonitrile solubility was in neat ethyl acetate at T = 318.15 K (1.346 × 10−3 in methanol, 1.082 × 10−2 in n-propanol, 1.159 × 10−2 in ethanol, 0.8765 × 10−3 in isopropanol, and 14.22 × 10−2 in ethyl acetate). The lowest 4nitrobenzonitrile solubility was observed in neat isopropanol (0.1624 × 10−2 at T = 278.15 K). The solubility dependence on both ethyl acetate composition and temperature was mathematically described by the Apelblat−Jouyban−Acree, van’t Hoff−Jouyban−Acree, and Jouyban−Acree models. The acquired values of relative average deviation and root-mean-square deviation were not, respectively, greater than 2.13% and 11.72 × 10−4.

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distillation technique.16 Isomer purification can also be made by several other methods usually used in industry, for example, adsorption,17,18 adjusting pH,19 chemical conversion,20 pervaporation21 and so on. In recent years, membrane has been used to separate isomeric mixtrues,7 however the cost of membrane is very high at present. Compared to the separation techniques described above, the solvent crystallization is suitable energy cost, easy operation, and high purity, so this method is an effective method to separate the isomers.22−24 It is well-known that the solid solubility in pure solvents and solvent mixtures is of significant importance during the process of solvent crystallization. As a result, the solubility is significant in the purification process of 4-nitrobenzonitrile through crystallization. In order to remove 3-nitrobenzonitrile from crude 4-nitrobenzonitrile product, the knowledge of 3/4nitrobenzonitrile solubility in different neat solvents and solvent mixtures is a crucial procedure. It is known to us that mixed solvents with temperature change is a common method to change solubility of a solid. The knowledge concerning solubility in solvent mixtures can enable us to discover suitable solvents in purifying 4-nitrobenzonitrile. Recently, the solubility of 3nitrobenzonitrile in some pure organic solvents and solvent mixtures determined with static method at several temperatures are reported.25,26 So as to explore a novel purification procedure

INTRODUCTION 4-Nitrobenzonitrile (CAS No. 619-72-7, structure presented in Figure 1) is an important aromatic nitrile which is generally

Figure 1. Chemical structure of 4-nitrobenzonitrile.

widely used for the pharmaceuticals, dyestuffs, and pesticides production.1−3 At present, it is commonly produced by benzonitrile nitration with HNO3 or other nitrating agent.4−15 Nevertheless, during the nitration process of benzonitrile, the 3nitrobenzonitrile isomer is also generated simultaneously as a byproduct. So further use of 4-nitrobenzonitrile is limited in some fields because of the isomeric byproduct. As the rapid development of dyestuff industry and pharmaceutical industry, the required purity of 4-nitrobenzonitrile is becoming very high. In general, the 4-nitrobenzonitrile production is made in some solvents, for instance, acetonitrile, acetone and methanol.5,10 The 3/4-nitrobenzonitrile solubility in these solvents influences greatly the yield of product and reaction rate. The separation for organic isomers has been attracting extensive attention owing to the great requirements and importance in industry. Nevertheless, due to their similar boiling points, it is not successfully realized by using the © XXXX American Chemical Society

Received: June 29, 2018 Accepted: September 7, 2018

A

DOI: 10.1021/acs.jced.8b00555 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Detailed Description of 4-Nitrobenzonitrile and the Selected Solvents chemicals

molar mass g·mol−1

4-nitrobenzonitrile

148.12

methanol ethanol n-propanol

32.04 46.07 60.06

isopropanol ethyl acetate

60.06 88.11

source Shangdong Shuojia Chemical Co., Ltd., China

Sinopharm Chemical Reagent Co., Ltd.,China

initial mass fraction purity

purification method

final mass fraction purity

analytical method

0.970

recrystallization

0.996

HPLCa

0.993 0.995 0.994

0.993 0.995 0.994

GCb GC GC

0.994 0.995

0.994 0.995

GC GC

a

High-performance liquid chromatography bGas chromatography.

temperature was displayed using a mercury glass microthermometer inserted in the jacket. The reliability of this apparatus was confirmed via measuring the benzoic acid solubility in toluene before experiment.27,28 The mixtures were prepared by the analytical balance having a model of BSA224S, and standard uncertainty was 0.0001 g. The composition range of ethyl acetate in the mixed solvents was from 0 to 1.0. The local ambient pressure was 101.1 kPa during determination. The solubility determination of 4-nitrobenzonitrile in (ethanol + ethyl acetate), (methanol + ethyl acetate), (isopropanol + ethyl acetate), and (n-propanol + ethyl acetate) mixtures were carried out through the isothermal equilibrium technique.25−28 Saturated solutions of 4-nitrobenzonitrile were prepared in the flask through introducing excess 4-nitrobenzonitrile to the flask filled with about 60 mL mixed solutions. Then the solutions were stirred with about 200 rpm at the desired temperatures. As soon as the solutions were in equilibration, the stirring was stopped and and the solid was allowed to precipitate from the mixtures. Triple samples were taken out cautiously with a 2 mL precooled or preheated syringe connected with a PTFE filter (0.2 μm) and moved instantly into a preweighed volumetric bottle. The samples were diluted with a certain amount of methanol, and then 1 μL of liquor was withdrawn for test with the HPLC. Analysis Technique. The compositions of equilibrium samples were tested with the HPLC (Agilent-1260). The chromatographic column was an unimicro Kromasil C18, 5 μm (250 mm × 4.6 mm). The temperature of the column was kept at around 303 K, and the wavelength of the detector was set to 256 nm. The water + methanol mixture having a volume ratio of 30:70 was used as the mobile phase in which flow speed was 0.8 mL·min−1. Each analysis was performed in triplicate. The mean data was considered as the solubility. The relative standard uncertainty of evaluated solubility in mole fraction was 0.026. The 4-nitrobenzonitrile solubility in mole fraction (xw,T) in the selected neat solvents and mixed solvents are achieved using eq 1. In addition, the original composition of the solution (w) is obtained by using eqs 2 and 3.

for nitrobenzonitrile isomers, the goals of the present paper are to determine the solubility of 4-nitrobenzonitrile in solvent mixtures of (ethanol + ethyl acetate), (methanol + ethyl acetate), (isopropanol + ethyl acetate), and (n-propanol + ethyl acetate) and correlate the obtained solubility data with different models.

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EXPERIMENTAL SECTION Materials. 4-Nitrobenzonitrile, having a mass fraction of 0.970, was purchased from Shangdong Shuojiao Chemical Co., Ltd., China. The crude 4-nitrobenzonitrile was crystallized repeatedly in ethanol. The mass fraction purity of the purified 4nitrobenzonitrile was 0.996, which was analyzed through an Agilent-1260 HPLC (high-performance liquid chromatography). The neat solvents, namely, n-propanol, ethanol, ethyl acetate, methanol, and isopropanol, were not treated before use. The mass fractions of these neat solvents were no less than 0.993 determined with gas chromatography (type: GC-2018)}. Table 1 presents the details of 4-nitrobenzonitrile and these solvents. Apparatus and 4-Nitrobenzonitrile Solubility Measurement. The apparatus shown in Figure 2 is similar to that

Figure 2. Schematic diagram of experimental apparatus: I, smart thermostatic water bath; II, mercury-in-glass thermometer; III, magnetic stirrer; IV, stirrer controller; V, jacketed glass vessel; VI, sampling port; VII, condenser.

x w,T =

used in our published works.25−28 This apparatus comprised a circulating water system, a stirrer, and a jacketed vessel. The water temperature was regulated through a water bath (QYHX1030) produced by Shanghai Joyn Electronic Co., Ltd., China, in which standard uncertainty was 0.05 K. Between the inner and outer walls of the flask was circulating water. The actual

m1 M1

w1 = w =

w2 = B

+

m1 M1 m2 M2

+

m2 m 2 + m3

m3 m 2 + m3

m3 M3

(1)

(2)

(3) DOI: 10.1021/acs.jced.8b00555 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

where m1 signifies the 4-nitrobenzonitrile mass; m2 signifies the ethyl acetate mass. m3 denotes the mass of methanol, ethanol, npropanol, or isopropanol. Mi (i = 1−3) stands for the corresponding molar masses of solute and solvents, respectively. X-ray Powder Diffraction. In an attempt to confirm the presence of polymorph transformation or solvate formation of 4nitrobenzonitrile in the experimental process, the solid equilibrated with liquor was gathered and analyzed using the powder X-ray diffraction (XRD). The test was performed on the HaoYuan DX-2700B (China) instrument at normal temperature. The wavelength of Cu Ka radiation was λ = 1.5405 nm, and the tube voltage and current were set at 40 kV and 40 mA, respectively. The data was collected at room temperature from 10° to 80° (2θ) at a step size of 0.01° with a scanning rate of 0.1s/step.

solvate formation or polymorph transformation exists in the experimental procedure. Solubility Data. The determined solubility of 4-nitrobenzonitrile in neat solvents, namely, methanol, ethyl acetate, ethanol, isopropanol and n-propanol, covering the temperature range from 278.15 to 318.15 K are tabulated in Tables 2−5 and plotted in Figure 4. As may be found, for a given pure solvent the 4-nitrobenzonitrile solubility rises with an increase in temperature. At a certain temperature, the 4-nitrobenzonitrile solubility in mole fraction is maximum in ethyl acetate, and minimum in isopropanol. The dissolving capacity of 4-nitrobenzonitrile in the five pure solvents are ethyl acetate > methanol > ethanol > npropanol > isopropanol. The solubility of 4-nitrobenzonitrile in the five neat solvents displays the positive dependence upon temperature studied. For instance, as the temperature rises from 278.15 to 318.15 K, the 4-nitrobenzonitrile solubility in ethyl acetate rises from 0.04044 to 0.1422; in methanol, it rises from 0.003201 to 0.01346. They increase about 4 times. For the 4nitrobenzonitrile + alcohol mixtures, the 4-nitrobenzonitrile solubility decreases with decreasing Hildebrand solubility parameters (δH), polarities, and dielectric constants of the selected alcohols with the exception of isopropanol.29 This is perhaps caused by strong polarity of the 4-nitrobenzonitrile molecule. The methanol polarity is highest among the alcohols, so the 4-nitrobenzonitrile solubility in methanol is the highest. The 4-nitrobenzonitrile solubility in (ethanol + ethyl acetate), (methanol + ethyl acetate), (isopropanol + ethyl acetate), and (n-propanol + ethyl acetate) mixtures is also tabulated in Tables 2−5. Moreover, the dependence of 4-nitrobenzonitrile solubility on temperature and solvent composition is shown graphically in Figures 5−8. As may be revealed from Figures 5−8 that the mole fraction solubility of 4-nitrobenzonitrile is a function of temperature and solvent composition. It rises with rising ethyl acetate composition and temperature for the (ethanol + ethyl acetate), (methanol + ethyl acetate), (isopropanol + ethyl acetate), and (n-propanol + ethyl acetate) mixed solvents. Solubility Modeling. Several models have been proposed and employed in correlating the solid solubility in solvent mixtures in literatures.26,27,30 In this work, three models, Jouyban−Acree,26,27,30 Apelblat−Jouyban−Acree26,27 and van’t Hoff−Jouyban−Acree26,27 are used in correlating the solubility of 4-nitrobenzonitrile in binary mixed solvents.

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RESULTS AND DISCUSSION X-ray Powder Diffraction Analysis. The obtained XRD patterns of raw 4-nitrobenzonitrile and equilibrated solids with mixtures are presented in Figure 3. It can be observed from

Figure 3. XRD patterns of 4-nitrobenzonitrile: (a) raw material; (b) in ethyl acetate; (c) in methanol; (d) in ethanol; (e) in n-propanol; (f) in isopropanol; (g) in ethyl acetate + methanol mixture; (h) in ethyl acetate + ethanol mixture; (i) in ethyl acetate + n-propanol mixture; (j) in ethyl acetate + isopropanol mixture.

Figure 3 that all XRD patterns of solids equilibrating in solutions have the identical characteristic peaks with raw 4-nitrobenzonitrile. Therefore, the conclusion can be made that no

Table 2. Experimental Mole Fraction Solubility (xeT,w × 102) of 4-Nitrobenzonitrile in Solvent Mixtures of Ethyl Acetate (w) + Methanol (1 − w) with Various Mass Fractions at the Temperatures Ranging from T/K = 278.15−318.15 under p = 101.1 kPaa w T/K

0

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

0.3201 0.3699 0.4478 0.5407 0.6520 0.7878 0.9550 1.145 1.346

0.652 0.747 0.894 1.066 1.271 1.52 1.826 2.173 2.542

1.05 1.197 1.422 1.681 1.990 2.364 2.826 3.350 3.913

1.456 1.656 1.956 2.299 2.709 3.204 3.818 4.519 5.281

1.825 2.074 2.441 2.857 3.356 3.958 4.709 5.573 6.526

2.152 2.448 2.873 3.351 3.929 4.624 5.498 6.510 7.642

2.301 2.777 3.329 3.967 4.699 5.535 6.485 7.560 8.771

2.654 3.201 3.835 4.567 5.407 6.366 7.455 8.687 10.07

3.318 3.783 4.412 5.099 5.947 6.964 8.273 9.821 11.63

3.415 4.117 4.930 5.868 6.943 8.170 9.563 11.14 12.91

4.044 4.627 5.381 6.190 7.205 8.420 10.01 11.92 14.22

a

Standard uncertainties u are u(T) = 0.02 K, u(p) = 0.45 kPa; relative standard uncertainty ur is ur(x) = 0.026. Solvent mixtures were prepared by mixing different masses of the solvents with relative standard uncertainty ur(w) = 0.0002. w represents the mass fraction of ethyl acetate in mixed solvents of ethyl acetate + methanol. C



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Table 3. Experimental Mole Fraction Solubility (xeT,w × 102) of 4-Nitrobenzonitrile in Mixed Solvent of Ethyl Acetate (w) + Ethanol (1 − w) with Various Mass Fractions at the Temperatures Ranging from T/K = 278.15 to 318.15 under p = 101.1 kPaa w T/K

0

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.6998

0.8000

0.9000

1

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

0.2552 0.3023 0.3758 0.4537 0.5564 0.6724 0.8213 0.9841 1.159

0.568 0.6642 0.814 0.9697 1.172 1.400 1.693 2.012 2.355

0.9619 1.116 1.353 1.597 1.912 2.268 2.725 3.225 3.767

1.366 1.578 1.897 2.226 2.648 3.128 3.742 4.423 5.168

1.729 1.991 2.378 2.779 3.293 3.878 4.631 5.473 6.408

2.047 2.353 2.798 3.260 3.848 4.525 5.397 6.383 7.494

2.381 2.734 3.235 3.759 4.424 5.194 6.189 7.328 8.628

2.577 3.113 3.736 4.455 5.282 6.228 7.303 8.520 9.892

2.983 3.600 4.316 5.142 6.091 7.175 8.407 9.800 11.37

3.389 4.087 4.897 5.831 6.902 8.126 9.515 11.09 12.86

4.044 4.627 5.381 6.190 7.205 8.420 10.01 11.92 14.22

a

Standard uncertainties u are u(T) = 0.02 K, u(p) = 0.45 kPa; relative standard uncertainty ur is ur(x) = 0.026. Solvent mixtures were prepared by mixing different masses of the solvents with relative standard uncertainty ur(w) = 0.0002. w represents the mass fraction of ethyl acetate in mixed solvents of ethyl acetate + ethanol.

Table 4. Experimental Mole Fraction Solubility (xeT,w × 102) of 4-Nitrobenzonitrile in Mixed Solvent of Ethyl Acetate (w) + nPropanol (1 − w) with Various Mass Fractions at the Temperatures Ranging from T/K = 278.15−318.15 under p = 101.1 kPaa w T/K

0

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

0.2265 0.2714 0.3300 0.4070 0.5050 0.6193 0.7585 0.9085 1.082

0.5325 0.6268 0.7524 0.9130 1.116 1.349 1.635 1.940 2.293

0.9269 1.081 1.286 1.543 1.866 2.236 2.692 3.179 3.745

1.333 1.546 1.828 2.175 2.610 3.110 3.727 4.396 5.175

1.692 1.956 2.305 2.725 3.251 3.858 4.614 5.443 6.413

2.004 2.312 2.717 3.197 3.797 4.493 5.365 6.337 7.478

2.17 2.631 3.169 3.793 4.513 5.338 6.280 7.350 8.560

2.526 3.058 3.678 4.395 5.220 6.166 7.243 8.466 9.846

2.945 3.559 4.272 5.097 6.046 7.130 8.364 9.761 11.34

3.699 4.235 4.931 5.693 6.648 7.783 9.254 10.99 13.07

4.044 4.627 5.381 6.190 7.205 8.420 10.01 11.92 14.22

a

Standard uncertainties u are u(T) = 0.02 K, u(p) = 0.45 kPa; relative standard uncertainty ur is ur(x) = 0.026. Solvent mixtures were prepared by mixing different masses of the solvents with relative standard uncertainty ur(w) = 0.0002. w represents the mass fraction of ethyl acetate in mixed solvents of ethyl acetate + n-propanol.

Table 5. Experimental Mole Fraction Solubility (xeT,w × 102) of 4-Nitrobenzonitrile in Mixed Solvent of Ethyl Acetate (w) + Isopropanol (1 − w) with Various Mass Fractions at the Temperatures Ranging from T/K = 278.15 to 318.15 under p = 101.1 kPaa w T/K

0

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

0.1624 0.1958 0.246 0.3039 0.3744 0.4597 0.5722 0.7077 0.8765

0.4473 0.5316 0.6543 0.7937 0.9604 1.163 1.425 1.739 2.123

0.8459 0.9942 1.208 1.447 1.733 2.077 2.522 3.052 3.697

1.257 1.468 1.767 2.100 2.497 2.975 3.591 4.325 5.214

1.606 1.867 2.234 2.638 3.124 3.707 4.460 5.358 6.442

1.899 2.201 2.621 3.081 3.637 4.304 5.167 6.196 7.438

2.037 2.487 3.015 3.630 4.345 5.169 6.116 7.197 8.425

2.402 2.922 3.531 4.239 5.058 6.001 7.079 8.308 9.701

2.858 3.465 4.173 4.994 5.941 7.026 8.265 9.672 11.26

3.673 4.209 4.913 5.672 6.615 7.743 9.215 10.98 13.10

4.044 4.627 5.381 6.190 7.205 8.420 10.01 11.92 14.22

a

Standard uncertainties u are u(T) = 0.02 K, u(p) = 0.45 kPa; relative standard uncertainty ur is ur(x) = 0.026. Solvent mixtures were prepared by mixing different masses of the solvents with relative standard uncertainty ur(w) = 0.0002. w represents the mass fraction of ethyl acetate in mixed solvents of ethyl acetate + isopropanol.

to, respectively, the mass fraction of solvent 1 (ethyl acetate) and solvent 2 (ethanol, methanol, isopropanol, and n-propanol) in 4nitrobenzonitrile-free mixtures; x1,T and x2,T stand for the 4nitrobenzonitrile solubility in neat solvent 1 and solvent 2; and Ji are the model parameters. The van’t Hoff−Jouyban−Acree equation can be derived by substituting the van’t Hoff equation into Jouyban−Acree equation. This equation can be described as eq 526,27

The Jouyban−Acree model described as eq 4 has been widely used to describe the dependence of solute solubility on both temperature and solvent composition for mixed solvents26,27,30 ln x w,T = w1

ln x1,T + w2

ln x 2,T +

w1w2 T /K

2

∑ Ji (w1 − w2)i i=0

(4)

here xw,T denotes the 4-nitrobenzonitrile solubility in mole fraction in mixed solvents at temperature T/K; w1 and w2 refer D



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Figure 7. Mole fraction solubility (x) of 4-nitrobenzonitrile in ethyl acetate (w) + n-propanol (1 − w) solvent mixtures with various mass fractions at several temperatures: w, mass fraction of ethyl acetate; ×, w = 1; ☆, w = 0.9000; ★, w = 0.8000; ◇, w = 0.7000; △, w = 0.6000; ○, w = 0.5000; □, w = 0.4000; ◆, w = 0.3000; ▲, w = 0.2000; ●, w = 0.1000; ■, w = 0; , calculated curves by the Jouyban−Acree model.

Figure 4. Mole fraction solubility (ln x) of 4-nitrobenzonitrile in pure solvents at different temperatures: ■, methanol; ●, ethanol; ▼, isopropanol; ○, n-propanol; ◆, ethyl acetate.

Figure 5. Mole fraction solubility (x) of 4-nitrobenzonitrile in ethyl acetate (w) + methanol (1 − w) mixed solutions with various mass fractions at several temperatures: w, mass fraction of ethyl acetate; ×, w = 1; ☆, w = 0.9000; ★, w = 0.8000; ◇, w = 0.7000; △, w = 0.6000; ○, w = 0.5000; □, w = 0.4000; ◆, w = 0.3000; ▲, w = 0.2000; ●, w = 0.1000; ■, w = 0; , calculated curves by the Jouyban−Acree model.

Figure 8. Mole fraction solubility (x) of 4-nitrobenzonitrile in ethyl acetate (w) + isopropanol (1 − w) solvent mixtures with various mass fractions at several temperatures: w, mass fraction of ethyl acetate; ×, w = 1; ☆, w = 0.9000; ★, w = 0.8000; ◇, w = 0.7000; △, w = 0.6000; ○, w = 0.5000; □, w = 0.4000; ◆, w = 0.3000; ▲, w = 0.2000; ●, w = 0.1000; ■, w = 0; , calculated curves by the Jouyban−Acree model. i i B1 yz B2 yz ww zz + 1 2 zz + w2jjjA 2 + ln x w,T = w1jjjjA1 + z T /K j z T T /K /K { k { k

2

∑ Ji (w1 − w2)i i=0

(5)

The Apelblat equation is expressed as ln x T = A +

B + C ln(T /K) T /K

(6)

here A, B, and C are model parameters; xT is 4-nitrobenzonitrile solubility in neat solvents at corresponding temperature. Combining eq 6 and eq 4, the Apelblat−Jouyban−Acree equation is acquired and described as26,27 ÉÑ ÅÄÅ ÑÑ B1 Å ln x w,T = w1ÅÅÅÅA1 + + C1 ln (T /K )ÑÑÑÑ ÑÑÖ ÅÅÇ T /K ÅÄÅ ÉÑ ÅÅ ÑÑ B2 ww + w2ÅÅÅÅA 2 + + C2 ln (T /K )ÑÑÑÑ + 1 2 ÅÅ ÑÑÖ T /K T /K ÅÇ

Figure 6. Mole fraction solubility (x) of 4-nitrobenzonitrile in ethyl acetate (w) + ethanol (1 − w) solvent mixtures with various mass fractions at several temperatures: w, mass fraction of ethyl acetate; ×, w = 1; ☆, w = 0.9000; ★, w = 0.8000; ◇, w = 0.7000; △, w = 0.6000; ○, w = 0.5000; □, w = 0.4000; ◆, w = 0.3000; ▲, w = 0.2000; ●, w = 0.1000; ■, w = 0; , calculated curves by the Jouyban−Acree model.

2

∑ Ji (w1 − w2)i i=0

(7)

The mole fraction solubility of 4-nitrobenzonitrile in (ethanol + ethyl acetate), (methanol + ethyl acetate), (isopropanol + ethyl E



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Table 6. Values of Parameters Obtained Using Solubility Models Jouyban−Acree parameter J0 J1 J2

RAD × 102 RMSD × 104

van’t Hoff− Jouyban−Acree value 713.04 544.14 414.55

value

parameter

value

Ethyl Acetate + Methanol A1 B1 A2 B2 J0 J1 J2

6.213 −3347.6 7.309 −2954.0 722.02 539.06 437.01

A1 B1 C1 A2 B2 C2 J0 J1 J2

−90.33 1000.65 14.38 −278.65 9899.02 42.62 715.75 574.85 425.39 1.23 7.49

A1 B1 C1 A2 B2 C2 J0 J1 J2

−26.39 −1978.87 4.89 −278.65 9899.02 42.62 764.1 644.46 453.1 1.54 10.53

A1 B1 C1 A2 B2 C2 J0 J1 J2

−22.01 −2289.42 4.28 −278.65 9899.02 42.62 828.68 746.08 563.97 1.47 8.57

A1 B1 C1 A2 B2 C2 J0 J1 J2

−182.02 4648.21 28.23 −278.65 9899.02 42.62 942.47 919.12 707.71 1.27 9.69

0.93 9.41 J0 J1 J2

RAD × 102 RMSD × 104

781.99 650.9 497.82

1.74 10.76 Ethyl Acetate + Ethanol A1 B1 A2 B2 J0 J1 J2

RAD × 102 RMSD × 104

824.05 711.39 552.39

1.40 9.25 Ethyl Acetate + n-Propanol A1 B1 A2 B2 J0 J1 J2

RAD × 102 RMSD × 104

951.41 909.22 730.05

1.60 10.78 Ethyl Acetate + Isopropanol A1 B1 A2 B2 J0 J1 J2

2.13 11.72

RAD =

using eqs 4, 5, and 7. Equation 8 is the objective function

i=1

7.531 −3907.3 7.309 −2954.0 964.26 911.19 762.18

1.02 8.95

acetate), and (n-propanol + ethyl acetate) mixtures is fitted by

e − ∑ (ln x w,T

6.748 −3586.1 7.309 −2954.0 831.52 703.54 571.06

0.87 7.71 J0 J1 J2

F=

6.411 −3456.8 7.309 −2954.0 789.21 642.61 515.89

0.96 9.96 J0 J1 J2

c ln x w,T )2

Apelblat− Jouyban−Acree

parameter

1 N

c e ij |x w,T − x w,T | yzz zz e z x w,T k {

∑ jjjj

(9)

N

(8)

RMSD =

Moreover, the relative average deviation (RAD) and the root-

c e ∑i = 1 (x w,T )2 − x w,T

N

(10)

where N refers to the number of experimental data points. xew,T denotes the measured solubility data in this study; and xcw,T, the calculated value with solubility model.

mean-square deviation (RMSD) are used in order to assess these equations F



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On the basis of the 4-nitrobenzonitrile solubility, the parameters of the three models are regressed and listed in Table 6, together with the RMSD and RAD values. The solubility of 4-nitrobenzonitrile in the solvent mixtures such as (ethanol + ethyl acetate), (methanol + ethyl acetate), (isopropanol + ethyl acetate), and (n-propanol + ethyl acetate) are back-calculated based on the regressed values of model parameters. The back-calculated data by using the Jouyban− Acree equation are given in Figures 5−8. The results of Table 6 illustrate that the maximum value of RAD is 2.13%, which is attained by using the van’t Hoff−Jouyban−Acree equation for (ethyl acetate + isopropanol) mixture. The obtained values of RMSD are all larger than 11.72 × 10−4. It can also be found that from Table 6 that the acquired RAD and RMSD values are lower using the Jouyban−Acree equation than the van’t Apelblat− Jouyban−Acree and Hoff−Jouyban−Acree models. In general, the three selected models may all be employed to describe the 4nitrobenzonitrile solubility in (ethanol + ethyl acetate), (methanol + ethyl acetate), (isopropanol + ethyl acetate), and (n-propanol + ethyl acetate) mixed solvents.

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CONCLUSION 4-Nitrobenzonitrile solubility in mixed solvents of ethyl acetate (1) + (ethanol, methanol, isopropanol, and n-propanol) (2) measured via isothermal equilibrium technique was reported covering the temperatures ranging from 278.15 to 318.15 K under p = 101.1 kPa. It increased with increasing temperature and ethyl acetate composition, and the maximum solubility value was found in ethyl acetate. The dependence of mole fraction solubility of 4-nitrobenzonitrile upon solvent composition and temperature was described through the Apelblat− Jouyban−Acree model, van’t Hoff−Jouyban−Acree model, and Jouyban−Acree model. The obtained root-mean-square deviations and mean relative deviations were, respectively, lower than 2.13% and 11.72 × 10−4 for correlative studies.

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AUTHOR INFORMATION

Corresponding Author

*Tel: +86 514 87975568. Fax: +86 514 87975244. E-mail: [email protected]. ORCID

Hongkun Zhao: 0000-0001-5972-8352 Funding

The authors thank the Project Funded by the Excellent Specialties Program Development of Jiangsu Higher Education Institutions, Jiangsu Provincial Department of Technology (No. BY2016066-07) for the finanical support. Notes

The authors declare no competing financial interest.

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REFERENCES

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Solubility Determination and Modeling for 4-Nitrobenzonitrile in Binary

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