Solubility Measurement and Thermodynamic Modeling of 4

Article pubs.acs.org/jced

Solubility Measurement and Thermodynamic Modeling of 4‑Nitrophthalimide in Twelve Pure Solvents at Elevated Temperatures Ranging from (273.15 to 323.15) K Shuo Han, Long Meng, Cunbin Du, Jian Xu, Chao Cheng, Jian Wang, and Hongkun Zhao* College of Chemistry & Chemical Engineering, Yangzhou University, Yangzhou, Jiangsu 225002, People’s Republic of China S Supporting Information *

ABSTRACT: The solubility of 4-nitrophthalimide in different solvents are of great importance for the design of its purification process via crystallization. The work reported new solubility data for 4-nitrophthalimide in 12 pure solvents of methanol, ethanol, isopropanol, cyclohexanone, acetone, acetonitrile, ethyl acetate, 2-butanone, chloroform, 1,4-dioxane benzyl alcohol and N,N-dimethylformamide. They were determined by a high-performance liquid chromatography at T = (273.15 to 323.15) K under pressure of 0.1 MPa. The 4-nitrophthalimide solubility in the selected solvents increased with the temperature increase. At a given temperature, the solubility of 4nitrophthalimide is largest in N,N-dimethylformamide and lowest in chloroform. The solubility data in the these solvents ranked as N,Ndimethylformamide > cyclohexanone > (1,4-dioxane, acetone, 2-butanone, benzyl alcohol) > ethyl acetate > acetonitrile > methanol > ethanol > isopropanol > chloroform. The experimental solubility data were correlated by modified Apelblat equation, λh equation, Wilson model, and NRTL model. The obtained values of root-mean-square deviation and relative average deviation are all less than 16.17 × 10−4 and 1.58%, respectively. The modified Apelblat equation achieved the best correlating results in totally.

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INTRODUCTION 4-Nitrophthalimide (IUPAC name: 5-nitroisoindole-1,3-dione; CAS No. 89-40-7), which chemical structure is shown in Figure 1, is an important intermediate of fine chemical by which 4-

It is well known that solvent crystallization is a crucial step to separation a compound.17 Thermodynamic calculations are fundamental to design and control the crystallization procedure. In addition, they can also provide the database to evaluate the uses and limitations of the solution models describing the thermodynamic properties. Therefore, knowledge of (solid + liquid) equilibrium of 4-nitrophthalimide in organic solvents and solution property are of clear importance for the quality of termination product when crystallization separation processes are designed.12−15 In order to acquire more systematic thermodynamic information on the crystallization of 4-nitrophthalimide from some organic solvents, the aims of the paper are to (1) acquire the melting enthalpy of 4-nitrophthalimide at 0.1 MPa; (2) measure the solubility of 4-nitrophthalimide in different pure solvents at temperature range from 273.15 to 323.15 K using the high-performance liquid phase chromatograph; (3) correlate the solubility data; and (4) compute the solution property for the solution procedure of 4-nitrophthalimide in organic solvents to better understand its solubility behavior.

Figure 1. Chemical structure of 4-nitrophthalimide.

aminophthalimide1−3 and 4-cyanophthalide4 can be made. The former may be used to prepare azo-dye5,6 and the latter is a key synthetic intermediate in the preparation of the antidepressant drug Citalopram.7,8 In addition, 4-nitrophthalimide is also an important material to synthesize phthalocyanine dye.9,10 Nowadays, 4-nitrophthalimide is prepared through nitration of o-phthalimide by mixed nitric acid and sulfuric acid.11−16 During the production process of 4-nitrophthalimide, however, the isomeric 3-nitrophthalimide is also generated as byproduct. The crude product containing isomeric 3-nitrophthalimide limits its further use in various areas. For example, when it is used as a medicine, the impurities may limit its clinical application and even lead to some side effects. The purity of 4nitrophthalimide is very significant for its further application. © XXXX American Chemical Society

Received: March 16, 2016 Accepted: June 15, 2016

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DOI: 10.1021/acs.jced.6b00230 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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Table 1. Source and Purity of Materials Used in the Work chemicals 4-nitrophthalimide

molar mass

melting point

g·mol−1

K

192.13

474.71a

a

melting enthalpy

density (298.15 K)

molar volume (298.15 K)

kJ·mol−1

kg·m−3

cm3·mol−1

34.60a

1594.7g

mass fraction purity

purification method

method for purity determination

Shanghai Xuxin Chemical Technology Co., Ltd.

0.997

recrystallization

HPLCi

Sinopharm Chemical Reagent Co., Ltd.,China

0.994

GCj

source

476b 470−475c 467.7−468.2d 490−492e 471−472f methanol

32.04

40.4h

ethanol isopropanol cyclohexanone acetone acetonitrile ethyl acetate 2-butanone chloroform benzyl alcohol 1,4-dioxane N,Ndimethylformamide carbon tetrachloride toluene benzoic acid

46.07 60.06 98.14 58.08 41.05 88.11 72.11 119.38 108.14 88.11 73.10

58.68h 76.92h 104.2h 73.4h 52.86h 98.5h 89.44h 80.41h

0.994 0.995 0.997 0.995 0.997 0.995 0.993 0.994

GC GC GC GC GC GC GC GC

85.1h 77.43h

0.995 0.992

GC GC

153.84 92.14 122.12

97.5h 106.85h

0.995 0.995 0.993

GC GC HPLC

This work, determined under 0.1 MPa. The standard uncertainties u are u(T) = 0.5 K, u(p) = 450 Pa, u(ΔfusH) = 400 J·mol−1. b,c,d,e,fTaken from refs 34, 35, 36, 37, and 38, respectively. gThis work, determined at 298.15 K and 0.1 MPa. The standard uncertainty u are u(T) = 0.02 K, u(p) = 450 Pa, u(ρ) = 0.9 kg·m−3. hTaken from ref 35. iHigh-performance liquid chromatography. jGas chromatography. a

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⎛1 ⎡ λ(1 − x) ⎤ 1 ⎞ ln⎢1 + ⎟ ⎥ = λh⎜ − ⎣ ⎦ x Tm ⎠ ⎝T

SOLUBILITY MODELS

The thermodynamic modeling of solubility data facilitates researchers to represent mathematical aspects of solubility.18 Many methods have been proposed to describe the solubility of a solute in different pure solvents.19 In this work, the solubility of 4-nitrophthalimide in the selected solvents at different temperatures are correlated with the modified Apelblat equation,18−23 Buchowski−Ksiaz̨ ċ zak λh equation,18,19,22−24 Wilson model,19,25 and NRTL model.19,26 Modified Apelblat Equation. The modified Apelblat equation is expressed in eq 1.18−23 It is used extensively in correlating the solute solubility in pure solvents ln x = A +

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

(2)

Tm denotes the melting temperature of 4-nitrophthalimide in Kelvin. Wilson Model. On the basis of the basic (solid−liquid) phase equilibrium theory, the solid−liquid phase equilibrium of 4-nitrophthalimide in the pure solvents can be expressed in a very universal manner as follows:27 ln(x·γ ) =

ΔfusH ⎛ 1 1 ⎞ ΔCp ⎛ 1 1⎞ ⎜ − ⎟− ⎜ − ⎟ R ⎝ Tt T⎠ R ⎝ Tt T⎠ −

(1)

ΔCp ⎛ Tt ⎞ ln⎜ ⎟ R ⎝T ⎠

(3)

where R is the universal gas constant, 8.314 J·K−1·mol−1. γ and ΔfusH are the activity coefficient and fusion enthalpy of 4nitrophthalimide, respectively. Tt denotes the triple-point temperature; ΔCP is the difference of the heat capacity of a solute between the liquid state and the solid state. Generally, the ΔCP value is so minor that the terms containing ΔCP in eq 3 can be neglected because they are less important than the first term on the right side.28 For solid−liquid equilibrium, small changes of pressure do not affect significantly on equilibrium unless the pressure changes are very large (10−100 MPa).29 The triple point temperature Tt is almost equal to the normal melting temperature, Tm. So, eq 3 can be simplified to eq 4

In eq 1, x denotes the mole fraction solubility of 4nitrophthalimideate in the 12 organic solvents at studied temperature T in Kelvin; A, B, and C are the modified Apelblat equation parameters. The parameters A and B show the variety in activity coefficient of a mixture and provide an indication of the influence of solution nonideality on the solubility of a solute; the C illustrates the effect of temperature on the enthalpy of fusion. λh Equation. Equation 2 is the expression for the λh equation.18,19,22−24 In this equation, two parameters, λ and h, are demanded to correlate the experimental solubility B


Journal of Chemical & Engineering Data ln(xi) =

ΔfusH ⎛ 1 1⎞ − ⎟ − ln(γi) ⎜ R ⎝ Tm T⎠

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acid, which were bought from Sinopharm Chemical Reagent Co., Ltd., China. The mass fraction purity of these solvents were all higher than 0.992. The detailed information on all chemicals used in the present work was tabulated in Table 1. Apparatus and Procedure. The equilibrium solubility of the 4-nitrophthalimide in the selected organic solvents were determined by the high-performance liquid chromatography (HPLC).19,32 The experimental apparatus illustrated in Figure 2 for the solubility measurements included a 100 mL jacketed

(4)

The expression of the binary solution activity coefficient γi described by Wilson model can be simplified as eqs 5-(7)19,25 ⎤ ⎡ Λ12 Λ 21 ln γ1 = −ln(x1 + Λ12x 2) + x 2⎢ − ⎥ x 2 + Λ 21x1 ⎦ ⎣ x1 + Λ12x 2 (5)

Λ12 =

V2 ⎛ λ12 − λ11 ⎞ V2 ⎛ Δλ12 ⎞ ⎟ = exp⎜ − ⎟ exp⎜ − V1 ⎝ RT ⎠ V1 ⎝ RT ⎠

(6)

Λ 21 =

⎛ Δλ ⎞ V1 ⎛ λ 21 − λ11 ⎞ V ⎟ = 1 exp⎜ − 21 ⎟ exp⎜ − V2 ⎝ RT ⎠ V2 ⎝ RT ⎠

(7)

Here, V1 is the molar volume of 4-nitrophthalimide, and V2, the solvent. Δλij are cross interaction energy parameters (J·mol−1) between the components i and j. NRTL Model. The NRTL model is based on the molecular local composition concept.19,26 It has been widely used in correlating and predicting of fluid phase equilibrium. Similar to Wilson model, the NRTL model is also an activity coefficient equation, and expressed as eq 8 N

ln γi =

∑ j = 1 τjiGjixj N

∑i = 1 Gijxi

N

+

∑ j=1

⎡ ∑N x τ G ⎤ ⎢τ i = 1 i ij ij ⎥ ij N N ∑i = 1 Gijxi ⎢⎣ ∑i = 1 Gijxi ⎥⎦ xjGij

Figure 2. Schematic diagram of the 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.

(8)

Gji = exp( −αjiτji)

(9)

αij = αji τij =

gij − gjj RT

glass vessel with a magnetic stirrer and a circulating (water + isopropanol mixture) bath used to keep the temperature. A condenser was employed to prevent the escaping of the solvent. The isothermal water bath (Type of DZKW-4 with a standard uncertainty of 0.02 K) bought from Ningbo Scientz Biotechnology Co., Ltd. was used to control the system temperature. The actual temperature of the mixture was displayed via a mercury glass thermometer (standard uncertainty: 0.02 K) inserted in the solution. The mass of solution, solute and solvent were determined with an analytical balance (model, BSA224S; standard uncertainty, 0.0001 g) provided by Sartorius Scientific Instruments (Beijing) Co., Ltd. An excess amount of 4-nitrophthalimide and 50 mL of solvent were placed into the 100 mL jacketed glass vessel equipped with a magnetic stirring. The solution was maintained at a fixed temperature via circulating water + isopropanol mixture (volume ratio of isopropanol to water was about 10:90) from the bath through the outside jacket. The system was stirred for 24 h to ensure equilibrium being reached. The equilibrium was identified by analyzing respectively the concentrations of solution at an interval of 60 min. Results indicated that 13 h was enough to build the solid−liquid equilibrium in the glass vessel. Once the equilibrium was reached, the magnetic stirring was stopped to allow the solids settle down. Then a sample of about 1 mL of the saturated liquid phase was removed from the glass vessel using a syringe connected with a 0.2 μm pore syringe filter. The sample was transferred quickly to a preweighed volumetric flask of 25 mL with a cover to prevent the loss of solvent. The volumetric flask containing the sample was weighed again using the analytical balance. The solution was diluted to 25 mL with methanol, and then analyzed by HPLC. After the solubility was determined at

(10)

=

Δgij RT

(11)

where Δgij are model parameters relating to the cross interaction energy (J·mol−1); α denotes the parameter relating to the nonrandomness of the solution, which value is generally in the range from 0.2 to 0.47. As described in the previous works,30,31 the binary crossinteraction parameters in the Wilson and NRTL models are supposed to have a linear relationship with temperature as eq 12

kij = aij + bijT

(12)

In which aij, bij, and kij stand for the parameters employed to correlate the solubility data and the interaction parameters, respectively.

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EXPERIMENTAL SECTION Materials. In this study, reagent grade chemical 4nitrophthalimide was supplied by Shanghai Xuxin Chemical Technology Co., Ltd., and the mass fraction was 0.985 at first. It was crystallized in aqueous solutions of methanol (volume ration of methanol to water is 95:5) and analyzed by highperformance liquid phase chromatograph (Agilent 1260, Agilent Technologies, U.S.A.). The mass fraction of the purified sample used in solubility measurement was 0.997. All other chemicals used were also of reagent grade, including methanol, ethanol, isopropanol, cyclohexanone, acetone, acetonitrile, ethyl acetate, 2-butanone, chloroform, 1,4-dioxane, benzyl alcohol, N,N-dimethylformamide, toluene, and benzoic C



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phase column (250 mm × 4.6 mm). Pure methanol was used as the mobile phase at a flow rate of 1 mL·min−1. Before analysis, the HPLC system was calibrated with standard solutions prepared by means of electronic balance. The calibration curves were established on the basis of different peak area ratios standing for different mole fraction of the standard solutions. Each analysis was performed three times to inspect the repeatability and three samples were taken for every saturated solution at a certain temperature. The mean value was regarded as the final solubility value. The relative standard uncertainty of the determined solubility data was less than 2.13% in mole fraction.

one temperature, the rest solution containing excess solid was heated to another temperature, and the determinations procedure was carried out repeatedly. In order to validate the experimental method, the solubility of benzoic acid in toluene was measured by using this apparatus. The determined solubility data and the literature values33 were presented in Table S1 of Supporting Information and plotted in Figure 3. It indicated that the experimental solubility data agreed well with those in the literature. So the reliability of the experimental apparatus was validated.

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RESULTS AND DISCUSSION Pure Component Properties. The acquired DSC results of 4-nitrophthalimide are shown graphically in Figure 4. It can

Figure 3. Solubility of benzoic acid in toluene: ■, literature values;33 ●, experimental values.

Thermal Analysis. The melting temperature Tm of 4nitrophthalimide was reported in the previous works.34−38 In the present paper, the melting enthalpy for 4-nitrophthalimide was determined using the differential scanning calorimetry (DSC) (Pyris-Diamond, PerkinElmer) under nitrogen atmosphere. Before determination, the instrument was precalibrated with the reference material (indium). Accurately weighed samples (6 to 10 mg) of 4-nitrophthalimide was introduced into a DSC pan, and then heated with a heating rate of 5 K· min−1 under nitrogen flow. The temperature ranges from 290 to 530 K. Stand uncertainties of the experiments were evaluated to be 0.5 K for temperature and no more than 400 J·mol−1 for the enthalpy of melting. Density Measurement. The flotation method39 was used to determine the density of 4-nitrophthalimide at 298.15 K and 0.1 MPa. The determination was carried out in a glass tube of 15 mm diameter. The temperature of the glass tube was kept by the smart thermostatic water (model: DZKW-4) having a standard uncertainty of 0.02 K through the outside jacket. Because of lower solubility of 4-nitrophthalimide in carbon tetrachloride and isopropanol at 298.15 K, the two solvents were used in density measurement. Isopropanol was added dropwisely to the glass tube filled with 10.00 mL of carbon tetrachloride and a given quantity of 4-nitrophthalimide. After every isopropanol addition, the solution in the glass tube was fully mixed. When the solid 4-nitrophthalimide was suspended in the mixture of carbon tetrachloride and isopropanol, the addition of isopropanol was stopped. The 4-nitrophthalimide density was equal to the liquid pair. Analytic Technique. The compositions of the equilibrium liquid was analyzed on an Agilent 1260 HPLC system (Agilent Technologies, U.S.A.) equipped with a quaternary pump with a vacuum degasser itself (type G1311C), an autosampler (type G1329B) and an UV detector (type G1314F). The detection wavelength was set to 229 nm determined by continuous UVscanning. The separation column was a Waters C18 reverse

Figure 4. DSC scan of 4-nitrophthalimide.

be seen from the DSC curve of 4-nitrophthalimide that the melting temperature Tm and the enthalpy of fusion (ΔfusH) are 474.71 K and 34.60 kJ·mol−1, respectively. In this work, the melting point is used as the onset point of the DSC curve which is the intersection of the extension of the baseline with the tangent at the point of greatest slope (inflection point) of the DSC curve. The obtained value of melting point is higher than those presented in refs 36−38, but in the range of that in ref 35. The case may be due to the difference in samples, equipment, or determined conditions. The density of 4-nitrophthalimide at 298.15 K is determined by the composition of carbon tetrachloride and isopropanol mixture. The densities for mixtures of (carbon tetrachloride + isopropanol) at 295.15 and 303.15 K are reported in the literature.40 The values at 298.15 K are acquired with interpolation method. The 4-nitrophthalimide density is calculated to be 1594.7 kg·m−3 at 298.15 K and also presented in Table 1. The standard uncertainty u for density determination was evaluated to be 0.9 kg·m−3. Solubility Data. The obtained mole fraction solubility (x) of 4-nitrophthalimide in methanol, ethanol, isopropanol, cyclohexanone, acetone, acetonitrile, ethyl acetate, 2-butanone, chloroform, 1,4-dioxane, benzyl alcohol and N,N-dimethylformamide over the temperature range from (273.15 to 323.15) K are tabulated in Table 2, and the plots of the solubility data of 4-nitrophthalimide in the selected solvents at different temperatures are shown in Figures 5 and 6. Each solubility data point is a mean value of three measurements. Furthermore, the plots of ln(x) versus 1/T for 4-nitrophthalimide in 12 pure solvents at different temperatures are given in Figure 7. From Table 2 and Figures 5 and 6, it is found that the solubility of 4D



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Table 2. Experimental and Calculated Mole Fraction Solubility x of 4-Nitrophthalimide and RAD with Four Models in Different Solvents at the Temperature Range from T = (273.15 to 323.15) K under 0.1 MPaa 100·xexp

100·xApel

273.15 275.65 278.15 283.15 285.65 288.15 293.15 295.65 298.15 303.15 305.65 308.15 313.15 315.65 318.15 323.15 100·RAD

0.1397 0.1506 0.1666 0.1955 0.2121 0.2329 0.2724 0.2954 0.3185 0.3716 0.3967 0.4273 0.4934 0.5271 0.5656 0.6456

0.1386 0.1516 0.1656 0.1966 0.2137 0.2321 0.2725 0.2946 0.3182 0.3699 0.3981 0.4279 0.4928 0.5280 0.5652 0.6455 0.34

273.15 275.65 278.15 283.15 285.65 288.15 293.15 295.65 298.15 303.15 305.65 308.15 313.15 315.65 318.15 323.15 100·RAD

0.07129 0.07989 0.08972 0.1118 0.1234 0.1368 0.1660 0.1825 0.2014 0.2435 0.2654 0.2879 0.3474 0.3778 0.4053 0.4793

0.07163 0.08016 0.08951 0.1109 0.1231 0.1364 0.1664 0.1834 0.2017 0.2427 0.2657 0.2903 0.3451 0.3754 0.4078 0.4793 0.40

273.15 275.65 278.15 283.15 285.65 288.15 293.15 295.65 298.15 303.15 305.65 308.15 313.15 315.65 318.15 323.15 100·RAD

0.05861 0.06434 0.07411 0.09370 0.1039 0.1146 0.1433 0.1588 0.1753 0.2141 0.2345 0.2573 0.3105 0.3399 0.3702 0.4434

0.05859 0.06594 0.07405 0.09284 0.1037 0.1155 0.1427 0.1581 0.1750 0.2132 0.2347 0.2581 0.3106 0.3400 0.3717 0.4423 0.45

2.952 3.074 3.213 3.524 3.674

2.928 3.069 3.215 3.527 3.693

T/K

100·xλh

100·xNRTL

100·xwilson

0.1393 0.1521 0.1660 0.1966 0.2136 0.2318 0.2718 0.2938 0.3173 0.3689 0.3971 0.4271 0.4926 0.5284 0.5663 0.6490 0.41

0.1387 0.1517 0.1657 0.1967 0.2138 0.2321 0.2724 0.2945 0.3181 0.3696 0.3978 0.4276 0.4927 0.5280 0.5653 0.6463 0.34

0.1397 0.1513 0.1653 0.1963 0.2135 0.2319 0.2723 0.2945 0.3181 0.3698 0.3980 0.4279 0.4929 0.5282 0.5654 0.6460 0.29

0.07215 0.08056 0.08979 0.1109 0.1230 0.1361 0.1658 0.1826 0.2008 0.2418 0.2648 0.2895 0.3450 0.3759 0.4091 0.4829 0.54

0.07197 0.08041 0.08966 0.1109 0.1229 0.1361 0.1659 0.1828 0.2010 0.2421 0.2650 0.2898 0.3452 0.3760 0.4090 0.4824 0.49

0.07191 0.08036 0.08963 0.1109 0.1230 0.1361 0.1660 0.1829 0.2011 0.2422 0.2652 0.2899 0.3452 0.3759 0.4088 0.4817 0.46

0.05856 0.06588 0.07397 0.09269 0.1035 0.1153 0.1424 0.1578 0.1746 0.2128 0.2344 0.2579 0.3107 0.3404 0.3724 0.4442 0.52

0.05845 0.06579 0.07389 0.09265 0.1034 0.1153 0.1424 0.1579 0.1747 0.2130 0.2346 0.2580 0.3108 0.3405 0.3724 0.4440 0.52

0.05840 0.06575 0.07387 0.09266 0.1035 0.1153 0.1425 0.1580 0.1748 0.2131 0.2347 0.2581 0.3108 0.3404 0.3722 0.4434 0.50

2.910 3.057 3.209 3.531 3.700

2.923 3.068 3.218 3.534 3.701

2.950 3.078 3.215 3.516 3.679

Methanol

Ethanol

Isopropanol

Cyclohexanone 273.15 275.65 278.15 283.15 285.65

E



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Table 2. continued 100·xexp

100·xApel

288.15 293.15 295.65 298.15 303.15 305.65 308.15 313.15 315.65 318.15 323.15 100·RAD

3.868 4.219 4.399 4.613 5.062 5.270 5.524 6.041 6.288 6.552 7.079

3.865 4.230 4.424 4.625 5.052 5.277 5.512 6.008 6.270 6.541 7.116 0.31

273.15 275.65 278.15 283.15 285.65 288.15 293.15 295.65 298.15 303.15 305.65 308.15 313.15 315.65 318.15 323.15 100·RAD

1.753 1.846 1.932 2.114 2.199 2.297 2.502 2.611 2.713 2.933 3.046 3.167 3.400 3.526 3.660 3.917

1.758 1.842 1.929 2.110 2.204 2.301 2.502 2.606 2.713 2.933 3.047 3.164 3.405 3.529 3.656 3.916 0.13

273.15 275.65 278.15 283.15 285.65 288.15 293.15 295.65 298.15 303.15 305.65 308.15 313.15 315.65 318.15 323.15 100·RAD

0.3593 0.3816 0.4031 0.4489 0.4736 0.5032 0.5553 0.5836 0.6181 0.6794 0.7089 0.7492 0.8217 0.8579 0.8945 0.9763

0.3589 0.3804 0.4028 0.4502 0.4753 0.5014 0.5566 0.5857 0.6158 0.6792 0.7125 0.7469 0.8191 0.8569 0.8958 0.9772 0.25

273.15 275.65 278.15 283.15 285.65 288.15 293.15 295.65 298.15 303.15 305.65

0.9192 0.9807 1.043 1.172 1.234 1.312 1.463 1.547 1.627 1.805 1.900

0.9225 0.9803 1.041 1.170 1.239 1.310 1.463 1.544 1.628 1.806 1.900

T/K

100·xλh

100·xNRTL

100·xwilson

3.876 4.245 4.440 4.641 5.065 5.288 5.519 6.004 6.259 6.523 7.079 0.46

3.874 4.240 4.432 4.632 5.053 5.275 5.506 5.992 6.249 6.515 7.077 0.43

3.851 4.221 4.417 4.622 5.056 5.284 5.521 6.017 6.277 6.545 7.104 0.20

1.777 1.856 1.937 2.108 2.198 2.291 2.485 2.588 2.693 2.916 3.032 3.153 3.406 3.540 3.678 3.968 0.56

1.763 1.846 1.932 2.110 2.203 2.298 2.497 2.600 2.706 2.927 3.042 3.160 3.405 3.532 3.663 3.936 0.21

1.758 1.842 1.929 2.110 2.204 2.301 2.502 2.606 2.712 2.933 3.047 3.163 3.405 3.529 3.656 3.919 0.13

0.3622 0.3828 0.4043 0.4501 0.4744 0.4998 0.5537 0.5824 0.6123 0.6757 0.7094 0.7445 0.8190 0.8586 0.8998 0.9874 0.46

0.3594 0.3808 0.4031 0.4503 0.4753 0.5013 0.5562 0.5852 0.6152 0.6785 0.7118 0.7463 0.8188 0.8569 0.8964 0.9792 0.26

0.3598 0.3808 0.4028 0.4499 0.4750 0.5011 0.5562 0.5854 0.6155 0.6790 0.7123 0.7468 0.8191 0.8570 0.8961 0.9780 0.24

0.9272 0.9838 1.043 1.170 1.237 1.308 1.458 1.538 1.622 1.800 1.895

0.9211 0.9794 1.040 1.170 1.239 1.311 1.464 1.545 1.628 1.806 1.900

0.9212 0.9795 1.041 1.170 1.239 1.311 1.464 1.544 1.628 1.806 1.900

Cyclohexanone

Acetone

Acetonitrile

Ethyl Acetate

F



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100·xApel

308.15 313.15 315.65 318.15 323.15 100·RAD

2.000 2.201 2.307 2.425 2.664

1.998 2.204 2.312 2.425 2.661 0.14

273.15 275.65 278.15 283.15 285.65 288.15 293.15 295.65 298.15 303.15 305.65 308.15 313.15 315.65 318.15 323.15 100·RAD

1.609 1.687 1.775 1.954 2.047 2.145 2.341 2.439 2.557 2.794 2.901 3.023 3.273 3.388 3.535 3.798

1.606 1.688 1.774 1.953 2.047 2.144 2.345 2.450 2.559 2.783 2.900 3.020 3.269 3.397 3.529 3.801 0.15

273.15 275.65 278.15 283.15 285.65 288.15 293.15 295.65 298.15 303.15 305.65 308.15 313.15 315.65 318.15 323.15 100·RAD

0.05352 0.05768 0.06252 0.07222 0.07745 0.08365 0.09590 0.1020 0.1087 0.1241 0.1313 0.1404 0.1598 0.1685 0.1784 0.2006

0.05366 0.05790 0.06240 0.07221 0.07755 0.08319 0.09542 0.1020 0.1090 0.1240 0.1321 0.1406 0.1588 0.1686 0.1788 0.2006 0.25

273.15 275.65 278.15 283.15 285.65 288.15 293.15 295.65 298.15 303.15 305.65 308.15 313.15 315.65 318.15 323.15 100·RAD

1.343 1.426 1.538 1.747 1.883 2.018 2.298 2.453 2.610 2.944 3.122 3.314 3.715 3.932 4.172 4.659

1.334 1.432 1.537 1.763 1.886 2.015 2.294 2.445 2.603 2.942 3.124 3.315 3.723 3.941 4.169 4.655 0.25

T/K

100·xλh

100·xNRTL

100·xwilson

1.993 2.203 2.315 2.431 2.679 0.33

1.997 2.203 2.311 2.424 2.661 0.13

1.997 2.203 2.311 2.424 2.662 0.13

1.622 1.700 1.781 1.952 2.042 2.135 2.332 2.435 2.542 2.768 2.887 3.010 3.269 3.406 3.547 3.846 0.49

1.609 1.691 1.776 1.953 2.046 2.142 2.342 2.446 2.554 2.778 2.896 3.016 3.268 3.399 3.534 3.816 0.19

1.605 1.688 1.774 1.954 2.048 2.144 2.346 2.451 2.559 2.784 2.900 3.020 3.268 3.396 3.528 3.800 0.15

0.05389 0.05808 0.06252 0.07220 0.07748 0.08305 0.09516 0.1017 0.1087 0.1237 0.1318 0.1403 0.1588 0.1687 0.1792 0.2018 0.36

0.05353 0.05780 0.06234 0.07222 0.07759 0.08326 0.09553 0.1022 0.1091 0.1241 0.1322 0.1407 0.1588 0.1685 0.1786 0.2003 0.25

0.05358 0.05784 0.06237 0.07222 0.07757 0.08323 0.09547 0.1021 0.1090 0.1240 0.1321 0.1406 0.1588 0.1685 0.1787 0.2006 0.24

1.333 1.432 1.537 1.764 1.886 2.015 2.294 2.444 2.602 2.941 3.123 3.313 3.722 3.941 4.170 4.659 0.25

1.326 1.427 1.534 1.765 1.890 2.021 2.303 2.454 2.612 2.950 3.130 3.319 3.720 3.933 4.156 4.628 0.33

1.342 1.431 1.531 1.757 1.881 2.012 2.295 2.448 2.607 2.949 3.131 3.321 3.726 3.941 4.165 4.639 0.26

Ethyl Acetate

2-Butanone

Chloroform

Benzyl Alcohol

G



Article


100·xApel

283.15 285.65 288.15 293.15 295.65 298.15 303.15 305.65 308.15 313.15 315.65 318.15 323.15 100·RAD

2.278 2.383 2.493 2.713 2.823 2.948 3.181 3.308 3.449 3.706 3.842 3.991 4.249

2.277 2.382 2.490 2.713 2.828 2.946 3.189 3.315 3.442 3.705 3.840 3.977 4.259 0.13

273.15 275.65 278.15 283.15 285.65 288.15 293.15 295.65 298.15 303.15 305.65 308.15 313.15 315.65 318.15 323.15 100·RAD

3.570 3.899 4.253 4.970 5.346 5.859 6.817 7.316 7.890 9.125 9.761 10.45 11.98 12.79 13.67 15.46

3.568 3.888 4.229 4.983 5.397 5.838 6.804 7.332 7.891 9.108 9.768 10.47 11.97 12.79 13.64 15.48 0.23

T/K

100·xλh

100·xNRTL

100·xwilson

2.287 2.388 2.492 2.709 2.822 2.938 3.179 3.305 3.434 3.702 3.841 3.985 4.283 0.21

2.282 2.385 2.491 2.711 2.825 2.942 3.185 3.310 3.438 3.704 3.841 3.981 4.270 0.15

3.465 3.813 4.184 4.999 5.444 5.913 6.927 7.472 8.041 9.252 9.893 10.56 11.95 12.68 13.44 15.00 1.58

3.583 3.895 4.230 4.975 5.387 5.827 6.796 7.326 7.889 9.114 9.779 10.48 11.99 12.80 13.64 15.45 0.24

1,4-Dioxane

a

2.297 2.394 2.495 2.705 2.816 2.930 3.170 3.296 3.426 3.699 3.843 3.992 4.305 0.42 N,N-Dimethylformamide 3.536 3.863 4.212 4.983 5.406 5.856 6.838 7.372 7.935 9.155 9.812 10.50 11.98 12.77 13.59 15.34 0.55

Standard uncertainties u are u(T) = 0.02 K, u(p) = 450 Pa; relative standard uncertainty ur is ur(x) = 2.13%.

Figure 5. Solubility (x) of 4-nitrophthalimide with mole fraction in selected solvents at different temperatures: ◀, N,N-Dimethylformamide; ▶, cyclohexanone; ▼, 1,4-dioxane; ■, acetone; ◆, ethyl acetate.

Figure 6. Solubility (x) of 4-nitrophthalimide with mole fraction in different solvents at studied temperatures: ■, 2-butanone; ◇, benzyl alcohol; ●, acetonitrile; ▲, methanol; ▼, ethanol; ◆, isopropanol; ◀, chloroform.

nitrophthalimide increase with the increase in temperature for all the selected solvents. At a fixed temperature, the solubility of 4-nitrophthalimide is largest in N,N-dimethylformamide and lowest in chloroform. Moreover, the solubility in N,Ndimethylformamide, benzyl alcohol, and 2-butanone change faster with temperature than those in the other solvents. This may be advantageous to the crystallization process of 4nitrophthalimide. By and large, the solubility of 4-nitro-

phthalimide in all the selected solvents from high to low obey the following order: N,N-dimethylformamide > cyclohexanone > (1,4-dioxane, acetone, 2-butanone, benzyl alcohol) > ethyl acetate > acetonitrile > methanol > ethanol > isopropanol > chloroform. For the solvents of 1,4-dioxane, acetone, 2-butanone, the solubility of 4-nitrophthalimide rank as 1,4-dioxane > acetone > 2-butanone. The solubility is lower in 2-butanone than in benzyl alcohol at below 295 K; however, H



Article

with the dielectric constants (ε) and polarity with the exception of the solvents of acetonitrile and 1,4-dioxane. The solubility values are greater in N,N-dimethylformamide than in the other solvents, which indicates the property of the proton donor of the NH group in 4-nitrophthalimide. Furthermore, the 4nitrophthalimide molecule has an amino group, and N,Ndimethylformamide molecule also has an amino group. Therefore, the group similarity between 4-nitrophthalimide molecule and N,N-dimethylformamide due to the amino group also increases the solubility greatly, which corresponds to the empirical rule that “like dissolves like”. It is too complex to elucidate the case shown in Figures 5 and 6 based on a single factor. It may result from many factors, for example, hydrogen bond, the rule of “like dissolves like”, van der Waals force and polarity, and so on. The chief reason is still unclear and needs additional investigation. Solubility Correlation and Calculation. The parameters in the modified Apelblat equation, λh equation, Wilson model and NRTL model can be obtained by regression of the experimental solubility data using a nonlinear optimization method.42 The regression process is performed by using the Mathcad software. During the process of data regression, the molar volumes of the studied solvents given in Table 1 are taken from the reference,41 and the density of 4-nitrophthalimide is taken from this work. The regression is based on the minimum of the objective function (F) described as

Figure 7. Experiment plots of ln(x) versus 1/T for 4-nitrophthalimide in 12 pure solvents at different temperatures: □, 2-butanone; ○, acetone; ▼, ethyl acetate; ◆, acetonitrile; ◀, chloroform; ▶, 1,4dioxane; △, methanol; ▽, ethanol; ◁, N,N-Dimethylformamide; ◇, benzyl alcohol; ●, isopropanol; ■, cyclohexanone.

when the temperature is greater than 313 K, the solubility is larger in benzyl alcohol than in 1,4-dioxane. Compared with the properties, such as the polarities, dipole moments (μ), dielectric constants (ε), and Hildebrand solubility parameters (δH) of the selected solvents,41 it indicates that these properties of solvents are important factor affecting the solubility of 4-nitrophthalimide in the pure solvents. For the solutions of 4-nitrophthalimide + alcohol, the order of the solubility values is about in consistent with the tendency of the dielectric constants (ε), Hildebrand solubility parameters (δH), polarity and dipole moments (μ); and for the other systems, the sequence of the solubility is approximately in accordance

N

F=

∑ (xic − xie)2

(13)

i=1

Table 3. Parameters of the Equations and RMSD Values for 4-Nitrophthalimide in Different Solvents solvent methanol ethanol isopropanol cyclohexanone acetone acetonitrile ethyl acetate 2-butanone chloroform benzyl alcohol 1,4-dioxane N,N-dimethylformamide solvent

modified Apelblat equation A

B

−1.71 14.62 2.72 −43.36 0.43 −4.96 −9.94 −0.79 −10.15 −12.95 10.77 3.04

−2491.03 −3780.11 −3439.97 451.34 −1383.01 −1510.97 −1334.10 −1422.81 −1834.15 −1466.20 −1859.59 −2452.74

λ methanol ethanol isopropanol cyclohexanone acetone acetonitrile ethyl acetate 2-butanone chloroform benzyl alcohol 1,4-dioxane N,N-dimethylformamide

0.08 0.12 0.14 0.21 0.08 0.03 0.11 0.09 0.02 0.34 0.08 2.45

10 ·RMSD

C 0.76 −1.43 0.43 6.80 0.10 0.87 1.81 0.33 1.66 2.50 −1.41 0.46 λh equation

h 33 056.73 27 461.76 25 235.61 6461.66 13 852.27 44 411.39 14 634.04 13 134.86 1.44 × 105 6238.57 12 794.72 1109.25

Wilson model

4

b12

3.73 2.06 1.73 4.60 6.07 6.11 7.32 5.96 7.00 3.65 6.06 −0.87

−1450.63 −816.19 −595.83 −2340.22 −2726.80 −2393.68 −2495.02 −2619.64 −1862.14 −1890.97 −2705.18 −864.87

1971.04 −637.71 8801.82 17.35 5245.16 46.62 −0.62 1804.82 1.07 70.12 11 439.73 5.60 NRTL

−5.37 −7.58 −7.53 −4149.84 −3.87 −11 125.89 182.91 −81 684.96 2.76 −18 084.5 −1.52 −1252.95 model

a12

b12

a21

b21

α

104·RMSD

217.43 148.50 125.84 −3.11 164.71 −349.93 157.51 165.68 131.69 10.99 −231.40 11.52

1.14 × 10 55 950.17 17 034.54 −7683.59 93 441.59 −31 218.13 84 397.12 95 561.74 61 527.87 66 854.34 −18 167.90 74 267.19

5.52 3.82 3.22 25.91 7.54 8.04 6.59 7.23 7.87 4.71 7.39 0.23

−1471.04 −827.87 −606.85 17 083.00 −2732.42 −2422.13 −2287.89 −2622.31 −1852.77 −1877.06 −2713.99 −939.87

0.2 0.2 0.2 0.3 0.2 0.3 0.2 0.2 0.2 0.2 0.2 0.2

0.10 0.16 0.09 2.43 0.75 0.19 0.24 0.75 0.04 1.16 1.14 16.17

0.10 0.13 0.08 1.79 0.36 0.18 0.25 0.53 0.04 0.67 0.61 1.98

104·RMSD 0.15 0.17 0.09 2.43 1.91 0.40 0.63 1.70 0.06 0.67 1.93 5.08

I

a21

104·RMSD

a12

5

b21 × 10 × 105 × 105 5

× 105

× 105

0.09 0.15 0.09 1.24 0.36 0.18 0.13 0.55 0.04 0.83 0.75 1.99



Article

In order to evaluate the four solubility models and find the difference between the measured solubility and calculated ones, the relative average deviation (RAD) and root-mean-square deviation (RMSD) are used and expressed as eqs 14 and 15 RAD =

1 N

N

∑ i=1

xie − xic xie

⎡ ∑N (x c − x e)2 ⎤1/2 i i ⎥ RMSD = ⎢ i = 1 ⎢⎣ ⎥⎦ N

positive deviations except for acetonitrile. The main reason may be due to the complicated hydrogen bond in the systems.

■

CONCLUSION The mole fraction solubility of 4-nitrophthalimide were measured in a variety of organic solvents (methanol, ethanol, isopropanol, cyclohexanone, acetone, acetonitrile, ethyl acetate, 2-butanone, chloroform, 1,4-dioxane, benzyl alcohol, and N,Ndimethylformamide) at temperatures from (273.15 to 323.15) K. On the basis of the results, we can find that with the increase in temperature, the 4-nitrophthalimide solubility in the studied solvents increase. At a certain temperature, the order of the solubility data from high to low in these solvents is N,Ndimethylformamide > cyclohexanone > (1,4-dioxane, acetone, 2-butanone, benzyl alcohol) > ethyl acetate > acetonitrile > methanol > ethanol > isopropanol > chloroform. The determined solubility data were correlated with four models (modified Apelblat equation, λh equation, Wilson model and NRTL model) by using a nonlinear optimization method. The four models were all successful at correlating the solubility of 4nitrophthalimide in the solvents. The obtained values of relative average deviations and the root-mean-square deviations by the four models are all less than 1.58% and 16.17 × 10−4, respectively. The four models can all be used to correlate the solubility data of 4-nitrophthalimide in the studied solvents at different temperatures. Generally, the modified Apelblat equation provides the better results than the other three models due to lower RMSD values.

(14)

(15)

Here, xei is the experimental solubility; and xci , computed ones. N is the number of experimental data points for each system. The obtained parameters’ values for the four models and the corresponding root-mean-square deviations (RMSD) are presented in Table 3, and the calculated solubility and corresponding relative average deviations (RAD) are given in Table 2. In addition, the calculated solubility values for 4nitrophthalimide with the modified Apelblat model are plotted in Figures 5 and 6. The results show that, for each solvents, the λh equation provide the largest RMSD values except for the system of 4-nitrophthalimide + N,N-dimethylformamide. However, the largest RMSD value, 16.17 × 10−4, is obtained with NRTL model for the solvent of N,N-dimethylformamide. On the other hand, the obtained values of RAD with the four models are no greater than 1.58%. In general, the computed solubility values with the four models agree well with the experimental ones for the selected solvents. So, the four models can all give the better description for the solubility of 4nitrophthalimide in the studied solvents at different temperatures. The activity coefficient of solute in a saturated solution can illustrate the solvent−solute intermolecular interactions. Figure 8 shows the activity coefficient of 4-nitrophthalimide in the

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.6b00230. Table S1. Mole fraction solubilities (x) of benzoic acid in toluene within the temperature range from T/K = (273.15 to 323.15) under 0.1 MPa. (PDF)

■

AUTHOR INFORMATION

Corresponding Author

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

This work was supported by the National Natural Science Foundation of China (Project number: 21406192) and the Priority Academic Program Development of Jiangsu Higher Education Institutions. Notes

The authors declare no competing financial interest.

Figure 8. Calculated logarithm of activity coefficient of 4-nitrophthalimide as a function of temperature at measured solubility data points: ○, chloroform; ■, isopropanol; ▼, acetone; ◀, 1,4-dioxane; ▶, cyclohexanone; ◆, methanol; □, N,N-Dimethylformamide; ▲, benzyl alcohol; ◇, 2-butanone; △, ethanol; ▽, acetonitrile; ●, ethyl acetate.

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REFERENCES

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Article

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Solubility Measurement and Thermodynamic Modeling of 4

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