Thermodynamic Functions for the Solubility of 3-Nitrobenzonitrile in 12

Oct 5, 2017 - The solubilities of 3-nitrobenzonitrile in 12 organic solvents including methanol, ethanol, n-propanol, isopropanol, acetone, n-butanol,...
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Thermodynamic Functions for the Solubility of 3‑Nitrobenzonitrile in 12 Organic Solvents from T/K = (278.15 to 318.15) Jiao Chen, Gaoquan Chen, Min Zheng, and Hongkun Zhao* College of Chemistry & Chemical Engineering, YangZhou University, YangZhou, Jiangsu 225002, People’s Republic of China S Supporting Information *

ABSTRACT: The solubilities of 3-nitrobenzonitrile in 12 organic solvents including methanol, ethanol, n-propanol, isopropanol, acetone, n-butanol, 2methyl-1-propanol, acetonitrile, acetic acid, ethyl acetate, cyclohexane, and toluene were measured by the static method within the temperature range from (278.15 to 318.15) K under atmospheric pressure of 101.1 kPa. The mole fraction solubility of 3-nitrobenzonitrile in the selected solvents increased with a rise in temperature. In general, they ranked as acetone > (acetonitrile, ethyl acetate) > toluene > acetic acid > methanol > ethanol > npropanol > n-butanol > isopropanol >2-methyl-1-propanol > cyclohexane. The achieved solubilities of 3-nitrobenzonitrile were correlated via the λh equation, modified Apelblat equation, NRTL model, and Wilson model. The maximum relative average deviation and root-mean-square deviation were 1.87% and 2.399 × 10−3, respectively. Finally, the mixing properties, e.g., change in Gibbs energy, enthalpy, entropy, activity coefficient at infinitesimal concentration, and reduced excess enthalpy, were also derived on the basis of the Wilson model. The mixing process of 3-nitrobenzonitrile in these solvents was endothermic and spontaneous.

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INTRODUCTION The separation of isomers is attracting worldwide attention owing to its high demands and scientific importance in the chemical industry. Nevertheless, isomer separation is not attained successfully using the distillation operation because of the similar boiling points of the mixed pairs.1 Some other methods are also frequently employed in industry to purify the isomers, such as adjusting the pH value of solutions,2 adsorption processes,3,4 low-temperature crystallization, chemical conversion,5 and so on. However, these operations are very energy-expensive and complex.6 Isomer separation by using membranes has been employed in recent years,7 but the membranes are very expensive. By comparison with separation methods mentioned above, we have found crystallization in solvent to be a promising method because this method has many advantages such as low energy cost, high purity, and easy operation. Recently, the technique of solvent crystallization has been successfully employed to separate organic isomers.8,9 Aromatic nitriles are essential intermediates and reactants in the fine chemical field and are used for the synthesis of pharmaceuticals, dyestuff, and pesticides.10,11 4-Nitrobenzonitrile is synthesized using traditional methods of organic chemistry, for instance, the nitration of benzonitrile using HNO3 or another nitrating agent in the presence of a catalyst.12−23 However, isomer (3-nitrobenzonitrile) is also produced as a byproduct. Its additional applications are restricted in several areas by the isomeric byproduct. With the development of pharmaceutical and dyestuff industries, the purity of products is increasing. Thus, isomeric 3-nitro© XXXX American Chemical Society

benzonitrile must be removed from crude 4-nitrobenzonitrile. Generally, the production process of 4-nitrobenzonitrile is carried out in organic solvents, such as methanol, 13 acetonitrile,13 and acetone.18 The solubility of 3-nitrobenzonitrile and 4-nitrobenzonitrile in organic solvents significantly affects the reaction rate and the yield of product. With the intention of optimizing the technical conditions, a knowledge of solubility and solution thermodynamics for 3-nitrobenzonitrile and 4-nitrobenzonitrile in different solvents is required. On the other hand, 3-nitrobenzonitrile is removed from the isomeric mixtures of nitrobenzonitrile by steam distillation.23 However, the cost of the separation process is very high. Therefore, it is essential to develop a new separation process of 3-nitrobenzonitrile and 4-nitrobenzonitrile mixtures. It is generally known that solvent crystallization is an effective technique in solid purification procedures. The solubility of a solid in neat solvents and mixed solvents is an important physicochemical property that helps us to understand the liquid−solid equilibrium in the improvement of a crystallization procedure. In addition, the accurate solubility is very crucial in designing a crystallization process and carrying out further thermodynamic studies. These solubility values are very important in 4-nitrobenzonitrile purification by using the method of solvent crystallization. With the intention of removing 3-nitrobenzonitrile from the crude product, informaReceived: July 6, 2017 Accepted: September 25, 2017

A

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capacity of a solid state and that of the assumed supercooled liquid state. The value of ΔCp can be regarded approximately as the fusion entropy (ΔfusS).31−33 A detailed discussion of the hypothesis has been made in ref 34. Thus, eq 3 can be written as29−31

tion on 3-nitrobenzonitrile and 4-nitrobenzonitrile solubility in various neat solvents at different temperatures and the thermodynamic dissolution properties is essential. According to the considerations mentioned above, in order to optimize the reaction conditions of 4-nitrobenzonitrile production and develop a new separation process of nitrobenzonitrile mixtures, in this work we determine the solubility of 3-nitrobenzonitrile in some organic solvents and discover better models for describing the solubility behavior. From many species of neat solvents, we select 12 common organic solvents including methanol, ethanol, n-propanol, isopropanol, acetone, n-butanol, 2-methyl-1-propanol, acetonitrile, acetic acid, ethyl acetate, cyclohexane, and toluene in the industrial purification process. The main purposes of this work are to (1) determine the solubility of 3-nitrobenzonitrile in these solvents; (2) correlate the solubility data with different models; and (3) compute the mixing properties for the dissolution process of 3nitrobenzonitrile in the neat solvents. For the reason that the temperatures of benzonitrile nitration and solvent crystallization are below 320 K, the selected temperatures are within the range from (278.15 to 318.15) K. It is noteworthy that the melting temperature of acetic acid is about 289.9 K and that of cyclohexane, 279.7 K. Accordingly, the temperature range of solubility determination is from (283.15 to 318.15) K for cyclohexane and from 293.15 to 318.15 K for acetic acid.

ln(xγ ) =

⎛ T ⎞⎤ + ln⎜ ⎟⎥ ⎝ Tfus ⎠⎥⎦

N

ln γi =

N

∑i = 1 Gijxi

N

+

∑ j=1

N ⎡ ∑ xτ G ⎤ ⎢τ − i = 1 i ij ij ⎥ ij N N ∑i = 1 Gijxi ⎢⎣ ∑i = 1 Gijxi ⎥⎦

xjGij

Gji = exp( −αjiτji)

(6)

αij = αji

(7)

τij =

gij − gjj RT

=

Δgij (8)

RT

Δgij are adjustable equation parameters relevant to the interaction energy. Generally, these parameters are regarded as constant. α is a parameter relating to the nonrandomness of the solution. Wilson Model. The Wilson model28 can be expressed as eqs 9−12. ⎤ ⎡ Λ12 Λ 21 ln γ1 = −ln(x1 + Λ12x 2) + x 2⎢ − ⎥ x 2 + Λ 21x1 ⎦ ⎣ x1 + Λ12x 2 (9)

⎤ ⎡ Λ 21 Λ12 ln γ2 = −ln(x 2 + Λ 21x1) + x1⎢ − ⎥ x1 + Λ12x 2 ⎦ ⎣ x 2 + Λ 21x1

where x is the mole fraction solubility of 3-nitrobenzonitrile in 12 organic solvents. A, B, and C are the adjustable parameters of the equation. λh Equation. The λh equation put forward by Buchowski and co-workers is described as eq 2,26 which is an alternative equation describing the solid−liquid equilibrium of 3-nitrobenzonitrile in neat solvents.

(10)

(2)

Λ12 =

⎛ λ − λ11 ⎞ V2 ⎛ Δλ ⎞ V2 ⎟= exp⎜ − 12 exp⎜ − 12 ⎟ ⎝ ⎝ RT ⎠ V1 RT ⎠ V1

(11)

Λ 21 =

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

(12)

Here, V1 and V2 denote the mole volumes of the solute and solvent, respectively. Δλij are the cross interaction energy parameters (expressed as J·mol−1) that may be correlated through experimental solubility. The solubilities of 3-nitrobenzonitrile in the studied neat solvents are correlated with eqs 1−12. The objective function is expressed as eq 13 for the Wilson and NRTL equations.

Here, λ and h are equation parameters. Tm is the melting temperature of 3-nitrobenzonitrile. NRTL Model. On the basis of the rigorous thermodynamics, the liquid−solid phase equilibrium for a nonelectrolyte solute can be described in a universal manner as eq 3.29−31 ΔCp ⎡ (Tfus − T ) −ΔfusH(Tfus − T ) ⎢ + RTfusT R ⎢⎣ T

⎛ T ⎞⎤ + ln⎜ ⎟⎥ ⎝ Tfus ⎠⎥⎦

∑ j = 1 τjiGjixj

(5)

SOLID−LIQUID PHASE EQUILIBRIUM MODELS With the purpose of finding the appropriate model to describe the solubility behavior of 3-nitrobenzonitrile in these solvents, four models (the modified Apelblat equation, 24,25 λh equation,26 NRTL model,27 and Wilson model28) are employed to correlate the 3-nitrobenzonitrile solubility. Modified Apelblat Equation. The solubilities of 3nitrobenzonitrile against temperature can be described by using the following modified Apelblat equation24,25 B ln x T = A + + C ln(T /K ) (1) T /K

ln(xγ ) =

(4)

For a binary liquid−solid system, the activity coefficient described by the NRTL model is given as eqs 5−8.27

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

−ΔfusH(Tfus − T ) Δ S ⎡ (T − T ) + fus ⎢ fus RTfusT R ⎢⎣ T

F=

∑ (ln γie − ln γic)2 i=1

(13)

For the modified Apelblat equation and λh equation, the objective function is expressed as eq 14.

(3)

Here, ΔfusH denotes the melting enthalpy at melting temperature Tfus. ΔCp is the difference between the molar heat

F=

∑ (xie − xic)2 i=1

B

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Table 1. Detailed Information on the Materials Used in This Work molar mass

melting point

melting enthalpy

density

g·mol−1

K

kJ·mol−1

kg·m−3

source

3-nitrobenzonitrile

148.12

389.7a

20.49a

1310b

methanol ethanol n-propanol isopropanol n-butanol 2-methyl-1propanol acetone ethyl acetate acetonitrile toluene cyclohexane acetic acid

32.04 46.07 60.10 60.10 74.12 74.12

786.5c 789.3c 805.3c 803.5c 810.9c 801.8c

Beijing HWRK Chemical Co., Ltd. Sinopharm Chemical Reagent Co., Ltd., China

58.05 88.11 41.05 92.14 84.16 60.05

784.5c 900.3c 776.8c 871.0c 778.1c 1044.6c

chemicals

initial mass fraction purity

final mass fraction purity

purification method

analytical method

0.970

0.996

recrystallization

HPLCd

̀

0.995 0.993 0.995 0.993 0.994 0.995

GCe GC GC GC GC GC

0.994 0.995 0.993 0.994 0.995 0.995

GC GC GC GC GC GC

a

Take from ref 44. bCalculated using Advanced Chemistry Development (ACD/Laboratories) Software V11.02 (copyright 1994−2017 ACD/ Laboratories). cTake from ref 43. dHigh-performance liquid-phase chromatography. eGas chromatography.

mL, a circulating (water + isopropanol) system, and a magnetic stirrer. A thermostatic bath (model QYHX-1030) was employed to control the temperature of the (water + isopropanol) solution. The bath having a standard uncertainty of 0.05 K was purchased from Shanghai Joyn Electronic Co., Ltd., China. A mercury glass microthermometer having a standard uncertainty of 0.02 K was inserted into the inner chamber of the vessel to display the true temperature of the solution. Before the experiment, the reliability of the apparatus was validated by measuring the solubility of benzoic acid in toluene.35,36 Solubility Determination. The liquid−solid equilibrium for the 3-nitrobenzonitrile + solvent systems was built with the static method37−43 over the temperature range of (278.15 to 318.15) K, and the solubility of 3-nitrobenzonitrile in neat solvents was determined using HPLC. A 60 mL portion of neat solvent and an excess amount of 3nitrobenzonitrile were placed in a 100 mL vessel. The solution temperature was retained at a certain value by using circulating mixed solvents of (water + isopropanol) from the thermostatic bath through the outer jacket. The liquid−solid equilibrium was confirmed by repeated analyses of concentration in an interval of 1 h. It was observed that 13 h was long enough to establish equilibrium for all of the selected solvents. With the purpose of confirming that sampling was performed under equilibrium conditions, a preliminary experiment was carried out in which the liquor was analyzed as a function of time. Two types of experiments were conducted. One was started from a supersaturated mixture in which the solid precipitated to reach equilibrium, and the other was started from a nonsaturated mixture in which the solid dissolved to reach equilibrium. The largest relative error value for the two types of experiments was estimated to be 0.93%. After arriving at equilibrium, the stirring was stopped to let any particles settle down from the system. About 2 mL of the saturated solution was taken out with a 2 mL syringe preheated or precooled in the thermostatic bath. The solution was quickly transferred to a 25 mL preweighed volumetric flask to prevent the loss of solvent. Then the sample was diluted to the mark with the corresponding solvent, and 1 μL was withdrawn to analyze by

Additionally, to identify the difference between the measured and calculated solubility data, the relative deviation (RD), relative average deviation and (RAD), and root-mean-square deviation (RMSD) are employed. RD =

xe − xc xe

RAD =

1 N

N

∑ i=1

(15)

xie − xic xie

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

(16)

(17)

Here, ln γei stands for the logarithm of the activity coefficient computed using eq 4 and ln γci is evaluated with the solubility models. N refers to the number of data points, xci represents the computed solubility values of 3-nitrobenzonitrile, and xie represents the the experimental values.

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EXPERIMENTAL SECTION Materials and Apparatus. 3-Nitrobenzonitrile having a mass fraction of 0.970 was purchased from Beijing HWRK Chemical Co., Ltd. The crude material was crystallized three times in methanol. The mass fraction purity of 3-nitrobenzonitrile was 0.996, which was tested using an Agilent1260 high-performance liquid chromatograph (HPLC). The neat solvents (methanol, ethanol, n-propanol, isopropanol, acetone, n-butanol, 2-methyl-1-propanol, acetonitrile, acetic acid, ethyl acetate, cyclohexane, and toluene) were all provided by Sinopharm Chemical Reagent Co., Ltd., China. They were used directly in solubility determinations without any further treatment. Detailed information on these solvents and 3nitrobenzonitrile is tabulated in Table 1. The mass of the solvent, solute, and saturated solutions was determined with an analytical balance (model CPA225D) produced by Satorius Scientific Instrument (Beijing). The experimental apparatus is given in Figure S1 of the Supporting Information, which comprised a jacketed glass vessel of 100 C

DOI: 10.1021/acs.jced.7b00615 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 2. Experimental Mole Fraction Solubility (x) of 3-Nitrobenzonitrile in Different Solvents over the Temperature Range from T = (278.15 to 318.15) K under 101.1 kPaa 100x T/K

a

methanol

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 T/K

0.4100 0.5010 0.6219 0.7598 0.9258 1.116 1.341 1.621 1.949 ethyl acetate

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

3.528 4.400 5.652 7.055 8.758 10.86 13.47 16.61 20.27

n-propanol

ethanol 0.3116 0.3804 0.4734 0.5820 0.7146 0.8726 1.061 1.304 1.587 acetonitrile 4.732 5.651 6.818 8.143 9.726 11.64 13.82 16.35 19.64

isopropanol

0.2497 0.3077 0.3803 0.4749 0.5917 0.7295 0.8974 1.111 1.351

0.1696 0.2155 0.2741 0.3499 0.4462 0.5649 0.7109 0.9054 1.143 acetone

toluene 2.588 3.043 3.738 4.576 5.571 6.703 8.129 9.817 11.87

7.889 9.054 10.60 12.32 14.25 16.41 18.71 21.33 24.16

n-butanol 0.2330 0.2863 0.3489 0.4279 0.5382 0.6831 0.8477 1.037 1.293 cyclohexane 0.03655 0.04722 0.05990 0.07677 0.09699 0.1215 0.1532 0.1931

2-methyl-1-propanol

100xid

0.1616 0.2066 0.2650 0.3300 0.4093 0.5040 0.6235 0.7726 0.9589 acetic acid

11.85 13.27 14.82 16.52 18.39 20.43 22.65 25.08 27.72 100xid

3.544 4.002 4.593 5.251 6.078 7.132

11.85 13.27 14.82 16.52 18.39 20.43 22.65 25.08 27.72

Standard uncertainties u are u(T) = 0.02 K and u(p) = 0.4 kPa. The relative standard uncertainty ur is ur(x) = 0.024.

Figure 1. Mole fraction solubility (x) of 3-nitrobenzonitrile in selected solvents at different temperatures: ◀, methanol; □, ethanol; ⧫, n-propanol; ▶, isopropanol; ●, acetone; ☆, n-butanol; ★, 2-methyl-1-propanol; △, acetonitrile; ▽, acetic acid; ■, toluene; ▼, ethyl acetate; ◊, cyclohexane. , Calculated values via the modified Apelblat equation.

triplicate, and the mean value was considered to be the final solubility value. In this work, the relative standard uncertainty of the mole fraction solubility determination was evaluated to be 2.4%. X-ray Powder Diffraction. Crystals of 3-nitrobenzonitrile were identified by X-ray powder diffraction (XRD), which was carried out on a Rigaku D/max-2500 (Rigaku, Japan) using Cu Kα radiation (1.5405 Å) in the 2θ range of 10 to 60°, and the tube current and voltage were set to 30 mA and 40 kV, respectively. The scanning rate was 6 deg·min−1 under atmospheric pressure.

HPLC. Once the solubility determination was made at one temperature, the residue containing the excess amount of solid was heated to another temperature and the determination was carried out repeatedly. The local atmospheric pressure was around 101.1 kPa during our experiment. Analysis Method. The content of 3-nitrobenzonitrile in equilibrium in the liquid phase was analyzed by the Agilent1260 high-performance liquid-phase chromatograph. A reversephase column with a type of LP-C18 (250 mm × 4.6 mm) was employed, whose temperature was set to about 303 K. The wavelength of the UV detector was 218 nm, attained via continuous UV scanning. The mobile phase was a mixture of (methanol + water) with a flow rate of 0.8 mL·min−1, whose volume ratio of methanol to water was 3:1. During the experiment process, each determination was recorded in

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RESULTS AND DISCUSSION X-ray Powder Diffraction Analysis. With the purpose of illustrating the existence of the solvate formation or D

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acetone is highest among the selected neat solvents. In general, it is too difficult to elucidate the solubility behavior presented in Table 1 in terms of a single reason. The behavior may result from many factors, e.g., solute−solvent and solvent−solvent interactions, molecular sizes and shapes, and so on. Solubility Correlation and Calculation. In the course of the regression process, the densities of the neat solvents are taken from ref 44. The density of 3-nitrobenzonitrile is estimated with Advanced Chemistry Development (ACD/ Laboratories) Software V11.02 (copyright 1994−2016, ACD/ Laboratories), and the fusion temperature Tm, fusion enthalpy (ΔfusH), and fusion entropy of 3-nitrobenzonitrile are taken from ref 45 and are 389.7 K, 20.49 kJ·mol−1, and 52.57 J·(K· mol)−1, respectively. The attained parameters’ values of λ and h in the λh equation, A, B, and C in the modified Apelblat equation, Δλij in the Wilson model, and Δgij in the NRTL model, together with the RMSD values, are presented in Table S2 of the Supporting Information. The 3-nitrobenzonitrile solubilities in these neat solvents are computed according to the acquired parameters’ values. The calculated RAD and RD values are tabulated in Table S3 of the Supporting Information. To show the difference between the experimental solubilities and the calculated ones, the computed solubility values using the modified Apelblat equation are shown graphically in Figure 1. Tables S2 and S3 reveal that the evaluated 3-nitrobenzonitrile solubilities in 12 neat solvents agree well with the experimental ones. The maximum value of RMSD is 23.99 × 10−4, which is obtained with the Wilson model for the ethyl acetate solvent. The values of RAD are no greater than 1.87%. We can conclude that the four models can all be suitable for correlating the 3-nitrobenzonitrile solubility in the neat solvents at temperatures ranging from (278.15 to 318.15) K under 101.1 kPa. Activity Coefficients. The ideal solubility of 3-nitrobenzonitrile (xid) can be computed by using eq 1829−31 and is presented in Table 2.

polymorphic transformation of 3-nitrobenzonitrile during the course of the experiment, the undissolved solid was collected, dried, and characterized by XRD. The XRD patterns of the 3nitrobenzonitrile raw material and the undissolved solid in different solvents are given in Figure S2 of the Supporting Information. The results exhibit that all of the XRD patterns of undissolved 3-nitrobenzonitrile in equilibrium with its mixture have the same characteristic peaks with the raw material. Accordingly, no polymorphic transformation or solvate formation is observed during the entire experiment. Solubility Data. The determined mole fraction solubility of 3-nitrobenzonitrile in methanol, ethanol, n-propanol, isopropanol, acetone, n-butanol, 2-methyl-1-propanol, acetonitrile, acetic acid, ethyl acetate, cyclohexane, and toluene over the temperature range of (278.15 to 318.15) K is presented in Table 2 and plotted in Figure 1. The van’t Hoff plots of ln(x) versus 1/T in the selected neat solvents are shown graphically in Figure S3 of the Supporting Information. It can be seen in Figure 1 that the mole fraction solubility of 3-nitrobenzonitrile is a function of temperature; therefore, an increase in temperature corresponds to an increase in 3-nitrobenzonitrile solubility. At a fixed temperature, the mole fraction solubility of 3-nitrobenzonitrile is highest in acetone and lowest in cyclohexane. The solubility of 3-nitrobenzonitrile in ethyl acetate shows the strongest positive dependence on temperature. For example, if the temperature increases from (278.15 to 318.15) K, then the 3-nitrobenzonitrile solubility in acetone increases from 0.07889 to 0.2416, whereas in ethyl acetate it increases from 0.03528 to 0.2027. The solubility decreases in the following order in different neat solvents: acetone > (acetonitrile, ethyl acetate) > toluene > acetic acid > methanol > ethanol > n-propanol > n-butanol > isopropanol >2-methyl-1propanol > cyclohexane. To demonstrate the difference in the 3-nitrobenzonitrile solubility, some properties of the studied solvents, e.g., dipole moments (μ), polarities, dielectric constants (ε), and Hildebrand solubility parameters (δH), are collected and presented in Table S1 of the Supporting Information.44 It can be seen from Tables 2 and S1 that for 3-nitrobenzonitrile + alcohol systems the solubility of 3-nitrobenzonitrile decreases with the decrease in dielectric constants (ε), polarity, and Hildebrand solubility parameter (δH) of these alcohols except for isopropanol. The trend in mole fraction solubility is in agreement with similar structural changes in the series methanol/ethanol/n-propanol/n-butanol. This case may be due to the strong polarity of the 3-nitrobenzonitrile molecule. The polarity of methanol is relatively strong, so the solubility of 3-nitrobenzonitrile in methanol is relative high. Besides, the polarity of cyclohexane is weakest among the selected solvents, so the 3-nitrobenzonitrile solubility in cyclohexane is also lowest. The solvent polarity seems to be an essential factor affecting the solubility of 3-nitrobenzonitrile in the alcohols and cyclohexane. Nevertheless, a similar case cannot be observed for the other neat solvents. The polarity of the acetic acid molecule is larger than that of the acetonitrile molecule; however, the mole fraction solubility of 3-nitrobenzonitrile is smaller in acetic acid than in acetonitrile. Moreover, the 3nitrobenzonitrile molecule has a −NO2 group and an −CN group, so it has large dipole moments and provides strong nonspecific dipole−dipole interactions with the solvent. It can form H-bonds with acetone molecules with electron donor sites, which significantly affects the 3-nitrobenzonitrile solubility. As a result, the solubility of 3-nitrobenzonitrile in

ln x id =

ΔCp ⎡ (Tfus − T ) −ΔfusH(Tfus − T ) ⎢ + RTfusT R ⎢⎣ T

⎛ T ⎞⎤ + ln⎜ ⎟⎥ ⎝ Tfus ⎠⎥⎦

(18)

Therefore, the activity coefficients (γ3) of solid 3-nitrobenzonitrile in the selected neat solvents are calculated with eq 19.30,32 γ3 = x idl /x3

(19)

The obtained values of activity coefficients (γ3) for 3nitrobenzonitrile in 12 neat solvents at different temperatures are listed in Table S4 of the Supporting Information. These values of the activity coefficients are a measure of the deviation found in the real dissolution procedure from the ideal dissolution procedure. The solute−solvent intermolecular interactions can be obtained on the basis of eq 20 from γ3 values.31,46 ln γ3 = (e11 + e33 − 2e13)

V3φ12 RT

(20)

Here, subscript 1 denotes the respective neat solvent, and 3, solute 3-nitrobenzonitrile. Hence, e11, e13, and e33 denote the E

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⎡ ∂(GE/T ) ⎤ H E = − T 2⎢ ⎥ ⎣ ∂T ⎦

solvent−solute, solvent−solvent, and solute−solute interaction energies, respectively; V3 refers to the molar volume of the supercooled liquid solute; and φ1 refers to the volume fraction of the neat solvents. For s solid with low solubility, the term V3φ21/RT can be considered to be nearly constant. Therefore, γ3 will depend mainly on e11, e33, and e13.30,34 Generally, the terms containing e11 and e33 are unfavorable for the dissolution procedure, whereas the term containing e13 favors the procedure.30,46 The contribution of the e33 term to the γ3 values can be regarded as constant in all of the neat solvents. As a qualitative approach, the subsequent analysis can be made on the basis of the energy quantities and magnitudes described in eq 20. The term e11 is highest in cyclohexane and lowest in acetone. The obtained values of e11 are similar in ethyl acetate, acetonitrile, toluene, and acetic acid because their solubility values are also similar. The e11 values are also much higher in methanol, ethanol, n-propanol, isopropanol, n-butanol, and 2methyl-1-propanol in comparison to those of ethyl acetate, acetonitrile, toluene, acetic acid, and acetone. Neat methanol, ethanol, n-propanol, isopropanol, n-butanol, cyclohexane, and 2-methyl-1-propanol have larger γ values, suggesting high e11 and low e13 values. However, in ethyl acetate, acetonitrile, toluene, acetic acid, and acetone (having low γ values), the e11 values are relatively low but the e13 values may be high. Hence, the solvation of 3-nitrobenzonitrile may be higher in these neat solvents. Thermodynamic Mixing Properties. The evaluation of thermodynamic functions of solutions is a necessity for studies involving the modeling of liquid−solid equilibrium. The mixing enthalpy (ΔmixH) is related to the solvent−solvent, solvent− solute, and solute−solute interactions, whereas the change in entropy (ΔmixS) is a function of the degree of disorder or randomness of a mixture system.47 Therefore, so as to understand the dissolution procedure of 3-nitrobenzonitrile in the neat solvents, the dissolution thermodynamic functions are required. If the solution is nonideal, then the mixing Gibbs energy, mixing enthalpy, and mixing entropy can be attained with eq 21. Δmix M = ME + Δmix M id

⎛ Δλ12 Λ12 Δλ 21Λ 21 ⎞ = x1x 2⎜ + ⎟ x 2 + Λ 21x1 ⎠ ⎝ x1 + Λ12x 2

SE =

The activity coefficient at infinitesimal concentration may be evaluated on the basis of the Wilson model by50 ln γ1∞ = −ln Λ12 + 1 − Λ 21

⎡ ∂ ln γ ∞ ⎤ 1 ⎢ ⎥ ⎣ ∂(1/T ) ⎦

Δmix H id = 0

(24)

P ,x

H1E, ∞ R

(29)

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CONCLUSIONS The equilibrium solubility data were obtained experimentally for 3-nitrobenzonitrile in a total of 12 neat organic solvents over the temperature range of (278.15 to 318.15) K under 101.1 kPa. The mole fraction solubility of 3-nitrobenzonitrile in the selected neat solvents increased with a rise in temperature. At a given temperature, they ranked as acetone > (acetonitrile, ethyl acetate) > toluene > acetic acid > methanol > ethanol > npropanol > n-butanol > isopropanol >2-methyl-1-propanol > cyclohexane. The experimental solubility was fitted by using the modified Apelblat equation, λh equation, and NRTL and Wilson models. The maximum values of RMSD and RAD were 2.399 × 10−3 and 1.87%, respectively. Furthermore, on the basis of the Wilson model, the mixing thermodynamic functions were computed. The mixing process of 3-nitrobenzonitrile in these neat solvents was spontaneous and endothermic.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b00615. Experimental apparatus, XPRD patterns, van’t Hoff plots, mixing Gibbs energy, physical properties of the solvents, parameters of the equations, values of solubility, RD and RAD, activity coefficients, and mixing properties (PDF)

Here, x1 and x2 denote the mole fractions of solute and solvent, respectively. The excess properties can be obtained using eqs 25−27 on the basis of the Wilson model.49

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GE = RT (x1 ln γ1 + x 2 ln γ2) = −RT[x1 ln(x1 + x 2 Λ12) + x 2 ln(x 2 + x1Λ 21)]

=

The obtained mixing properties of ΔmixG, ΔmixH, ΔmixS, ln E,∞ γ∞ are tabulated in Table S5 of the Supporting 1 , and H1 Information. The values of ΔmixH and ΔmixS are positive in all cases, which indicates that the mixing process is endothermic and entropy-driven. The mixing procedure needs more energy to overcome the cohesive forces between the neat solvent and solute. The change in mixing Gibbs energy (Figure S4 in the Supporting Information) decreases with increasing temperature, indicating an increase in solubility. Consequently, the lowest Gibbs energy is acquired for the acetone system as a result of the highest solubility of 3-nitrobenzonitrile.

(22) (23)

(28)

The excess enthalpy at infinite dilution can be obtained using eq 29.51,52

(21)

Δmix S id = −R(x1 ln x1 + x 2 ln x 2)

(27)

(γ∞ 1 )

Here, ME is the excess property in real mixtures. ΔmixG, ΔmixH, and ΔmixS are, respectively, the changes in mixing Gibbs energy, mixing enthalpy, and mixing entropy. For an ideal system, the mixing properties are described as48 Δmix Gid = RT (x1 ln x1 + x 2 ln x 2)

HE − GE T

(26)

AUTHOR INFORMATION

Corresponding Author

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

(25) F

DOI: 10.1021/acs.jced.7b00615 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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ORCID

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Hongkun Zhao: 0000-0001-5972-8352 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions.

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H

DOI: 10.1021/acs.jced.7b00615 J. Chem. Eng. Data XXXX, XXX, XXX−XXX