Solubility Modeling, SoluteâSolvent Interactions, and Thermodynamic

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

pubs.acs.org/jced

Solubility Modeling, Solute−Solvent Interactions, and Thermodynamic Dissolution Properties of p‑Nitrophenylacetonitrile in Sixteen Monosolvents at Temperatures Ranging from 278.15 to 333.15 K Gaoquan Chen, Jinhua Liang, Jingchao Han, and Hongkun Zhao* College of Chemistry & Chemical Engineering, YangZhou University, YangZhou, Jiangsu 225002, People’s Republic of China

J. Chem. Eng. Data Downloaded from pubs.acs.org by UNIV OF WINNIPEG on 12/21/18. For personal use only.

S Supporting Information *

ABSTRACT: The investigation on p-nitrophenylacetonitrile solubility in ethanol, methanol, isopropanol, n-propanol, acetonitrile, acetone, ethyl acetate, toluene, n-butanol, cyclohexane, 2-butanone, isobutanol, acetic acid, 1,4dioxane, water, and ethylbenzene was performed via the shake-flask technique covering the temperature range from 278.15 to 333.15 K at local atmospheric pressure. The mole fraction solubility of p-nitrophenylacetonitrile increased with an increase of the studied temperature and followed a sequence in the 16 solvents with the exception of 1,4-dioxane: ethyl acetate > acetone > (acetonitrile, 2-butanone) > toluene > acetic acid > ethylbenzene > methanol > ethanol > n-propanol > n-butanol > isopropanol > isobutanol > cyclohexane > water. There was no solvation or polymorphic transformation during the experiment process. Correlation was made for the obtained p-nitrophenylacetonitrile solubility in the 16 solvents using the λh, Apelblat, Wilson, and NRTL models. The obtained maximum relative average deviation was 2.67%, and root-mean-square deviation, 2.57 × 10−3. The solute−solvent and solvent−solvent interactions were studied based on the linear solvation energy relationship approach. Furthermore, the thermodynamic dissolution properties, reduced excess enthalpy, and activity coefficient under infinitesimal condition were also computed.

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INTRODUCTION Nitration is of great importance in organic synthesis because many nitro aromatics may be employed as pharmaceutical intermediates to give aromatic amines via reduction.1,2 Aromatic nitriles are also needed as significant substances in both fine chemistry and bioactivity antitumor activities for many pteridine derivatives.3−6 As a representative derivative of aromatic nitriles, p-nitrophenylacetonitrile (CAS No. 555-21-5, structure given as Figure S1 of Supporting Information) is a significant compound for the synthesis of pharmaceuticals, adrenoreceptor blocker atenolol, and antidepressant drugs, as well as liquid crystal and agricultural chemicals.7−10 Various approaches for p-nitrophenylacetonitrile synthesis have been given in the literature.7−13 In general, p-nitrophenylacetonitrile is synthesized by conventional methods, for example, by benzylcyanide nitration using nitric and sulfuric acid mixtures.7−10 Nevertheless, the isomer (o-nitrophenylacetonitrile) is also produced as a byproduct during the nitration procedure of benzylcyanide. The ratio of p-nitrophenylacetonitrile to o-nitrophenylacetonitrile depends on the type of nitrating agent and reaction conditions. It is wellknown that the material purity is very significant in industry, and the solid solubility may influence the yield, crystal size distribution, and purity of the product. Therefore, the thermodynamic solubility is quite valuable for the design © XXXX American Chemical Society

procedure of separation and the improvement of solid solubility models.14,15 The impurities will considerably affect the p-nitrophenylacetonitrile properties and restrict its additional usage in different aspects, e.g., liquid crystal.10 Thus, isomeric o-nitrophenylacetonitrile must be removed from crude p-nitrophenylacetonitrile. Considering the similar boiling point of the two isomers, it is rather difficult to separate by means of distillation operation. So, it is essential to develop a novel separation process of the two isomeric mixtures. Crystallization operation is a common method in the separation procedure. The accurate solid solubility is essential in the design of crystallization operation and further thermodynamic investigation. Literature survey shows that onitrophenylacetonitrile can be removed by addition of ethanol or aqueous ethanol mixtures to the reaction system.7,9 Nevertheless, few solubility values are available in the publications. So, to obtain sufficient purity p-nitrophenylacetonitrile, the knowledge of solubility and dissolution thermodynamics for p-nitrophenylacetonitrile in different solvents at different temperatures is desired. Received: September 10, 2018 Accepted: December 7, 2018

A

DOI: 10.1021/acs.jced.8b00811 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

ÅÄÅ ÑÉÑ Λ12 Λ 21 Å ÑÑ ÑÑ ln γ1 = −ln(x1 + Λ12x 2) + x 2ÅÅÅÅ − ÅÅÇ x1 + Λ12x 2 x 2 + Λ 21x1 ÑÑÑÖ

Journal of Chemical & Engineering Data

Article

Based on the above considerations, the objectives of this paper are (1) determination of the solubility of p-nitrophenylacetonitrile in ethanol, methanol, isopropanol, npropanol, acetonitrile, acetone, ethyl acetate, toluene, nbutanol, cyclohexane, 2-butanone, isobutanol, acetic acid, water, ethylbenzene, and 1,4-dioxane at temperature range from 278.15 to 333.15 K via the shake-flask technique; (2) correlating the experimental solubility obtained in several models; and (3) calculating the dissolution properties of pnitrophenylacetonitrile in different solvents.

ÉÑ ÄÅ ÑÑ ÅÅ Λ 21 Λ12 ÑÑ Å ln γ2 = −ln(x 2 + Λ 21x1) + x1ÅÅÅ − Ñ ÅÅÇ x 2 + Λ 21x1 x1 + Λ12x 2 ÑÑÑÖ

(5)

■

Λ12 =

SOLID−LIQUID PHASE EQUILIBRIUM MODELS In our work, five solubility models are applied in correlating the solubility in the selected pure solvents, which are Apelblat, 16,17 Buchowski−Ksiazaczak λh, 18 Wilson, 19 NRTL,20 and Kamlet−Taft linear solvation energy relationship equations.21 Modified Apelblat Equation. The Apelblat equation16,17 has been successfully employed to link theoretical and experimental solubility of different solids. It expression is given as eq 1. This equation provides a simple empirical description of solubility. B ln x = A + + C ln T (1) T where x denotes the solubility of p-nitrophenylacetonitrile in mole fraction in different solvents at temperature T in kelvin. The equation parameters are denoted as A, B, and C. Buchowski−Ksiazaczak λh Equation. Buchowski−Ksiazaczak λh equation is employed to study the solubility of hydrogen-bonding solutes.18 This equation described as eq 2 is used to correlate the p-nitrophenylacetonitrile solubility in different solvents. ÄÅ É ij 1 ÅÅ λ(1 − x) ÑÑÑÑ 1 yzz lnÅÅÅ1 + ÑÑ = λhjjj − z jT x Tm zz{ ÅÅÇ ÑÑÖ (2) k Here, h and λ are two parameters; Tm signifies fusion temperature of p-nitrophenylacetonitrile. Wilson Model. According to the (liquid−solid) phase equilibrium theory, the mole fraction solubility of p-nitrophenylacetonitrile in different neat solvents is expressed using the nonideal eq 3.22 ln(x·γ ) =

ΔfusH ijj 1 1 yz 1 − zzz − jj R jk Tm T z{ RT 1 T ΔCp dT + R Tm T

∫T

Λ 21 =

(10)

αij = αji

(11)

gij − gjj RT

=

Δgij (12)

RT

Here Δgij are equation parameters relating to cross interaction energy. α denotes a parameter indicating nonrandomness of the mixtures. Generally, the value of α is from 0.20 to 0.47. Supposing that the dependence of parameters in Wilson model and NRTL model on temperature is a linear relationship,23,24 Λij and τij mentioned above can be expressed as eqs 13 and 14. τij = aij +

bij

T/K ÄÅ É ÅÅ i bij yzÑÑÑÑ Vj ÅÅ jj zzÑÑ expÅÅ−jjaij + Λij = z ÅÅ j T /K z{ÑÑÑÑÖ Vi ÅÇ k

ΔCp dT

(13)

(14)

Here, aij and b ij are equation parameters which are independent of temperature and composition. KAT-LSER Model. So, to study the role played by some types of solvation interaction on solid solubility in neat solvents, a MLRA (multiple linear regression analysis) covering several parameters of solvent is used. In general, some modes of solute−solvent interactions are suggested. It is normal to express some linear properties concerning the Gibbs energy (XYZ) of a solvent−solute mixture in terms of the relationship of linear solvation energy (LSER) through eq 15.25,26

(3) −1

Here, R having a value of 8.314 J·K ·mol refers to the universal gas constant. Tm, ΔfusH, and γ1 stand for melting point, fusion enthalpy, and activity coefficient of p-nitrophenylacetonitrile; ΔCp denotes the difference of heat capacities between subcooled liquid state and solid state, respectively. In general, the value of ΔCp is very small. So, the terms comprising ΔCp may be ignored. As a result, this equation may be simplified to Δ H ij 1 1 yzz ln(x·γ ) = fus jjj − z j R k Tm/K T /K zz{

(8)

Gji = exp( −αjiτji)

τij =

m

−1

V1 V i λ − λ11 zy i Δλ y zz = 1 expjjj− 21 zzz expjjj− 21 V2 RT V k { k RT { 2

(7)

Here V signifies the molar volume. Δλ refers to energy parameters (J·mol−1) regarding cross interactions between the solvent and the solute. NRTL Model. This equation20 was proposed in terms of the concept of local composition. The activity coefficient in binary solution expressed through the NRTL equation is given as eqs 9−12. ÑÉÑ ÅÄÅ 2 ÑÑ τ21G21 τ12G12 2Å Å Ñ Å ln γ1 = x 2 ÅÅ + 2Ñ ÅÅÇ (x1 + G21x 2)2 (x 2 + G12x1) ÑÑÑÖ (9)

T

∫

V2 i λ − λ 22 yz V2 i Δλ y zz = expjjj− 12 expjjj− 12 zzz V1 RT V k { k RT { 1

(6)

XYZ = XYZ0 + cavity formation energy + ∑ solute−solvent interaction energy

(4)

(15)

where XYZ0 means a constant. The summation comprises all the solvent−solute interaction modes. The AT-LSER model developed by Kamlet and Taft has been widely used in

The activity coefficient in pure solvents described by the Wilson equation19 may be expressed as B



Article

Table 1. Detailed Description on the Experimental Materials Used in This Work Chemicals

Molar mass (g·mol−1)

p-Nitrophenylacetonitrile

162.15

Melting Point (K) 384.23a 388−390b 387−389c 385−386d 381−386e

Melting Enthalpy (kJ·mol−1) 16.05a

Density (kg·m−3) (298 K)

Initial mass fraction purity

Final mass fraction purity

0.983

0.996

Recrystallization

HPLCh

0.995 0.997 0.995 0.995 0.997 0.996 0.995 0.996 0.995 0.996 0.997 0.995 0.996 0.996 0.995 Distillation

none none none none none none none none none none none none none none none Conductivity meter none

GCi GC GC GC GC GC GC GC GC GC GC GC GC GC GC

Source

1272f

Purification method

Analytical method

Shanghai Macklin Biochem. Tech. Co., Ltd.

Methanol Ethanol n-Propanol Isopropanol Acetone 2-Butanone Acetonitrile Ethyl acetate n-Butanol Isobutanol 1,4-Dioxane Toluene Acetic acid Cyclohexane Ethylbenzene Water

32.04 46.07 60.10 60.10 58.08 72.11 41.05 88.11 74.12 74.12 88.11 92.14 60.05 84.16 106.16 18.02

786.5g 789.4g 805.3g 803.6g 789.9g 805.4g 776.8g 900.6g 809.7g 806.8g 1033.6g 871.1g 1044.6g 778.5g 870.0g 1000.0

Benzoic acid

122.12

1265.9

Sinopharm Chemical Reagent Co., Ltd., China

̀

Our lab

Conductivity acetone > (acetonitrile, 2-butanone) > toluene > acetic acid > ethylbenzene > methanol > ethanol > n-propanol > n-butanol > isopropanol > isobutanol > cyclohexane > water. For the p-nitrophenylacetonitrile + alcohol systems, the pnitrophenylacetonitrile solubility order is consistent with the altering tendency of solvents’ polarity except for isobutanol and isopropanol, which shows that the solvent polarity is significant to influence the solubility of p-nitrophenylacetonitrile in the selected alcohols. For example, the methanol polarity is largest among the studied alcohols,35 and as a result the solubility data in methanol is largest among the alcohols. On the other hand, the water polarity is higher than that of the other solvents; nevertheless, the solubility is lowest in water. On the whole, it is very difficult to demonstrate the solubility behavior based on a single factor. In fact, the solubility of solute in solvent is affected by many factors, e.g., molecular geometry (i.e., steric and structural effect), molecular size, molecule polarity, solvent−solute interactions, and solvent−solvent interactions.36 Solvent Effect on Solubility. So as to acquire the detailed aspects upon solvent effect, the KAT-LSER model is employed for the p-nitrophenylacetonitrile solubility in 16 neat solvents at 298.15 K. The parameters required, α, β, π* and δH, tabulated in Table S2 of Supporting Information, are cited in refs 35 and 37−40. The parameters concerning the cavity term described as Vsδ2H /(100RT) are dimensionless and have the

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RESULTS AND DISCUSSION Melting Properties of p-Nitrophenylacetonitrile. The DSC scan of p-nitrophenylacetonitrile given in Figure 1 shows that a single endotherm is found with a peak. The average extrapolated onset temperature (melting temperature, Tm) is 384.23 K, which is a little lower than the values reported in refs 7, 28, and 29, but in good agreement with that presented in ref 30. The small difference may be a result of the different determination method, purity of raw material, experimental environment, measured conditions and so on. In addition, the determined melting enthalpy ΔfusH of p-nitrophenylacetonitrile is 16.05 kJ·mol−1. Characterization of p-Nitrophenylacetonitrile. Raw pnitrophenylacetonitrile and excess p-nitrophenylacetonitrile in the selected pure solvents were analyzed by XRPD in the present work. The patterns given in Figure S3 of Supporting Information show that the crystal forms of excess solids from 16 solutions are consistent with raw material p-nitroD



Article

Table 2. Experimental Mole Fraction Solubility (100x) of p-Nitrophenylacetonitrile in 16 Pure Solvents at the Temperature Range from T = 278.15 to 333.15 K under Atmospheric Pressure (p = 101.2 kPa)a T/K 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 T/K 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

methanol

ethanol

n-propanol

isopropanol

acetone 5.698 6.582 7.527 8.593 9.736 11.10 12.60 14.32 16.18 18.31 20.64

0.2367 0.2737 0.3360 0.4295 0.5474 0.6948 0.8650 1.097 1.361 1.700 2.117 2.616 1,4-dioxane

0.1834 0.2227 0.2786 0.3524 0.4295 0.5357 0.6536 0.7883 0.9856 1.218 1.486 1.781 cyclohexane

0.1328 0.1652 0.2043 0.2601 0.3318 0.4203 0.5265 0.6732 0.8471 1.074 1.350 1.703 isobutanol

0.09012 0.1186 0.1531 0.1928 0.2525 0.3321 0.4243 0.5346 0.6833 0.8639 1.098 1.383 ethyl acetate

n-butanol

4.606 5.672 7.153 8.880 10.92 13.41 16.06 19.30 23.21 28.35

0.009175 0.01107 0.01344 0.01664 0.02086 0.02584 0.03270 0.04089 0.05051 0.06393 0.08217

0.08417 0.1080 0.1390 0.1785 0.2293 0.2989 0.3829 0.4925 0.6304 0.8056 1.022 1.292

12.20 13.04 13.95 14.86 15.88 16.98 18.23 19.59 21.04 22.77 24.62 26.80

0.1281 0.1471 0.1900 0.2405 0.3062 0.3876 0.5008 0.6428 0.8070 1.024 1.289 1.595

2-butanone

acetonitrile

toluene

4.577 5.343 6.171 7.174 8.276 9.533 10.93 12.56 14.38 16.55 18.94 21.61 acetic acid

3.613 4.370 5.192 6.277 7.491 8.987 10.48 12.44 14.49 16.93 19.64 22.79 ethylbenzene

0.7906 0.9657 1.168 1.478 1.768 2.084 2.518 2.978 3.540 4.323 5.298 6.567 water

1.401 1.662 1.954 2.313 2.716 3.186 3.746 4.382 5.157

0.5635 0.6848 0.7836 0.9689 1.182 1.353 1.627 2.013 2.380 2.842 3.428 4.462

0.001499 0.001936 0.002478 0.002975 0.003549 0.004273 0.005202 0.006401 0.007888 0.009631 0.01169 0.01425

a

Standard uncertainties u are u(T) = 0.02 K, u(p) = 0.4 kPa; Relative standard uncertainty ur is ur(x) = 0.024.

Figure 2. Mole fraction solubility (x) of p-nitrophenylacetonitrile in the selected solvents at studied temperatures: ■, ethyl acetate; ●, acetone; Δ, acetonitrile; ▼, 2-butanone; ×, 1,4-dioxane; ◇, toluene; ☆, acetic acid; ▲, ethylbenzene; Ω, methanol; ◆, ethanol; ▽, n-butanol; right-facing triangle, isopropanol; □, n-propanol; ○, isobutanol; ★, cyclohexane; ◁, water; , calculated values via modified Apelblat equation.

similar range as the other properties of solvent, α, β, and π*. The experimental solubility of p-nitrophenylacetonitrile is fitted by using the solvent properties via the analysis of multiple linear regression. The regressed results are expressed with eq 17 for all the selected monosolvents.

Here R2 represents the coefficient of squared correlation; F refers to F-test; and RSS refers to residual sum of squares. The numbers in the squared bracket are the standard deviation for every coefficient. Equation 17 shows that the KAT-LSER equation containing all variables may provide an acceptable characterization for the determined p-nitrophenylacetonitrile solubility in the 16 neat solvents. The coefficient magnitude shows that the relative contributions to the solubility of pnitrophenylacetonitrile are 6.41%, 5.70%, 46.07%, and 41.82% for hydrogen bond basicity, hydrogen bond acidity, Hildebrand solubility parameter, and dipolarity/polarizability, respectively. Therefore, the Hildebrand solubility parameter, described as c4, plays a significant role in solubility values, which indicates the negative contributions of the solvent cohesive energy and

ln(x) = −7.148(0.640) − 1.313(0.778)α + 1.478(1.044)β + 9.636(1.244)π * ij V δ 2 yz − 10.616(1.414)jjj s H zzz j 100RT z k {

(17)

n = 16, R2 = 0.90, RSS = 6.20, F = 33.28 E



Article

Table 3. Parameters of the Correlation Equations/Models and RMSD Values for p-Nitrophenzylcyanide in the Selected Solvents Modified Apelblat equation Solvent

A

Methanol Ethanol n-Propanol Isopropanol Acetone Acetonitrile Toluene 2-Butanone Ethyl acetate 1,4-Dioxane n-Butanol Acetic acid Isobutanol Ethylbenzene Cyclohexane Water

−121.36 −94.81 −173.87 −108.06 −57.08 −14.67 −227.6 −72.21 −105.98 −46.10 −106.34 −104.92 −123.17 −303.59 −297.76 −160.01

B 1686.9 754.59 3924.4 713.64 475.12 −2093.1 7212.5 945.16 3605.0 −1250.2 765.60 1991.1 1347.2 10705.6 9687.6 3647.0 λh equation

Wilson model 4

C

10 RMSD

a12

b12

19.39 15.24 27.20 17.50 9.33 3.35 34.99 11.68 16.16 8.37 17.20 16.52 19.76 46.2 45.03 24.14

0.80 0.81 0.23 0.26 1.89 3.73 5.06 2.41 5.94 13.41 0.67 0.60 0.17 5.39 0.03 0.01

−6.17 −2.81 −4.12 −4.28 −0.89 −4.04 −1.23 −1.32 3.02 −5.45 −5.74 −1.23 −4.40 −0.54 −1.27 1.87

2575.6 1600.2 2173.3 2228.0 178.02 1019.9 964.62 444.21 −1042.8 1859.6 2836.0 673.99 2357.1 1052.0 2560.3 1239.8

a21 8.20 8.78 24.6 32.35 3.41 55.83 2.51 3.50 2.06 2.80 6.89 50.0 27.27 3.42 6.08 24920633.57 NRTL model

b21

104 RMSD

−1898.9 −1764.1 −6218.6 −8001.8 −420.09 −14169.9 −352.45 −576.94 −189.06 −600.54 −1793.7 1.00 −6888.5 −865.46 −1676.3 1.00

3.40 1.09 0.19 0.33 2.29 3.79 5.22 2.50 2.07 15.96 2.59 0.42 0.29 4.44 0.022 0.01

Solvent

λ

h

104 RMSD

a12

b12

a21

b21

α

104 RMSD

Methanol Ethanol n-Propanol Isopropanol Acetone Acetonitrile Toluene 2-Butanone Ethyl acetate 1,4-Dioxane n-Butanol Acetic acid Isobutanol Ethylbenzene Cyclohexane Water

0.09789 0.05537 0.06792 0.06518 0.3624 0.6726 0.1658 0.4032 0.02731 1.5399 0.06671 0.09437 0.06130 0.09783 0.00273 0.000383

39557.5 62967.1 59588.5 66715.5 5398.1 4411.2 18762.4 5606.3 6593.3 2630.2 61622.0 26574.5 71470.5 30277.0 1377231 8554671

1.76 1.03 1.65 0.41 2.94 5.09 8.63 3.09 3.15 25.73 1.30 1.83 0.77 9.56 0.13 0.0068

61.60 −116.3 26.67 29.45 3.54 6.21 0.50 2.75 1.72 2.57 49.72 2.29 −7.29 1.33 2.50 −19.22

−15768.4 43284.8 −6513.5 −7207.6 −574.28 −1361.8 −159.69 −503.31 −209.76 −451.6 −12823.6 86.52 3049.9 −776.35 −1302.8 7162.39

1.84 −0.09 −3.05 −0.88 −1.44 −3.56 −0.96 −0.86 3.17 −5.43 0.67 −0.10 −2.92 −1.50 −8.40 −0.39

132.59 1275.1 1762.2 1385.3 382.76 1203.2 1122.9 427.05 −1032.4 1792.7 735.23 635.56 1784.2 1910.0 5788.3 2517.9

0.20 0.40 0.25 0.35 0.20 0.43 0.20 0.46 0.25 0.28 0.25 0.46 0.21 0.20 0.35 0.39

0.98 0.52 0.23 0.27 2.36 4.12 4.69 2.51 2.13 16.16 0.35 0.91 0.59 3.81 0.03 0.0088

solvent−solvent interaction to the entire solvent effect. The contributions of nonspecific dipolarity/polarizability interactions to solubility are almost the same strength as the cavity term. Specific interactions accounted for by α and β of the solvent have lower contribution to the p-nitrophenylacetonitrile solubility. The coefficients of π* and β are positive, which shows that the p-nitrophenylacetonitrile solubility rises with increasing dipolarity/polarizability and hydrogen bond basicity of the solvent. On the contrary, the p-nitrophenylacetonitrile solubility decreases as the density of cohesive energy and hydrogen bond acidity of the selected solvents increases. Data Correlation. The solubility of p-nitrophenylacetonitrile is correlated based on the objective function expressed as eq 18 for NRTL and Wilson models. F=

∑ (lnγie − lnγic)2 i=1

The RD (relative deviation), RAD (relative average deviation), and RMSD (root-mean-square deviation) are also employed in order to estimate the selected solubility models. RD =

RAD =

∑ (xie − xic)2 i=1

1 N

N

∑

(20)

xie − xic xie

ÄÅ N É ÅÅ ∑ (x c − x e)2 ÑÑÑ1/2 ÅÅ i = 1 i ÑÑ i ÑÑ RMSD = ÅÅÅ ÑÑ ÅÅ N ÑÑÖ ÅÇ i=1

(21)

(22)

Here, the activity coefficient described in eq 18 is denoted as γei ; and the activity coefficient calculated using solubility models, γci , xci , and xei refer to, respectively, the computed and determined solubilities of p-nitrophenylacetonitrile. N refers to the experimental data number. The density values of the studied organic solvents tabulated in Table 1 are cited in ref 33; and the p-nitrophenylacetonitrile density is evaluated through the Advanced Chemistry Development (ACD/Laboratories) Software v 11.02. The

(18)

whereas the objective function for the λh and Apelblat equations is represented as F=

xe − xc xe

(19) F


ÅÄÅ ÑÉ i b Λ Å ∂(GE /T ) ÑÑÑ ÑÑ = Rx1x 2jjjj 12 12 HE,o = −T 2ÅÅÅÅ jx + Λ x ÅÅÇ ∂T ÑÑÑÖ 12 2 k 1 b21Λ 21 zyz + z x 2 + Λ 21x1 zz{

Journal of Chemical & Engineering Data melting point (Tm) and melting enthalpy (ΔfusH) of pnitrophenylacetonitrile are determined in this work, which are 384.23 K and 16.05 kJ·mol−1, respectively. The parameters’ values in Apelblat equation, Buchowski−Ksiazaczak λh equation, NRTL model, and Wilson model as well as the values of RMSD are listed in Table 3. In addition, The computed solubility of p-nitrophenylacetonitrile in the 16 pure solvents are presented in Table S3 together with the RD and RAD values. Furthermore, the calculated solubility values by using the Apelblat equation is plotted in Figure 2 of this work. As observed from Tables S3 and 3, the calculated pnitrophenylacetonitrile solubility in 16 solvents coincides well with the experimental ones. The maximum value of RMSD is 25.73 × 10−4 attained using the Buchowski−Ksiazaczak λh equation for 1,4-dioxane. The RAD values are no greater than 2.67%. So, the computed solubility by using the selected models provides good agreement with the experimental data. On the whole, for the four solubility equations studied, the attained values of RAD are smaller with NRTL equation than with the other three equations. So, the NRTL model offers the best correlation results among the four models. Dissolution Properties. It is very important to investigate the thermodynamic aspect of dissolution properties for a solute in solutions. The dissolution procedure may be presumed as the steps: heating, mixing, cooling, and fusion. In the present work, the properties of dissolution process (ΔdM°) of pnitrophenylacetonitrile are studied and may be evaluated using the following equation:41 Δd M o = (Δh M o + ΔfusM o + ΔcM o)x1 + Δmix M o

S E,o =

ÄÅ É ÅÅ ∂ ln γ ∞ ÑÑÑ H E, ∞ 1 Ñ ÅÅ ÑÑ = 1 ÅÅ ÅÅÇ ∂(1/T ) ÑÑÑÖ R P ,x

(26)

Δmix H id = 0

(27)

■

CONCLUSION The p-nitrophenylacetonitrile solubilities in 16 neat solvents were attained over the temperature range from 278.15 to 333.15 K under ambient pressure p = 101.2 kPa. They obeyed the order except for 1,4-dioxane as ethyl acetate > acetone > (acetonitrile, 2-butanone) > toluene > acetic acid > ethylbenzene > methanol > ethanol > n-propanol > n-butanol > isopropanol > isobutanol > cyclohexane > water. The solubility determined was described mathematically though the Buchowski−Ksiazaczak λh equation, Apelblat equation, NRTL, and Wilson models. The maximum values of RMSD (×10−3) and RAD (×10−2) were 2.573 and 2.67, respectively. To some degree, the values of RAD acquired using the NRTL model were lower than that using the other three models. KAT-LSER relationship analysis showed that the dipolarity/ polarizability interactions and Hildebrand solubility parameter of solvents contributed mainly to the solubility. The dissolution thermodynamic properties were evaluated in terms of the Wilson equation. The dissolution procedure of p-nitrophenylacetonitrile in the studied solvents is entropydriven, endothermic, and favorable in the investigated solvents.

■

where x1 denotes the solubility of solute in mole fraction; and x2, the mole fraction of corresponding solvent in equilibrium liquor. Based on the Wilson model, the excess thermodynamic mixing properties are described by eqs 28−30.43

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.8b00811. Chemical structure of p-nitrophenzylcyanide; solubility of benzoic acid in toluene; XPRD patterns; dissolution Gibbs energy change; benzoic acid solubility in toluene; Hildebrand solubility parameters and solvatochromic

GE,o = RT (x1ln γ1 + x 2 ln γ2) = −RT[x1ln(x1 + x 2 Λ12) + x 2 ln(x 2 + x1Λ 21)]

(32)

The calculated values of ΔdG°, ΔdH°, ΔdS°, and HE,∞ 1 are presented in Table S4. The values of ΔdH° and ΔdS° are positive in any case, showing that the dissolution process of pnitrophenylacetonitrile in the selected solvents is endothermic and entropy-driven. The dissolution process needs to absorb energy from environment to destroy the attractive force between the pure solvent and the solute. As shown in Figure S4, the ΔdG° values are negative in any cases and rise with rising temperature. Consequently, the dissolution procedure of p-nitrophenylacetonitrile is favorable and spontaneous in the selected 16 solvents.

Here, ΔmixMid,o refers to mixing property for ideal solution; ME,o represents the excess properties for the nonideal solution. The mixing Gibbs energy, enthalpy, and entropy of an ideal system may be described by the following equations based on the Lewis-Randall rule.

Δmix S id = −R(x1ln x1 + x 2 ln x 2)

(31)

lnγ∞ 1 ,

(24)

(25)

(30)

ln γ1∞ = −ln Λ12 + 1 − Λ 21

(23)

Δmix Gid = RT (x1ln x1 + x 2 ln x 2)

(29)

Here, γ1 and γ2 denote the activity coefficient of solute and solvent, respectively, in the actual system, which can be obtained with the help of the Wilson equation. Moreover, the E,∞ activity coefficient (γ∞ 1 ) and reduced excess enthalpy (H1 ) 44,45 under infinitesimal concentration can be computed by

where M denotes Gibbs energy G, enthalpy H, and entropy S; ΔmixM°, ΔhM°, ΔcM°, and ΔfusM° signify, respectively, the property variation of mixing, heating, cooling, and melting procedures. Since the values of heating and cooling processes (ΔhM° and ΔcM°) are lower than that of the fusion procedure, the two terms can be ignored in the equation.41,42 For the nonideal system, the mixing thermodynamic properties can be attained via eq 24. Δmix M o = ME,o + Δmix M id,o

HE,o − GE,o T

Article

(28) G



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parameters for neat solvents; values of RD and RAD; dissolution thermodynamic properties (PDF)

AUTHOR INFORMATION

Corresponding Author

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

Hongkun Zhao: 0000-0001-5972-8352 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge the award of Science and Technology Research Key Project of the Education Department of Jiangsu Province (Project number: SJCX17̅0621) and the Practice Innovation Project of Jiangsu Province for Post Graduate Students (Project number: XKYCX17̅039).

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