Solubility Determination and Thermodynamic Mixing Properties of 5

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

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Solubility Determination and Thermodynamic Mixing Properties of 5‑Methyl-2-pyrazinecarboxylic Acid in Different Solvents Zehui Yang,* Danfeng Shao,* and Guoquan Zhou

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School of Materials and Chemical Engineering, Ningbo University of Technology, Ningbo City, Zhejiang Province 315211, PRC ABSTRACT: The solubility of 5-methyl-2-pyrazinecarboxylic acid (MPCA) in 12 pure solvents within the temperature range from 273.15 to 313.15 K under 101.3 kPa was determined and correlated by some thermodynamic models including the modified Apelblat equation, λh equation, and Wilson model. The results increased with the rising temperature, and it decreased with the following sequence (at a certain temperature): 1,4-dioxane > ethanol > n-propanol > 1-butanol > methanol > isopropanol > acetone > 2-butanone > ethyl acetate > water > acetonitrile > toluene. Moreover, the solvent effect and solute−solvent intermolecular interaction were analyzed during the dissolution process of MPCA in pure organic solvents. The maximum values of the relative average deviation and root-mean-square deviation were no more than 1.67% and 3.43 × 10−4, respectively. Furthermore, the mixing Gibbs energy, mixing enthalpy, and mixing entropy were calculated by the Wilson model as well, and the values of ΔmixG and ΔmixH are all negative, while those of the ΔmixS are all positive. The calculated results of thermodynamic properties indicate that the mixing process is not only exothermic but also entropy-driven. in water.8−11 However, butanone is controlled by the Drug Enforcement Administration, which brings inconvenience to industrial production. In order to obtain the satisfying yield and purity of the product, it is of great significance to study the dissolution and purification process of MPCA. Up to now, the dissolution process of MPCA in different solvents has not been reported. Hence, we studied the dissolution behavior of MPCA in methanol, ethanol, npropanol, isopropanol, 1-butanol, acetone, 2-butanone, toluene, ethyl acetate, acetonitrile, 1,4-dioxane, and water at temperatures ranging from 273.15 to 313.15 K by using the isothermal saturation method, and the results were correlated by the modified Apelblat equation, λh equation, and Wilson model. Moreover, the solvent effect and solute−solvent intermolecular interaction were analyzed during the dissolution process of MPCA in pure organic solvents. Furthermore, the mixing Gibbs energy, mixing enthalpy, and mixing entropy were also evaluated by the Wilson model.

1. INTRODUCTION 5-Methyl-2-pyrazinecarboxylic acid (CAS no. 5521-55-1, its chemical structure is shown in Figure 1) as a pyrazine

Figure 1. Chemical structure of 5-methyl-2-pyrazinecarboxylic acid.

derivative is an important pharmaceutical intermediate. It is mainly used to synthesize the second generation sulfonylurea hypoglycemic drug glipizide, a new generation of long-acting lipid-lowering drug acimox, and an effective drug for tuberculosis, methyl 5-methylpyrazine-2-carboxylate.1−4 At the same time, MPCA is a good ligand containing nitrogen heterocycles and carboxyl groups on heterocycles.5,6 It is used to synthesize metal complexes for the preparation of catalysts.7 Currently, there are many synthetic methods of MPCA, which can be divided into chemical synthesis, electrochemical synthesis, and microbial synthesis.8−11 According to the different raw materials used, they can be divided into 2,3dicyanyl-5-methylpyrazine, 2-methylbenzopyrazine, 2-methyl5-hydroxymethylpyrazine, 2,5-dimethylpyrazine, etc. as the starting materials.8−11 Among them, Zhang9,10 reported the synthesis of MPCA by cyclization of methylglyoxal and ophenylenediamine in the presence of a catalyst, oxidation with KMnO4, sulfuric acid acidification, and decarboxylation.11 The process of this method is simple and easy to control. It has been industrialized at home and abroad. No matter which synthetic method is used, the final crude product needs to be extracted with 2-butanone and then purified by crystallization © XXXX American Chemical Society

2. SOLUBILITY MODELS In this work, the experimental solubility data were evaluated by some thermodynamic models including the modified Apelblat equation,12,13 λh equation,14 and Wilson model.15 2.1. Modified Apelblat Equation. It is an accurate mathematical description and usually used to correlate the solubility data (x, the mole fraction in this work) for a binary solid−liquid system, as shown in eq 1.12,13 A, B, and C are the Received: May 7, 2019 Accepted: August 2, 2019

A

DOI: 10.1021/acs.jced.9b00406 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. The Materials Used in the Work chemicals

molar mass (g·mol−1)

melting point (K)

5-methyl-2-pyrazinecarboxylic acid

138.12

440.35a

methanol ethanol n-propanol isopropanol 1-butanol acetone 2-butanone toluene ethyl acetate acetonitrile 1,4-dioxane water

32.04 46.07 60.06 60.06 74.12 58.05 72.11 92.14 88.11 41.05 88.11 18.01

CAS no.

melting enthalpy (kJ·mol−1)

density (kg·m−3) (293 K)

5521-55-1

28.60a

1425b 786.5c 789.3c 805.3c 803.5c 809.8c 784.5c 810c 871.0c 900.3c 776.8c 1040c 1000c

67-56-1 64-17-5 71-23-8 67-63-0 71-36-3 67-64-1 78-93-3 108-88-3 141-78-6 75-05-8 123-91-1 7732-18-5

source Beijing Ouhe Technology Co., Ltd., China Sinopharm Chemical Reagent Co., Ltd., China.

mass fraction purity

analysis method

0.993

HPLCd

0.997 0.995 0.995 0.996 0.996 0.995 0.994 0.996 0.996 0.995 0.995 secondary distilled water

none

a This work, determined at 101.2 kPa. The standard uncertainties u are u(T) = 0.5 K, u(p) = 0.45 kPa, and u(ΔfusH) = 0.4 kJ·mol−1. bReported by ChemSpider, which was obtained experimentally by ChongQing Acemol Technology Co., Ltd. China. cTaken from ref 21. dHigh-performance liquid phase chromatography.

equation parameters. T represents the experimental temperature in Kelvin. ln x = A +

B + C ln T T

During the process of calculation, the activity coefficient of the solid solute can be calculated by the Wilson equation. In the equation, V1 and V2 are the molar volumes of the solute and solvent, respectively. Δλij is the interaction parameter (J· mol−1). ÄÅ ÉÑ ÅÅ ÑÑ Λ 21 Λ12 Å ÑÑ Å ln γ1 = −ln(x1 + Λ12x 2) + x 2ÅÅ − Ñ ÅÅÇ x1 + Λ12x 2 x 2 + Λ 21x1 ÑÑÑÖ

(1)

2.2. Buchowski−Ksiazaczak λh Equation. The λh equation is another semiempirical calculation and proposed by Buchowski and co-workers.14 In eq 2, it has two parameters, λ and h; x is the mole fraction solubility of MPCA in 12 organic solvents; Tm is the melting temperature of MPCA in Kelvin. ÄÅ É ij 1 ÅÅ λ(1 − x) ÑÑÑÑ 1 yzz lnÅÅÅ1 + ÑÑ = λhjjj − z jT ÅÅÇ ÑÑÖ x Tm zz{ (2) k

Λ12 = Λ 21 =

2.3. Wilson Equation. In solid−liquid solution at different temperatures, the solubility data of the solid solute can be expressed as eq 315 when the system reaches equilibrium. As described above, x is the mole fraction solubility of the solute in solvent. R is the universal gas constant. γ stands for the activity coefficient, and ΔV and ΔCp stand for the differences of volume and heat capacity of a solute between the solid phase and liquid phase at the melting temperature, respectively. ln(xiγi) =

ΔHtp ijj 1 Ttp y 1 zy ΔCp ijj Ttp jj − zzzz − − + 1zzzz jjln j R j Ttp Tz R k T T { k { ΔV (p − ptp ) − (3) RT

ΔfusH ijj 1 1 yz − zzz jjj R k Tm T z{

V1 ij λ 21 − λ11 yz V i Δλ y zz = 1 expjjj− 21 zzz expjj− V2 k RT { V2 k RT {

(6)

(7)

In eqs 6 and 7, it is considered that the interaction parameters in the equation are linear with temperature. Therefore, the Λij in eqs 6 and 7 can be expressed as eq 8. Ä É bij yzÑÑÑÑ Vj ÅÅÅÅ ij j z Å Λij = expÅÅ−jjaij + zzÑÑÑ ÅÅ j T z{ÑÑÑÖ Vi (8) ÅÇ k where aij and bij are model parameters.

3. EXPERIMENTAL SECTION 3.1. Materials. 5-Methyl-2-pyrazinecarboxylic acid with a mass fraction of 0.986 was purchased from Beijing Ouhe Technology Co., Ltd., China. The crude MPCA was crystallized in ethanol, and the final purity was 0.993, which was determined by high-performance liquid chromatography. The selected analytical grade solvents including 1,4-dioxane, ethanol, n-propanol, 1-butanol, methanol, isopropanol, acetone, 2-butanone, ethyl acetate, acetonitrile, and toluene were purchased from Sinopharm Chemical Reagent Co., Ltd., China. These 11 organic solvents were used directly without any additional purification. Distilled water was obtained in our laboratory. The sources and purity of these materials are presented in Table 1.

In eq 3, ΔV and ΔCp can be ignored, and the triple-point temperature Ttp is nearly the same with the normal melting temperature Tm. Substituting the Ttp and ΔHtp with Tm and normal melting enthalpy ΔfusH, respectively, the solubility of the solute can be calculated by eq 4.15 ln(xiγi) =

V2 ij λ12 − λ11 yz V2 ij Δλ12 yz zz = expjj− zz expjj− V1 k RT { V1 k RT {

(5)

(4) B



Article

3.2. Properties Measurement. So far, the melting point of MPCA has been reported by many of the literature. Compared with the melting point, the enthalpy of fusion (ΔfusH) has not been reported by any reference. Therefore, the ΔfusH of MPCA in this work was measured by a differential scanning calorimetric instrument (Pyris-Diamond, PerkinElmer). Indium is a reference material and under a nitrogen atmosphere. Then, we weighed approximately 5 mg of the sample and took it into a DSC pan and then heat up in the temperature range from 293.15 to 480.15 K at a rate of 5 K· min−1. During the experiment, the standard uncertainties of the temperature and the melting enthalpy were 0.5 K and 450 J·mol−1, respectively. 3.3. Solubility Determination. In this work, the reliability of verification of the experimental apparatus was verified in our previous work.16,17 Excess solid compounds were added into the jacketed glass vessel with 60 mL of the solvent. The jacketed glass vessel was connected with a condenser, a magnetic stirrer, and a circulating water system. The condenser was used to prevent solvent volatilization. The temperature of the circulating water was controlled by a smart thermostatic water bath with the standard uncertainty of 0.02 K. Moreover, the true temperature was shown by a mercury glass microthermometer. After 48 h, the magnetic stirrer was stopped, and the solid was allowed to be precipitated from the mixture. The upper portion was taken out with a 5 mL preheated syringe connected with a filter (PTFE 0.2 μm) and transferred into a volumetric flask of 25 mL preweighed. The total mass of the solution and flask was weighed again by using the balance. Then, we completed the dilution with corresponding solvents. After that, 5 μL of the diluent was taken out with a microsyringe, and the concentration of MPCA was analyzed with high-performance liquid chromatography. Each determination was repeated three times. During the testing process, pure methanol at a flow rate of 1.0 mL·min−1 was the mobile phase. A reverse-phase column LP-C18 (250 mm × 4.6 mm) at the temperature of 303.15 K and a UV detector with the wavelength of 276 nm was applied to determine the concentration of MPCA in different solvents.

be found that the experimental melting temperature Tm of MPCA is 440.35 K, which is close to the values reported by Iovel et al. and Chen et al.18,19 Moreover, the melting enthalpy ΔfusH of MPCA is 28.60 kJ·mol−1. Since no 5-methyl-2pyrazinecarboxylic acid polymorphs have been reported in the literature, DSC equipment was used to check whether the solvate was produced during the dissolution process. From the analysis of Figure 2, we can see that no endothermic peak occurs before the melting point temperature. 4.2. Solubility Data. The obtained results of solubility data in methanol, ethanol, n-propanol, isopropanol, 1-butanol, acetone, 2-butanone, toluene, ethyl acetate, acetonitrile, 1,4dioxane, and water at temperatures ranging from 273.15 to 313.15 K are listed in Table 2 and presented in Figure 3. The maximum data was obtained in 1,4-dioxane at 313.15 K, and the minimum value was in toluene. Moreover, at all investigated temperatures, the solubility data obey the following sequence: 1,4-dioxane > ethanol > n-propanol > 1butanol > methanol > isopropanol > acetone > 2-butanone > ethyl acetate > water > acetonitrile > toluene. Therefore, we can select suitable solvents according to different preparation methods to separate and purify the objective compound. In these pure solvents, the solubility data in alcohols is obviously larger than that in other solvents except for 1,4-dioxane. The main reason is the formation of hydrogen bonds between hydroxyl groups in alcohols and solute molecules. Besides, the electron-pushing effect of methyl in toluene increases the electron cloud density in the benzene ring. However, the electron-attracting effect of the N atom on the pyrazine ring in the objective compound increases the electron cloud density in the pyrazine ring, and the repulsion of the solvent and solute makes the solubility in toluene smaller. Moreover, the KAT-LSER method20 is applied to further research the influence of solvation interaction on solubility, which is derived from the linear solvation energy relationship (LSER) and shown as eq 9.

4. RESULTS AND DISCUSSION 4.1. DSC Curves. The results of the DSC curve for the raw material and excess solid in solution are presented in Figure 2. Because the DSC curves obtained from experiments are almost the same, one of them is presented here. From Figure 2, it can

In eq 9, the values of solvent properties including hydrogen bond acidity (α), hydrogen bond basicity (β), dipolarity/ polarizability (π*), and the Hildebrand solubility parameter (δH2) are tabulated in Table 3.20,21 In addition, T, Vs, and R represent the temperature in Kelvin, molar volume of the solute, and gas constant, respectively. The data of Vs is 96.93 cm3/mol and reported by ChemSpider, which is obtained experimentally by ChongQing Acemol Technology Co., Ltd., China. It is close to the data predicted (104.7 cm3/mol) by the ACD/Labs Percepta platform. Each coefficient in the equation has different physical meanings. c0 is a constant term, and ci,(i = 1,2,3,4) presents the situation of the solute−solvent interaction through the specific hydrogen bonding interaction, the solute’s sensitivity to the nonspecific electrostatic solute− solvent interactions, and the self-cohesiveness related to the solvent−solvent interaction. In order to obtain ideal fitting results, 1,4-dioxane is neglected here. Hence, MLRA can be presented in eq 10.

ln(x) = c0 + c1α + c 2β + c3π * + c4

Vsδ H 2 100RT

(9)

ln(x) = −7.508 + 0.297α + 3.178β + 2.633π * Figure 2. DSC curve of 5-methyl-2-pyrazinecarboxylic acid raw and excess solid in solution.

− 2.432 C

Vsδ H 2 F = 47.68, R = 0.92 100RT

(10)



Article

Table 2. Experimental and Calculated Mole Fraction Solubility (x) of 5-Methyl-2-pyrazinecarboxylic Acid in Twelve Pure Solvents at T = 273.15 to 313.15 K under 101.2 kPaa,b x

x T (K) methanol 273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 100 RAD ethanol 273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 100 RAD n-propanol 273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 100 RAD isopropanol 273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 100 RAD 1-butanol 273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 100 RAD acetone 273.15 278.15

xexp

xapelblat

xλh

xWilson

0.0085 0.0100 0.0116 0.0136 0.0156 0.0177 0.0201 0.0229 0.0257

0.0085 0.0100 0.0117 0.0135 0.0155 0.0178 0.0202 0.0228 0.0257 0.33

0.0086 0.0100 0.0116 0.0134 0.0154 0.0176 0.0201 0.0229 0.0260 0.72

0.0086 0.0100 0.0116 0.0134 0.0154 0.0177 0.0202 0.0229 0.0259 0.53

0.0109 0.0127 0.0148 0.0171 0.0197 0.0225 0.0258 0.0293 0.0333 0.26

0.0109 0.0127 0.0148 0.0171 0.0196 0.0225 0.0257 0.0293 0.0333 0.26

0.0109 0.0127 0.0148 0.0171 0.0197 0.0226 0.0258 0.0293 0.0332 0.21

0.0101 0.0117 0.0136 0.0157 0.0181 0.0207 0.0236 0.0269 0.0305 0.46

0.0101 0.0117 0.0136 0.0157 0.0180 0.0207 0.0236 0.0269 0.0305 0.46

0.0100 0.0117 0.0136 0.0157 0.0181 0.0207 0.0236 0.0269 0.0304 0.37

0.0078 0.0090 0.0104 0.0119 0.0137 0.0156 0.0178 0.0202 0.0229 0.33

0.0078 0.0090 0.0104 0.0120 0.0137 0.0156 0.0178 0.0202 0.0228 0.35

0.0078 0.0090 0.0104 0.0119 0.0137 0.0156 0.0178 0.0202 0.0229 0.34

0.0094 0.0108 0.0125 0.0144 0.0165 0.0190 0.0218 0.0251 0.0287 0.22

0.0092 0.0108 0.0125 0.0145 0.0167 0.0191 0.0219 0.0250 0.0284 0.73

0.0094 0.0108 0.0124 0.0143 0.0165 0.0190 0.0219 0.0251 0.0287 0.16

0.0068 0.0080

0.0069 0.0080

0.0068 0.0079

0.0109 0.0127 0.0149 0.0171 0.0197 0.0225 0.0257 0.0293 0.0333

0.0100 0.0117 0.0136 0.0158 0.0182 0.0207 0.0234 0.0268 0.0306

0.0078 0.0091 0.0104 0.0119 0.0136 0.0156 0.0178 0.0203 0.0228

0.0094 0.0108 0.0125 0.0143 0.0165 0.0190 0.0219 0.0251 0.0287

0.0067 0.0080

T (K) acetone 283.15 288.15 293.15 298.15 303.15 308.15 313.15 100 RAD 2-butanone 273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 100 RAD toluene 273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 100 RAD acetonitrile 273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 100 RAD ethyl acetate 273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 100 RAD 1,4-dioxane 288.15 293.15 298.15 303.15

D

xexp

xapelblat

xλh

xWilson

0.0093 0.0107 0.0121 0.0139 0.0156 0.0178 0.0200

0.0092 0.0106 0.0122 0.0139 0.0157 0.0178 0.0200 0.67

0.0092 0.0106 0.0121 0.0138 0.0157 0.0178 0.0202 0.93

0.0092 0.0106 0.0121 0.0138 0.0157 0.0178 0.0201 0.78

0.0058 0.0068 0.0080 0.0093 0.0106 0.0121 0.0139 0.0158 0.0179

0.0058 0.0068 0.0080 0.0092 0.0106 0.0122 0.0139 0.0158 0.0179 0.38

0.0059 0.0068 0.0079 0.0092 0.0106 0.0121 0.0139 0.0158 0.0180 0.60

0.0058 0.0068 0.0079 0.0092 0.0106 0.0122 0.0139 0.0158 0.0179 0.41

0.00097 0.00110 0.00125 0.00142 0.00165 0.00189 0.00218 0.00250 0.00289

0.00097 0.00110 0.00125 0.00143 0.00164 0.00189 0.00217 0.00250 0.00289 0.32

0.00094 0.00109 0.00126 0.00146 0.00167 0.00191 0.00219 0.00249 0.00283 1.42

0.00094 0.00109 0.00127 0.00146 0.00168 0.00192 0.00219 0.00248 0.00281 1.67

0.00248 0.00292 0.00344 0.00401 0.00460 0.00534 0.00605 0.00688 0.00779

0.00248 0.00293 0.00343 0.00400 0.00462 0.00531 0.00607 0.00689 0.00778 0.26

0.00251 0.00294 0.00342 0.00396 0.00458 0.00527 0.00604 0.00691 0.00789 0.83

0.00249 0.00293 0.00342 0.00397 0.00459 0.00528 0.00605 0.00691 0.00787 0.55

0.00431 0.00504 0.00582 0.00663 0.00750 0.00840 0.00945 0.01068 0.01200

0.0044 0.0050 0.0058 0.0066 0.0075 0.0084 0.0095 0.0107 0.0120 0.61

0.0044 0.0050 0.0058 0.0065 0.0074 0.0084 0.0095 0.0107 0.0121 0.75

0.0043 0.0050 0.0057 0.0065 0.0074 0.0084 0.0095 0.0107 0.0120 0.60

0.01876 0.02161 0.02477 0.02842

0.0189 0.0215 0.0247 0.0285

0.0186 0.0216 0.0250 0.0288

0.0186 0.0216 0.0250 0.0288



Article

Table 2. continued x

x T (K) 1,4-dioxane 308.15 313.15 100 RAD water 273.15 278.15 283.15 288.15 293.15 298.15

xexp

xapelblat

xλh

xWilson

T (K)

0.03286 0.03843

0.0330 0.0384 0.33

0.0331 0.0379 0.92

0.0331 0.0378 0.95

water 303.15 308.15 313.15 100 RAD

0.00332 0.00383 0.00446 0.00516 0.00586 0.00674

0.00333 0.00385 0.00444 0.00511 0.00587 0.00674

0.00330 0.00384 0.00445 0.00514 0.00591 0.00677

0.00330 0.00384 0.00445 0.00513 0.00590 0.00676

xexp

xapelblat

xλh

xWilson

0.00770 0.00883 0.01012

0.00773 0.00884 0.01010 0.37

0.00774 0.00883 0.01004 0.47

0.00773 0.00882 0.01005 0.64

a

x denotes the experimental mole fraction solubility; RAD is the relative average deviation. bStandard uncertainties u are u(T) = 0.02 K, u(p) = 450 Pa; relative standard uncertainty ur is ur(x) = 0.039. xexp: experiment data, xapelblat: calculated by the Apelblat model, xλh: calculated by the λh model, and xWilson: calculated by the Wilson model.

Figure 3. Mole solubility (x) of 5-methyl-2-pyrazinecarboxylic acid in 12 pure solvents over a temperature range from 273.15 to 313.15 K.

of MPCA. The total proportion of the hydrogen bond acidity, hydrogen bond basicity, dipolarity/polarizability of the solvent, and the cavity term is 53.22%. Among them, the proportion of the selected parameter including α, β, π*, and δH2 are 1.85%, 19.80%, 16.41%, and 15.15%, respectively. 4.3. Solubility Correlation. The nonlinear regression method was used to correlate the solubility results of MPCA in selected pure solvents by software Mathcad. Usually, the resultant correlation of thermodynamic models is evaluated by the relative average deviation (RAD) and root-mean-square deviation (RMSD), and mathematical descriptions of the RAD and RMSD are presented in eqs 11 and 12. In the equation, xci and xei are the calculated and experimental values, respectively. N is the number of experimental data points.

Table 3. Hildebrand Solubility Parameters (δH) and Solvatochromic Parameters α, β, and π* for the Selected solventsa solvent

α

β

π*

δH2/1000 (J·cm−3)

methanol ethanol n-propanol isopropanol 1-butanol acetone ethyl acetate toluene 2-butanone acetonitrile 1,4-dioxane water

0.98 0.86 0.84 0.76 0.84 0.08 0 0 0.06 0.19 0 1.17

0.66 0.75 0.9 0.84 0.84 0.43 0.45 0.11 0.48 0.4 0.37 0.18

0.60 0.54 0.52 0.48 0.47 0.71 0.55 0.54 0.67 0.75 0.55 1.09

0.8797 0.7516 0.6025 0.552 0.5333 0.3994 0.3858 0.3315 0.3648 0.5806 0.4194 2.294

RAD =

1 N

N

∑

xie − xic xie

ÅÄÅ N ÑÉ1/2 ÅÅ ∑i = 1 (xic − xie)2 ÑÑÑ Å ÑÑ RMSD = ÅÅÅ ÑÑ ÅÅ ÑÑ N ÅÇ ÑÖ

a

Taken from refs 20 and 21.

As shown in eq 10, the values of c1, c2, and c3 are positive, which indicates that the dissolution capacity of MPCA increases with the increasing values of these three parameters. Hence, solute−solvent interaction through the specific hydrogen bonding interaction and polar interactions favors the solute’s solubility. As shown in Figure 3, because of the hydrogen bond, the solubility of solutes in alcohols is obviously higher than that of polar aprotic solvents except for 1,4-dioxane

i=1

(11)

(12)

During the process of calculation, the melting temperature (Tm) and melting enthalpy (ΔfusH) of MPCA were taken from this work, and the densities of solvents and the solute are listed in Table 1. The values of RAD are tabulated in Table 2. The values of the regressed parameters and RMSD are listed in Table 4. The maximum values of RAD and RMSD were no more than 1.67% and 3.43 × 10−4, respectively, which indicated that the calculated and experimental values agreed very well. However, the values of RAD in the modified Apelblat equation are all less than 0.67%, and the largest

2

and water. The coefficient of Vsδ H is negative, it indicates that 100RT the solubility decreases as the self-cohesiveness of the solvent increases. Therefore, the self-cohesiveness related to the solvent−solvent interaction is disadvantageous to the solubility E



Article

Table 4. Parameters of the Modified Apelblat Equation, λh Equation, and NRTL Model for 5-Methyl-2-pyrazinecarboxylic Acid in Different Solvents λh equation

modified Apelblat equation 4

Wilson model 4

solvent

A

B

C

10 RMSD

λ

h

10 RMSD

a12

b12/K

a21

b21/K

104 RMSD

methanol ethanol n-propanol isopropanol 1-butanol acetone 2-butanone toluene acetonitrile ethyl acetate 1,4-dioxane water

35.317 −18.320 −19.544 −37.659 −84.372 17.785 4.473 −152.390 36.561 −5.631 −227.271 −71.119

−3736.825 −1392.800 −1334.742 −493.227 1474.085 −2926.216 −2433.012 4393.481 −3915.741 −1797.064 7834.207 871.247

−4.706 3.370 3.535 6.170 13.245 −2.150 −0.127 23.059 −5.031 1.208 34.627 11.092

0.63 0.51 1.08 0.58 0.39 0.79 0.45 0.061 0.15 0.47 0.87 0.23

0.177 0.237 0.214 0.142 0.205 0.125 0.125 0.018 0.056 0.06 0.337 0.067

12455.687 9443.965 10412.471 14954.263 11001.586 16942.265 17801.83 120163.37 40179.378 32080.891 7263.436 32956.74

1.51 0.51 1.06 0.63 1.48 1.17 0.68 0.28 0.48 0.57 3.07 0.38

2.075 3.003 2.809 2.373 0.900 3.170 3.187 5.489 3.348 4.453 1.775 3.784

−1091.74 −1115.87 −1090.53 −628.31 −418.279 −1158.88 −1066.74 −1146.95 −1024.83 −1307.67 −879.30 −1200.85

15.054 0.762 1.571 2.015 7.191 17.781 14.629 1262.08 15.747 15.479 136.294 1.563

1303.14 30.541 9.794 −544.470 −1781.55 1101.77 4678.03 −88193.2 1903.33 1261.53 −30565.6 −0.292

1.11 0.49 1.09 0.61 0.31 0.93 0.49 0.36 0.33 0.52 3.43 0.43

Table 5. The Calculated Values of the Mixing Gibbs Energy (ΔmixG), Mixing Enthalpy (ΔmixH), and Mixing Entropy (ΔmixS) T (K)

ΔmixG (J·mol−1)

methanol 273.15 −111.72 278.15 −128.41 283.15 −145.67 288.15 −166.41 293.15 −186.5 298.15 −206.91 303.15 −229.37 308.15 −254.52 313.15 −278.75 isopropanol 273.15 −102.4 278.15 −116.63 283.15 −130.46 288.15 −145.92 293.15 −162.86 298.15 −182.08 303.15 −202.45 308.15 −224.7 313.15 −246.16 2-butanone 273.15 −76.2 278.15 −87.36 283.15 −100.29 288.15 −113.83 293.15 −126.98 298.15 −141.63 303.15 −158.5 308.15 −175.65 313.15 −193.86 ethyl acetate 273.15 −56.54 278.15 −64.21 283.15 −72.66 288.15 −80.84 293.15 −89.71 298.15 −98.29 303.15 −107.47 308.15 −118.91 313.15 −129.87

ΔmixH (J·mol−1)

ΔmixS (J·K−1·mol−1)

−76.92 −90.42 −104.78 −122.7 −140.55 −159.22 −180.47 −205.14 −229.65

0.127 0.137 0.144 0.152 0.157 0.160 0.161 0.160 0.157

−83.65 −95.65 −107.23 −120.42 −135.14 −152.25 −170.69 −191.29 −211.22

0.069 0.075 0.082 0.088 0.095 0.1 0.105 0.108 0.112

−51.28 −60.08 −70.61 −81.98 −93.32 −106.36 −121.94 −138.3 −156.27

0.091 0.098 0.105 0.111 0.115 0.118 0.121 0.121 0.12

−46.61 −54.15 −62.75 −71.32 −80.94 −90.51 −101.1 −114.81 −128.42

0.036 0.036 0.035 0.033 0.03 0.026 0.021 0.013 0.005

ΔmixG (J·mol−1) ethanol −143.06 −163.12 −186.74 −209.69 −235.83 −263.02 −292.92 −325.23 −359.64 1-butanol −123.35 −138.65 −156.74 −175.45 −197.63 −222.07 −249.48 −278.73 −310.49 toluene −12.66 −14.11 −15.73 −17.51 −19.83 −22.17 −24.87 −27.74 −31.07 1,4-dioxane

−230.07 −258.79 −290.51 −324.94 −366.08 −413.93

ΔmixH (J·mol−1)


−98.6 −114.69 −134.28 −153.76 −176.63 −201.07 −228.75 −259.57 −293.37

0.163 0.174 0.185 0.194 0.202 0.208 0.212 0.213 0.212

−107.65 −114.09 −122.48 −130.65 −141.24 −153.07 −166.74 −181.31 −197.36

0.057 0.088 0.121 0.155 0.192 0.231 0.273 0.316 0.361

−9.22 −10.45 −11.86 −13.46 −15.62 −17.86 −20.56 −23.53 −27.11

0.013 0.013 0.014 0.014 0.014 0.014 0.014 0.014 0.013

−136.61 −156.75 −179.69 −205.4 −237.39 −276.25

F

0.324 0.348 0.372 0.394 0.418 0.44

ΔmixG (J·mol−1) n-propanol −131.28 −150.2 −170.68 −193.57 −217.68 −241.97 −267.31 −297.85 −330.51 acetone −88.23 −102.58 −116.48 −130.96 −145.01 −162.35 −178.21 −197.86 −216.74 acetonitrile −32.79 −37.29 −42.72 −48.99 −55.08 −61.92 −69.45 −76.73 −84.61 water −43.28 −48.83 −56.29 −63.51 −70.52 −78.25 −87.54 −97.36 −108.48

ΔmixH (J·mol−1)


−90.09 −105.3 −122.25 −141.8 −163.05 −185.06 −208.7 −238.3 −271.11

0.151 0.161 0.171 0.18 0.186 0.191 0.193 0.193 0.19

−64.36 −76.78 −89.17 −102.47 −115.73 −132.72 −148.69 −169.26 −189.7

0.087 0.093 0.096 0.099 0.1 0.099 0.097 0.093 0.086

−21.23 −24.61 −28.83 −33.88 −38.91 −44.75 −51.41 −58.02 −65.43

0.042 0.046 0.049 0.052 0.055 0.058 0.06 0.061 0.061

−32.64 −37.5 −44.26 −50.96 −57.58 −65.06 −74.31 −84.3 −95.88

0.039 0.041 0.042 0.044 0.044 0.044 0.044 0.042 0.04



Article

Figure 4. Calculated mixing Gibbs energy at measured solubility points based on the Wilson model.

RMSD is 1.08 × 10−4; the results show that the modified Apelblat equation could be used preferentially to correlate solubility data. 4.4. Mixing Properties of Solutions. It is important to study the dissolution behavior of solute in various solvents for practical solutions. Based on the Lewis−Randall rule, the mixing properties of solutions could be obtained by the Wilson model. Moreover, for an ideal binary solution, the mixing properties including the mixing Gibbs energy, mixing enthalpy, and mixing entropy could be described as eqs 13−15.22 Δmix Gid = RT (x1 ln x1 + x 2 ln x 2)

(13)

Δmix S id = −R(x1 ln x1 + x 2 ln x 2)

(14)

Δmix H id = 0

(15)

indicate that the mixing process is not only exothermic but also entropy-driven.

5. CONCLUSIONS The solubility of MPCA in 12 pure solvents within the temperature range from 273.15 to 313.15 K under atmospheric pressure (101.3 kPa) was determined. It increased with increasing temperature, and at a certain temperature, it decreased with the following sequence: 1,4-dioxane > ethanol > n-propanol > 1-butanol > methanol > isopropanol > acetone > 2-butanone > ethyl acetate > water > acetonitrile > toluene. The results were correlated by the modified Apelblat equation, λh equation, and Wilson model, and the maximum values of RAD and RMSD were no more than 1.67% and 3.43 × 10−4, respectively. The values of RAD in the modified Apelblat equation are all less than 0.67%, and the largest RMSD is 1.08 × 10−4; the results show that the modified Apelblat equation could be used preferentially to correlate solubility data. Furthermore, the results of the mixing Gibbs energy, mixing enthalpy, and mixing entropy show that the mixing process is not only exothermic but also entropy-driven. Understanding the dissolution process of MPCA is of great industrial significance.

where x1 is the mole fraction of the solute, and x2 the corresponding solvent. For the nonideal solution, the three mixing properties can be described as eqs 16 and 17. Δmix M = ME + Δmix M id

(16)

for M = G , H , and S

■

(17)

In eq 16, ΔmixM, M , and ΔmixM are the mixing property in practical solutions, excess property in nonideal solutions, and mixing property at the ideal state, respectively. Moreover, the excess mixing property could be calculated by eqs 18−2022 E

id

Corresponding Authors

*E-mail: [email protected] (Z.Y.). *E-mail: [email protected] (D.S.). ORCID

GE = RT (x1 ln γ1 + x 2 ln γ2)

Zehui Yang: 0000-0001-7588-366X Danfeng Shao: 0000-0001-7934-089X

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

ÄÅ É Å ∂(GE /T ) ÑÑÑ E 2Å Å ÑÑ = x x ijjj b12 Λ12 + b21Λ 21 yzzz H = −T ÅÅÅ Ñ 1 2j jx + Λ x ÅÅÇ ∂T ÑÑÑÖ x 2 + Λ 21x1 zz{ 12 2 k 1 E

(18)

Notes

(19)

■

The authors declare no competing financial interest.

ACKNOWLEDGMENTS The research is supported by the China National Key Research and Invention program of the thirteenth Five-Year Plan (no. 2017YFD0200707). The authors also want to give thanks to the Ministry of Education Scientific Research Foundation (no. XM20131225085213994) as well as the Zhejiang Province Public Technology Project (no. 2013C31G2290019) and Ningbo Natural Science Foundations (nos. 2013A610094 and 2018A610411).

E

H −G (20) T The results of the mixing properties including the mixing Gibbs energy, mixing enthalpy, and mixing entropy are obtained and shown in Table 5. The mixing Gibbs energy (ΔmixG) was plotted in Figure 4, which is consistent with the dissolution capacity of MPCA in different solvents. Moreover, the values of ΔmixG are all negative and decrease with the increasing temperature. From Table 5, the negative values of ΔmixH and the positive values of ΔmixS can be found, which SE =

AUTHOR INFORMATION

■

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Solubility Determination and Thermodynamic Mixing Properties of 5

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