Journal of Molecular Liquids 275 (2019) 815–828
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Solubility and thermodynamic properties of 5-nitrofurazone form γ in mono-solvents and binary solvent mixtures Xin Li a, Xin Huang a,b,⁎, Yanan Luan a, Jing Li a, Na Wang a, Xuling Zhang a, Steven Ferguson c, Xianze Meng a, Hongxun Hao a,b,⁎ a b c
National Engineering Research Center of Industrial Crystallization Technology, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin 300072, China School of Chemical and Bioprocess Engineering, University College Dublin, Belfield, Dublin 4, Ireland
a r t i c l e
i n f o
Article history: Received 25 September 2018 Received in revised form 13 November 2018 Accepted 23 November 2018 Available online 26 November 2018 Keywords: 5-Nitrofurazone Solubility UV spectroscopy Mixing thermodynamic properties Dissolution thermodynamic properties
a b s t r a c t In this work, the solubility of the γ - polymorphic form of 5-nitrofurazone (5-nitro-2-furaldehyde semicarbazone) in mono-solvent systems and binary solvent mixtures was measured from 278.15 to 313.15 K, using a UV spectroscopic method. The results revealed that the solubility increased with increasing temperature in all investigated solvents within this temperature range. The experimental solubility data in the single solvent systems was well represented with the modified Apelblat equation and the NRTL model, while the λh equation and the NRTL model were used to correlate the experimental solubility data in the case of the binary solvent mixtures. In all cases, these models were shown to have an average relative deviation of lower than 5%. In addition, the thermodynamic mixing and dissolution properties of the γ - form of 5-nitrofurazone, in all investigated mono-solvent systems and binary solvent mixtures, were calculated based on NRTL model and experimental solubility data. © 2018 Elsevier B.V. All rights reserved.
1. Introduction 5-Nitrofurazone (Fig. 1, C6H6N4O4, CAS registry No: 59-87-0) is an anti-infective agent with bacteriostatic effects against Gram-positive and Gram-negative bacteria, used in the treatment of wounds, burns, ulcers and skin infections [1]; in addition to the treatment of American trypanosomiasis caused by the etiologic parasitic agent Trypanosoma cruzi [2]. Olszak et al. published the first crystal structure of 5-nitrofurazone (α-form). Subsequently, Pogoda et al. discovered two new polymorphic forms (the β and γ forms) [1]. Most studies of 5-nitrofurazone polymorphs were focused on intermolecular interaction and molecule conformation in the different crystalline forms [1–3]. Few publications to date have investigated the solubilities and thermodynamic properties of the three polymorphs of 5-nitrofurazone. Solution crystallization is the final step to refine the 5-nitrofurazone products for commercial supply. As such, accurate solubility data and additional thermodynamic data, such as the dissolution thermodynamics of 5-nitrofurazone in relevant solvents are needed for the development, optimization and design of 5-nitrofurazone manufacturing and crystallization processes [4].
Three polymorphs; the α, β, and γ forms, have been published to date in literature. Of the three polymorphs, the γ - form is the most stable form and hence will not transform into the other polymorphs on storage or during application and for this reason is typically chosen for commercial applications. This motivated this work, where the solubility of the γ - form of 5-nitrofurazone is experimentally determined in nine solvents (water, n-propanol, isopropanol, methanol, ethanol, acetonitrile, acetone, N, N-dimethylformamide and formamide) and in binary solvent mixtures of N, N-dimethylformamide and water/isopropanol by UV spectroscopy from 278.15 K to 313.15 K. The experimental solubility data in mono-solvent systems were fitted with the modified Apelblat equation and the NRTL model. The λh equation and the NRTL model were applied to fit the experimental solubility data in binary solvent mixtures. Furthermore, the mixing and dissolution thermodynamic properties of the 5-nitrofurazone γ - form in solvent and binary solvent mixtures were determined by using the NRTL model and experimental solubility data. 2. Experimental 2.1. Materials
⁎ Corresponding authors at: National Engineering Research Center of Industrial Crystallization Technology, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China. E-mail addresses:
[email protected] (X. Huang),
[email protected] (H. Hao).
https://doi.org/10.1016/j.molliq.2018.11.123 0167-7322/© 2018 Elsevier B.V. All rights reserved.
The β - form of 5-nitrofurazone was purchased from Tokyo Chemical Industry Co., Ltd., Shanghai, China. The γ - form of 5-nitrofurazone was prepared by solution crystallization, and the purity of the obtained
816
X. Li et al. / Journal of Molecular Liquids 275 (2019) 815–828
Fig. 1. Chemical structure of 5-nitrofurazone.
product was measured with UV spectroscopy. All solvents were supplied by Jizhun Chemical Technology Co., Ltd., (Tianjin, China), Guangda Pharmaceutical Co. Ltd., (Tianjin, China), Yuxiang Chemical Technology Co., Ltd., (Tianjin, China). The solvents were used without further purification. Details of the materials used in this work can be found in Table 1. Fig. 2. Calibration curve of 5-nitrofurazone concentration in UV method diluent (DMF and Water).
2.2. X-ray powder diffraction The powder X-ray diffraction (p-XRD) patterns of 5-nitrofurazone were measured before and after solution crystallization to confirm that the final isolated products were the γ - form of 5-nitrofurazone. Wet solid samples from solution following solubility measurements were also tested to analyze the polymorphic purity of 5-nitrofurazone present. The XRD measurements were conducted on a Rigaku D/max2500 (Rigaku, Japan) using Cu Kα radiation (1.5405 Å), with step size of 0.02° and scanning rate of 0.067°/s over diffraction angle (2θ) range of 5°–50°. 2.3. Thermogravimetric analysis Thermogravimetric analysis (TGA) was used to determine the stability of the γ - form of 5-nitrofurazone at its melting point. All TGA measurements were analyzed using a Mettler Toledo TGA/DSC/SF (Greifensee, Switzerland) machine with a temperature ramp/cycle from 348.15 K to 573.15 K with a heating rate of 10 K/min, conducted in a controlled inert environment of nitrogen gas. 2.4. Solubility measurements by UV spectroscopy In this work, a UV spectroscopic method was used to determine the concentration of the γ - form of 5-nitrofurazone in nine mono-solvent systems (water, n-propanol, isopropanol, methanol, ethanol,
acetonitrile, acetone, N, N-dimethylformamide and formamide) and two binary solvent mixtures (N, N-dimethylformamide and water/ isopropanol). At first, an excess amount of 5-nitrofurazone was put into a water-jacketed glass vessel (80 ml) with approximately 60 ml solvent or solvent mixture. A thermostat (Xianou Laboratory Instrument Works Co., Ltd., Nanjing) with an accuracy of ±0.1 K was used to keep the system at a specific temperature. The suspended solution was agitated adequately for N10 h by a magnetic stirrer (200 rpm) to guarantee solid-liquid equilibrium. Next, the solution was kept at the same temperature without agitation for about 4 h to ensure the undissolved solids had settled. Following settling, the upperpart of the clear saturated solutions was withdrawn by syringe through a membrane filter (0.22 μm, Tianjin Legg Technology Co., Ltd., Tianjin, China). These mother liquor samples were then diluted to the concentration range that was appropriated for UV measurement of concentration. Finally, the concentration was determined using a UV-2600 spectrophotometer (SHIMADZU, Japan). After initial screening of all of the single solvents, it was found that the solubility of 5-nitrofurazone was the lowest in water and highest in N, N-dimethylformamide. For this reason, all solutions were diluted first by N, N-dimethylformamide after filtration, and then diluted further with water to do the final detection. The effects of the original solvent mixtures in the saturated solution on absorbance (A) could be
Table 1 The sources and mass fraction based purity of experimental materials. Chemical name
Source
5-Nitrofurazone form β 5-Nitrofurazone form γ Propanol Isopropanol Methanol Ethanol Acetonitrile Acetone N, N-dimethylformamide Formamide
Tokyo Chemical Industry Co., Ltd., Shanghai, China Tokyo Chemical Industry Co., Ltd., Shanghai, China Jizhun Chemical Technology Co., Ltd., Tianjin, China Guangda Pharmaceutical Co. Ltd., Tianjin, China Guangda Pharmaceutical Co. Ltd., Tianjin, China Guangda Pharmaceutical Co. Ltd., Tianjin, China Yuxiang Chemical Technology Co., Ltd., Tianjin, China Guangda Pharmaceutical Co. Ltd., Tianjin, China Jizhun Chemical Technology Co., Ltd., Tianjin, China Fuchen Chemical Technology Co., Ltd., Tianjin, China
a b c d e f
Mass purity
Purification method
Analysis method
N0.98 ≥0.9865 ≥0.998 ≥0.997 ≥0.995 ≥0.997 ≥0.995 ≥0.995 ≥0.995 ≥0.993
None
HPLCa UVb GCc GCd GCd GCd GCe GCd GCc GCf
High-performance liquid chromatography, conducted by Tokyo Chemical Industry Co., Ltd., Shanghai, China. UV spectroscopy, conducted by our lab, Tianjin, China. Gas chromatography, conducted by Jizhun Chemical Technology Co., Ltd., Tianjin, China. Gas chromatography, conducted by Guangda Pharmaceutical Co. Ltd., Tianjin, China. Gas chromatography, conducted by Yuxiang Chemical Technology Co., Ltd., Tianjin, China. Gas chromatography, conducted by Fuchen Chemical Technology Co., Ltd., Tianjin, China.
None None None None None None None None
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ignored since the amount of it was much lower than the amount of diluent utilized [5]. The calibration curve of 5-nitrofurazone in water was obtained at room temperature and atmospheric pressure before measuring the concentration of the saturated solution. The maximum absorption wavelength in water was tested to be 374 nm. The fitted linear calibration is shown in Fig. 2 and the line has a slope of 0.0821 and intercept of −0.0079 with an R2 = 0.9998. Each experiment was repeated three times and the average absorbance was used to calculate the equilibrium mole fraction, which was used as the primary unit of solubility in this study, using Eqs. (1) and (2) [4,6,7]:
mN ¼ NV
xN ¼
A−b a
ð1Þ
mN =MN P mN =M N þ mi =Mi
ð2Þ
where A is the absorbance value presented by UV spectrophotometer, a and b represent the slope and intercept of the calibration curve, V is the initial sample volume, N is dilution volumes used; mN and MN represent the mass and the molar mass of 5-nitrofurazone; mi, Mi, represent the mass and the molar mass of solvents, respectively.
Fig. 3. Powder X-ray diffraction patterns of 5-nitrofurazone. β0 and γ0 are the β - form and γ - form obtained from the Cambridge Crystallographic Data Centre respectively (WERVEU01 for the β - form and WERVEU02 for the γ - form). β1 and γ1 is the purchased sample and the products prepared by solution crystallization in this work, respectively.
3. Thermodynamic models 3.1. Modified Apelblat equation The modified Apelblat equation is a widely used model to correlate solid–liquid equilibrium data. It is often used to express the relation between temperature T and the solubility of solute. It can be shown as Eq. (3) [8–10]: ln xN ¼ A þ
B þ C lnT T
ð3Þ
where xN is the mole fraction solubility of solute. T is the absolute temperature. A, B, and C are fitted model parameters.
G12 ¼ eð−ατ12 Þ
ð7Þ
G21 ¼ eð−ατ21 Þ
ð8Þ
τ12 ¼
g 12 −g 22 Δg 12 ¼ RT RT
ð9Þ
τ21 ¼
g 21 −g 11 Δg 21 ¼ RT RT
ð10Þ
where R is gas constant (8.314 J·mol−1·K−1). T represents thermodynamic temperature. Δg12 and Δg21 are the two model parameters. The
3.2. NRTL model The general thermodynamic model for expressing the solid-liquid equilibrium can be written as per Eq. (4) [11,12]. ZT ZT ΔHfus 1 1 1 1 ΔCp dT − − ln γi − ΔCpdT þ ln xN ¼ R Tm T RT R T Tm
ð4Þ
Tm
where R, ΔfusH, Tm, γi, xN, and T are the gas constant, the enthalpy of fusion, the melting point of the solute, the activity coefficient, the equilibrium mole fraction of the solute, and the absolute temperature, respectively. In Eq. (4), the last 2 parts are generally much lower in value than the first two due to the negligible value of ΔCp. Therefore, Eq. (4) can be simplified into Eq. (5) [12]. ln xN ¼
ΔHfus 1 1 − − ln γi R Tm T
ð5Þ
γi can be calculated by many thermodynamic models. Among all these models, the NRTL model is widely used. According to NRTL model, in mono-solvent systems, the activity coefficient of γi can be calculated by Eqs. (6)–(10) [13]. " ln γ1 ¼
x22
τ 21 G221
ðx1 þ G21 x2 Þ2
þ
τ 12 G12 ðx2 þ G12 x1 Þ2
# ð6Þ
Fig. 4. Powder X-ray diffraction (p-XRD) patterns of products after solubility measurements in single solvent systems. The p-XRD patterns from top to bottom are the undissolved phase in water, n-propanol, isopropanol, methanol, ethanol, acetonitrile, acetone, N, N-dimethylformamide and formamide.
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Fig. 7. Thermal analysis (TGA/DSC) data of γ - form 5-nitrofurazone.
Fig. 5. Powder X-ray diffraction patterns of products after solubility measurements in N, Ndimethylformamide and water binary solvents. The p-XRD patterns from top to bottom are the undissolved phase in binary solvents mixture from xD = 0.1000 to xD = 0.9005 with a increment about 0.1000.
Table 2 Experimental mole fraction solubility and calculated mole fraction solubility of 5nitrofurazone (γ - form) based on the modified Apelblat equation and NRTL model in the investigated mono-solvents systems from 278.15 K to 313.15 K (p = 101.3 kPa).a,b T/K
parameter α in Eqs. (7) and (8) represents the non-randomness of the system and is an adjustable constant. In binary solvent systems, the activity coefficient γi can be calculated by Eq. (11) [12].
lnγi ¼
Gij x j þ Gkj xk τ ji Gji x j þ τki Gkj xk τ ij Gij x j 2 þ Gij Gkj x j xk τji −τ ki þ 2 2 xi þ Gijx j þ Gki xk xi þ Gij xi þ Gkj xk 2 τik Gkxk þ Gik Gjk x j xk τ ik −τjk þ 2 xk þ Gik xi þ Gjk xk
ð11Þ
Fig. 6. Powder X-ray diffraction patterns of products after solubility measurements in N, Ndimethylformamide and isopropanol, The p-XRD patterns from top to bottom are the undissolved phase in the binary solvent mixtures from xD = 0.1000 to xD = 0.9000 with a increment about 0.1000.
104xNexp
ABC
NRTL
104xNcal
104xNcal
0.8532 1.061 1.295 1.492 1.879 2.355 2.849 3.679
0.8681 1.041 1.259 1.535 1.885 2.331 2.901 3.632
0.7853 0.9931 1.248 1.558 1.935 2.388 2.932 3.581
Ethanol 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15
Isopropanol 278.15 0.7039 283.15 0.9569 288.15 1.128 293.15 1.312 298.15 1.686 303.15 2.164 308.15 2.623 313.15 3.445
0.7312 0.8949 1.102 1.366 1.702 2.131 2.680 3.385
Water 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15
0.1310 0.1618 0.1880 0.2286 0.2925 0.3660 0.4503 0.5887
Methanol 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 Formamide 278.15 283.15 288.15 293.15
Propanol 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15
T/K
104xNexp
ABC
NRTL
104xNcal
104xNcal
0.6966 0.8331 1.005 1.212 1.433 1.755 2.133 2.533
0.6961 0.8348 1.003 1.206 1.452 1.750 2.111 2.548
0.6714 0.8226 1.003 1.217 1.470 1.768 2.117 2.525
0.6629 0.8529 1.089 1.382 1.741 2.179 2.711 3.354
Acetonitrile 278.15 0.8460 283.15 1.026 288.15 1.227 293.15 1.462 298.15 1.762 303.15 2.112 308.15 2.475 313.15 2.882
0.8446 1.023 1.232 1.476 1.760 2.088 2.467 2.901
0.8520 1.027 1.233 1.475 1.757 2.084 2.464 2.903
0.1323 0.1575 0.1902 0.2328 0.2884 0.3615 0.4578 0.5854
0.1156 0.1480 0.1882 0.2379 0.2988 0.3732 0.4636 0.5727
Acetone 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15
2.994 3.425 3.909 4.452 5.060 5.740 6.497 7.341
2.988 3.422 3.908 4.453 5.063 5.743 6.501 7.343
1.484 1.724 2.012 2.332 2.821 3.260 3.867 4.398
1.474 1.727 2.024 2.371 2.778 3.253 3.808 4.457
1.446 1.714 2.025 2.384 2.797 3.271 3.814 4.432
N, N-Dimethylformamide 278.15 219.4 217.9 283.15 227.0 227.3 288.15 235.4 237.7 293.15 246.2 249.2 298.15 264.9 261.7 303.15 279.6 275.4 308.15 289.1 290.4 313.15 305.0 306.6
221.9 227.8 235.7 246.0 259.8 274.7 290.5 309.9
16.86 19.11 20.84 23.87
16.82 18.94 21.27 23.83
16.88 18.97 21.28 23.82
298.15 303.15 308.15 313.15
26.62 29.70 33.08 36.80
2.980 3.447 3.916 4.429 5.120 5.677 6.471 7.384
26.74 29.83 33.45 36.43
26.64 29.72 33.10 36.78
a Standard uncertainty is u(T) = 0.05 K, u(p) = 0.3 kPa. Relative standard uncertainty is ur(x1) = 0.05. b xNexp is the experimental mole fraction solubility, xNcal is the calculated mole fraction solubility of 5-nitrofurazone (γ - form).
X. Li et al. / Journal of Molecular Liquids 275 (2019) 815–828
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Table 4 Model parameters of NRTL model for 5-nitrofurazone (γ – form) in single solvent systems (p = 101.3 kPa).a,b,c Parameters
10−4Δg12
10−4Δg21
ARD%
106RMSD
Propanol Isopropanol water Methanol Ethanol Acetonitrile Acetone N, N-Dimethylformamide Formamide Overall ARD% Overall 106RMSD
2.798844 2.391687 3.426946 4.435531 3.816274 4.186797 5.260288 −2.589181 4.778898
−0.8373013 −0.6959889 −0.4996499 −1.150401 −0.9451692 −1.021375 −1.305321 3.970817 −1.721175 1.957 41.29
4.047 4.421 4.281 0.6557 1.230 0.6268 0.6319 0.9395 0.7778
6.757 6.904 1.139 1.765 1.804 1.409 3.802 322.5 25.55
a The values of Δg12, Δg21 were obtained by correlating the experimental data with the NRTL model. b ARD is average relative deviation, RMSD is the root-mean-square deviation. c Standard uncertainty is u(p) = 0.3 kPa.
Fig. 8. Mole fraction solubility of 5-nitrofurazone (γ – form) in seven mono-solvent solutions at temperatures ranging from 278.15 K to 313.15 K.
τij ¼
Δg ij RT
ð13Þ
α ij ¼ α ji
ð14Þ
Δgij is the model parameter, α is an adjustable constant between 0 and 1. 3.3. λh equation The λh equation is an empirical equation and it can be used to describe the relationship between temperature T and solubility (xN). The equation can be described as Eq. (15) [13–15]. 1−xN 1 1 ln 1 þ λ ¼ λh − T Tm xN
ð15Þ
where λ and h are two model parameters in the equation, T is absolute temperature and Tm is the melting temperature of solute. 3.4. Thermodynamics of mixing and dissolution Fig. 9. Mole fraction solubility of 5-nitrofurazone (γ – form) in N, N-dimethylformamide and formamide at temperatures ranging from 278.15 K to 313.15 K.
where, i, j and k are the component of the solution system, Gij, Gji, Gik, Gjk, Gkj, Gki, τij, τji, τik, τjk, τkj, and τki are parameters which can be calculated by Eqs. (12)–(14): Gij ¼ eð−αij τij Þ
ð12Þ
To investigate the mixing properties of non-ideal binary solution mixtures, the mixing Gibbs free energy, mixing enthalpy, and mixing entropy can be calculated through Eqs. (16)–(18) [16–18]. Δmix G ¼ GE þ ΔGid
ð16Þ
Δmix S ¼ SE þ ΔSid
ð17Þ
Table 3 Model parameters of modified Apelblat model for 5-nitrofurazone (γ – form) in single solvent systems (p = 101.3 kPa).a,b,c Parameters
A
B
Propanol Isopropanol Water Methanol Ethanol Acetonitrile Acetone N, N-Dimethylformamide Formamide Overall ARD% Overall 106RMSD
−325.8336 −290.6613 −443.7778 −118.5058 −169.5436 −23.67748 −53.49451 −87.24896 −37.97374
10,959.51 9189.055 15,960.27 2520.108 4337.738 −1953.508 123.1961 2963.894 −244.9943
a b c
The values of A, B, C were obtained by correlating the experimental data with the Apelblat equation. ARD is average relative deviation, RMSD is the root-mean-square deviations. Standard uncertainty is u(p) = 0.3 kPa.
C 49.23107 44.08219 66.65848 17.87854 25.65245 3.788349 7.984485 12.92911 5.768670 1.143 32.10
ARD%
106RMSD
1.721 2.894 1.439 0.9672 0.5304 0.5113 0.6332 0.8346 0.7609
3.418 4.529 0.4279 3.638 1.194 1.243 3.753 246.1 24.59
820
X. Li et al. / Journal of Molecular Liquids 275 (2019) 815–828
Table 5 Experimental equilibrium mole fraction (solubility) and calculated mole fraction solubility of 5-nitrofurazone (γ - form) in binary solvent mixtures from 278.15 K to 313.15 K (p = 101.3 kPa).a,b xD
278.15 K
283.15 K
288.15 K
293.15 K
298.15 K
303.15 K
308.15 K
313.15 K
0.1000 0.2000 0.3001 0.4001 0.5000 0.6002 0.7003 0.8004 0.9005
0.4395 1.525 5.008 13.92 31.77 57.32 95.54 135.1 178.6
0.5504 1.903 6.191 16.40 35.77 63.00 103.5 139.5 182.7
0.6872 2.390 7.296 18.72 38.87 68.66 109.7 151.2 196.3
0.8211 2.857 8.432 20.23 43.21 74.92 116.2 158.3 205
1.047 3.597 10.39 24.53 49.08 81.59 126.2 169.2 215.5
1.356 4.685 13.05 29.09 55.70 91.60 137.8 181.0 228.3
1.735 5.805 15.08 34.35 62.38 100.8 148.6 194.4 241.6
2.208 7.415 18.72 40.08 73.17 112.6 161.9 208.4 256.5
xND/W,NRTL 0.1000d 0.2000 0.3000 0.4000 0.5004 0.6000 0.7005 0.7999 0.9000
0.4179 1.994 6.330 15.74 33.15 59.61 96.62 137.6 181.5
0.5217 2.344 7.204 17.50 36.10 63.76 101.9 141.3 184.7
0.6503 2.769 8.208 19.51 39.21 68.63 107.6 149.3 193.1
0.8073 3.269 9.380 21.59 43.26 74.54 114.5 156.9 201.6
1.005 3.892 10.91 24.82 48.48 81.49 124.1 167.6 212.6
1.252 4.679 12.85 28.62 54.74 90.94 135.7 180.2 226.3
1.558 5.614 14.94 33.23 61.88 101.2 148.5 195.3 242.3
1.940 6.810 17.82 38.72 71.96 114.2 164.1 212.7 261.0
xND/W,λh 0.1000e 0.2000 0.3001 0.4001 0.5000 0.6002 0.7003 0.8004 0.9005
0.3896 1.382 4.749 13.09 30.23 55.86 93.88 131.8 175.3
0.5110 1.797 5.877 15.56 34.51 62.05 101.7 140.9 185.1
0.6640 2.315 7.221 18.39 39.25 68.74 110.0 150.4 195.4
0.8552 2.957 8.812 21.63 44.48 75.95 118.9 160.5 206.1
1.092 3.747 10.68 25.30 50.23 83.73 128.2 171.0 217.4
1.384 4.712 12.88 29.47 56.53 92.10 138.1 182.2 229.2
1.741 5.883 15.43 34.17 63.45 101.1 148.7 193.9 241.5
2.174 7.293 18.39 39.45 71.01 110.8 159.8 206.3 254.6
xND/I,exp 0.1000f 0.2000 0.3001 0.4001 0.5000 0.6002 0.7003 0.8004 0.9005
1.331 3.517 7.844 13.90 25.30 43.45 69.69 108.8 158.3
1.535 3.936 8.463 15.18 26.84 46.59 73.14 113.6 165.0
1.699 4.300 9.374 15.94 28.77 48.53 75.87 119.5 172.6
2.064 4.991 10.21 17.69 31.05 51.87 79.02 122.5 178.2
2.515 5.773 11.61 20.03 33.44 55.49 84.72 129.8 185.5
2.919 6.687 12.5 21.74 35.41 57.78 89.73 136.3 194.7
3.545 7.616 14.29 24.43 38.88 62.43 95.09 140.6 207.0
4.253 8.863 15.91 26.77 41.70 66.74 99.98 149.4 215.7
xND/I,NRTL 0.1000g 0.2000 0.3001 0.4001 0.5000 0.6002 0.7003 0.8004 0.9005
1.502 3.597 7.607 14.50 26.14 44.37 71.67 110.9 163.0
1.744 4.009 8.228 15.41 27.30 46.05 73.49 113.0 165.6
2.027 4.487 9.001 16.44 28.85 47.93 75.89 116.7 170.2
2.377 5.080 9.890 17.83 30.80 50.66 79.15 120.6 175.7
2.797 5.779 11.01 19.54 33.11 53.98 83.95 127.0 183.4
3.286 6.605 12.22 21.40 35.69 57.49 89.33 134.3 193.4
3.884 7.561 13.75 23.72 39.01 62.21 95.67 142.0 206.2
4.596 8.710 15.48 26.28 42.62 67.47 102.7 152.5 219.4
xND/I,λh 0.1000h 0.2000 0.3001 0.4001 0.5000 0.6002 0.7003 0.8004 0.9005
1.204 3.288 7.527 13.36 24.88 43.24 68.69 108.6 157.2
1.464 3.828 8.425 14.84 26.85 46.04 72.50 113.5 164.4
1.768 4.435 9.402 16.44 28.94 48.97 76.49 118.7 171.8
2.122 5.116 10.46 18.17 31.16 52.06 80.68 124.1 179.6
2.533 5.876 11.61 20.04 33.50 55.31 85.07 129.7 187.8
3.007 6.724 12.86 22.04 35.99 58.74 89.67 135.7 196.3
3.552 7.667 14.21 24.21 38.63 62.35 94.52 141.9 205.2
4.175 8.712 15.67 26.53 41.42 66.15 99.61 148.4 214.6
xND/W,exp c
a b c d e f g h
Standard uncertainty is u(T) = 0.05 K, u(p) = 0.3 kPa. Relative standard uncertainty is ur(x1) = 0.05. xD is the initial mole fraction of N, N-dimethylformamide in the binary solvents mixture. xND/W,exp is the experimental mole fraction solubility of 5-nitrofurazone (γ - form) in N, N-dimethylformamide + water binary solvents. xND/W,NRTL is the calculated mole fraction solubility of 5-nitrofurazone (γ - form) in N, N-dimethylformamide + water binary solvents correlated by NRTL model. xND/W,λh is the calculated mole fraction solubility of 5-nitrofurazone (γ - form) in N, N-dimethylformamide + water binary solvents correlated by λh equation. xND/I,exp is the experimental mole fraction solubility of 5-nitrofurazone (γ - form) in N, N-dimethylformamide + isopropanol binary solvents. xND/I,NRTL is the calculated mole fraction solubility of 5-nitrofurazone (γ - form) in N, N-dimethylformamide + isopropanol binary solvents correlated by NRTL model. xND/I,λh is the calculated mole fraction solubility of 5-nitrofurazone (γ - form) in N, N-dimethylformamide + isopropanol binary solvents correlated by λh equation.
X. Li et al. / Journal of Molecular Liquids 275 (2019) 815–828
821
Fig. 10. Mole fraction solubility of 5-nitrofurazone (γ - form) in N, N-dimethylformamide and water mixtures at temperatures ranging from 278.15 K to 313.15 K.
Δmix H ¼ H E þ ΔHid
ð18Þ
where ΔGid, ΔSid and ΔHid stand for the mixing properties of the ideal solution, and GE, SE and HE are the excess properties of the real solution.
The mixing properties for an ideal solution can be described as per Eqs. (19)–(21) [17,18]. ΔGid ¼ RT
n X
xN ln xN
j¼1
Fig. 11. Mole fraction solubility of 5-nitrofurazone (γ - form) in N, N-dimethylformamide and isopropanol mixtures at temperatures ranging from 278.15 K to 313.15 K.
ð19Þ
822
X. Li et al. / Journal of Molecular Liquids 275 (2019) 815–828
ΔSid ¼
ΔGid T
ð20Þ
ΔH id ¼ 0
ð21Þ
where, xN is the mole fraction of each component in solution. The term n represents the number of components in the system. Hence, in monosolvent systems, n has a value of 2 and n has a value of 3 for ternary systems (i.e. those with two solvents). For non-ideal solutions, the excess mixing properties can be calculated using Eqs. (22)–(24) [17,18]. GE ¼ RT
n X
x j ln γ j
ð22Þ
j¼1
SE ¼
E
H E −GE T
H ¼ −RT
2
Table 6 Model parameters of NRTL model for 5-nitrofurazone (γ - form) in binary solvent mixtures (p = 101.3 kPa).a,b,c Parameters Δgij Δgik Δgji Δgjk Δgki Δgkj 104RMSD ARD%
N, N-Dimethylformamide + water
N, N-Dimethylformamide + isopropanol
−8212.134 −3700.461 19,463.84 −4089.048 57,643.67 4371.924 0.4944 4.506
−8275.720 −6345.898 20,061.00 −13,842.27 23,129.36 7440.413 1.284 2.983
a The values of Δgij, Δgik, Δgji, Δgjk, Δgki, and Δgkj were obtained by correlating the experimental solubility data with NRTL model. b ARD is the average relative deviation, RMSD is the root-mean-square deviations. c Standard uncertainty is u(p) = 0.3 kPa.
ð23Þ
n X
xN
∂ ln γ j
j¼1
∂T
! ð24Þ p;x
4.1. Identification and characterization of materials
where γj is the activity coefficient of component j in non-ideal solution, which can be calculated from the NRTL model. Furthermore, the thermodynamic dissolution properties can be calculated based on the mixed thermodynamic properties. The thermodynamic properties of the dissolution process of compounds equate to the summation of thermodynamic properties of heating, melting, cooling, and mixing process [13,18]. heating
fusion
SoluteðsolidÞ at T → SoluteðsolidÞ at T m → SoluteðliquidÞ at T m cooling
4. Results and discussion
mixing
→ SoluteðliquidÞ at T → SoluteðsolutionÞ at T
The p-XRD data of 5-nitrofurazone from the Cambridge Crystallographic Data Centre (WERVEU01 for form β and WERVEU02 for form γ) were compared with the p-XRD data of purchased materials and the solids prepared by solution crystallization in this work. The results are shown in Fig. 3. It can be found that the purchased material is the β polymorphic form of 5-nitrofurazone while the products prepared in this work via recrystallization are the γ - form. The UV spectroscopic method developed in the Experimental section (2.4), was used to measure the purity of the γ - form product, which was determined to be 98.65%, via the UV method.
The entire dissolution thermodynamics can thus be expressed as: Δdis M ¼ xN ðΔheat M þ Δfus M þ Δcool M Þ þ Δmix M
ð25Þ
where M can be replaced by Gibbs energy (G), enthalpy (H) and entropy (S). xN is the mole fraction of solute and the value of ΔheatH, ΔcoolH, ΔheatS and ΔcoolS can be calculated using Eqs. (26)–(29): Δheat H ¼ C pðsÞ ðT m −T Þ
ð26Þ
Δcool H ¼ C pðlÞ ðT−T m Þ
ð27Þ
Δheat S ¼ C pðsÞ ln
Tm T
ð28Þ
Δcool S ¼ C pðlÞ ln
T Tm
ð29Þ
The Cp(l) and Cp(s) are the constant pressure heat capacity of liquid and solid, respectively, which have almost the same value because of the almost invariable volume of 5-nitrofurazone in the heating and cooling process, Therefore, the value of (ΔheatH + ΔcoolH), (ΔheatS + ΔcoolS) can be considered as zero. And the following equations can be used to calculate the dissolution thermodynamics: Δdis H ¼ xN Δfus H þ Δmix H
ð30Þ
Δdis S ¼ xN Δfus S þ Δmix S
ð31Þ
Δdis G ¼ Δdis H−TΔdis S
ð32Þ
The value of Tm, ΔfusS and ΔfusH were calculated by a group contributions method to be 508.9 K, 64.79 J·K−1·mol−1, 32,971 J·mol−1.
Table 7 Model parameters of λh equation for 5-nitrofurazone (γ - form) in binary solvent mixtures (p = 101.3 kPa).a,b,c 10−4 h
ARD%
104RMSD
N, N-Dimethylformamide + water 0.1000 4.095132 0.2000 11.55048 0.3001 10.99111 0.4001 10.39398 0.5000 7.746674 0.6002 6.107469 0.7003 4.125709 0.8004 3.079146 0.9005 1.881298 Overall ARD Overall 104RMSD
10.42379 3.573820 3.040694 2.588456 2.596644 2.485094 2.494496 2.381740 2.347488 2.349 1.005
4.295 3.664 3.001 3.288 2.599 1.329 1.151 1.036 0.7739
3.498e−2 0.1069 0.2878 0.7605 1.301 1.240 1.641 1.849 1.825
N, N-Dimethylformamide + isopropanol 0.1000 1.734135 0.2000 1.451138 0.3000 1.034229 0.4000 1.431064 0.5004 0.8951634 0.6000 0.7714654 0.7005 0.6710267 0.7999 0.3307270 0.9000 0.4835527 Overall ARD Overall 104RMSD
17.60457 16.10280 15.95473 10.54143 10.44128 8.119306 6.199301 4.885649 3.354396 1.422 0.5186
3.355 2.450 1.535 1.898 0.7263 0.7417 0.8329 0.5475 0.7089
0.07381 0.1300 0.2128 0.3683 0.2960 0.4849 0.8002 0.8857 1.416
Parameters
102λ
a The values of λ, h were obtained by correlating the experimental solubility data with the λh equation. b ARD is the average relative deviation, RMSD is the root-mean-square deviations. c Standard uncertainty is u(p) = 0.3 kPa.
X. Li et al. / Journal of Molecular Liquids 275 (2019) 815–828 Table 8 The mixing thermodynamic properties of 5-nitrofurazone (γ - form) in mono-solvent systems (p = 101.3 kPa).a,b ΔmixG (J·mol−1)
ΔmixS (J·K−1·mol−1)
ΔmixH (J·mol−1)
Propanol 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15
−1.456 −1.785 −2.151 −2.465 −3.045 −3.741 −4.456 −5.597
0.2047 0.2300 0.2512 0.2561 0.2811 0.3013 0.3039 0.3153
55.49 63.34 70.24 72.61 80.77 87.60 89.19 93.14
Isopropanol 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15
−1.205 −1.599 −1.874 −2.170 −2.733 −3.434 −4.105 −5.241
9.504e−3 1.735e−2 4.183e−2 7.303e−2 0.1245 0.1983 0.2862 0.4349
1.438 3.313 10.18 19.24 34.37 56.67 84.09 130.9
Water 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15
−0.2224 −0.2713 −0.3140 −0.3775 −0.4734 −0.5819 −0.7044 −0.8956
1.082e−2 8.927e−3 5.293e−3 2.256e−3 1.050e−2 2.254e−2 3.917e−2 6.592e−2
2.787 2.256 1.211 0.284 2.657 6.253 11.36 19.75
Methanol 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15
−2.553 −2.925 −3.363 −3.841 −4.545 −5.170 −6.007 −6.732
1.613 1.821 2.063 2.320 2.721 3.046 3.497 3.845
446.0 512.6 591.1 676.3 806.7 918.2 1071 1197
Ethanol 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15
−1.197 −1.412 −1.678 −1.991 −2.321 −2.785 −3.316 −3.870
0.4589 0.5245 0.6037 0.6932 0.7789 0.9045 1.040 1.165
126.5 147.1 172.3 201.2 229.9 271.4 317.1 361.0
Acetonitrile 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15
−1.462 −1.742 −2.050 −2.403 −2.841 −3.341 −3.850 −4.411
0.7335 0.8585 0.9896 1.135 1.316 1.515 1.703 1.899
202.6 241.3 283.1 330.4 389.5 455.9 520.8 590.2
Acetone 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15
−5.146 −5.847 −6.537 −7.277 −8.247 −9.016 −10.08 −11.28
4.597 5.214 5.805 6.430 7.276 7.893 8.798 9.811
1274 1471 1666 1878 2161 2384 2701 3061
N, N-Dimethylformamide 278.15 −373.3 283.15 −379.1 288.15 −386.1 293.15 −396.3 298.15 −417.0 303.15 −431.8
681.8 680.0 680.0 686.2 712.7 726.4
1.893e5 1.921e5 1.956e5 2.008e5 2.121e5 2.198e5
T (K)
823
Table 8 (continued) ΔmixG (J·mol−1)
ΔmixS (J·K−1·mol−1)
ΔmixH (J·mol−1)
308.15 313.15
−439.5 −455.3
725.6 739.8
2.231e5 2.312e5
Formamide 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15
−29.12 −32.43 −34.92 −39.19 −43.14 −47.28 −52.02 −55.83
30.04 33.45 35.83 40.30 44.31 48.50 53.34 56.97
8326 9439 1.029e4 1.177e4 1.317e4 1.466e4 1.639e4 1.778e4
T (K)
a
The values of ΔmixG, ΔmixH and ΔmixS were calculated by Eqs. (16)–(18). The combined expanded uncertainties U are Uc(ΔHm) = 0.060ΔHm, Uc(ΔSm) = 0.065ΔSm, Uc(ΔGm) = 0.065ΔGm (0.95 level of confidence). b
The p-XRD patterns of 5-nitrofurazone in different mono-solvent systems and binary solvent mixtures after solubility measurement experiments are shown in Figs. 4, 5 and 6. It can be seen that all the samples remain as γ - form within detectable limits of p-XRD. No measurable polymorphic transformation during the solubility experiments was observed. The TGA and DSC curves of the γ - form of 5-nitrofurazone are shown in Fig. 7, with a small endothermic peak at 506.76 K and a sharp exothermic peak at 519.25 K. The endothermic peak corresponds to the melting of the γ - form of 5-nitrofurazone while the exothermic peak corresponds to chemical decomposition of 5-nitrofurazone. The melt and decomposition peaks are overlapping, indicating that 5nitrofurazone form γ undergoes immediate decomposition when melted [19]. For this reason, it was not possible to get accurate enthalpy of fusion and melting temperature through TGA and DSC. Jain et al. [20,21] proposed a method of combination of additive group contributions and non-additive molecular parameters to estimate melting temperature. This method has been applied to over 2200 compounds. According to this method, the melting temperature and enthalpy of fusion can be estimated by Eqs. (33)–(36): T m ¼ Δfus H=Δfus S Δfus H ¼
X
ni mi þ
ð33Þ X
n jm j
ð34Þ
Δfus S ¼ 50−R ln σ þ R ln ϕ
ð35Þ
ϕ ¼ 2:435SP3þ0:5SP2þ0:5RING−1
ð36Þ
where ΔfusH and ΔfusS are the enthalpy and entropy of fusion respectively; ni is the number of times a group i appears in a compound, mi is the contribution of group i to the enthalpy of melting. nj is the number of times a proximity factor j appears; mj is the corresponding contribution of the proximity factor j to the enthalpy of melting; σ refers to the rotational symmetry number; ϕ indicates the molecular flexibility which is an exponential function of the chain length and can be calculated by Eq. (19). SP3 stands for the number of non-terminal, non-ring sp3 atoms; SP2 represents the number of non-terminal, non-ring sp2 atoms; RING is the number of single or fused aromatic ring systems. And when applied to aliphatic cyclic compounds, the −1 in Eq. (19) should be replaced with −3. Using this model, the melting temperature of the γ – form of 5-nitrofurazone was calculated to be 508.9 K, which seems qualitatively consistent with Fig. 7 and the enthalpy and entropy of fusion were calculated to be 32,971 J·mol−1 and 64.79 J·K−1·mol−1, respectively.
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X. Li et al. / Journal of Molecular Liquids 275 (2019) 815–828
Table 9 The mixing thermodynamic properties of 5-nitrofurazone (γ - form) in binary solvent mixtures (p = 101.3 kPa).a,b,c xDW
xDI
N, N-Dimethylformamide + water ΔmixG (kJ·mol−1)
ΔmixS (J·K−1·mol−1)
N, N-Dimethylformamide + isopropanol ΔmixG (kJ·mol−1)
ΔmixS (J·K−1·mol−1)
ΔmixH (kJ·mol−1)
5.945 63.84 137.1 206.2 261.9 295.6 308.7 291.6 252.4
T = 278.15 K 0.1000 0.2000 0.3000 0.4000 0.5004 0.6000 0.7005 0.7999 0.9000
−3.569 −5.383 −6.213 −6.395 −6.119 −5.503 −4.604 −3.484 −2.123
2521 4537 5678 6037 5800 5137 4171 3035 1790
697.7 1257 1573 1673 1607 1423 1155 840.8 495.7
21.21 227.7 491.4 742.8 945.9 1070 1120 1042 895.8
5.094 63.02 137.3 208.2 265.7 300.8 315.0 293.5 252.4
T = 283.15 K 0.1000 0.2000 0.3000 0.4000 0.5004 0.6000 0.7005 0.7999 0.9000
−3.528 −5.338 −6.177 −6.373 −6.108 −5.503 −4.611 −3.495 −2.135
2462 4453 5596 5972 5752 5108 4151 3022 1779
693.6 1255 1578 1685 1623 1441 1171 852.1 501.7
−0.9209 −1.475 −1.851 −2.085 −2.191 −2.172 −2.027 −1.730 −1.249
17.94 221.1 483.3 735.9 939.1 1068 1116 1052 908.1
4.248 62.23 137.4 210.0 268.4 305.7 319.5 301.5 260.4
T = 288.15 K 0.1000 0.2000 0.3000 0.4000 0.5004 0.6000 0.7005 0.7999 0.9000
−3.489 −5.295 −6.144 −6.351 −6.098 −5.502 −4.617 −3.507 −2.148
2405 4371 5517 5907 5706 5075 4129 3010 1771
689.5 1254 1584 1696 1638 1457 1185 863.8 508.1
T = 293.15 K 0.1000 0.2000 0.3001 0.4001 0.5000 0.6002 0.7003 0.8004 0.9005
−0.9313 −1.490 −1.870 −2.106 −2.216 −2.198 −2.051 −1.751 −1.266
14.77 214.6 475.3 726.6 935.7 1068 1112 1047 904.6
3.398 61.41 137.5 210.9 272.1 310.9 324.0 305.3 263.9
T = 293.15 K 0.1000 0.2000 0.3000 0.4000 0.5004 0.6000 0.7005 0.7999 0.9000
−3.453 −5.255 −6.112 −6.331 −6.090 −5.504 −4.624 −3.517 −2.159
2351 4293 5441 5845 5662 5046 4108 2992 1757
685.7 1253 1589 1707 1654 1474 1200 873.5 513.0
T = 298.15 K 0.1000 0.2000 0.3001 0.4001 0.5000 0.6002 0.7003 0.8004 0.9005
−0.9420 −1.506 −1.890 −2.131 −2.242 −2.225 −2.079 −1.777 −1.286
11.76 208.7 469.4 724.9 936.2 1068 1118 1052 905.4
2.565 60.72 138.1 214.0 276.9 316.1 331.3 311.9 268.7
T = 298.15 K 0.1000 0.2000 0.3000 0.4000 0.5004 0.6000 0.7005 0.7999 0.9000
−3.419 −5.218 −6.082 −6.313 −6.083 −5.506 −4.634 −3.531 −2.172
2299 4218 5368 5787 5618 5017 4092 2982 1747
682.1 1252 1594 1719 1669 1490 1215 885.5 518.8
T = 303.15 K 0.1000 0.2000 0.3001 0.4001 0.5000 0.6002 0.7003 0.8004 0.9005
−0.9529 −1.522 −1.911 −2.155 −2.269 −2.255 −2.109 −1.804 −1.309
8.894 203.5 465.1 723.4 937.8 1076 1127 1058 911.2
1.743 60.17 139.1 217.1 282.0 323.9 339.4 318.9 274.9
T = 303.15 K 0.1000 0.2000 0.3000 0.4000 0.5004 0.6000 0.7005 0.7999 0.9000
−3.387 −5.182 −6.054 −6.295 −6.076 −5.507 −4.644 −3.544 −2.187
2250 4146 5295 5727 5573 4985 4074 2970 1740
678.6 1252 1599 1730 1683 1506 1230 896.7 525.3
T = 308.15 K 0.1000 0.2000 0.3001 0.4001 0.5000 0.6002 0.7003 0.8004 0.9005
−0.9639 −1.539 −1.932 −2.181 −2.297 −2.285 −2.138 −1.833 −1.332
6.144 198.4 459.1 723.0 938.7 1080 1131 1067 917.0
0.9293 59.61 139.5 220.6 287.0 330.6 346.5 326.8 281.2
T = 308.15 K 0.1000 0.2000 0.3000 0.4000 0.5004 0.6000 0.7005 0.7999 0.9000
−3.357 −5.148 −6.028 −6.280 −6.071 −5.511 −4.654 −3.556 −2.205
2202 4077 5227 5671 5532 4958 4056 2953 1738
675.3 1251 1605 1741 1699 1522 1245 906.5 533.3
T = 278.15 K 0.1000 0.2000 0.3001 0.4001 0.5000 0.6002 0.7003 0.8004 0.9005
−0.9005 −1.444 −1.814 −2.042 −2.144 −2.121 −1.977 −1.684 −1.213
24.61 234.7 499.3 748.8 949.3 1070 1117 1054 911.9
T = 283.15 K 0.1000 0.2000 0.3001 0.4001 0.5000 0.6002 0.7003 0.8004 0.9005
−0.9106 −1.459 −1.832 −2.064 −2.168 −2.146 −2.003 −1.702 −1.224
T = 288.15 K 0.1000 0.2000 0.3001 0.4001 0.5000 0.6002 0.7003 0.8004 0.9005
ΔmixH (kJ·mol−1)
X. Li et al. / Journal of Molecular Liquids 275 (2019) 815–828
825
Table 9 (continued) xDW
xDI
N, N-Dimethylformamide + water ΔmixG (kJ·mol
T = 313.15 K 0.1000 0.2000 0.3001 0.4001 0.5000 0.6002 0.7003 0.8004 0.9005
−1
ΔmixS (J·K
)
−0.9752 −1.557 −1.954 −2.207 −2.329 −2.317 −2.170 −1.862 −1.357
−1
·mol
3.515 194.2 456.5 723.2 949.2 1090 1141 1075 925.2
−1
)
−1
ΔmixH (kJ·mol
) T = 313.15 K 0.1000 0.2000 0.3000 0.4000 0.5004 0.6000 0.7005 0.7999 0.9000
0.1255 59.24 141.0 224.3 294.9 339.1 355.2 334.7 288.4
N, N-Dimethylformamide + isopropanol ΔmixG (kJ·mol−1)
ΔmixS (J·K−1·mol−1)
ΔmixH (kJ·mol−1)
−3.329 −5.117 −6.003 −6.265 −6.066 −5.515 −4.664 −3.572 −2.220
2157 4010 5159 5615 5490 4930 4036 2944 1729
672.2 1251 1610 1752 1713 1538 1259 918.3 539.1
a
The values of ΔmixG, ΔmixH and ΔmixS are calculated by Eqs. (16)–(18). The combined expanded uncertainties U are Uc(ΔHm) = 0.060ΔHm, Uc(ΔSm) = 0.065ΔSm, Uc(ΔGm) = 0.065ΔGm (0.95 level of confidence). c xDW and xDIare the mole fraction of N, N-dimethylformamide in the initial binary solvents of N, N-dimethylformamide + water and N, N-dimethylformamide + isopropanol, respectively. b
4.2. Solubility of 5-nitrofurazone (γ – form) in single solvent systems Solubility data of the γ – form of 5-nitrofurazone in water, npropanol, isopropanol, methanol, ethanol, acetonitrile, acetone, N, Ndimethylformamide and formamide at temperatures from 278.15 K to 313.15 K were measured experimentally as outlined in Section 2.4. The results are listed in Table 2 and are graphically shown in Fig. 8 for water, n-propanol, isopropanol, methanol, ethanol, acetonitrile, acetone, and Fig. 9 for N, N-dimethylformamide and formamide. Two graphs were used to enable the individual solvent trends to be discernable in the plots despite to the large increase in saturation mole fraction shown across the investigated temperature range for formamide and particularly N, N-dimethylformamide. The solubility data of 5nitrofurazone (γ – form) in these selected single solvent systems increases with increasing temperature in all cases. The solubility of 5nitrofurazone in N, N-dimethylformamide is the highest and second highest in Formamide. The solubility in each of the other solvents is between 40 times to 1600 times lower than N, N-dimethylformamide. Hence, N, N-dimethylformamide would be a good choice of solvent for the crystallization of 5-nitrofurazone, offering the highest volumetric productivity, and minimizing solvent consumption. All of the other solvents with the exception formamide show potential for use as antisolvents. It is obviously that solubilities of 5-nitrofurazone don't follow the rule of thumb of “like dissolves like” at given temperature. This means that the dissolution of 5-nitrofurazone is a complex process which will be affected by many factors, such as polarity and ability to form hydrogen bonds. The modified Apelblat equation and the NRTL model were fitted to the solubility of 5-nitrofurazone in these single solvent systems The average relative deviation (ARD) and the root-mean-square deviations (RMSD) were used to evaluate reliability and accuracy of the models [6]:
ARD ¼
N exp cal
1X
xi −xi
N i¼1 xexp i "
RMSD ¼
2 1 N exp ∑ x −xcal i N i¼1 i
The value of ARD and RMSD are shown in Tables 3 and 4. The ARD% of the modified Apelblat model in all selected solvents are under 3%, while ARD% was under 5% for NRTL model in all cases. Therefore, the two models can give satisfactory correlation to experimental data, with the Apelblat model providing a better fit of experimental results than NRTL model. 4.3. Solubility of 5-nitrofurazone (γ – form) in binary solvent mixtures The experimental solubility data of the γ – form of 5-nitrofurazone in mixtures of N, N-dimethylformamide and water/isopropanol are listed in Table 5 and graphically shown in Figs. 10 and 11. The equilibrium concentration (solubility) data of 5-nitrofurazone in the binary solvent mixtures are a function of both the temperature and solvent composition. The solubility in the binary solvent mixtures was found to increase with temperature and mole fraction of N, Ndimethylformamide. No local maximum in terms of solubility was found in the concentration ranges investigated that can often describe a local synergistic maximum in solubility in mixed solvent systems at low anti-solvent concentrations. The λh equation and the NRTL model were applied to fit the solubility data of 5-nitrofurazone (γ - form) in the experimentally measured mixtures of N, N-dimethylformamide and water/isopropanol. The calculated solubility data are also listed in Table 5 and the parameters of these two models are given in Tables 6 and 7, respectively. The ARD and RMSD values were calculated and used to evaluate the suitability of the models. The obtained ARD and RMSD values are shown in Tables 8 and 9. ARD (%) derived from the λh equation and the NRTL model in all the tested solvents with all compositions are lower than 5%. Therefore, the two models could be used to accurately predict the solubility data of 5-nitrofurazone γ - form in binary solvent mixtures and provide accurate results. 4.4. Thermodynamic mixing and dissolution properties
ð37Þ
#1=2 ð38Þ
exp where xcal represent the calculated mole fraction solubility i and xi and the experimental mole fraction solubility respectively. N stands for the number of the experimental data points.
The thermodynamic mixing properties of 5-nitrofurazone (γ - form) in mono-solvents and in binary mixed solvent systems of N, Ndimethylformamide and water/isopropanol are calculated by using the NRTL model from the experimental solubility data. The results are listed in Tables 8 and 9. The negative ΔmixG values and the positive ΔmixS values illustrate that the mixing processes in the tested solvent systems are spontaneous and entropy-driven processes, respectively. Furthermore, the thermodynamic dissolution properties were calculated by using Eqs. (30)–(32). The obtained thermodynamic
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X. Li et al. / Journal of Molecular Liquids 275 (2019) 815–828
Table 10 The dissolution thermodynamic properties of 5-nitrofurazone (γ - form) in mono-solvents systems (p = 101.3 kPa).a,b ΔdisG (J·mol−1)
ΔdisH (J·mol−1)
ΔdisS (J·K−1·mol−1)
Propanol 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15
−0.1809 −0.2333 −0.2987 −0.3794 −0.4793 −0.6017 −0.7506 −0.9315
58.31 66.84 74.51 77.53 86.96 95.36 98.59 105.3
0.2103 0.2369 0.2596 0.2658 0.2933 0.3166 0.3224 0.3391
Isopropanol 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15
−0.1530 −0.1994 −0.2608 −0.3363 −0.4312 −0.5491 −0.6940 −0.8725
3.759 6.468 13.90 23.56 39.93 63.81 92.74 142.3
1.406e2 2.355e2 4.913e2 8.153e2 0.1354 0.2123 0.3032 0.4572
−2.652e−2 −3.470e−2 −4.510e−2 −5.794e−2 −7.407e−2 −9.406e−2 −0.1187 −0.1490
3.219 2.790 1.831 1.038 3.621 7.459 12.85 21.69
1.167e−2 9.976e−3 6.511e−3 3.737e−3 1.239e−2 2.492e−2 4.208e−2 6.974e−2
Methanol 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15
−0.3343 −0.4037 −0.4853 −0.5811 −0.6936 −0.8247 −0.9771 −1.154
450.9 518.3 597.8 684.0 816.0 928.9 1084 1212
1.622 1.832 2.076 2.335 2.739 3.067 3.522 3.874
Ethanol 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15
−0.1552 −0.1936 −0.2403 −0.2966 −0.3642 −0.4455 −0.5423 −0.6573
128.8 149.9 175.6 205.2 234.6 277.2 324.2 369.3
0.4635 0.5299 0.6102 0.7011 0.7882 0.9159 1.054 1.182
Acetonitrile 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15
−0.1970 −0.2419 −0.2955 −0.3595 −0.4355 −0.5253 −0.6313 −0.7557
205.4 244.7 287.2 335.2 395.3 462.8 529.0 599.7
0.7390 0.8651 0.9976 1.145 1.327 1.528 1.719 1.917
Acetone 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15
−0.6915 −0.8060 −0.9369 −1.086 −1.256 −1.448 −1.667 −1.913
1283 1482 1679 1892 2178 2403 2722 3085
4.617 5.236 5.830 6.459 7.309 7.930 8.840 9.859
1.900e5 1.929e5 1.963e5 2.016e5 2.129e5 2.207e5
683.2 681.4 681.5 687.8 714.4 728.2
T (K)
Water 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15
Table 10 (continued) ΔdisG (J·mol−1)
ΔdisH (J·mol−1)
ΔdisS (J·K−1·mol−1)
308.15 313.15
−63.51 −68.49
2.241e5 2.322e5
727.4 741.8
Formamide 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15
−3.918 −4.482 −5.116 −5.829 −6.627 −7.520 −8.516 −9.627
8381 9502 1.036e4 1.185e4 1.326e4 1.475e4 1.650e4 1.790e4
30.15 33.58 35.97 40.45 44.48 48.69 53.56 57.20
T (K)
a
The values of ΔdisG, ΔdisH and ΔdisS were calculated by Eqs. (30)–(32). The combined expanded uncertainties U are Uc(ΔHd) = 0.060ΔHd, Uc(ΔSd) = 0.065ΔSd, Uc(ΔGd) = 0.065ΔGd (0.95 level of confidence). b
dissolution properties of 5-nitrofurazone in single solvent systems and binary mixed solvents of N, N-dimethylformamide and water/ isopropanol are listed in Tables 10 and 11, respectively. Similar to mixing, the negative ΔdisG values and the positive ΔdisS values for all tested solvents illustrate that the dissolution processes are also spontaneous and entropy-driven. The positive ΔdisH values indicate that the dissolution processes are endothermic, which is consistent with the observed trend that increasing temperature improves the solubility of 5-nitrofurazone. 5. Conclusions
N, N-Dimethylformamide 278.15 −45.31 283.15 −47.12 288.15 −49.39 293.15 −52.13 298.15 −55.32 303.15 −59.10
In this work, a UV spectroscopic method was used to experimentally measure the solubility data of 5-nitrofurazone in nine single solvents systems (water, n-propanol, isopropanol, methanol, ethanol, acetonitrile, acetone, N, N-dimethylformamide and formamide) and two binary solvent systems (N, N-dimethylformamide and water/isopropanol) from temperatures of 278.15 K to 313.15 K. The ranked order of 5-nitrofurazone's solubility data in mono-solvents systems at investigated temperatures below 298.15 K from highest to lowest is N, N-dimethylformamide N formamide N acetone N methanol N n-propanol N acetonitrile N isopropanol N ethanol N water. At temperatures above 298.15 K, the sequence remains unchanged except that the solubility in isopropanol is higher than that of acetonitrile in the remainder of the investigated temperature range. In all tested mono-solvent systems and binary solvent mixtures, the solubility data of 5nitrofurazone increases with increasing of temperature. This data set can provide a reference for the selection of solvents and antisolvents in crystallization process. The experimental solubility of 5-nitrofurazone in mono-solvents systems were successfully represented by the modified Apelblat equation and the NRTL model with an ARD% of the modified Apelblat model in all selected solvents under 3%, and ARD% was under 5% for NRTL model in all cases. Similarly, the λh equation and the NRTL model were applied to the binary solvent mixtures and described the experimental data well, with the ARD (%) calculated to be lower than 5% from the λh equation and the NRTL model in all the tested solvents with all compositions. The entropy and Gibbs energy of mixing and dissolution of 5-nitrofurazone (γ – form) in single and binary solvent mixtures were calculated and the results indicated that both the mixing process and the dissolution processes were spontaneous and entropy-driven in all tested solvents. Acknowledgements This research is financially supported by the National Key Research and Development Program (No. 2016YFB0600504).
X. Li et al. / Journal of Molecular Liquids 275 (2019) 815–828
827
Table 11 The mixing thermodynamic properties of 5-nitrofurazone (γ - form) in binary solvent mixtures (p = 101.3 kPa).a,b,c xDW
xDI
N, N-Dimethylformamide + water ΔdisG (kJ·mol−1)
ΔdisS (J·K−1·mol−1)
N, N-Dimethylformamide + isopropanol ΔdisG (kJ·mol−1)
ΔdisS (J·K−1·mol−1)
ΔdisH (kJ·mol−1)
24.61 234.7 499.3 748.9 949.5 1071 1117 1055 913.0
T = 278.15 K 0.1000 0.2000 0.3000 0.4000 0.5004 0.6000 0.7005 0.7999 0.9000
−3.567 −5.377 −6.201 −6.375 −6.081 −5.438 −4.500 −3.321 −1.886
697.8 1257 1573 1673 1607 1424 1156 841.2 496.2
2521 4537 5678 6037 5800 5138 4171 3036 1791
5.096 63.02 137.3 208.3 265.8 301.0 315.4 293.9 253.0
21.21 227.7 491.4 742.9 946.1 1070 1120 1043 897.0
T = 283.15 K 0.1000 0.2000 0.3000 0.4000 0.5004 0.6000 0.7005 0.7999 0.9000
−3.525 −5.332 −6.165 −6.350 −6.069 −5.435 −4.504 −3.329 −1.893
693.6 1255 1578 1685 1623 1441 1171 852.5 502.3
2462 4453 5596 5972 5752 5108 4151 3022 1781
−0.9199 −1.471 −1.841 −2.059 −2.135 −2.074 −1.870 −1.513 −0.9680
4.250 62.24 137.4 210.0 268.5 305.9 319.9 302.0 261.1
17.94 221.1 483.3 736.0 939.4 1069 1117 1053 909.4
T = 288.15 K 0.1000 0.2000 0.3000 0.4000 0.5004 0.6000 0.7005 0.7999 0.9000
−3.486 −5.289 −6.130 −6.328 −6.057 −5.433 −4.509 −3.336 −1.901
689.5 1254 1584 1696 1638 1457 1185 864.2 508.7
2405 4371 5517 5907 5707 5076 4129 3011 1772
T = 293.15 K 0.1000 0.2000 0.3001 0.4001 0.5000 0.6002 0.7003 0.8004 0.9005
−0.9302 −1.486 −1.858 −2.078 −2.155 −2.093 −1.888 −1.530 −0.9799
3.401 61.42 137.5 211.0 272.2 311.1 324.4 305.8 264.6
14.77 214.6 475.4 726.7 936.0 1068 1113 1048 906.0
T = 293.15 K 0.1000 0.2000 0.3000 0.4000 0.5004 0.6000 0.7005 0.7999 0.9000
−3.450 −5.248 −6.097 −6.306 −6.047 −5.431 −4.514 −3.346 −1.909
685.7 1253 1589 1707 1654 1474 1200 873.9 513.6
2351 4293 5441 5845 5662 5046 4108 2993 1758
T = 298.15 K 0.1000 0.2000 0.3001 0.4001 0.5000 0.6002 0.7003 0.8004 0.9005
−0.9406 −1.501 −1.876 −2.097 −2.175 −2.113 −1.907 −1.546 −0.9922
2.568 60.73 138.1 214.1 277.0 316.4 331.7 312.5 269.4
11.77 208.7 469.5 725.1 936.5 1068 1119 1053 906.8
T = 298.15 K 0.1000 0.2000 0.3000 0.4000 0.5004 0.6000 0.7005 0.7999 0.9000
−3.415 −5.210 −6.066 −6.285 −6.037 −5.430 −4.519 −3.354 −1.918
682.1 1252 1594 1719 1669 1491 1216 885.9 519.4
2299 4218 5368 5787 5618 5017 4092 2983 1748
T = 303.15 K 0.1000 0.2000 0.3001 0.4001 0.5000 0.6002 0.7003 0.8004 0.9005
−0.9511 −1.516 −1.894 −2.117 −2.195 −2.133 −1.926 −1.563 −1.005
1.748 60.19 139.1 217.2 282.2 324.2 339.9 319.5 275.7
8.903 203.5 465.2 723.5 938.2 1077 1127 1059 912.7
T = 303.15 K 0.1000 0.2000 0.3000 0.4000 0.5004 0.6000 0.7005 0.7999 0.9000
−3.383 −5.173 −6.037 −6.267 −6.029 −5.430 −4.524 −3.363 −1.927
678.6 1252 1599 1730 1683 1506 1231 897.2 526.0
2250 4146 5295 5727 5573 4985 4074 2971 1741
T = 308.15 K 0.1000 0.2000 0.3001 0.4001 0.5000 0.6002 0.7003 0.8004
−0.9617 −1.532 −1.912 −2.136 −2.216 −2.153 −1.945 −1.580
0.9350 59.63 139.6 220.7 287.2 331.0 347.0 327.5
6.155 198.5 459.2 723.2 939.1 1081 1132 1068
T = 308.15 K 0.1000 0.2000 0.3000 0.4000 0.5004 0.6000 0.7005 0.7999
−3.352 −5.139 −6.009 −6.248 −6.020 −5.430 −4.530 −3.373
675.3 1251 1605 1741 1699 1522 1245 906.9
2202 4077 5227 5671 5532 4958 4056 2954
T = 278.15 K 0.1000 0.2000 0.3001 0.4001 0.5000 0.6002 0.7003 0.8004 0.9005
−0.8999 −1.442 −1.806 −2.021 −2.097 −2.035 −1.834 −1.482 −0.9457
5.946 63.85 137.1 206.3 262.0 295.8 309.0 292.0 253.0
T = 283.15 K 0.1000 0.2000 0.3001 0.4001 0.5000 0.6002 0.7003 0.8004 0.9005
−0.9098 −1.457 −1.823 −2.040 −2.116 −2.054 −1.851 −1.498 −0.9571
T = 288.15 K 0.1000 0.2000 0.3001 0.4001 0.5000 0.6002 0.7003 0.8004 0.9005
ΔdisH (kJ·mol−1)
(continued on next page)
828
X. Li et al. / Journal of Molecular Liquids 275 (2019) 815–828
Table 11 (continued) xDW
xDI
N, N-Dimethylformamide + water ΔdisG (kJ·mol
−1
)
ΔdisS (J·K
−1
·mol
−1
)
ΔdisH (kJ·mol
−1
)
N, N-Dimethylformamide + isopropanol ΔdisG (kJ·mol−1)
ΔdisS (J·K−1·mol−1)
ΔdisH (kJ·mol−1)
0.9005
−1.018
282.0
918.5
0.9000
−1.936
534.0
1739
T = 313.15 K 0.1000 0.2000 0.3001 0.4001 0.5000 0.6002 0.7003 0.8004 0.9005
−0.9724 −1.547 −1.931 −2.156 −2.236 −2.174 −1.965 −1.598 −1.032
0.1327 59.27 141.1 224.4 295.2 339.5 355.7 335.4 289.2
3.529 194.2 456.6 723.5 949.7 1091 1142 1076 926.9
T = 313.15 K 0.1000 0.2000 0.3000 0.4000 0.5004 0.6000 0.7005 0.7999 0.9000
−3.323 −5.106 −5.983 −6.231 −6.013 −5.431 −4.537 −3.382 −1.946
672.2 1251 1610 1752 1713 1538 1260 918.8 539.8
2157 4010 5159 5615 5490 4930 4037 2945 1730
a
The values of ΔdisG, ΔdisH and ΔdisS are calculated by Eqs. (30)–(32). The combined expanded uncertainties U are Uc(ΔHm) = 0.060ΔHm, Uc(ΔSm) = 0.065ΔSm, Uc(ΔGm) = 0.065ΔGm (0.95 level of confidence). c xDW and xDIare the mole fraction of N, N-dimethylformamide in the initial binary solvents of N, N-dimethylformamide + water and N, N-dimethylformamide + isopropanol, respectively. b
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