Solubility determination and correlation for 3-nitropyrazole in four binary solvents (water?+?methanol, ethanol, 1-propanol and acetone) from 283.15?K to 323.15?K

Article abstract of DOI:10.1016/j.molliq.2021.117332

The solubility of 3-nitropyrazole in four binary solvents (water + methanol, ethanol, 1-propanol and acetone) was measured by a dynamic laser monitoring over the temperature range of 283.15 K, 288.15 K, 293.15 K, 298.15 K, 303.15 K, 308.15 K, 313.15 K, 318.15 K and 323.15 K at pressure of 0.1 MPa. The solubility of 3-nitropyrazole increased positively with increasing temperature, while increased with decreasing mass-fraction of water in each binary system. Moreover, the experimental solubility values of 3-nitropyrazole in this work were correlated well with four thermodynamic models namely “the modified Apelblat equation, λh equation, Jouyban-Acree model and CNIBS/R-K model” obtaining average relative deviations (10⁴RMSD) lower than 4.79 for correlative studies, which shows that all the four models have a good correlation. Through the comparison of R² and 10⁴RMSD, it was found that the modified Apelblat equation can get more satisfactory results. In addition, Hansen solubility parameters were used to explain and predict the solubility behavior. Solute-solvent interaction was calculated by molecular simulation to investigate the solubility behavior deeply. Finally, the thermodynamic parameters (Δ_disG^o, Δ_disH^o, Δ_disS^o) of 3-nitropyrazole dissolution processes in investigated four binary solvents were evaluated utilizing the van't Hoff equation. The positive Δ_disH^o and Δ_disS^o, indicate that the dissolution processes of 3-nitropyrazole are endothermic and entropy-driven in all chosen binary solvents. And the main contributor of Δ_disG^o is positive enthalpy. The solubility of 3-nitropyrazole in mixed solvents (water + methanol, water + ethanol, water + 1-propanol and water + acetone) will provide essential support for the further researches of crystallization and spheroidization of 3-nitropyrazole.

Full text of DOI:10.1016/j.molliq.2021.117332

Journal of Molecular Liquids 342 (2021) 117332
Contents lists available at ScienceDirect
Journal of Molecular Liquids
journal homepage: www.elsevier.com/locate/molliq
Solubility determination and correlation for 3-nitropyrazole in four
binary solvents (water + methanol, ethanol, 1-propanol and acetone)
from 283.15 K to 323.15 K
Wen-Dong Liu , Yong-Xiang Li , Duan-Lin Cao , Heng-Jie Guo , Zi-Yang Li c
a
a
a
b,
⇑
a
School of Chemical Engineering and Technology, North University of China, Taiyuan 030051, China
Beijing Fukangren Biopharmaceutical Technology Co., Ltd. Jinan Branch, Jinan 250307, China
Research Institute of Gan Su Yin Guang Chemical Industry Group, Baiyin 730900, China
b
c
a r t i c l e i n f o
a b s t r a c t
Article history:
The solubility of 3-nitropyrazole in four binary solvents (water + methanol, ethanol, 1-propanol and ace-
tone) was measured by a dynamic laser monitoring over the temperature range of 283.15 K, 288.15 K,
Received 26 July 2021
Revised 12 August 2021
Accepted 18 August 2021
Available online 23 August 2021
293.15 K, 298.15 K, 303.15 K, 308.15 K, 313.15 K, 318.15 K and 323.15 K at pressure of 0.1 MPa. The sol-
ubility of 3-nitropyrazole increased positively with increasing temperature, while increased with
decreasing mass-fraction of water in each binary system. Moreover, the experimental solubility values
of 3-nitropyrazole in this work were correlated well with four thermodynamic models namely ‘‘the mod-
ified Apelblat equation, kh equation, Jouyban-Acree model and CNIBS/R-K model” obtaining average rel-
Keywords:
Solubility
4
ative deviations (10 RMSD) lower than 4.79 for correlative studies, which shows that all the four models
3
-nitropyrazole
2
4
have a good correlation. Through the comparison of R and 10 RMSD, it was found that the modified
Apelblat equation can get more satisfactory results. In addition, Hansen solubility parameters were used
to explain and predict the solubility behavior. Solute-solvent interaction was calculated by molecular
simulation to investigate the solubility behavior deeply. Finally, the thermodynamic parameters
Measurement
Correlation
Hansen solubility parameters
Thermodynamic
o
o
o
(D
disG ,
D
disH ,
D
disS ) of 3-nitropyrazole dissolution processes in investigated four binary solvents were
o
o
evaluated utilizing the van’t Hoff equation. The positive
dis
D H and DdisS , indicate that the dissolution
processes of 3-nitropyrazole are endothermic and entropy-driven in all chosen binary solvents. And
o
the main contributor of
water + methanol, water + ethanol, water + 1-propanol and water + acetone) will provide essential sup-
port for the further researches of crystallization and spheroidization of 3-nitropyrazole.
Ó 2021 Elsevier B.V. All rights reserved.
dis
D G is positive enthalpy. The solubility of 3-nitropyrazole in mixed solvents
(
1
. Introduction
tal. The melting point, density, getonation velocity and detonation
ꢁ3
ꢁ1
pressure of 3-nitropyrazole is 174–175 ℃, 1.57 gꢀcm , 7.02 kmꢀs
Due to the large number of N-N, C-N bonds and large ring ten-
and 20.08 GPa, respectively [3]. As a typical nitrogen heterocyclic
compound, it is an important intermediate for the synthesis of
new explosives such as 3,4-dinitropyrazole (DNP). It can also be
used directly as an energetic material or as an intermediate to fur-
ther prepare other energetic compounds.
sion in the azacyclic compound, the enthalpy of formation is very
high. And this type of compound has the characteristics of high
nitrogen and low carbon hydrogen, so it has a higher density. In
addition, the electronegativity of nitrogen and oxygen atoms in
nitrogen heterocyclic molecules are high, especially the nitrogen
heteroaromatic ring system can also form a large benzene-like
structure of the bond, which has the characteristics of insensitivity
and good thermal stability. It is highly valued in the research of
The solubility of solid substances in different solvents is one of
the most important parameters in fundamental research, which
can also show the knowledge of physical properties and optimal
crystallization conditions. It can help estimate a suitable solvents
ratio for maximum solubility, playing an important role in the
determination of appropriate solvents for the crystallization pro-
cess [4]. Moreover, many studies have focused on the synthesis
of 3-nitropyrazole (e.g., Janssen [5], Klebe [6], Cuiping Li [7], Hongli
Li [8] and Xin Tian [9] et al.), but only a few have attempted to
establish purification methods to obtain products with high purity
energetic materials [1,2]. 3-Nitropyrazole (C
No. 26621–44-3, molar mass 113.07 gꢀmol ) is a light yellow crys-
3 3
H N
3
O
2
, Fig. 1, CAS
ꢁ1
⇑
Corresponding author.
E-mail address: 2604125064@qq.com (H.-J. Guo).
https://doi.org/10.1016/j.molliq.2021.117332
167-7322/Ó 2021 Elsevier B.V. All rights reserved.
0

Wen-Dong Liu, Yong-Xiang Li, Duan-Lin Cao et al.
Journal of Molecular Liquids 342 (2021) 117332
used in this experiment, such as methanol, ethanol, 1-propanol
and acetone, were purchased from local reagent factories without
further purification, and their mass fraction purity was
not<0.990. The distilled water received the production in a pure
water machine (IQ-7005, Milli-Q). More information of all the
materials used in this experiment is presented in Table 1.
2.2. Differential scanning calorimetry
The differential scanning calorimetry (DSC 1/500, Mettler-
Toledo, Switzerland) was used to determine the melting tempera-
ture (T ) and fusion enthalpy ( fusH) of 3-nitropyrazole. The stan-
dard uncertainties of the measurement were a temperature of
m
D
ꢁ
1
0
.5 K and a fusion enthalpy of 400 Jꢀmol . Fig. 3 indicates that
Fig. 1. The molecular structure of 3-nitropyrazole.
ꢁ1
the fusion enthalpy is 16.72 kJꢀmol and the melting temperature
is 447.05 K.
and yield. The industrial crystallization process based on the solu-
bility data has many advantages, such as high efficiency, high yield,
low energy consumption, low pollution, high product purity, etc.
Furthermore, it is especially suitable for industrial fields of solid
products, such as fine chemicals and biopharmaceuticals. At the
same time, the study of solubility data defines the separation limit
for the crystallization separation process, and provides basic data
for the design of the equipment structure size and the determina-
tion of operating conditions, which is an important prerequisite for
realizing chemical production. The solubility data of 3-
nitropyrazole has important research significance for the crystal-
lization process of 3-nitropyrazole.
In this work, to optimize the crystallization process of 3-
nitropyrazole (e.g., yield, stability, whiteness, fluidity and so on).
The solid–liquid equilibrium solubility of 3-nitropyrazole in four
kinds of binary solvent mixtures (including water + methanol,
water + ethanol, water + 1-propanol and water + acetone) was
2.3. X-ray diffraction
Since the solubility may change with the crystal structure, it is
necessary to confirm the crystal structure before the measurement
of its solubility. The 3-nitropyrazole crystal used to measure the
solubility was identified by X-ray diffraction (XRD) using Bruker
D8 Advance (Bruker Corporation, Germany). The data was carried
out in the range of 2h from 5° to 80°, with a voltage of 45 kV and
a scanning rate of 10 °ꢀmin . The XRD curves of 3-nitropyrazole
in four binary solvents were showed in Fig. 4. The results showed
that no polymorph transformation of 3-nitropyrazole was
identified.
ꢁ
1
2.4. Hansen solubility parameter
The concept of Hansen solubility parameter (HSP) has been
determined with
a temperature ranging from 283.15 K to
widely used for selecting suitable solvents for solute [10]. The basis
of the HSP approach is to assume that the total cohesive energy (E
of a pure compound consists of three parts, including nonpolar
dispersion) interactions (E ), polar (dipole–dipole and dipole-
induced dipole) interactions (E ) and hydrogen bonding or other
specific association interactions including Lewis acid-base interac-
tions (E ):
3
23.15 K under approximately 0.1 MPa. The Hansen solubility
t
)
parameter for 3-nitropyrazole and the selected solvents was
employed to analyze the probabilities of miscibility between solute
and solvents. The solubility behavior was studied by molecular
simulation. In addition, four thermodynamic models (i.e., the mod-
ified Apelblat equation, kh equation, Jouyban-Acree model and
CNIBS/R-K model) were selected to correlate the experimental
data. The solubility data are of guiding significance to the crystal-
lization process of 3-nitropyrazole. Furthermore, the thermody-
namic properties of the solution process, including the standard
molar Gibbs energy, standard molar enthalpy and standard molar
entropy, were calculated by the van’t Hoff analysis.
(
d
p
h
E
t
¼ E þ E
Dividing each contribution by the molar volume:
d
p
þ E
h
ð1Þ
Et Ed Ep Eh
2
d
2
p
2
h
¼
þ
þ ¼ d þ d þ d
V
ð2Þ
V
V
V
Therefore, the total solubility parameter (d
t
) can be expressed
2
. Experimental
.1. Chemical materials
-Nitropyrazole was synthesized from pyrazole by a two-step
as:
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
2
d
2
p
2
h
d
t
¼
d þ d þ d
ð3Þ
3
d p
Where d , d and dh represent the Hansen dispersion solubility
reaction of nitration and rearrangement [7], and the synthetic
route is showed in Fig. 2. It was purified by crystallization in
methanol and its mass fraction purity, measured by High Perfor-
mance Liquid Chromatography (HPLC), was 0.990. All solvents
parameter, polar solubility parameter and hydrogen bonding solu-
bility parameter, respectively. The values of d , dp and dh for
d
selected solvents can be obtained from literature [10]. The solubil-
ity parameter for binary solvents (dmix) can be expressed as: [11]
d
mix
¼
ad
1
þ ð1 ꢁ
aÞd
2
ð4Þ
Where
a
stands for the volume fraction of water; d
1
and d
2
are
the Hansen solubility parameters of water and methanol, ethanol,
1
-propanol and acetone.
The group contribution (Hoftyzer-Van Krevelen) method was
used to calculate the values of d
12]. The molar volume of 3-nitropyrazole, V
was taken from the SciFinder database [13].
d
, d
p
and d
h
of 3-nitropyrazole
3
ꢁ1
[
s
= 61.5 cm ꢀmol
,
Fig. 2. Synthesis route of 3-nitropyrazole.
2

Wen-Dong Liu, Yong-Xiang Li, Duan-Lin Cao et al.
Journal of Molecular Liquids 342 (2021) 117332
Table 1
The detailed information of the materials used in this paper.
Material
-nitropyrazole
Methanol
Ethanol
Molar mass/(gꢀmolꢁ1)
Source
Purity
Purification method
Analysis method
HPLCa
3
113.07
32.04
46.07
60.10
58.08
18.02
Synthesized by us
0.990
0.995
0.995
0.990
0.990
/
crystallization
b
Sinopharm Chemical Reagent Co., Ltd
Sinopharm Chemical Reagent Co., Ltd
Sinopharm Chemical Reagent Co., Ltd
Sinopharm Chemical Reagent Co., Ltd
prepared by the laboratory
none
none
none
none
/
GC
GC
GC
GC
b
b
1
-propanol
b
Acetone
Water
/
a
High-performance liquid chromatography.
Gas chromatography.
b
In addition, the difference of total solubility parameter between
solute and solvent (
D
d
t
) can be used to estimate the miscibility of
two compounds: [14]
D
d
t
¼ jdt2 ꢁ dt1
j
ð5Þ
Where dt1 and dt2 are total Hansen solubility parameters of
solute and binary solvents, respectively. Values of d , d , d , d
and of four binary solvents and solute are listed in Table 2.
d
p
h
t
Dd
t
2.5. Simulation methods
The calculations based on density functional theory (DFT) were
3
conducted with the Dmol module implemented in Materials Stu-
dio [15] to determine the solubility sequence of 3-nitropyrazole. In
the present study, molecules of 3-nitropyrazole and solvents were
optimized with adopting the DFT method in the generalized gradi-
ent approximation (GGA) and with the Perdew-Burke-Ernzerhof
(
PBE) functional form [16]. The double numerical polarized (DNP)
Fig. 3. DSC plot of 3-nitropyrazole.
basis sets were applied [17], equivalent to 6-31G* basis sets. The
self-consistent-field calculation complied with the convergence
criteria of 10- Hartree, and the tolerances of energy, maximal
force, and maximal displacement for the geometry optimization
were set to 1.0 ꢂ 10 au, 0.002 au and 0.005 au, respectively. After
the geometries of all involving molecules were optimized at this
level, the interaction energy Einter was obtained as:
6
-5
ꢁE
inter
¼
D
E ¼ Etotal ꢁ Esolute ꢁ Esolvent
ð6Þ
Herein, parameters Etotal and Esolute represent the energies of 3-
nitropyrazole + binary solvent and 3-nitropyrazole, respectively;
solvent stands for energy of selected solvent. Values of solvent
E
3
polarity and interaction energy Einter calculated by Dmol are pre-
sented in Table 3.
2.6. Experimental procedures
In this research work, the solubility of 3-nitropyrazole in four
selected binary solvents including ‘‘water + methanol, ethanol, 1-
propanol and acetone” at 283.15–323.15 K was investigated by a
laser monitoring method. The experimental approach and appara-
tus were similar to our previous published paper and briefly
Fig. 4. XRD pattern of 3-nitropyrazole.
2
.342
2
.342
2
.342
1.433
2.342
2
.576
2
.004
1.678
(a)
(b)
(c)
(d)
Fig. 5. Optimized structures between 3-nitropyrazole and methanol + water (a), ethanol + water (b), 1-propanol + water (c) and acetone + water (d), respectively. The dashed
lines indicate hydrogen bonds with a distance (Unit: Å, 1 Ã. . . = 0.1 nm).
3

Wen-Dong Liu, Yong-Xiang Li, Duan-Lin Cao et al.
Journal of Molecular Liquids 342 (2021) 117332
Table 2
Hansen solubility parameter of selected binary solvents and 3-nitropyrazole.
w
1
d
(
d
d
p
d
h
d
t
Dd
t
(MPa)
MPa)0.5
(MPa)
0.5
(MPa)
0.5
(MPa)
0.5
0.5
Water + methanol
0
0
0
0
0
0
0
0
0
.1000
.2000
.3000
.4000
.5000
.6000
.7000
.8000
.9000
13.9
25.8
35.4
42.3
46.1
46.4
42.6
34.1
20.2
13.8
15.4
17.1
18.9
20.7
22.6
24.6
26.7
29.0
23.3
24.3
25.3
26.4
27.6
28.8
30.1
31.4
32.8
30.4
38.6
46.8
53.3
57.6
59.1
57.7
53.5
48.2
0.17
8.38
16.5
23.1
27.3
28.9
27.4
23.3
17.9
Water + ethanol
0
0
0
0
0
0
0
0
0
.1000
.2000
.3000
.4000
.5000
.6000
.7000
.8000
.9000
14.4
26.7
36.7
43.9
47.9
48.2
44.3
35.5
21.0
10.6
12.5
14.5
16.6
18.7
21.0
23.4
25.9
28.5
20.7
21.9
23.2
24.6
26.0
27.5
29.1
30.7
32.5
27.4
36.8
45.8
53.0
57.6
59.4
57.9
53.6
48.1
2.91
6.52
15.5
22.7
27.4
29.1
27.7
23.4
17.8
Water + 1-propanol
0
0
0
0
0
0
0
0
0
.1000
.2000
.3000
.4000
.5000
.6000
.7000
.8000
.9000
14.7
27.2
37.2
44.4
48.3
48.5
44.4
35.5
20.9
8.80
10.9
13.1
15.3
17.7
20.2
22.8
25.5
28.3
18.8
20.2
21.7
23.3
24.9
26.6
28.4
30.3
32.2
25.4
35.6
45.0
52.4
57.1
58.9
57.4
53.1
47.7
4.86
5.30
14.7
22.1
26.9
28.6
27.2
22.9
17.5
Water + acetone
0
0
0
0
0
0
0
0
0
3
.1000
.2000
.3000
.4000
.5000
.6000
.7000
.8000
14.1
26.1
35.9
43.0
47.0
47.3
43.6
34.9
20.7
16.6
12.1
13.8
15.7
17.6
19.6
21.7
23.9
26.2
28.7
22.0
9.22
11.5
13.9
16.4
19.0
21.8
24.7
27.7
30.9
12.5
20.7
31.7
41.5
49.2
54.3
56.4
55.5
51.7
47.0
30.3
9.58
1.45
11.3
19.0
24.1
26.2
25.2
21.5
16.7
0.00
.9000
-nitropyrazole
Table 3
Values of interaction energy Einter calculated by Dmol3,a
agitator was used for accelerating the dissolution rate of 3-
nitropyrazole in selected binary solvents. The mixture solution
was stirred for>30 min. After 30 min, the selected binary solvents
of known weight were added dropwise into mixture solution by
a syringe with the dropping rate of 2–3 drops per minute till the
last trace of 3-nitropyrazole was dissolved in mixture solution.
The mixture solution reached saturation and the electrical signal
of laser monitoring arrived at its maximum at this moment. The
weights of solute and solvent were weighed by an electronic ana-
lytical balance (type AB 204, Mettler Toledo, Switzerland) with an
accuracy of 0.0001 g. Three parallel experiments for each temper-
ature point were performed in this work and the average values
were considered the final results.
.
Solvents
E
total
/
E
solvent/Esolute
/
inter
E /
(Hartree)
(Hartree)
(kJꢀmolꢁ1)
Methanol
Ethanol
ꢁ970.00
ꢁ115.65
ꢁ154.94
ꢁ187.36
ꢁ213.21
ꢁ104.32
ꢁ219.97
ꢁ259.26
ꢁ291.68
48.44
62.17
52.25
17.18
4.18
26.26
57.76
34.13
ꢁ1009.28
ꢁ1041.71
ꢁ1067.55
ꢁ958.65
1
-propanol
Acetone
Water
Water + methanol
Water + ethanol
Water + 1-
ꢁ1074.31
ꢁ1113.61
ꢁ1146.02
propanol
Water + acetone
ꢁ1171.87
ꢁ317.53
ꢁ854.33
21.00
3
-nitropyrazole
The mole-fraction solubility (x
1
) of 3-nitropyrazole in binary
a
Hartree = 2625.5 kJꢀmolꢁ1
1
.
solvents can be expressed as:
m
1
=M
=M
1
2
x
1
¼ m
¼ m
ð7Þ
1
2
=M
1
þ m
2
3 3
þ m =M
described here [18–20]. Firstly, about 50 mL binary solvent was
added into a double-layer glass bottle (customized through the
glasswork). The temperature of solvent was controlled by circulat-
ing water bath (type 501, Gongyi Yuhua Instrument Co., Ltd.,
China) with an uncertainty of 0.05 K and determined by ther-
mometer mercury. Then, excess amount of solid was added into
double-layer glass bottle at the setting temperature. A magnetic
m
=M
2
=M
2
x
2
ð8Þ
ð9Þ
2
þ m
3
=M
3
m2
þ m
w
1
¼ m
2
3
4

Wen-Dong Liu, Yong-Xiang Li, Duan-Lin Cao et al.
Journal of Molecular Liquids 342 (2021) 117332
Table 4
Mole fraction solubility (x
) of 3-nitropyrazole in binary solvent mixtures at different temperatures from 283.15 K to 323.15 K and P = 0.1 MPaa,b
.
1
3
exp
3
AP
3
kh
3
JA
3
RK
T/K
10 ꢀx
1
10 ꢀx
1
10 ꢀx
1
10 ꢀx
1
10 ꢀx
1
Water + methanol (w
1
1
1
1
1
1
1
1
= 0.1000)
= 0.2000)
= 0.3000)
= 0.4000)
= 0.5000)
= 0.6000)
= 0.7000)
= 0.8000)
2
2
2
2
3
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
3.83
4.85
6.02
3.49
4.64
6.12
3.52
4.67
6.13
3.72
4.80
6.16
3.85
4.87
6.04
7.49
7.98
7.98
7.88
7.50
9.88
10.31
13.19
16.73
21.04
26.24
10.30
13.17
16.70
21.03
26.27
10.03
12.73
16.09
20.26
25.41
9.90
13.62
16.79
21.30
26.03
13.61
16.77
21.31
26.07
Water + methanol (w
2
2
2
2
3
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
3.73
4.58
3.93
4.66
3.17
4.14
3.37
4.35
3.69
4.54
5.62
5.61
5.37
5.60
5.55
6.87
6.85
6.90
7.17
6.83
8.57
8.47
8.79
9.15
8.51
10.62
13.49
17.30
21.97
10.60
13.41
17.15
22.14
11.11
13.94
17.37
21.50
11.62
14.71
18.54
23.30
10.72
13.60
17.30
21.89
Water + methanol (w
2
2
2
2
3
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
3.52
4.31
3.54
4.30
2.98
3.91
3.06
3.96
3.52
4.34
5.31
5.29
5.09
5.10
5.36
6.57
6.55
6.57
6.54
6.58
8.14
8.18
8.40
8.36
8.15
10.29
13.10
16.61
21.36
10.30
13.05
16.64
21.35
10.67
13.44
16.81
20.88
10.63
13.47
17.01
21.39
10.10
12.85
16.50
21.32
Water + methanol (w
2
2
2
2
3
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
3.16
4.01
3.25
3.96
2.67
3.55
2.75
3.56
3.24
4.02
5.01
4.88
4.66
4.59
5.03
6.13
6.07
6.07
5.90
6.17
7.69
7.62
7.84
7.54
7.73
9.61
9.67
10.04
12.76
16.09
20.14
9.61
9.69
12.17
15.86
20.73
12.35
15.91
20.62
12.19
15.42
19.42
12.28
15.90
20.77
Water + methanol (w
2
2
2
2
3
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
2.87
3.50
3.08
3.62
2.35
3.11
2.39
3.10
2.80
3.49
4.39
4.34
4.09
4.00
4.37
5.36
5.30
5.32
5.15
5.36
6.74
6.58
6.87
6.61
6.76
8.45
8.31
8.80
8.43
8.57
10.62
13.80
18.21
10.66
13.85
18.24
11.17
14.08
17.63
10.72
13.58
17.15
10.89
14.11
18.52
Water + methanol (w
2
2
2
2
3
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
2.24
2.78
3.46
4.23
5.39
6.79
8.98
11.54
15.05
2.24
2.75
3.41
4.27
5.41
6.90
8.89
11.53
15.06
1.83
2.45
3.24
4.26
5.55
7.17
9.18
11.67
14.72
1.96
2.56
3.31
4.28
5.50
2.24
2.79
3.45
4.22
5.32
6.72
8.67
11.17
14.65
7.04
8.98
11.40
14.43
Water + methanol (w
2
2
2
2
3
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
1.71
2.16
2.61
3.21
3.97
5.02
6.53
8.29
10.89
1.76
2.12
2.58
3.19
3.99
5.05
6.46
8.35
10.87
1.41
1.87
2.46
3.20
4.13
5.28
6.70
8.45
10.59
1.49
1.95
2.54
3.29
4.25
5.46
6.99
8.92
11.33
1.65
2.05
2.50
3.06
3.84
4.79
6.33
8.08
10.58
Water + methanol (w
2
2
2
83.15
88.15
93.15
0.99
1.25
1.54
1.00
1.23
1.53
0.81
1.09
1.45
1.02
1.34
1.75
1.12
1.41
1.73
(
continued on next page)
5

Wen-Dong Liu, Yong-Xiang Li, Duan-Lin Cao et al.
Journal of Molecular Liquids 342 (2021) 117332
Table 4 (continued)
3
exp
3
AP
3
kh
3
JA
3
RK
T/K
10 ꢀx
1
10 ꢀx
1
10 ꢀx
1
10 ꢀx
1
10 ꢀx
1
2
3
3
3
3
3
98.15
1.90
2.43
3.07
4.07
5.23
6.84
1.92
2.43
3.11
4.02
5.23
6.85
1.91
2.50
3.23
4.15
5.29
6.70
2.28
2.97
3.83
4.94
6.33
8.08
2.15
2.72
3.39
4.55
5.81
7.62
03.15
08.15
13.15
18.15
23.15
1
Water + methanol (w = 0.9000)
2
2
2
2
3
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
0.78
1.02
1.33
1.70
2.25
2.85
3.86
5.02
6.63
0.79
1.02
1.32
1.71
2.23
2.91
3.82
5.03
6.63
0.67
0.93
1.26
1.70
2.26
2.99
3.91
5.07
6.54
0.60
0.80
1.05
1.39
1.81
2.36
3.07
3.96
5.09
0.71
0.94
1.23
1.59
2.13
2.75
3.68
4.79
6.32
Water + ethanol (w
1
1
1
1
1
1
= 0.1000)
= 0.2000)
= 0.3000)
= 0.4000)
= 0.5000)
= 0.6000)
2
2
2
2
3
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
14.42
16.36
18.56
21.24
24.23
28.92
34.12
40.34
47.36
14.40
16.26
18.54
21.31
24.69
28.82
33.86
40.04
47.63
13.00
15.51
18.39
21.70
25.48
29.78
34.66
40.17
46.38
13.19
15.59
18.39
21.63
25.38
29.70
34.67
40.38
46.93
14.41
16.34
18.54
21.22
24.20
28.89
34.07
40.28
47.27
Water + ethanol (w
2
2
2
2
3
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
8.47
9.72
8.53
9.71
7.44
9.09
7.60
9.15
8.53
9.80
11.20
13.07
15.51
18.25
21.69
26.67
32.23
11.20
13.05
15.37
18.27
21.91
26.49
32.28
11.03
13.30
15.94
19.01
22.56
26.64
31.32
10.98
13.14
15.68
18.66
22.15
26.22
30.96
11.30
13.20
15.65
18.44
21.97
27.03
32.67
Water + ethanol (w
2
2
2
2
3
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
4.75
5.58
4.86
5.58
4.10
5.12
4.25
5.21
4.63
5.43
6.56
6.51
6.35
6.37
6.36
7.71
7.68
7.81
7.76
7.46
9.27
9.18
9.56
9.42
9.00
11.07
13.45
16.91
20.78
11.10
13.57
16.75
20.86
11.62
14.05
16.89
20.20
11.41
13.77
16.58
19.90
10.70
12.93
16.26
20.03
Water + ethanol (w
2
2
2
2
3
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
2.54
3.05
3.67
4.34
5.31
6.40
7.83
9.99
12.58
2.61
3.05
3.60
4.32
5.23
6.42
7.95
9.95
12.56
2.18
2.77
3.49
4.37
5.43
6.71
8.23
10.05
12.19
2.36
2.95
3.67
4.55
5.63
6.93
8.51
10.42
12.71
2.52
3.02
3.61
4.30
5.22
6.33
7.78
9.86
12.32
Water + ethanol (w
2
2
2
2
3
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
1.22
1.47
1.79
2.22
2.69
3.38
4.19
5.23
6.61
1.22
1.47
1.79
2.20
2.71
3.36
4.19
5.25
6.60
1.07
1.37
1.75
2.21
2.78
3.46
4.29
5.29
6.48
1.34
1.70
2.16
2.73
3.43
4.30
5.37
6.68
8.28
1.46
1.79
2.20
2.71
3.30
4.10
5.11
6.48
8.20
Water + ethanol (w
2
2
2
2
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
1.02
1.27
1.59
2.03
2.50
3.15
3.99
5.02
1.02
1.27
1.59
1.99
2.50
3.15
3.98
5.04
0.91
1.20
1.55
2.00
2.55
3.23
4.06
5.07
0.81
1.05
1.35
1.73
2.21
2.82
3.57
4.51
0.94
1.17
1.48
1.92
2.35
2.98
3.76
4.76
6

Wen-Dong Liu, Yong-Xiang Li, Duan-Lin Cao et al.
Journal of Molecular Liquids 342 (2021) 117332
Table 4 (continued)
3
exp
3
AP
3
kh
3
JA
3
RK
T/K
10 ꢀx
1
10 ꢀx
1
10 ꢀx
1
10 ꢀx
1
10 ꢀx
1
3
23.15
6.40
6.39
6.30
5.68
6.08
Water + ethanol (w
1
1
1
= 0.7000)
= 0.8000)
= 0.9000)
2
2
2
2
3
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
0.80
1.02
1.35
1.85
2.28
2.93
3.75
4.80
6.16
0.81
1.05
1.37
1.77
2.29
2.94
3.77
4.82
6.14
0.76
1.02
1.35
1.77
2.30
2.97
3.81
4.84
6.10
0.54
0.71
0.93
1.21
1.57
2.03
2.61
3.35
4.27
0.69
0.86
1.12
1.50
1.86
2.37
3.04
3.84
4.94
Water + ethanol (w
2
2
2
2
3
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
0.58
0.70
0.87
1.06
1.31
1.59
2.10
2.65
3.37
0.57
0.69
0.85
1.05
1.31
1.65
2.08
2.64
3.37
0.49
0.64
0.82
1.06
1.35
1.70
2.14
2.67
3.31
0.42
0.56
0.74
0.98
1.29
1.69
2.20
2.85
3.68
0.56
0.71
0.92
1.22
1.54
1.93
2.53
3.21
4.12
Water + ethanol (w
2
2
2
2
3
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
0.45
0.59
0.75
0.90
1.21
1.46
1.98
2.56
3.25
0.45
0.57
0.73
0.93
1.19
1.52
1.96
2.53
3.27
0.40
0.53
0.70
0.93
1.21
1.56
2.00
2.55
3.22
0.41
0.55
0.73
0.98
1.29
1.71
2.24
2.93
3.82
0.49
0.63
0.79
0.91
1.20
1.42
1.94
2.51
3.16
Water + 1-propanol (w = 0.1000)
1
1
1
1
1
2
2
2
2
3
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
11.78
13.63
15.53
17.63
20.06
23.22
26.92
32.30
38.26
12.11
13.52
15.27
17.42
20.05
23.29
27.27
32.17
38.21
10.88
12.88
15.18
17.80
20.77
24.15
27.96
32.25
37.09
10.91
12.84
15.07
17.64
20.59
23.98
27.86
32.29
37.33
11.80
13.64
15.55
17.65
20.10
23.26
26.97
32.45
38.35
Water + 1-propanol (w
= 0.2000)
2
2
2
2
3
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
9.18
10.51
12.01
13.95
16.21
19.02
22.85
27.77
32.79
9.19
10.45
12.00
13.92
16.29
19.23
22.86
27.37
32.99
8.17
9.87
8.31
9.95
9.10
10.44
11.91
13.83
16.01
18.88
22.67
27.09
32.46
11.86
14.18
16.85
19.93
23.46
27.49
32.09
11.86
14.11
16.73
19.78
23.33
27.45
32.20
Water + 1-propanol (w
= 0.3000)
2
2
2
2
3
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
6.59
7.74
9.00
10.62
12.42
15.14
18.35
21.63
27.55
6.69
7.69
8.95
10.53
12.51
15.01
18.17
22.18
27.28
5.79
7.16
8.78
10.71
12.97
15.63
18.73
22.33
26.49
6.11
7.44
9.02
10.90
13.14
15.79
18.92
22.60
26.92
6.71
7.81
9.12
10.76
12.69
15.24
18.47
22.57
27.82
Water + 1-propanol (w
= 0.4000)
2
2
2
2
3
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
4.82
5.65
6.74
8.04
9.70
11.59
14.12
18.26
22.51
4.89
5.67
6.67
7.94
9.59
11.70
14.42
17.96
22.57
4.08
5.16
6.47
8.06
9.96
12.24
14.94
18.13
21.88
4.30
5.32
6.57
8.08
9.91
12.10
14.74
17.89
21.65
4.78
5.68
6.77
8.08
9.70
11.78
14.33
18.01
22.75
Water + 1-propanol (w
= 0.5000)
2
2
2
83.15
88.15
93.15
3.35
4.05
4.90
3.45
4.05
4.83
2.87
3.67
4.67
2.86
3.61
4.55
3.29
3.96
4.78
(
continued on next page)
7

Wen-Dong Liu, Yong-Xiang Li, Duan-Lin Cao et al.
Journal of Molecular Liquids 342 (2021) 117332
Table 4 (continued)
3
exp
3
AP
3
kh
3
JA
3
RK
T/K
10 ꢀx
1
10 ꢀx
1
10 ꢀx
1
10 ꢀx
1
10 ꢀx
1
2
3
3
3
3
3
98.15
5.88
7.20
8.76
10.72
13.73
17.44
5.82
7.10
8.75
10.91
13.72
17.40
5.88
7.36
9.15
11.29
13.86
16.90
5.69
7.10
8.83
10.94
13.50
16.61
5.76
7.01
8.54
10.50
13.46
17.19
03.15
08.15
13.15
18.15
23.15
Water + 1-propanol (w = 0.6000)
1
1
1
2
2
2
2
3
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
2.15
2.65
3.21
3.95
4.79
5.96
7.48
9.60
12.28
2.20
2.62
3.17
3.88
4.80
5.99
7.54
9.58
12.26
1.82
2.37
3.05
3.90
4.95
6.23
7.79
9.68
11.95
1.79
2.31
2.96
3.78
4.80
6.08
7.67
9.64
12.06
2.15
2.61
3.17
3.86
4.74
5.79
7.26
9.39
11.95
Water + 1-propanol (w
= 0.7000)
2
2
2
2
3
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
1.27
1.56
1.92
2.37
2.95
3.64
4.74
6.09
7.86
1.34
1.59
1.91
2.34
2.91
3.67
4.69
6.05
7.91
1.05
1.39
1.82
2.35
3.03
3.86
4.89
6.14
7.67
1.04
1.37
1.79
2.34
3.03
3.91
5.03
6.44
8.21
1.30
1.59
1.96
2.42
3.00
3.72
4.77
6.19
7.82
Water + 1-propanol (w
= 0.8000)
2
2
2
2
3
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
0.57
0.70
0.91
1.15
1.44
1.89
2.42
3.16
4.11
0.57
0.72
0.90
1.14
1.46
1.88
2.43
3.15
4.12
0.48
0.65
0.86
1.14
1.49
1.94
2.49
3.19
4.04
0.56
0.75
1.00
1.34
1.77
2.33
3.06
4.00
5.20
0.70
0.87
1.14
1.43
1.80
2.33
3.02
3.99
5.07
Water + 1-propanol (w
1
= 0.9000)
2
2
2
2
3
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
0.47
0.60
0.82
1.06
1.35
1.80
2.30
3.24
4.11
0.47
0.61
0.80
1.04
1.37
1.80
2.38
3.14
4.14
0.40
0.56
0.76
1.04
1.39
1.84
2.42
3.16
4.09
0.27
0.37
0.51
0.70
0.94
1.27
1.71
2.28
3.02
0.32
0.42
0.62
0.81
1.05
1.48
1.89
2.64
3.53
Water + acetone (w
1
1
1
= 0.1000)
2
2
2
2
3
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
1.26
1.47
1.67
1.94
2.17
2.43
2.86
3.35
3.87
1.29
1.46
1.66
1.89
2.16
2.49
2.87
3.33
3.87
1.22
1.42
1.65
1.91
2.21
2.54
2.91
3.33
3.80
1.11
1.33
1.56
1.88
2.15
2.45
2.94
3.49
4.03
1.15
1.42
1.65
1.95
2.06
2.40
2.83
3.32
3.89
Water + acetone (w
= 0.2000)
2
2
2
2
3
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
1.09
1.26
1.42
1.63
1.88
2.19
2.58
3.12
3.66
1.12
1.25
1.42
1.62
1.88
2.19
2.59
3.08
3.69
0.99
1.18
1.40
1.66
1.95
2.28
2.66
3.09
3.58
0.98
1.15
1.34
1.56
1.84
2.17
2.59
3.18
3.72
1.23
1.40
1.58
1.80
2.07
2.40
2.81
3.31
3.83
Water + acetone (w
= 0.3000)
2
2
2
2
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
1.00
1.13
1.28
1.47
1.68
1.97
2.32
2.70
0.99
1.13
1.29
1.48
1.70
1.97
2.29
2.67
0.93
1.09
1.28
1.50
1.74
2.01
2.32
2.68
0.91
1.06
1.22
1.42
1.65
1.94
2.29
2.66
0.82
0.95
1.08
1.26
1.46
1.73
2.07
2.50
8

Wen-Dong Liu, Yong-Xiang Li, Duan-Lin Cao et al.
Journal of Molecular Liquids 342 (2021) 117332
Table 4 (continued)
3
exp
3
AP
3
kh
3
JA
3
RK
T/K
10 ꢀx
1
10 ꢀx
1
10 ꢀx
1
10 ꢀx
1
10 ꢀx
1
3
23.15
3.10
3.13
3.07
3.02
2.96
Water + acetone (w
1
1
1
1
1
1
= 0.4000)
= 0.5000)
= 0.6000)
= 0.7000)
= 0.8000)
= 0.9000)
2
2
2
2
3
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
0.87
1.01
1.15
1.33
1.54
1.81
2.16
2.55
3.03
0.88
1.00
1.15
1.33
1.55
1.82
2.14
2.54
3.03
0.80
0.96
1.14
1.35
1.59
1.87
2.19
2.55
2.97
0.83
0.97
1.12
1.30
1.52
1.79
2.13
2.50
2.94
0.82
0.95
1.08
1.25
1.45
1.71
2.05
2.45
2.89
Water + acetone (w
2
2
2
2
3
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
0.79
0.90
1.04
1.20
1.40
1.67
1.99
2.41
2.86
0.79
0.90
1.04
1.21
1.42
1.67
1.99
2.39
2.88
0.71
0.85
1.03
1.23
1.46
1.73
2.04
2.40
2.81
0.78
0.90
1.04
1.21
1.41
1.67
1.97
2.36
2.76
0.86
0.98
1.12
1.30
1.50
1.77
2.11
2.51
2.96
Water + acetone (w
2
2
2
2
3
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
0.71
0.82
0.95
1.12
1.32
1.56
1.89
2.32
2.76
0.72
0.82
0.95
1.12
1.32
1.57
1.89
2.28
2.78
0.63
0.77
0.94
1.13
1.36
1.63
1.94
2.29
2.71
0.74
0.85
0.98
1.15
1.34
1.58
1.88
2.27
2.65
0.78
0.89
1.03
1.20
1.41
1.67
1.99
2.41
2.87
Water + acetone (w
2
2
2
2
3
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
0.63
0.73
0.85
1.01
1.20
1.43
1.73
2.13
2.62
0.64
0.73
0.85
1.00
1.19
1.43
1.74
2.12
2.62
0.55
0.68
0.83
1.02
1.23
1.49
1.79
2.14
2.54
0.69
0.80
0.93
1.08
1.26
1.47
1.75
2.10
2.52
0.60
0.70
0.82
0.97
1.16
1.40
1.70
2.11
2.59
Water + acetone (w
2
2
2
2
3
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
0.55
0.65
0.76
0.91
1.07
1.32
1.61
1.95
2.41
0.55
0.64
0.76
0.91
1.09
1.32
1.60
1.96
2.41
0.49
0.60
0.75
0.92
1.12
1.36
1.64
1.97
2.36
0.65
0.75
0.87
1.01
1.18
1.40
1.66
1.95
2.33
0.45
0.55
0.65
0.79
0.95
1.18
1.46
1.83
2.30
Water + acetone (w
2
2
2
2
3
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
0.43
0.55
0.64
0.81
0.95
1.24
1.51
1.84
2.28
0.43
0.53
0.65
0.80
0.99
1.21
1.50
1.85
2.28
0.40
0.51
0.64
0.80
1.00
1.24
1.52
1.85
2.25
0.60
0.70
0.81
0.96
1.10
1.34
1.58
1.86
2.22
0.48
0.59
0.69
0.86
1.00
1.29
1.57
1.89
2.33
a
The standard uncertainty u are u(T) = 0.05 K and u(P) = 0.2 kPa; Relative standard uncertainty u
r
is u
r 1
(x ) = 0.05.
b
exp
AP
kh
JA
RK
x
1
1 1 1 1
is the experimental solubility; x , x , x and x
represent the calculated mole fraction solubility correlated by the modified Apelblat equation, kh equation,
Jouyban-Acree model and CNIBS/R-K model, respectively.
Where x
solvents; x
is the mass fraction of water in binary solvents mixtures; m
, m , and M , M , M represent the mass and molar mass of 3-
1
represents the solubility of 3-nitropyrazole in binary
is the mole fraction of water in binary mixed solvents;
3. Results and discussion
2
w
m
1
1
,
3.1. Solubility models
2
3
1
2
3
nitropyrazole, water and (methanol, ethanol, 1-propanol and ace-
tone), respectively.
In order to demonstrate the error and evaluate the different
models, the root-mean-square deviation (RMSD) is employed,
which is expressed as Eq. (10).
9

Wen-Dong Liu, Yong-Xiang Li, Duan-Lin Cao et al.
Journal of Molecular Liquids 342 (2021) 117332
"
À
Á
#
1=2
P
2
n
i ¼ 1
c
e
i
Where Tm represents the melting temperature of the corre-
x ꢁ x
i
4
RMSD ¼
ð10Þ
sponding solid. The values of model parameters k, h, 10 RMSD
N
2
and R are presented in Table 6.
Where xe and x denote experimental data and the calculated
values, respectively, and N is the number of experimental data.
c
3
.1.3. Jouyban-Acree model
The Jouyban-Acree model [25,26] is a semi-empirical thermo-
dynamic model that it is widely used to correlate the relationship
between both temperature and solvent composition with the solu-
bility. The equation can be expressed as:
3
.1.1. The modified Apelblat equation
The temperature and solubility of 3-nitropyrazole were corre-
lated by the modified Apelblat equation [21–23]. It is simple and
commonly to be written as follows:
2
3
lnx
1
¼ A
1
þ A
2
=T þ A
3
lnT þ A
4
x
2
þ A
5
x
2
=T þ A
6
ðx
2
Þ =T þ A
7
ðx
2
Þ =T
4
B
þA
8
ðx
2
Þ =T þ A
9 2
x lnT
lnx
1
¼ A þ T þ ClnT
ð11Þ
ð13Þ
Where A, B, C are the empirical constants and T is the absolute
Where A
1
-A
9
are empirical model parameters. Table 7 contains
temperature. The values of A and B reflect the variation of the activ-
ity coefficient, C represents the temperature effect upon the fusion
enthalpy. Table 5 contains data of the model parameters A, B, C,
4
2
the model parameters, 10 RMSD and R .
4
2
3.1.4. CNIBS/R-K model
1
0 RMSD and R .
The CNIBS/R-K equation, which was proposed by Acree [27,28],
is suitable for binary mixed systems. It is mainly used to describe
the relationship between the solubility and the composition of
mixed solvent when the temperature is constant, which can be
expressed as follows:
3
.1.2. kh equation
kh equation was proposed by Buchowski et al. that can give an
excellent solubility correlation for most systems with only two
variable parameters, k and h. The equation can be written as [24]:
ꢄ
ꢂ
ꢀ
ꢁꢃ
ꢅ
2
3
4
2
lnx
1
¼ B
0
þ B
1
x
2
þ B
2
x þ B
3
x þ B
4
x
ð14Þ
1
1 ¼ 1k exp kh
1
T
1
2
2
ꢁ
ꢁ T
m
ꢁ 1
ð12Þ
x
1
Table 5
4
Model parameters and 10 RMSD of the modified Apelblat equation in different binary solvents.
4
R2
w
1
A
B
C
10 RMSD
Water + methanol
0
0
0
0
0
0
0
0
0
.1000
.2000
.3000
.4000
.5000
.6000
.7000
.8000
.9000
36.74
ꢁ5792.00
17482.63
12489.24
14115.39
22019.44
14316.37
16808.12
14396.86
8693.58
ꢁ3.89
70.91
54.92
60.68
86.31
61.78
69.38
62.20
44.86
3.18
1.14
0.28
0.97
1.12
0.56
0.40
0.26
0.26
0.9981
0.9996
0.9999
0.9997
0.9995
0.9998
0.9998
0.9998
0.9998
ꢁ467.65
ꢁ359.84
ꢁ398.18
ꢁ570.86
ꢁ405.49
ꢁ457.45
ꢁ408.93
ꢁ291.15
Water + ethanol
0
0
0
0
0
0
0
0
0
.1000
.2000
.3000
.4000
.5000
.6000
.7000
.8000
.9000
ꢁ298.07
ꢁ365.97
ꢁ425.46
ꢁ431.36
ꢁ306.54
ꢁ244.07
ꢁ116.74
ꢁ343.1
10928.40
13702.86
16114.13
16133.89
10249.65
7157.71
1033.90
11689.04
7959.14
45.21
55.40
64.33
65.26
46.69
37.53
18.77
52.14
41.27
2.28
1.07
0.90
0.61
0.14
0.16
0.32
0.22
0.31
0.9995
0.9998
0.9997
0.9996
0.9999
0.9999
0.9997
0.9994
0.9988
ꢁ268.83
Water + 1-propanol
0
0
0
0
0
0
0
0
0
.1000
.2000
.3000
.4000
.5000
.6000
.7000
.8000
.9000
ꢁ328.22
ꢁ328.08
ꢁ373.48
ꢁ429.65
ꢁ429.28
ꢁ408.71
ꢁ516.71
ꢁ348.36
ꢁ258.12
12368.34
12100.86
13885.54
16160.89
15962.02
14818.15
19552.99
11554.79
7074.93
49.61
49.71
56.58
65.05
65.04
62.03
78.12
53.15
39.93
2.03
1.66
2.27
1.61
0.87
0.39
0.42
0.11
0.47
0.9994
0.9995
0.9988
0.9992
0.9996
0.9999
0.9996
0.9999
0.9984
Water + acetone
0.1000
0.2000
0.3000
0.4000
0.5000
0.6000
0.7000
0.8000
0.9000
ꢁ213.74
ꢁ362.39
ꢁ215.36
ꢁ277.81
ꢁ319.58
ꢁ351.16
ꢁ381.06
ꢁ314.90
ꢁ195.13
7251.71
13713.33
7174.28
9801.89
11575.02
12884.17
14102.91
10993.43
5245.31
32.16
54.40
32.43
41.83
48.10
52.86
57.37
47.57
29.91
0.29
0.20
0.16
0.09
0.11
0.15
0.06
0.07
0.17
0.9988
0.9994
0.9994
0.9998
0.9997
0.9995
0.9999
0.9999
0.9991
10

Wen-Dong Liu, Yong-Xiang Li, Duan-Lin Cao et al.
Journal of Molecular Liquids 342 (2021) 117332
Table 6
4
Model parameters and the 10 RMSD of the kh equation in different binary solvents.
4
R2
w
1
k
h
10 RMSD
Water + methanol
0
0
0
0
0
0
0
0
0
.1000
.2000
.3000
.4000
.5000
.6000
.7000
.8000
.9000
1.40
0.93
0.96
1.08
0.93
0.89
0.54
0.41
0.56
3300.73
4724.45
4628.19
4300.05
4965.35
5359.74
8438.84
11628.68
9220.77
3.18
3.81
3.51
4.11
3.91
2.71
2.20
1.17
0.79
0.9981
0.9961
0.9965
0.9950
0.9940
0.9960
0.9948
0.9965
0.9984
Water + ethanol
0
0
0
0
0
0
0
0
0
.1000
.2000
.3000
.4000
.5000
.6000
.7000
.8000
.9000
0.51
0.49
0.44
0.34
0.21
0.27
0.36
0.14
0.19
5565.59
6615.63
8263.44
11481.66
19298.76
16354.43
13342.34
31965.23
24929.63
8.23
6.57
4.41
2.72
0.95
0.71
0.44
0.62
0.47
0.9938
0.9928
0.9930
0.9931
0.9972
0.9984
0.9994
0.9958
0.9975
Water + 1-propanol
0
0
0
0
0
0
0
0
0
.1000
.2000
.3000
.4000
.5000
.6000
.7000
.8000
.9000
0.35
0.43
0.49
0.57
0.53
0.47
0.37
0.26
0.38
7614.56
7156.40
6955.86
6673.90
7554.48
9182.82
12252.31
18752.95
13843.78
7.69
6.36
6.09
5.20
3.72
2.43
1.48
0.57
0.62
0.9918
0.9933
0.9918
0.9920
0.9935
0.9947
0.9955
0.9978
0.9974
Water + acetone
-2
-2
-2
-2
-2
-2
-2
-2
-2
0.1000
0.2000
0.3000
0.4000
0.5000
0.6000
0.7000
0.8000
0.9000
2.63 ꢂ 10
3.58 ꢂ 10
2.47 ꢂ 10
3.17 ꢂ 10
3.54 ꢂ 10
4.03 ꢂ 10
4.53 ꢂ 10
4.67 ꢂ 10
6.17 ꢂ 10
91284.04
77756.01
0.54
0.68
0.37
0.47
0.50
0.48
0.52
0.39
0.27
0.9958
0.9935
0.9972
0.9955
0.9946
0.9949
0.9937
0.9959
0.9980
103604.77
90079.54
85616.54
79697.24
75293.19
75551.75
63000.60
Table 7
Model parameters and 10 RMSD of Jouyban-Acree model in binary solvent systems.
4
Water + methanol Water + ethanol
Water + 1-propanol
Water + acetone
A
A
A
A
A
A
A
A
A
1
1
2
3
4
5
6
7
8
9
ꢁ87.85
26.19
14.54
A
A
A
A
A
A
A
A
A
1
2
3
4
5
6
7
8
9
ꢁ55.93
153.74
9.13
A
A
A
A
A
A
A
A
A
1
2
3
4
5
6
7
8
9
ꢁ52.54
A
A
A
A
A
A
A
A
A
1
2
3
4
5
6
7
8
9
ꢁ39.22
40.16
8.52
ꢁ2.86
5.58
ꢁ7.42
ꢁ59.72
ꢁ53.55
15138.62
330.05
ꢁ0.02
0.96
11.13
34.26
5.05
324.15
ꢁ319.81
ꢁ405.29
1.09
ꢁ760.66
212.90
850.94
9.70
ꢁ287.66
ꢁ335.04
ꢁ68.43
9.07
0.01
ꢁ2555.10
4
4
4
4
0 RMSD
5.30
0.9905
10 RMSD
R
5.41
0.9961
10 RMSD
R
4.73
0.9968
10 RMSD
R
3.71
2
2
2
2
R
0.9900
4
Where x
, B , B , B
ters values of B
2
is the mole fraction of water in binary mixed solvents;
observed easily that the average values of 10 RMSD of selected
four models: the modified Apelblat equation, kh equation,
Jouyban-Acree model and CNIBS/R-K model are 0.70, 2.47, 4.79
and 1.51, respectively. In addition, the average values R2 of 3-
nitropyrazole within the experimental temperature range of these
equations are 0.9995 (the modified Apelblat equation), 0.9954 (kh
equation), 0.9934 (Jouyban-Acree model) and 0.9972 (CNIBS/R-K
B
0
1
2
3
and B
4
are the model parameters. The model parame-
4
2
0 1 2 3 4
, B , B , B , B , 10 RMSD and R are displayed in
Table 8.
3
.2. Solubility data
2
4
In four correlation models, it can be showed that small differ-
model). And the values of R and the values of 10 RMSD indicated
that all the four equations can present a satisfactory fitting results
in the mixed solvents and well correlated with experimental data
of 3-nitropyrazole. Therefore, by comparing the data of 10 RMSD
and R , the correlation between solubility and temperature good-
ences exist between the calculated values and experimental data
at different temperature in mixed binary systems, which provide
a convincing evidence for the accuracy of experimental data.
According to Table 4, it can be seen clearly that the calculated val-
ues are close to the experimental values. From Tables 5-8, it can be
4
2
ness order is the modified Apelblat equation > CNIBS/R-K mod-
11

Wen-Dong Liu, Yong-Xiang Li, Duan-Lin Cao et al.
Journal of Molecular Liquids 342 (2021) 117332
Table 8
4
Model parameters and the 10 RMSD of the CNIBS/R-K model in different binary solvents.
4
R2
T/K
B
0
B
1
B
2
B
3
B
4
10 RMSD
Water + methanol
2
2
2
2
3
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
ꢁ5.49
ꢁ5.16
ꢁ4.87
ꢁ4.62
ꢁ4.19
ꢁ3.66
ꢁ3.53
ꢁ3.27
ꢁ3.12
ꢁ1.08
ꢁ2.36
ꢁ3.64
ꢁ4.07
ꢁ6.29
ꢁ9.32
ꢁ8.09
ꢁ8.48
ꢁ7.91
4.07
8.97
ꢁ8.70
3.43
7.31
0.19
0.69
1.13
0.61
1.79
2.12
1.81
4.11
1.63
0.9965
0.9971
0.9973
0.9972
0.9979
0.9978
0.9964
0.9973
0.9973
ꢁ16.10
ꢁ25.41
ꢁ28.11
ꢁ39.16
ꢁ52.65
ꢁ45.86
ꢁ49.52
ꢁ49.17
14.63
16.27
24.07
34.11
29.55
31.64
30.79
12.37
13.95
19.43
25.76
22.41
24.43
24.50
Water + ethanol
2
2
2
2
3
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
ꢁ3.91
ꢁ3.79
ꢁ3.69
ꢁ3.64
ꢁ3.57
ꢁ3.35
ꢁ3.19
ꢁ3.08
ꢁ2.97
ꢁ1.82
ꢁ1.95
ꢁ1.59
ꢁ0.23
0.64
ꢁ16.72
ꢁ15.50
ꢁ16.69
–23.02
ꢁ25.01
–23.16
–22.18
–23.61
ꢁ25.04
24.90
23.16
25.95
38.14
39.91
38.66
37.06
37.90
39.87
ꢁ10.18
ꢁ9.39
0.42
2.33
4.22
1.08
8.43
1.85
6.36
3.71
0.46
0.9995
0.9993
0.9990
0.9987
0.9985
0.9984
0.9980
0.9975
0.9971
ꢁ11.32
ꢁ18.78
ꢁ19.14
ꢁ19.31
ꢁ18.38
ꢁ18.36
ꢁ19.45
0.04
ꢁ0.05
0.72
1.32
Water + 1-propanol
2
2
2
2
3
3
3
3
3
83.15
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
ꢁ4.25
ꢁ4.05
ꢁ3.86
ꢁ3.77
ꢁ3.64
ꢁ3.51
ꢁ3.45
ꢁ3.19
ꢁ2.99
ꢁ1.47
ꢁ2.36
ꢁ3.36
ꢁ2.99
ꢁ3.01
ꢁ3.01
ꢁ1.75
ꢁ2.89
ꢁ3.53
ꢁ5.09
ꢁ1.15
4.07
3.51
4.47
5.78
1.31
6.60
10.64
6.89
0.86
ꢁ5.15
ꢁ1.99
3.41
3.48
4.48
6.86
3.36
7.57
11.54
0.07
0.28
0.35
0.15
0.18
0.16
0.05
0.52
0.37
0.9995
0.9995
0.9994
0.9993
0.9990
0.9991
0.9989
0.9971
0.9987
ꢁ8.27
7.93
ꢁ9.71
ꢁ13.01
ꢁ6.20
ꢁ14.34
ꢁ21.49
Water + acetone
283.15
288.15
293.15
298.15
303.15
308.15
313.15
318.15
323.15
ꢁ2.28
ꢁ2.41
ꢁ2.48
ꢁ2.57
ꢁ2.62
ꢁ2.64
ꢁ2.82
ꢁ3.00
ꢁ3.19
ꢁ41.78
ꢁ39.22
ꢁ37.33
ꢁ35.19
–33.27
ꢁ31.73
ꢁ28.50
ꢁ25.07
ꢁ21.76
128.37
120.28
113.96
107.36
100.68
96.40
86.11
74.68
63.87
ꢁ164.55
ꢁ154.38
ꢁ145.58
ꢁ137.21
ꢁ127.59
ꢁ122.80
ꢁ109.25
ꢁ93.54
73.48
69.18
64.95
61.35
56.57
54.86
48.64
41.14
34.31
0.57
1.81
2.04
0.94
0.95
0.90
0.30
1.19
0.52
0.9951
0.9949
0.9946
0.9942
0.9942
0.9939
0.9934
0.9956
0.9960
ꢁ78.91
el > kh equation > Jouyban-Acree model, which indicated that the
modified Apelblat equation correlated the relationship between
equilibrium solubility and temperature is more suitable for equa-
tion research and fitting the solubility values of 3-nitropyrazole
in the binary systems than other three models. The results men-
tioned above suggest that the fitted models and the values of sol-
ubility in this study provide
a certain foundation for the
crystallization process of 3-nitropyrazole in the future.
For further study of 3-nitropyrazole solubility behavior, Hansen
solubility parameters of selected solvents and 3-nitropyrazole
were investigated in this work. From Table 2, values of d
methanol, ethanol and 1-propanol are mainly contributed by d
However, values of d for water and acetone are mainly contributed
by d . It indicates that the major forces of methanol, ethanol and 1-
t
for
h
.
t
d
propanol differ from theses of water and acetone. Therefore, solu-
bility of 3-nitropyrazole in methanol, ethanol and 1-propanol is
higher than that in water and acetone. In addition, values of
Dd
t
between 3-nitropyrazole and binary solvents (water + methanol,
ethanol, 1-propanol and acetone) decrease as the mass fraction
Fig. 6. Experimental data correlated by the modified Apelblat equation for 3-
nitropyrazole in (water + methanol) binary solvent mixtures.
of water decreases. For four binary solvents, the difference of d
d
between mixed solvent and 3-nitropyrazole reduces as mass frac-
tion of water decreases. So the solubility of 3-nitropyrazole
increases with the decrease of mass fraction of water.
of temperature and increases with the increasing temperature,
while decreases with the rising water mass fraction ranging from
0.1000 to 0.9000 at a constant temperature. As the mass fraction
of water increases, the interaction of water and organic solvent will
be weakened. So the solubility of 3-nitropyrazole decreases with
Solubility of 3-nitropyrazole in four binary solvents (water
+
methanol, ethanol, 1-propanol and acetone) with different mass
fraction of water was presented in Table 4 and Figs. 6-9. The results
further illustrate that the solubility of 3-nitropyrazole is a function
12

Wen-Dong Liu, Yong-Xiang Li, Duan-Lin Cao et al.
Journal of Molecular Liquids 342 (2021) 117332
Fig. 10. lnx
against 10 (1/T-1/Tmean).
1
of 3-nitropyrazole in (water + methanol) binary solvent mixtures
Fig. 7. Experimental data correlated by the modified Apelblat equation for 3-
nitropyrazole in (water + ethanol) binary solvent mixtures.
4
Fig. 8. Experimental data correlated by the modified Apelblat equation for 3-
nitropyrazole in (water + 1-propanol) binary solvent mixtures.
Fig. 11. lnx
1
of 3-nitropyrazole in (water + ethanol) binary solvent mixtures against
4
10 (1/T-1/Tmean).
Fig. 9. Experimental data correlated by the modified Apelblat equation for 3-
nitropyrazole in (water + acetone) binary solvent mixtures.
Fig. 12. lnx
against 10 (1/T-1/Tmean).
1
of 3-nitropyrazole in (water + 1-propanol) binary solvent mixtures
4
13

Wen-Dong Liu, Yong-Xiang Li, Duan-Lin Cao et al.
Journal of Molecular Liquids 342 (2021) 117332
general. It can be inferred that the solubility order of 3-
nitropyrazole is ethanol > 1-propanol > methanol > acetone > wa-
ter. However, the polarity order of pure solvents is water (100)
>
methanol (76.2) > ethanol (65.4) > 1-propanol (61.7) > acetone
(
35.5) [29], which is not strictly consistent with the solubility
sequence of 3-nitropyrazole. The principle of ‘like dissolves like’
rule was not obvious. Generally, polarity mainly influences the
strength of solute–solvent Van der Waals interactions. Whereas,
hydrogen-bonding may also play an important role in the solute–
solvent interactions. For instance, a similar phenomenon has been
revealed in other compounds, such as EA [30], CNP [31] and FM
[
32]. Obviously, dissolution is a complex process and polarity is
not the unique factor to affect it. In fact, many factors (e.g., molec-
ular geometry, molecule polarity, molecule size, solute–solvent
and solvent–solvent interactions, dielectric constant, ionization
constant [33] and surface tension of different solvents) might affect
the solute solubility dissolved in a solvent. A similar phenomenon
was identified the solubility measurement of other compounds
(
e.g., sorbic acid [34] and sulbactam [35]).
According to Mauricio A. Filippa [29], dissolution process can be
Fig. 13. lnx
1
of 3-nitropyrazole in (water + acetone) binary solvent mixtures against
4
1
0 (1/T-1/Tmean).
divided into three steps: First, the bonds between adjacent solute
molecules are broken. Next, some hollow space are produced in
solvent. After that, the hollow space are filled by solute molecules.
Therefore, the Einter plays a key role in solubility behavior. In this
work, solute–solvent interaction was analyzed by using Dmol3
module. Fig. 5 displays interactions between 3-nitropyrazole and
methanol + water (a), ethanol + water (b), 1-propanol + water (c)
the increasing mass fraction of water in the determined tempera-
ture. At a given temperature and mass fraction of water, the solu-
bility order of 3-nitropyrazole in four binary solvents is water
+
ethanol (w
1
= 0.1000) > water + 1-propanol (w
1
= 0.1000) > wa-
ter + methanol (w
1
= 0.1000) > water + acetone (w = 0.1000) in
1
Table 9
H S
%f , %f , standard molar enthalpy, entropy and Gibbs energy of 3-nitropyrazole in four binary solvents at mean temperature (302.60 K) and P = 0.1 MPa.
o
ꢁ1
o
K-1
ꢁ1
o
ꢁ1
w
1
D
disH /(kJ
̣
mol
)
D
disS /(J
̣
̣
mol
)
D
disG /(kJ
̣
mol
)
%f
H
%f
S
Water + methanol
0
0
0
0
0
0
0
0
0
.1000
.2000
.3000
.4000
.5000
.6000
.7000
.8000
.9000
37.39
33.57
34.22
35.15
34.77
36.11
34.74
36.57
40.49
85.33
71.57
73.33
75.86
73.55
76.19
69.19
71.06
83.12
11.57
11.92
12.03
12.19
12.52
13.06
13.80
15.07
15.34
59.15
60.79
60.66
60.49
60.97
61.03
62.39
62.97
61.68
40.85
39.21
39.34
39.51
39.03
38.97
37.61
37.03
38.32
Water + ethanol
0
0
0
0
0
0
0
0
0
.1000
.2000
.3000
.4000
.5000
.6000
.7000
.8000
.9000
22.74
25.37
27.90
30.02
32.15
34.92
38.81
33.50
37.49
44.57
49.38
53.50
56.58
57.28
65.67
77.59
55.75
67.99
9.25
10.43
11.71
12.89
14.82
15.05
15.33
16.63
16.92
62.77
62.93
63.28
63.68
64.98
63.73
62.31
66.51
64.57
37.23
37.07
36.72
36.32
35.02
36.27
37.69
33.49
35.43
Water + 1-propanol
0
0
0
0
0
0
0
0
0
.1000
.2000
.3000
.4000
.5000
.6000
.7000
.8000
.9000
21.95
24.29
26.79
29.16
30.95
32.74
34.47
37.60
41.42
40.28
46.29
52.37
58.05
61.44
64.09
65.72
70.15
82.13
9.76
10.29
10.94
11.60
12.36
13.35
14.58
16.37
16.57
64.30
63.43
62.83
62.41
62.47
62.80
63.42
63.92
62.50
35.70
36.57
37.17
37.59
37.53
37.20
36.58
36.08
37.50
Water + acetone
0
0
0
0
0
0
0
0
0
.1000
.2000
.3000
.4000
.5000
.6000
.7000
.8000
.9000
20.91
22.92
21.86
23.60
24.61
28.95
26.97
28.11
31.47
18.21
23.80
19.34
24.39
26.99
40.76
33.41
36.35
46.48
15.40
15.71
16.01
16.22
16.44
16.61
16.86
17.11
17.40
79.15
76.09
78.88
76.18
75.08
70.12
72.73
71.87
69.11
20.85
23.91
21.12
23.82
24.92
29.88
27.27
28.13
30.89
14

Wen-Dong Liu, Yong-Xiang Li, Duan-Lin Cao et al.
Journal of Molecular Liquids 342 (2021) 117332
and acetone + water (d), respectively. Hydrogen bonds are built
between solvent and solute molecules according to the calcula-
tions, while the HꢀꢀꢀAcceptor distances (shown in Fig. 5) imply that
hydrogen bonds are the main origin of intermolecular interactions
in the studied cases [36]. The order of hydrogen bonds distance (Å)
is 3-nitropyrazole-ethanol–water (1.433, 2.342) < 3-nitropyrazole-
which indicates that 3-nitropyrazole in all solvents investigated
is a non-spontaneous and favorable process [48,49]. Meanwhile,
o
it is found that the lower the value of
D
disG , the greater the 3-
nitropyrazole solubility, which conforms to the general thermody-
namic principle [50]. In brief, these results are helpful for the opti-
mization of the mixing and crystallization processes of 3-
nitropyrazole. Moreover, it can be observed that all the values of
1
-propanol-water (1.678, 2.342) < 3-nitropyrazole-methanol–wat
er (2.004, 2.342) < 3-nitropyrazole-acetone–water (2.576, 2.342).
The weakening of the (solute + solvent) interactions gives rise to
the elongation of HꢀꢀꢀAcceptor distances. It illustrates that a high
solubility in ethanol + water can be mainly attributed to a strong
hydrogen bond interactions between 3-nitropyrazole and etha-
nol/water. When 3-nitropyrazole interacted with ethanol + water,
the atom H of amino group (H-bond donor) in pyrazole form
hydrogen bond with the atom O of hydroxyl group (H-bond accep-
tor) in ethanol + water. It is reasonable since the delocalized elec-
tron pyrazole ring attracts the lone pair electrons of nitrogen of
amino group along with the CAO bond so that the electron density
around O decreases and H atom becomes more positive [37]. As is
shown in Table 3, order of Einter is same to that of solubility order.
H S
%f were greater than those of %f in the 4 kinds of binary mixed
o
o
solvents, revealing that
[51].
dis dis
D H is the main factor affecting D G
5
. Conclusions
In this paper, the solubility of 3-nitropyrazole was measured by
the dynamic laser method in four binary solvents such as (water
+
+
methanol), (water + ethanol), (water + 1-propanol) and (water
acetone) in the temperature range from 283.15 K to 323.15 K. It
is easy to be found that the solubility of 3-nitropyrazole generally
increases with the increasing temperature in binary system at con-
stant solvent and decreases with the increasing in the mass frac-
tion of water. Moreover, the dissolving capacity of 3-
nitropyrazole in four binary solvent mixtures at constant temper-
For binary solvents, the order of
E
inter is water + ethanol
ꢁ1
ꢁ1
(
+
57.76 kJꢀmol ) > water + 1-propanol
(34.13 kJꢀmol ) > water
ꢁ1
ꢁ1
methanol (26.26 kJꢀmol ) > water + acetone (21.00 kJꢀmol ). A
ature ranked as water + ethanol (w
propanol (w = 0.1000) > water + methanol (w
acetone (w = 0.1000). Hansen solubility parameters were
1
= 0.1000) > water + 1-
larger value of Einter indicates a stronger interaction force. Stronger
1
1
= 0.1000) > water
solute–solvent interaction indicates stronger dissolution ability of
+
1
3
-nitropyrazole in selected solvents [38,39].
employed to provide a reasonable illustration for the solubility
order of 3-nitropyrazole in the 4 binary mixed solvents, and the
order of 3-nitropyrazole solubility in each binary solvent mixture
is the result of the combined effects of hydrogen bonding, disper-
sion and polarity. And solute–solvent interaction was calculated
by molecular simulation to investigate the solubility behavior dee-
ply. The analytic results show that solubility behavior can be
explained well by them. In addition, the data of experiment was
correlated by the modified Apelblat equation, kh equation,
Jouyban-Acree model and CNIBS/R-K model, which have been ver-
ified to be capable of the correlation of the solubility of 3-
nitropyrazole in binary system. In general, the four models give a
very satisfactory results, and the modified Apelblat equation shows
best consistency with the experimental data than the other three
4
. Thermodynamic properties
o
The standard molar enthalpy (
D
disH ) [40] could be related to
the temperature and the solubility with Eq. (15).
ꢀ
ꢁ
@
lnx
1
O
D
dis
H
¼ ꢁR ꢂ
ð15Þ
@
ð1=TÞ
Over
enthalpy (
mean = 302.60 K, in the present work) [41]. Therefore, Eq. (16)
a limited temperature interval, the standard molar
o
D
disH ) would be valid for the mean temperature
(T
can be presented as:
ꢀ
ꢁ
@
lnx
1
O
4
2
D
dis
H
¼ ꢁR ꢂ
ð16Þ
equations by comparing the 10 RMSD and R in different binary
solvents. Meanwhile, the thermodynamic properties of solution
in different binary solvent mixtures, such as the standard molar
@
ð1=T ꢁ 1=Tmean
Þ
o
The standard molar Gibbs energy (
D
disG ) can be calculated by
o
o
the following equation [42]:
Gibbs energy (
D
disG ), standard molar enthalpy (
D
disH ) and stan-
o
dard molar entropy (
D
disS ) were obtained and discussed. Accord-
O
D
dis
G
¼ ꢁRTmean ꢂ intercept
ð17Þ
ing to the data fitting, the mixing process of 3-nitropyrazole in all
solvents investigated is a non-spontaneous, and the main contribu-
Where the intercept is obtained in plots of lnx
1
versus (1/T ꢁ 1/
o
o
tion of DdisG comes from the positive enthalpy. Furthermore, the
Tmean). The standard molar entropy (DdisS ) is obtained by [43]:
solubility data and correlation results are worthwhile and very
useful for choosing a suitable solvent for the purification process
of 3-nitropyrazole on an industrial scale and further theoretical
studies.
O
O
D
disH ꢁ
dis
D G
O
D
disS ¼
ð18Þ
T
mean
The %f
H
and %f
S
represent the comparison of the relative contri-
bution to the standard Gibbs energy by enthalpy and entropy in
the solution process [44,45], respectively.
Declaration of Competing Interest
j
D
mixHj
%
fH
¼
ꢂ 100
ð19Þ
The authors declare that they have no known competing finan-
cial interests or personal relationships that could have appeared
to influence the work reported in this paper.
j
D
mixHj þ jT
m
D
mixSj
jT
D
mixSj
%
fS ¼
ꢂ 100
ð20Þ
j
D
mixHj þ jT
D
mixSj
Acknowledgments
The curves of lnx
tures were displayed in Figs. 10–13. The data of %f
listed in Table 9 together with
1
vs (1/T ꢁ 1/Tmean) in four binary solvent mix-
H
and %f
S
is
We would like to acknowledge editors and reviewers, thank you
for your valuable advice.
o
o
o
D
disG ,
D
disH and
D
disS . It is clear
o
o
that the values of
D
disH and
D
disS are all positive, which indicate
Notes
that the dissolution process of 3-nitropyrazole is endothermic and
This research did not receive any specific grant from funding
agencies in the public, commercial, or not-for-profit sectors.
o
driven by entropy [46,47]. The values of
dis
D G are all positive,
15

Wen-Dong Liu, Yong-Xiang Li, Duan-Lin Cao et al.
Journal of Molecular Liquids 342 (2021) 117332
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