Solubility, thermodynamic modeling and Hansen solubility parameter of a new type of explosive in four binary solvents (benzene + ethanol, n-propanol, n-butanol and isoamyl alcohol) from 283.15 K to 323.15 K

Article abstract of DOI:10.1016/j.molliq.2020.114842

The solubility of 3,4-dinitropyrazole (DNP) in four binary solvents (benzene + ethanol, n-propanol, n-butanol and isoamyl alcohol) was measured by a dynamic laser monitoring at the temperature from 283.15 K to 323.15 K at pressure of 0.1 MPa. The solubility of DNP increased positively with increasing temperature, while increased with decreasing molar fraction of benzene in each binary system. Moreover, the experimental solubility values of DNP in this work were correlated well with four thermodynamic models namely “the modified Apelblat equation, Jouyban-Acree model, NRTL model and Wilson model” obtaining average root-mean-square deviation (10⁴RMSD) lower than 98.93 for correlative studies. In addition, Hansen solubility parameters were used to explain and predict the solubility behavior. Finally, mixing thermodynamic properties were estimated and analyzed based on solubility data and the Wilson model, and it's easy to understand that the dissolution was a spontaneous process from the results.

Full text of DOI:10.1016/j.molliq.2020.114842

Journal of Molecular Liquids 328 (2021) 114842
Contents lists available at ScienceDirect
Journal of Molecular Liquids
journal homepage: www.elsevier.com/locate/molliq
Solubility, thermodynamic modeling and Hansen solubility parameter
of a new type of explosive in four binary solvents (benzene + ethanol,
n-propanol, n-butanol and isoamyl alcohol) from 283.15 K to 323.15 K
a
b,
a
c
Hao-qi Guo , Yong-xiang Li ⁎, Yu-lin Yang , Zi-yang Li
a
School of Chemistry and Chemical Engineering, Harbin Institute of Technology, Harbin 150001, China
School of Chemical Engineering and Technology, North University of China, Taiyuan 030051, China
Research Institute of Gan Su Yin Guang Chemical Industry Group, Baiyin 730900, People's Republic of China
b
c
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 6 August 2020
Received in revised form 23 October 2020
Accepted 19 November 2020
Available online 24 January 2021
The solubility of 3,4-dinitropyrazole (DNP) in four binary solvents (benzene + ethanol, n-propanol, n-butanol
and isoamyl alcohol) was measured by a dynamic laser monitoring at the temperature from 283.15 K to
323.15 K at pressure of 0.1 MPa. The solubility of DNP increased positively with increasing temperature, while
increased with decreasing molar fraction of benzene in each binary system. Moreover, the experimental solubil-
ity values of DNP in this work were correlated well with four thermodynamic models namely “the modified
Apelblat equation, Jouyban-Acree model, NRTL model and Wilson model” obtaining average root-mean-square
Keywords:
Solubility
4
deviation (10 RMSD) lower than 98.93 for correlative studies. In addition, Hansen solubility parameters were
3
,4-dinitropyrazole
used to explain and predict the solubility behavior. Finally, mixing thermodynamic properties were estimated
and analyzed based on solubility data and the Wilson model, and it's easy to understand that the dissolution
was a spontaneous process from the results.
Measurement
Correlation
Hansen solubility parameters
Thermodynamic
©
2020 Elsevier B.V. All rights reserved.
1
. Introduction
low-melting and low-explosive explosive, which is a potential melt-
cast explosive carrier and can replace TNT [3,4]. Furthermore, the single
crystal structure and spatial structure have been studied [5] and the re-
At present, due to the simple charge process of TNT-based melt-cast
explosives, the price is cheap, and it can adapt to various shapes of drug
rooms. It has good comprehensive performance and is widely used in
conventional weapons. Therefore, it is the most widely used military hy-
brid explosive in the world [1]. But such explosives have obvious defects
1
sults showed that DNP was monoclinic and the space group was P2 /c,
with unit cell parameters of a = 9.9801(8) Å, b = 11.9959(9) Å, c =
3
9.7192(7) Å, β = 94.232(1) °, V = 1160.41(15) Å , Z = 8, F (000) =
−3
c
640, D = 1.80969 g·cm . Due to the large number of intermolecular
[
2]. 2-Methyl-1,3,5-trinitrobenzene (TNT) is toxic to humans and can-
hydrogen bonds and the π-π stacking interactions between the DNP
molecules, the structure of DNP is very stable. The structure of DNP
have been characterized [6], and the experimental values of explosion
not meet the requirements in the standard test of insensitive ammu-
nition. In addition, it has high sensitivity and poor safety during
−
1
−1
transportation. 3,4-Dinitropyrazole (DNP, C
is a five-membered nitrogen heterocyclic nitro compound with
4n + 2) electrons, which has certain aromaticity, and the structure
3
H
2
O
4
N
4
, 158.09, Fig. 1)
heat and explosion velocity were 4326 kJ·kg
respectively.
and 7633 m·s
,
(
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 process [7]. Moreover, many studies have
focused on the synthesis of DNP [8–10], but only a few have attempted
to establish purification methods to obtain products with high purity
and yield. The industrial crystallization process based on the solubility
data has many advantages, such as high efficiency, high yield, low en-
ergy consumption, low pollution, high product purity, etc. Furthermore,
it is especially suitable for industrial fields of solid products, such as fine
contains N–N, C–N, N–O and other heights generate thermal
groups to make the material have a higher energy (energy output of
8
−3
210.32 kJ·cm ). In addition, due to high nitrogen (35.67%), high oxy-
gen (40.67%), low carbon (22.93%) and other characteristics, the density
of DNP is higher than TNP (DNP of 1.87 g·cm− , TNT of 1.64 g·cm ),
and it is easy to reach oxygen balance (25.48%). Compared with
cyclotrimethylenetrinitramine (RDX), octahydro-1,3,5,7-tetranitro-
3
−3
1
,3,5,7-tetrazocine (HMX) and other explosives, it is a high-energy,
⁎
Corresponding author.
E-mail address: 574732638@qq.com (Y. Li).
https://doi.org/10.1016/j.molliq.2020.114842
167-7322/© 2020 Elsevier B.V. All rights reserved.
0

H. Guo, Y. Li, Y. Yang et al.
Journal of Molecular Liquids 328 (2021) 114842
purchased from local reagent factories without further purification,
and their mass fraction purity was not less than 0.990. 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 temperature (T )
m
and fusion enthalpy (ΔfusH) of DNP. The standard uncertainties of the
measurement were a temperature of 0.5 K and a fusion enthalpy of
−
1
4
1
00 J·mol
. Fig. 3 indicates that the fusion enthalpy is
−
1
1.744 kJ·mol and the melting temperature is 360.98 K.
2.3. X-ray diffraction
Since the solubility may change with the crystal structure, it is nec-
essary to confirm the crystal structure before the measurement of its
solubility. The DNP crystal used to measure the solubility was identified
by X-ray diffraction (XRD) using Bruker D8 Advance (Bruker Corpora-
tion, Germany). The data was carried out in the range of 2θ from 5° to
Fig. 1. The molecular structure of DNP.
−1
8
0°, with a voltage of 45 kV and a scanning rate of 10°·min . The
XRD curves of DNP in binary solvents were showed in Fig. 4. The results
showed that no polymorph transformation of DNP was identified.
chemicals and biopharmaceuticals. At the same time, the study of solu-
bility data defines the separation limit for the crystallization separation
process, and provides basic data for the design of the equipment struc-
ture size and the determination of operating conditions, which is an im-
portant prerequisite for realizing chemical production. The solubility
data of DNP has important research significance for the crystallization
process of DNP.
The solubility of DNP in four binary solvent mixtures has been deter-
mined at temperatures ranging from (283.15 to 323.15) K with a dy-
namic laser monitor. The solubility data was regressed with different
thermodynamic models including the modified Apelblat equation,
Jouyban-Acree model, NRTL model and Wilson model. Hansen solubility
parameters of DNP and mixed binary solvents were applied to investi-
gate the dissolution behavior. Besides, the mixing thermodynamic
properties of DNP in different binary solvent mixtures, including mixing
enthalpy, mixing entropy and mixing Gibbs energy, were calculated and
discussed by Wilson model. Additionally, the identification of DNP crys-
tal was verified by using X-ray diffraction (XRD).
2.4. Hansen solubility parameter
The concept of Hansen solubility parameter (HSP) has been widely
used for selecting suitable solvents for solute [12]. The basis of the HSP
approach is to assume that the total cohesive energy (E ) of a pure com-
pound consists of three parts, including nonpolar (dispersion) interac-
tions (E ), polar (dipole-dipole and dipole-induced dipole)
interactions (E ) and hydrogen bonding or other specific association in-
t
d
p
teractions including Lewis acid-base interactions (E
h
):
Et ¼ E þ Ep þ E
ð1Þ
d
h
Dividing each contribution by the molar volume:
Et
V
Ed Ep Eh
2
2
2
¼
þ
þ
¼ δd þ δp þ δh
V
ð2Þ
V
V
Therefore, the total solubility parameter (δ
t
) can be expressed as:
ð3Þ
represent the Hansen dispersion solubility pa-
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2. Experimental
2
d
2
p
2
h
δt ¼ δ þ δ þ δ
2.1. Chemical materials
Where δ , δ
d p
and δ
H
DNP was synthesized from pyrazole by a three-step reaction of nitra-
rameter, polar solubility parameter and hydrogen bonding solubility pa-
tion, rearrangement and nitration [11], and the synthetic route is
showed in Fig. 2. It was purified by crystallization in benzene and its
mass fraction purity, measured by High Performance Liquid Chromatog-
raphy (HPLC), was 0.990. All solvents used in this experiment, such
as benzene, ethanol, n-propanol, n-butanol and isoamyl alcohol, were
rameter, respectively. The values of δ , δ and δ for selected solvents
can be obtained from literature [12]. The solubility parameter for binary
solvents (δmix) can be expressed as: [13]
d
p
H
δmix ¼ αδ1 þ ð1−αÞδ2
ð4Þ
O N
O N
NO2
2
2
,
H
HNO3 2SO
4
HNO3
benzonitrile
heat
N
N
N
N
Ac O
2
N
H
N
H
N
H
N
NO2
Fig. 2. Synthetic route of DNP.
2

H. Guo, Y. Li, Y. Yang et al.
Journal of Molecular Liquids 328 (2021) 114842
Table 1
The detailed information of the materials used in this paper.
Material
Molar mass/(g·mol−1)
ρa/(g·cm−3)
Source
Purity
Purification method
Analysis method
HPLCb
DNP
Benzene
Ethanol
n-propanol
n-butanol
Isoamyl alcohol
158.09
78.11
46.07
60.11
74.12
88.15
1.810
0.879
0.789
0.804
0.810
0.809
Synthesized by us
0.990
0.995
0.995
0.990
0.990
0.990
crystallization
none
none
none
none
c
Sinopharm Chemical Reagent Co., Ltd
Sinopharm Chemical Reagent Co., Ltd
Sinopharm Chemical Reagent Co., Ltd
Sinopharm Chemical Reagent Co., Ltd
Sinopharm Chemical Reagent Co., Ltd
GC
GC
GC
GC
c
c
c
c
none
GC
a
The density of solvents at temperature 293.15 K.
High-performance liquid chromatography.
Gas chromatography.
b
c
In addition, the difference of total solubility parameter between
t
solute and solvent (Δδ ) can be used to estimate the miscibility of two
compounds: [16]
Δδt ¼ jδt2−δt1j
ð5Þ
Where δt1 and δt2 are total Hansen solubility parameters of solute
and binary solvents, respectively.
2.5. Experimental procedures
In this research work, the solubility of DNP in four selected binary
solvents including “benzene + ethanol, n-propanol, n-butanol and
isoamyl alcohol” at 283.15–323.15 K was investigated by laser monitor-
ing method. The experimental approach and apparatus were similar to
our previous published paper and briefly described here [17–19]. 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 circulating water bath (type 501, Gongyi Yuhua Instru-
ment Co., Ltd., China) with an uncertainty of 0.05 K and determined
by thermometer mercury. Then, excess amount of solid was added
into double-layer glass bottle at the setting temperature. A magnetic ag-
itator was used for accelerating the dissolution rate of DNP in selected
binary solvents. The mixture solution was stirred for more than
Fig. 3. DSC plot of DNP.
3
0 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 DNP was dis-
solved 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 elec-
tronic analytical balance (type AB 204, Mettler Toledo, Switzerland)
with an accuracy of 0.0001 g. Three parallel experiments for each tem-
perature point were performed in this work and the average values
were considered the final results.
The mole-fraction solubility of DNP (x
expressed as:
1
) in binary solvents can be
m1=M1
m1=M1 þ m2=M2 þ m3=M3
x1 ¼
x2 ¼
ð6Þ
ð7Þ
m2=M2
m2=M2 þ m3=M3
Fig. 4. XRD pattern of DNP.
x3 ¼ 1−x2
m2
ð8Þ
ð9Þ
w1 ¼
Where α stands for the volume fraction of solvent 1 (benzene); δ
1
2
m þ m
3
and δ
and solvent 2 (ethanol / n-propanol / n-butanol / isoamyl alcohol).
The group contribution (Hoftyzer-Van Krevelen) method was
used to calculate the values of δ , δ and δ of DNP [14]. The molar
= 95.0 cm ·mol , was taken from the SciFinder
2
are the Hansen solubility parameters of solvent 1 (benzene)
w2 ¼ 1−w1
ð10Þ
d
p
−1
H
Where x1 represents the solubility of DNP in binary solvents; x2
is the mole fraction of benzene in binary mixed solvents; x3 is the
mole fraction of (ethanol / n-propanol / n-butanol / isoamyl alcohol)
3
volume of DNP, V
database [15].
s
3

H. Guo, Y. Li, Y. Yang et al.
Journal of Molecular Liquids 328 (2021) 114842
in binary solvents; w
1
is the mass fraction of benzene in binary solvents
When introducing constant term, Eq. (16) can be further simplified
mixtures; w
isoamyl alcohol) in binary solvents; m
2
is the mass fraction of (ethanol / n-propanol / n-butanol /
, m , m , and M , M , M re-
as Eq. (17):
1
2
3
1
2
3
2
3
ln x1 ¼ A1 þ A2=T þ A3 ln T þ A4x2 þ A5x2=T þ A6ðx2Þ =T þ A7ðx2Þ =T
present the mass and molar mass of DNP, benzene and (ethanol,
n-propanol, n-butanol and isoamyl alcohol), respectively.
4
þA ðx Þ =T þ A x ln T
8
2
9
2
ð17Þ
3. Results and discussion
Where A
parameters.
1
, A
2
, A
3
, A
4
, A
5
, A
6
, A
7
, A
8
and A
9
are empirical model
3.1. Solubility models
Since (solid + liquid) equilibrium is usually not available, correla-
3
.1.3. NRTL model
Based on Scott's two-liquid approach, Renon and Prausnitz's NRTL
model has some similarities to Guggenheim's quasi-chemical approach
25,26]. Rather than using interaction potential energies and volume
tion and prediction schemes are frequently utilized. The modified
Apelblat equation, Jouyban-Acree model, NRTL model and Wilson
model are used to correlate the experimental values. The root-mean-
square deviation (RMSD) of four binary solvents is used to evaluate
the fitting results of the correlation models. The RMSD is defined as:
[
fractions, NRTL model was described by using Gibbs energies of interac-
tion (Gij and Gii), mole fractions and a non-randomness parameter of the
molecular distribution (αij and αji). The NRTL expression of g for ter-
nary mixture can be given by:
E
"
À
Á#1=2
n
i¼1
2
c
e
i
∑
x −x
i
RMSD ¼
ð11Þ
N
gE
RT
3
τjixjGji
¼
∑ xi
ð18Þ
3
e
c
i¼1
Where x and x denote experimental data and the calculated values,
respectively, and N is the number of experimental data.
∑
xlGli
l¼1
Where the adjustable parameters (τij and τji) can be expressed by
using the difference between energy parameter characteristics (Δgij
and Δgji) as:
3
.1.1. The modified Apelblat equation
The temperature and solubility of DNP were correlated by the mod-
ified Apelblat equation [20–22]. It is simple and commonly to be written
as follows:
gij−gjj Δgij
RT
τij ¼
¼
RT
ð19Þ
B
T
ln x1 ¼ A þ þ C ln T
ð12Þ
Where A, B, C are the empirical constants and T is the absolute tem-
perature. The values of A and B reflect the variation of the activity coef-
ficient, C represents the temperature effect upon the fusion enthalpy.
Table 2
Hansen solubility parameter of selected binary solvents and solute.
(MPa)0.5 (MPa)0.5 (MPa)0.5 (MPa)0.5
benzene + ethanol
w
1
δ
d
δ
p
δ
H
δ
t
Δδ
t
(MPa)0.5
3.1.2. Jouyban-Acree model
The Jouyban-Acree model [23,24] is a semi-empirical thermody-
0.86
17.3
17.1
16.9
16.7
16.5
16.3
16.2
2.1
3.2
4.1
4.7
5.7
6.5
7.2
4.5
6.9
9.0
10.4
12.5
14.3
15.8
18.0
18.7
19.6
20.3
21.5
22.6
23.7
9.8
9.1
8.2
7.5
6.3
5.2
4.1
namic model that it is widely used to correlate the relationship between
temperature and solvent composition with the solubility. The equation
can be expressed as:
0.72
0.60
0
0
0
0
.52
.40
.30
.21
2
i
J ðx2−x3Þ
i
ln x1 ¼ x2 ln ðx1Þ þ x3 ln ðx1Þ þ x2x3 ∑
ð13Þ
2
3
i¼0
T
benzene + n-propanol
0
0
0.66
0.56
0
0
0
.88
.77
17.4
17.2
17.0
16.9
16.7
16.5
16.3
1.7
2.3
3.0
3.6
4.1
4.7
5.3
3.8
5.5
7.2
8.8
10.3
11.9
13.4
17.9
18.2
18.7
19.3
20.0
20.9
21.8
9.9
9.6
9.1
8.5
7.8
6.9
6.0
i
Where J is the model constant.
In order to extent the application of the temperature ranges where
non-linear solubility behavior is observed, Jouyban et al. proposed a
combination of Jouyban-Acree model and the modified Apelblat equa-
tion to correlate the solubility of a solute in binary solvent mixtures at
different temperatures. According to the modified Apelblat equation,
.46
.36
.26
benzene + n-butanol
1 2 1 3
ln(x ) and ln(x ) can be expressed by Eqs. (14) and (15):
0
0
0
0
0.50
0
0
.90
.80
.70
.60
17.4
17.3
17.1
17.0
16.8
16.6
16.5
1.5
1.9
2.4
2.9
3.4
3.8
4.3
3.4
4.8
6.1
7.5
8.9
10.3
11.7
17.8
18.0
18.3
18.8
19.3
19.9
20.6
10.0
9.8
9.5
9.0
8.5
7.9
7.2
ln ðx1Þ ¼ A2 þ B2=T þ C2 ln T ln ðx1Þ ¼ A2 þ B2=T þ C2 ln T
ð14Þ
ð15Þ
2
2
ln ðx1Þ ¼ A3 þ B3=T þ C3 ln T
3
.40
.30
Put Eqs. (14), (15) and x
be obtained:
3
= 1 - x
2
into Eq. (13), a new equation can
benzene + isoamyl alcohol
0
0
.75
.65
17.2
17.0
16.8
16.6
16.4
16.2
16.0
18.0
1.8
2.2
2.5
2.8
3.2
3.5
3.9
18.2
5.0
6.1
7.3
8.5
17.9
18.2
18.5
18.9
19.4
20.0
20.6
27.8
9.9
9.6
9.3
8.9
8.4
7.8
7.2
0.0
x2
T
ln x1 ¼ A2 þ B2=T þ C2 ln T þ ðA2−A3Þx2 þ ðB2−B3 þ J −J þ J Þ
0
1
2
0.55
0.45
0.34
0.23
0.12
DNP
x22
x23
þð3J −J −5J Þ
þ ð8J −2J Þ
1
0
2
2
1
9.8
T
T
x24
11.1
12.4
10.8
þð−4J2Þ T þ ðC2−C3Þx2 ln T
ð16Þ
4

H. Guo, Y. Li, Y. Yang et al.
Journal of Molecular Liquids 328 (2021) 114842
Table 3
1
Mole fraction solubility (x .
) of DNP in binary solvent mixtures at different temperatures from 283.15 K to 323.15 K and P = 0.1 MPaa,b
exp
AP
JA
NRTL
Wilson
T/K
x
1
x
1
x
1
x
1
x
1
benzene + ethanol (w
1
2
= 0.86/x = 0.8426)
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
0.07206
0.08252
0.09708
0.1141
0.1320
0.1394
0.1590
0.1813
0.2098
0.07342
0.08443
0.09680
0.1106
0.1261
0.1433
0.1624
0.1835
0.2069
0.07177
0.08099
0.09191
0.1049
0.1202
0.1385
0.1601
0.1859
0.2165
0.07209
0.08246
0.09712
0.1142
0.1319
0.1394
0.1590
0.1814
0.2098
0.07495
0.08474
0.09679
0.1109
0.1269
0.1401
0.1597
0.1825
0.2109
benzene + ethanol (w
1
= 0.72/x
2
= 0.6914)
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
0.1190
0.1195
0.1353
0.1524
0.1711
0.1912
0.2128
0.2360
0.2608
0.2872
0.1166
0.1308
0.1474
0.1671
0.1902
0.2175
0.2497
0.2877
0.3326
0.1190
0.1296
0.1588
0.1721
0.1936
0.2139
0.2292
0.2598
0.2901
0.1210
0.1335
0.1529
0.1688
0.1891
0.2107
0.2319
0.2622
0.2951
0.1297
0.1588
0.1721
0.1936
0.2139
0.2292
0.2598
0.2901
benzene + ethanol (w
1
1
1
1
1
= 0.60/x
2
= 0.5665)
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
0.1693
0.1644
0.1854
0.2100
0.2387
0.2723
0.3117
0.3578
0.4118
0.4751
0.1705
0.1903
0.2134
0.2405
0.2724
0.3097
0.3535
0.4049
0.4653
0.1693
0.1849
0.2068
0.2332
0.2717
0.3126
0.3642
0.4125
0.4721
0.1659
0.1857
0.2094
0.2369
0.2718
0.3112
0.3599
0.4117
0.4749
0.1849
0.2069
0.2332
0.2717
0.3125
0.3643
0.4125
0.4721
benzene + ethanol (w
= 0.52/x
2
= 0.4856)
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
0.2126
0.2077
0.2338
0.2644
0.3001
0.3419
0.3907
0.4480
0.5150
0.5936
0.2057
0.2290
0.2563
0.2882
0.3255
0.3691
0.4201
0.4797
0.5496
0.2127
0.2318
0.2601
0.3009
0.3369
0.3947
0.4504
0.5169
0.5909
0.2091
0.2339
0.2636
0.3007
0.3395
0.3915
0.4479
0.5153
0.5938
0.2319
0.2601
0.3009
0.3368
0.3948
0.4504
0.5169
0.5909
benzene + ethanol (w
= 0.40/x
2
= 0.3674)
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
0.2294
0.2235
0.2530
0.2867
0.3254
0.3698
0.4207
0.4791
0.5459
0.6226
0.2434
0.2706
0.3024
0.3394
0.3825
0.4326
0.4911
0.5593
0.6388
0.2294
0.2501
0.2808
0.3252
0.3684
0.4252
0.4810
0.5454
0.6213
0.2275
0.2537
0.2853
0.3248
0.3676
0.4203
0.4778
0.5451
0.6252
0.2501
0.2808
0.3253
0.3684
0.4252
0.4810
0.5454
0.6213
benzene + ethanol (w
= 0.30/x
2
= 0.2719)
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
0.2562
0.2561
0.2840
0.3166
0.3547
0.3993
0.4513
0.5122
0.5834
0.6667
0.2592
0.2883
0.3221
0.3614
0.4071
0.4601
0.5218
0.5935
0.6769
0.2563
0.2842
0.3113
0.3598
0.4000
0.4556
0.5116
0.5741
0.6717
0.2551
0.2843
0.3158
0.3574
0.3999
0.4528
0.5111
0.5778
0.6704
0.2842
0.3115
0.3596
0.3999
0.4556
0.5117
0.5739
0.6717
benzene + ethanol (w
= 0.21/x
2
= 0.1881)
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
0.2800
0.2816
0.3134
0.3498
0.3913
0.4386
0.4927
0.5544
0.6249
0.7053
0.2720
0.3027
0.3382
0.3794
0.4272
0.4826
0.5468
0.6212
0.7077
0.2798
0.3108
0.3520
0.3938
0.4414
0.4962
0.5526
0.6123
0.7132
0.2813
0.3127
0.3505
0.3916
0.4385
0.4925
0.5522
0.6190
0.7134
0.3103
0.3522
0.3940
0.4415
0.4961
0.5523
0.6125
0.7132
(continued on next page)
5

H. Guo, Y. Li, Y. Yang et al.
Journal of Molecular Liquids 328 (2021) 114842
Table 3 (continued)
T/K
exp
AP
JA
NRTL
Wilson
x
1
x
1
x
1
x
1
x
1
1
1
1
1
1
1
1
2
benzene + n-propanol (w = 0.88/x = 0.8495)
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
0.07112
0.08188
0.09504
0.1105
0.1230
0.1360
0.1569
0.1737
0.1991
0.07219
0.08262
0.09455
0.1076
0.1222
0.1384
0.1563
0.1759
0.1975
0.06632
0.07616
0.08747
0.1003
0.1152
0.1321
0.1515
0.1737
0.1991
0.07127
0.08178
0.09502
0.1105
0.1230
0.1360
0.1569
0.1738
0.1991
0.07389
0.08335
0.09453
0.1077
0.1210
0.1358
0.1554
0.1750
0.2009
benzene + n-propanol (w
= 0.77/x
2
= 0.7204)
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
0.1045
0.1062
0.1227
0.1406
0.1598
0.1805
0.2024
0.2255
0.2498
0.2751
0.1065
0.1219
0.1394
0.1595
0.1824
0.2086
0.2384
0.2725
0.3113
0.1045
0.1192
0.1421
0.1655
0.1816
0.2079
0.2155
0.2455
0.2805
0.1106
0.1237
0.1406
0.1594
0.1774
0.2011
0.2186
0.2481
0.2834
0.1193
0.1421
0.1654
0.1817
0.2079
0.2155
0.2454
0.2805
benzene + n-propanol (w
= 0.66/x
2
= 0.5990)
= 0.4948)
= 0.3959)
= 0.3021)
= 0.2128)
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
0.1501
0.1484
0.1697
0.1946
0.2238
0.2581
0.2984
0.3458
0.4015
0.4670
0.1474
0.1684
0.1924
0.2199
0.2512
0.2869
0.3277
0.3741
0.4270
0.1501
0.1671
0.1990
0.2165
0.2609
0.3004
0.3443
0.4028
0.4662
0.1500
0.1698
0.1967
0.2209
0.2584
0.2979
0.3435
0.4017
0.4687
0.1672
0.1990
0.2166
0.2609
0.3004
0.3442
0.4029
0.4661
benzene + n-propanol (w
= 0.56/x
2
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
0.1712
0.1680
0.1950
0.2254
0.2596
0.2978
0.3406
0.3881
0.4409
0.4993
0.1790
0.2047
0.2341
0.2676
0.3059
0.3496
0.3995
0.4563
0.5211
0.1712
0.1942
0.2223
0.2574
0.2930
0.3517
0.3928
0.4289
0.5034
0.1748
0.1978
0.2246
0.2566
0.2920
0.3410
0.3869
0.4345
0.5076
0.1943
0.2223
0.2573
0.2930
0.3517
0.3928
0.4289
0.5034
benzene + n-propanol (w
= 0.46/x
2
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
0.2015
0.1990
0.2302
0.2660
0.3067
0.3531
0.4058
0.4656
0.5334
0.6102
0.2026
0.2321
0.2659
0.3045
0.3487
0.3992
0.4568
0.5226
0.5976
0.2015
0.2318
0.2623
0.3033
0.3487
0.4136
0.4714
0.5257
0.6118
0.2055
0.2338
0.2651
0.3033
0.3474
0.4047
0.4648
0.5288
0.6176
0.2317
0.2623
0.3033
0.3487
0.4136
0.4715
0.5256
0.6118
benzene + n-propanol (w
= 0.36/x
2
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
0.2282
0.2301
0.2558
0.2869
0.3245
0.3697
0.4243
0.4900
0.5693
0.6651
0.2184
0.2508
0.2881
0.3307
0.3796
0.4356
0.4997
0.5729
0.6565
0.2281
0.2593
0.2824
0.3292
0.3695
0.4236
0.4900
0.5674
0.6662
0.2278
0.2571
0.2862
0.3276
0.3702
0.4237
0.4891
0.5672
0.6666
0.2592
0.2824
0.3292
0.3694
0.4235
0.4901
0.5674
0.6662
benzene + n-propanol (w
= 0.26/x
2
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
0.2405
0.2385
0.2704
0.3076
0.3510
0.4015
0.4604
0.5291
0.6093
0.7028
0.2285
0.2633
0.3033
0.3493
0.4021
0.4627
0.5322
0.6117
0.7028
0.2405
0.2768
0.3025
0.3452
0.3951
0.4673
0.5383
0.6042
0.7015
0.2404
0.2737
0.3065
0.3486
0.3976
0.4617
0.5317
0.6059
0.7052
0.2767
0.3025
0.3452
0.3951
0.4673
0.5383
0.6041
0.7016
6

H. Guo, Y. Li, Y. Yang et al.
Journal of Molecular Liquids 328 (2021) 114842
Table 3 (continued)
exp
AP
JA
NRTL
Wilson
T/K
x
1
x
1
x
1
x
1
x
1
1
1
1
1
1
1
1
2
benzene + n-butanol (w = 0.90/x = 0.8952)
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
0.04476
0.04907
0.05437
0.06440
0.07089
0.07798
0.08833
0.1048
0.04450
0.04956
0.05544
0.06226
0.07018
0.07937
0.09004
0.1024
0.03667
0.04203
0.04833
0.05576
0.06453
0.07487
0.08707
0.1015
0.04477
0.04907
0.05436
0.06439
0.07089
0.07797
0.08834
0.1048
0.04465
0.04955
0.05519
0.06308
0.07035
0.07850
0.08893
0.1036
0.1161
0.1168
0.1185
0.1161
0.1168
benzene + n-butanol (w
= 0.80/x
2
= 0.7915)
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
0.08034
0.07975
0.08817
0.09766
0.1083
0.1204
0.1339
0.1491
0.1663
0.1855
0.07057
0.08010
0.09125
0.1043
0.1196
0.1375
0.1585
0.1832
0.2121
0.08033
0.08823
0.09738
0.1067
0.1188
0.1390
0.1477
0.1648
0.1861
0.07773
0.08628
0.09592
0.1064
0.1188
0.1357
0.1491
0.1675
0.1898
0.08822
0.09738
0.1067
0.1188
0.1390
0.1477
0.1648
0.1861
benzene + n-butanol (w
= 0.70/x
2
= 0.6889)
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
0.1133
0.1190
0.1319
0.1476
0.1664
0.1892
0.2165
0.2494
0.2891
0.3370
0.1133
0.1278
0.1447
0.1643
0.1872
0.2139
0.2451
0.2814
0.3239
0.1133
0.1341
0.1530
0.1687
0.1881
0.2161
0.2461
0.2871
0.3396
0.1160
0.1325
0.1501
0.1681
0.1893
0.2165
0.2474
0.2875
0.3387
0.1341
0.1530
0.1687
0.1881
0.2162
0.2461
0.2871
0.3396
benzene + n-butanol (w
= 0.60/x
2
= 0.5874)
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
0.1476
0.1511
0.1709
0.1938
0.2204
0.2511
0.2867
0.3280
0.3758
0.4312
0.1567
0.1760
0.1985
0.2246
0.2548
0.2900
0.3309
0.3785
0.4338
0.1476
0.1706
0.2004
0.2208
0.2497
0.2852
0.3251
0.3782
0.4314
0.1506
0.1714
0.1964
0.2206
0.2502
0.2852
0.3256
0.3766
0.4327
0.1706
0.2004
0.2209
0.2497
0.2852
0.3249
0.3783
0.4314
benzene + n-butanol (w
= 0.50/x
2
= 0.4869)
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
0.1809
0.1825
0.2074
0.2363
0.2699
0.3089
0.3542
0.4069
0.4683
0.5396
0.1921
0.2154
0.2424
0.2737
0.3099
0.3520
0.4007
0.4572
0.5227
0.1809
0.2081
0.2356
0.2730
0.3083
0.3544
0.4039
0.4693
0.5402
0.1835
0.2088
0.2367
0.2708
0.3076
0.3526
0.4037
0.4683
0.5424
0.2081
0.2357
0.2730
0.3083
0.3543
0.4038
0.4694
0.5402
benzene + n-butanol (w
= 0.40/x
2
= 0.3875)
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
0.2161
0.2205
0.2416
0.2675
0.2990
0.3371
0.3832
0.4388
0.5061
0.5875
0.2145
0.2405
0.2706
0.3054
0.3457
0.3922
0.4461
0.5085
0.5807
0.2161
0.2406
0.2711
0.3052
0.3389
0.3833
0.4327
0.5006
0.5929
0.2159
0.2407
0.2699
0.3032
0.3395
0.3841
0.4356
0.5021
0.5903
0.2406
0.2710
0.3052
0.3389
0.3834
0.4327
0.5006
0.5929
benzene + n-butanol (w
= 0.30/x
2
= 0.2891)
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
0.2304
0.2265
0.2534
0.2845
0.3207
0.3626
0.4112
0.4676
0.5331
0.6092
0.2241
0.2516
0.2833
0.3199
0.3622
0.4111
0.4676
0.5329
0.6085
0.2304
0.2632
0.2903
0.3293
0.3625
0.4125
0.4617
0.5318
0.6007
0.2325
0.2613
0.2909
0.3270
0.3643
0.4117
0.4631
0.5296
0.6019
0.2632
0.2904
0.3293
0.3625
0.4125
0.4616
0.5319
0.6007
(continued on next page)
7

H. Guo, Y. Li, Y. Yang et al.
Journal of Molecular Liquids 328 (2021) 114842
Table 3 (continued)
T/K
exp
AP
JA
NRTL
Wilson
x
1
x
1
x
1
x
1
x
1
benzene + isoamyl alcohol (w
1
1
1
1
1
1
1
= 0.75/x
0.1345
0.1457
0.1559
0.1690
0.1801
0.1945
0.2078
0.2247
0.2408
2
2
2
2
2
2
2
= 0.7720)
= 0.6770)
= 0.5797)
= 0.4801)
= 0.3676)
= 0.2521)
= 0.1334)
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
0.1349
0.1452
0.1562
0.1680
0.1807
0.1942
0.2087
0.2242
0.2407
0.1247
0.1355
0.1475
0.1606
0.1752
0.1912
0.2088
0.2283
0.2497
0.1345
0.1457
0.1559
0.1690
0.1801
0.1945
0.2078
0.2247
0.2408
0.1185
0.1314
0.1449
0.1606
0.1766
0.1952
0.2148
0.2374
0.2614
benzene + isoamyl alcohol (w
= 0.65/x
0.1502
0.1653
0.1795
0.1920
0.2076
0.2234
0.2405
0.2693
0.2955
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
0.1532
0.1641
0.1766
0.1907
0.2066
0.2247
0.2451
0.2681
0.2941
0.1543
0.1675
0.1820
0.1981
0.2158
0.2353
0.2567
0.2803
0.3063
0.1502
0.1653
0.1795
0.1920
0.2076
0.2234
0.2405
0.2693
0.2955
0.1346
0.1503
0.1670
0.1844
0.2043
0.2259
0.2497
0.2810
0.3136
benzene + isoamyl alcohol (w
= 0.55/x
0.1806
0.1993
0.2170
0.2336
0.2562
0.2849
0.3076
0.3420
0.3837
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
0.1830
0.1978
0.2148
0.2343
0.2566
0.2820
0.3109
0.3439
0.3816
0.1785
0.1939
0.2108
0.2294
0.2499
0.2724
0.2972
0.3245
0.3545
0.1806
0.1993
0.2170
0.2336
0.2561
0.2850
0.3076
0.3421
0.3836
0.1660
0.1854
0.2061
0.2281
0.2541
0.2847
0.3153
0.3540
0.3999
benzene + isoamyl alcohol (w
= 0.45/x
0.1810
0.2033
0.2193
0.2443
0.2734
0.2965
0.3190
0.3554
0.3985
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
0.1832
0.2013
0.2213
0.2435
0.2680
0.2952
0.3252
0.3583
0.3949
0.1967
0.2138
0.2327
0.2535
0.2764
0.3015
0.3292
0.3596
0.3929
0.1810
0.2034
0.2192
0.2443
0.2734
0.2965
0.3191
0.3555
0.3985
0.1727
0.1931
0.2133
0.2381
0.2667
0.2953
0.3259
0.3656
0.4124
benzene + isoamyl alcohol (w
= 0.34/x
0.2143
0.2389
0.2503
0.2746
0.3024
0.3205
0.3588
0.3895
0.4316
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
0.2173
0.2339
0.2528
0.2742
0.2984
0.3258
0.3566
0.3913
0.4304
0.2110
0.2298
0.2506
0.2734
0.2984
0.3260
0.3564
0.3897
0.4263
0.2144
0.2387
0.2503
0.2745
0.3025
0.3203
0.3589
0.3895
0.4315
0.2008
0.2230
0.2428
0.2685
0.2976
0.3250
0.3635
0.4017
0.4490
benzene + isoamyl alcohol (w
= 0.23/x
0.2298
0.2451
0.2709
0.2882
0.3163
0.3347
0.3807
0.4111
0.4505
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
0.2298
0.2472
0.2669
0.2892
0.3144
0.3428
0.3748
0.4108
0.4513
0.2227
0.2431
0.2655
0.2902
0.3174
0.3473
0.3801
0.4163
0.4560
0.2298
0.2451
0.2709
0.2882
0.3163
0.3347
0.3807
0.4111
0.4505
0.2180
0.2373
0.2614
0.2845
0.3133
0.3404
0.3820
0.4197
0.4653
benzene + isoamyl alcohol (w
= 0.12/x
0.2339
0.2573
0.2780
0.3237
0.3500
0.3682
0.4039
0.4426
0.4941
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
0.2352
0.2587
0.2843
0.3120
0.3420
0.3744
0.4095
0.4474
0.4883
0.2364
0.2585
0.2829
0.3097
0.3392
0.3717
0.4075
0.4468
0.4900
0.2339
0.2574
0.2779
0.3238
0.3499
0.3681
0.4039
0.4427
0.4941
0.2398
0.2605
0.2819
0.3138
0.3415
0.3680
0.4044
0.4453
0.4968
a
r r 1
The standard uncertainty u are u(T) =0.05 K and u(P) = 0.2 kPa; Relative standard uncertainty u is u (x ) = 0.05.
b
exp
AP JA NRTL
Wilson
x
1
is the experimental solubility; x
1
, x
1
x
1
and x
1
represent the calculated mole fraction solubility correlated by the modified Apelblat equation, Jouyban-Acree model, NRTL
model and Wilson model, respectively.
8

H. Guo, Y. Li, Y. Yang et al.
Journal of Molecular Liquids 328 (2021) 114842
gji−g
ii
Δgji
between mixed solvent and DNP reduces as mass fraction of benzene
decreases. So the solubility of DNP increases with the decrease of mass
fraction of benzene. Moreover, the values of the Hildebrand solubility
parameter δ increases with decreasing the content of benzene, and the
solubility of DNP also increases.
The solubility data is fitted by the modified Apelblat equation,
Jouyban-Acree model, NRTL model and Wilson model, the results
were listed in Table 3. And the experimental values correlated by
NRTL model are given in Figs. 5-8. The results showed that solubility
data increases with increasing temperature in all selected solvents,
and as the benzene content in the mixed solvents decreases, the solubil-
ity data also increases, which suggests that cooling crystallization using
the above solvents is appropriate for crystallization of DNP. At a given
temperature and mass fraction of benzene, the solubility order of DNP
τji ¼
¼ RT
ð20Þ
RT
The expressions of Gij and Gji can be given by:
À
Á
Gij ¼ exp −αij⋅τij
ð21Þ
ð22Þ
À
ÁÀ
Á
Gji ¼ exp −αji⋅τji αij ¼ αji
For a solute in binary solvent, the lnγ
1
can be expressed as:
ðτ21x2G21 þ τ31x3G31Þðx2G21 þ x3G31Þ
ln γ1
¼
2
ðx1 þ x2G21 þ x3G31Þ
x2G12ðτ12x2 þ τ12x3G32−τ32x3G32Þ
þ
ð23Þ
2
ðx1G12 þ x2 þ x3G32Þ
x3G13ðτ13x3 þ τ13x2G23−τ23x2G23Þ
þ
2
ðx1G13 þ x2G23 þ x3Þ
Where x
1
represents the mole fraction of DNP; x
2
and x
3
stand for the
mole fraction of benzene and (ethanol, n-propanol, n-butanol and
isoamyl alcohol) in ternary mixture solution.
3.1.4. Wilson model
The Wilson model based on the Flory-Huggins non-thermal
mixture expression has been widely used for correlating solubility
data. The expression of Wilson model for ternary mixtures could
be expressed as: [27,28].
!
gE
RT
3
3
¼
− ∑ xi ln ∑ xjΛij
ð24Þ
i¼1
j¼1
E
Where g stands for the excess Gibbs energy; Λij and Λij are ad-
justable parameters of Wilson model, which can be estimated by
corresponding molar volumes of pure-component (ν
characteristic energy differences (Δλij and Δλji):
i
and ν
j
) and
ꢀ
ꢀ
ꢁ
ꢁ
ꢀ
ꢀ
ꢁ
ꢁ
vj
Λij ¼ exp
vi
λij−λii
RT
vj
vi
Δλij
RT
−
¼
¼
exp
exp
−
ð25Þ
ð26Þ
Fig. 5. Experimental data correlated by the NRTL model for DNP in (benzene + ethanol)
binary solvent mixtures.
vi
Λji ¼ exp
vj
λji−λjj
RT
vi
vj
Δλji
RT
−
−
For ternary mixture system, activity coefficient of ln γ
1
could be
expressed as:
ln γ1 ¼ 1− ln ðx1 þ x2Λ12 þ x3Λ13Þ
x1
x2
x3
−
−
−
ð27Þ
x1 þ x2Λ12 þ x3Λ13
x1Λ21 þ x2 þ x3Λ23
x1Λ31 þ x2Λ32 þ x3
1 2 3
Where x represents the mole fraction of DNP; x and x stand for the
mole fraction of benzene and (ethanol, n-propanol, n-butanol and
isoamyl alcohol) in ternary mixture solution.
3.2. Solubility data
d p h t t
The Hansen solubility parameters (δ , δ , δ , δ and Δδ ) of four bi-
nary systems and DNP are listed in Table 2. As can be seen from
Table 2, values of δ for ethanol and n-propanol are mainly contributed
by δ . However, values of δ
are mainly contributed by δ
t
H
t
for benzene, n-butanol and isoamyl alcohol
d
. It indicates that the major forces of ethanol
and n-propanol differ from theses of benzene, n-butanol and isoamyl
alcohol. Therefore, solubility of DNP in ethanol and n-propanol is hi-
gher than that in benzene, n-butanol and isoamyl alcohol. In addition,
values of Δδ
n-propanol, n-butanol and isoamyl alcohol) decrease as the mass frac-
tion of benzene decreases. For four binary solvents, the difference of δ
t
between DNP and binary solvents (benzene + ethanol,
Fig. 6. Experimental data correlated by the NRTL model for DNP in (benzene +
n-propanol) binary solvents.
d
9

H. Guo, Y. Li, Y. Yang et al.
Journal of Molecular Liquids 328 (2021) 114842
the increasing mole fraction of alcohols. Moreover, when the increasing
mole fraction of benzene, the interaction of benzene and organic solvent
will be weakened. Therefore, the solubility of DNP decreases with the
increasing mole fraction of benzene in the determined temperature.
When the temperature is changed from 283.15 K to 323.15 K, the max-
imum increased solubility of DNP in each mixed solvents (benzene +
ethanol, benzene + n-propanol, benzene + n-butanol and benzene +
isoamyl alcohol) with different mole fractions of benzene are 191.15%
(
(
w
1
= 0.86), 179.92% (w
= 0.75), respectively.
The calculated solubility data by these models, along with the va-
1 1
= 0.88), 159.36% (w = 0.90) and 79.05%
w
1
4
lues of 10 RMSD, were presented in Tables 4-7. It can be easily obser-
ved that for the studied binary solvent mixtures, the maximum
values of 10 RMSD of selected four models: the modified Apelblat
4
equation, Jouyban-Acree model, NRTL model and Wilson model are
6
1
4.38, 128.41, 2.17 and 120.21, respectively. In addition, the average
0 RMSD within the experimental temperature range of these models
4
are 36.07 (the modified Apelblat equation), 98.93 (Jouyban-Acree
model), 0.52 (NRTL model) and 43.80 (Wilson model). Because the av-
4
4
erage 10 RMSD and the maximum 10 RMSD of NRTL model are the
smallest in four binary mixtures of (benzene + ethanol), (benzene +
n-propanol), (benzene + n-butanol) and (benzene + isoamyl alcohol)
Fig. 7. Experimental data correlated by the NRTL model for DNP in (benzene + n-butanol)
binary solvent systems.
2
at all initial composition ranges, and R is close to 1, the NRTL model can
better correlate the solubility data than other three models. The accu-
racy of the correlation is acceptable for industrial design and operation
purpose. From the result, it can be concluded that, the solubility as a
function of temperature is correlated well with the NRTL model as a
function of solvent composition in binary solvent mixtures. The experi-
mental solubility and correlation models in this paper can be used as
basic data and applicable simulation equations in the industrial separa-
tion and purification process of DNP. The results mentioned above
in four binary solvents is benzene + ethanol (w
n-propanol (w = 0.26) > benzene + n-butanol (w
isoamyl alcohol (w = 0.23) in general. It can be inferred that the sol-
ubility order of DNP is ethanol > n-propanol > n-butanol > isoamyl al-
cohol > benzene. In addition, the polarity order of pure solvents is
ethanol (65.4) > n-propanol (61.7) > n-butanol (60.2) > isoamyl alco-
hol (56.5) > benzene (11.1) [29], which is strictly consistent with the
solubility sequence of DNP. The phenomenon can be explained by the
1
= 0.30) > benzene +
1
1
= 0.30) > benzene
+
1
Table 4
“like dissolves like” rule [30] that the solubility of materials highly cor-
4
2
Model parameters, 10 RMSD and R of the modified Apelblat equation for solubility of
responds to the similarities between the solutes and the solvents. As
DNP in different binary solvents.
displayed in Fig. 1, DNP is a five-membered ring structure. Because
4
R2
w
1
A
B
C
10 RMSD
2
-NO is an electron-withdrawing group, the electron cloud density of
benzene + ethanol
the H atoms on N is reduced, and DNP molecule exhibits N–H hydrogen
bonding donor group, meaning that a hydrogen bond can be formed be-
tween the DNP and solvent molecules, so the solubility increases with
0.86
0.72
0.60
0.52
0.40
0.30
0.21
−30.03
12.39
−758.66
−2341.11
6028.98
6129.90
3540.35
6960.20
4318.70
5.33
31.93
38.81
36.07
34.12
34.27
45.25
54.32
0.9946
0.9949
0.9987
0.9992
0.9993
0.9988
0.9984
−1.11
27.98
28.23
19.47
30.27
21.24
−181.05
−182.58
−123.90
−196.82
−136.42
benzene + n-propanol
0.88
0.77
0.66
0.56
0.46
0.36
0.26
−22.26
78.71
−1056.35
−5386.07
5373.85
−1376.08
726.82
4.14
16.37
50.45
32.99
62.77
48.32
26.59
58.22
0.9984
0.9916
0.9990
0.9966
0.9987
0.9996
0.9985
−10.62
26.45
3.69
10.88
41.94
25.35
−170.24
−17.76
−65.64
−274.45
−162.90
10,248.82
5190.89
benzene + n-butanol
0.90
0.80
0.70
0.60
0.50
0.40
0.30
−176.52
−114.04
−272.10
−150.39
−152.49
−295.07
−168.63
5950.46
3396.55
10,287.59
4668.45
4703.91
11,331.78
5622.11
26.99
17.63
41.91
23.38
23.76
44.91
26.09
13.90
20.06
32.56
28.85
16.76
43.60
60.62
0.9965
0.9966
0.9979
0.9990
0.9998
0.9986
0.9994
benzene + isoamyl alcohol
0
0
0
0
0
0
0
.75
.65
.55
.45
.34
.23
.12
−48.43
−146.36
−161.76
−84.59
−140.56
−138.38
−41.73
976.56
7.61
5.55
0.9997
0.9974
0.9989
0.9975
0.9978
0.9973
0.9938
5251.13
5793.26
2254.57
4944.64
4865.29
408.24
22.31
24.73
13.27
21.53
21.21
6.88
23.14
21.37
38.87
32.24
37.46
64.38
Fig. 8. Experimental data correlated by the NRTL model for DNP in (benzene + isoamyl
alcohol) mixed solvents.
10

H. Guo, Y. Li, Y. Yang et al.
Journal of Molecular Liquids 328 (2021) 114842
Table 5
4
2
Model parameters, 10 RMSD and R of Jouyban-Acree model for solubility of DNP in binary solvent systems.
benzene + ethanol
benzene + n-propanol
benzene + n-butanol
benzene + isoamyl alcohol
A
1
−158.69
A
1
−94.96
A
1
−143.01
A
1
−77.39
A
A
A
A
A
A
A
A
2
3
4
5
6
7
8
9
5382.06
24.60
A
A
A
A
A
A
A
A
2
3
4
5
6
7
8
9
1932.39
15.37
A
A
A
A
A
A
A
A
2
3
4
5
6
7
8
9
4392.65
22.31
A
A
A
A
A
A
A
A
2
3
4
5
6
7
8
9
2002.53
12.22
−68.30
1643.83
5374.14
−8576.01
4078.43
10.14
−3.66
559.51
329.14
−504.15
−256.73
0.20
−40.31
2004.64
286.23
−865.39
−199.94
5.90
−16.74
816.37
581.45
−733.98
−35.63
2.28
4
4
4
4
10 RMSD
128.41
0.9917
10 RMSD
R
111.95
0.9938
10 RMSD
R
75.41
0.9970
10 RMSD
R
79.97
0.9900
2
2
2
2
R
E
id
suggest that the experimental data provide a certain foundation for
crystallization process of DNP in the future.
ΔmixH ¼ H þ ΔmixH
ð29Þ
E
id
ΔmixS ¼ S þ ΔmixS
ð30Þ
4. Thermodynamic properties
E
id
E
id
E
id
Where G and ΔmixG , S and ΔmixS , H and Δmix
H
stand for the
For a non-ideal solution, it is necessary to study the mixing thermo-
excess properties and mixing properties of ideal systems.
dynamic properties of the solute in different binary solvent mixtures,
such as the mixing enthalpy, the mixing Gibbs energy and the mixing
entropy.
The mixing thermodynamic properties of the ideal solution can be
calculated by the following equations [32].
n
id
The mixing properties can be calculated by the following equations [31].
ΔmixG ¼ RT ∑ xi ln xi
ð31Þ
ð32Þ
i
E
id
ΔmixHid ¼ 0
ΔmixG ¼ G þ ΔmixG
ð28Þ
Table 6
4
2
Model parameters, 10 RMSD and R of NRTL model for solubility of DNP in binary solvent mixtures.
Δg12/(J·mol−1)
Δg13/(J·mol−1
)
Δg21/(J·mol−1
)
Δg23/(J·mol−1
)
Δg31/(J·mol−1
)
Δg32/(J·mol−1
)
10 RMSD
4
R2
w
1
ɑ
benzene + ethanol
0.86
0.72
0.60
0.52
0.40
0.30
0.21
0.15
1.20
1.06
0.49
0.99
1.02
0.24
6450.91
4513.78
7603.23
8502.85
−1096.34
−1908.88
−98,564.04
−36,861.79
−2375.47
−1367.72
−10,011.11
7772.37
463.29
618.79
−5175.26
−9713.64
−11,894.43
6073.04
−12,273.08
−12,124.42
44,446.46
94,504.11
19,818.08
25,781.57
3200.37
1445.45
714.35
−9386.71
−1194.30
−11,964.42
−15,171.84
0.98
0.57
0.24
0.43
0.65
0.27
1.09
2.17
0.9999
0.9998
0.9998
0.9999
0.9994
0.9995
0.9995
1390.87
157.61
26,936.80
24,903.40
120,333.75
7004.92
−53,735.52
4.58
48,612.40
−71,412.23
benzene + n-propanol
0.88
0.77
0.66
0.56
0.46
0.36
0.26
0.31
0.51
0.74
0.45
0.41
0.91
0.20
−18,955.20
171,153.24
6628.61
−12,109.09
11,756.23
−4626.12
32,286.37
6293.38
694.07
−119,877.24
1181.53
2801.76
−951.74
1081.89
−8757.05
−108,020.58
2047.75
−16,329.02
−18,704.59
0.72
−4032.22
−45.94
38,401.32
−134.07
3815.82
9.09
−9549.20
−64,281.02
−10,574.48
9828.95
8964.30
−11,526.65
14,189.66
0.40
0.50
0.52
0.27
0.47
0.38
0.24
0.9994
0.9998
0.9999
0.9999
0.9994
0.9997
0.9996
−19,484.45
−4090.50
8401.54
−11,072.58
4931.02
−22,093.15
−11,246.40
−36,611.34
8011.65
benzene + n-butanol
0.90
0.80
0.70
0.60
0.50
0.40
0.30
1.40
0.05
1.56
0.51
0.65
0.98
1.08
555.24
55,314.40
3721.18
−3840.45
−17,926.63
−2384.07
−9731.67
12,156.23
6743.22
207.44
19,318.72
475.97
−368.58
11,634.80
1358.85
24,786.69
−5407.40
19.47
−3057.87
7850.77
−16,284.89
−1392.96
−12,036.54
12,312.99
−10,498.33
18,168.45
2777.98
3298.33
33.88
2678.89
0.10
0.13
0.28
0.54
0.80
0.43
0.62
0.9991
0.9997
0.9991
0.9996
0.9995
0.9999
0.9998
−13,928.83
−9825.85
−12,836.31
−12,493.82
−3397.21
−4491.53
6905.07
−3212.95
−3891.79
−1532.49
6935.99
683.02
benzene + isoamyl alcohol
0.75
0.65
0.55
0.45
0.34
0.23
0.12
1.35
0.25
0.41
0.54
0.21
0.77
1.31
1480.07
−2288.62
0.82
−148.63
143,944.30
24,580.38
3213.40
−70,578.84
383.54
1941.37
−2790.81
−38,899.72
32,889.51
56.71
23,983.54
955.53
−3837.58
−19,530.79
−11,205.98
5063.34
−26,466.78
−13,387.85
−3490.19
0.01
0.16
0.60
0.68
0.88
0.07
0.94
0.9998
0.9994
0.9995
0.9998
0.9992
0.9997
0.9999
−81,080.49
389,562.89
−8095.70
23,339.98
5424.01
−23,224.87
62,727.08
−15,023.97
−25,842.99
53.99
361,276.59
9197.81
−6556.66
−6149.87
4753.31
−2662.24
244.01
−10,248.49
42.47
11

H. Guo, Y. Li, Y. Yang et al.
Journal of Molecular Liquids 328 (2021) 114842
Table 7
4
2
Model parameters, 10 RMSD and R of Wilson model for solubility of DNP in mixed solvents.
Δλ12/(J·mol−1)
Δλ13/(J·mol−1
)
Δλ21/(J·mol−1
)
Δλ23/(J·mol−1
)
Δλ31/(J·mol−1
)
Δλ32/(J·mol−1
)
10 RMSD
4
R2
w
1
benzene + ethanol
0.86
0.72
0.60
0.52
0.40
0.30
0.21
46,426.60
51,145.33
1575.62
−369.89
−632.68
32,347.06
98,325.89
−1999.58
−2244.79
−1030.60
−363.57
−624.61
−1750.69
−1777.75
37,579.67
65,185.98
41,898.71
41,807.55
7370.67
−6959.46
0.86
11.75
−37.13
44.74
−1.41
−14,387.52
31,746.26
5857.20
−194,520.12
−37,593.34
−7.74
24.23
38.36
26.28
26.45
31.23
23.43
29.88
0.9969
0.9957
0.9993
0.9995
0.9994
0.9997
0.9995
6292.39
−12.68
38,563.73
40,585.40
75,367.42
−323,267.64
−10,884.87
1.07
6095.27
93,178.56
48,175.32
benzene + n-propanol
0.88
0.77
0.66
0.56
0.46
0.36
0.26
4922.39
6257.11
503.59
−114.57
−371.70
−1710.12
6285.52
−2728.70
−2655.27
496.96
−112.93
−365.68
29,776.56
−1016.80
2.34
−723,220.03
−1447.16
−39,459.71
−42,885.30
−7.92
14,827.61
36,598.87
3126.33
−34,009.64
−10,772.38
22.90
−0.16
−32,618.75
0.71
17.82
45.34
24.07
50.69
46.68
16.18
38.68
0.9981
0.9932
0.9994
0.9978
0.9988
0.9999
0.9993
56,366.86
34,578.93
38,530.17
4147.74
−598.03
2662.53
6239.80
39,871.99
33,774.31
46,998.11
17.74
11,628.13
−10.32
benzene + n-butanol
0.90
0.80
0.70
0.60
0.50
0.40
0.30
31,912.93
67,793.74
36,979.40
349.61
4.05
−2550.75
8567.87
−1979.07
−1811.85
−1492.08
345.51
5.21
33,706.76
−1464.95
29,860.19
132,113.16
8889.54
31,898.63
67,278.09
9371.51
−3463.81
−25,490.16
−14,384.52
−10,779.47
−14,220.33
12,757.25
0.10
1233.07
94,003.37
1997.55
10,506.96
5906.22
−161,640.63
147,103.37
29.62
0.59
7.88
0.9989
0.9985
0.9995
0.9996
0.9998
0.9998
0.9998
22.71
15.98
18.42
16.07
16.37
16.91
−315.09
−233.31
6.84
−170,719.49
2.80
33,993.47
benzene + isoamyl alcohol
0.75
0.65
0.55
0.45
0.34
0.23
0.12
76,592.08
437,427.78
−1252.39
−1861.10
−2869.97
−4008.89
−5846.77
−1776.45
−1301.65
71,809.87
236,353.47
80,685.63
67,857.63
12,424.88
37,095.63
588,689.36
133,156.26
147,151.38
102,190.83
100,914.26
36,658.47
−527,655.51
3737.30
25,494.07
0.54
−2518.64
5555.15
−6710.01
70,291.52
1,082,028.37
103,346.01
89,928.84
96,272.60
69,082.45
43,025.12
−8603.84
420,496.47
−2236.69
3.49
−2438.61
−3351.98
−11,362.82
120.21
117.75
106.62
84.06
107.52
84.36
0.9991
0.9990
0.9996
0.9987
0.9990
0.9989
0.9960
52.17
Table 8
mixH, ΔmixS and ΔmixG of DNP in different binary solvents from T = (283.15 K to 323.15 K) and P = 0.1 MPa.
Δ
T/K
Δ
mixG/(kJ·mol−1)
Δ
mixH/(kJ·mol−1
)
Δ
mixS/(J·K−1·mol−1
)
T/K
Δ
mixG/(kJ·mol−1
)
Δ
mixH/(kJ·mol−1
= 0.88)
)
Δ
mixS/(J·K−1·mol−1
)
benzene + ethanol (w
−2.510
−2.573
−2.649
−2.728
−2.804
−2.851
−2.926
−3.000
1
1
1
= 0.86)
−2.356
−2.412
−2.480
−2.550
−2.618
−2.660
−2.726
−2.792
−2.862
benzene + n-propanol (w
1
2
2
2
2
3
3
3
3
3
83.15
0.544
0.559
0.577
0.597
0.615
0.622
0.638
0.654
0.670
283.15
288.15
293.15
298.15
303.15
308.15
313.15
318.15
323.15
−2.416
−2.480
−2.549
−2.623
−2.684
−2.745
−2.822
−2.885
−2.959
−2.273
−2.329
−2.391
−2.456
−2.511
−2.565
−2.634
−2.690
−2.756
0.508
0.523
0.540
0.558
0.571
0.584
0.601
0.614
0.629
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
−3.078
benzene + ethanol (w
−3.102
−3.165
−3.267
−3.331
−3.406
−3.474
−3.533
−3.605
= 0.72)
−2.883
−2.939
−3.030
−3.086
−3.153
−3.214
−3.266
−3.330
−3.386
1
benzene + n-propanol (w = 0.77)
283.15
288.15
293.15
298.15
303.15
308.15
313.15
318.15
323.15
0.774
0.785
0.810
0.819
0.833
0.844
0.851
0.863
0.871
283.15
288.15
293.15
298.15
303.15
308.15
313.15
318.15
323.15
−2.935
−3.010
−3.100
−3.185
−3.250
−3.328
−3.375
−3.448
−3.517
−2.734
−2.801
−2.881
−2.956
−3.015
−3.084
−3.126
−3.191
−3.252
0.709
0.725
0.747
0.765
0.777
0.792
0.796
0.809
0.819
−3.668
benzene + ethanol (w
−3.402
−3.470
−3.545
−3.620
−3.699
−3.766
−3.820
−3.857
= 0.60)
−3.150
−3.211
−3.277
−3.344
−3.414
−3.473
−3.522
−3.551
−3.558
1
benzene + n-propanol (w = 0.66)
283.15
288.15
293.15
298.15
303.15
308.15
313.15
318.15
323.15
0.891
0.901
0.914
0.926
0.939
0.948
0.952
0.959
0.968
283.15
288.15
293.15
298.15
303.15
308.15
313.15
318.15
323.15
−3.289
−3.362
−3.455
−3.520
−3.609
−3.678
−3.735
−3.775
−3.788
−3.049
−3.114
−3.197
−3.255
−3.334
−3.396
−3.446
−3.477
−3.482
0.847
0.860
0.880
0.889
0.907
0.917
0.922
0.935
0.948
−3.870
12

H. Guo, Y. Li, Y. Yang et al.
Journal of Molecular Liquids 328 (2021) 114842
Table 8 (continued)
T/K
Δ
mixG/(kJ·mol−1)
Δ
mixH/(kJ·mol−1
)
Δ
mixS/(J·K−1·mol−1
)
T/K
Δ
mixG/(kJ·mol−1
)
Δ
mixH/(kJ·mol−1
= 0.56)
)
Δ )
mixS/(J·K−1·mol−1
benzene + ethanol (w
−3.515
−3.581
−3.651
−3.722
−3.779
−3.824
−3.848
−3.853
1
1
1
1
= 0.52)
−3.250
−3.309
−3.372
−3.435
−3.485
−3.525
−3.543
−3.540
−3.542
benzene + n-propanol (w
1
2
2
2
2
3
3
3
3
3
83.15
0.934
0.943
0.954
0.964
0.968
0.969
0.974
0.985
0.995
283.15
288.15
293.15
298.15
303.15
308.15
313.15
318.15
323.15
−3.436
−3.516
−3.597
−3.676
−3.746
−3.809
−3.852
−3.885
−3.908
−3.180
−3.251
−3.323
−3.394
−3.456
−3.512
−3.545
−3.570
−3.585
0.904
0.918
0.933
0.947
0.956
0.963
0.978
0.989
0.999
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
−3.864
benzene + ethanol (w
−3.490
−3.553
−3.620
−3.684
−3.734
−3.766
−3.779
−3.785
= 0.40)
−3.228
−3.284
−3.344
−3.401
−3.445
−3.470
−3.476
−3.473
−3.468
1
benzene + n-propanol (w = 0.46)
283.15
288.15
293.15
298.15
303.15
308.15
313.15
318.15
323.15
0.924
0.933
0.942
0.950
0.952
0.959
0.967
0.980
0.997
283.15
288.15
293.15
298.15
303.15
308.15
313.15
318.15
323.15
−3.494
−3.575
−3.647
−3.717
−3.775
−3.813
−3.829
−3.835
−3.839
−3.232
−3.304
−3.368
−3.431
−3.482
−3.513
−3.521
−3.517
−3.508
0.926
0.941
0.952
0.962
0.967
0.975
0.985
0.998
1.025
−3.790
benzene + ethanol (w
−3.369
−3.430
−3.484
−3.536
−3.574
−3.593
−3.601
−3.605
= 0.30)
−3.121
−3.175
−3.223
−3.269
−3.300
−3.311
−3.311
−3.307
−3.305
1
benzene + n-propanol (w = 0.36)
283.15
288.15
293.15
298.15
303.15
308.15
313.15
318.15
323.15
0.878
0.886
0.891
0.895
0.901
0.915
0.926
0.938
0.958
283.15
288.15
293.15
298.15
303.15
308.15
313.15
318.15
323.15
−3.442
−3.514
−3.573
−3.637
−3.684
−3.716
−3.721
−3.742
−3.759
−3.186
−3.250
−3.302
−3.359
−3.401
−3.430
−3.425
−3.437
−3.443
0.906
0.918
0.924
0.932
0.934
0.930
0.945
0.958
0.978
−3.615
benzene + ethanol (w
−3.159
−3.211
−3.259
−3.294
−3.315
−3.318
−3.302
−3.125
= 0.21)
−2.934
−2.980
−3.022
−3.052
−3.064
−3.057
−3.030
−2.842
−2.845
1
benzene + n-propanol (w = 0.26)
283.15
288.15
293.15
298.15
303.15
308.15
313.15
318.15
323.15
0.796
0.802
0.806
0.812
0.829
0.845
0.869
0.888
0.902
283.15
288.15
293.15
298.15
303.15
308.15
313.15
318.15
323.15
−3.266
−3.335
−3.388
−3.441
−3.479
−3.489
−3.498
−3.504
−3.516
−3.029
−3.090
−3.138
−3.184
−3.217
−3.218
−3.221
−3.219
−3.225
0.838
0.849
0.855
0.860
0.865
0.879
0.885
0.897
0.902
−3.136
benzene + n-butanol (w
−2.203
−2.243
−2.288
−2.354
−2.402
−2.453
−2.515
−2.595
1
= 0.90)
benzene + isoamyl alcohol (w
1
= 0.75)
= 0.65)
= 0.55)
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
−2.082
−2.119
−2.159
−2.217
−2.260
−2.305
−2.360
−2.432
−2.485
0.424
0.433
0.442
0.459
0.469
0.479
0.493
0.513
0.526
283.15
288.15
293.15
298.15
303.15
308.15
313.15
318.15
323.15
−3.069
−3.130
−3.187
−3.249
−3.306
−3.367
−3.424
−3.485
−3.542
−2.854
0.761
0.771
0.779
0.789
0.797
0.806
0.813
0.821
0.828
−2.908
−2.958
−3.013
−3.064
−3.118
−3.170
−3.224
−3.275
−2.655
benzene + n-butanol (w
−2.765
1
= 0.80)
benzene + isoamyl alcohol (w
1
283.15
288.15
293.15
298.15
303.15
308.15
313.15
318.15
323.15
−2.583
0.643
0.654
0.665
0.676
0.689
0.709
0.716
0.729
0.744
283.15
288.15
293.15
298.15
303.15
308.15
313.15
318.15
323.15
−3.305
−3.374
−3.439
−3.500
−3.565
−3.627
−3.688
−3.757
−3.817
−3.063
0.853
0.864
0.874
0.882
0.891
0.898
0.906
0.915
0.922
−2.822
−2.882
−2.942
−3.009
−3.095
−3.148
−3.220
−3.295
−2.634
−2.688
−2.741
−2.800
−2.877
−2.924
−2.988
−3.055
−3.125
−3.183
−3.237
−3.295
−3.350
−3.405
−3.466
−3.520
benzene + n-butanol (w
−3.129
1
= 0.70)
benzene + isoamyl alcohol (w
1
283.15
288.15
293.15
298.15
303.15
308.15
313.15
318.15
323.15
−2.907
0.784
0.805
0.821
0.833
0.846
0.862
0.874
0.886
0.894
283.15
288.15
293.15
298.15
303.15
308.15
313.15
318.15
323.15
−3.458
−3.529
−3.595
−3.658
−3.724
−3.790
−3.846
−3.901
−3.946
−3.200
0.912
0.923
0.933
0.940
0.948
0.957
0.961
0.965
0.966
−3.219
−3.299
−3.369
−3.442
−3.523
−3.599
−3.674
−3.737
−2.987
−3.058
−3.120
−3.185
−3.258
−3.325
−3.392
−3.448
−3.263
−3.322
−3.378
−3.436
−3.495
−3.545
−3.594
−3.634
(continued on next page)
13

H. Guo, Y. Li, Y. Yang et al.
Journal of Molecular Liquids 328 (2021) 114842
Table 8 (continued)
T/K
Δ
mixG/(kJ·mol−1)
Δ
mixH/(kJ·mol−1
)
Δ
mixS/(J·K−1·mol−1
)
T/K
Δ
mixG/(kJ·mol−1
)
Δ
mixH/(kJ·mol−1
)
Δ )
mixS/(J·K−1·mol−1
benzene + n-butanol (w
−3.359
−3.445
−3.536
−3.605
−3.680
−3.751
−3.813
−3.863
1
= 0.60)
benzene + isoamyl alcohol (w
1
= 0.45)
= 0.34)
= 0.23)
= 0.12)
2
2
2
2
3
3
3
3
3
83.15
−3.112
−3.188
−3.269
−3.331
−3.397
−3.461
−3.516
−3.560
−3.581
0.874
0.891
0.910
0.921
0.932
0.943
0.950
0.952
0.965
283.15
288.15
293.15
298.15
303.15
308.15
313.15
318.15
323.15
−3.458
−3.535
−3.598
−3.669
−3.738
−3.797
−3.851
−3.903
−3.944
−3.200
0.912
0.926
0.934
0.944
0.954
0.959
0.963
0.966
0.978
88.15
93.15
98.15
03.15
08.15
13.15
18.15
23.15
−3.268
−3.325
−3.388
−3.449
−3.501
−3.549
−3.596
−3.628
−3.893
benzene + n-butanol (w
−3.470
1
= 0.50)
benzene + isoamyl alcohol (w
1
283.15
288.15
293.15
298.15
303.15
308.15
313.15
318.15
323.15
−3.210
0.917
0.933
0.945
0.958
0.966
0.970
0.979
0.989
0.103
283.15
288.15
293.15
298.15
303.15
308.15
313.15
318.15
323.15
−3.396
−3.465
−3.517
−3.579
−3.637
−3.687
−3.737
−3.777
−3.807
−3.145
0.888
0.899
0.903
0.911
0.917
0.920
0.923
0.928
0.936
−3.553
−3.630
−3.707
−3.771
−3.828
−3.868
−3.883
−3.897
−3.285
−3.353
−3.421
−3.479
−3.529
−3.562
−3.568
−3.864
−3.206
−3.253
−3.307
−3.359
−3.403
−3.448
−3.482
−3.504
benzene + n-butanol (w
−3.474
1
= 0.40)
benzene + isoamyl alcohol (w
1
283.15
288.15
293.15
298.15
303.15
308.15
313.15
318.15
323.15
−3.214
0.918
0.929
0.939
0.947
0.951
0.952
0.965
0.978
0.989
283.15
288.15
293.15
298.15
303.15
308.15
313.15
318.15
323.15
−3.175
−3.228
−3.287
−3.336
−3.387
−3.430
−3.471
−3.503
−3.524
−2.948
0.802
0.808
0.817
0.821
0.826
0.828
0.836
0.845
0.860
−3.544
−3.613
−3.676
−3.731
−3.776
−3.806
−3.807
−3.814
−3.276
−3.338
−3.394
−3.442
−3.483
−3.504
−3.495
−3.494
−2.995
−3.047
−3.091
−3.137
−3.175
−3.210
−3.234
−3.246
benzene + n-butanol (w
−3.344
1
= 0.30)
benzene + isoamyl alcohol (w
1
283.15
288.15
293.15
298.15
303.15
308.15
313.15
318.15
323.15
−3.099
0.868
0.880
0.887
0.893
0.895
0.900
0.912
0.925
0.938
283.15
288.15
293.15
298.15
303.15
308.15
313.15
318.15
323.15
−2.774
−2.826
−2.872
−2.925
−2.961
−2.993
−3.019
−3.035
−3.048
−2.591
0.646
0.655
0.661
0.670
0.672
0.687
0.698
0.708
0.721
−3.415
−3.474
−3.531
−3.577
−3.611
−3.630
−3.648
−3.665
−3.162
−3.214
−3.265
−3.306
−3.334
−3.344
−3.354
−3.362
−2.637
−2.678
−2.725
−2.757
−2.781
−2.800
−2.810
−2.815
n
ΔmixSid ¼ −R ∑ xi ln xi
process in binary solvents is exothermic. The values of ΔmixS in all tested
solvents are positive and increase with increasing temperature, which
indicates that the mixing process is also entropy-driven [31]. In brief,
these results are helpful for the optimization of the mixing and crystal-
lization processes of DNP.
ð33Þ
ð34Þ
i
n
E
G ¼ RT ∑ xi ln γ
i
i
i i
Where x and γ are the mole fraction and activity coefficient of
component i in real solution, respectively. i = 2 means a binary solution
5
. Conclusions
and i = 3 means a ternary solution.
The solubility of DNP in four binary mixed solvents like benzene +
In addition, the activity coefficient can be calculated by the given
Wilson model. The excess mixing properties can be calculated by the
following equations [33].
ethanol, benzene + n-propanol, benzene + n-butanol and benzene +
isoamyl alcohol was investigated by laser monitoring technique in the
temperature range from 283.15 K to 323.15 K under 0.1 MPa. Experi-
mental solubility increases with increasing temperature at given solvent
composition and increases with decreasing mass fraction of benzene at
constant temperature. Hansen solubility parameters (HSP) were used to
explain and predict the solubility behavior. If the Hildebrand solubility
parameter δ of some solvent was known, the solubility of DNP in
some solvent may be predicted based on solubility and selected sol-
vents. In addition, four correlation models (i.e., the modified Apelblat
equation, Jouyban-Acree model, NRTL model and Wilson model) se-
lected in this study can all be used to fit the solubility values of DNP pre-
cisely. What's more, all of the 252 experimental values are used to
correlate the parameters of NRTL model and the correlated results are
superior to the other three models by comparing the average
ꢀ∂ ln γi
ꢁ
n
HE ¼ −RT ∑ xi
2
ð35Þ
ð36Þ
i
∂T
P,x
E
E
H −G
E
S ¼
T
The calculated mixing thermodynamic properties in four binary sol-
vent mixtures are given in Table 8, in addition, these mixing thermody-
namic parameters are calculated based on per mole mixture. As shown
in Table 8, it can be found that the values of ΔmixG are all negative and
decrease with increasing temperature, which indicates that the dissolu-
tion process of DNP in all investigated solvents is a spontaneous and fa-
vorable process [34]. The negative ΔmixH illustrates that the dissolution
4
2
10 RMSD and R . Moreover, mixing properties of DNP in selected binary
14

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