Measurement, correlation of solubility and thermodynamic properties analysis of 2,4,6-trinitroresorcinol hydrate in pure and binary solvents

Article abstract of DOI:10.1016/j.molliq.2021.115639

The solubility of 2,4,6-trinitroresorcinol hydrate (TNR?2/3H₂O) in the pure solvents (methanol, ethanol, isopropanol and water) and the binary mixed solvents (methanol-water, ethanol-water and isopropanol-water) was measured by the laser dynamic method from 298.15 K to 323.15 K under the atmospheric pressure. The TNR?2/3H₂O do not change before and after the solubility measurement in the selected solvents. The solubility increases with the increase of the temperature, and methanol is more suitable for the cooling crystallization of TNR?2/3H₂O. In the pure solvents, the solubility order at the same temperature is: methanol > ethanol > isopropanol > water, which may be affected by the properties (such as hydrogen bond, polarity, dielectric constant, cohesive energy density etc.) of the alcohol solvents, self-association of water molecules, the hydrophobic wing of the TNR?2/3H₂O and so on. In the mixed solvents, the solubility has different sensitivity to the content of organic components (x₂) in the solvent. The possible reason is that: the interaction between solvent and solvent plays an important role (the formation of azeotropic mixtures of alcohols and water, the interaction between water and alcohol solvents, the properties of the solvents etc.). The solubility data of TNR?2/3H₂O were compared with that of 2,4,6-trinitrophenol (TNP) that have been reported. It can be found that the solubility of TNP is always greater than that of TNR?2/3H₂O with the same solvent and temperature, and x₂ = 0.63–0.69 (ethanol-water) and x₂ ≈ 0.73 (isopropanol-water) are more suitable as the solvents for solution crystallization to separate TNR?2/3H₂O from the mixture of TNP and TNR?2/3H₂O. The experimental mole fraction solubility data (x^exp) of TNR?2/3H₂O were correlated by the modified Apelblat, Van't Hoff, CNIBS R-K, and Jouyban-Acree-modified Apelblat model. All of these models give satisfactory results, and the Van't Hoff model has better correlation and helps to expand the solubility data of TNR?2/3H₂O. The thermodynamic properties during the dissolution process were analyzed based on the Van't Hoff. And the dissolution of TNR?2/3H₂O in the solvents used is considered to be an “endothermic, non-spontaneous and entropy-driven” process and the enthalpy is the main contributor to the Gibbs free energy in the process of dissolution.

Full text of DOI:10.1016/j.molliq.2021.115639

Journal of Molecular Liquids 330 (2021) 115639
Contents lists available at ScienceDirect
Journal of Molecular Liquids
journal homepage: www.elsevier.com/locate/molliq
Measurement, correlation of solubility and thermodynamic properties
analysis of 2,4,6-trinitroresorcinol hydrate in pure and binary solvents
Mei Xue a, Dao-zhen Huangb, Kai-xin Yang a, Li-zhen Chena, Zhi-hua Zheng a, Yong Xiang c,
Qing-wu Huang c, Jian-long Wanga,
⁎
a
School of Chemical Engineering and Technology, North University of China, Taiyuan 030051, China
Shandong Teneng Environmental Technology Co., Ltd., Dezhou 253000, China
Sichuan North Hongguang Special Chemical Co., Ltd., Yibin 644104, 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 2,4,6-trinitroresorcinol hydrate (TNR∙2/3H2O) in the pure solvents (methanol, ethanol,
isopropanol and water) and the binary mixed solvents (methanol-water, ethanol-water and isopropanol-
water) was measured by the laser dynamic method from 298.15 K to 323.15 K under the atmospheric pressure.
The TNR∙2/3H2O do not change before and after the solubility measurement in the selected solvents. The solubil-
ity increases with the increase of the temperature, and methanol is more suitable for the cooling crystallization of
TNR∙2/3H2O. In the pure solvents, the solubility order at the same temperature is: methanol > ethanol >
isopropanol > water, which may be affected by the properties (such as hydrogen bond, polarity, dielectric con-
stant, cohesive energy density etc.) of the alcohol solvents, self-association of water molecules, the hydrophobic
wing of the TNR∙2/3H2O and so on. In the mixed solvents, the solubility has different sensitivity to the content of
organic components (x2) in the solvent. The possible reason is that: the interaction between solvent and solvent
plays an important role (the formation of azeotropic mixtures of alcohols and water, the interaction between
water and alcohol solvents, the properties of the solvents etc.). The solubility data of TNR∙2/3H2O were compared
with that of 2,4,6-trinitrophenol (TNP) that have been reported. It can be found that the solubility of TNP is
always greater than that of TNR∙2/3H2O with the same solvent and temperature, and x2 = 0.63–0.69 (ethanol-
water) and x2 ≈ 0.73 (isopropanol-water) are more suitable as the solvents for solution crystallization to sepa-
rate TNR∙2/3H2O from the mixture of TNP and TNR∙2/3H2O. The experimental mole fraction solubility data
(xexp) of TNR∙2/3H2O were correlated by the modified Apelblat, Van't Hoff, CNIBS R-K, and Jouyban-Acree-
modified Apelblat model. All of these models give satisfactory results, and the Van't Hoff model has better corre-
lation and helps to expand the solubility data of TNR∙2/3H2O. The thermodynamic properties during the dissolu-
tion process were analyzed based on the Van't Hoff. And the dissolution of TNR∙2/3H2O in the solvents used is
considered to be an “endothermic, non-spontaneous and entropy-driven” process and the enthalpy is the main
contributor to the Gibbs free energy in the process of dissolution.
Received 19 December 2020
Received in revised form 3 February 2021
Accepted 8 February 2021
Available online 11 February 2021
Keywords:
Solubility
2,4,6-Trinitroresorcinol hydrate
Dissolution thermodynamic properties
Laser dynamic method
© 2021 Elsevier B.V. All rights reserved.
1. Introduction
2,4,6-trinitroresorcinol (also known as styphnic acid, TNR, 0.5–6.5%)
was obtained from the nitration of nitrobenzene with the mixed acid
m-Dinitrobenzene is of great importance for the manufacture of
m-nitroaniline, m-phenylenediamine, dyes etc. in the organic chemical
industry. Two-step nitration of benzene through the mixed acid of nitric
acid and sulfuric acid is a common method for preparing m-
dinitrobenzene [1]. However, some by-products are often produced
during the reaction process. Bennett et al. [2] mentioned that the by-
products of phenols produced from the nitration of benzene with the
mixed acid of nitric acid and sulfuric acid are: 2,4,6-trinitrophenol
(also known as picric acid, TNP), 2,4-dinitrophenol (2,4-DNP, 0.03%);
of nitric acid and sulfuric acid; and the formation pathway of phenols
was analyzed. Wang et al. [3] pointed out that the side reaction of oxida-
tion will occur and the nitrophenols will be generated in the production
process of dinitrobenzene. It is also mentioned in this patent [4] that
nitrophenols were produced as by-products during the process of nitra-
tion of benzene to dinitrobenzene, which are mainly TNR and TNP. It can
be seen that the by-products produced by the nitration of benzene to di-
nitrobenzene with the mixed acid of nitric acid and sulfuric acid mainly
point to the polynitrophenols. And in previous experiments, our labora-
tory also found that the main by-products are TNR (76.7% by HPLC),
followed by TNP (14.6% by HPLC) [5]. It is worth noting that TNR and
its derivatives have important applications in the field of energetic
⁎
Corresponding author.
E-mail address: wangjianlong@nuc.edu.cn (J. Wang).
https://doi.org/10.1016/j.molliq.2021.115639
0167-7322/© 2021 Elsevier B.V. All rights reserved.

M. Xue, D. Huang, K. Yang et al.
Journal of Molecular Liquids 330 (2021) 115639
(methanol+water, ethanol+water, and isopropanol+water) and in
corresponding pure solvents (methanol, ethanol, isopropanol, and
water) was measurement at 298.15 to 323.15 K by laser dynamic
method in this work. The four well-known models (the modified
Apelblat, Van't Hoff, CNIBS/R-K, and Jouyban-Acree-modified Apelblat
model) were used to correlate the solubility data to expand the data.
Furthermore, the dissolution thermodynamic properties of TNR∙2/
3H2O in these solvents were further analyzed.
2. Experimental section
2.1. Materials
The crystalline TNR∙2/3H2O was obtained in our laboratory by the ni-
tration of resorcinol with nitric‑sulfuric mixed acid, and the recrystalli-
zation of crude product with aqueous ethanol, following Urbanski's
preparation procedure of styphnic acid of high purity [1]. The TNR∙2/
3H2O used in this research is the same as that used in our previous
work [5]. The reaction route is as follows:
Fig. 1. Ellipsoid models of TNR∙2/3H2O.
materials [6–10]. If the TNR can be recycled and reused, it can not only
solve the problems of solid waste pollution and danger brought by the
by-products, but also continue to generate value. However, there are
few reports on the recovery and reuse of TNR from the by-products of
benzene nitration.
It is well known that solution crystallization is usually an important
method of separation and purification in the production processes, and
even is an important means to study the crystal morphology. The solu-
bility of substances in different solvents is a significant physical prop-
erty, and is the crucial basic data for the selection of crystallization
conditions and process optimization in solution crystallization. At the
same time, it can be seen in previous experiments that the solution crys-
tallization is an effective method to separate TNR∙2/3H2O from the by-
products which come from the nitration of benzene to dinitrobenzene
with the mixed acid of nitric acid and sulfuric acid [5].
As a result of the composition analysis of the by-products produced
by the nitration of benzene to dinitrobenzene in the previous work, the
organic component with the highest content is the 2,4,6-trinit-
roresorcinol hydrate, which specifically is 2,4,6-trinitroresorcinol∙2/
3H2O (TNR∙2/3H2O, C6H3N3O8∙2/3H2O, Fig. 1.) [5]. Therefore, in order
to separate TNR∙2/3H2O from the by-products by solution crystalliza-
tion, it is necessary to get its solubility data in different solvents. At pres-
ent, the existing literatures only have reported the solubility of TNR∙2/
3H2O in the single solvent such as dichloromethane, chloroform, 1,2-di-
chloroethane, toluene, xylene and anisole and the solubility of TNR in
nitric acid, sulfuric acid, mixed acid of nitric acid and sulfuric acid, and
water [1,5,11,12], which shows the solubility data are very limited. So
in order to provide the basic solubility data and related thermodynamic
information for the crystallization of TNR∙2/3H2O from some mixed sol-
vents, the solubility of TNR∙2/3H2O in common binary mixed solvents
(1)
The organic solvents considered in this research are of analytical
grade, and used without further purification. The deionized water was
made in our laboratory by a Millipore Milli-Q Plus water system.
The detailed aspects of all materials used in this work were summa-
rized in Table 1.
2.2. Thermal analysis
The thermal analysis of TNR∙2/3H2O was performed by the differen-
tial scanning calorimeter (DSC) (DSC 3, METTLER TOLEDO, Switzerland)
and thermogravimetry (TG) (TGA1, METTLER TOLEDO, Switzerland),
with the heating rate of 5 K∙min−1, from 298.15 K to 473.15 K and
under the protection of nitrogen. The sample mass used in DSC and
TG were 0.8 mg and 1.0–1.5 mg, respectively.
The results of thermal analysis are shown in Fig. 2. It can be seen that
there are three endothermic peaks in the DSC curve, and the percentage
of mass loss reaches to 4.8% before 449.8 K in the TG curve, which is con-
sistent with the proportion of water in the molecule. Therefore, the first
two endothermic peaks in DSC represent the process of losing crystal
water, while the third one indicates the melting process of TNR. The
Tm (melting temperature) of TNR∙2/3H2O is the temperature of the in-
tersection between the tangent to the starting point of the third endo-
thermic peak and the tangent to the maximum slope of the curve. The
value of Tm is 450.20 K, which was computed by the STARe software
(METTLER TOLEDO, Switzerland).
Table 1
The detailed information of all materials used in this research.
Chemicals
Source
Molar mass/(g∙mol−1
)
Purification method
Purity (mass faction)
Analysis method
TNR∙2/3H2O
Methanol
Ethanol
Isopropanol
Water
Synthesized by us
257.12
32.04
46.07
60.06
18.02
Recrystallization
None
None
>0.990
>0.995
>0.997
>0.997
HPLCa
GCb
Damao Chemical Reagent Factory
Tianjin Beichen District Fangzheng Reagent Factory
Sinopharm Chemical Reagent Co., Ltd.
Prepared in our laboratory
GCb
None
GCb
a
High-performance liquid chromatography.
Gas chromatography.
b
2

M. Xue, D. Huang, K. Yang et al.
Journal of Molecular Liquids 330 (2021) 115639
2.3. Solubility measurement
Record the amounts of the solute and solvent that have been added to
the container at this time, and calculate the mole fraction solubility of
TNR∙2/3H2O by Eq. (2). At each temperature, the determination was
performed three times in parallel and the average value was taken as
the final mole fraction solubility.
The laser dynamic method was used to measure the solubility of
TNR∙2/3H2O in the pure solvents (methanol, ethanol, isopropanol and
water) and the binary solvents (methanol-water, ethanol-water and
isopropanol-water) from 298.15 K to 323.15 K under the atmospheric
pressure. The experimental devices are shown in Fig. 3, which are the
same as the ones we used to study the solubility of TNR∙2/3H2O in
some single solvents [5].
The test process is as follows: install the experimental devices as
shown in Fig. 3, and set the thermostatic bath to the specified tempera-
ture (the temperature uncertainty is 0.05 K). Prepare the solvent with
specified content, and take a certain amount of the solvent accurately
with a pipette (standard uncertainty of 0.01 ml) and place it in the
jacketed glass container. Then, add a small amount of TNR∙2/3H2O (sol-
ute) frequently and stir for 30 min after each addition. Stop add the sol-
ute and start add the solvent with a burette (standard uncertainty of
0.01 ml) several times in a small amount when the undissolved solute
is visible to the naked eye (the laser intensity indicator is obviously re-
duced), and stir for 30 min after each addition of solvent. When the laser
intensity indicator reaches a stable value within 30 min and no longer
increases, it is considered that the solute has been completely dissolved.
m1=M1
m1=M1 þ m2=M2 þ m3=M3
x1
x2
¼
¼
ð2Þ
ð3Þ
m2=M2
m2=M2 þ m3=M3
In which, x1 represents the mole fraction solubility, x2 represents the
mole fraction of organic solvent (methanol, ethanol or isopropanol) in
the solvents; m1, m2 and m3 are the mass of solute, organic solvent
and water, respectively; M1, M2 and M3 are the molar mass of solute, or-
ganic solvent and water, respectively.
2.4. Powder X-ray diffraction analysis
In order to check whether the substance will change (transforma-
tion of crystal form, loss of crystal water, formation of solvent com-
pounds, reaction, etc.) before and after the solubility measurement,
the powder X-ray diffraction analysis (PXRD) (DX-2700B, Haoyuan In-
strument Co., Ltd., China) was performed on the raw material and the
equilibrium solid phases obtained from the solubility measurement.
After the solubility test of TNR∙2/3H2O at 323.15 K, the system was
cooled down and the solids were precipitated. Then the equilibrium
solid phases could be obtained by vacuum filtering and drying at 40 °C
after the system was cooled down to room temperature. During the
PXRD analysis, Cu Kα radiation (λ = 1.54 nm) was used and the tube
voltage and current were set at 40 kV and 30 mA, respectively. The
data were collected over the diffraction angle (2θ) range of 5–60° with
a scanning rate of 5°/min and a step size of 0.02°.
3. Thermodynamic models
3.1. Modified Apelblat equation
The modified Apelblat model is a semi-empirical thermodynamic
model derived from the Clausius-Clapeyron equation, which has been
widely used to correlate the experimental solubility and temperature,
Fig. 2. Thermal analysis of TNR∙2/3H2O.
Fig. 3. Experiment device schematic diagram for solubility measurement: 1-laser generator; 2-jacketed glass container; 3-condenser pipe; 4-burette; 5‑mercury thermometer; 6-digital
display; 7-thermostatic bath; 8-signal receiver; 9-magnetic stirrer.
3

M. Xue, D. Huang, K. Yang et al.
Journal of Molecular Liquids 330 (2021) 115639
Fig. 4. The PXRD patterns of raw material and equilibrium solid phases of TNR∙2/3H2O in pure solvents (a), methanol-water (b), ethanol-water (c), and isopropanol-water (d).
and reflects the dependence of solubility on temperature [13,14]. The
3.3. CNIBS/R-K model
equation can be expressed as Eq. (4):
The CNIBS/R-K (Combined Nearly Ideal Binary Solvent/
RedichKister) model was proposed by Acree and colleagues to explain
the relationship between the experimental solubility of a solute and
the composition of a binary solvent mixture at the specified tempera-
ture. It reflects the dependence of solubility on the solvent composition
[17–19]. The expression is as follows:
B
T
ln x1 ¼ A þ þ C ln T
ð4Þ
Where, x1 is the mole fraction solubility of TNR∙2/3H2O, T represents
the absolute temperature (K), and A, B and C are the empirical constants
determined by the experimental solubility data based on this model.
N
i
ln x1 ¼ x2 ln X2 þ x3 ln X3 þ x2x3 ∑ Siðx2−x3Þ
ð6Þ
i¼0
3.2. Van't Hoff equation
The Van't Hoff equation is a semi-empirical and simplified form of
the activity coefficients in solid-liquid equilibrium. It shows that the log-
arithm of the mole fraction solubility has a significant linear correlation
with the reciprocal of the absolute temperature of the system, which re-
flects the dependence of solubility on temperature [15,16]. The expres-
sion of the equation is as follows:
Here, x1 is the mole fraction solubility of TNR∙2/3H2O; x2, x3 respec-
tively represent the mole fraction of organic solvent (methanol, ethanol
or isopropanol) and water in the initial mixed solvent; X2, X3 represent
the mole fraction solubility of the solute in the single organic solvent
(methanol, ethanol or isopropanol) and water, respectively. Si is the
model constant. For the binary solvent system, N = 2 and x3 = 1-x2.
The Eq. (6) can be further simplified to Eq. (7) by representing the pa-
rameters as constants.
B
ln x1 ¼ A þ
ð5Þ
T
ln x1 ¼ B0 þ B1x2 þ B2x22 þ B3x23 þ B4x24
ð7Þ
In which，x1 is the mole fraction solubility of TNR∙2/3H2O, T repre-
sents the absolute temperature of the system, A and B are the model pa-
rameters of the Van't Hoff equation.
In which, B0, B1, B2, B3, and B4 are model parameters and they can be
acquired by least-squares regression.
4

M. Xue, D. Huang, K. Yang et al.
Journal of Molecular Liquids 330 (2021) 115639
Table 2
Experimental mole fraction solubility values xexp and calculated solubility values xcal of TNR∙2/3H2O in methanol-water solvents at the temperature T a
.
T / K
100 xexp
The modified Apelblat
Van't Hoff
CNIBS R-K
Jouyban-Acree-
modified Apelblat
100xcal
RD
100xcal
RD
100xcal
RD
100xcal
RD
x2 = 0.0000
298.15
303.15
308.15
313.15
0.0312
0.0343
0.0396
0.0451
0.0529
0.0608
0.0313
0.0352
0.0399
0.0458
0.0530
0.0618
−0.0032
−0.0262
−0.0076
−0.0155
−0.0019
−0.0164
0.0300
0.0348
0.0402
0.0463
0.0530
0.0604
0.0385
0.0286
0.0319
0.0360
0.0418
0.0495
0.0611
0.0833
0.070
0.0909
0.0732
0.0643
−0.0049
0.0255
0.0307
0.0368
0.0440
0.0525
0.0625
0.1827
0.1050
0.0707
0.0244
0.0076
−0.0280
−0.0146
−0.0152
−0.0266
−0.0019
0.0066
318.15
323.15
x2 = 0.0472
298.15
303.15
308.15
313.15
0.0350
0.0436
0.0521
0.0614
0.0709
0.0843
0.0347
0.0419
0.0502
0.0595
0.0699
0.0815
0.0086
0.0390
0.0365
0.0309
0.0141
0.0332
0.0358
0.0429
0.0511
0.0606
0.0714
0.0837
−0.0229
0.0161
0.0192
0.0130
−0.0071
0.0071
0.0349
0.0401
0.0464
0.0542
0.0645
0.0773
0.0029
0.0803
0.1094
0.1173
0.0903
0.0830
0.0332
0.0397
0.0473
0.0563
0.0668
0.0790
0.0514
0.0894
0.0921
0.0831
0.0578
0.0629
318.15
323.15
x2 = 0.1004
298.15
303.15
308.15
313.15
0.0416
0.0503
0.0603
0.0710
0.0869
0.1029
0.0422
0.0508
0.0611
0.0733
0.0877
0.1047
−0.0144
−0.0099
−0.0133
−0.0324
−0.0092
−0.0175
0.0413
0.0501
0.0605
0.0727
0.0867
0.1030
0.0072
0.0040
−0.0033
−0.0239
0.0023
0.0448
0.0527
0.0620
0.0728
0.0864
0.1013
−0.0769
−0.0477
−0.0282
−0.0254
0.0058
0.0450
0.0534
0.0632
0.0747
0.0880
0.1034
−0.0817
−0.0616
−0.0481
−0.0521
−0.0127
−0.0049
318.15
323.15
−0.0010
0.0155
x2 = 0.1606
298.15
303.15
308.15
313.15
0.0598
0.0691
0.0795
0.0950
0.1096
0.1296
0.0589
0.0680
0.0790
0.0923
0.1083
0.1276
0.0151
0.0159
0.0063
0.0284
0.0119
0.0154
0.0581
0.0688
0.0810
0.0948
0.1105
0.1281
0.0284
0.0043
−0.0189
0.0021
−0.0082
0.0116
0.0610
0.0726
0.0859
0.1010
0.1191
0.1374
−0.0201
−0.0507
−0.0805
−0.0632
−0.0867
−0.0602
0.0634
0.0746
0.0876
0.1027
0.1201
0.1403
−0.0602
−0.0796
−0.1019
−0.0811
−0.0958
−0.0826
318.15
323.15
x2 = 0.2293
298.15
303.15
308.15
313.15
0.0915
0.1060
0.1215
0.1418
0.1678
0.1934
0.0929
0.1074
0.1246
0.1449
0.1690
0.1975
−0.0153
−0.0132
−0.0255
−0.0219
−0.0072
−0.0212
0.0898
0.1058
0.1239
0.1444
0.1674
0.1933
0.0186
0.0019
−0.0198
−0.0183
0.0024
0.0878
0.1046
0.1236
0.1449
0.1690
0.1929
0.0404
0.0132
−0.0173
−0.0219
−0.0072
0.0026
0.0929
0.1083
0.1261
0.1465
0.1700
0.1969
−0.0153
−0.0217
−0.0379
−0.0331
−0.0131
−0.0181
318.15
323.15
0.0005
x2 = 0.3086
298.15
303.15
308.15
313.15
0.1308
0.1528
0.1811
0.2055
0.2392
0.2721
0.1311
0.1541
0.1797
0.2080
0.2391
0.2730
−0.0023
−0.0085
0.0077
−0.0122
0.0004
0.1317
0.1539
0.1789
0.2069
0.2383
0.2732
−0.0069
−0.0072
0.0121
−0.0068
0.0038
0.1333
0.1574
0.1840
0.2143
0.2462
0.2797
−0.0191
−0.0301
−0.0160
−0.0428
−0.0293
−0.0279
0.1413
0.1630
0.1879
0.2162
0.2485
0.2854
−0.0803
−0.0668
−0.0375
−0.0521
−0.0389
−0.0489
318.15
323.15
−0.0033
−0.0040
x2 = 0.4010
298.15
303.15
308.15
313.15
0.2089
0.2444
0.2868
0.3292
0.3740
0.4244
0.2104
0.2469
0.2870
0.3304
0.3771
0.4268
−0.0072
−0.0102
−0.0007
−0.0036
−0.0083
−0.0057
0.2119
0.2460
0.2843
0.3270
0.3744
0.4270
−0.0144
−0.0065
0.0087
0.0067
−0.0011
−0.0061
0.2115
0.2449
0.2816
0.3242
0.3665
0.4155
−0.0124
−0.0020
0.0181
0.0152
0.0201
0.2213
0.2524
0.2877
0.3276
0.3728
0.4239
−0.0594
−0.0327
−0.0031
0.0049
0.0032
0.0012
318.15
323.15
0.0210
x2 = 0.5101
298.15
303.15
308.15
313.15
0.3509
0.3982
0.4457
0.5091
0.5620
0.6307
0.3513
0.3982
0.4495
0.5053
0.5657
0.6310
−0.0011
0.0000
−0.0085
0.0075
−0.0066
−0.0005
0.3495
0.3959
0.4467
0.5021
0.5623
0.6275
0.0040
0.0058
−0.0022
0.0137
−0.0005
0.0051
0.3448
0.3890
0.4391
0.4977
0.5543
0.6266
0.0174
0.0231
0.0148
0.0224
0.0137
0.0065
0.3540
0.3986
0.4488
0.5052
0.5686
0.6397
−0.0088
−0.0010
−0.0070
0.0077
−0.0117
−0.0143
318.15
323.15
x2 = 0.6410
298.15
303.15
308.15
313.15
0.5673
0.6215
0.6919
0.7641
0.8472
0.9521
0.5799
0.6374
0.7038
0.7807
0.8696
0.9723
−0.0222
−0.0256
−0.0172
−0.0217
−0.0264
−0.0212
0.5564
0.6222
0.6934
0.7699
0.8522
0.9402
0.0192
0.5696
0.6270
0.6972
0.7757
0.8553
0.9578
−0.0041
−0.0088
−0.0077
−0.0152
−0.0096
−0.0060
0.5776
0.6414
0.7126
0.7920
0.8805
0.9792
−0.0182
−0.0320
−0.0299
−0.0365
−0.0393
−0.0285
−0.0011
−0.0022
−0.0076
−0.0059
0.0125
318.15
323.15
x2 = 0.8007
298.15
303.15
308.15
313.15
0.9900
1.0730
1.1821
1.2885
1.4157
1.5493
1.0121
1.1052
1.2084
1.3228
1.4494
1.5895
−0.0223
−0.0300
−0.0222
−0.0266
−0.0238
−0.0259
0.9766
1.0760
1.1819
1.2942
1.4132
1.5390
0.0135
−0.0028
0.0002
−0.0044
0.0018
0.0066
0.9850
1.0677
1.1778
1.2829
1.4078
1.5475
0.0051
0.0049
0.0036
0.0043
0.0056
0.0012
1.0065
1.0995
1.2027
1.3169
1.4434
1.5835
−0.0167
−0.0247
−0.0174
−0.0220
−0.0196
−0.0221
318.15
323.15
(continued on next page)
5

M. Xue, D. Huang, K. Yang et al.
Journal of Molecular Liquids 330 (2021) 115639
Table 2 (continued)
T / K
100 xexp
The modified Apelblat
Van't Hoff
CNIBS R-K
Jouyban-Acree-
modified Apelblat
100xcal
RD
100xcal
RD
100xcal
RD
100xcal
RD
x2 = 1.0000
298.15
303.15
308.15
313.15
2.3250
2.4846
2.6561
2.8271
3.0438
3.3018
2.3828
2.5320
2.7030
2.8978
3.1189
3.3693
−0.0249
−0.0191
−0.0177
−0.0250
−0.0247
−0.0204
2.3009
2.4794
2.6654
2.8587
3.0593
3.2671
0.0104
0.0021
−0.0035
−0.0112
−0.0051
0.0105
2.3052
2.4724
2.6516
2.8156
3.0197
3.3041
0.0085
0.0049
0.0017
0.0041
0.0079
−0.0007
2.3764
2.5367
2.7139
2.9095
3.1252
3.3628
−0.0221
−0.0210
−0.0218
−0.0291
−0.0267
−0.0185
318.15
323.15
a
Values of the standard uncertainty u are u(x) =0.001, u(T) =0.05 K.
Table 3
Experimental mole fraction solubility values xexp and calculated solubility values xcal of TNR∙2/3H2O in ethanol-water solvents at the temperature T a
.
T / K
100 xexp
The modified Apelblat
Van't Hoff
CNIBS R-K
Jouyban-Acree-
modified Apelblat
100xcal
RD
100xcal
RD
100xcal
RD
100xcal
RD
x2 = 0.0000
298.15
303.15
308.15
313.15
0.0312
0.0343
0.0396
0.0451
0.0529
0.0608
0.0313
0.0352
0.0399
0.0458
0.0530
0.0618
−0.0032
−0.0262
−0.0076
−0.0155
−0.0019
−0.0164
0.0300
0.0348
0.0402
0.0463
0.0530
0.0604
0.0385
0.0168
0.0223
0.0283
0.0349
0.0414
0.0471
0.4615
0.3499
0.2854
0.2262
0.2174
0.2253
0.0206
0.0242
0.0283
0.0329
0.0381
0.0439
0.3397
0.2945
0.2854
0.2705
0.2798
0.2780
−0.0146
−0.0152
−0.0266
−0.0019
0.0066
318.15
323.15
x2 = 0.0332
298.15
303.15
308.15
313.15
0.0351
0.0429
0.0510
0.0605
0.0729
0.0858
0.0353
0.0425
0.0510
0.0610
0.0725
0.0859
−0.0057
0.0093
0.0000
−0.0083
0.0055
−0.0012
0.0350
0.0424
0.0509
0.0609
0.0723
0.0855
0.0028
0.0117
0.0020
−0.0066
0.0082
0.0035
0.0283
0.0364
0.0451
0.0549
0.0647
0.0742
0.1937
0.1515
0.1157
0.0926
0.1125
0.1352
0.0335
0.0391
0.0454
0.0525
0.0603
0.0690
0.0456
0.0886
0.1098
0.1322
0.1728
0.1958
318.15
323.15
x2 = 0.0718
298.15
303.15
308.15
313.15
0.0472
0.0582
0.0694
0.0840
0.0987
0.1162
0.0478
0.0584
0.0706
0.0844
0.1000
0.1173
−0.0127
−0.0034
−0.0173
−0.0048
−0.0132
−0.0095
0.0479
0.0579
0.0696
0.0831
0.0987
0.1166
−0.0148
0.0052
−0.0029
0.0107
0.0000
−0.0034
0.0484
0.0606
0.0730
0.0877
0.1028
0.1183
−0.0254
−0.0412
−0.0519
−0.0440
−0.0415
−0.0181
0.0555
0.0642
0.0740
0.0848
0.0968
0.1100
−0.1758
−0.1031
−0.0663
−0.0095
0.0193
318.15
323.15
0.0534
x2 = 0.1170
298.15
303.15
308.15
313.15
0.0768
0.0958
0.1129
0.1341
0.1527
0.1754
0.0785
0.0954
0.1139
0.1338
0.1548
0.1765
−0.0221
0.0042
−0.0089
0.0022
−0.0138
−0.0063
0.0805
0.0954
0.1123
0.1315
0.1533
0.1778
−0.0482
0.0042
0.0053
0.0194
−0.0039
−0.0137
0.0834
0.1015
0.1196
0.1413
0.1643
0.1890
−0.0859
−0.0595
−0.0593
−0.0537
−0.0760
−0.0775
0.0924
0.1061
0.1213
0.1381
0.1565
0.1766
−0.2031
−0.1075
−0.0744
−0.0298
−0.0249
−0.0068
318.15
323.15
x2 = 0.1709
298.15
303.15
308.15
313.15
0.1257
0.1574
0.1891
0.2204
0.2571
0.2924
0.1280
0.1562
0.1873
0.2208
0.2562
0.2930
−0.0183
0.0076
0.0095
−0.0018
0.0035
−0.0021
0.1319
0.1567
0.1852
0.2177
0.2546
0.2963
−0.0493
0.0044
0.0206
0.0123
0.0097
0.1436
0.1700
0.1961
0.2282
0.2622
0.3002
−0.1424
−0.0801
−0.0370
−0.0354
−0.0198
−0.0267
0.1536
0.1750
0.1986
0.2244
0.2526
0.2832
−0.2220
−0.1118
−0.0502
−0.0181
0.0175
318.15
323.15
−0.0133
0.0315
x2 = 0.2362
298.15
303.15
308.15
313.15
0.2508
0.2863
0.3228
0.3648
0.4074
0.4653
0.2567
0.2901
0.3279
0.3704
0.4183
0.4723
−0.0235
−0.0133
−0.0158
−0.0154
−0.0268
−0.0150
0.2507
0.2858
0.3244
0.3668
0.4130
0.4634
0.0004
0.0017
−0.0050
−0.0055
−0.0137
0.0041
0.2423
0.2794
0.3169
0.3630
0.4113
0.4664
0.0339
0.0241
0.0183
0.0049
−0.0096
−0.0024
0.2505
0.2833
0.3192
0.3583
0.4007
0.4466
0.0012
0.0105
0.0112
0.0178
0.0164
0.0402
318.15
323.15
x2 = 0.3169
298.15
303.15
308.15
313.15
0.4025
0.4507
0.5033
0.5677
0.6412
0.7140
0.4049
0.4549
0.5109
0.5737
0.6439
0.7225
−0.0060
−0.0093
−0.0151
−0.0106
−0.0042
−0.0119
0.3961
0.4485
0.5058
0.5682
0.6360
0.7094
0.0159
0.0049
−0.0050
−0.0009
0.0081
0.3900
0.4398
0.4927
0.5565
0.6203
0.6938
0.0311
0.0242
0.0211
0.0197
0.0326
0.0283
0.3911
0.4396
0.4922
0.5492
0.6107
0.6771
0.0283
0.0246
0.0221
0.0326
0.0476
0.0517
318.15
323.15
0.0064
x2 = 0.4191
298.15
303.15
308.15
313.15
0.5630
0.6318
0.7059
0.7832
0.5470
0.6122
0.6820
0.7563
0.0284
0.0310
0.0339
0.0343
0.5682
0.6345
0.7060
0.7829
−0.0092
−0.0043
−0.0001
0.0004
0.5789
0.6418
0.7133
0.7976
−0.0282
−0.0158
−0.0105
−0.0184
0.5674
0.6344
0.7069
0.7852
−0.0078
−0.0041
−0.0014
−0.0026
6

M. Xue, D. Huang, K. Yang et al.
Journal of Molecular Liquids 330 (2021) 115639
Table 3 (continued)
T / K
100 xexp
The modified Apelblat
Van't Hoff
CNIBS R-K
Jouyban-Acree-
modified Apelblat
100xcal
RD
100xcal
RD
100xcal
RD
100xcal
RD
318.15
323.15
0.8551
0.9508
0.8352
0.9186
0.0233
0.0339
0.8653
0.9534
−0.0119
−0.0027
0.8753
0.9646
−0.0236
−0.0145
0.8696
0.9602
−0.0170
−0.0099
x2 = 0.5530
298.15
303.15
308.15
313.15
0.7740
0.8504
0.9397
1.0416
1.1374
1.2442
0.7588
0.8399
0.9268
1.0198
1.1189
1.2243
0.0196
0.0123
0.0137
0.0209
0.0163
0.0160
0.7745
0.8577
0.9468
1.0418
1.1429
1.2503
−0.0006
−0.0086
−0.0076
−0.0002
−0.0048
−0.0049
0.7695
0.8451
0.9334
1.0407
1.1313
1.2388
0.0058
0.0062
0.0067
0.0009
0.0054
0.0043
0.7470
0.8324
0.9249
1.0247
1.1321
1.2476
0.0349
0.0212
0.0157
0.0162
0.0047
−0.0027
318.15
323.15
x2 = 0.7357
298.15
303.15
308.15
313.15
0.9409
1.0341
1.1320
1.2598
1.3827
1.5420
0.9167
1.0053
1.1062
1.2209
1.3513
1.4995
0.0257
0.0279
0.0228
0.0309
0.0227
0.0276
0.9293
1.0335
1.1456
1.2656
1.3938
1.5304
0.0123
0.0006
−0.0120
−0.0046
−0.0080
0.0075
0.9430
1.0324
1.1286
1.2659
1.3829
1.5393
−0.0022
0.0016
0.0030
−0.0048
−0.0001
0.0018
0.9231
1.0269
1.1394
1.2611
1.3922
1.5335
0.0189
0.0070
−0.0065
−0.0010
−0.0069
0.0055
318.15
323.15
x2 = 1.0000
298.15
303.15
308.15
313.15
1.4235
1.5499
1.7102
1.8751
2.0725
2.3324
1.4411
1.5675
1.7178
1.8955
2.1052
2.3520
−0.0124
−0.0114
−0.0044
−0.0109
−0.0158
−0.0084
1.3955
1.5524
1.7210
1.9017
2.0948
2.3005
0.0197
1.4264
1.5452
1.6992
1.8873
2.0651
2.3284
−0.0020
0.0030
0.0064
−0.0065
0.0036
0.0017
1.4113
1.5631
1.7276
1.9057
2.0979
2.3053
0.0086
−0.0016
−0.0063
−0.0142
−0.0108
0.0137
−0.0085
−0.0102
−0.0163
−0.0123
0.0116
318.15
323.15
a
Values of the standard uncertainty u are u(x) =0.001, u(T) =0.05 K.
Table 4
Experimental mole fraction solubility values xexp and calculated solubility values xcal of TNR∙2/3H2O in isopropanol-water solvents at the temperature T a
.
T / K
100 xexp
The modified Apelblat
Van't Hoff
CNIBS R-K
Jouyban-Acree-
modified Apelblat
100xcal
RD
100xcal
RD
100xcal
RD
100xcal
RD
x2 = 0.0000
298.15
303.15
308.15
313.15
0.0312
0.0343
0.0396
0.0451
0.0529
0.0608
0.0313
0.0352
0.0399
0.0458
0.0530
0.0618
−0.0032
−0.0262
−0.0076
−0.0155
−0.0019
−0.0164
0.0300
0.0348
0.0402
0.0463
0.0530
0.0604
0.0385
0.0251
0.0313
0.0386
0.0467
0.0559
0.0669
0.1955
0.0875
0.0253
−0.0355
−0.0567
−0.1003
0.0339
0.0381
0.0427
0.0478
0.0534
0.0596
−0.0865
−0.1108
−0.0783
−0.0599
−0.0095
0.0197
−0.0146
−0.0152
−0.0266
−0.0019
0.0066
318.15
323.15
x2 = 0.0256
298.15
303.15
308.15
313.15
0.0327
0.0396
0.0486
0.0585
0.0686
0.0812
0.0321
0.0393
0.0475
0.0570
0.0677
0.0797
0.0183
0.0076
0.0226
0.0256
0.0131
0.0185
0.0329
0.0399
0.0481
0.0576
0.0686
0.0812
−0.0061
−0.0076
0.0103
0.0154
0.0000
0.0402
0.0489
0.0595
0.0710
0.0840
0.0991
−0.2294
−0.2348
−0.2243
−0.2137
−0.2245
−0.2204
0.0522
0.0584
0.0652
0.0726
0.0808
0.0897
−0.5963
−0.4747
−0.3416
−0.2410
−0.1778
−0.1047
318.15
323.15
0.0000
x2 = 0.0558
298.15
303.15
308.15
313.15
0.0480
0.0588
0.0721
0.0868
0.1056
0.1254
0.0486
0.0598
0.0730
0.0885
0.1066
0.1274
−0.0125
−0.0170
−0.0125
−0.0196
−0.0095
−0.0159
0.0482
0.0592
0.0722
0.0875
0.1054
0.1262
−0.0042
−0.0068
−0.0014
−0.0081
0.0019
0.0655
0.0781
0.0936
0.1100
0.1286
0.1496
−0.3646
−0.3282
−0.2982
−0.2673
−0.2178
−0.1930
0.0819
0.0912
0.1013
0.1124
0.1245
0.1377
−0.7063
−0.5510
−0.4050
−0.2949
−0.1790
−0.0981
318.15
323.15
−0.0064
x2 = 0.0920
298.15
303.15
308.15
313.15
0.1009
0.1201
0.1451
0.1714
0.2008
0.2310
0.0996
0.1204
0.1439
0.1700
0.1986
0.2298
0.0129
−0.0025
0.0083
0.0082
0.0110
0.0052
0.1018
0.1214
0.1439
0.1698
0.1992
0.2325
−0.0089
−0.0108
0.0083
0.0093
0.0080
0.1083
0.1265
0.1493
0.1730
0.1997
0.2289
−0.0733
−0.0533
−0.0289
−0.0093
0.0055
0.1302
0.1443
0.1596
0.1763
0.1946
0.2144
−0.2904
−0.2015
−0.0999
−0.0286
0.0309
318.15
323.15
−0.0065
0.0091
0.0719
x2 = 0.1361
298.15
303.15
308.15
313.15
0.1892
0.2189
0.2549
0.2921
0.3321
0.3779
0.1919
0.2233
0.2581
0.2963
0.3381
0.3836
−0.0143
−0.0201
−0.0126
−0.0144
−0.0181
−0.0151
0.1901
0.2202
0.2538
0.2913
0.3329
0.3788
−0.0048
−0.0059
0.0043
0.0027
−0.0024
−0.0024
0.1793
0.2055
0.2387
0.2727
0.3111
0.3518
0.0523
0.0612
0.0636
0.0664
0.0632
0.0691
0.2072
0.2287
0.2522
0.2777
0.3054
0.3354
−0.0951
−0.0448
0.0106
0.0493
0.0804
318.15
323.15
0.1125
(continued on next page)
7

M. Xue, D. Huang, K. Yang et al.
Journal of Molecular Liquids 330 (2021) 115639
Table 4 (continued)
T / K
100 xexp
The modified Apelblat
Van't Hoff
CNIBS R-K
Jouyban-Acree-
modified Apelblat
100xcal
RD
100xcal
RD
100xcal
RD
100xcal
RD
x2 = 0.1911
298.15
303.15
308.15
313.15
0.3078
0.3473
0.3954
0.4448
0.5016
0.5623
0.3034
0.3443
0.3896
0.4397
0.4949
0.5555
0.0143
0.0086
0.0147
0.0115
0.0134
0.0121
0.3058
0.3480
0.3944
0.4452
0.5006
0.5609
0.0065
−0.0020
0.0025
−0.0009
0.0020
0.0025
0.2914
0.3293
0.3762
0.4245
0.4785
0.5345
0.0533
0.0518
0.0486
0.0456
0.0461
0.0494
0.3243
0.3572
0.3929
0.4317
0.4737
0.5193
−0.0536
−0.0285
0.0063
0.0295
0.0556
318.15
323.15
0.0765
x2 = 0.2617
298.15
303.15
308.15
313.15
0.4526
0.5018
0.5614
0.6236
0.6962
0.7719
0.4506
0.5023
0.5597
0.6231
0.6932
0.7707
0.0044
−0.0010
0.0030
0.0008
0.0043
0.0016
0.4466
0.5011
0.5602
0.6240
0.6927
0.7665
0.0133
0.0014
0.0021
−0.0006
0.0050
0.0070
0.4519
0.5061
0.5689
0.6351
0.7084
0.7835
0.0015
0.4851
0.5342
0.5875
0.6454
0.7082
0.7762
−0.0718
−0.0646
−0.0465
−0.0350
−0.0172
−0.0056
−0.0086
−0.0134
−0.0184
−0.0175
−0.0150
318.15
323.15
x2 = 0.3554
298.15
303.15
308.15
313.15
0.6283
0.7025
0.7794
0.8645
0.9601
1.0523
0.6347
0.7091
0.7892
0.8751
0.9670
1.0649
−0.0102
−0.0094
−0.0126
−0.0123
−0.0072
−0.0120
0.6261
0.6990
0.7777
0.8623
0.9530
1.0500
0.0035
0.0050
0.0022
0.0025
0.0074
0.0022
0.6425
0.7171
0.7942
0.8792
0.9729
1.0679
−0.0226
−0.0208
−0.0190
−0.0170
−0.0133
−0.0148
0.6649
0.7346
0.8105
0.8933
0.9832
1.0810
−0.0583
−0.0457
−0.0399
−0.0333
−0.0241
−0.0273
318.15
323.15
x2 = 0.4859
298.15
303.15
308.15
313.15
0.8201
0.9125
1.0001
1.0982
1.2152
1.3311
0.8184
0.9035
0.9961
1.0969
1.2064
1.3252
0.0021
0.0099
0.0040
0.0012
0.0072
0.0044
0.8187
0.9077
1.0030
1.1047
1.2131
1.3283
0.0017
0.0053
−0.0029
−0.0059
0.0017
0.8076
0.9006
0.9866
1.0848
1.1966
1.3058
0.0152
0.0130
0.0135
0.0122
0.0153
0.0190
0.7993
0.8909
0.9916
1.1021
1.2230
1.3553
0.0254
0.0237
0.0085
−0.0036
−0.0064
−0.0182
318.15
323.15
0.0021
x2 = 0.6802
298.15
303.15
308.15
313.15
0.8875
0.9835
1.0824
1.1872
1.3234
1.4411
0.8753
0.9677
1.0682
1.1774
1.2958
1.4240
0.0137
0.0161
0.0131
0.0083
0.0209
0.0119
0.8873
0.9847
1.0891
1.2007
1.3196
1.4462
0.0002
0.8891
0.9865
1.0841
1.1894
1.3216
1.4394
−0.0018
−0.0031
−0.0016
−0.0019
0.0014
0.8323
0.9438
1.0680
1.2062
1.3597
1.5300
0.0622
0.0404
0.0133
−0.0160
−0.0274
−0.0617
−0.0012
−0.0062
−0.0114
0.0029
318.15
323.15
−0.0035
0.0012
x2 = 1.0000
298.15
303.15
308.15
313.15
0.5127
0.6260
0.7606
0.9240
1.0954
1.3078
0.5005
0.6131
0.7449
0.8980
1.0746
1.2769
0.0238
0.0206
0.0206
0.0281
0.0190
0.0236
0.5147
0.6280
0.7614
0.9175
1.0991
1.3093
−0.0039
−0.0032
−0.0011
0.0070
−0.0034
−0.0011
0.5144
0.6282
0.7597
0.9187
1.0889
1.3037
−0.0033
−0.0035
0.0012
0.0057
0.0059
0.5762
0.6769
0.7927
0.9255
1.0775
1.2511
−0.1239
−0.0813
−0.0422
−0.0016
0.0163
318.15
323.15
0.0031
0.0434
a
Values of the standard uncertainty u are u(x) =0.001, u(T) =0.05 K.
3.4. Jouyban-Acree-modified Apelblat model
Jouyban-Acree-modified Apelblat model. For the binary solvent system,
N = 2 and x3 = 1-x2 are introduced at the same time. The Eq. (8) can be
further simplified to Eq. (11).
Jouyban and colleagues proposed the Jouyban-Acree model, which
correlates solubility with the temperature and composition of the
mixed solvents. It reflects the dependence of solubility on temperature
and initial solvent composition. Compared with the CNIBS/R-K model,
Jouyban-Acree model can correlate the solubility data of the binary sol-
vent system not only at the same temperature, but also at the different
temperatures [20–23]. The Jouyban-Acree model is shown as Eq. (8).
B
T
ln X2 ¼ Að2Þ þ ð2Þ þ C ln T
ð9Þ
ð2Þ
B
T
ln X3 ¼ Að3Þ þ ð3Þ þ C ln T
ð10Þ
ð3Þ
ln x1 ¼ A0 þ A1=T þ A2 ln T þ A3x2 þ A4x2=T þ A5x22=T þ A6x23=T
þ A7x42=T þ A8x2 ln T
N
x2x3
T
i
ð11Þ
ln x1 ¼ x2 ln X2 þ x3 ln X3
þ
∑ Jiðx2−x3Þ
ð8Þ
i¼0
Where, A0, A1, A2, A3, A4, A5, A6, A7 and A8 are model parameters,
Among them, Ji is the model constant, T represents the absolute tem-
perature of the solution. The other symbols have the same meanings as
Eq. (6).
which can be estimated by least-squares method.
4. Results and discussion
However, Eq. (8) ignores the relationship between the solubility of
the solute in the pure solvent and the temperature. In order to fit the
solubility data more accurately, the mole fraction solubility of TNR∙2/
3H2O in pure solvents X2 and X3 can be expressed by the modified
Apelblat equation, such as Eq. (9) and Eq. (10). The modified Apelblat
equation is introduced into the Jouyban-Acree model to obtain the
4.1. Powder X-ray diffraction analysis
The equilibrium solid phases obtained from the solubility measure-
ment were compared with the raw material by Powder X-ray diffraction
(PXRD), and the results are shown in the Fig. 4. It can be seen that the
8

M. Xue, D. Huang, K. Yang et al.
Journal of Molecular Liquids 330 (2021) 115639
Table 5
Table 6
Values of model parameters, RMSD (%) and R2 of the modified Apelblat equation in the sol-
Values of model parameters, RMSD (%) and R2 of Van't Hoff equation in the solvents
(methanol/ ethanol/ isopropanol-water).
vents (methanol/ ethanol/ isopropanol-water).
x2
A
B
C
R2
RMSD(%)
x2
A
B
R2
RMSD(%)
Methanol+water
Methanol+water
0.0000
0.0472
0.1004
0.1606
0.2293
0.3086
0.4010
0.5101
0.0000
0.0472
0.1004
0.1606
0.2293
0.3086
0.4010
0.5101
0.6410
0.8007
1.0000
−355.47
99.11
13,782.10
−7718.15
785.88
8946.59
6014.46
−5934.48
−8172.68
−2589.41
7131.94
3014.19
6255.15
52.86
−14.25
13.81
38.44
28.75
−10.01
−17.55
−1.07
29.40
15.32
24.46
0.9989
0.9986
0.9993
0.9993
0.9993
0.9994
0.9999
0.9993
0.9997
0.9998
0.9994
0.0006
0.0018
0.0013
0.0016
0.0026
0.0013
0.0021
0.0027
0.0170
0.0320
0.0619
0.94
3.04
4.03
2.77
2.89
2.80
2.90
1.91
1.59
1.25
0.76
−2698.81
−3272.00
−3525.10
−3047.22
−2953.20
−2812.28
−2700.32
−2255.97
−2021.89
−1752.78
−1351.18
0.9946
0.9983
0.9990
0.9977
0.9981
0.9992
0.9991
0.9993
0.9970
0.9987
0.9952
0.0008
0.0008
0.0007
0.0012
0.0016
0.0013
0.0022
0.0034
0.0073
0.0075
0.0229
−89.09
−256.46
−190.96
70.30
121.24
9.13
−196.58
−101.99
−164.08
0.6410
0.8007
1.0000
Ethanol+water
Ethanol+water
0.0000
0.0332
0.0718
0.1170
0.1709
0.2362
0.3169
0.4191
0.0000
0.0332
0.0718
0.1170
0.1709
0.2362
0.3169
0.4191
0.5530
0.7357
1.0000
−355.47
13,782.10
−1797.58
−8298.22
−15,750.46
−16,293.44
2006.74
52.86
5.26
0.9989
0.9997
0.9998
0.9992
0.9994
0.9994
0.9997
0.9993
0.9997
0.9997
0.9996
0.0006
0.0003
0.0009
0.0013
0.0014
0.0068
0.0057
0.0237
0.0169
0.0326
0.0206
0.94
3.58
3.85
3.11
3.83
1.95
2.00
1.52
1.33
1.77
2.19
−2698.81
−3439.72
−3426.85
−3051.31
−3118.93
−2366.86
−2245.42
−1994.76
−1845.77
−1922.63
−1926.63
0.9946
0.9997
0.9995
0.9962
0.9958
0.9989
0.9991
0.9993
0.9997
0.9976
0.9946
0.0008
0.0004
0.0005
0.0021
0.0037
0.0026
0.0041
0.0049
0.0053
0.0101
0.0228
−31.89
109.07
277.57
288.54
−92.69
−86.77
28.58
−4.02
−157.02
−253.63
−15.60
−40.70
−42.22
14.04
13.17
−4.02
0.79
1855.53
−3245.10
−1598.78
5411.25
0.5530
0.7357
1.0000
23.55
37.95
9888.57
Isopropanol+water
Isopropanol+water
0.0000
0.0256
0.0558
0.0920
0.1361
0.1911
0.2617
0.3554
0.0000
0.0256
0.0558
0.0920
0.1361
0.1911
0.2617
0.3554
0.4859
0.6802
1.0000
−355.47
99.87
33.68
150.12
52.90
−28.10
−70.16
8.57
−46.89
−40.90
47.44
13,782.10
−7933.70
−5046.06
−9956.41
−4981.80
−943.99
1232.90
−2314.01
367.51
79.55
52.86
−14.27
−4.28
−21.70
−7.45
4.47
10.64
−1.03
7.17
0.9989
0.9997
0.9999
0.9998
0.9999
0.9999
0.9999
0.9999
0.9997
0.9993
0.9999
0.0006
0.0011
0.0013
0.0014
0.0045
0.0055
0.0017
0.0091
0.0060
0.0171
0.0209
0.94
3.65
4.80
3.79
2.65
2.05
1.57
1.61
1.45
1.59
6.80
−2698.81
−3479.01
−3708.16
−3184.29
−2658.17
−2337.47
−2081.44
−1992.68
−1864.99
−1882.75
−3598.50
0.9946
0.9994
0.9998
0.9991
0.9998
0.9999
0.9995
0.9999
0.9995
0.9992
0.9999
0.0008
0.0004
0.0005
0.0014
0.0010
0.0012
0.0036
0.0037
0.0038
0.0067
0.0033
0.4859
0.6802
1.0000
6.30
−6.03
−5480.21
PXRD patterns of the equilibrium solid phases from the pure and mixed
solvents are consistent with that of the raw material, and there is no
peak shift. Which shows that TNR∙2/3H2O did not change before and
after the solubility measurement. In addition, the crystal water still ex-
ists even in the equilibrium solid phases from pure methanol, ethanol,
and isopropanol, which means TNR and the crystal water have a strong
binding ability, and even stronger than that between methanol/ etha-
nol/ isopropanol and water.
Table 7
Values of model parameters, RMSD (%) and R2 of CNIBS R-K model in the solvents (meth-
anol/ ethanol/ isopropanol-water).
T / K
B0
B1
B2
B3
B4
R2
RMSD(%)
Methanol+water
298.15
303.15
308.15
313.15
318.15
323.15
−8.16
−8.05
−7.93
−7.78
−7.61
−7.40
3.90
4.67
5.30
5.48
5.59
4.90
7.14
4.37
1.83
1.05
−0.12
1.98
−13.95 7.30
−10.78 6.09
1.0000 0.0068
1.0000 0.0057
1.0000 0.0047
0.9999 0.0076
1.0000 0.0096
1.0000 0.0053
−7.48
−6.68
−4.82
−7.56
4.65
4.36
3.46
4.67
4.2. Solubility data
Ethanol+water
The experimental mole fraction solubility data (xexp) of TNR∙2/3H2O
in different concentrations of methanol/ ethanol/ isopropanol-water
solvent systems are listed in the Table 2-4, with the temperature ranged
from 298.15 K to 323.15 K and at normal pressure.
298.15
303.15
308.15
313.15
318.15
323.15
−8.69
16.49
15.61
−26.01 17.89
−24.51 16.81
−3.93
−3.67
−2.6
−2.88
−3.63
−5.05
0.9995 0.0102
0.9997 0.0080
0.9998 0.0076
0.9998 0.0084
0.9997 0.0110
0.9998 0.0106
−8.41
−8.17
−7.96
−7.79
−7.66
14.735 −22.31 14.27
14.32
14.21
14.47
−21.91 14.46
−22.55 15.88
−24.34 18.82
Isopropanol+water
4.3. Solubility correlation
298.15
303.15
308.15
313.15
318.15
323.15
−8.29
−8.07
−7.86
−7.67
−7.49
−7.31
19.41
18.46
17.89
17.29
16.81
16.20
−42.00 42.87
−38.98 38.70
−37.91 37.59
−36.29 35.40
−35.24 34.31
−33.55 32.02
−17.26 0.9989 0.0104
−15.18 0.9989 0.0113
−14.59 0.9989 0.0124
−13.42 0.9990 0.0136
−12.91 0.9990 0.0149
−11.70 0.9989 0.0177
The modified Apelblat, Van't Hoff, CNIBS R-K, and Jouyban-Acree-
modified Apelblat model were used to correlate the experimental
mole fraction solubility data (xexp) of TNR∙2/3H2O, and the values of
model parameters and the correlation graphs are presented in the
Table 5-8, Fig. 5-11 and Fig. S1-S6, respectively. The corresponding cor-
relation equations were further used to calculate the mole fraction sol-
ubility and get the values of the calculated mole fraction solubility (xcal).
And then the relative deviation (RD) and the root-mean-square devia-
tion (RMSD) were calculated combining the corresponding xexp by
Eq. 12–13 (in which N represents experimental points), to evaluate
the accuracy of the correlation. The values of xcal and RD are listed in
the Table 2-4, and the values of the model parameters, RMSD and R2
are shown in the Table 5-8.
xexp−xcal
xexp
RD ¼
ð12Þ
9

M. Xue, D. Huang, K. Yang et al.
Journal of Molecular Liquids 330 (2021) 115639
Table 8
increases with the increase of temperature, that is, the kinetic energy
that appears with the increase of temperature makes the solvent mole-
cules more effectively break apart the solute molecules that held to-
gether by intermolecular forces. Which means the dissolution of
TNR∙2/3H2O in these solvents is an endothermic process. From
298.15 K to 323.15 K, the solubility increment (Δ100xexp) is different
in different solvent systems and the value of Δ100xexp all increases
with the increase of x2. The maximum values of Δ100xexp are: 0.9768
(methanol), 0.9089 (ethanol) and 0.7951 (isopropanol) respectively.
Therefore, pure methanol, ethanol, and isopropanol are suitable for
the cooling crystallization of TNR∙2/3H2O, and the methanol is more
advantageous.
Values of model parameters, RMSD (%) and R2 of Jouyban-Acree-modified Apelblat model
in the solvents (methanol/ ethanol/ isopropanol-water).
Methanol+water
Ethanol+water
Isopropanol+water
A0
A1
A2
A3
A4
A5
A6
A7
−71.82
5.09
11.15
10.33
−3334.31
−1.34
−47.68
−6.20
6.97
−37.47
4019.82
620.65
−2390.74
1474.64
5.18
−38.84
6206.72
−7342.62
5172.93
−1185.06
5.88
−1.16
3954.45
−11,291.99
10,995.12
−4166.08
1.00
A8
RMSD(%)
0.0231
0.9999
0.0137
0.9995
0.0276
0.9961
R2
4.4.2. The influence of different solvents on the solubility of TNR∙2/3H2O
(1) Pure solvents. In pure solvents, the solubility order of TNR∙2/
3H2O at the same temperature is: methanol > ethanol > isopropanol
> water. The solubility is influenced by many factors, and the
dissolution of substances generally conforms to the principle of “similar
compatibility”. The TNR molecular structure is an axisymmetric struc-
ture with relatively small polarity, but the order of solubility is not con-
sistent with the order of polarity of the selected solvents, which
indicates that the polarity of the solvents is not the main factor affecting
the solubility of TNR∙2/3H2O. In the literature [24], the influence of alco-
hol solvents on the solubility was analyzed. For alcohols, the solvent-
solvent interaction is strong due to the existence of hydrogen bonds,
which explains that the order of solubility and that of polarity of sol-
vents may not be parallel to each other in alcohol solvents. And in nor-
mal alcohols, the solubility decreases with the increase of the number of
CH2 units, which explains the solubility order of TNR∙2/3H2O at the
same temperature is: methanol > ethanol > isopropanol. Furthermore,
as shown in the Table 9, the order of π, Σα, μ, dielectric constant and co-
hesive energy density is consistent with the order of solubility, and the
order of Σβ is opposite to the order of solubility, which shows that
TNR∙2/3H2O is easier to dissolve in methanol, followed by ethanol and
isopropanol. In addition, the literature [24] also mentioned that the
low solubility of the dye in water is probably due to the presence of
the hydrophobic wing of the dye, and there is a tendency for water mol-
ecules to maintain self-association by hydrogen bonding. These can also
explain the low solubility of TNR∙2/3H2O in water.
Fig. 5. Experimental mole fraction solubility values (xexp) of TNR∙2/3H2O correlated by the
modified Apelblat equation in the pure solvents.
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
N
À
Á
1
2
RMSD ¼
∑ xexp−xcal
ð13Þ
N i¼1
(2) Binary solvents with different concentrations. The solubility of
TNR∙2/3H2O in these three binary mixed solvents has different sensitiv-
ity to the content of organic components in the solvent, that is, the
change rate of the solubility values with the change of x2 (dx1/dx2) is dif-
ferent. As shown in Fig. 9-11, x2 from 0 to 1, x1 and dx1/dx2 increase with
the increase of x2 (methanol-water mixed system); x1 increases but dx1/
dx2 successively presents increase, decrease, and then increase with the
increase of x2 (ethanol-water mixed system); for isopropanol-water
4.4. Discussion
4.4.1. The influence of temperature on the solubility of TNR∙2/3H2O
It can be seen from the Table 2-4 and Fig. 5-8 that all the solubility
test results of TNR∙2/3H2O in this article show that the solubility
Fig. 6. Experimental mole fraction solubility values (xexp) of TNR∙2/3H2O correlated by the modified Apelblat equation in methanol-water solvents.
10

M. Xue, D. Huang, K. Yang et al.
Journal of Molecular Liquids 330 (2021) 115639
Fig. 7. Experimental mole fraction solubility values (xexp) of TNR∙2/3H2O correlated by the modified Apelblat equation in ethanol-water solvents.
Fig. 8. Experimental mole fraction solubility values (xexp) of TNR∙2/3H2O correlated by the modified Apelblat equation in isopropanol-water solvents.
mixed system, x1 and dx1/dx2 increase first and then decrease with the
increase of x2, and TNR∙2/3H2O has the highest solubility at x2
There are many factors that affect the solubility and its changed
trends. In addition to the interaction between the solvents, the interac-
tion between the solute and the solvent, the properties of solvent and
solute (such as dielectric constant, polarity, dipole moment, cohesive
energy, ionization constant, the surface tension etc.) and so on will
also affect the solubility. The influencing factors are numerous and com-
plex, and the specific reasons that affecting the solubility of TNR∙2/3H2O
need to be further studied.
=
0.6802. There is no obvious difference about the change trends between
298.15 K and 323.15 K. And these trends are similar to those reported in
the literatures for the solubility trends of 2,4,6-trinitrophenol (an ana-
logue of TNR) [26,27]. Referring to the literatures [24,26,27], the possi-
ble reason for these trends is: the interaction between solvent and
solvent plays an important role.
In ethanol-water mixed system, the minimum of dx1/dx2 appears at
x2 = 0.7357, which is close to the proportions of ethanol in the
azeotropic mixture of ethanol-water (ethanol mass fraction: 95.0%). In
isopropanol-water mixed system, dx1/dx2 ≈ 0 and x1 reaches the max-
imum when x2 = 0.6802, which is close to the proportions of iso-
propanol in the azeotropic mixture of isopropanol-water (isopropanol
mass fraction: 87.9%). Therefore, the aforementioned changed trends
of solubility may be related to the azeotropes formed by the alcohols
and water. Moreover, water is a highly structured solvent with a high
self-cohesiveness, and this property is expected to change as a co-
solvent (methanol/ ethanol/ isopropanol) is added to it [24]. This may
be the result of the dissociation of the associated water molecules by
the alcohol solvents and the subsequent association of alcohol mole-
cules with water.
4.4.3. Comparison of the solubility of TNR∙2/3H2O and TNP
Since TNR has a similar structure to 2,4,6-trinitrophenol (TNP), the
solubility data of TNR∙2/3H2O were compared with that of TNP reported
in the literature [26], and the comparison charts are shown in the
Fig. S7-S10. It can be found that, at the same temperature, the solubility
of TNR∙2/3H2O and TNP in the methanol-water and isopropanol-water
mixed systems respectively have the same changing trend with the in-
crease of x2. However, there are different trends in the ethanol-water
mixed system. The reasons for the difference may be: TNR∙2/3H2O con-
tains crystal water, the properties of the two substances are different,
and they have different interactions with the same solvent, etc. In addi-
tion, with the same solvent and temperature, the solubility of TNP is al-
ways greater than that of TNR∙2/3H2O. And among the four pure
solvents (methanol, ethanol, isopropanol and water), the solubility dif-
ference between TNP and TNR∙2/3H2O is obviously the largest in
isopropanol. In methanol-water mixed system, the difference in solubil-
ity between the two is the largest with x2 ≈ 0.80. When x2 = 0.63–0.69
(ethanol-water) and x2 ≈ 0.73 (isopropanol-water), the solubility
Therefore, it may be that the formation of azeotropic mixtures of al-
cohols and water, the interaction between water and alcohol solvents,
the properties of the solvents (such as cohesion, etc.) and so on can
make the solubility of TNR∙2/3H2O (x1) and dx1/dx2 show different
changed trends with the change of x2.
11

M. Xue, D. Huang, K. Yang et al.
Journal of Molecular Liquids 330 (2021) 115639
Fig. 9. Experimental mole fraction solubility values (xexp) of TNR∙2/3H2O correlated by
CNIBS R-K model in methanol-water solvents.
Fig. 11. Experimental mole fraction solubility values (xexp) of TNR∙2/3H2O correlated by
CNIBS R-K model in isopropanol-water solvents.
Apelblat); 0.0026 (isopropanol-Water)
< 0.0045 (methanol-
water) < 0.0057 (isopropanol-water) (for Van't Hoff model); 0.0066
(methanol-water) < 0.0093 (ethanol-water) < 0.0134 (isopropanol-
water) (for CNIBS R-K model); 0.0137 (ethanol-water) < 0.0231 (meth-
anol-water)
< 0.0276 (isopropanol-water) (for Jouyban-Acree-
modified Apelblat model). Therefore, it is more suitable for the modified
Apelblat and Van't Hoff models to correlate the xexp from the
isopropanol-water system, and the CNIBS R-K model and the Jouyban-
Acree-modified Apelblat model are more suitable for correlating the
x
exp from the methanol-water and ethanol-water system, respectively.
For these three mixed solvent systems, the order of the average RMSD
(%) values is: 0.0045 (VH) < 0.0066 (RK) < 0.0114 (AP) < 0.0231(JA)
(for methanol-water system); 0.0057 (VH) < 0.0093 (RK) < 0.0110
(AP) < 0.0137 (JA) (for ethanol-water system); 0.0026 (VH) < 0.0069
(AP) < 0.0134(RK) < 0.0276(JA) (for isopropanol-water system). It is
shown that the values of xexp in these three systems are all most suitable
for being correlated with the Van't Hoff model, which is more beneficial
to extend the solubility data of TNR∙2/3H2O, and followed by the CNIBS
R-K and the modified Apelblat model.
5. Thermodynamic properties of dissolution
Fig. 10. Experimental mole fraction solubility values (xexp) of TNR∙2/3H2O correlated by
CNIBS R-K model in ethanol-water solvents.
From an energy point of view, the dissolution of substances in sol-
vents is related to some thermodynamic properties describing the
structure of the solution. The thermodynamic properties of the dissolu-
tion process are of great significance to the study of solution structure.
The graphical method based on the Van't Hoff equation has been fre-
quently used to analyze the thermodynamic properties of the dissolu-
tion process, aiming to calculate the apparent thermodynamic
parameters (standard dissolution enthalpy (ΔH°dis), standard dissolu-
tion entropy (ΔS°dis) and the standard Gibbs energy (ΔG°dis)) at the
mean temperature (Tmean) [28–34]. And the specific analysis process
is as follows:
difference between the two is the largest and the difference gradually
increases as the temperature rises, and the difference is the largest
when T = 323.15 K. From the comparison charts, we can see that
x2 = 0.63–0.69 (ethanol-water) and x2 ≈ 0.73 (isopropanol-water)
are more suitable as the solvents for solution crystallization to separate
TNR∙2/3H2O from the mixture of TNP and TNR∙2/3H2O, for the solubility
of TNP is greater than that of TNR∙2/3H2O and the large solubility differ-
ence between them in the same solvent and temperature.
Basing on the Eq. 14–15, the linear regression of lnx1 value to 1/T-1/
Tmean was run. Calculate the value of ΔH°dis and ΔGd° is from the slope and
intercept, and further calculate the value of ΔS°dis. The calculation formu-
las are shown as Eq. 15–17.
4.4.4. The results of solubility correlation
It can be seen that all the values of R2 are greater than 0.99 and these
four models all have good correlation/curve fitting to the experimental
mole fraction solubility data (xexp) of TNR∙2/3H2O (as shown in
Fig. 5-11, Fig. S1-S6 and Table 5-8). For the four models, the order of
the average RMSD (%) values is: 0.0069 (isopropanol-water) < 0.0110
(ethanol-water) < 0.0114 (methanol-water) (for The modified
N
Tmean
¼
ð14Þ
N
∑ð1=TÞ
i¼1
12

M. Xue, D. Huang, K. Yang et al.
Journal of Molecular Liquids 330 (2021) 115639
Table 9
Table 12
Solvent property parameters of selected solvents [25].
%ξH,%ξTmeanS,the standard dissolution enthalpy, standard dissolution entropy and the stan-
dard Gibbs energy of TNR∙2/3H2O in ethanol-water solvents.
Solvent
π a
Σα b
Σβ c
μ d
Dielectric
constant e
Cohesive energy
density f
x2
ΔH°dis /kJ∙mol−1
ΔS°dis/J∙mol−1
ΔG°dis/kJ∙mol−1
%ξH
%ξTmeanS
Methanol
Ethanol
Isopropanol
Water
0.60
0.54
0.48
1.09
0.43
0.37
0.33
1.17
0.47
0.48
0.56
0.47
1.70
1.69
1.56
1.87
32.61
24.85
19.26
78.36
808.26
618.87
489.11
2095.93
0.0332
0.0718
0.1170
0.1709
0.2362
0.3169
0.4191
0.5530
0.7357
28.53
28.77
26.14
26.81
19.55
18.50
16.63
15.33
15.77
29.56
32.90
28.29
34.67
15.77
16.14
12.76
10.97
14.03
19.35
18.56
17.36
16.05
14.65
13.49
12.67
11.92
11.42
75.66
73.80
74.85
71.36
79.98
78.69
80.77
81.82
78.37
24.34
26.20
25.15
28.64
20.02
21.31
19.23
18.18
21.63
a
Polarity/dipolarity of the solvent.
b
c
d
e
f
Summation of the hydrogen bond donor propensities of the solvent.
Summation of the hydrogen bond acceptor propensities of the solvent.
Dipole moment, μ/D.
Dielectric constant at T = 293.15 K.
Cohesive energy density in the unit of J mol/ml.
Table 10
Table 13
%ξH,%ξTmeanS,the standard dissolution enthalpy, standard dissolution entropy and the stan-
dard Gibbs energy of TNR∙2/3H2O in different pure solvents.
%ξH,%ξTmeanS,the standard dissolution enthalpy, standard dissolution entropy and the stan-
dard Gibbs energy of TNR∙2/3H2O in isopropanol-water solvents.
Solvent
ΔH°dis /kJ∙mol−1 ΔS°dis/J∙mol−1 ΔGd° is/kJ∙mol−1 %ξH
%ξTmeanS
x2
ΔH°dis /kJ∙mol−1
ΔS°dis/J∙mol−1
ΔG°dis/kJ∙mol−1
%ξH
%ξTmeanS
Water
Methanol
Ethanol
21.78
11.09
15.69
5.68
5.85
17.16
56.85
20.02
9.27
10.37
12.37
92.51 7.49
0.0256
0.0558
0.0920
0.1361
0.1911
0.2617
0.3554
0.4859
0.6802
29.23
30.88
26.80
22.19
19.38
17.19
16.57
15.45
15.59
31.35
40.03
32.56
22.32
16.89
12.73
13.43
11.87
13.00
19.50
18.45
16.69
15.26
14.14
13.24
12.40
11.76
11.56
75.02
71.30
72.62
76.21
78.71
81.31
79.90
80.74
79.44
24.98
28.70
27.38
23.79
21.29
18.69
20.10
19.26
20.56
85.92 14.08
74.66 25.34
62.98 37.02
Isopropanol 30.02
Table 11
%ξH,%ξTmeanS,the standard dissolution enthalpy, standard dissolution entropy and the stan-
dard Gibbs energy of TNR∙2/3H2O in methanol-water solvents.
This graphical method was used to study the thermodynamic prop-
erties of TNR∙2/3H2O in the selected solvents to understand their disso-
x2
ΔH°dis /kJ∙mol−1
ΔS°dis/J∙mol−1
ΔG°dis/kJ∙mol−1
%ξH
%ξTmeanS
0.0472
0.1004
0.1606
0.2293
0.3086
0.4010
0.5101
0.6410
0.8007
27.58
28.98
24.83
24.13
23.51
22.72
18.77
16.54
14.44
26.51
32.42
21.44
22.64
23.69
24.96
15.95
12.38
10.00
19.35
18.91
18.18
17.10
16.16
14.97
13.82
12.70
11.34
77.02
74.22
78.86
77.44
76.18
74.57
79.13
81.15
82.32
22.98
25.78
21.14
22.56
23.82
25.43
20.87
18.85
17.68
lution behavior. The linear regression graphs of lnx1 verse (1/T-1/Tmean
)
are shown in Fig. S11-S14, and the R2 values are all in the range of
0.9907 to 0.9999. The calculation results of relevant parameters are pre-
sented in Table 10-13. It can be seen from the results that the values of
ΔH°dis and ΔG°dis are both positive in all solvents used. The order of solu-
bility is opposite to that of ΔH°dis and ΔGd° is in each pure and binary sol-
vents consisted to the phenomenon reported in the literatures [35–37].
Which indicates the dissolution is an endothermic, non-spontaneous
and favorable process. In addition, the values of ΔS°dis are also positive
means that the process is the entropy-driven [38]. Moreover, all the
values of %ξH are greater than that of corresponding %ξTmeanS which
shows that enthalpy is the main contributor to the Gibbs free energy
during the dissolution process. In conclusion, the dissolution of TNR∙2/
3H2O in the selected solvents is considered as an “endothermic, non-
spontaneous and entropy-driven” process.
ꢀ
ꢁ
ΔHꢀdis ¼ −R
ð15Þ
∂ ln x1
∂ð1=T−1=Tmean
Þ
ΔGꢀdis ¼ −RTmean⋅intercept
ΔHꢀdis−ΔGꢀdis
ð16Þ
ð17Þ
ΔSꢀdis
¼
Tmean
6. Conclusion
In which, N represents the number of temperature points, T repre-
sents the absolute temperature, R is the universal gas constant
(8.314 J·K−1·mol−1), x1 is the mole fraction solubility of TNR∙2/3H2O
at the temperature T, and the “intercept” is the intercept of the plot of
lnx1 verse (1/T-1/Tmean).
In addition, the relative contributions of enthalpy (%ξH) and entropy
(%ξTmeanS) to the dissolution process of TNR∙2/3H2O were determined by
the Eq. 18–19.
In this work, the laser dynamic method was used to measure the sol-
ubility of 2,4,6-trinitroresorcinol hydrate (TNR∙2/3H2O) in the pure sol-
vents (methanol, ethanol, isopropanol and water) and the binary mixed
solvents (methanol-water, ethanol-water and isopropanol-water) from
298.15 K to 323.15 K under the atmospheric pressure. And the powder
X-ray diffraction (PXRD) was used to compare the equilibrium solid
phases and the raw material, which shows that the TNR∙2/3H2O do
not change before and after the solubility measurement in the selected
solvents, and TNR has a strong binding ability with the crystal water.
Among all the solvents used, the solubility of TNR∙2/3H2O increases
with the increase of temperature, which means that the dissolution in
these solvents is an endothermic process, and methanol is more suitable
for the cooling crystallization of TNR∙2/3H2O. In the pure solvents, the
solubility order of TNR∙2/3H2O at the same temperature is: methanol
> ethanol > isopropanol > water, which may be affected by the
jΔHdis
j
%ξH
¼
ꢁ 100
ð18Þ
ð19Þ
jΔHdisj þ jTmeanΔSdisj
jTmeanΔSdisj
%ξT
¼
ꢁ 100
mean S
jΔHdisj þ jTmeanΔSdisj
13

M. Xue, D. Huang, K. Yang et al.
Journal of Molecular Liquids 330 (2021) 115639
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The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influ-
ence the work reported in this paper.
Appendix A. Supplementary data
Supplementary data to this article can be found online at https://doi.
org/10.1016/j.molliq.2021.115639.
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