3-Methyl-6-nitroindazole in some aqueous co-solvent mixtures: Solubility determination, preferential solvation and solvent effect analysis

Journal Pre-proofs 3-Methyl-6-nitroindazole in some aqueous co-solvent mixtures: Solubility determination, preferential solvation and solvent effect analysis Wanxin Li, Ali Farajtabar, Rong Xing, Yiting Zhu, Hongkun Zhao, Rongguan Lv PII: DOI: Reference:

S0021-9614(20)30030-6 https://doi.org/10.1016/j.jct.2020.106066 YJCHT 106066

To appear in:

J. Chem. Thermodynamics

Received Date: Revised Date: Accepted Date:

12 January 2020 15 January 2020 20 January 2020

Please cite this article as: W. Li, A. Farajtabar, R. Xing, Y. Zhu, H. Zhao, R. Lv, 3-Methyl-6-nitroindazole in some aqueous co-solvent mixtures: Solubility determination, preferential solvation and solvent effect analysis, J. Chem. Thermodynamics (2020), doi: https://doi.org/10.1016/j.jct.2020.106066

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3-Methyl-6-nitroindazole in some aqueous co-solvent mixtures: Solubility determination, preferential solvation and solvent effect analysis Wanxin Lia, Ali Farajtabarb, Rong Xinga, Yiting Zhua, Hongkun Zhaoc*, Rongguan Lva* a School

of Chemistry and Environmental Engineering, Yancheng Teachers University, Yancheng, Jiangsu

224002, People’s Republic of China b Department

c College

of Chemistry, Jouybar Branch, Islamic Azad University, 4776186131, Jouybar, Iran

of Chemistry & Chemical Engineering, YangZhou University, YangZhou, Jiangsu 225002, People’s

Republic of China

Corresponding author. Tel: + 86 514 87975568; Fax: + 86 514 87975244.

c,*E-mail

address: [email protected] (Hongkun Zhao).

Tel: + 86 515 88258980; Fax: + 86 515 88628866.

a,*E-mail

address: [email protected] (Rongguan Lv).

ABSTRACT The equilibrium solubility of 3-methyl-6-nitroindazole in co-solvent mixtures of acetonitrile (1) + water (2), ethanol (1) + water (2) and n-propanol (1) + water (2) is reported. Experiments were performed by using the saturation shake-flask technique at temperature range from 278.15 to 328.15 K. The maximum solubility value was observed in neat acetonitrile (ethanol or n-propanol) for each co-solvent mixtures. By using the Jouyban-Acree model, the 3-methyl-6-nitroindazole solubility was well correlated obtaining RAD values smaller

1

than 4.50 % and RMSD values smaller than 3.3610-4. Quantitative values for the local mole fraction of acetonitrile (ethanol, n-propanol, DMF or acetone) and water around the 3-methyl-6-nitroindazole were computed by using the Inverse Kirkwood–Buff integrals method applied to the solubility data. 3-Methyl-6-nitroindazole was preferentially solvated by water in water-rich compositions; while within co-solvent-rich and intermediate compositions, 3-methyl-6-nitroindazole is preferentially solvated by acetonitrile (ethanol, n-propanol, DMF or acetone) in the acetonitrile (ethanol, n-propanol, DMF or acetone) + water mixtures. The experimental solubility data were correlated by Kamlet and Taft linear solvation energy relationships to examine the main factors describing solvent effect. The results showed that the change in cavity formation

energy

over

the

composition

played

the

main

role

on

the

solubility

variation

of

3-methyl-6-nitroindazole in all aqueous mixtures.

Keywords: 3‑Methyl-6-nitroindazole; Solubility; Jouyban-Acree; Preferential solvation; Solvent effect

1. Introduction Investigation upon the solubility of pharmaceutical intermediates and drugs together with their improvement is one of the most increasing subjects in pharmaceutical regions [1–5]. The solid solubility in co-solvent solutions as a function of the co-solvent compositions and temperature is very important for raw material purification and mechanisms understanding with regard to the chemical and physical stability of dissolutions of solid compounds [3-5]. Co-solvency is an operational solubilization method to adjust the solid solubility, since the co-solvent mixtures are generally employed as a synthesis reaction medium or a re-crystallization solvent in purifying process for a lot of substances [1,3,4,6]. As well, the solubility of solids in co-solvent solutions allows us to make the thermodynamic analysis to deeply insight the molecular mechanisms 2

regarding the dissolution process of drugs and the preferential solvation of solutes by co-solvent components [7-13]. 3-Methyl-6-nitroindazole (CAS registry number: 6494-19-5) is a critical intermediate of Pazopanib production [14], which is a tyrosine kinase inhibitor for treating patients with soft tissue sarcoma and advanced renal cell carcinoma [15,16]. The chemical structure of 3-methyl-6-nitroindazole is graphically shown in Figure 1. Recently Wang and coworkers reported the solubility of 3-methyl-6-nitroindazole in neat solvents and mixed solvents of N,N-dimethylformamide (DMF) + water and acetone + water from 278.15 to 328.15 K under atmospheric pressure [17]. According to the literature results, the 3-methyl-6-nitroindazole presents lower aqueous solubility [17]. In addition, 3-methyl-6-nitroindazole shows up to about 102-103-fold increase in mole fraction solubility in going from water to the DMF, alcohols, acetone and acetonitrile. The high increment of solubility magnitude strongly suggests the presence of preferential solvation of 3-methyl-6-nitroindazole in the aqueous co-solvent mixtures [9-13]. This case encourages us to perform in-depth investigation upon the solubility and thermodynamic aspects of 3-methyl-6-nitroindazole in some aqueous co-solvent mixtures. Furthermore, although the co-solvency method has been extensively used in the pharmacies many years ago [1,3,5], only just at present the mechanism relating to increasing or decreasing the drugs’ solubility starts to be investigated from a deep thermodynamic point of view, as well as the analysis of preferential solvation of a solute by the solvent components in aqueous co-solvent mixtures [7-13]. For these reasons, the main objectives of this contribution are to report the solubility of 3-methyl-6-nitroindazole (component 3) in three co-solvent mixtures of (acetonitrile + water), (ethanol + water) and (n-propanol + water) so as to evaluate the thermodynamic aspects of the 3

mixtures and investigate on the solvent effect as well as the preferential solvation analysis of 3-methyl-6-nitroindazole by the organic solvents. The present work does enrich the available solubility of 3-methyl-6-nitroindazole [3,17] and also permits us to carry out the thermodynamic analysis of solvation process. It is noteworthy that the aqueous solutions of acetonitrile have been intensively studied owing to its importance for numerous chemistry branches and its simple structure. In addition, the CN group is an environmental sensor. Previous study demonstrates that the influence of acetonitrile on water structure is quite different from that of the other solvents [18]. The solvent of ethanol is a co-solvent commonly employed in the pharmaceutical fields. Because of its high solubilization ability, ethanol is normally used in the liquid formulation process. Moreover, it effects the drug’s distribution, excretion, absorption and metabolism [19]. In contrast, although the solvent of n-propanol is not expansively employed as a co-solvent in the design of liquid medicines, it is generally used as a solvent in the pharmaceuticals for the cellulose resins and esters [20]. The knowledge on the molecular interactions is generally employed to predict the solid solubility and condition selection for the improvement of lower aqueous solubility of drugs in mixed solvents. In this aspect, the linear solvation energy relationships, LSER, may provide a satisfactory method through quantitatively handling the solvent effect. LSER treats it by means of making correlations between the solvent polarity and corresponding solvent-induced energy variations [21]. In this manner, the solvent polarity as a universal definition for the solvent properties stands for the solvent ability to procedure all possible kinds of solvent-solute interactions except for bringing about the chemical changes and molecular structure. Kamlet, Abboud and Taft parameters, termed as the KAT parameters, are introduced to quantitatively describe the solvent polarity [21-24]. These 4

descriptors may be attainable from direct determination of the solvent-induced variations in energetic stabilization of the electronic states of solvent-sensitive probes due to presenting distinct solute-solvent interactions at a molecular level. This method separates the solvent polarity to its components by means of building the *,  and  scales. The term * refers to the dipolarity-polarizability of a solvent, and presents a measurement of relative affinity of the solvent participation in the non-specific electrostatic interactions. The terms  and  designate the ability of hydrogen-bond acceptance and hydrogen-bond donation of a solvent, respectively. The concept of LSER on the basis of the KAT model affords a multi-parametric method, KAT-LSER, to get the information upon type and strength of the intermolecular interactions which describes the solvent effect on solid solubility [23,25-27]. It is evident that the KAT-LSER model has disclosed remarkable success in explaining many chemical phenomena, e.g. solubility, in pure solvents and solvent mixturs [23,25-27]. Accordingly, another objective of this contribution is to analyze the solvent effect upon the solubility variation of 3-methyl-6-nitroindazole in aqueous solutions of acetonitrile, ethanol and n-propanol as well as the DMF and acetone via the KAT-LSER model with the intention of explaining the nature of intermolecular interactions and relative significance that result in the solvent effect.

2. Theoretical aspects In this contribution, the Jouyban−Acree model [26,28,29] is applied to mathematically describe the 3-methyl-6-nitroindazole solubility in aqueous co-solvent solutions of acetonitrile, ethanol and n-propanol. In addition, the Kamlet-Taft linear solvation energy relationships, KAT-LSER, is used herein to mathematically describe the solvent effect upon the solubility of 3-methyl-6-nitroindazole [21,23,25]. 5

2.1. Jouyban-Acree model This model, Eq. (1), may provide accurate mathematical description for the solid solubility dependence on both solvent composition and temperature for mixed solvents [26,28,29]. ln xw,T  w1 ln x1,T  w2 ln x2,T 

w1w2 2 i J i  w1  w2   T / K i=0

(1)

wherein xw,T denotes the mole fraction solubility of a solute in solutions at temperature T/K; w1 and w2 refer to the mass fraction of co-solvents 1 (acetonitrile, ethanol and n-propanol) and 2 (water) in the co-solvent solutions free of the solute (3-methyl-6-nitroindazole), respectively; x1,T and x2,T stand for the mole fraction solubility of 3-methyl-6-nitroindazole in neat co-solvent and water. Ji are parameters of the Jouyban-Acree model. 2.2. KAT-LSER model The KAT-LSER model is experienced here for the 3-methyl-6-nitroindazole solubility to describe the co-solvency effect upon 3-methyl-6-nitroindazole solubility in mixtures. Eq. (2) is a general form of the KAT-LSER model [21,23,25].  Vs H2  ln xw  c0  c1 * c2   c3  c4    100 RT 

(2)

Through definition, the c1 c2 and c3 refer to the energy terms for non-specific and specific solute-solvent interactions, for which ci=1-3 reveal the sensitivity of solute solubility to corresponding energy terms. The last term in Eq. (2) is cavity term referring to energy term for the solvent-solvent interactions. This term measures the energy of solute accommodation as a product of Hildebrand solubility parameter, H, of solvent and solute molar volume, Vs. The temperature T/K and gas constant R are also considered here in denominator so as to get a dimensionless value for the cavity term. Hence, the coefficient c4 indicates the susceptibility of solute solubility to the 6

solvent-solvent interactions. In practice, the mole fraction solubility is firstly converted to lnxw, and then mathematically correlated with Eq. (2) by the use of the multiple linear regression analysis. The objective function used here is defined as Eq. (3). e c  ln xw,T F   ln xw,T 

2

(3)

In an attempt to evaluate the Jouyban-Acree model, the relative average deviation (RAD) and root-mean-square deviation (RMSD) are also employed and described as Eqs. (4) and (5), respectively. 1 RAD  N

e c  xw,T  xw,T   xe w,T 



RMSD 

N i 1

   

(4)

c e ( xw,T )2  xw,T

(5)

N

e here xw,T signifies the mole fraction solubility of 3-methyl-6-nitroindazole determined by us; and c xw,T , computed value through the Jouyban-Acree model. N designates the number of experimental

data points. 2.3. Preferential solvation The method of Inverse Kirkwood–Buff integrals (IKBI) describes the local solvent compositions nearby a solute compared with the global solution compositions [7-13,26,27,30]. It is expressed as Eq. (6). In general, it is a powerful tool to investigate the preferential solvation of a nonelectrolyte or a weak electrolyte in the co-solvent + water solutions. Gi ,3  

rcor

0

( gi ,3  1)4 r 2 dr

(6)

In Eq. (6), r is the distance between the molecule centers of 3-methyl-6-nitroindazole (3) and that of co-solvent (1) or water (2); rcor refers to the correlation distance. gi,3 represents the pair correlation function for the solvent molecule i in the co-solvent (1) + water (2) solutions adjacent 7

3-methyl-6-nitroindazole (3). For r is greater than rcor, the gi,3 value is approximately equal to 1. Consequently, for r>rcor up to infinity, the integral value is essentially zero. The parameter of preferential solvation (δx1,3) of 3-methyl-6-nitroindazole (3) by the co-solvent (1) in co-solvent (1) + water (2) solutions may be described as Eqs. (7) [7-13,26,27,30]. L  x1,3  x1,3  x1   x2,3

(7)

L herein x1,3 denotes the local mole fraction composition of the co-solvent (1) adjacent the solute

3-methyl-6-nitroindazole (3); and x1, the bulk mole fraction of the co-solvent (1) in the initial mixtures. If the δx1,3 magnitude is higher than 0, the solute is preferentially solvated by the co-solvent (1); whereas if it is smaller than 0, then the solute is said to be preferentially solvated by water (2). The values of δx1,3 can be attainable from the IKBI method for individual solvent compositions [7-13,26,27,30].

 x1,3 

x1 x2  G1,3  G2,3 

(8)

x1G1,3  x2G2,3  Vcor

with G1,3  RT  T  V3 

x2 V2 D Q

(9)

G2,3  RT  T  V3 

x1V1 D Q

(10)



L L Vcor  2522.5  r3  0.1363 x1,3 V 1  x2,3 V2 



1/3

 0.085 

3

(11)

wherein, V 1 and V 2 stand for the partial molar volumes of the components in the aqueous mixtures free of 3-methyl-6-nitroindazole; V 3 is partial molar volume of 3-methyl-6-nitroindazole in mixtures. κT stands for the isothermal compressibility of the co-solvent (1) + water (2) solutions; The function D {Eq. (12)} is the derivative of standard molar Gibbs energy of transfer of 8

3-methyl-6-nitroindazole from pure water (2) to the co-solvent (1) + water (2) solutions with respect to the co-solvent compositions. The function Q described as Eq. (13) is the second derivative of excess molar Gibbs energy of mixing of the two solvents ( G1Exc  2 ) with respect to water proportions in the aqueous co-solvent solutions. Vcor refers to the correlation volume; and r3, the molecular radius of 3-methyl-6-nitroindazole obtained from Eq. (14) with NAv as Avogadro’s number.

  G o  D   tr (3,21 2)    x1  T , P

(12)

   2G1Exc 2 Q  RT  x1 x2   2  x2 T , p

(13)

r3 

3

3 1021V 3 4 N AV

(14)

Because of the dependence of κT value upon solvents compositions, thus it is not known for the studied co-solvent mixtures. However, the contribution of RTκT to the IKBI is minor, so, the value of κT may be approximately estimated by considering an additive property through the solution compositions and available values for pure solvents by [9-13,26,27,30]: o o  T  x1 T,1  x2 T,2

(15)

o where  T,i is isothermal compressibility of the neat component i; xi is the mole fraction of

component i in solutions. The standard molar Gibbs energies of transfer of 3-methyl-6-nitroindazole from neat water (2) to aqueous co-solvent mixtures are computed by the use of Eq. (16) from the solubility and fitted with an empirical Eq. (17) for the ethanol (1) + water (2),n-propanol (1) + water (2) and DMF (1) + water (2) mixtures; and an empirical Eq. (18) for the acetonitrile (1) + water (2) and acetone (1) + water (2) mixtures, where A0, A1, A2, t1 and t2 refer to the equation parameters. 9

 x3,2  o  tr G3,2  1 2  RT ln  x  3,1 2 

 tr G

o 3,2 1 2

 tr G

o 3,2 1 2

 A0  A1e  A0  A1e



x1 t1



x1 t1

 A2 e

(16) 

x1 t2

(17) (18)

The definitive correlation volume needs to be iterated because it is dependent upon the local mole fractions nearby the solute. The iteration procedure may be performed through substituting L δx1,3 and Vcor in Eqs. (7), (8) to (11) to recalculate x1,3 until a non-variant Vcor value is obtained.

2. Experimental 2.1. Materials The raw material 3-methyl-6-nitroindazole having a mass fraction purity of 0.986 was provided by the Sigma Chemical Co., Ltd., China. After recrystallizing in methanol for three times, the 3-methyl-6-nitroindazole had a mass fraction composition of 0.995, which was confirmed by means of an Agilent 1260 high-performance liquid chromatography (HPLC). The water used in this contribution was twice-distilled water with a conductivity of less than 2µS·cm-1. The organic solvents of acetonitrile, ethanol, and n-propanol were bought from the Sinopharm Chemical Reagent Co., Ltd., China, which mass fraction purity was no less than 0.994 analyzed by using a gas chromatography {Smart (GC-2018)}. The details of the solvents and 3-methyl-6-nitroindazole were presented in Table 1. 2.2. Preparation of solvent mixtures The co-solvent + water mixtures were prepared through the analytical balance having a model of BSA224S. The amount of mixtures employed in each experiment was about 15 ml. The mass fraction compositions of the co-solvent varied from 0 to 1 in the initial solvent mixtures. The flask was covered by using a rubber stopper so as to prevent the solvent(s) from escaping. The local 10

atmospheric pressure was approximately 101.2 kPa in the course of the experiments. 2.3. Solubility measurement The solid-liquid equilibrium of 3-methyl-6-nitroindazole dissolved in the three co-solvent mixtures was constructed by using the saturation shake-flask method which has been widely used in the literatures [31,32]. The reliability of the apparatus was checked by using the benzoic acid solubility in toluene [32]. The HPLC (Agilent-1260) was used to determine the solubility of 3-methyl-6-nitroindazole in saturated liquid phase. An excessive amount of 3-methyl-6-nitroindazole was added into the 25 ml flask, which filled with approximately 15 ml of respective co-solvent + water mixtures. After mixed completely, it was placed to the thermostatic mechanical shaker, which provided by Tianjin Ounuo Instrument Co. Ltd., China and had a standard uncertainty of 0.02 K for temperature. The solutions were continually shaken with a shaking speed of 100 rpm. In order to obtain the equilibration time for the studied solid-liquid systems, approximately 0.5 mL of liquor was taken out by means of a 2 ml preheated syringe connected with a pore PTFE syringe filter (0.2 μm) at intervals of 1 hour and tested by using the HPLC. The results revealed that it took about 10 h to be equilibrium for all the systems. Then the solutions were kept static at the desired temperature to ensure that any un-dissolved solid precipitated from the solutions. The saturated liquid phase was withdrawn by means of the 2 mL of preheated or precooled syringe, and transferred quickly into a 25 mL volumetric flask. The extracted sample was diluted (if necessary) to 25 mL with neat methanol, and then analyzed by using the Agilent-1260 HPLC. 2.4. Analysis method The composition of 3-methyl-6-nitroindazole in saturated liquid phase was tested through the 11

Agilent-1260 HPLC, which included a reverse phase column (LP-C18, 250 mm × 4.6 mm). The column temperature was set to about 303 K during the analysis process. The wavelength of UV detector was 254 nm [33]. The mixture of acetonitrile and 0.1 % H3PO4 with a mass ratio of 5 to 95 was used as the mobile phase with a flow speed of 0.8 mlmin-1. Each sample was analyzed repeated triple times to check the repeatability and three samples were taken for each system at the desired temperature. The final solubility data were calculated through the average value. The relative standard uncertainty was assessed to be less than 5.43 % for mole fraction solubility. 2.5. X-ray powder diffraction So as to show the absence of polymorph transformation or solvate formation of 3-methyl-6-nitroindazole in experiments, the equilibrium solid phase was recognized by using the X-ray powder diffraction (XRD). The solid determinations were carried upon a HaoYuan DX-2700B (HaoYuan, China) apparatus through Cu Ka radiation with a wavelength of λ=1.54184 nm under ambient conditions. The tube voltage and tube current were set at 40 kV and 30 mA, respectively. The obtained data were gathered from 5° to 80° (2-Theta) at a scan speed of 6 deg·min−1.

3. Results and discussion 3.1. X-ray powder diffraction analysis The XRD patterns of raw material 3-methyl-6-nitroindazole as well as the equilibrium solid phase are given in Figure S1 of Supporting material. It is observed that the XRD patterns of equilibrated solids with equilibrium liquid phases have the characteristic peaks similar with the raw 3-methyl-6-nitroindazole and that in neat solvents [17]. As a result, no polymorph transformation as well as solvate formation takes place in all the determinations. 12

3.2. Solubility data The obtained mole fraction solubility of 3-methyl-6-nitroindazole in co-solvent solutions of (acetonitrile + water), (ethanol + water) and (n-propanol + water) is presented in Tables 2-4, respectively. The dependence of the solubility data upon the co-solvent compositions and temperature is graphically shown in Figure 2 as well. As revealed from Tables 2-4 and Figure 2 that, for the three mixtures studied, the 3-methyl-6-nitroindazole solubility in mole fraction scale is a function of temperature and co-solvent compositions. It increases with rising temperature and mass fraction of co-solvent. At the same co-solvent compositions and investigated temperature, the 3-methyl-6-nitroindazole solubility is larger in (acetonitrile + water) mixture than in (ethanol + water) and (n-propanol + water) mixtures. For comparison, the 3-methyl-6-nitroindazole solubility in neat acetonitrile, ethanol, n-propanol, and water attained by us as well as that reported in the previous publication [17] is graphically shown in Figure S2 of Supporting material. It may be observed that the mole fraction solubility of 3-methyl-6-nitroindazole determined in the present contribution is very close to that reported by Wang and co-workers [17]. The maximum relative average deviations (RAD) are, respectively, 16.08 % and 12.21 % for the solvent of water and ethanol at 278.15 K. At the other temperatures, the difference is relative slight. The small difference may be resulted from many factors, such as purity of equilibration time, raw material, sampling, determination method and so forth. 3.3. Solvent effect KAT-LSER model is applied to investigate solvent effect on the solubility. The properties of solvent mixtures including ,  and * are reported for (acetonitrile + water), (ethanol + water), (n-propanol + water), (DMF + water) and (acetone + water) mixtures in literatures [34-37]. As these 13

values are obtained from different works, a small discrepancy is expected for data in the neat solvents. As a result, the KAT parameters are considered for neat solvents in Ref. [38] as the reference points, and then correct them for aqueous co-solvent mixtures by the method used previously [35]. The corrected data are tabulated in Tables S1 and S2 of Supporting material. The

 values for binary mixtures are calculated by using the expression  [7] from the volume fractions, i, and Hi of neat solvents [39]. The evaluated  values for mixtures are also given in Tables S1 and S2. The molar volume of 3-methyl-6-nitroindazole is 123.2 cm3mol-1, taken from the Scifinder database [40]. The analysis of stepwise multiple linear regression is made so as to find the best form of KAT-LSER model to mathematically describe the 3-methyl-6-nitroindazole solubility. As well as Eq. (2), 14 expressions of KATA-LSER model are made from different exclusion and inclusion of the interaction terms on the right hand side of the Eq. (2). Then, the solubility data in (acetonitrile + water), (ethanol + water) and (n-propanol + water) mixtures determined in this work and in (DMF + water) and (acetone + water) mixtures taken from Ref. (17) is regressed by using these equations. The correlation results are presented in Tables S3-S7 of Supporting material. The selection of suitable model is made by considering the following statistical and physical criteria [35]. The solute-solvent interactions in both specific and non-specific types favor the solubility, while the cavity term plays a hampering role. Through imposing the constraints mentioned above, the models with negative ci=1-3 values as well as positive ci=4 values are rejected. Another criterion to consider is the coefficient c0 in KAT-LSER model. This solvent-independent constant, c0, terms the effect of crystal lattice properties of the solute on the solid solubility that in turn is generally denoted as the ideal solubility, xideal, which can be assessed by means of the Eq. 14

(19) [41].

ln xideal  

H m  Tm  T  Cp  Tm  T T   ln m     R  TmT  R  T T 

(19)

where Tm, Hm and Cp denote the melting temperature, melting enthalpy and the difference in heat capacity of solute between in its liquid and in its solid forms, respectively. The values of Hm, Cp and Tm for 3-methyl-6-nitroindazole are10.66 kJ.mol-1, 23.18 J.mol-1.K-1 and 460.15 K, respectively [17]. Therefore, an estimated value of -1.20 for lnxideal is obtained at 298.15 K. In this manner, c0 should be close to the value for an appropriate model to meet the criterion. After bearing in mind the above physical criteria, the KAT-LSER model is statistically judged as the most appropriate equation with the largest F-statistic and squared correlation coefficient, r2, and smallest standard deviations [26,27,35]. The best KAT-LSER model for the five mixtures are bolded in the Tables S3-S7. Analysis of results in Tables S3-S7 shows that the change in cavity term is determinant in the solubility variation of 3-methyl-6-nitroindazole in all studied mixtures. The single-parametric KAT-LSER based on cavity term is the best predictive model according to the criteria mentioned above. Cavity formation has a negative contribution to the solubility; meaning that the stronger the solvent-solvent interactions are in a mixture, the more work should be done on system to make cavity

for

solute

accommodation

and

thus

the

lower

solubility

is.

Although

3-methyl-6-nitroindazole is a polar and potent hydrogen-bonding acceptor solute, its solubility is very low in water because of the high cohesive energy of water molecules. As the mole fraction of organic solvent increases in aqueous mixtures, the solubility increases because the cavity formation energy decreases. The complexity of intermolecular interactions in these aqueous mixtures perhaps leads to the 15

difference in behaviour of the solvents in solvation shell of solute and the bulk on account of occurrence of preferential solvation. Therefore, a further analysis of preferential solvation is carried out to show how solvent affects the chemical properties in the aqueous co-solvent mixtures in the next section. 3.4. Preferential solvation of 3-methyl-6-nitroindazole According to the solubility data of 3-methyl-6-nitroindazole in (acetonitrile + water), (ethanol + water) and (n-propanol + water) mixtures determined in this work and in (DMF + water) and o (acetone + water) mixtures taken from Ref. (17), the calculated values of  tr G3,2 1 2 at 298.15 K

are presented in Table S8 of Supplementary material. In addition, they are plotted in Figure S3 of Supplementary material. The curve-fitting coefficients achieved by means of regression are tabulated in Table S9 of Supplementary material. Thus, the values of D can be computed from the first derivative of Eq. (17) solved based on the co-solvent compositions varying by 0.05 in mole fraction of acetonitrile, ethanol, n-propanol, DMF and acetone and are presented in Tables S10-S14 of Supplementary material. The values of RTκT and Q as well as the partial molar volumes of the co-solvent and water in the co-solvent mixtures of (acetonitrile + water), (ethanol + water), (n-propanol + water) and (DMF + water) at 298.15 K may be accessible from the publications [9-11]. For the (acetone + water) mixture, the dependence of κT upon the solvent compositions is approximated by the Eq. (15) with the help of the reported  To values for acetone (1.324 GPa–1) and water (0.457 GPa–1) at 298.15 K [42], taken as independent of the temperature [7-13]. The G1Exc values are calculated at 298.15 K through Eq. (20) for the acetone (1) + water (2) 2

mixture, as reported by Marcus [7]. 16

2   G1Exc  2  x1 (1  x1 )  4560  163(1  2 x1 )  1140(1  2 x1 ) 

(20)

In similar way, the partial molar volumes of acetone and water in mixtures can be evaluated from the densities of acetone (1) + water (2) mixture at 298.15 K under investigation by Estradabaltazar [43], by using Eqs. (21) and (22), where V is the molar volume of the solutions evaluated as V =(x1·M1 + x2·M2)/ρ. The molar mass M1 is 58.08 g·mol–1 for acetone and M2 is 18.02 g·mol–1 for water.

V1  V  x2

dV dx1

(21)

V2  V  x1

dV dx1

(22)

The values of G1,3 and G2,3 in the five aqueous mixtures are calculated through the Eqs. (9) and (10) and also presented in Tables S10-S14. Additionally, the partial molar volumes of 3-methyl-6-nitroindazole (3) in these solutions cannot be accessible from previous works, herein they are regarded as similar with that of neat 3-methyl-6-nitroindazole [7-13]. Therefore, the radius (r3) of the 3-methyl-6-nitroindazole may be calculated through Eq. (14) as 0.366 nm. The attained values through iteration of Vcor and δx1,3 are also presented in the Tables S10-S14 for the (acetonitrile + water), (ethanol + water), (n-propanol + water), (DMF + water) and acetone (1) + water (2) mixtures, respectively. Furthermore, the dependence of δx1,3 upon the co-solvent compositions is plotted in Figure 3. It reveals that the values of δx1,3 non-linearly vary with the co-solvent (1) proportions in all the mixtures studied. According to Figure 3, addition of the co-solvent (1) makes negative the δx1,3 values of 3-methyl-6-nitroindazole (3) from pure water up to x1 = 0.257 mole fraction of acetonitrile; x1 = 0.25 mole fraction of ethanol; and x1 = 0.20 mole fraction of n-propanol, DMF and acetone. In these regions, the local mole fractions of acetonitrile 17

(ethanol, n-propanol, DMF or acetone) (1) are lower than those of the solutions and consequently the δx1,3 values are negative, which indicates that 3-methyl-6-nitroindazole is preferentially solvated by

water.

The

structuring

of

water

molecules

around

the

nonpolar

groups

of

3-methyl-6-nitroindazole (i.e. hydrophobic hydration of methyl groups and aromatic ring) maybe contribute to lowering of the net δx1,3 values to negative in the acetonitrile (ethanol, n-propanol, DMF or acetone) mixtures. Minimum negative value is observed with the compositions x1 = 0.15 with δx1,3 = −10.28×10−2 for the acetonitrile (1) + water (2) mixture, x1 = 0.10 with δx1,3 = −2.146×10−2 for the ethanol (1) + water (2) mixture, x1 = 0.05 with δx1,3 = −1.728×10−2 for the n-propanol (1) + water (2) mixture, x1 = 0.05 with δx1,3 = −4.720×10−2 for the DMF (1) + water (2) mixture, and x1 = 0.15 with δx1,3 = −14.17×10−2 for the acetone (1) + water (2) mixture. 3-Methyl-6-nitroindazole could be mainly acting as a Lewis base in front to water because the water is more acidic than acetonitrile, ethanol, n-propanol, DMF and acetone as described by the Kamlet– Taft hydrogen bond donor parameters, i.e. α = 1.17 for water, α = 0.86 for ethanol, α = 0.19 for acetonitrile, α = 0.00 for DMF, α = 0.84 for n-propanol and α = 0.08 for acetone, respectively [42]. In the ethanol (1) + water (2) mixture with compositions 0.25 < x1 < 1, n-propanol (1) + water (2) and DMF (1) + water (2) mixtures with compositions 0.20 < x1 < 1, the local mole fractions of ethanol (n-propanol or DMF) are higher than that of the solutions and therefore the δx1,3 values show positive, indicating preferential solvation of 3-methyl-6-nitroindazole by the ethanol (n-propanol or DMF). The co-solvents action to improve the 3-methyl-6-nitroindazole solubility may be related to the breaking of the ordered structure of water round the polar moiety of 3-methyl-6-nitroindazole which rises the solvation having maximum values near to x1 = 0.65 with δx1,3 = 6.882×10−2 for the ethanol (1) + water (2), x1 = 0.50 with δx1,3 = 3.135×10−2 for the 18

n-propanol (1) + water (2) and x1 = 0.40 with δx1,3 = 2.212×10−2 for the DMF (1) + water (2) mixtures. It is conjecturable that in these regions 3-methyl-6-nitroindazole is mainly acting as Lewis acid with ethanol, n-propanol or DMF molecules because the co-solvents are more basic than water as described by the respective Kamlet-Taft hydrogen bond acceptor parameters, as follows: β = 0.75 for ethanol, β = 0.69 for DMF, β = 0.86 for n-propanol and β = 0.47 for water [42]. In the case of acetonitrile (1) + water (2) and acetone (1) + water (2) mixtures, the exhibited behaviour in the intermediate and co-solvent-rich mixtures is erratic because even negative δx1,3 values can be found within the regions 0.56 < x1 < 0.83 for the acetonitrile (1) + water (2) mixture and 0.20 < x1 < 0.44 for the acetone (1) + water (2) mixture, This case is perhaps due to negative Q values in the mixtures as a consequence of the highly positive excess Gibbs energy of mixing. Similar behaviours may also be observed for other substances in different aqueous mixtures also exhibiting high positive excess Gibbs energies of mixing [44,45]. Nevertheless, as a qualitative result for the acetonitrile (1) + water (2) in the region 0.257 < x1 < 1 and acetone (1) + water (2) mixture in the region 0.20 < x1 < 1, the positive values of δx1,3 could be attributed to polarization effects because water is more acidic and basic than acetonitrile and acetone. Thus the preferential solvation of 3-methyl-6-nitroindazole by acetonitrile and acetone molecules could not be resulted from specific Lewis-acid base interactions [10,44,45]. 3.5. Solubility modelling Based on the solubility data determined in this contribution, the parameters of the Jouyban−Acree model are regressed by using the Mathcad software and tabulated in Table S15 of the Supporting material along with the RAD and RMSD values. The back-evaluated 3-methyl-6-nitroindazole solubility in the solutions of (ethanol + water), (n-propanol+ water) and 19

(acetonitrile + water) is graphically shown in Figure 2. It is shown from the Table S15 that for the co-solvent mixtures studied the values of relative average deviations (RAD) are 3.12 % for ethanol + water mixture, 2.84 % for n-propanol + water and 4.50 % for acetonitrile + water mixtures. Additionally, the maximum RMSD value is 3.36ⅹ10-4, which is got for the (acetonitrile + water) mixture. On the whole, the Jouyban-Acree model presents satisfied correlation results for the three mixtures.

4. Conclusion The solubility of 3-methyl-6-nitroindazole in three co-solvent mixtures of ethanol (1) + water (2), n-propanol (1) + water (2) and acetonitrile (1) + water (2) at temperatures from 278.15 to 328.15 K was reported. At a same co-solvent composition of ethanol, n-propanol or acetonitrile and temperature, the maximum value of the mole fraction solubility of 3-methyl-6-nitroindazole is in acetonitrile (1) + water (2) mixture. The 3-methyl-6-nitroindazole solubility was well correlated through the Jouyban-Acree model obtaining RAD lower than 4.50 % and RMSD lower than 3.3610-4. The analysis of solvent effect by KAT-LSER model revealed that the decrease in the cavity formation energy when the mole fraction of organic solvent increased in the mixture mainly led to the enhancement of solubility in all studied aqueous mixtures. Quantitative values for the local mole fraction of acetonitrile (ethanol, n-propanol, DMF or acetone) and water around the 3-methyl-6-nitroindazole were computed via the IKBI method applied to the solubility data. 3-methyl-6-nitroindazole was preferentially solvated by the co-solvent for the ethanol (1) + water (2), n-propanol (1) + water (2), acetonitrile (1) + water (2), DMF (1) + water (2) and acetone (1) + water (2) mixtures in intermediate and co-solvent-rich compositions.

20

Acknowledgments The authors express sincere thanks to National Natural Science Foundation of China (Project number: 41877118), Natural Science Foundation of Jiangsu Province Higher Education (Grant No.11KJD480002), Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Project number: 17KJB610013), Natural Science Foundation of Jiangsu Province of China (Project number: BK20181479) and Jiangsu Province Education Department Major Project (19KJA140003) for their financial support.

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25

Figure 1. The chemical structure of 3-methyl-6-nitroindazole.

26

300 ( a)

250

200

4

100

100 50

50 330

( b)

150

150

10 x

4

10 x

200

320

310

300

T/K

290

0.2 280

0.4

1.0 0.8 0.6

330 320 310

T/K

w

0.0

300

0.4 290

0.2 280

0.6

1.0 0.8

w

0.0

200

(c)

4

10 x

150

100 50

330 320 310

T/K 300 290

0.2 280

0.4

0.6

1.0 0.8

w

0.0

Figure 2. Mole fraction solubility (x) of 3‑methyl-6-nitroindazole in (a) acetonitrile (w) + water (1-w), (b) ethanol (w) + water (1-w) and (c) n-propanol (w) + water (1-w) mixed solutions with various mass fractions at different temperatures: w, mass fraction; ■, w = 0; ●, w = 0.1000; ▲, w = 0.2000; ◆, w = 0.3000; ▼, w = 0.4000; ★, w = 0.5000; △, w = 0.6000; ○, w = 0.7000; ☆, w = 0.8000; ◀, w = 0.9000; □，w = 1. —, calculated curves by the Jouyban−Acree model.

27

 x1,3

20

10

0

-10 0.0

0.2

0.4

x1

0.6

0.8

1.0

Figure 3. δx1,3 values of 3-methyl-6-nitroindazole (3) in acetonitrile (1) + water (2), ethanol (1) + water (2), n-propanol (1) + water (2), DMF (1) + water (2) and acetone (1) + water (2) mixtures at 298.15 K. ■, acetonitrile (1) + water (2); ●, ethanol (1) + water (2); ▲, n-propanol (1) + water (2); ▼, DMF (1) + water (2); ◆, acetone (1) + water (2).

28

Table 1 Detailed information on the materials used in the present work. Chemicals

Molar mass/ g·mol−1

3-methyl-6-nitroindazole

177.16

Acetonitrile

41.05

Source

Initial mass fraction purity

Final mass fraction purity

Purification method

Analytical method

0.986

0.995

Recrystallization

HPLCa

0.996

0.996

none

GCb

0.995

0.995

none

GC

0.994

0.994

none

GC

Sigma Chemical Co., Ltd., China

Sinopharm ethanol

46.06

Chemical Reagent Co., Ltd., China

n-propanol

60.10

water

18.01

Conductivity a

Our lab

< 2 µS·cm-1

High-performance liquid phase chromatography;

b Gas

chromatography.

29

Distillation

Conductivity meter

Table 2 e Experimental mole fraction solubility ( xT,W 104 ) of 3-methyl-6-nitroindazole in mixed solvent of acetonitrile (w) +

water (1-w) with various mass fractions within the temperature range from T/K = (278.15 to 328.15) under p=101.2 kPa.a e xT,W 104

W T/K 0

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1

278.15

0.2058

0.3947

0.7885

1.578

3.246

6.356

12.01

21.83

37.84

61.32

85.61

283.15

0.2702

0.4948

0.9443

1.967

3.786

7.935

14.83

26.31

45.92

72.44

98.82

288.15

0.3521

0.6443

1.226

2.434

4.597

9.849

17.64

32.24

54.41

83.93

112.6

293.15

0.4672

0.8256

1.567

2.925

5.525

12.13

21.95

39.52

65.83

96.81

129.9

298.15

0.6148

1.059

1.953

3.551

6.943

14.72

26.22

46.44

75.93

110.9

147.5

303.15

0.7912

1.328

2.448

4.412

8.562

17.74

32.83

58.43

90.54

126.2

166.5

308.15

0.9981

1.683

3.062

5.421

10.62

21.42

40.31

68.01

102.9

144.4

186.5

313.15

1.227

2.101

3.756

6.789

13.11

25.83

48.02

79.62

119.1

162.2

207.2

318.15

1.512

2.592

4.634

8.579

16.03

31.01

56.04

93.11

135.6

181.7

228.5

323.15

1.824

3.204

5.672

10.71

19.74

36.92

65.65

107.1

154.3

203.1

251.8

328.15

2.221

3.874

7.245

13.62

24.72

44.44

77.52

120.7

171.3

221.9

277.4

a Standard

uncertainties u are u(T) = 0.02 K, u(p) = 0.45 kPa; Relative standard uncertainty ur is ur (x) = 0.0543.

Solvent mixtures were prepared by mixing different masses of the solvents with relative standard uncertainty ur(w) = 0.0002. w represents the mass fraction of acetonitrile in mixed solvents of acetonitrile (w) + water (1-w).

30

Table 3 e Experimental mole fraction solubility ( xT,W 104 ) of 3-methyl-6-nitroindazole in mixed solvents of ethanol (w) +

water (1-w) with various mass fractions within the temperature range from T/K = (278.15 to 328.15) under p=101.2 kPa.a e 104 xT,W

W T/K

a

0

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1

278.15

0.2058

0.3754

0.6538

1.123

1.977

3.396

5.979

9.777

16.39

28.15

47.13

283.15

0.2702

0.4790

0.8361

1.440

2.480

4.078

7.354

11.30

18.78

32.38

53.95

288.15

0.3521

0.6113

1.037

1.838

3.078

4.898

8.617

13.26

22.17

38.52

61.89

293.15

0.4672

0.7856

1.302

2.236

3.767

5.881

10.06

15.72

26.23

45.29

72.95

298.15

0.6148

1.003

1.594

2.672

4.453

6.988

11.65

18.58

30.68

51.80

86.60

303.15

0.7912

1.194

2.002

3.194

5.352

8.463

13.72

21.80

35.55

60.16

102.3

308.15

0.9981

1.588

2.586

4.124

6.717

10.31

16.36

25.95

41.65

70.86

117.8

313.15

1.227

2.012

3.121

5.119

8.164

12.58

19.78

30.68

49.27

84.02

137.1

318.15

1.512

2.446

3.794

6.178

9.65

15.33

24.04

37.07

59.46

99.39

159.6

323.15

1.824

2.952

4.741

7.509

11.81

18.95

29.76

46.02

72.93

117.7

189.5

328.15

2.221

3.563

5.722

9.063

14.56

22.89

36.77

57.03

90.95

142.1

220.3

Standard uncertainties u are u(T) = 0.02 K, u(p) = 0.45 kPa; Relative standard uncertainty ur is ur (x) = 0.0543.

Solvent mixtures were prepared by mixing different masses of the solvents with relative standard uncertainty ur(w) = 0.0002. w represents the mass fraction of ethanol in mixed solvents of ethanol (w) + water (1-w).

31

Table 4 e Experimental mole fraction solubility ( xT,W 104 ) of 3-methyl-6-nitroindazole in mixed solvents of n-propanol (w)

+ water (1-w) with various mass fractions within the temperature range from T/K = (278.15 to 328.15) under p=101.2 kPa.a e 104 xT,W

W T/K

a

0

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1

278.15

0.2058

0.3714

0.7011

1.271

2.407

4.227

7.102

11.91

20.42

33.44

51.01

283.15

0.2702

0.4868

0.9001

1.585

2.859

5.033

8.231

13.83

23.74

38.83

57.42

288.15

0.3521

0.6340

1.116

2.014

3.459

5.942

9.717

16.34

28.02

44.61

68.24

293.15

0.4672

0.8158

1.436

2.467

4.134

7.279

11.71

19.52

31.82

51.63

79.32

298.15

0.6148

1.050

1.759

3.022

5.064

8.623

14.13

22.71

37.11

59.02

90.11

303.15

0.7912

1.318

2.155

3.701

6.053

10.12

16.42

26.30

43.03

69.73

103.3

308.15

0.9981

1.604

2.623

4.506

7.282

11.91

18.94

30.70

49.44

79.55

117.6

313.15

1.227

1.989

3.253

5.452

8.699

14.04

22.02

34.53

55.72

89.31

133.2

318.15

1.512

2.407

3.936

6.465

10.31

16.51

25.41

39.44

62.93

100.8

149.1

323.15

1.824

3.003

4.788

7.880

12.42

19.52

29.64

45.82

72.51

112.9

169.9

328.15

2.221

3.611

5.906

9.407

15.11

22.83

34.82

53.51

83.62

128.7

194.3

Standard uncertainties u are u(T) = 0.02 K, u(p) = 0.45 kPa; Relative standard uncertainty ur is ur (x) = 0.0543.

Solvent mixtures were prepared by mixing different masses of the solvents with relative standard uncertainty ur(w) = 0.0002. w represents the mass fraction of n-propanol in mixed solvents of n-propanol (w) + water (1-w).

32

Author statement

Wanxin Li: Methodology, Writing-Original Draft. Ali Farajtabar: Formal analysis, Data Curation. Rong Xing: Investigation. Yiting Zhu, Data Curation ， Resources. Hongkun Zhao: Conceptualization, Supervision. Rongguan Lv: Project administration.

33

The authors declared that they have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that repres ents a conflict of interest in connection with the work submitted.

34

Graphic abstract

20

200

100

 x1,3

4

10 x

150

ethanol (w) + water (1-w)

50

330 320 310

T/K

300

0.4 290

0.2 280

0.6

1.0 0.8

acetonitrile (1) + water (2) ethanol (1) + water (2) n-propanol (1) + water (2) acetone (1) + water (2) DMF (1) + water (2)

10

0

-10

w 0.0

0.0

35

0.2

0.4

x1

0.6

0.8

1.0

Highlights ► 3-Methyl-6-nitroindazole solubility in three aqueous co-solvent mixtures of alcohols was determined and correlated. ► Preferential solvation of 3-methyl-6-nitroindazole in five mixtures were derived via IKBIs method. ► Solvent effect was studied in terms of solute-solvent and solvent-solvent interactions.

36