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Thermodynamic study of solubility for pyrazinamide in ten solvents from T = (283.15 to 323.15) K
Accepted Manuscript Thermodynamic study of solubility for pyrazinamide in ten solvents from T = (283.15 to 323.15) K Keke Zhang, Huan Shen, Shijie Xu, Huihui Zhang, Minghe Zhu, Peng Shi, Xiaoyan Fu, Yaoyao Yang, Junbo Gong PII: DOI: Reference:
S0021-9614(17)30126-X http://dx.doi.org/10.1016/j.jct.2017.04.014 YJCHT 5048
To appear in:
J. Chem. Thermodynamics
Received Date: Revised Date: Accepted Date:
9 January 2017 5 April 2017 23 April 2017
Please cite this article as: K. Zhang, H. Shen, S. Xu, H. Zhang, M. Zhu, P. Shi, X. Fu, Y. Yang, J. Gong, Thermodynamic study of solubility for pyrazinamide in ten solvents from T = (283.15 to 323.15) K, J. Chem. Thermodynamics (2017), doi: http://dx.doi.org/10.1016/j.jct.2017.04.014
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Thermodynamic study of solubility for pyrazinamide in ten solvents from T = (283.15 to 323.15) K Keke Zhanga,b, Huan Shen a,b, Shijie Xu a,b, Huihui Zhang a,b, Minghe Zhu a,b, Peng Shi a,b, Xiaoyan Fu a,b, Yaoyao Yang a,b, Junbo Gong a,b,* a
School of Chemical Engineering and Technology, State Key Laboratory of Chemical
Engineering, Tianjin University, Tianjin 300072, People’s Republic of China. b
The Co-Innovation Center of Chemistry and Chemical Engineering of Tianjin,
Tianjin University, Tianjin 300072, People’s Republic of China. ABSTRACT: The solubility of pyrazinamide in ten solvents (water, methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, 2-butanol, acetone, acetonitrile and ethyl acetate) at temperatures ranging from (278.15 to 323.15) K was determined by using the gravimetric method. The experimental results indicated that in different solvents, the solubility of pyrazinamide was temperature dependent and increased with the increasing temperature. Besides, the modified Apelblat equation, λh equation, Wilson model and NRTL model were employed to correlate the solubility data in the solvents. The results show that the correlated data are in good agreement with the experimental solubility. Furthermore, the mixing thermodynamic properties of pyrazinamide in different solvents were calculated based on the Wilson model. The outcome indicates that the mixing process of pyrazinamide is endothermic. Keywords: pyrazinamide; solubility; thermodynamic model
1. Introduction Pyrazinamide (pyrazine-2-carboxamide, abbreviated as PZA, C5H5N3O) is one of the first-line drugs against Mycobacterium tuberculosis [1]. Tuberculosis (TB) results in cough, fever, sweats, fatigue and weight loss, which, if remained untreated, eventually deteriorates to death. Despite the widespread use of a vaccine, more than eight million people are infected with TB each year, of which 1.8 million will die [2].
Tuberculosis treatment is through a course of antibiotics for periods up to 26 weeks. Pyrazinamide allows the treatment shortening from (9 to 12) months to 6 months on account of its activity against the persisting tubercle bacilli at an acidic pH [3]. World Health Organization guidelines recommended the administration of PZA in association with two other drugs (rifampicin and isoniazid), in order to reduce bacterial growth during the initial phase of tuberculosis treatment [1]. Pyrazinamide is categorized as a class II agent and its dissolution is the rate-limiting step for its absorption. The low aqueous solubility and bioavailability have impeded the efficient therapeutic use of BCS Class II drugs [4]. Due to the crucial role of pyrazinamide in the pharmaceutical industry, it is necessary to find a proper way to enhance its solubility. Various formulation strategies such as the synthesis of co-crystals, complexation with cyclodextrin, amorphous solid dispersions, lipid-based formulations, and particle size reduction can be applied to solve this problem [5]. As pyrazinamide has strong hydrogen bonding properties and ability to act as ligands in various complexes, the synthesis of co-crystals is apparently a good choice [6，7]. For the preparation of co-crystals, the solubility performance of drugs is significant in the method of solution crystallization [8] (slow evaporation from solution and reaction crystallization [9]). Appropriate solubility of the two different solutes in the solvent can promote the production of co-crystals. Also in the preparation of co-crystals, the choice of solvents and the initial concentration of solution can determine the particle size distribution and crystalline morphology of co-crystals. Besides, as fundamental data, the solubility data of pyrazinamide reflect the interactions between solvent and solute. Moreover, based on the solubility, one can design different degree of supersaturation, initial temperature and initial concentration to investigate the nucleation and growth behaviour of pyrazinamide in different solvents. The solubility studies of pyrazinamide can also provide data support for synthesizing and investigating pyrazinamide’s derivatives [10, 11]. In conclusion, it is necessary to implement the solubility studies of pyrazinamide. However, to the best of the authors’ present knowledge, values of solubility of pyrazinamide in various solvents at different temperatures are very scarce in previous publications [12].
Thus, the solubility of pyrazinamide in ten solvents (water, methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, 2-butanol, acetone, acetonitrile and ethyl acetate) at temperatures ranging from (278.15 to 323.15) K was determined by employing gravimetric method. The experiment solubility data was correlated by the Apelblat equation, λh equation, Wilson model and NRTL model. As we all know, the enthalpy of mixing and heat of crystallization, which play an important part in influencing the crystallization system, are not ignorable in the industrial scale-up process. Thus, the thermodynamic properties of mixing process for the solutions ought to be calculated precisely. Meanwhile, our work provided the thermodynamic basis (material balance and heat balance) for further research. 2. Experimental 2.1. Materials Pyrazinamide (0.99 mass fraction purity) was obtained from Shanghai Baoman Biological technology Co., Ltd. All the organic solvents (methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, 2-butanol, acetone, acetonitrile and ethyl acetate) purchased from Tianjin Jiangtian Chemical Reagent Co. (Tianjin, China) were of analytical grade. All the materials were used without further disposal. Distilled-deionized water (conductivity < 0.5 µS∙cm-1) was prepared in our laboratory. The detailed information is given in Table 1. 2.2. X-ray powder diffraction In this work, the X-ray powder diffraction (XRPD) was applied to monitor the crystal form of pyrazinamide during the process. The XPRD was carried out using the D/MAX-2500 (Rigaku, Japan) by Cu Kα radiation (0.15405 nm) over a diffraction angle (2θ) range of 2° to 50° with a scanning rate of 8°·min-1. Raw pyrazinamide and excess solid state pyrazinamide in different solvents were analysed by XRPD and the patterns are shown in Figure 2. 2.3. Solubility determination The solubility of pyrazinamide in pure water, methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, 2-butanol, acetone, acetonitrile, and ethyl acetate was analysed across the temperature range of (278.15 to 318.15) K under atmospheric pressure by
using a solid-liquid equilibrium method. In the experiment, all measurements of mass were performed on an analytic balance (AB204-N, Mettler-Toledo, Switzerland) with uncertainty of ±0.0001 g. In this method, excess amount of pyrazinamide were added into a 50 mL capped glass vial containing 25 mL preheated/cooled solvent. Then, the (solid + liquid) mixture were put into a thermostat shaker (type 501A, Shanghai Laboratory Instrument Works Co., Ltd., China, with the precision of T = ±0.1 K) at 150 rpm for about 12 h to reach the (solid - liquid) equilibrium. The pre-experiments indicated that 12 h was enough to ensure saturation. After stopping the shaker, all the samples were standing for 2 h to make the un-dissolved substances deposit. Followed 5 mL saturated solution was extracted by a preheated/cooled syringe filter (0.45 µm) and transferred into a pre-weighed beaker. Then the total weight was measured immediately by the balance. Subsequently the weighed beaker was placed into a vacuum oven (type DZ-1BCII, Yichuan Appearance of Bearing Co., Ltd, China) at T= 323.15 K until the weight of sample remained constant . Each experiment was repeated three times under the same conditions and the mean value was used as the final result to calculate the solubility. The experimental mole fraction solubility of pyrazinamide in each solvent was calculated by equation (1) as follows: ⁄ (1) = ⁄ + ⁄
where the m1 represents the mass of pyrazinamide in saturated solution; m2 represents the mass of solvent(water, methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, 2-butanol, acetone, acetonitrile or ethyl acetate); and M1 and M2 are the molar masses of pyrazinamide and solvent, respectively. 3. Thermodynamic models In this work, the modified Apelblat equation [13，14], λh equation [15], Wilson model [16] and NRTL model [17] were applied to correlate the solubility of pyrazinamide in different solvents, respectively. 3. 1. Modified Apelblat equation The modified Apelblat equation is a semi-empirical equation, which has been successfully used to link experimental and theoretical solubility results of different
drugs/pharmaceuticals. In this work, the dependence of the mole fraction solubility of pyrazinamide on the absolute temperature T is correlated by the modified Apelblat equation (equation (2)) [13，14]:
ln = + ⁄⁄K + ln⁄K
(2)
where x is the mole fraction solubility of pyrazinamide, T is the absolute experimental temperature (K), A, B, and C are adjustable parameters. The A and B indicate the effect of solution on the solubility, while C represents the effect of temperature on the fusion enthalpy. 3. 2. λh equation The Buchowski–Ksiazaczak λh equation suggested by Buchowski is also a semi-empirical equation. This equation has two empirical parameters and has been widely applied to describe the solubility of solute in pure solvents. The expression of λh equation is described as equation (3) [15]:
ln 1 +
1 − 1 1 = ℎ − ⁄K ⁄K
(3)
where T m is the melting point; λ and h are two empirical equation parameters. The value of λ correlates to the association number of solute molecules in the associating system, and h value relates to the excess enthalpy of solution. 3. 3. Wilson model In the solid-liquid phase equilibrium, Wilson equation is widely used to describe the solubility of a solute in solvents at different temperatures. The model can be expressed as equation (4) [16]: ln x1 =
∆ fus H 1 1 − R Tm T
∆C p − R
Tm Tm − + 1 -ln γ 1 ln T T
(4)
where, ∆fusH is the molar enthalpy of fusion of the pure solute (at the melting point), Tm is the absolute melting point, T is the absolute solution temperature, R is the gas constant (8.314 J·K-1·mol-1), and ∆Cp is the difference between the molar heat capacity of the crystalline form and the molar heat capacity of the hypothetical super cooled liquid form, both at the solution temperature [18]. Since ∆Cp cannot be easily determined experimentally, therefore, two approaches are always employed to
identify a reasonable range of values for ∆Cp [19]. In this study, we assume that ∆Cp is approximated by the entropy of fusion, ∆fusS [20]. Considering that, equation (4) can be expressed as: ln x1 =
∆ fus H 1 1 ∆ fus S − − R Tm T R
Tm Tm − + 1 -lnγ 1 ln T T
(5)
Therefore, on the basis of equation (5) the activity coefficient must be known to deduce the solubility of solute. In the pure solvent system, the activity coefficient can be expressed by the following Wilson mode
ln = −ln + Λ +
Λ Λ − + Λ + Λ
(6)
where x2 is the mole fraction of solvent; Λ12, Λ21 are the model parameters.
− Δ !− # = !− # " " − Δ = !− # = !− # " "
Λ = Λ
(7) (8)
where V1 is the mole volume of the solute, and V2, the solvent. ∆λ12 and ∆λ21 are model parameters (J·mol-1) indicating interaction energy between the solute and the solvent. The values of two model parameters can be deduced by relevant experimental solubility. 3. 4. NRTL model Based on molecular local composition concept, the NRTL (Non Random Two Liquid) model is first proposed by Renon and is widely applied in describing fluid phase equilibrium. The activity coefficient represented by NRTL model is expressed as equations (8)-(11) [17]. )
∑) ' +'% ∑) '( *'% +'% ' %( % *%' +%' ln % = + , * − %' ) ) ∑%( +'% % ∑%( +'% % ∑) %( +%' % +%' = exp0−1%' *%' 2 1%' = 1'% = 1 *%' =
'(
03%' − 3'' 2 Δ3%' = " "
(9) (10) (11) (12)
where ∆gij is the model parameters relevant to the interaction energy; α is an adjustable parameter ranging from 0.20 to 0.47 , which reveals the non-randomness of
the solution. 4. Results and discussion 4.1. Characterization and identification of pyrazinamide Raw pyrazinamide and excess pyrazinamide in different solvents were analyzed by XRPD in this work. The patterns proved that the forms of both the raw material and residual solids were stable form α [21]. According to Figure 2, the results show that the crystal forms of material and excess solids from ten solutions are consistent with crystalline pyrazinamide of form α reported by literature. Therefore, it can be concluded that there is no crystal transformation in the solubility measurements. 4.2. Solubility results The measured solubility in mole fraction of pyrazinamide in water, methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, 2-butanol, acetone, acetonitrile and ethyl acetate at the temperatures ranging from (278.15 to 323.15) K is presented in Table 2 and shown graphically in Figure 3. The results indicate that the solubility of pyrazinamide in ten solvents increased with the increasing of temperature. However, the increasing extent of solubility varies in different pure solvents. At same temperature, the mole fraction solubility is highest in acetone, and lowest in 2-butanol. In general, the solubility of pyrazinamide in different solvents decreases according to the following order: acetone > methanol > ethyl acetate > acetonitrile > ethanol > 1-butanol > 1-propanol > 2-propanol > 2-butanol. For the solvents methanol, ethanol, 1-butanol and 2-propanol, the sequence of the pyrazinamide solubility values from high to low is in keeping with the changing trend of polarity of the four solvents [22]. While this case is not found for the solvents 1-propanol and
2-butanol. In general, it is rather hard to explain the phenomenon shown in Figure 3 only on the basis of a single factor. In fact, the solubility is determined by the mutual competition of the interaction between the solute-solvent and solvent-solvent. Figure1 shows that the pyrazinamide molecule contains both hydrogen donor and hydrogen acceptor groups, then between the solute and solvents molecules the hydrogen bond can be formed [23]. Thus in this system, both the van de Waals interaction (represented by polarity) and hydrogen bonding (represented by hydrogen bond donor/acceptor propensity) contribute to the solute–solvent interaction. Besides, the degree of solvent–solvent association could be represented by the cohesive energy density [22]. Though 1-propanol’s polarity in these alcohols is lowest, its hydrogen bond donor and acceptor propensity are identical to 1-butanol. Therefore pyrazinamide have similar solubility values in 1-propanol and 1-butanol. For 2-butanol, possessing greater steric hindrance because of the branched chains, which makes it harder to form hydrogen bonds with the solute and this results in lower solubility in alcohols. The order of solubility in acetone, ethyl acetate and acetonitrile is not strictly in accordance with the polarity order, while it is similar with the sequences of the hydrogen bond acceptor propensity as shown in Table 3. In addition, though water’s polarity and capacity to form the hydrogen bond with the solute are the highest, the cohesive energy density of water is extremely higher than any other selected solvents [22], the solubility is not the highest. 4.3. Solubility correlation and calculation To evaluate the applicability and accuracy of the four models used in this work, the
average relative deviation (ARD) and the root-mean-square deviation (RMSD) are defined as follows [24]: )
1 % − %;<= ARD = , 8 8 9: 7 % 9:
%(
RMSD = @
(13)
9: ∑) − %;<= 2 %(0 %
7
(14)
where xiexp and xical are the experimental and calculated solubility values, respectively; N refers to the numbers of experimental points. During the regression process, the melting temperature (Tm) and melting enthalpy (∆fusH) of pyrazinamide are taken from the reference [25]. The regressed values of the parameters in Apelblat equation, λh equation, Wilson model and NRTL model are listed in Tables 4-7, respectively. The obtained ARD and RMSD values for all models are also shown in Tables 4-7. As the results shown, the ARD values obtained from the Apelblat equation are smaller than those associated with the other three models. The largest value of RMSD is 5.040 × 10 -4, which is calculated by the NRTL equation for the system (pyrazinamide + methanol). The ARD values are no greater than 8.82%. Generally speaking, the calculated solubility with the four models suits well with the experimental values. The ARD values and RMSD values obtained with the modified Apelblat equation are no greater than 3.72% and 1.271×10 -4 respectively, which show that the modified Apelblat equation provides more accurate results for the same solvent. 4.4. Mixing properties of solution
Thermodynamic property of a solute dissolved in solvent may provide essential information for the dissolution procedure. The mixing properties of solution can be obtained according to the Lewis-Randall rule. For the ideal solution, the mixing Gibbs energy, mixing enthalpy, and mixing entropy in pure solvent can be calculated by the following equations [26]:
∆CD + CE = " ln + ln
∆CD F CE = −" ln + ln ∆CD GCE = 0
(15) (16) (17)
where x1 refers to the mole fraction of solute; and x2, the corresponding solvent. For the non-ideal solution, the three mixing properties can be calculated using the following equations:
∆CD + = + I + ∆CD + CE ∆CD F = F I + ∆CD F CE
∆CD G = GJ +∆CD GCE
(18) (19) (20)
Here GE, S E and HE represent for the excess properties. According to the Wilson model, the excess properties are expressed as the following equations [27]:
+ I = " ln + ln
= −"0ln + Λ + ln + Λ 2
(21)
∆ Λ ∆ Λ = ! + # + Λ + Λ GI − + I FI =
(22)
L+ I ⁄ GI = − K M L
(23)
On the basis of the regressed parameters in Wilson model and the experimental solubility values, the Δ mixG and ΔmixH are obtained and presented in Table 8. The values of mixing Gibbs energy (Δ mixG) can be applied to elaborate the dissolution capacity of a solute. The connection between mixing Gibbs energy (Δ mixG) and temperature is shown in Figure 4. The results in Table 8 illustrates that the values of ΔmixG are all negative and decrease with increasing temperature, therefore, the mixing process of pyrazinamide is spontaneous and favourable in the solvents selected. Table 8 demonstrates that the Δ mixH values of pyrazinamide are all positive. We also calculated the relative standard uncertainties of the mixing enthalpy, and found that the relative standard uncertainties of the mixing enthalpy in 1-butanol and 2-butanol are respectively 1.165 and 7.450 (the maximum value). It means the Wilson model is not applicable in calculating the mixing enthalpy of pyrazinamide in 1-butanol and 2-butanol. That is also the reason that the trends of mixing enthalpies are not consistent with the trends of solubility data in some solvents. The net variation in ∆mixH values results from the contributions of several kinds of intermolecular interactions [28, 29]. The enthalpy of cavity formation (needed for solute accommodating) is endothermic in order to overcome the cohesive forces of the solvent. In addition, the interaction enthalpy between solute and solvent, which is depended predominantly upon interactions of van der Waals and hydrogen bonding, is exothermic. The positive mixing enthalpy for pyrazinamide demonstrates that the intermolecular interactions of cross associating formed between pyrazinamide and the selected solvents are weaker than the self-associating interactions. In this context, the
mixing process is slightly endothermic and the values of HE increase with an increase in temperature. 5. Conclusions In this study, the mole fraction solubility of pyrazinamide in water, methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, 2-butanol, acetone, acetonitrile and ethyl acetate was determined by a gravimetric method over the temperature range of (278.15 to 323.15) K. For all the selected solvents, the solubility of pyrazinamide increased with the increase in temperature. The experimental solubility results in ten solvents were well correlated based on the modified Apelblat equation, λh equation, Wilson model and NRTL model. The relative average deviations obtained by the four models are all less than 8.82%, and the root-mean-square deviations, less than 5.040 × 10-4. The Wilson model was used to calculate the mixing Gibbs energy, the mixing enthalpy and mixing entropy. The results indicated that the mixing process of pyrazinamide was endothermic in the solvents selected. On the basis of the experimental solubility and thermodynamic results of pyrazinamide, it can be helpful in the aspects of the preparation of co-crystals and the synthesis and investigation of pyrazinamide’s derivatives.
AUTHOR INFORMATION Notes The authors declare no competing financial interest. Acknowledgment We are grateful to the financial support of National Natural Science Foundation of China (NNSFC 81361140344 and NNSFC 21376164), National 863 Program (2015AA021002), Major Science and Technology Program for Water Pollution Control and Treatment (NO.2015ZX07202-013) and Tianjin Science and Technology Project (15YFJZC00800). Corresponding Author *Tel.: 86-22-27405754. Fax: +86-22-27374971. E-mail: [email protected]
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Table captions: Table 1. Sources and mass fraction purity of materials used in the experiments. Table 2. Experimental and calculated mole fraction solubility (x) of Pyrazinamide in different solvents at the temperature range from T = (278.15–323.15) K under 100 kPa. Table 3. Physical properties for the selected solvents. Table 4. Parameters of the modified Apelblat equation for pyrazinamide in different solvent. Table 5. Parameters of the λh equation for pyrazinamide in different solvents. Table 6. Parameters of the NRTL equation for pyrazinamide in different solvents. Table 7. Parameters of the Wilson equation for pyrazinamide in different solvents. Table 8. The mixing thermodynamic properties of pyrazinamide in different mono-solvents (p = 0.1 MPa).
Figure captions: Figure 1. Molecular structure of pyrazinamide. Figure 2. Powder X-ray diffraction (PXRD) patterns of excess solid from ten solvents. ( (a) raw material; (b) water; (c) methanol; (d) ethanol; (e) 1-propanol; (f) 2-propanol; (g) 1-butanol; (h) 2-butanol; (i) acetone; (j) acetonitrile; (k) ethyl acetate ) Figure 3. The solubility of pyrazinamide in ten pure solvents. Figure 4. Calculated mixing Gibbs energy at measured solubility points.
Figures
Figure 1. Molecular structure of pyrazinamide.
Figure 2. Powder X-ray diffraction (PXRD) patterns of excess solid from ten solvents. ( (a) raw material; (b) water; (c) methanol; (d) ethanol; (e) 1-propanol; (f) 2-propanol; (g) 1-butanol; (h) 2-butanol; (i) acetone; (j) acetonitrile; (k) ethyl acetate )
Figure 3. The solubility of pyrazinamide in ten pure solvents.
Figure 4. Calculated mixing Gibbs energy at measured solubility points.
Tables Table 1. Sources and mass fraction purity of materials used in the experiments. Mass Fraction Analysis Chemical Molar mass/(g·mol-1) Purity Method Pyrazinamide
123.11
≥0.990
HPLCa
Methanol
32.04
≥0.995
GCb
Ethanol
46.07
≥0.995
GCb
1-Propanol
60.06
≥0.995
GCb
60.06
≥0.995
GCb
1-Butanol
74.12
≥0.995
GCb
2-Butanolc
74.12
≥0.995
GCb
Acetone
58.08
≥0.995
GCb
Acetonitrile
41.05
≥0.995
GCb
Ethyl acetate
88.11
≥0.995
GCb
2-Propanol
Both the analysis method and the mass fraction purity were provided by the suppliers. a High performance liquid chromatography b Gas liquid chromatography. Both the analysis method and the mass fraction purity were provided by the suppliers. c 2-Butanol used in this work is a racemic mixture (RS-), namely, (RS)-2-butanol.
Table 2. Experimental and calculated mole fraction solubility (x) of Pyrazinamide in different solvents at the temperature range from T = (278.15 to 323.15) K under 100 kPa. a, b, c, d 1000 xexp
1000 xApel
1000 xλh
1000 xNRTL
1000 xwilson
278.15
1.048
1.059
1.051
1.102
1.111
283.15
1.312
1.311
1.308
1.332
1.351
288.15
1.684
1.614
1.617
1.622
1.643
293.15
1.941
1.977
1.986
1.933
1.982
298.15
2.396
2.409
2.423
2.345
2.398
303.15
2.839
2.923
2.938
2.821
2.889
308.15
3.622
3.532
3.543
3.487
3.507
313.15
4.211
4.248
4.250
4.188
4.210
318.15
5.210
5.089
5.073
5.176
5.100
323.15
6.000
6.073
6.028
6.222
6.111
278.15
2.078
2.115
2.093
2.182
2.167
283.15
2.652
2.604
2.599
2.642
2.646
288.15
3.278
3.192
3.205
3.191
3.217
293.15
3.841
3.898
3.924
3.803
3.882
298.15
4.698
4.740
4.775
4.611
4.704
303.15
5.633
5.743
5.775
5.575
5.680
308.15
7.098
6.932
6.945
6.925
6.923
313.15
8.278
8.338
8.309
8.346
8.316
318.15
10.028
9.996
9.892
10.301
10.074
278.15
1.025
1.057
1.078
1.130
1.167
283.15
1.406
1.383
1.388
1.410
1.464
288.15
1.878
1.785
1.772
1.772
1.835
T/K Water
Methanol
Ethanol
293.15
2.307
2.274
2.244
2.177
2.263
298.15
2.806
2.862
2.820
2.678
2.784
303.15
3.439
3.560
3.519
3.330
3.435
308.15
4.327
4.380
4.361
4.250
4.282
313.15
5.402
5.334
5.369
5.464
5.342
318.15
6.514
6.432
6.571
6.921
6.593
278.15
0.775
0.813
0.833
0.898
0.956
283.15
1.228
1.092
1.100
1.170
1.245
288.15
1.451
1.446
1.437
1.405
1.518
293.15
1.795
1.888
1.862
1.726
1.876
298.15
2.453
2.434
2.391
2.248
2.402
303.15
2.971
3.098
3.047
2.787
2.962
308.15
3.935
3.898
3.852
3.698
3.799
313.15
5.033
4.850
4.835
4.888
4.835
318.15
6.158
5.972
6.028
6.324
6.047
323.15
7.065
7.281
7.467
7.782
7.322
278.15
0.619
0.714
0.699
0.745
0.843
283.15
0.973
0.952
0.942
0.967
1.093
288.15
1.360
1.256
1.255
1.243
1.396
293.15
1.813
1.644
1.657
1.599
1.775
298.15
2.240
2.120
2.167
2.003
2.207
303.15
2.787
2.729
2.809
2.544
2.757
308.15
3.652
3.550
3.612
3.404
3.539
313.15
4.665
4.594
4.608
4.559
4.520
318.15
5.742
5.880
5.835
6.000
5.688
323.15
6.916
7.463
7.336
7.816
7.090
1-Propanol
2-Propanol
1-Butanol 278.15
0.772
0.802
0.827
0.895
0.954
283.15
1.157
1.088
1.097
1.145
1.232
288.15
1.479
1.452
1.440
1.415
1.532
293.15
1.922
1.908
1.873
1.780
1.925
298.15
2.370
2.471
2.416
2.208
2.381
303.15
3.091
3.157
3.090
2.857
3.028
308.15
3.956
3.981
3.922
3.719
3.842
313.15
5.124
4.960
4.941
4.973
4.937
318.15
6.228
6.108
6.182
6.411
6.155
323.15
7.313
7.439
7.683
8.073
7.533
278.15
0.530
0.551
0.563
0.637
0.684
283.15
0.810
0.773
0.777
0.818
0.899
288.15
1.084
1.067
1.060
1.029
1.147
293.15
1.496
1.451
1.432
1.336
1.495
298.15
1.879
1.945
1.913
1.684
1.882
303.15
2.522
2.572
2.533
2.244
2.464
308.15
3.318
3.359
3.324
3.024
3.222
313.15
4.345
4.334
4.323
4.162
4.233
318.15
5.643
5.527
5.578
5.831
5.572
323.15
6.956
6.973
7.141
7.879
7.108
278.15
2.488
2.493
2.546
2.570
2.664
283.15
3.040
3.006
3.024
3.031
3.120
288.15
3.574
3.590
3.572
3.562
3.642
293.15
4.239
4.250
4.200
4.175
4.242
2-Butanol
Acetone
298.15
4.948
4.989
4.915
4.880
4.927
303.15
5.744
5.810
5.727
5.690
5.711
308.15
6.738
6.716
6.646
6.620
6.608
313.15
7.840
7.709
7.686
7.684
7.630
318.15
8.967
8.788
8.857
8.896
8.789
323.15
9.749
9.955
10.180
10.260
10.081
278.15
1.255
1.270
1.329
1.398
1.447
283.15
1.625
1.610
1.630
1.683
1.733
288.15
2.046
2.009
1.984
2.017
2.070
293.15
2.480
2.468
2.401
2.409
2.463
298.15
2.936
2.989
2.889
2.866
2.920
303.15
3.513
3.571
3.457
3.401
3.457
308.15
4.197
4.212
4.116
4.025
4.084
313.15
4.969
4.908
4.877
4.750
4.814
318.15
5.801
5.655
5.753
5.590
5.660
323.15
6.334
6.444
6.760
6.538
6.604
278.15
1.599
1.665
1.691
1.721
1.755
283.15
2.191
2.038
2.046
2.067
2.101
288.15
2.401
2.471
2.461
2.462
2.494
293.15
3.118
2.971
2.944
2.935
2.966
298.15
3.496
3.543
3.503
3.475
3.500
303.15
4.156
4.192
4.147
4.110
4.129
308.15
4.748
4.924
4.886
4.840
4.849
313.15
5.812
5.744
5.733
5.703
5.703
318.15
6.663
6.657
6.700
6.685
6.671
323.15
7.754
7.666
7.802
7.826
7.794
Acetonitrile
Ethyl acetate
a
exp
x
Apel
is the experimentally determined solubility; x
λh
NRTL
,x ,x
and x
wilson
, are the calculated
solubility by Apelbat, λh , NRTL and Wilson equation, respectively. b The standard uncertainty of temperature is u (T) = 0.1 K. c The relative standard uncertainty of the solubility measurement is ur (x) = 0.039. d The relative standard uncertainty of pressure is ur (P) = 0.05.
Table 3. Physical properties for the selected solvents.a solvent
Water Methanol Ethanol 1-Propanol 2-Propanol 1-Butanol 2-Butanol Acetonitrile Acetone Ethyl acetate a
Polarity ∑αb （water100） 100 76.2 65.4 11.9 54.6 60.2 55.2 46 35.5 23
1.17 0.43 0.37 0.37 0.33 0.37 0.33 0.07 0.04 0
∑βc
10-4δH d /
(J·m-3)1/2 0.47 151.4 0.47 93.8 0.48 86.7 0.48 399.1 0.56 74.4 0.48 73.7 0.56 69.2 0.32 77.0 0.49 64.7 0.45 58.9
µ e/
ε f/
D 1.87 1.7 1.7 1.7 1.66 1.66 1.7 3.2 2.9 1.7
F*m-1 79.7 32.6 22.4 20.1 18.3 18.2 17.7 37.5 20.6 6.02
Taken from Ref. [15]. Summation of the hydrogen bond donor propensities of the solvent. c Summation of the hydrogen bond acceptor propensities of the solvent. d Hildebrand solubility parameters. e Dipole moment in the unit of debye. f Dielectric constant. b
Cohesive energy density/ mN∙m-1 2095.93 808.26 618.87 520.37 489.11 446.01 416.88 522.95 362.07 300.64
Table 4. Parameters of the modified Apelblat equation for pyrazinamide in different solvents. Solvents
A
B/10 3
C
ARD /%
RMSD /10-4
Water
-40.8
-1411.8
6.9
1.763
0.6571
Methanol
-58.319
-572.37
9.63
1.541
0.8166
Ethanol
104.1
-8281.1
-14.4
2.256
0.6922
1-Propanol
134
-10035
-19
2.644
0.8893
2-Propanol
103.7
-9222.5
-13.9
2.246
0.5144
1-Butanol
105.2
-8692.6
-14.4
3.724
1.271
2-Butanol
301
-17707
-44
3.405
0.8376
Acetone
51.2
-5134.8
-7
2.709
1.007
Acetonitrile
182
-11143
-26
1.365
0.6746
Ethyl acetate
68.3
-5640.6
-9.6
1.011
0.9991
Table 5. Parameters of the λh equation for pyrazinamide in different solvents. ARD Solvents λ h /%
RMSD /10-4
Water
0.1398
24547
1.761
0.6656
Methanol
0.2627
12897
1.680
0.9653
Ethanol
0.3131
12693
2.201
0.5793
1-Propanol
0.4657
9524.8
2.986
1.366
2-Propanol
0.7846
6461.5
2.359
0.6857
1-Butanol
0.4221
10334
4.158
1.610
2-Butanol
0.5618
8338.9
4.661
1.545
Acetone
0.115
25783
2.632
0.9627
Acetonitrile
0.1222
25965
2.689
1.481
Ethyl acetate
0.1097
24150
1.371
1.527
Table 6. Parameters of the NRTL equation for pyrazinamide in different solvents. ARD RMSD Solvents ∆g12 ∆g21 α /% /10-4 Water
-3085
13329
0.47
2.219
0.8917
Methanol
-3179
12188
0.2
6.119
5.040
Ethanol
-3622
15325
0.25
4.298
1.641
1-Propanol
-3669
15966
0.47
6.382
2.683
2-Propanol
-3769
16766
0.47
8.729
3.376
1-Butanol
-3677
16007
0.47
6.551
2.846
2-Butanol
-3805
17250
0.47
8.817
3.410
Acetone
4188.2
2315.8
0.2
1.753
1.797
Acetonitrile
-581.5
7265.5
0.225
4.016
1.452
Ethyl acetate
-558.2
6756.7
0.2
2.853
0.9815
Table 7. Parameters of the Wilson equation for pyrazinamide in different solvents. ARD RMSD Solvents ∆λ12 a /kJ·mol-1 ∆λ21 a /kJ·mol-1 /% /10-4 Water
3.651±0.2508
3.599±0.1831
2.253
0.7010
Methanol
5.537±0.2471
0.6385±0.1141
1.172
0.7403
Ethanol
9.497±0.3156
1.034±0.092
2.646
0.6638
1-Propanol
11.26±0.4956
-1.866±0.1078
4.926
1.355
2-Propanol
11.76±0.4282
-1.9880.0851
6.547
1.167
1-Butanol
12.35±0.4412
-2.519±0.0796
4.705
1.213
2-Butanol
13.61±0.3371
-2.6640.0438
5.727
0.9433
Acetone
2.684±0.2382
6.344±2.288
2.268
1.570
Acetonitrile
4.358±0.6231
2.647±0.9917
3.839
1.349
Ethyl acetate
4.851±0.4120
2.421±1.138
2.805
0.9433
a
The number in the right side of ‘‘±” means the standard error of each coefficient in different solvents (0.95 level of confidence).
Table 8. The mixing thermodynamic properties of pyrazinamide in different solvents (p = 0.1 MPa).a ∆mixG/ ∆mixH/ ∆mixG ∆mixH/ T/K T/K -1 -1 -1 J·mol J·mol /J·mol J·mol-1 Water
1-Butanol
278.15
-11.50
7.48
278.15
-8.56
2.93
283.15
-14.15
9.47
283.15
-12.20
4.00
288.15
-17.72
12.28
288.15
-15.24
4.88
293.15
-20.38
14.31
293.15
-19.27
5.91
298.15
-24.70
17.83
298.15
-23.33
6.91
303.15
-28.95
21.32
303.15
-29.53
8.03
308.15
-35.86
27.37
308.15
-36.79
9.01
313.15
-41.34
32.06
313.15
-46.24
9.68
318.15
-49.88
39.85
318.15
-55.18
10.25
323.15
-56.99
46.19
323.15
-64.01
10.84
Methanol
2-Butanol
278.15
-22.63
13.17
278.15
-5.91
2.01
283.15
-28.25
16.67
283.15
-8.57
2.71
288.15
-34.32
20.43
288.15
-11.13
3.32
293.15
-39.94
23.79
293.15
-14.81
3.95
298.15
-48.00
28.78
298.15
-18.24
4.52
303.15
-56.74
34.14
303.15
-23.68
4.89
308.15
-69.57
42.27
308.15
-30.25
4.92
313.15
-80.30
48.71
313.15
-38.48
4.37
318.15
-95.29
57.92
318.15
-48.63
2.96
323.15
-58.85
1.41
Ethanol
Acetone
278.15
-11.29
6.52
278.15
-27.46
7.79
283.15
-14.96
8.69
283.15
-32.89
9.58
288.15
-19.38
11.25
288.15
-38.18
11.33
293.15
-23.45
13.51
293.15
-44.56
13.51
298.15
-28.12
16.04
298.15
-51.29
15.86
303.15
-33.88
19.07
303.15
-58.72
18.52
308.15
-41.63
23.00
308.15
-67.66
21.84
313.15
-50.79
27.38
313.15
-77.37
25.54
318.15
-60.25
31.65
318.15
-87.25
29.36
323.15
-94.71
32.12
1-Propanol
Acetonitrile
278.15
-8.64
4.14
278.15
-14.05
7.11
283.15
-12.88
6.09
283.15
-17.71
9.23
288.15
-15.11
7.12
288.15
-21.79
11.64
293.15
-18.39
8.55
293.15
-25.97
14.14
298.15
-24.20
10.85
298.15
-30.35
16.77
303.15
-28.88
12.65
303.15
-35.72
20.09
308.15
-36.98
15.27
308.15
-41.92
24.02
313.15
-46.03
17.79
313.15
-48.78
28.45
318.15
-55.24
20.10
318.15
-56.10
33.21
323.15
-62.95
22.15
323.15
-61.36
36.34
2-Propanol
Ethyl acetate
278.15
-7.05
3.33
278.15
-17.73
8.85
283.15
-10.45
4.88
283.15
-23.34
12.12
288.15
-14.05
6.41
288.15
-25.74
13.31
293.15
-18.16
8.02
293.15
-32.36
17.26
298.15
-22.05
9.50
298.15
-36.25
19.37
303.15
-26.90
11.18
303.15
-42.42
23.02
308.15
-34.18
13.26
308.15
-48.11
26.30
313.15
-42.52
15.26
313.15
-57.39
32.12
318.15
-51.32
17.09
318.15
-65.08
36.79
323.15
-60.83
18.79
323.15
-74.54
42.74
a
The mean relative standard uncertainty of ∆mixH is ur (∆mixH) = 0.167 (the relative standard uncertainties of the mixing enthalpy in 1-butanol and 2-butanol are respectively 1.165 and 7.450 ), the mean relative standard uncertainty of ∆mixG is ur (∆ mixG) = 0.097.
Highlights The solubility of pyrazinamide in ten pure solvents was determined by using gravimetric method. The modified Apelblat equation, λh equation, Wilson model and NRTL model were employed to correlate the solubility data of pyrazinamide in the selected solvents. The mixing thermodynamic properties of pyrazinamide in different solvents were calculated and discussed.
S0021-9614(17)30126-X http://dx.doi.org/10.1016/j.jct.2017.04.014 YJCHT 5048
To appear in:
J. Chem. Thermodynamics
Received Date: Revised Date: Accepted Date:
9 January 2017 5 April 2017 23 April 2017
Please cite this article as: K. Zhang, H. Shen, S. Xu, H. Zhang, M. Zhu, P. Shi, X. Fu, Y. Yang, J. Gong, Thermodynamic study of solubility for pyrazinamide in ten solvents from T = (283.15 to 323.15) K, J. Chem. Thermodynamics (2017), doi: http://dx.doi.org/10.1016/j.jct.2017.04.014
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Thermodynamic study of solubility for pyrazinamide in ten solvents from T = (283.15 to 323.15) K Keke Zhanga,b, Huan Shen a,b, Shijie Xu a,b, Huihui Zhang a,b, Minghe Zhu a,b, Peng Shi a,b, Xiaoyan Fu a,b, Yaoyao Yang a,b, Junbo Gong a,b,* a
School of Chemical Engineering and Technology, State Key Laboratory of Chemical
Engineering, Tianjin University, Tianjin 300072, People’s Republic of China. b
The Co-Innovation Center of Chemistry and Chemical Engineering of Tianjin,
Tianjin University, Tianjin 300072, People’s Republic of China. ABSTRACT: The solubility of pyrazinamide in ten solvents (water, methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, 2-butanol, acetone, acetonitrile and ethyl acetate) at temperatures ranging from (278.15 to 323.15) K was determined by using the gravimetric method. The experimental results indicated that in different solvents, the solubility of pyrazinamide was temperature dependent and increased with the increasing temperature. Besides, the modified Apelblat equation, λh equation, Wilson model and NRTL model were employed to correlate the solubility data in the solvents. The results show that the correlated data are in good agreement with the experimental solubility. Furthermore, the mixing thermodynamic properties of pyrazinamide in different solvents were calculated based on the Wilson model. The outcome indicates that the mixing process of pyrazinamide is endothermic. Keywords: pyrazinamide; solubility; thermodynamic model
1. Introduction Pyrazinamide (pyrazine-2-carboxamide, abbreviated as PZA, C5H5N3O) is one of the first-line drugs against Mycobacterium tuberculosis [1]. Tuberculosis (TB) results in cough, fever, sweats, fatigue and weight loss, which, if remained untreated, eventually deteriorates to death. Despite the widespread use of a vaccine, more than eight million people are infected with TB each year, of which 1.8 million will die [2].
Tuberculosis treatment is through a course of antibiotics for periods up to 26 weeks. Pyrazinamide allows the treatment shortening from (9 to 12) months to 6 months on account of its activity against the persisting tubercle bacilli at an acidic pH [3]. World Health Organization guidelines recommended the administration of PZA in association with two other drugs (rifampicin and isoniazid), in order to reduce bacterial growth during the initial phase of tuberculosis treatment [1]. Pyrazinamide is categorized as a class II agent and its dissolution is the rate-limiting step for its absorption. The low aqueous solubility and bioavailability have impeded the efficient therapeutic use of BCS Class II drugs [4]. Due to the crucial role of pyrazinamide in the pharmaceutical industry, it is necessary to find a proper way to enhance its solubility. Various formulation strategies such as the synthesis of co-crystals, complexation with cyclodextrin, amorphous solid dispersions, lipid-based formulations, and particle size reduction can be applied to solve this problem [5]. As pyrazinamide has strong hydrogen bonding properties and ability to act as ligands in various complexes, the synthesis of co-crystals is apparently a good choice [6，7]. For the preparation of co-crystals, the solubility performance of drugs is significant in the method of solution crystallization [8] (slow evaporation from solution and reaction crystallization [9]). Appropriate solubility of the two different solutes in the solvent can promote the production of co-crystals. Also in the preparation of co-crystals, the choice of solvents and the initial concentration of solution can determine the particle size distribution and crystalline morphology of co-crystals. Besides, as fundamental data, the solubility data of pyrazinamide reflect the interactions between solvent and solute. Moreover, based on the solubility, one can design different degree of supersaturation, initial temperature and initial concentration to investigate the nucleation and growth behaviour of pyrazinamide in different solvents. The solubility studies of pyrazinamide can also provide data support for synthesizing and investigating pyrazinamide’s derivatives [10, 11]. In conclusion, it is necessary to implement the solubility studies of pyrazinamide. However, to the best of the authors’ present knowledge, values of solubility of pyrazinamide in various solvents at different temperatures are very scarce in previous publications [12].
Thus, the solubility of pyrazinamide in ten solvents (water, methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, 2-butanol, acetone, acetonitrile and ethyl acetate) at temperatures ranging from (278.15 to 323.15) K was determined by employing gravimetric method. The experiment solubility data was correlated by the Apelblat equation, λh equation, Wilson model and NRTL model. As we all know, the enthalpy of mixing and heat of crystallization, which play an important part in influencing the crystallization system, are not ignorable in the industrial scale-up process. Thus, the thermodynamic properties of mixing process for the solutions ought to be calculated precisely. Meanwhile, our work provided the thermodynamic basis (material balance and heat balance) for further research. 2. Experimental 2.1. Materials Pyrazinamide (0.99 mass fraction purity) was obtained from Shanghai Baoman Biological technology Co., Ltd. All the organic solvents (methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, 2-butanol, acetone, acetonitrile and ethyl acetate) purchased from Tianjin Jiangtian Chemical Reagent Co. (Tianjin, China) were of analytical grade. All the materials were used without further disposal. Distilled-deionized water (conductivity < 0.5 µS∙cm-1) was prepared in our laboratory. The detailed information is given in Table 1. 2.2. X-ray powder diffraction In this work, the X-ray powder diffraction (XRPD) was applied to monitor the crystal form of pyrazinamide during the process. The XPRD was carried out using the D/MAX-2500 (Rigaku, Japan) by Cu Kα radiation (0.15405 nm) over a diffraction angle (2θ) range of 2° to 50° with a scanning rate of 8°·min-1. Raw pyrazinamide and excess solid state pyrazinamide in different solvents were analysed by XRPD and the patterns are shown in Figure 2. 2.3. Solubility determination The solubility of pyrazinamide in pure water, methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, 2-butanol, acetone, acetonitrile, and ethyl acetate was analysed across the temperature range of (278.15 to 318.15) K under atmospheric pressure by
using a solid-liquid equilibrium method. In the experiment, all measurements of mass were performed on an analytic balance (AB204-N, Mettler-Toledo, Switzerland) with uncertainty of ±0.0001 g. In this method, excess amount of pyrazinamide were added into a 50 mL capped glass vial containing 25 mL preheated/cooled solvent. Then, the (solid + liquid) mixture were put into a thermostat shaker (type 501A, Shanghai Laboratory Instrument Works Co., Ltd., China, with the precision of T = ±0.1 K) at 150 rpm for about 12 h to reach the (solid - liquid) equilibrium. The pre-experiments indicated that 12 h was enough to ensure saturation. After stopping the shaker, all the samples were standing for 2 h to make the un-dissolved substances deposit. Followed 5 mL saturated solution was extracted by a preheated/cooled syringe filter (0.45 µm) and transferred into a pre-weighed beaker. Then the total weight was measured immediately by the balance. Subsequently the weighed beaker was placed into a vacuum oven (type DZ-1BCII, Yichuan Appearance of Bearing Co., Ltd, China) at T= 323.15 K until the weight of sample remained constant . Each experiment was repeated three times under the same conditions and the mean value was used as the final result to calculate the solubility. The experimental mole fraction solubility of pyrazinamide in each solvent was calculated by equation (1) as follows: ⁄ (1) = ⁄ + ⁄
where the m1 represents the mass of pyrazinamide in saturated solution; m2 represents the mass of solvent(water, methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, 2-butanol, acetone, acetonitrile or ethyl acetate); and M1 and M2 are the molar masses of pyrazinamide and solvent, respectively. 3. Thermodynamic models In this work, the modified Apelblat equation [13，14], λh equation [15], Wilson model [16] and NRTL model [17] were applied to correlate the solubility of pyrazinamide in different solvents, respectively. 3. 1. Modified Apelblat equation The modified Apelblat equation is a semi-empirical equation, which has been successfully used to link experimental and theoretical solubility results of different
drugs/pharmaceuticals. In this work, the dependence of the mole fraction solubility of pyrazinamide on the absolute temperature T is correlated by the modified Apelblat equation (equation (2)) [13，14]:
ln = + ⁄⁄K + ln⁄K
(2)
where x is the mole fraction solubility of pyrazinamide, T is the absolute experimental temperature (K), A, B, and C are adjustable parameters. The A and B indicate the effect of solution on the solubility, while C represents the effect of temperature on the fusion enthalpy. 3. 2. λh equation The Buchowski–Ksiazaczak λh equation suggested by Buchowski is also a semi-empirical equation. This equation has two empirical parameters and has been widely applied to describe the solubility of solute in pure solvents. The expression of λh equation is described as equation (3) [15]:
ln 1 +
1 − 1 1 = ℎ − ⁄K ⁄K
(3)
where T m is the melting point; λ and h are two empirical equation parameters. The value of λ correlates to the association number of solute molecules in the associating system, and h value relates to the excess enthalpy of solution. 3. 3. Wilson model In the solid-liquid phase equilibrium, Wilson equation is widely used to describe the solubility of a solute in solvents at different temperatures. The model can be expressed as equation (4) [16]: ln x1 =
∆ fus H 1 1 − R Tm T
∆C p − R
Tm Tm − + 1 -ln γ 1 ln T T
(4)
where, ∆fusH is the molar enthalpy of fusion of the pure solute (at the melting point), Tm is the absolute melting point, T is the absolute solution temperature, R is the gas constant (8.314 J·K-1·mol-1), and ∆Cp is the difference between the molar heat capacity of the crystalline form and the molar heat capacity of the hypothetical super cooled liquid form, both at the solution temperature [18]. Since ∆Cp cannot be easily determined experimentally, therefore, two approaches are always employed to
identify a reasonable range of values for ∆Cp [19]. In this study, we assume that ∆Cp is approximated by the entropy of fusion, ∆fusS [20]. Considering that, equation (4) can be expressed as: ln x1 =
∆ fus H 1 1 ∆ fus S − − R Tm T R
Tm Tm − + 1 -lnγ 1 ln T T
(5)
Therefore, on the basis of equation (5) the activity coefficient must be known to deduce the solubility of solute. In the pure solvent system, the activity coefficient can be expressed by the following Wilson mode
ln = −ln + Λ +
Λ Λ − + Λ + Λ
(6)
where x2 is the mole fraction of solvent; Λ12, Λ21 are the model parameters.
− Δ !− # = !− # " " − Δ = !− # = !− # " "
Λ = Λ
(7) (8)
where V1 is the mole volume of the solute, and V2, the solvent. ∆λ12 and ∆λ21 are model parameters (J·mol-1) indicating interaction energy between the solute and the solvent. The values of two model parameters can be deduced by relevant experimental solubility. 3. 4. NRTL model Based on molecular local composition concept, the NRTL (Non Random Two Liquid) model is first proposed by Renon and is widely applied in describing fluid phase equilibrium. The activity coefficient represented by NRTL model is expressed as equations (8)-(11) [17]. )
∑) ' +'% ∑) '( *'% +'% ' %( % *%' +%' ln % = + , * − %' ) ) ∑%( +'% % ∑%( +'% % ∑) %( +%' % +%' = exp0−1%' *%' 2 1%' = 1'% = 1 *%' =
'(
03%' − 3'' 2 Δ3%' = " "
(9) (10) (11) (12)
where ∆gij is the model parameters relevant to the interaction energy; α is an adjustable parameter ranging from 0.20 to 0.47 , which reveals the non-randomness of
the solution. 4. Results and discussion 4.1. Characterization and identification of pyrazinamide Raw pyrazinamide and excess pyrazinamide in different solvents were analyzed by XRPD in this work. The patterns proved that the forms of both the raw material and residual solids were stable form α [21]. According to Figure 2, the results show that the crystal forms of material and excess solids from ten solutions are consistent with crystalline pyrazinamide of form α reported by literature. Therefore, it can be concluded that there is no crystal transformation in the solubility measurements. 4.2. Solubility results The measured solubility in mole fraction of pyrazinamide in water, methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, 2-butanol, acetone, acetonitrile and ethyl acetate at the temperatures ranging from (278.15 to 323.15) K is presented in Table 2 and shown graphically in Figure 3. The results indicate that the solubility of pyrazinamide in ten solvents increased with the increasing of temperature. However, the increasing extent of solubility varies in different pure solvents. At same temperature, the mole fraction solubility is highest in acetone, and lowest in 2-butanol. In general, the solubility of pyrazinamide in different solvents decreases according to the following order: acetone > methanol > ethyl acetate > acetonitrile > ethanol > 1-butanol > 1-propanol > 2-propanol > 2-butanol. For the solvents methanol, ethanol, 1-butanol and 2-propanol, the sequence of the pyrazinamide solubility values from high to low is in keeping with the changing trend of polarity of the four solvents [22]. While this case is not found for the solvents 1-propanol and
2-butanol. In general, it is rather hard to explain the phenomenon shown in Figure 3 only on the basis of a single factor. In fact, the solubility is determined by the mutual competition of the interaction between the solute-solvent and solvent-solvent. Figure1 shows that the pyrazinamide molecule contains both hydrogen donor and hydrogen acceptor groups, then between the solute and solvents molecules the hydrogen bond can be formed [23]. Thus in this system, both the van de Waals interaction (represented by polarity) and hydrogen bonding (represented by hydrogen bond donor/acceptor propensity) contribute to the solute–solvent interaction. Besides, the degree of solvent–solvent association could be represented by the cohesive energy density [22]. Though 1-propanol’s polarity in these alcohols is lowest, its hydrogen bond donor and acceptor propensity are identical to 1-butanol. Therefore pyrazinamide have similar solubility values in 1-propanol and 1-butanol. For 2-butanol, possessing greater steric hindrance because of the branched chains, which makes it harder to form hydrogen bonds with the solute and this results in lower solubility in alcohols. The order of solubility in acetone, ethyl acetate and acetonitrile is not strictly in accordance with the polarity order, while it is similar with the sequences of the hydrogen bond acceptor propensity as shown in Table 3. In addition, though water’s polarity and capacity to form the hydrogen bond with the solute are the highest, the cohesive energy density of water is extremely higher than any other selected solvents [22], the solubility is not the highest. 4.3. Solubility correlation and calculation To evaluate the applicability and accuracy of the four models used in this work, the
average relative deviation (ARD) and the root-mean-square deviation (RMSD) are defined as follows [24]: )
1 % − %;<= ARD = , 8 8 9: 7 % 9:
%(
RMSD = @
(13)
9: ∑) − %;<= 2 %(0 %
7
(14)
where xiexp and xical are the experimental and calculated solubility values, respectively; N refers to the numbers of experimental points. During the regression process, the melting temperature (Tm) and melting enthalpy (∆fusH) of pyrazinamide are taken from the reference [25]. The regressed values of the parameters in Apelblat equation, λh equation, Wilson model and NRTL model are listed in Tables 4-7, respectively. The obtained ARD and RMSD values for all models are also shown in Tables 4-7. As the results shown, the ARD values obtained from the Apelblat equation are smaller than those associated with the other three models. The largest value of RMSD is 5.040 × 10 -4, which is calculated by the NRTL equation for the system (pyrazinamide + methanol). The ARD values are no greater than 8.82%. Generally speaking, the calculated solubility with the four models suits well with the experimental values. The ARD values and RMSD values obtained with the modified Apelblat equation are no greater than 3.72% and 1.271×10 -4 respectively, which show that the modified Apelblat equation provides more accurate results for the same solvent. 4.4. Mixing properties of solution
Thermodynamic property of a solute dissolved in solvent may provide essential information for the dissolution procedure. The mixing properties of solution can be obtained according to the Lewis-Randall rule. For the ideal solution, the mixing Gibbs energy, mixing enthalpy, and mixing entropy in pure solvent can be calculated by the following equations [26]:
∆CD + CE = " ln + ln
∆CD F CE = −" ln + ln ∆CD GCE = 0
(15) (16) (17)
where x1 refers to the mole fraction of solute; and x2, the corresponding solvent. For the non-ideal solution, the three mixing properties can be calculated using the following equations:
∆CD + = + I + ∆CD + CE ∆CD F = F I + ∆CD F CE
∆CD G = GJ +∆CD GCE
(18) (19) (20)
Here GE, S E and HE represent for the excess properties. According to the Wilson model, the excess properties are expressed as the following equations [27]:
+ I = " ln + ln
= −"0ln + Λ + ln + Λ 2
(21)
∆ Λ ∆ Λ = ! + # + Λ + Λ GI − + I FI =
(22)
L+ I ⁄ GI = − K M L
(23)
On the basis of the regressed parameters in Wilson model and the experimental solubility values, the Δ mixG and ΔmixH are obtained and presented in Table 8. The values of mixing Gibbs energy (Δ mixG) can be applied to elaborate the dissolution capacity of a solute. The connection between mixing Gibbs energy (Δ mixG) and temperature is shown in Figure 4. The results in Table 8 illustrates that the values of ΔmixG are all negative and decrease with increasing temperature, therefore, the mixing process of pyrazinamide is spontaneous and favourable in the solvents selected. Table 8 demonstrates that the Δ mixH values of pyrazinamide are all positive. We also calculated the relative standard uncertainties of the mixing enthalpy, and found that the relative standard uncertainties of the mixing enthalpy in 1-butanol and 2-butanol are respectively 1.165 and 7.450 (the maximum value). It means the Wilson model is not applicable in calculating the mixing enthalpy of pyrazinamide in 1-butanol and 2-butanol. That is also the reason that the trends of mixing enthalpies are not consistent with the trends of solubility data in some solvents. The net variation in ∆mixH values results from the contributions of several kinds of intermolecular interactions [28, 29]. The enthalpy of cavity formation (needed for solute accommodating) is endothermic in order to overcome the cohesive forces of the solvent. In addition, the interaction enthalpy between solute and solvent, which is depended predominantly upon interactions of van der Waals and hydrogen bonding, is exothermic. The positive mixing enthalpy for pyrazinamide demonstrates that the intermolecular interactions of cross associating formed between pyrazinamide and the selected solvents are weaker than the self-associating interactions. In this context, the
mixing process is slightly endothermic and the values of HE increase with an increase in temperature. 5. Conclusions In this study, the mole fraction solubility of pyrazinamide in water, methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, 2-butanol, acetone, acetonitrile and ethyl acetate was determined by a gravimetric method over the temperature range of (278.15 to 323.15) K. For all the selected solvents, the solubility of pyrazinamide increased with the increase in temperature. The experimental solubility results in ten solvents were well correlated based on the modified Apelblat equation, λh equation, Wilson model and NRTL model. The relative average deviations obtained by the four models are all less than 8.82%, and the root-mean-square deviations, less than 5.040 × 10-4. The Wilson model was used to calculate the mixing Gibbs energy, the mixing enthalpy and mixing entropy. The results indicated that the mixing process of pyrazinamide was endothermic in the solvents selected. On the basis of the experimental solubility and thermodynamic results of pyrazinamide, it can be helpful in the aspects of the preparation of co-crystals and the synthesis and investigation of pyrazinamide’s derivatives.
AUTHOR INFORMATION Notes The authors declare no competing financial interest. Acknowledgment We are grateful to the financial support of National Natural Science Foundation of China (NNSFC 81361140344 and NNSFC 21376164), National 863 Program (2015AA021002), Major Science and Technology Program for Water Pollution Control and Treatment (NO.2015ZX07202-013) and Tianjin Science and Technology Project (15YFJZC00800). Corresponding Author *Tel.: 86-22-27405754. Fax: +86-22-27374971. E-mail: [email protected]
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Table captions: Table 1. Sources and mass fraction purity of materials used in the experiments. Table 2. Experimental and calculated mole fraction solubility (x) of Pyrazinamide in different solvents at the temperature range from T = (278.15–323.15) K under 100 kPa. Table 3. Physical properties for the selected solvents. Table 4. Parameters of the modified Apelblat equation for pyrazinamide in different solvent. Table 5. Parameters of the λh equation for pyrazinamide in different solvents. Table 6. Parameters of the NRTL equation for pyrazinamide in different solvents. Table 7. Parameters of the Wilson equation for pyrazinamide in different solvents. Table 8. The mixing thermodynamic properties of pyrazinamide in different mono-solvents (p = 0.1 MPa).
Figure captions: Figure 1. Molecular structure of pyrazinamide. Figure 2. Powder X-ray diffraction (PXRD) patterns of excess solid from ten solvents. ( (a) raw material; (b) water; (c) methanol; (d) ethanol; (e) 1-propanol; (f) 2-propanol; (g) 1-butanol; (h) 2-butanol; (i) acetone; (j) acetonitrile; (k) ethyl acetate ) Figure 3. The solubility of pyrazinamide in ten pure solvents. Figure 4. Calculated mixing Gibbs energy at measured solubility points.
Figures
Figure 1. Molecular structure of pyrazinamide.
Figure 2. Powder X-ray diffraction (PXRD) patterns of excess solid from ten solvents. ( (a) raw material; (b) water; (c) methanol; (d) ethanol; (e) 1-propanol; (f) 2-propanol; (g) 1-butanol; (h) 2-butanol; (i) acetone; (j) acetonitrile; (k) ethyl acetate )
Figure 3. The solubility of pyrazinamide in ten pure solvents.
Figure 4. Calculated mixing Gibbs energy at measured solubility points.
Tables Table 1. Sources and mass fraction purity of materials used in the experiments. Mass Fraction Analysis Chemical Molar mass/(g·mol-1) Purity Method Pyrazinamide
123.11
≥0.990
HPLCa
Methanol
32.04
≥0.995
GCb
Ethanol
46.07
≥0.995
GCb
1-Propanol
60.06
≥0.995
GCb
60.06
≥0.995
GCb
1-Butanol
74.12
≥0.995
GCb
2-Butanolc
74.12
≥0.995
GCb
Acetone
58.08
≥0.995
GCb
Acetonitrile
41.05
≥0.995
GCb
Ethyl acetate
88.11
≥0.995
GCb
2-Propanol
Both the analysis method and the mass fraction purity were provided by the suppliers. a High performance liquid chromatography b Gas liquid chromatography. Both the analysis method and the mass fraction purity were provided by the suppliers. c 2-Butanol used in this work is a racemic mixture (RS-), namely, (RS)-2-butanol.
Table 2. Experimental and calculated mole fraction solubility (x) of Pyrazinamide in different solvents at the temperature range from T = (278.15 to 323.15) K under 100 kPa. a, b, c, d 1000 xexp
1000 xApel
1000 xλh
1000 xNRTL
1000 xwilson
278.15
1.048
1.059
1.051
1.102
1.111
283.15
1.312
1.311
1.308
1.332
1.351
288.15
1.684
1.614
1.617
1.622
1.643
293.15
1.941
1.977
1.986
1.933
1.982
298.15
2.396
2.409
2.423
2.345
2.398
303.15
2.839
2.923
2.938
2.821
2.889
308.15
3.622
3.532
3.543
3.487
3.507
313.15
4.211
4.248
4.250
4.188
4.210
318.15
5.210
5.089
5.073
5.176
5.100
323.15
6.000
6.073
6.028
6.222
6.111
278.15
2.078
2.115
2.093
2.182
2.167
283.15
2.652
2.604
2.599
2.642
2.646
288.15
3.278
3.192
3.205
3.191
3.217
293.15
3.841
3.898
3.924
3.803
3.882
298.15
4.698
4.740
4.775
4.611
4.704
303.15
5.633
5.743
5.775
5.575
5.680
308.15
7.098
6.932
6.945
6.925
6.923
313.15
8.278
8.338
8.309
8.346
8.316
318.15
10.028
9.996
9.892
10.301
10.074
278.15
1.025
1.057
1.078
1.130
1.167
283.15
1.406
1.383
1.388
1.410
1.464
288.15
1.878
1.785
1.772
1.772
1.835
T/K Water
Methanol
Ethanol
293.15
2.307
2.274
2.244
2.177
2.263
298.15
2.806
2.862
2.820
2.678
2.784
303.15
3.439
3.560
3.519
3.330
3.435
308.15
4.327
4.380
4.361
4.250
4.282
313.15
5.402
5.334
5.369
5.464
5.342
318.15
6.514
6.432
6.571
6.921
6.593
278.15
0.775
0.813
0.833
0.898
0.956
283.15
1.228
1.092
1.100
1.170
1.245
288.15
1.451
1.446
1.437
1.405
1.518
293.15
1.795
1.888
1.862
1.726
1.876
298.15
2.453
2.434
2.391
2.248
2.402
303.15
2.971
3.098
3.047
2.787
2.962
308.15
3.935
3.898
3.852
3.698
3.799
313.15
5.033
4.850
4.835
4.888
4.835
318.15
6.158
5.972
6.028
6.324
6.047
323.15
7.065
7.281
7.467
7.782
7.322
278.15
0.619
0.714
0.699
0.745
0.843
283.15
0.973
0.952
0.942
0.967
1.093
288.15
1.360
1.256
1.255
1.243
1.396
293.15
1.813
1.644
1.657
1.599
1.775
298.15
2.240
2.120
2.167
2.003
2.207
303.15
2.787
2.729
2.809
2.544
2.757
308.15
3.652
3.550
3.612
3.404
3.539
313.15
4.665
4.594
4.608
4.559
4.520
318.15
5.742
5.880
5.835
6.000
5.688
323.15
6.916
7.463
7.336
7.816
7.090
1-Propanol
2-Propanol
1-Butanol 278.15
0.772
0.802
0.827
0.895
0.954
283.15
1.157
1.088
1.097
1.145
1.232
288.15
1.479
1.452
1.440
1.415
1.532
293.15
1.922
1.908
1.873
1.780
1.925
298.15
2.370
2.471
2.416
2.208
2.381
303.15
3.091
3.157
3.090
2.857
3.028
308.15
3.956
3.981
3.922
3.719
3.842
313.15
5.124
4.960
4.941
4.973
4.937
318.15
6.228
6.108
6.182
6.411
6.155
323.15
7.313
7.439
7.683
8.073
7.533
278.15
0.530
0.551
0.563
0.637
0.684
283.15
0.810
0.773
0.777
0.818
0.899
288.15
1.084
1.067
1.060
1.029
1.147
293.15
1.496
1.451
1.432
1.336
1.495
298.15
1.879
1.945
1.913
1.684
1.882
303.15
2.522
2.572
2.533
2.244
2.464
308.15
3.318
3.359
3.324
3.024
3.222
313.15
4.345
4.334
4.323
4.162
4.233
318.15
5.643
5.527
5.578
5.831
5.572
323.15
6.956
6.973
7.141
7.879
7.108
278.15
2.488
2.493
2.546
2.570
2.664
283.15
3.040
3.006
3.024
3.031
3.120
288.15
3.574
3.590
3.572
3.562
3.642
293.15
4.239
4.250
4.200
4.175
4.242
2-Butanol
Acetone
298.15
4.948
4.989
4.915
4.880
4.927
303.15
5.744
5.810
5.727
5.690
5.711
308.15
6.738
6.716
6.646
6.620
6.608
313.15
7.840
7.709
7.686
7.684
7.630
318.15
8.967
8.788
8.857
8.896
8.789
323.15
9.749
9.955
10.180
10.260
10.081
278.15
1.255
1.270
1.329
1.398
1.447
283.15
1.625
1.610
1.630
1.683
1.733
288.15
2.046
2.009
1.984
2.017
2.070
293.15
2.480
2.468
2.401
2.409
2.463
298.15
2.936
2.989
2.889
2.866
2.920
303.15
3.513
3.571
3.457
3.401
3.457
308.15
4.197
4.212
4.116
4.025
4.084
313.15
4.969
4.908
4.877
4.750
4.814
318.15
5.801
5.655
5.753
5.590
5.660
323.15
6.334
6.444
6.760
6.538
6.604
278.15
1.599
1.665
1.691
1.721
1.755
283.15
2.191
2.038
2.046
2.067
2.101
288.15
2.401
2.471
2.461
2.462
2.494
293.15
3.118
2.971
2.944
2.935
2.966
298.15
3.496
3.543
3.503
3.475
3.500
303.15
4.156
4.192
4.147
4.110
4.129
308.15
4.748
4.924
4.886
4.840
4.849
313.15
5.812
5.744
5.733
5.703
5.703
318.15
6.663
6.657
6.700
6.685
6.671
323.15
7.754
7.666
7.802
7.826
7.794
Acetonitrile
Ethyl acetate
a
exp
x
Apel
is the experimentally determined solubility; x
λh
NRTL
,x ,x
and x
wilson
, are the calculated
solubility by Apelbat, λh , NRTL and Wilson equation, respectively. b The standard uncertainty of temperature is u (T) = 0.1 K. c The relative standard uncertainty of the solubility measurement is ur (x) = 0.039. d The relative standard uncertainty of pressure is ur (P) = 0.05.
Table 3. Physical properties for the selected solvents.a solvent
Water Methanol Ethanol 1-Propanol 2-Propanol 1-Butanol 2-Butanol Acetonitrile Acetone Ethyl acetate a
Polarity ∑αb （water100） 100 76.2 65.4 11.9 54.6 60.2 55.2 46 35.5 23
1.17 0.43 0.37 0.37 0.33 0.37 0.33 0.07 0.04 0
∑βc
10-4δH d /
(J·m-3)1/2 0.47 151.4 0.47 93.8 0.48 86.7 0.48 399.1 0.56 74.4 0.48 73.7 0.56 69.2 0.32 77.0 0.49 64.7 0.45 58.9
µ e/
ε f/
D 1.87 1.7 1.7 1.7 1.66 1.66 1.7 3.2 2.9 1.7
F*m-1 79.7 32.6 22.4 20.1 18.3 18.2 17.7 37.5 20.6 6.02
Taken from Ref. [15]. Summation of the hydrogen bond donor propensities of the solvent. c Summation of the hydrogen bond acceptor propensities of the solvent. d Hildebrand solubility parameters. e Dipole moment in the unit of debye. f Dielectric constant. b
Cohesive energy density/ mN∙m-1 2095.93 808.26 618.87 520.37 489.11 446.01 416.88 522.95 362.07 300.64
Table 4. Parameters of the modified Apelblat equation for pyrazinamide in different solvents. Solvents
A
B/10 3
C
ARD /%
RMSD /10-4
Water
-40.8
-1411.8
6.9
1.763
0.6571
Methanol
-58.319
-572.37
9.63
1.541
0.8166
Ethanol
104.1
-8281.1
-14.4
2.256
0.6922
1-Propanol
134
-10035
-19
2.644
0.8893
2-Propanol
103.7
-9222.5
-13.9
2.246
0.5144
1-Butanol
105.2
-8692.6
-14.4
3.724
1.271
2-Butanol
301
-17707
-44
3.405
0.8376
Acetone
51.2
-5134.8
-7
2.709
1.007
Acetonitrile
182
-11143
-26
1.365
0.6746
Ethyl acetate
68.3
-5640.6
-9.6
1.011
0.9991
Table 5. Parameters of the λh equation for pyrazinamide in different solvents. ARD Solvents λ h /%
RMSD /10-4
Water
0.1398
24547
1.761
0.6656
Methanol
0.2627
12897
1.680
0.9653
Ethanol
0.3131
12693
2.201
0.5793
1-Propanol
0.4657
9524.8
2.986
1.366
2-Propanol
0.7846
6461.5
2.359
0.6857
1-Butanol
0.4221
10334
4.158
1.610
2-Butanol
0.5618
8338.9
4.661
1.545
Acetone
0.115
25783
2.632
0.9627
Acetonitrile
0.1222
25965
2.689
1.481
Ethyl acetate
0.1097
24150
1.371
1.527
Table 6. Parameters of the NRTL equation for pyrazinamide in different solvents. ARD RMSD Solvents ∆g12 ∆g21 α /% /10-4 Water
-3085
13329
0.47
2.219
0.8917
Methanol
-3179
12188
0.2
6.119
5.040
Ethanol
-3622
15325
0.25
4.298
1.641
1-Propanol
-3669
15966
0.47
6.382
2.683
2-Propanol
-3769
16766
0.47
8.729
3.376
1-Butanol
-3677
16007
0.47
6.551
2.846
2-Butanol
-3805
17250
0.47
8.817
3.410
Acetone
4188.2
2315.8
0.2
1.753
1.797
Acetonitrile
-581.5
7265.5
0.225
4.016
1.452
Ethyl acetate
-558.2
6756.7
0.2
2.853
0.9815
Table 7. Parameters of the Wilson equation for pyrazinamide in different solvents. ARD RMSD Solvents ∆λ12 a /kJ·mol-1 ∆λ21 a /kJ·mol-1 /% /10-4 Water
3.651±0.2508
3.599±0.1831
2.253
0.7010
Methanol
5.537±0.2471
0.6385±0.1141
1.172
0.7403
Ethanol
9.497±0.3156
1.034±0.092
2.646
0.6638
1-Propanol
11.26±0.4956
-1.866±0.1078
4.926
1.355
2-Propanol
11.76±0.4282
-1.9880.0851
6.547
1.167
1-Butanol
12.35±0.4412
-2.519±0.0796
4.705
1.213
2-Butanol
13.61±0.3371
-2.6640.0438
5.727
0.9433
Acetone
2.684±0.2382
6.344±2.288
2.268
1.570
Acetonitrile
4.358±0.6231
2.647±0.9917
3.839
1.349
Ethyl acetate
4.851±0.4120
2.421±1.138
2.805
0.9433
a
The number in the right side of ‘‘±” means the standard error of each coefficient in different solvents (0.95 level of confidence).
Table 8. The mixing thermodynamic properties of pyrazinamide in different solvents (p = 0.1 MPa).a ∆mixG/ ∆mixH/ ∆mixG ∆mixH/ T/K T/K -1 -1 -1 J·mol J·mol /J·mol J·mol-1 Water
1-Butanol
278.15
-11.50
7.48
278.15
-8.56
2.93
283.15
-14.15
9.47
283.15
-12.20
4.00
288.15
-17.72
12.28
288.15
-15.24
4.88
293.15
-20.38
14.31
293.15
-19.27
5.91
298.15
-24.70
17.83
298.15
-23.33
6.91
303.15
-28.95
21.32
303.15
-29.53
8.03
308.15
-35.86
27.37
308.15
-36.79
9.01
313.15
-41.34
32.06
313.15
-46.24
9.68
318.15
-49.88
39.85
318.15
-55.18
10.25
323.15
-56.99
46.19
323.15
-64.01
10.84
Methanol
2-Butanol
278.15
-22.63
13.17
278.15
-5.91
2.01
283.15
-28.25
16.67
283.15
-8.57
2.71
288.15
-34.32
20.43
288.15
-11.13
3.32
293.15
-39.94
23.79
293.15
-14.81
3.95
298.15
-48.00
28.78
298.15
-18.24
4.52
303.15
-56.74
34.14
303.15
-23.68
4.89
308.15
-69.57
42.27
308.15
-30.25
4.92
313.15
-80.30
48.71
313.15
-38.48
4.37
318.15
-95.29
57.92
318.15
-48.63
2.96
323.15
-58.85
1.41
Ethanol
Acetone
278.15
-11.29
6.52
278.15
-27.46
7.79
283.15
-14.96
8.69
283.15
-32.89
9.58
288.15
-19.38
11.25
288.15
-38.18
11.33
293.15
-23.45
13.51
293.15
-44.56
13.51
298.15
-28.12
16.04
298.15
-51.29
15.86
303.15
-33.88
19.07
303.15
-58.72
18.52
308.15
-41.63
23.00
308.15
-67.66
21.84
313.15
-50.79
27.38
313.15
-77.37
25.54
318.15
-60.25
31.65
318.15
-87.25
29.36
323.15
-94.71
32.12
1-Propanol
Acetonitrile
278.15
-8.64
4.14
278.15
-14.05
7.11
283.15
-12.88
6.09
283.15
-17.71
9.23
288.15
-15.11
7.12
288.15
-21.79
11.64
293.15
-18.39
8.55
293.15
-25.97
14.14
298.15
-24.20
10.85
298.15
-30.35
16.77
303.15
-28.88
12.65
303.15
-35.72
20.09
308.15
-36.98
15.27
308.15
-41.92
24.02
313.15
-46.03
17.79
313.15
-48.78
28.45
318.15
-55.24
20.10
318.15
-56.10
33.21
323.15
-62.95
22.15
323.15
-61.36
36.34
2-Propanol
Ethyl acetate
278.15
-7.05
3.33
278.15
-17.73
8.85
283.15
-10.45
4.88
283.15
-23.34
12.12
288.15
-14.05
6.41
288.15
-25.74
13.31
293.15
-18.16
8.02
293.15
-32.36
17.26
298.15
-22.05
9.50
298.15
-36.25
19.37
303.15
-26.90
11.18
303.15
-42.42
23.02
308.15
-34.18
13.26
308.15
-48.11
26.30
313.15
-42.52
15.26
313.15
-57.39
32.12
318.15
-51.32
17.09
318.15
-65.08
36.79
323.15
-60.83
18.79
323.15
-74.54
42.74
a
The mean relative standard uncertainty of ∆mixH is ur (∆mixH) = 0.167 (the relative standard uncertainties of the mixing enthalpy in 1-butanol and 2-butanol are respectively 1.165 and 7.450 ), the mean relative standard uncertainty of ∆mixG is ur (∆ mixG) = 0.097.
Highlights The solubility of pyrazinamide in ten pure solvents was determined by using gravimetric method. The modified Apelblat equation, λh equation, Wilson model and NRTL model were employed to correlate the solubility data of pyrazinamide in the selected solvents. The mixing thermodynamic properties of pyrazinamide in different solvents were calculated and discussed.