Comment/Reply pubs.acs.org/jced
Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Comment on “Measurement and Correlation of the Solubility of 2,6-Dihydroxybenzoic Acid in Alcohols and Binary Solvents” Elaheh Rahimpour,† Abolghasem Jouyban,‡,§ and William E. Acree, Jr.*,∥ †
Food and Drug Safety Research Center, Tabriz University of Medical Sciences, Tabriz, Iran Pharmaceutical Analysis Research Center and Faculty of Pharmacy, Tabriz University of Medical Sciences, Tabriz, Iran § Kimia Idea Pardaz Azarbayjan (KIPA) Science Based Company, Tabriz University of Medical Sciences, Tabriz, Iran ∥ Department of Chemistry, University of North Texas, Denton, Texas 76203-5070, United States ‡
ABSTRACT: The experimental solubility data of 2,6-dihydroxybenzoic acid in neat organic solvents and binary aqueous solvent systems at temperature range from (278.15 to 318.15) K have carefully been reanalyzed and some recommendations were proposed. In addition, a combined form of the Jouyban−Acree−van’t Hoff model and the Abraham solvation parameters was used to predict the solubility of 2,6-dihydroxybenzoic acid in the binary solvent mixtures at various temperatures.
I
n a recent paper published in this journal, Wang et al.1 reported the experimental solubility of 2,6-dihydroxybenzoic acid in methanol, ethanol, 2-propanol, 1-butanol, and three binary solvent systems (methanol + water, ethanol + water, and 2-propanol + water) from (278.15 to 318.15) K along with some numerical analyses. The experimental solubility data were correlated using the modified Apelblat model for neat monosolvents, and derived versions of the previously proposed cosolvency models for aqueous−organic binary solvent mixtures. The accuracy of the authors’ computations were evaluated using the average relative deviation (ARD) defined as ⎛ |x cal − x obs | ⎞ 100 %ARD = ∑ ⎜⎜ m,T obs m,T ⎟⎟ N xm , T ⎠ ⎝
Wang et al.1 also used a previously derived equation3 (eq 3) based on the combined nearly ideal binary solvent/Redlich− Kister model (CNIBS/R-K) to correlate their measured solubility data of 2,6-dihydroxybenzoic acid in each of the investigated binary aqueous−organic mixtures at each temperature. ln xm = B0 + B1w1 + B2 (w1)2 + B3(w1)3 + B4 (w1)4
(3)
Equation 3 can be derived by replacing w2 (fraction of water) with 1 − w1 from CNIBS/R-K model (eq 4).4 The original version of the CNIBS/R-K model is 2
ln xm = w1 ln(x1)B + w2 ln(x1)C + w1w2∑ Ji (w1 − w2)i i=0
(1)
(4)
where N is the number of experimental points, is the calculated solubility and xobs m,T is the experimental solubility. The aqueous solubility of 2,6-dihydroxybenzoic acid at various temperatures was not reported, and there are some problems with the reported computations. The aim of this communication is to report the recalculation results and to provide additional computations. We offer several comments on the work of Wang et al.1 in the hope that research groups in this field will consider our comments in future works. As stated above, Wang et al.1 correlated the mole fraction solubility data of 2,6-dihydroxybenzoic acid in neat solvents at different temperatures with the modified Apelblat model.
Although both the general single (eq 3) and the CNIBS/R-K models (eq 4) produce the same accuracy for the correlation of the solubility data of a given drug in a certain cosolvent + water mixture at a constant temperature, we recommend using the original version of the CNIBS/R-K model in future works. We also recommend that researchers use its extended version (i.e., the Jouyban−Acree model and/or its combined version with the van’t Hoff equation), which consider both solvent composition and temperature. Compared to various other cosolvency models, the Jouyban−Acree model is perhaps the more versatile model. The Jouyban−Acree model affords good predictability power over a broad temperature range and solvent composition.5−7 The general form of Jouyban−Acree−van’t Hoff model is expressed as8,9
xcal m,T
ln x sat = A +
B + C ln(T /K) T /K
(2)
⎛ ⎛ B ⎞ B ⎞ ln xmsat, T = w1⎜A1 + 1 ⎟ + w2⎜A 2 + 2 ⎟ ⎝ ⎝ T⎠ T⎠
sat
where x is the mole fraction solubility of the 2,6-dihydroxybenzoic acid in the investigated solvents and the terms A, B, and C are the coefficients of the model. The recalculated parameters for eq 2 by SPSS software version 16.0,2 show an inconsistency for constants obtained for 2-propanol (Table 1). In addition, a negative sign in parameter “C” of ethanol was inadvertently omitted. The recalculated ARD% for eq 2 in 2-propanol solvent is 0.1%, which is reported as 2.7% in Table S2 of Wang et al. © XXXX American Chemical Society
2
+
w1·w2 ∑ J (w1 − w2)i T i=0 i
(5)
Received: January 28, 2018 Accepted: May 8, 2018
A
DOI: 10.1021/acs.jced.8b00092 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Comment/Reply
Table 1. Recalculated (recacld) Parameters of the Modified Apelblat Model (Equation 2 of the Published Paper) for Describing the Solubility of 2,6-Dihydroxybenzoic Acid in Neat Solvents methanol
2-propanol
ethanol
1-butanol
parameters
recalcd
Table 5 ref 1
recalcd
Table 5 ref 1
recalcd
Table 5 ref 1
recalcd
Table 5 ref 1
A B C
73.60 −4181.20 −10.70
72.856 −4148.912 −10.582
79.320 −4261.813 −11.636
−33148.00 17945.00 1.00
40.157 −2523.91 −5.791
41.80 −2598.70 6.00
8.708 −1360.328 −0.975
8.80 −1362.50 −1.00
sat where xm,T is the mole fraction solubility of solute (2,6dihydroxybenzoic acid in this case) in the solvent mixtures at temperature T/K, w1 and w2 are the mass fractions of monosolvents 1 and 2, in the absence of the solute, and A1, B1, A2, B2, and Ji are constants of the model obtained by a regression analysis. When eq 5 is fitted/correlated using the solubility data of 2,6dihydroxybenzoic acid in {alcohols (1) + water (2)} solvent mixtures at various temperatures, the obtained models are eqs 6−8 for the solubility of 2,6-dihydroxybenzoic acid in binary solvents mixtures of {methanol (1) + water (2)}, {ethanol (1) + water (2)}, and {2-propanol (1) + water (2)}, respectively.
where subscripts 1 and 2 denote the cosolvent and water, respectively, E is the excess molar refraction, S is the dipolarity/ polarizability of the solute, A denotes the solute’s hydrogen-bond acidity, B stands for the solute’s hydrogen-bond basicity, and V is the McGowan volume of the solute in units of 0.01 (cm3·mol−1). The c, e, s, a, b, and v (solvent’s coefficients) depend upon the solvent under investigation. The e is the tendency of the phase to interact with solutes through n- or π-electron pairs, s is a measure of the solvent phase dipolarity/polarity, the a- and b-coefficients represent the solvent phase hydrogen-bond basicity and acidity, respectively, and v is the general dispersion interaction energy between the solute and solvent phase. Numerical values of the coefficients for water-to-organic solvent systems have been reported in the literature12,13 and tabulated in Table 2.
⎛ 6281.255 ⎞⎟ ln xmsat, T = w1⎜13.953 − ⎝ ⎠ T w1w2 ⎛ ⎞ 1406.976 ⎟ + 1861.944 + w2⎜3.332 − ⎝ ⎠ T T R2 = 0.998
N = 90
p‐value < 0.2
Table 2. Abraham Parameters of the Investigated Solvents Taken from a Reference12,13
MRD = 12.8% (6)
⎛ 5520.414 ⎞⎟ = w1⎜11.501 − ln ⎝ ⎠ T w1. w2 ⎛ ⎞ 865.073 ⎟ + 2064.860 + w2⎜1.610 − ⎝ ⎠ T T ww ww + 1732.527 1 2 (w1 − w2) + 1173.663 1 2 (w1 − w2)2 T T xmsat, T
R2 = 0.998
N = 90
p‐value < 0.2
MRD = 12.1%
p‐value < 0.2
a
b
v
2- propanol ethanol methanol
0.099 0.222 0.276
0.343 0.471 0.334
−1.049 −1.035 −0.714
0.406 0.326 0.243
−3.827 −3.596 −3.320
4.033 3.857 3.549
+ J14 v 2 + J15a 2b2} ⎛ w w (w − w2) ⎞ +⎜ 1 2 1 ⎟{J16 + J17 c + J18 e + J19 s ⎝ ⎠ T
MRD = 8.1%
+ J20 a + J21b + J22 v + J23ab + J24 c 2 + J25e 2
To provide a more comprehensive model, it is possible to include the physicochemical properties of the solutes and solvents in the computations. In a recent work,10 by adding the Abraham solvation parameters of the solutes and the solvent coefficients, a significant improvement has been achieved for the solubility prediction of drugs in nonaqueous binary solvents. The basic quantitative structure property relationship (QSPR) is11 2
+ J26 s 2 + J27 a 2 + J28 b2 + J29 v 2 + J30 a 2b2} ⎛ w w (w − w )2 ⎞ 2 ⎟{J31 + J32 c + J33e + J34 s +⎜ 1 2 1 T ⎠ ⎝ + J35a + J36 b + J37 v + J38ab + J39 c 2 + J40 e 2
2
Ji = J1, i [(c1 − c 2) ] + J2, i [E(e1 − e 2) ] + J3, i [S(s1 − s2) ]
+ J41s 2 + J42 a 2 + J43b2 + J44 v 2 + J45a 2b2}
+ J4, i [A(a1 − a 2)2 ] + J5, i [B(b1 − b2)2 ] 2
s
+ J8 ab + J9 c 2 + J10 e 2 + J11s 2 + J12 a 2 + J13b2
(8)
2
e
⎛ ⎛ B ⎞ B ⎞ ln xm , T = w1⎜A1 + 1 ⎟ + w2⎜A 2 + 2 ⎟ ⎝ ⎠ ⎝ T T⎠ ⎛w w ⎞ + ⎜ 1 2 ⎟{J1 + J2 c + J3e + J4 s + J5a + J6 b + J7 v ⎝ T ⎠
⎛ 5322.321 ⎞⎟ = w1⎜11.121 − ln ⎝ ⎠ T w1w2 ⎛ ⎞ 683.304 ⎟ + 2045.194 + w2⎜1.004 − ⎝ ⎠ T T ww ww + 2265.529 1 2 (w1 − w2) + 2355.547 1 2 T T (w1 − w2)2 xmsat, T
N = 90
c
By simplifying eq 9 for a given solute in the aqueous solutions of cosolvents, the Jouyban−Acree−van’t Hoff model combined with the Abraham parameters of solvent coefficients for calculating the solubility in mixed solvents at various temperatures is expressed as
(7)
R2 = 0.999
solvent
2
+ J6, i [V (v1 − v2) ] + J7, i [A . B(a1b1 − a 2b2) ]
(10)
where Abraham solvent parameters belong to the alcohols and J terms are the model constants computed using a no intercept least-square analysis.
(9) B
DOI: 10.1021/acs.jced.8b00092 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Comment/Reply
solute solubility in water−cosolvent mixtures. Int. J. Pharm. 1999, 177, 93−101. (6) Martinez, F. Performance of the Jouyban-Acree model for correlating the solubility of indomethacin and ethylhexyl triazone in ethyl acetate+ ethanol mixtures. Vitae 2010, 17, 309−316. (7) Patel, S. V.; Patel, S. Prediction of the solubility in lipidic solvent mixture: investigation of the modeling approach and thermodynamic analysis of solubility. Eur. J. Pharm. Sci. 2015, 77, 161−169. (8) Jouyban, A.; Fakhree, M. A.; Acree, W. E., Jr Comment on “Measurement and correlation of solubilities of (Z)-2-(2-aminothiazol4-Yl)-2-methoxyiminoacetic acid in different pure solvents and binary mixtures of water+(ethanol, methanol, or glycol). J. Chem. Eng. Data 2012, 57, 1344−1346. (9) Sardari, F.; Jouyban, A. Solubility of nifedipine in ethanol+ water and propylene glycol+ water mixtures at 293.2 to 313.2 K. Ind. Eng. Chem. Res. 2013, 52, 14353−14358. (10) Jouyban, A.; Acree, W. E. Solubility prediction in non-aqueous binary solvents using a combination of Jouyban-Acree and Abraham models. Fluid Phase Equilib. 2006, 249, 24−32. (11) Jouyban, A.; Soltanpour, S.; Soltani, S.; Chan, H.; Acree, W. E., Jr Solubility prediction of drugs in water-cosolvent mixtures using Abraham solvation parameters. J. Pharm. Pharm. Sci. 2007, 10, 263−277. (12) Acree, W. E., Jr; Grubbs, L. M.; Abraham, M. H. Toxicity and Drug Testing; InTech Publisher: New York, 2012 pp: 100−2. (13) Stovall, D. M.; Givens, C.; Keown, S.; Hoover, K. R.; Barnes, R.; Harris, C.; Lozano, J.; Nguyen, M.; Rodriguez, E.; Acree, W. E., Jr Solubility of crystalline nonelectrolyte solutes in organic solvents: mathematical correlation of 4-chloro-3-nitrobenzoic acid and 2-chloro5-nitrobenzoic acid solubilities with the Abraham solvation parameter model. Phys. Chem. Liq. 2005, 43, 351−360.
All obtained solubility data of 2,6-dihydroxybenzoic acid in the binary solvent mixtures at various temperatures were fitted to eq 10 and the trained version of Jouyban−Acree−van’t Hoff model combined with the Abraham parameters of solvent coefficients, as a QSPR model, after excluding nonsignificant model constant is ⎛ 5632.722 ⎞⎟ ln xm , T = w1⎜11.990 − ⎝ ⎠ T ⎛ 1060.969 ⎞⎟ ⎛⎜ w1w2 ⎞⎟ + w2⎜2.255 − + ⎝ ⎠ ⎝ T ⎠ T {12456.956c 2 + 928.157e 2 + 11450.049a 2} ⎛ w w (w − w2) ⎞ +⎜ 1 2 1 ⎟{−18223.829c 2 ⎝ ⎠ T + 6034.465e 2 + 11213.910a 2} ⎛ w w (w − w )2 ⎞ 2 ⎟{−48148.395c 2 +⎜ 1 2 1 T ⎠ ⎝ + 835.770v}
(11)
The back-calculated MRD% values are 13.8% for solubility of 2,6dihydroxybenzoic acid in {methanol (1) + water (2)} mixture, 12.7% in {ethanol (1) + water (2)} mixture, and 9.8% in {2-propanol (1) + water (2)} mixture. The overall predicted MRD% is 12.1%. In brief, we have corrected a couple of mistakes in the modified Apelblat model curve-fit parameters reported by Wang et al.1 We also provide discussions regarding the Jouyban−Acree−van’t Hoff model and its combined version with the Abraham solvation parameters. The combined version can not only be used as a mathematical representation of some commonly observed phenomena in the solutions, but also provides a generally trained model to predict the solubility of 2,6-dihydroxybenzoic acid in given cosolvent + water mixtures.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Abolghasem Jouyban: 0000-0002-4670-2783 William E. Acree Jr.: 0000-0002-1177-7419 Notes
The authors declare no competing financial interest.
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REFERENCES
(1) Wang, Y.; Chen, Y.; Zhu, P.; Bao, Y.; Xie, C.; Gong, J.; Jiang, X.; Hou, B.; Chen, W. Measurement and correlation of the solubility of 2, 6dihydroxybenzoic acid in alcohols and binary solvents. J. Chem. Eng. Data 2017, 62, 3009−3014. (2) IBM SPSS Statistics Family. http://www.spss.com.hk/software/ statistics/ (accessed 2018). (3) Barzegar-Jalali, M.; Jouyban-Gharamaleki, A. A general model from theoretical cosolvency models. Int. J. Pharm. 1997, 152, 247−250. (4) Acree, W. E. Mathematical representation of thermodynamic properties: Part 2. Derivation of the combined nearly ideal binary solvent (NIBS)/Redlich-Kister mathematical representation from a two-body and three-body interactional mixing model. Thermochim. Acta 1992, 198, 71−79. (5) Jouyban-Gharamaleki, A.; Valaee, L.; Barzegar-Jalali, M.; Clark, B.; Acree, W., Jr Comparison of various cosolvency models for calculating C
DOI: 10.1021/acs.jced.8b00092 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
