Comment/Reply pubs.acs.org/jced
Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Comment on “Determination and Thermodynamic Modeling of Solid−Liquid Phase Equilibrium for Esomeprazole Sodium in Monosolvents and in the (Ethanol + Ethyl Acetate) Binary Solvent Mixtures” William E. Acree, Jr.* Department of Chemistry, 1155 Union Circle Drive #305070, University of North Texas, Denton, Texas 76203, United States ABSTRACT: Errors are found in several of the mathematical representations in the published paper by Zhao and co-workers. Published curve-fit parameters for several of the modified Apelblat model representations yield back-calculated mole fraction solubilities of esomeprazole sodium that exceed unity. Mole fraction concentrations cannot exceed unity. Back-calculated mole fraction solubilities for a mathematical representation, presumably based on the Jouyban−Acree model, were also found to exceed unity. n a recent paper appearing in Journal of Chemical & Engineering Data Zhao and co-workers1 reported the solubility of esomeprazole sodium in five organic monosolvents (ethyl acetate, acetonitrile, methyl isobutyl ketone, ethanol, methanol) and in the (ethanol + ethyl acetate) binary solvent system. Solubilities were determined at temperatures between 278.15 and 328.15 K using a gravimetric method. A one milliliter aliquot of the clear supernatant liquid was transferred into a precisely weighed covered beaker. The covered beaker and contents were quickly weighed, and placed uncovered in a large dryer. The solvent was evaporated leaving a solid residue. The solubility of esomeprazole sodium was calculated from the mass of the solid residue after solvent evaporation, and the mass of saturated solution taken for analysis. The purpose of the present communication is to inform journal readers that many of the mathematical correlations reported in the authors’ published paper are incorrect. For example, the authors used the modified Apelblat model:
I
ln x = A +
B + C ln T T
substituting the curve-fit parameters from Table S2 (A = −21.18; B/100 = 29.01; C = 4.43) into eq 1 above: ln x = −21.18 +
(5)
Again, I calculate mole fraction solubility, x = 9.75 × 10 , which exceeds unity. Similarly, I calculate back-calculate the mole fraction solubility of esomeprazole sodium in acetonitrile at 298.15 K using the authors’ curve-fit parameters of A = −20.77, B/100 = 29.02 and C = 4.45 from Table S2: 5
ln x = −20.77 +
2902 + 4.45 ln 298.15 298.15
(6)
ln x = −20.77 + 9.733 + 25.354
(7)
ln x = 14.32
(8)
This set of curve-fit parameters also yields a mole fraction solubility, x = 1.656 × 106, which exceeds unity. There are clearly problems with the modified Apelblat model equation coefficients reported in the Supporting Information that accompanies the published paper. Given that back-calculated mole fraction solubilities exceed unity, one must wonder if the authors actually performed the back-calculations using their reported curve-fit parameters. The back-calculations are easy to perform, and the errors would be immediately spotted. Unfortunately the problems in the published paper1 are not limited to this one mathematical representation. Backcalculations based on the mathematical representation of
(2)
Careful examination of eq 2 reveals that every term on the right-hand side of the equation is positive. Equation 2 will thus yield a numerical value of ln x > 0, irrespective of the solution temperature. Mole fraction concentrations cannot exceed unity. I next back-calculate the mole fraction solubility of esomeprazole sodium in ethyl acetate at 298.15 K by © XXXX American Chemical Society
(4)
ln x = 13.79
(1)
2917 + 0.64 ln T T
(3)
ln x = −21.18 + 9.730 + 25.240
to describe the variation in the mole fraction solubility, x, with temperature, T. Unfortunately the numerical values of the authors’ calculated curve-fit parameters (A, B, and C) fail to describe the measured solubility data. To illustrate this point, I back-calculate the solubility of esomeprazole sodium in methyl isobutyl ketone at 298.15 K by substituting the curve-fit parameters from Table S2 (A = 3.37; B/100 = 29.17; C = 0.64) into eq 1 above: ln x = 3.37 +
2901 + 4.43 ln 298.15 298.15
Received: January 6, 2018 Accepted: February 8, 2018
A
DOI: 10.1021/acs.jced.8b00022 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data ln x =
Comment/Reply
D0 + D1 + D2 ln T + D3x III T 2 3 4 D x + D5x III + D6x IIII + D7x III + 4 III + D8x III ln T T
in monosolvents and in the (ethanol + ethyl acetate) binary solvent mixtures. J. Chem. Eng. Data 2017, 62, 1965−1972.
(9)
also have serious problems. Equation 9 was used to describe the solubility in the binary (ethanol + ethyl acetate) solvent system, and was presumably obtained from the Jouyban−Acree model. The Supporting Information that accompanies the published paper gave the equation as D1 + D2 ln T + D3x III T 2 3 4 D x + D5xIII + D6x IIII + D7x III + 4 III + D8x III ln T T
ln x = D0 +
(10)
where D0 thru D8 are the curve-fit parameters for this particular model. To show the problems with eqs 9 and 10 I calculate the mole fraction solubility of esomeprazole sodium at 298.15 in the binary (ethanol + ethyl acetate) solvent system at a solvent composition of xIII = 0.0. Only the first two terms (eq 9) and/ or first three terms (eq 10) on the right-hand side of the respective equations contribute to the calculation whenever xIII = 0.0. Substitution of the authors’ calculated curve-fit parameters (D0 = −1.81; D1 = −82.20; D2 = 26.19) into eqs 9 and 10 yields ln x =
−1.81 − 82.20 + 26.19 ln 298.15 298.15
(11)
ln x = −0.282 + 149.220
(12)
ln x = 148.938
(13)
and ln x = −1.81 −
82.20 + 26.19 ln 298.15 298.15
(14)
ln x = −1.81 − 0.276 + 149.220
(15)
ln x = 147.134
(16)
at xIII = 0.0. Both equations give back-calculated mole fraction solubilities that significantly exceed unity at xIII = 0.0. In summary there are serious problems with several of the mathematical representations in the published paper by Zhao and co-workers.1 For several of the mathematical representations the curve-fit parameters reported in the Supporting Information fail to correctly back-calculate the observed solubility data. It is recommended that authors exercise caution when using the reported curve-fit parameters.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Fax: 940-565-4318. ORCID
William E. Acree Jr.: 0000-0002-1177-7419 Notes
The author declares no competing financial interest.
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REFERENCES
(1) Zhao, W.; Yang, W.; Hao, J. Determination and Thermodynamic modeling of solid−liquid phase equilibrium for esomeprazole sodium B
DOI: 10.1021/acs.jced.8b00022 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
