Comment/Reply pubs.acs.org/jced
Comment on “Solubility of Trimethoprim in Selected Pure Solvents and (Water + Ethanol/2-Propanol) Mixed-Solvent Systems” William E. Acree, Jr.,*,† Abolghasem Jouyban,‡,§ and Fleming Martinez∥ †
Department of Chemistry, University of North Texas, Denton, Texas 76203-5070, United States Pharmaceutical Analysis Research Center and Faculty of Pharmacy, and §Kimia Idea Pardaz Azarbayjan (KIPA) Science Based Company, Tabriz University of Medical Sciences, Tabriz 51664, Iran ∥ Grupo de Investigaciones Farmacéutico-Fisicoquímicas, Departamento de Farmacia, Facultad de Ciencias, Universidad Nacional de ColombiaSede Bogotá, Cra. 30 No. 45-03, Bogotá D.C., Colombia ‡
ABSTRACT: Mathematical representations reported by Yin and co-workers for the Combined Nearly Ideal Binary Solvent (NIBS)/Redlich−Kister model are carefully examined in regards to the model’s ability to predict the solubility of trimethoprim dissolved in binary aqueous-2-propanol and aqueous-ethanol solvent mixtures. The equation coefficients reported by Yin and coworkers were found to give calculated mole fraction solubilities in the two alcohol monosolvents that exceed unity. The narrow range of solvent composition over which the authors performed solubility measurements does not enable one to derive mathematical correlations for predicting the solubility of trimethoprim in the alcohol-rich solvent composition region. n a recent paper appearing in Journal of Chemical & Engineering Data Yin and co-workers1 reported the solubility of trimethoprim (TMP) in water, in four neat organic solvents (ethanol, ethyl acetate, acetonitrile, and 2-propanol) and in both binary aqueous−ethanol and aqueous−2-propanol solvent mixtures as a function of temperature. In the case of the two binary aqueous−organic solvent mixtures experimental measurements were performed at seven temperatures and at seven mixture compositions including both cosolvents. The authors correlated the mole fraction solubility data of TMP dissolved in the binary solvent mixtures in terms of polynomial equation derived from reported cosolvency models2
I
ln x1 = B0 + B1x 2o + B2 (x 2o)2 + B3(x 2o)3 + B4 (x 2o)4
fraction solubility of TMP in ethanol at 298.45 K would be calculated as ln x1 = −10.826 + 27.777 + 11.481
using the equation coefficients from Table 5 of the published paper by Jin and co-workers.1 Clearly there are serious problems with the equation coefficients as the calculated value of ln x1 = 241.266 leads to a mole fraction solubility that significantly exceeds unity. Mole fraction solubilities cannot exceed unity. The experimental mole fraction solubility that the authors give in Table 6 of their manuscript for TMP dissolved in ethanol at 298.45 K is significantly smaller, x1exp = 0.00091973. The problem is not limited to this one set of equation coefficients. Most of the equation coefficients in Table 5 of the manuscript yield mole fraction solubilities in neat ethanol and neat 2-propanol that are either ridiculously small or that exceed unity. Equation coefficients for TMP dissolved in binary aqueous−ethanol solvent mixtures at 308.15 K, when substituted into eq 1 for xo2 = 1.00, yield a numerical value of
(1)
which was obtained from the Combined Nearly Ideal Binary Solvent (NIBS)/Redlich−Kister equation3 N
ln x1 = x 2o ln(x1)2 + x3o ln(x1)3 + x 2ox3o ∑ Ji (x 2o − x3o)i i=0
(2)
ln x1 = −10.811 + 46.288 − 244.202
by replacing the initial mole fraction composition of component 3 in the binary solvent mixture, xo3, with 1 − xo2 and then expanding the summation term for N = 2.2 Mole fraction solubilities of trimethoprim in the binary mixtures and in the neat organic solvents are denoted as ln x1 and as ln(x1)2 and ln(x1)3, respectively. Numerical values Bi are obtained by regression analysis by curve-fitting the experimental mole fraction solubility data in accordance with eq 1. The purpose of the present commentary is to point out several serious flaws in the authors’ computation of the various Bi curve-fit parameters. The numerical values of the curve-fit equation coefficients do not provide a satisfactory representation of the mole fraction solubilities of trimethoprim in the two neat organic cosolvents. For example, in the case of the solubility of binary aqueous−ethanol solvent mixtures, the mole © 2017 American Chemical Society
(3)
− 362.056 + 574.890
+ 884.620 − 1374.839
(4)
which corresponds to a mole fraction solubility of x1 = exp (−698.944). The experimental mole fraction solubility of TMP in ethanol at this temperature is x1 = 0.00134110. Li and coworkers4 reported a slightly smaller solubility of about x1 = 0.001080 for trimethoprim dissolved in ethanol. There are clearly problems in using the authors’ tabulated equation coefficients pertaining to the Combined NIBS/Redlich−Kister equation to make solubility predictions in the alcohol-rich Received: November 9, 2016 Accepted: January 19, 2017 Published: February 2, 2017 1157
DOI: 10.1021/acs.jced.6b00940 J. Chem. Eng. Data 2017, 62, 1157−1160
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Comment/Reply
solvent region. As an informational note, this is not the first time that members of this research group have reported equation coefficients based on eq 1 that predict solute mole fraction solubilities in the organic cosolvent that exceed unity. Published equation coefficients for azithromycin in binary water + 1,2-propanediol solvent mixtures predict a value of x1 = exp (5925.1) at 289.35 K in 1,2-propanediol.5 We suspect that the reason for why the authors’ calculated equation coefficients fail to accurately describe the measured TMP solubility data in both ethanol and 2-propanol arises because the authors failed to include the experimental solubility data for TMP in the two organic cosolvents in their regression analysis. This would be an extremely serious curve-fitting mistake. Given our observations concerning the failure of the authors’ calculated equation coefficients to reproduce the measured solubility data in the two neat organic cosolvents, we must caution journal readers to exercise great care in using the coefficients to make solubility predictions outside the solvent concentration range of the experimental measurements. The experimental measurements were performed over a very narrow range of solvent composition, namely from xo2 = 0.00 to xo2 = 0.28 for binary aqueous−ethanol mixtures and from xo2 = 0.00 to xo2 = 0.23 for binary aqueous−2-propanol mixtures. Even with the measured solubility of TMP in neat ethanol and neat 2-propanol, the narrow range of solvent composition studied may not allow one to derive a mathematical representation capable of making solubility predictions over the entire composition range as discussed below. We curve-fit the experimental solubility data for TMP dissolved in binary 2-propanol (2) + water (3) mixtures at 298.45 K in accordance with eq 1, and the mathematical correlation that was obtained by including the solubility data in the two monosolvents is ln x1 = −10.432(0.234) +
Figure 1. Predicted values of ln x1 for trimethoprim dissolved in binary 2-propanol + water solvent mixtures based on eq 5 versus the initial mole fraction composition of 2-propanol. The solid circles indicate predicted values used to generate the curve, rather than experimental data points.
Jin and co-workers1 elected to mathematically describe how the solubility of TMP varies with the mole fraction composition of the binary solvent mixture. Volume fraction and mass fraction solvent compositions can also be used in conjunction with the Combined NIBS/Redlich−Kister equation. As part of the present commentary we have also regressed the natural logarithm of the experimental solubility data of TMP in 2propanol + water mixtures at 298.45 K in terms of the mass fraction composition of 2-propanol, wo2, ln x1 = −10.557(0.164) + 14.207(1.743)w2o − 13.138(3.936)(w2o)2 + 1.358(2.396)(w2o)4
35.991(5.196)x 2o
(7)
as experimental measurements covered a mass fraction range from xo2 = 0.00 to wo2 = 0.50, plus the neat solvent 2-propanol. The mass fraction composition range may provide for a better mathematical description. As shown in Figure 2, the calculated values of ln x1 no longer suggest a minimum in the experimental mole fraction solubility of TMP in the alcoholrich binary solvent concentration region. For comparison purposes we have converted the mass fraction compositions
− 88.191(22.643)(x 2o)2 + 54.499(17.842)(x 2o)4 (5)
where the standard errors in the equation coefficients are given in parentheses immediately following the respective equation coefficient. Large relative standard errors are observed both in the (xo2)2 and (xo2)4 coefficients. The SSPS statistical software eliminated the (x2o)3 term from the regression analysis. Equation 5 back-calculates the solubility data with an ARD of 15.3% and exhibits unusual behavior at the larger mole fraction compositions of 2-propanol as shown in Figure 1. At 2propanol mole fraction compositions of xo2 = 0.70 and xo2 = 0.90 the calculated mole fraction solubilities of TMP are x1 = 2.18 × 10−8 and x1 = 1.10 × 10−6, respectively, which give rise to the existence of a minimum solubility in a graph of ln x1 versus xo2. The minimum in the graph may simply be a calculation anomaly as there were no experimental data in this particular concentration region. Without additional solubility data the minimum solubility in the graph cannot be verified. The polynomial representation based on the solubility data for TMP in binary ethanol + water solvent mixtures at 298.45 K, ln x1 = −10.710(0.109) + 30.750(1.991)x 2o − 58.818(7.245)(x 2o)2 + 31.787(5.429)(x 2o)4
Figure 2. Predicted values of ln x1 for trimethoprim dissolved in binary 2-propanol + water solvent mixtures based on eq 7 versus the initial mole fraction composition of 2-propanol. The solid circles indicate predicted values used to generate the curve, rather than experimental data points.
(6)
exhibits similar behavior. Both a maximum and local minimum are predicted in the plot of the ln x1 values based on eq 6 versus xo2. 1158
DOI: 10.1021/acs.jced.6b00940 J. Chem. Eng. Data 2017, 62, 1157−1160
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that were used in generating the predicted ln x1 values into mole fractions in constructing Figure 2. The solvent concentration units used in the mathematical representation can have a significant effect on the predicted values, particularly whenever the set of concentrations covers such a very narrow range of solvent composition. The curve-fitting that we have presented thus far pertains to the polynomial version of the Combined NIBS/Redlich−Kister equation which calculates the solubility of a solute in the solvent mixtures at isothermal condition. We also described the solubility of TMP in binary ethanol + water solvent mixtures at 298.45 K with eq 2 using both the initial mole fraction solvent compositions of ethanol, xo2, ln x1 = x 2o ln(0.00091973) + x3o ln(0.00002485) − 10.592x 2ox3o − 79.764x 2ox3o(x 2o − x3o) −
49.190x 2ox3o(x 2o
−
x3o)2
Figure 4. Predicted values of ln x1 for trimethoprim dissolved in binary ethanol (2) + water (3) solvent mixtures based on eq 9 versus the initial mole fraction composition of ethanol. The solid circles indicate predicted values used to generate the curve, rather than experimental data points.
(8)
and initial mass fraction solvent compositions of ethanol, wo2, ln x1 = w2o ln(0.00091973) + w3o ln(0.00002485)
data measured within a very narrow range of solvent compositions and yet the representations have little if any extrapolative, predictive ability. We use “extrapolative, predictive” rather than “extrapolative” as the observed mole fraction solubility of TMP in ethanol was included in the regression analysis. Technically, we are interpolating between two experimental data points. As noted above the two polynomial representations for TMP dissolved in binary 2propanol + water solvent mixtures, eqs 5 and 7, also predicted very different solubility behavior in the alcohol-rich solvent composition region as shown in Figures 1 and 2. The primary purpose for developing mathematical representations is to make predictions at other experimental conditions. The current data set provides the opportunity for us to illustrate how a small relative absolute deviation between experimental and back-calculated values does not always properly determine the predictive ability of a mathematical representation. The equation coefficients that are reported in Table 5 of the paper by Jin and co-workers1 provide fairly accurate mathematical descriptions of the solubility behavior of TMP over the very narrow range of solvent compositions. When used to predict solubilities outside of the narrow range of composition studied, the mathematical representations give unrealistic values for the mole fraction solubility. The predictive applicability of the derived equations is poor when it comes to making predictions over the entire binary solvent range. Our mathematical correlation, eq 5, gave more realistic solubility predictions at the large organic cosolvent concentrations for TMP dissolved in binary 2-propanol + water mixtures at 298.45 K, but the predictions were still far out of line with other measured values. In proposing mathematical correlations for predicting solubilities we suggest that authors should carefully examine the correlation’s behavior over the entire concentration range to make sure that there are no calculation anomalies that would restrict the correlations applicability. Anomalies if detected need to be disclosed to journal readers so that they do not misuse the correlation to make predictions that are clearly incorrect as would be the case with the coefficients given in Table 5 of the paper by Yin and co-workers. The tabulated equation coefficients yield mole fraction solubilities in neat ethanol and 2-propanol that either exceed unity or are much smaller than the observed values. Given the above
+ 8.939w2ow3o − 8.510w2ow3o(w2o − w3o) − 14.790w2ow3o(w2o − w3o)2
(9)
to see whether this type of regression analysis yielded similar predicted solubility behavior over the entire range of solvent composition. Our calculations are summarized graphically in Figures 3 and 4 as the predicted ln x1 values versus xo2. As
Figure 3. Predicted values of ln x1 for trimethoprim dissolved in binary ethanol (2) + water (3) solvent mixtures based on eq 8 versus the initial mole fraction composition of ethanol. The solid circles indicate predicted values used to generate the curve, rather than experimental data points.
before, the mass fraction compositions that were used in generating the predicted ln x1 values for Figure 4 were converted into mole fractions so that journal readers could visually compare the predicted solubility behavior of eqs 8 and 9. Careful examination of the two figures clearly shows that the predicted solubility behavior is very similar at low ethanol concentrations. Significantly different behavior is observed; however, in the ethanol-rich concentration region where there are no experimental data points. Results of our regression analyses, combined with calculations based on our derived equations, clearly show that it is possible to derive mathematical representations that accurately describe experimental solubility 1159
DOI: 10.1021/acs.jced.6b00940 J. Chem. Eng. Data 2017, 62, 1157−1160
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observations and cautionary warnings we elect not to recommend any mathematical representations. Additional experimental measurements need to be performed in order to better define the solubility behavior of TMP in the alcohol-rich region of both binary solvent systems.
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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 Abolghasem Jouyban: 0000-0002-4670-2783 Notes
The authors declare no competing financial interest.
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REFERENCES
(1) Yin, D.-P.; Liu, M.-X.; Fu, H.-L.; Shu, G.; Zhou, J.-Y.; Qing, W. W.-B. Solubility of trimethoprim in selected pure solvents and (wáter + ethanol/2-propanol) mixed-solvent systems. J. Chem. Eng. Data 2016, 61, 404−411. (2) Barzegar-Jalali, M.; Jouyban-Gharamaleki, A. A general model from theoretical cosolvency models. Int. J. Pharm. 1997, 152, 247− 250. (3) Acree, W. E., Jr. Mathematical representation of thermodynamic properties. Part II. 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. (4) Li, Q.-S.; Li, Z.; Wang, S. Solubility of trimethoprim (TMP) in different organic solvents from (278 to 333) K. J. Chem. Eng. Data 2008, 53, 286−287. (5) Liu, M.-J.; Yin, D.-P.; Fu, H.-L.; Zhang, Y.-L.; Liu, M.-X.; Zhou, J.-Y.; Qing, X.-Y.; Wu, W.-B. Solid-liquid equilibrium of azithromycin in water + 1,2-propanediol solutions from (289.35 to 319.15) K. J. Mol. Liq. 2014, 199, 51−56.
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DOI: 10.1021/acs.jced.6b00940 J. Chem. Eng. Data 2017, 62, 1157−1160
