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Comment on “Measurement and Correlation of the Solubility of Maltitol in Different Pure Solvents, Methanol−Water Mixtures, and Ethanol−Water Mixtures” Abolghasem Jouyban,†,‡ Fleming Martinez,§ and William E. Acree, Jr.*,∥ †

Pharmaceutical Analysis Research Center and Faculty of Pharmacy, Tabriz University of Medical Sciences, Tabriz 51664, Iran 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 Colombia − Sede Bogotá, Cra. 30 No. 45-03, Bogotá D.C. Colombia ∥ Department of Chemistry, University of North Texas, Denton, Texas 76203-5070, United States ‡

ABSTRACT: Mathematical representations reported by Li et al. for a number of cosolvency models are carefully examined concerning the models’ abilities to predict the solubility of maltitol in binary aqueous mixtures of methanol and ethanol at various temperatures. Some further recommendations on computational methods are also provided to be employed in the future research works. Preferential solvation of the solution was also investigated to provide better understanding of the dissolution process.

I

S4 of the published paper by Li and co-workers,1 when substituted into eq 1 give calculated values of ln xA that significantly exceed unity for the solubilities of maltitol in neat ethanol. Mole fraction solubilities cannot exceed unity. There are clearly problems in using the authors’ tabulated equation coefficients pertaining to eq 1 to make solubility predictions in the alcohol-rich solvent region. The reason for why the authors’ calculated equation coefficients fail to predict maltitol solubility in ethanol arises because Li et al. did not possibly include the solubility data for maltitol in neat organic cosolvents in their regression analysis. This would be a serious curve-fitting mistake. The calculations according to eq 1 were repeated for solubility of maltitol in ethanol + water mixtures at T = 298.15 K by including the monosolvent data and without these data points, and the obtained models are

n a recent paper appearing in This Journal Li and coworkers1 reported the solubility of maltitol in water, methanol, N,N-dimethylformamide, ethanol, and 2-propanol and in two binary aqueous mixtures of methanol and ethanol at various temperatures. In the case of the two binary aqueousalcoholic solvent mixtures experimental measurements were performed at seven temperatures and at nine mixture compositions including both cosolvents. The authors correlated the mole fraction solubility data of maltitol in the binary solvent mixtures in terms of a polynomial equation derived from previously reported cosolvency models2 ln xA = B0 + B1x Bo + B2 (x Bo)2 + B3(x Bo)3 + B4 (x Bo)4

(1)

which was obtained from a number of cosolvency models including the combined nearly ideal binary solvent (NIBS)/ Redlich−Kister equation3

ln xA = −2.886 − 3.094x Bo − 4.437(x Bo)2

N

ln xA = x Bo ln(xA )B + xCo ln(xA )C + x BoxCo ∑ S i(x Bo − xCo)i

and ln xA = −3.426 + 3.089x Bo − 19.908(x Bo)2 + 10.265(x Bo)3

i=0

(2)

(4)

by replacing the initial mole fraction composition of component C in the binary solvent mixture, xoC, with 1 − xoB and then expanding the summation term for N = 2.2 Mole fraction solubilities of the binary mixtures and in the neat organic solvents are denoted as ln xA and as ln (xA)B and ln (xA)C, respectively. Numerical values of Bi are obtained by regression analysis by curve-fitting the experimental mole fraction solubility data in accordance with eq 1. The purpose of this report 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 maltitol in the two neat organic cosolvents. For example, as shown in the eighth column of Table 1 of this manuscript, the equation coefficients from Table © XXXX American Chemical Society

(3)

in which, there is no agreement between our computations with those reported by Li et al. One should consider that the solubility pattern in ethanol + water looks slightly unusual when comparing with the previously observed patterns. In eqs 3 and 4, the model constants with a p value >0.1 were excluded from the model. The predicted ln xA in ethanol at 298.15 K was −9.98 against 60.01 of Li et al.1 We curve-fit the experimental solubility data for maltitol dissolved in ethanol (B) + water (C) mixtures at various temperatures in accordance with eq 1, and the equation Received: February 22, 2017 Accepted: May 5, 2017

A

DOI: 10.1021/acs.jced.7b00204 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Comment/Reply

Table 1. Recalculated Parameters of eq 1 for Describing the Solubility of Maltitol in Ethanol + Water Mixtures, the Calculated Li Solubility in Ethanol Using Our Recalculated parameters (ln (xA)Cal C ) and the Parameters Reported by Li et al. (ln (xA)C ), and the Corresponding Experimental Values

a

T/K

B0

B1

B2

298.15 303.15 308.15 313.15 318.15 323.15

−2.886 −2.766 −2.590 −2.366 −2.197 −2.089

−3.094 −2.706 −2.490 −2.183 −1.571 −1.093

−4.437 −4.740 −4.954 −5.274 −5.942 −6.311

B3 NS NS NS NS NS NS

a

B4

ln (xA)Cal C

ln (xA)Li C

ln (xA)Exp C

NS NS NS NS NS NS

−10.417 −10.212 −10.034 −9.823 −9.710 −9.493

60.0126 31.0151 37.6063 −8.9488 95.3924 93.6395

−10.23 −10.03 −9.86 −9.69 −9.51 −9.27

Not significant.

coefficients were obtained by including the solubility data in the two monosolvents. We list in Table 1 the equation coefficients that we obtained. The p values for the B3 and B4 coefficients were more than 0.1, therefore these coefficients were not able to improve the prediction capability of the model. The SSPS statistical software eliminated the (xoB)3 and (xoB)4 terms from the regression analysis. The solubility of maltitol in binary ethanol + water mixtures at various temperatures was mathematically described using eq 2, and the obtained model constants along with the %ARDs were listed in Table 2 of this manuscript.

calculated value of the mole fraction solubility of maltitol in ethanol that greatly exceeds unity, whereas the obtained ln xA value using these constants (eqs 10−14) is −10.23. To correlate the solubility of maltitol in solvent mixtures at various temperatures, Li et al. employed a modified form of the combined version of the Jouyban−Acree and Apelblat equations as

Table 2. Calculated Parameters of the CNIBS/R-K Model for Describing the Solubility of Maltitol in Ethanol + Water Mixtures

(15)

T/K

S0

S1

S2

%ARD

298.15 303.15 308.15 313.15 318.15 323.15

4.165 4.491 4.753 5.079 5.803 6.213

−2.496 −2.478 −2.358 −1.869 −2.921 −3.170

−4.703 −4.135 −3.816 −2.770 −4.106 −5.201

10.5 8.6 6.9 5.6 6.2 6.2

xo A2 + A3 ln(T ) + A4 x Bo + A5 B T T o 2 o 3 o 4 (x ) (x ) (x ) + A 6 B + A 7 B + A8 B + A 9x Bo ln(T ) T T T

ln xA, T = A1 +

.Our previous observations showed that significant contributions of a number of A terms of eq 15 are questionable. In addition, the reported model constants in Table 5S resulted in nonacceptable predictions. To show this, when xoB = 1.0 and T = 298.15 K, the predicted solubility of maltitol in ethanol is 13542.71 + 57.7699 × ln(298.15) 298.15 3228.8 1048.943 9759.2 + 88.35621 − + − 298.15 298.15 298.15 7411.458 + − 13.4498 × ln(298.15) = 749.088 (16) 298.15

ln xA, T = 377.849 +

According to the basic derivation of eq 1 from eq 2, the B terms are2 B0 = ln(xA )C

(5)

B1 = ln(xA )B − ln(xA )C + S0 − S1 + S2

(6)

B2 = −S0 + 3S1 − 5S2

(7)

B3 = −2S1 + 8S2

(8)

B4 = −4S2

(9)

By considering xoB = 0.0 and T = 298.15 K, the predicted solubility of maltitol in water is ln xA, T = 377.849 +

Both calculated values are unacceptable in that mole fraction solubilities must be less unity. In addition, Li et al.1 have used a modified form of the combined version of the Jouyban−Acree and van’t Hoff equations as xo (x o)2 C2 + C3x Bo + C4 B + C5 B T T T o 3 o 4 (x ) (x ) + C6 B + C7 B T T

ln xA, T = C1 +

B1 = −10.23 + 2.79 + 4.165 + 2.496 − 4.703 = − 5.482 (11) (12)

B3 = 2 × 2.496 − 8 × 4.703 = − 32.632

(13)

B4 = 4 × 4.703 = 18.812

(14)

(17)

= 752.56

.Substitution of these terms for the obtained values for solubility data of maltitol in ethanol + water mixtures at 298.15 K for eq 2, yielded the B terms as B0 = −2.79 (10)

B2 = −4.165 − 3 × 2.496 + 5 × 4.703 = 11.862

13542.71 + 57.7699 × ln(298.15) 298.15

(18)

for representing the solubility data with respect to solvent composition and temperature effects. The predicted solubilities of maltitol in ethanol and water at 298.15 K employing Li et al. reported model constants in Table S6 were −3.30 and −8.76, respectively. The corresponding experimental values were −2.79 and −10.23. These predictions are more rational than those calculated from eqs 16 and 17; however, the difference

which differ significantly from the Bi values reported in Table 4S of Li et al.1 As noted above, the coefficients of Li et al. give a B



Comment/Reply

and 323.15 K (totally seven data points) and obtained a trained version of the model as

between the experimental and calculated values is still much larger than would be expected. In another recent work from the same research group4 similar computations were employed for solubility of L-histidine in binary solvent mixtures, which needs further attention. In addition, the measured solubility4 was not in the full composition range of the binary solvents which could produce less accurate results as discussed in a recent work.5 To provide more accurate and more acceptable predictions, we recommend to use the original versions of the Jouyban− Acree model and its combined version with the van’t Hoff equation. The original version of the Jouyban−Acree model is6 ln xA, T = x Bo ln(xA )B, T + xCo ln(xA )C, T +

⎛ 3698.868 ⎞⎟ ln xA, T = x Bo⎜2.174 − ⎝ ⎠ T o o ⎛ 2741.223 ⎞⎟ 1151.686x BxC + xCo⎜6.406 − + ⎝ ⎠ T T o o o o 929.459x BxC(x B − xC) 33.534x BoxCo(x Bo − xCo)2 − − T T

x BoxCo T

(23)

which is able to predict the solubility of maltitol at other solvent compositions of ethanol + water mixtures at various temperatures with the %ARD of 18.7%. Mathematical correlations that describe how the solute solubility varies with solvent composition can be used to examine the preferential solvation by the solvent components around the dissolved solute molecules. The preferential solvation parameter of maltitol (compound A) by the cosolvent (compound B) in the cosolvent (B) + water (C) mixtures is defined as13,14

N

∑ J i(xBo − xCo)i i=0

and its combined version with the van’t Hoff equation is

(19) 7,8

⎛ ⎛ β ⎞ β ⎞ ln xA, T = x Bo⎜αB + B ⎟ + xCo⎜αC + C ⎟ T⎠ T⎠ ⎝ ⎝ x ox o + B C T

N

∑ J i(xBo − xCo)i i=0

L δx B,A = x B,A − x B = −δxC,A

(20)

(24)

where, xLB,A is the local mole fraction of cosolvent (B) in the environment near to the maltitol molecules. The solute is preferentially solvated by cosolvent (B) whenever the numerical value of δxB,A is greater than zero. If this parameter is negative maltitol is preferentially solvated by water (C). Numerical values of δxB,A are determined from the inverse Kirkwood-Buff integrals (IKBI) for the individual solvent components as shown in eqs 25 and 26

.When eq 19 is trained using the solubility data of maltitol in ethanol + water mixtures at various temperatures, the obtained model is 1570.991x BoxCo T o o o o o o o 788.845x BxC(x B − xC) 1278.048x BxC(x B − xCo)2 − − T T

ln xA, T = x Bo ln(xA )B, T + xCo ln(xA )C, T +

(21)

G B,A = RTκT − VA + xCVCD/Q

(25)

which back-calculates the solubility data with the %ARD of 12.5%. By calculating α and β terms for neat ethanol and water, and substituting in eq 21, one obtains

GC,A = RTκT − VA + x BVBD/Q

(26)

where κT is the isothermal compressibility of the solvent mixtures (expressed in units of GPa−1), VB and VC are the partial molar volumes of the cosolvent (B) and water (C), respectively, and VA is the partial molar volume of maltitol. The function D is the derivative of the standard molar Gibbs energies of transfer of maltitol (A) from neat water (C) to the cosolvent (B) + water (C) mixtures, with respect to the mole fraction of cosolvent (B) in the mixtures. The second terms in the function Q contains the second derivative of the excess molar Gibbs energy of mixing of the two solvents with respect to the mole fraction of water (C) in the mixtures:

⎛ x Bo⎜1.811 ⎝

3594.008 ⎞⎟ ln xA, T = − ⎠ T o o ⎛ 2901.908 ⎞⎟ 1570.991x BxC + xCo⎜6.908 − + ⎝ ⎠ T T o o o o 788.845x BxC(x B − xC) 1278.048x BoxCo(x Bo − xCo)2 − − T T (22)

which back-calculates the solubility data with the %ARD of 13.1%. Equation 22 is able to predict the solubility of maltitol in all possible solvent compositions of ethanol + water mixtures at various temperatures including in neat ethanol and water without the requirement of any further experimental data, whereas eq 21 requires the solubility of maltitol in the monosolvents at each temperature of interest. It is also possible to train eq 20 employing a minimum number of experimental data, and then predict the rest of data points using the trained model. Our earlier results9−12 showed that the solubility data in xoB of 0.3, 0.5, and 0.7 provided the most reliable J values. Owing to the linear nature of the van’t Hoff equation, two data points in each monosolvent could be used to compute α and β terms of the equation. Therefore, we employed solubility data of maltitol in xoB of 0.2811, 0.4771, and 0.7787 (closest values to the above-mentioned fractions), and xoB of 0.0 and 1.0 at 298.15

o ⎛ ∂Δtr GA,C ⎞ →B+A D=⎜ ⎟ o ∂x B ⎝ ⎠T , p

(27)

⎛ ∂ 2G Exc ⎞ B+C ⎟ Q = RT + x BxC⎜ o2 ⎝ ∂xC ⎠T , p

(28)

The numerical values of the preferential solvation parameter of maltitol by cosolvent (B) were calculated at each solvent composition from the IKBI method as follows: δx B,A = C

x BxC(G B,A − GC,A ) x BG B,A + xCGC,A + Vcor

(29)



Comment/Reply

water (C) mixtures at 298.15 K. These values were calculated from the mole fraction solubility data reported by Li et al.1 through the following expression:

The correlation volume (Vcor) used in eq 29 was obtained by means of the following expression:15 L L Vcor = 2522.5(rA + 0.1363(xB,A VB + xC,A VC)1/3 − 0.085)3

⎛ xA,C ⎞ o ⎟⎟ Δtr GA,C ⎜ → B + C = RT ln⎜ ⎝ xA,B + C ⎠

(30)

where rA denotes the molecular radius of the solute (in nm) calculated by using eq 31 and NAv refers to Avogadro’s number. ⎛ 3·1021V ⎞1/3 A ⎟ r3 = ⎜ ⎝ 4πNAv ⎠

(32)

Δtr GoA,C→B+C

values were correlated according to the following fourth-order polynomials: o o o2 o3 Δtr GA,C → B + C = − 0.06 + 18.92x B − 44.96x B + 82.14x B

(31)

Several interactions were required to obtain the final numerical value of the definitive correlation volume. The iterations were accomplished by replacing δxB,A in the eq 24 to calculate xLB,A until a nonvariant value of Vcor was obtained. Figure 1 depicts the Gibbs energy of transfer behavior of maltitol (A) from neat water (C) to the various cosolvent (B) +

− 42.75x Bo4

(33)

o o o2 o3 Δtr GA,C → B + C = 0.44 + 7.80x B − 8.00x B + 51.75x B

− 33.58x Bo4

(34) 2

The determination coefficients (r ) were 0.9991 (eq 33) and 0.9976 (eq 34), for methanol (B) + water (C) and ethanol (B) + water (C) mixtures, respectively. The D values reported in Tables 3 and 4 were calculated from the first derivative of the polynomial models, solved according to the cosolvent proportions. The values of Q, RTκT, VB and VC of methanol (B) + water (C), and ethanol (B) + water (C) mixtures were taken from the literature.14,16 The molar volume of maltitol (A) was calculated as 203.73 cm3 mol−1 from the molar mass and reported density (1.69 g cm−3). The solute radius value (rA) was calculated to be 0.432 nm. The correlation volume was iterated three times by using eqs 24, 29, and 30 to obtain the values reported in Tables 3 and 4. The last columns of these tables list the preferential solvation parameters of maltitol by both cosolvents (component 1), δxB,A. The values of δxB,A vary nonlinearly with the alcohol proportion in these aqueous mixtures (Tables 3 and 4, Figure 2). In water-rich mixtures, the addition of methanol to water makes positive the δxB,A values of maltitol from pure water to

Figure 1. Gibbs energy of transfer of maltitol (A) from neat water (C) to cosolvent (B) + water (C) mixtures at 298.15 K. ●: methanol (B) + water (C); ○: ethanol (B) + water (C).

Table 3. Some Properties Associated to Preferential Solvation of Maltitol (A) in Methanol (B) + Water (C) Mixtures at 298.15 K

a o xB

xoBa

D/kJ mol−1

GB,A/cm3 mol−1

GC,A/cm3 mol−1

Vcor/cm3 mol−1

100δxB,A

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00

18.93 15.02 12.23 10.40 9.43 9.17 9.51 10.31 11.44 12.78 14.19 15.56 16.74 17.62 18.07 17.95 17.13 15.50 12.92 9.26 4.40

−64.5 −99.6 −121.9 −135.5 −142.5 −144.7 −143.4 −139.9 −135.6 −132.1 −130.9 −132.8 −138.1 −146.1 −155.9 −166.4 −176.5 −185.6 −192.9 −198.0 −200.6

−202.6 −191.4 −183.9 −177.5 −170.5 −160.9 −147.1 −127.8 −102.4 −71.5 −37.1 −2.7 27.8 50.9 64.0 65.8 55.7 33.1 −3.1 −55.2 −128.3

884 910 934 957 980 1003 1025 1047 1069 1089 1110 1130 1152 1174 1199 1225 1253 1283 1313 1343 1372

0.00 0.60 0.74 0.68 0.55 0.36 0.09 −0.30 −0.84 −1.52 −2.29 −3.05 −3.69 −4.08 −4.17 −3.90 −3.31 −2.47 −1.50 −0.59 0.00

is the mole fraction of methanol (B) in the methanol (B) + water (C) mixtures free of maltitol (A). D



Comment/Reply

Table 4. Some Properties Associated to Preferential Solvation of Maltitol (A) in Ethanol (B) + Water (C) Mixtures at 298.15 K

a o xB

xoBa

D/kJ mol−1

GB,A/cm3 mol−1

GC,A/cm3 mol−1

Vcor/cm3 mol−1

100δxB,A

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00

7.80 7.37 7.62 8.44 9.74 11.41 13.35 15.46 17.64 19.80 21.82 23.61 25.07 26.10 26.59 26.45 25.58 23.86 21.22 17.53 12.71

−145.7 −145.6 −141.9 −135.1 −125.9 −115.2 −103.8 −92.2 −80.7 −69.6 −59.4 −50.8 −45.6 −46.5 −57.5 −81.2 −115.1 −150.2 −177.4 −193.7 −200.9

−202.6 −193.6 −182.1 −165.8 −142.5 −109.7 −65.3 −6.3 70.4 169.2 295.0 452.3 641.6 851.1 1043.7 1151.2 1105.5 903.1 617.9 335.1 99.8

884 929 973 1016 1057 1095 1132 1165 1196 1225 1250 1274 1297 1321 1350 1391 1446 1515 1586 1649 1700

0.00 0.31 0.45 0.46 0.29 −0.10 −0.77 −1.73 −3.01 −4.59 −6.48 −8.59 −10.81 −12.86 −14.25 −14.29 −12.40 −8.82 −4.81 −1.69 0.00

is the mole fraction of ethanol (B) in the ethanol (B) + water (C) mixtures free of maltitol (A).

0.86 for water, methanol, and ethanol, respectively.19 Finally, Figure 2 also shows that the preferential solvation behavior of maltitol is similar regarding those exhibited by xylitol and arabinose in ethanol (B) + water (C) mixtures at 298.15 K.13,14 The combined NIBS/R-K and Jouyban−Acree models are often used to mathematically describe how the solubility behavior of crystalline nonelectrolyte solutes varies with solvent composition and temperature in both binary aqueous−organic solvent mixtures and binary organic solvent mixtures. The models are commonly used in the chemical and pharmaceutical industries. In the past two years there have been several incorrect applications5,20−26 of the models that have led to calculated mole fraction solubilities that have exceeded unity in one or both of the monosolvents used to prepare the binary solvent mixture. Several of the incorrect applications20,21,23 have involved solubility studies in which the authors performed experimental measurements in a very narrow range of binary solvent composition. To prevent future occurrences we suggest that if possible research groups using the Combined NIBS/R-K and Jouyban−Acree models should perform solubility measurements over the entire range of binary solvent composition, including both monosolvents. Moreover, we recommend that researchers quickly check for possible errors in the regressed equation coefficients by calculating the solute solubility in both monosolvents at all temperatures studied. If the calculated solubilities exceed unity then there are problems with the calculated equation coefficients or experimental design. Mathematical correlations should be reported only if the correlations have predictive ability over the entire range of solvent composition, including both monosolvents.

Figure 2. δxB,A values of some polyhydroxyl compounds (A) in cosolvent (B) + water (C) mixtures at 298.15 K. ●: maltitol (A) in methanol (B) + water (C); ○: maltitol (A) in ethanol (B) + water (C); □: xylitol (A) in ethanol (B) + water (C); △: arabinose (A) in ethanol (B) + water (C).

the mixture with xB = 0.32 reaching a maximum of 7.4 × 10−3 in the mixtures with xB = 0.10, whereas, the positive values of δxB,A are observed in the interval 0 < xB < 0.23 with a maximum in xB = 0.15 (δxB,A = 4.6 × 10−3). Nevertheless, these δxB,A values could not be attributed to preferential solvation effects by the alcohols because they are lower than 1.00 × 10−2, and thus, they could be due to uncertainties propagation in the IKBI calculations.17,18 Otherwise, from these alcohol proportions up to neat alcohols, the δxB,A values are negative, and hence, maltitol is preferentially solvated by water in alcohol-rich mixtures in both cosolvent systems. Moreover, the magnitude of preferential solvation by water is clearly higher in ethanolic mixtures regarding those with methanol. In this way, maltitol could act as a Lewis base due to the free electron pairs in the oxygen atoms of its hydroxyl and cyclic ether groups to interact with the acidic hydrogen atoms of water. This is because water is more acidic than both alcohols as described by their Kamlet−Taft hydrogen-bond donor parameters, that is, α = 1.17, 0.98, and

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax: 940-565-4318. ORCID

Abolghasem Jouyban: 0000-0002-4670-2783 William E. Acree Jr.: 0000-0002-1177-7419 E



Comment/Reply

Notes

(20) Yin, D.-P.; Liu, M.-X.; Fu, H.-L.; Shu, G.; Zhou, J.-Y.; Qing, X.y.; Wu, W.-B. Solubility of trimethoprim in selected pure solvents and (water + ethanol/2-propanol) mixed-solvent systems. J. Chem. Eng. Data 2016, 61, 404−411. (21) Yu, C.; Huang, Z.; Zeng, Z.; Xue, W. Thermodynamic models for correlation of solubility of hexaquocobalt(II) bis(p-toluenesulfonate) in liquid mixtures of water and ethanol from 288.15 to 333.15 K. J. Solution Chem. 2016, 45, 395−409. (22) Acree, W. E., Jr.; Jouyban, A.; Martinez, F. Comments on “Thermodynamic models for correlation of solubility of hexaquocobalt(II) bis(p-toluenesulfonate) in liquid mixtures of water and ethanol from 288.15 to 333.15 K. J. Solution Chem. 2017, 46, 734− 737. (23) Huang, Z.; Yu, C.; Xue, W.; Lin, F.; Zeng, Z. Solubility and dissolution thermodynamics of hexaquoiron(III)tris(p-toluenesulfonate) in (ethanol+water) binary mixtures within 291.15−333.15 K. Korean J. Chem. Eng. 2017, 34, 206−213. (24) Huang, Q.; Xie, C.; Li, Y.; Su, N.; Lou, Y.; Hu, X.; Wang, Y.; Bao, Y.; Hou, B. Thermody-namic equilibrium of hydroxyacetic acid in pure and binary solvent systems. J. Chem. Thermodyn. 2017, 108, 76− 83. (25) Acree, W. E., Jr. Commentary on Thermodynamic equilibrium of hydroxyacetic acid in pure and binary solvent systems. J. Chem. Thermodyn. 2017, 108, 199−201. (26) 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.

The authors declare no competing financial interest.

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REFERENCES

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