Comment/Reply pubs.acs.org/jced
Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Comment on “Measurement and Correlation of Solubility of Two Isomers of Cyanopyridine in Eight Pure Solvents from 268.15 to 318.15 K” William E. Acree, Jr.* Department of Chemistry, University of North Texas, 1155 Union Circle Drive #305070, Denton, Texas 76203, United States ABSTRACT: Several mathematical errors in the published paper by Zhang and co-workers are identified. The errors pertain to the published equation coefficients for the modified Apelblat, for the empirical fourth-order polynomial equation, and for the Buchlowski−Ksiazcyak λh. The published curve-fit equation coefficients do not yield the back-calculated mole fraction solubilities that are reported in the published paper. n a recent paper published in This Journal Zang and coworkers1 reported the experimental mole fraction solubility of both 3-cyanopyridine and 4-cyanopryrine in methanol, ethanol, 1-propanol, 1-butanol, 2-methyl-1-propanol, ethyl acetate, acetone, and tetrachloromethane. Solubilities were measured at seven temperatures from 268.15 to 318.15 K. The authors described the variation in the mole fraction solubility, x, with temperature, T, using the modified Apelblat equation,
I
ln x = a + (b/T ) + c ln T
Similarly I substitute the regressed modified Apelblat coefficients (a = −317.3; b = 8929; c = 49.9) for 4cyanopyridine in ethanol into eq 1:
(2)
the Buchowski−Ksiazcyak λh equation, ⎛1 ⎡ 1 − x⎤ 1 ⎞ ln⎢1 + λ = λh⎜ − ⎟ ⎥ ⎣ x ⎦ Tm ⎠ ⎝T
(3)
and the Wilson model. In eqs 1−3, Tm represents the melting point temperature of the cyanopyridine isomer. The curve-fit parameters are denoted as a, b, and c for the modified Apelblat equation, as Bi for the empirical fourth-order polynomial equation, and as λ and h for the Buchlowski-Ksiazcyak λh model. The purpose of the present commentary is to alert journal readers to the fact that many of the authors’ published mathematical representations fail to correctly back-calculate the observed mole fraction solubilities. To illustrate this point I will calculate the mole fraction solubility of 3-cyanopyridine in ethanol at 298.15 K by substituting the authors regressed modified Apelblat model equation coefficients (a = 779.8; b = −38210; c = −114.6) from Table 5 into eq 1 above: ln x = 779.8 − (38210/298.15) − 114.6 ln 298.15
(4)
ln x = 779.8 − 128.157 − 652.945
(5)
ln x = − 1.302
(6)
ln x = − 317.3 + 29.918 + 284.310
(8)
ln x = − 3.072
(9)
x = 0.8049 − (5.521 × 10−3)(298.15) − (0.0440 × 10−4)(298.15)2 + (0.1690 × 10−6)(298.15)3 + (622.5 × 10−3)(298.15)4
(10)
x = 0.8049 − 1.6461 − 0.3911 + 4.4791 + 4.919 × 109 (11)
x = 4.919 × 10
9
(12)
I calculate a mole fraction of 3-cyanopyridine in ethanol much greater than unity. Mole fractions cannot exceed unity. All sets of Bi values in the table give back-calculated mole fraction solubilities that exceed unity. Finally I consider the authors’ mathematical representations based on the Buchowski−Ksiazczak λh model. I calculate the solubility of 3-cyanopyridine in ethanol at 298.15 K by
I calculate a mole fraction solubility of x = 0.272 which is significantly smaller than the back-calculated value of x = 0.338 that the authors gave in Table 2 of their published paper.1 © XXXX American Chemical Society
(7)
I calculate a mole fraction of 4-cyanopyridine in ethanol of x = 0.0463 at 298.15 K. The authors’ back-calculated value in the table of x = 0.0699 is significantly larger. There are clearly problems with the authors’ tabulated equation coefficients for the modified Apelblat model. I next consider the empirical fourth-order polynomial equation. I substitute the authors’ tabulated Bi coefficients for 3-cyanopyridine dissolved in ethanol (B0 = 0.8049; B1 = −5.52 × 10−3; B2 = −0.0440 × 10−4; B3 = 0.1690 × 10−6; B4 = 622.5 × 10−3) into eq 2, along with a temperature of T = 298.15 K:
(1)
an empirical fourth-order polynomial equation, x = B0 + B1T + B2 T 2 + B3T 3 + B4 T 4
ln x = − 317.3 + (8920/298.15) + 49.9 ln 298.15
Received: January 22, 2018 Accepted: May 11, 2018
A
DOI: 10.1021/acs.jced.8b00073 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Comment/Reply
substituting the authors’ regressed coefficients (λ = 0.3834; h = 7007) from Table 7 into eq 3 above: ⎡ ⎛ 1 − x ⎞⎤ ⎟ ln⎢1 + (0.3834)⎜ ⎝ x ⎠⎥⎦ ⎣ ⎛ 1 1 ⎞ ⎟ = (0.3834)(7007)⎜ − ⎝ 298.15 325.05 ⎠
(13)
⎡ ⎛ 1 − x ⎞⎤ ⎟ = 0.74568 ln⎢1 + (0.3834)⎜ ⎝ x ⎠⎥⎦ ⎣
(14)
⎛1 − x ⎞ ⎟ = 1.1078708 (0.3834)⎜ ⎝ x ⎠
(15)
1−x = 2.889595 x
(16)
The melting point temperature of 3-cyanopyridine is 325.05 K. I calculate a mole fraction solubility of 3-cyanolpyridine in ethanol of x = 0.257 at 298.15 K, which is significantly smaller than the value of x = 0.328 that the authors give in Table 2 of their published paper. Readers should exercise caution in using the mathematical representations reported by Zhang and coworkers1 to calculate the solubility of 3-cyanopyridine and 4cyanopyridine. The authors’ calculated curve-fit parameters fail to yield the back-calculated solubilities reported in the paper.
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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) Zhang, R.; Feng, Z.; Ji, H. Measurement and correlation of solubility of two isomers of cyanopyridine in eight pure solvents from 268.15 to 318.15 K. J. Chem. Eng. Data 2017, 62, 3241−3251.
B
DOI: 10.1021/acs.jced.8b00073 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
