Comment/Reply pubs.acs.org/jced
Cite This: J. Chem. Eng. Data 2018, 63, 3157−3159
Comment on “Measurement and Correlation of the Solubility of Florfenicol Form A in Several Pure and Binary Solvents” Jiao Chen, Min Zheng, Gaoquan Chen, and Hongkun Zhao*
J. Chem. Eng. Data 2018.63:3157-3159. Downloaded from pubs.acs.org by DURHAM UNIV on 09/06/18. For personal use only.
College of Chemistry & Chemical Engineering, YangZhou University, YangZhou, Jiangsu 225002, People’s Republic of China ABSTRACT: Errors are found relating to the published equation coefficients of Zhang and co-workers [J. Chem. Eng. Data 2018, DOI: 10.1021/acs.jced.8b00043.] for correlating the solubility of florfenicol form A in eight pure organic solvents (propionic acid, ethanol, 1-propanol, 1-butanol, 2-propanol, 2-methyl-1-propanol, 3-methyl-1-butanol, and 2-ethyl-1-hexanol) with the nonrandom two-liquid (NRTL) model. The back-calculated values with the published equation coefficients for the NRTL model are not the mole fraction solubility as stated in the published paper.
I
In eqs 1−5, x1 is the mole fraction solubility of the solute; Δgij are the interaction parameter (J·mol−1). αij denote the adjustable empirical parameters in the NRTL model; ΔfusH is the molar enthalpy of fusion of the pure solute at the melting point, Tm; R is the gas constant (8.314 J·K−1·mol−1), and γ1 is the activity coefficient of the solute in the saturated solution. The objective of this communication is to point out some errors in the authors’ mathematical representations. In the case of the NRTL model, one can easily observes that the equation coefficients of NRTL model that the authors report in Table 6 of their published work yield the solubility that is different from the experimental values. The authors measured the melting point and melting enthalpy of florfenicol form A, which were 425.15 K and 18.98 kJ·mol−1, respectively.1 On the basis of the parameters’ values of the authors’ statement in Table 6, we carried out back-calculation in terms of the equation coefficients tabulated in Table 6 to demonstrate the error of equation coefficients in the NRTL model. The mole fraction solubility needs iteration because it depends on the activity coefficient of the solute. Here we use the graphical method to obtain the solubility value at a given temperature. Take the florfenicol form A + ethanol system as a sample. The evaluated activity coefficients (ln γ1) using eq 1 should be equal to that calculated using eq 5. If one substitutes the numerical values of the NRTL model coefficients tabulated in Table 6 into eqs 1 and 5, the functions f(x) and g(x) are obtained and expressed as follows. ÄÅ ÉÑ2 ÅÅ 1083.17 ÄÅÅ ÅÅ ÅÅexp −0.47 × 1083.17 ÑÑÑ Å Å ÑÑÖ RT Å RT Å Ç f (x) = (1 − x)2 ÅÅÅ Ä É2 ÅÅÅ ÅÅÅÅx + exp −0.47 × 1083.17 (1 − x)ÑÑÑÑ ÅÅ ÅÅ ÑÑÖ RT ÅÇ Ç É Ä É Ñ 14087.48 Å ÅÅexp −0.47 × 14087.48 ÑÑÑ ÑÑÑ Å ÑÑ ÑÑ RT Å RT ÅÇ ÑÖ ÑÑ + Ä ÅÅ ÑÉÑ2 ÑÑÑ 14087.48 ÅÅÅ1 − x + exp − 0.47 × RT x ÑÑÑ ÑÑÑÑ ÅÇ ÑÖ ÑÖ (6)
n the recent work published in the Journal of Chemical & Engineering Data, Zhang and co-workers reported the mole
Figure 1. Plots of f(x) and g(x) versus x for ethanol at 323.15 K.
fraction solubility of florfenicol form A in eight pure organic solvents (propionic acid, ethanol, 1-propanol, 1-butanol, 2propanol, 2-methyl-1-propanol, 3-methyl-1-butanol, and 2ethyl-1-hexanol) and three binary solvents (dimethyl sulfoxide + ethanol, dimethyl sulfoxide +1-propanol, and dimethyl sulfoxide +1-butanol) at temperatures ranging from 283.15 to 323.15 K determined by the laser dynamic method.1 The mole fraction solubility (x) with temperature, T, was correlated in terms of the nonrandom two-liquid (NRTL) model: ÉÑ ÄÅ 2 ÑÑ Å τ21G21 τ12G12 2Å ÑÑ Å ln γ1 = x 2 ÅÅÅ + Ñ ÅÅÇ (x1 + G21x 2)2 (x 2 + G12x1)2 ÑÑÑÖ (1) Gji = exp( −αjiτji)
(2)
αij = αji
(3)
τij =
gij − gjj
=
(
(
( (
Δgij
(4) RT RT The activity coefficient (ln γ1) in eq 1 is computed by using eq 5.
ln γ1 =
ΔfusH ijj 1 1 yz − zzz − ln x1 jjj R k Tm T z{
© 2018 American Chemical Society
)
)
) )
Received: May 26, 2018 Accepted: July 11, 2018 Published: July 24, 2018
(5) 3157
DOI: 10.1021/acs.jced.8b00435 J. Chem. Eng. Data 2018, 63, 3157−3159
Journal of Chemical & Engineering Data
Comment/Reply
Table 1. Comparison of the Back-Calculated Solubility Values (103 x) of Florfenicol Form A in Neat Solvents Using the NRTL Model T/K 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15
Zhang1
this work
Zhang1
Zhang1
this work
this work
Zhang1
this work
Ethanol
1-Propanol
1-Butanol
2-Propanol
1.587 30.91 1.977 35.60 2.450 40.80 3.022 46.58 3.715 52.96 4.554 59.99 5.568 67.72 6.800 76.21 8.303 85.49 2-Methyl-1-propanol 0.3223 28.23 0.4105 32.69 0.5195 37.68 0.6534 43.26 0.8174 49.45 1.018 56.33 1.262 63.94 1.559 72.34 1.920 81.60
1.039 31.69 1.318 36.67 1.666 42.24 2.101 48.47 2.648 55.39 3.338 63.07 4.221 71.56 5.368 80.95 6.902 91.30 3-Methyl-1-butanol 0.4873 25.57 0.6171 29.54 0.7766 33.97 0.9718 38.90 1.210 44.38 1.500 50.45 1.853 57.16 2.282 64.55 2.804 72.70
0.5284 29.18 0.6766 33.84 0.863 39.06 1.097 44.91 1.391 51.43 1.765 58.69 2.242 66.75 2.860 75.69 3.680 85.56 2-Ethyl-1-hexanol 0.1956 23.83 0.2510 27.59 0.3197 31.82 0.4047 36.53 0.5093 41.79 0.6374 47.62 0.794 54.09 0.985 61.25 1.218 69.15
0.6867 30.87 0.8653 35.67 1.084 41.04 1.351 47.00 1.676 53.62 2.071 60.94 2.550 69.01 3.133 77.90 3.842 87.65 Propionic Acid 0.2669 21.07 0.3460 24.78 0.4468 29.01 0.5752 33.84 0.7395 39.33 0.9510 45.58 1.227 52.66 1.593 60.68 2.096 69.77
Table 2. Regressed Parameters in the NRTL Models for Florfenicol Form A in the Selected Solvents solvent parameters
ethanol
1-propanol
1-butanol
2-propanol
2-methyl-1- propanol
3-methyl-1- butanol
2-ethyl-1- hexanol
propionic acid
Δg12 Δg21 α 100 ARD 104 RMSD
−666.88 9853.0 0.47 1.34 0.73
−2147.3 13570.2 0.47 3.89 2.53
−732.71 12702.9 0.60 2.02 0.66
−731.89 12287.1 0.60 2.30 0.96
−623.72 13794.8 0.60 1.34 0.17
−1216.5 13397.4 0.47 1.61 0.31
−2253 17573.9 0.47 2.18 0.11
−2797.2 18238.2 0.47 1.29 0.25
back-calculated data and those reported in the authors’ published paper. The back-calculated mole fraction solubility by us is 10 times the reported ones by using the published equation coefficients. To show the difference clearly, in the same way, the solubility data in all neat solvents at the studied temperatures is back-calculated according to the equation coefficients reported in Table 6 the authors’ published paper by using the NRTL model. The calculated results by us together with the authors’ evaluated ones are tabulated in Table 1 of this communication. As can be seen that the numerical values of the coefficients reported in Table 6 of the published paper1 do not correctly describe the measured solubility data. There is large differences between our back-calculated values and those reported in the authors’ published work. To give readers the correct information, we perform reregression for the reported experimental solubility (x) of florfenicol form A in the studied pure solvents. The values of regressed equation parameters are tabulated in Table 2 of this communication. In addition, the obtained average relative deviations (ARD) and root-mean-square (RMSD) deviation expressed as eqs 8 and 9, respectively, are also presented in Table 2.
Figure 2. Solubility of Florfenicol form A in ethanol: ■, experimental data; solid line, calculated with the regressed parameters of this work; dash line, calculated with the reported parameters of the published paper by Zhang.1
g (x ) =
18980 ij 1 1y jj − zzz − ln x R k 425.15 T{
(7)
where x is the mole fraction of florfenicol form A. Obviously, the intersection of the two curves f(x) and g(x) is the calculated solubility data at temperature T. The plots of f(x) and g(x) versus x at 323.15 K are shown in Figure 1 of this communication. As can be shown, the two curves intersect at x = 0.08549. The calculated mole fraction solubility is x = 0.008303 at 323.15 K as listed in Table 2 of the authors’ published paper.1 A larger difference is observed between our
ARD = 3158
1 N
N
∑ i=1
xi ,cal − xi ,exp xi ,cal
(8) DOI: 10.1021/acs.jced.8b00435 J. Chem. Eng. Data 2018, 63, 3157−3159
ÅÄÅ N ÑÉ1/2 ÅÅ ∑i = 1 (xi ,cal − xi ,exp)2 ÑÑÑ Å ÑÑ RMSD = ÅÅÅ ÑÑ ÅÅ ÑÑ N ÑÖ ÇÅ
Journal of Chemical & Engineering Data
Comment/Reply
(9)
The calculated solubility of florfenicol form A with the NRTL model by us in ethanol is shown in Figure 2. The obtained largest values of ARD and RMSD are 3.89% and 2.53 × 10−4, respectively. Readers need to be aware of this in using the authors’ tabulated equation coefficients.
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AUTHOR INFORMATION
Corresponding Author
*Tel: + 86 514 87975568. Fax: + 86 514 87975244. E-mail:
[email protected]. ORCID
Hongkun Zhao: 0000-0001-5972-8352 Notes
The authors declare no competing financial interest.
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REFERENCES
(1) Zhang, P. S.; Zhang, C.; Zhao, R.; Wan, Y. M.; Yang, Z. K.; He, R. Y.; Chen, Q. L.; Li, T.; Ren, B. Z. Measurement and Correlation of the Solubility of Florfenicol Form A in Several Pure and Binary Solvents. J. Chem. Eng. Data 2018, 63, 2046.
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DOI: 10.1021/acs.jced.8b00435 J. Chem. Eng. Data 2018, 63, 3157−3159
