Solubility Determination and Correlation for Pyridoxal 5-Phosphate

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Solubility Determination and Correlation for Pyridoxal 5‑Phosphate Monohydrate in Different Binary Solvents from 278.15 K to 318.15 K Hua Sun,† Xiaowu Zhang,† Baoshu Liu,*,† and Dong Liu‡ †

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College of Chemical and Pharmaceutical Engineering, Hebei University of Science and Technology, Shijiazhuang, Hebei 050018, People’s Republic of China ‡ Hebei MeiBang Engineering & Technology Co., Ltd., 98, Huanghe Road, Shijiazhuang City, Hebei Province High Tech Zone, Hebei 050000, People’s Republic of China ABSTRACT: The solubility of pyridoxal 5-phosphate monohydrate (PLP) in four binary mixed solvents (methanol + water, ethanol + water, isopropanol + water, and acetone + water) with various compositions were determined at the temperature from 278.15K to 318.15K by the isothermal dissolution equilibrium method under normal atmospheric pressure. The solubility of PLP increased with the increasing temperature and mole fraction of water for the binary mixed solvents ethanol + water, isopropanol + water, and acetone + water. For methanol + water, the mole fraction solubility increased with the temperature at a certain solvent composition, yet the solubility had a maximum value around the mole fraction of water fc = 0.8 when the temperature was higher than 308.15 K. The experimental solubility was correlated with the Wilson model, NRTL model, Apelblat equation, and λh equation, and the largest value of RMSD was 16.6649 × 10−5. The Apelblat equation could best describe the solubility behavior according to the result of AIC analysis. ΔGmix, ΔHmix, and ΔSmix in the mixed solutions were calculated. The dissolution process of PLP in the mixed solvents was spontaneous.

1. INTRODUCTION Pyridoxal 5-phosphate monohydrate(CAS Reg No.41468-25-1), also known as PLP, a kind of white or almost white crystalline powder, is one of the metabolically active forms of vitamin B6 and it is also a kind of coenzyme in various enzymatic reactions, including transamination, racemization, decarboxylation, and so on. It is also widely used to cure the Parkinson’s disease clinically. The chemical structure of PLP shown in Figure 1

process as well as an essential physicochemical property that makes great contributions to understanding the phase equilibrium. Though the solubility data of PLP is so significant in its purification process, seldom solubility data were determined in previous publications. So as to provide comprehensive and systematic basic data and useful thermodynamic information for engineering application, systematic experiments on solubility of PLP in several binary solvents were carried out. To opt reasonable solvent system applied to purification of PLP, a laser monitoring observation technique4−9 is employed to determine the solubility of PLP in four mixed solvents methanol + water, ethanol + water, isopropanol + water, and acetone + water with different solvent compositions and temperatures from 278.15K to 318.15K at normal atmospheric pressure. Four mathematical models are used to fit the solubility data of PLP in different binary mixed solvents, and the mixing properties of solutions are calculated.

Figure 1. Chemical structure of pyridoxal 5-phosphate monohydrate.

demonstrates a certain extent of hydrophilicity due to the existence of aldehyde, hydroxy, and phosphate groups in its molecule.1,2 In industry, the traditional separation and purification method in the productive process of PLP applied the ion exchange and freeze-drying technique, which has a series of shortcomings, such as that the traditional method is of low product qualities, is high cost, and causes pollution. Therefore, an environment friendly crystallization technique which is low cost is indispensable. It is well-known that crystallization is the primary technology to remove the impurities and other byproducts, and it is operated as a last and most significant process. The solubility behavior3 of solid in a variety of solvents is crucial for the design and improvement of the crystallization © XXXX American Chemical Society

2. SOLUBILITY MODELS Solubility models can provide a quantitative description of solid−liquid equilibrium and predict drug solubility in certain solvent systems.10 In this work, four models are used to correlate the solubility data, including Wilson model, NRTL model, modified Apelblat equation, and λh equation. Received: April 17, 2018 Accepted: July 4, 2018

A

DOI: 10.1021/acs.jced.8b00309 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data 2.1. Activity Coefficient Models. According to the solid− liquid phase equilibrium theory, eq 1 can be obtained. f iS = fiL ̂ = γixif iΘ

Λ13 =

(1)

Λ31 =

Here, γi is the activity coefficient of the solute i; xi is the mole fraction solubility in the binary mixed solvent; f Θi is the fugacity of the solute i in the standard state. The solubility of the solute i in the solvent can be calculated in a universal manner by eq 2.11,12

Λ 23 =

ΔHtp ijj 1 Ttp y 1 yzzz ΔCp ijj Ttp jj ln(γixi) = − − + 1zzzz jjln zz − j j z R Ttp T R k T T { k { ΔV (P − Ptp) − (2) RT

Λ32 =

(3)

N

∑ k=1

Λkixk (4)

(5)

For a ternary solution, eq 4 can be expressed as eq 6. ÄÅ ÅÅ Λ12x 2 + Λ13x3 ln γ1 = −ln[x1 + Λ12x 2 + Λ13x3] + ÅÅÅÅ ÅÅÇ x1 + Λ12x 2 + Λ13x3 ÑÉÑ Λ31x3 Λ 21x 2 ÑÑ ÑÑ − − Λ 21x1 + x 2 + Λ 23x3 Λ31x1 + Λ32x 2 + x3 ÑÑÑÖ

V1 V i λ − λ11 yz i Δλ y zz = 1 expjjj− 21 zzz expjjj− 21 V2 RT { V2 k k RT {

αij = αji

(15)

gij − gjj RT

=

Δgij (16)

RT

B + C ln(T /K) T /K

(17)

Here, xA is the mole fraction solubility of PLP in solvent while A, B, and C are the empirical parameters of this equation. 2.2.2. λh Equation. The λh equation,19 first proposed by Buchowski and co-workers in 1980, can be used to correlate the solubility data of the association system or slightly eutectic system, and it can be expressed as eq 18. ÄÅ É λ(1 − x) ÑÑÑÑ 1 zyz ÅÅÅ ji 1 lnÅÅ1 + − ÑÑ = λhjjj z j ÅÅÇ Ñ x Tm/K zz{ ÑÖ (18) k T /K

Λij can be expesssed as eqs 7−12.

Λ 21 =

(14)

ln xA = A +

(6)

V2 i λ − λ 22 yz V2 i Δλ y zz = expjjj− 12 expjjj− 12 zzz V1 RT { V1 k k RT {

(12)

Δgij, considered to be constant, denotes the interaction parameters relating to the interaction energy, and α represents an adjustable parameter showing the nonrandomness of the solution, which is in the range from 0.20 to 0.47. 2.2. Simplified Empirical Models. It is obviously that the activity coefficient models have quantities of calculations and a complex calculation process, which limit the practical applications of the models. So, the simplified empirical models are proposed to correlate the solid−liquid equilibrium data based on lots of experimental data made by many scholars. 2.2.1. Modified Apelblat Equation. The modified Apelblat equation,17,18 posed by Apelblat, is a semiempirical model which is widely used to correlate the solubility data versus absolute temperature at the same solvent composition and is given as follows.

For a binary solution, eq 4 can be expressed as eq 5. ÄÅ ÉÑ ÅÅ ÑÑ Λ12 Λ 21 Å ÑÑ ln γ1 = −ln(x1 + Λ12x 2) + x 2ÅÅÅ − Ñ ÅÅÇ x1 + Λ12x 2 x 2 + Λ 21x1 ÑÑÑÖ

Λ12 =

i λ − λ 22 yz V2 i Δλ y V2 zz = expjjjj− 32 expjjjj− 32 zzzz z V3 RT { V3 k k RT {

(11)

Gji = exp( −αjiτji)

τij =

N

∑ j = 1 Λkjxj

V3 V i λ − λ33 yz i Δλ y zz = 3 expjjj− 23 zzz expjjjj− 23 z j RT z V2 RT { V2 k k {

(10)

(13)

2.1.1. Wilson Model. Wilson equation,14,15 a general formula to calculate the activity coefficient γi, is deduced by introducing the local volume fraction as eq 4. ij N yz j z ln γi = 1 − lnjjj∑ Λijxjzzz − jj zz k j=1 {

i λ − λ11 yz i Δλ y V1 V zz = 1 expjjj− 31 zzz expjjjj− 31 z j RT z V3 RT { V3 k k {

(9)

Here, Vi represent the mole volume of component i; Δλij, relating to the interaction energy between the component i and j, represent the interaction parameters (J mol−1). The values of Δλij can be obtained by regressing from the experimental solubility data. 2.1.2. NRTL Model. The NRTL (Nonrandom Two Liquid) model16 was put forward by Renon and Prausnitzin in 1968 based on the local composition concept. It is widely used to correlate and calculate both solid−liquid and liquid−liquid phase equilibrium, and the activity coefficient of component i described by NRTL model can be expressed with eqs 13−16. ÅÄ ÑÉ N N N ∑ j = 1 τjiGjixj ∑i = 1 xiτijGij ÑÑÑÑ xjGij ÅÅÅÅ ln γi = +∑ N ÅÅÅτij − ÑÑ N N Å ∑j = 1 Gjixj ∑i = 1 Gijxi ÑÑÑÑ j = 1 ∑i = 1 Gijxi Å ÅÇ Ö

Here, R is the universal gas constant equal to 8.314 J K−1 mol−1; ΔCp and ΔV are the difference of the heat capacity and the volume between the liquid phase and solid phase at the melting point, respectively. In eq 2, the terms containing ΔCp are less important than the first term in the right side under normal pressure, so they can be ignored. For solid−liquid equilibrium, small changes of the pressure ( (ethanol + water) > (isopropanol + water) > (acetone +

(22)

4.2. Solubility Data. The measured mole fraction solubilities of PLP in binary mixed solvents of methanol + water, ethanol + water, isopropanol + water, and acetone + water at the temperature ranging from 278.15 to 318.15 K are presented in Table 2. In order to compare the experimental points, the solubility data is presented in Figures 5−8. Table 2 and Figures 5−8 show that the mole fraction solubility of PLP is a function of solvent composition and temperature. The solubility of PLP increases with the increasing temperature and mole fraction of water for the binary mixed solvents ethanol + water, isopropanol + water, and acetone + water, and the maximum solubility values embodied itself when the solvent is E


Journal of Chemical & Engineering Data

Article

Table 3. Parameters of the Wilson Model and RMSD Values for PLP in Various Solventsa Wilson model fc

Δλ12

methanol + water 0.0000 −24410.52 0.2001 −5972.82 0.4000 −3711.68 0.5999 60331.93 0.8001 2443.43 1.0000 −2030.15 ethanol + water 0.0000 −25671.46 0.2001 7429.91 0.3999 −5641.89 0.5997 −2582.82 0.8002 14031.29 1.0000 −2030.15 isopropanol + water 0.0000 −26793.70 0.2001 4216.61 0.3992 17481.76 0.5998 8705.60 0.8000 14846.99 1.0000 −2030.15 acetone + water 0.0000 −30344.71 0.1999 3552.93 0.3998 5404.93 0.5999 −4491.94 0.8000 941.57 1.0000 −2030.15

Δλ21

Δλ13

Δλ31

Δλ23

−20299.48 32800.06 4221.58 28748.40 −41466.75 4562.48

−471.11 1474.85 1607.31 −432.26 2441.00

2272.08 −493.37 36661.87 −2028.92 645.67

0.0671 −59379.15 8669.55 −53587.31 −55720.13

−57286.40 898.29 8886.39 276.33 −39991.49 4562.48

1150.35 7304.27 2496.76 2200.19 5478.07

2651.90 −32846.19 −53965.17 −5620.91 −2758.02

8845.25 8406.13 709.62 −1947.27 −23654.49 4562.48

947.45 17033.66 6076.78 15926.42 3274.76

−25474.87 7302.33 7790.89 6496.84 −23276.29 4562.48

3887.90 15358.63 16213.68 3467.41 1009.42

Δλ32

R2

105 RMSD

−26463.79 −8014.95 −36431.89 −3782.57 7614.90

0.9999 0.9994 0.9988 0.9284 0.9973 0.9966

0.0033 0.1526 0.2971 1.3169 0.8192 1.2742

23128.26 7553.66 25721.97 −53250.26 −46338.57

−28261.95 −44141.75 −61265.46 −8776.06 0.3104

0.9999 0.9997 0.9999 0.9945 0.9798 0.9966

0.0029 0.0397 0.0688 0.6347 0.9039 1.2742

1053.84 −3639.76 −15485.49 −28969.58 −3922.66

39331.68 42765.51 4665.41 −2.9007 −29166.74

−28318.84 −6407.32 −24140.35 −34117.84 −2658.59

0.9999 0.9997 0.9999 0.9992 0.9999 0.9966

0.0012 0.0225 0.0139 0.1312 0.0522 1.2742

−577.94 −3109.94 −4153.38 −18998.66 −26.09

2299.05 35084.83 32130.21 85099.80 −30783.15

−33301.36 −5712.01 −5297.93 −25511.36 3751.48

0.9999 0.9999 0.9999 0.9992 0.9986 0.9966

0.0017 0.0040 0.0074 0.0499 0.2235 1.2742

a

Standard uncertainties u are u(T) = 0.01 K, u(p) = 2 kPa, u(fc) = 0.0001.

Table 4. Parameters of the NRTL Model and RMSD Values for PLP in Various Solventsa NRTL model fc

Δg12

methanol + water 0.0000 −36770.52 0.2001 −5840.98 0.4000 −4208.91 0.5999 −169.89 0.8001 −8873.45 1.0000 −20.24 ethanol + water 0.0000 27871.19 0.2001 −692.25 0.3999 −4480.32 0.5997 −2437.10 0.8002 −64700.58 1.0000 −20.24 isopropanol + water 0.0000 26674.44 0.2001 −47022.85 0.3992 −1118.94 0.5998 −567.89 0.8000 −891.60 1.0000 −20.24 acetone + water 0.0000 −41535.86 0.1999 8811.58 0.3998 −41432.10

Δg21

Δg13

Δg31

Δg23

Δg32

R2

105 RMSD

−31211.64 16074.48 11140.27 3224.11 8885.83 2298.26

3293.97 −6465.13 −6931.69 34282.65 4119.95

−0.09 14036.45 8581.01 2826.20 14927.88

5666.28 −17795.98 −13768.69 214968.09 7846.76

110718.42 27272.94 22204.06 13555.01 −9817.97

0.9999 0.9996 0.9990 0.9259 0.9975 0.9998

0.0036 0.1390 0.2950 1.1100 0.9470 16.6649

−53313.20 15621.95 11807.23 8112.73 11293.92 2298.26

−1719.91 −11371.15 −558.17 −3456.37 −205099.65

4121.90 15007.31 11858.43 6411.66 1660.70

5247.97 −11051.78 28070.99 21665.45 0.80

104726.54 47048.57 34383.33 −11862.79 −63727.62

0.9999 0.9997 0.9965 0.9947 0.9910 0.9998

0.0012 0.0406 0.2040 2.7900 0.4630 16.6649

−58673.54 2885.44 5406.04 11350.85 6770.41 2298.26

−1843.52 −4817.66 −289.05 −4258.34 904.42

4428.70 2968.33 3037.14 11393.75 −2229.61

−55271.87 −8707.83 40495.85 34118.49 46425.94

104870.78 −46321.46 43883.62 28044.39 36539.03

0.9999 0.9996 0.9999 0.9988 0.9999 0.9998

0.0006 0.0228 0.0140 0.1210 0.0542 16.6649

−41529.04 689.06 1058.92

−1734.60 0.02 2060.95

3884.19 680.90 1098.63

−339.61 32273.28 16281.16

128079.70 19647.72 −41514.72

0.9999 0.9999 0.9999

0.0002 0.0045 0.0083

F



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Table 4. continued NRTL model fc

Δg12

0.5999 0.8000 1.0000

−25362.18 −11155.91 −20.24

Δg21 17618.36 13260.46 2298.26

Δg13

Δg31

−5916.95 913.61

17582.97 19712.37

Δg23 29919.35 45871.85

Δg32

R2

105 RMSD

−25562.93 −10700.72

0.9999 0.9987 0.9998

0.0498 0.2389 16.6649

a


Table 5. Parameters of the Apelblat Equation and RMSD Values for PLP in Various Solventsa Apelblat equation A

B

C

R2

105 RMSD

218.8209 158.4339 −162.9773 −1006.8824 −403.7448 −314.1977

−14958.7112 −10894.9951 2708.0945 38534.5101 13630.5636 11126.2509

−31.5196 −23.1163 25.3692 152.4956 61.4267 47.2186

0.9985 0.9986 0.9988 0.9989 0.9985 0.9998

0.0294 0.1471 0.2834 0.5585 0.8199 0.2622

−507.3427 −147.3976 708.6327 −241.3551 997.0223 −314.1977

19913.9031 3288.6344 −35688.9119 5941.3182 −50037.9549 11126.2509

75.1555 21.9723 −105.1245 37.2422 −147.0105 47.2186

0.9951 0.9976 0.9997 0.9959 0.9971 0.9998

0.0112 0.0388 0.0665 0.6038 0.8618 0.2622

−751.4945 −629.9198 45.6065 453.3982 192.8244 −314.1977

30221.6685 24604.7176 −5021.8606 −23587.2613 −12972.1313 11126.2509

111.9134 94.0215 −6.9013 −67.3794 −27.7404 47.2186

0.9995 0.9979 0.9998 0.9995 0.9999 0.9998

0.0038 0.0197 0.0132 0.0875 0.0406 0.2622

72.9096 −121.4301 −260.3491 708.7549 −62.3557 −314.1977

−8351.3437 2931.8325 8446.9411 −35096.0162 −1976.5528 11126.2509

−10.2083 17.3579 38.6452 −105.5372 10.4641 47.2186

0.9982 0.9984 0.9997 0.9992 0.9989 0.9998

0.0083 0.0038 0.0068 0.0504 0.2122 0.2622

fc methanol + water 0.0000 0.2001 0.4000 0.5999 0.8001 1.0000 ethanol + water 0.0000 0.2001 0.3999 0.5997 0.8002 1.0000 isopropanol + water 0.0000 0.2001 0.3992 0.5998 0.8000 1.0000 acetone + water 0.0000 0.1999 0.3998 0.5999 0.8000 1.0000 a


water).22 As a result, the solubility of PLP in methanol + water is larger than that in ethanol + water, isopropanol + water or acetone + water. 4.3. Solubility Correlation and Evaluation of Thermodynamic Models. The solubility of PLP in the these solutions is correlated with the four thermodynamic models mentioned above, with the method of nonlinear regression.23 Also, the objective function of the Wilson model and the NRTL model in this work is defined as eq 23. F=

∑ (ln γi

e

N

RMSD =

(23)

Here ln γei represent the logarithm of experimental mole fraction solubility, and ln γci , the calculated value. The objective function of the λh model and the Apelblat model in this work is defined as eq 24 F=

∑ (xie − xic)2 i=1

∑i = 1 (xie − xic)2 N

(25)

Here N represents the number of solubility data points; xei and xci represent the experimental mole fraction solubility and calculated value, respectively. Based on the experimental mole fraction solubility of PLP in pure and binary mixed solvents, the parameters of the four models are acquired by nonlinear regression method. The values of the parameters and RMSD are presented in Tables 3−6. Tables 2−6 demonstrate that the calculated solubility of PLP in four binary mixed solvents is in line well with the experimental data. The largest value of RMSD is 16.6649 × 10−5, which is determined using the NRTL model for the solvent

c 2

− ln γi )

i=1

where xei and xci represent the experimental mole fraction solubility and calculated value, respectively. The root-mean-square deviation (RMSD) is applied to judge the error computed with the four models. The RMSD are given as follows.

(24) G



Article

Table 6. Parameters of the λh Equation and RMSD Values for PLP in Various Solventsa

In order to demonstrate the results more intuitively, Akaike weight, ωi is applied to determine the best model with the highest value.

λh equation λ

fc

methanol + water 0.0000 0.09 0.2001 0.01 0.4000 0.06 0.5999 0.64 0.8001 0.04 1.0000 0.01 ethanol + water 0.0000 0.14 0.2001 0.12 0.3999 0.01 0.5997 0.02 0.8002 0.04 1.0000 0.01 isopropanol + water 0.0000 0.02 0.2001 0.08 0.3992 0.03 0.5998 0.02 0.8000 0.03 1.0000 0.01 acetone + water 0.0000 0.04 0.1999 0.03 0.3998 0.04 0.5999 0.04 0.8000 0.06 1.0000 0.01

h

R2

105 RMSD

107666.70 420532.51 122389.89 13227.49 117118.54 327734.51

0.9549 0.9808 0.9945 0.9969 0.9967 0.9977

0.7121 1.2834 1.8061 1.7781 1.5843 2.5130

87366.32 86633.90 442670.82 268963.36 144070.49 327734.51

0.9181 0.9471 0.9324 0.9945 0.9916 0.9977

0.2934 0.8025 1.2524 0.6787 1.8253 2.5130

427192.89 132379.58 280224.25 302403.43 195869.18 327734.51

0.9781 0.9602 0.9247 0.9331 0.9942 0.9977

0.2074 0.4613 1.2031 2.2786 1.7634 2.5130

308020.21 324780.16 233813.41 204737.40 124196.69 327734.51

0.9024 0.9243 0.9268 0.9233 0.9916 0.9977

0.0955 0.1966 0.4061 1.5331 1.7329 2.5130

ωi =

(28)

id ΔGmix = RT (x1 ln x1 + x 2 ln x 2 + x3 ln x3)

(29)

id ΔSmix = −R(x1 ln x1 + x 2 ln x 2 + x3 ln x3)

(30)

id ΔHmix =0

(31)

Here x1, x2, x3 are the mole fractions of solute, water, and organic solvent in the ternary solution, respectively. The superscript id represents the ideal conditions. For real solution, the mixing Gibbs energy (ΔGmix), mixing enthapy (ΔHmix), and mixing entropy (ΔSmix) can be calculated by eq 32.


id ΔM mix = ME + ΔM mix

(32)

with M = G, H, and S. Here, the superscript E represents the excess properties in real solutions. In addition, the mixing properties can be obtained by eqs 33−35 according to the Wilson model.30

water. On the whole, all four of the thermodynamic models can be used to correlate the solubility data of PLP in the four binary mixed solvents at the temperature from 278.15 K to 318.15 K under 101.1 kPa. In addition, the Akaike Information Criterion (AIC)24−27 is applied to compare the relative applicability of these models to find the best model for describing the solubility of PLP in various binary mixed solvents. Generally, the lower of the AIC value is, the better the solubility correlates. The AIC value of the four models can be obtained by eq 26.

GE = RT (x1 ln x1 + x 2 ln x 2 + x3 ln x3) = −RT[x1 ln(x1 + x 2 Λ12 + x3Λ13) + x 2 ln(x1Λ 21 + x 2 + x3Λ 23) + x3 ln(x1Λ31 + x 2 Λ32 + x3)]

(33)

ij ∂(GE /T ) yz zz HE = −T 2jjj j ∂T zz k { x x Λ Δλ + x1x3Λ13Δλ13 = 1 2 12 12 x1 + x 2 Λ12 + x3Λ13 x 2x1Λ 21Δλ 21 + x 2x3Λ 23Δλ 23 + x1Λ 21 + x 2 + x3Λ 23 x3x1Λ31Δλ31 + x3x 2 Λ32Δλ32 + x1Λ31 + x 2 Λ32 + x3

(26)

Here L(θ) represents the maximized likelihood value for the assessed model, and k is the number of parameters in the model. In the special case of the least-squares estimation with normal distributed error, except for an additive constant, AIC can be simplified as follows. AIC = 2N ln(RMSD) + 2k

n

∑i = 1 e((AICmin − AICi )/2)

Here n is the number of the compared models; AICmin is the minimum value of AIC for the compared models, and AICi is the AIC value of the ith model. The values of AIC and ωi of the four models are presented in Table 7. The lowest AIC value and highest ωi value show that Apelblat could best describe the solubility behavior among the four models. 4.4. Mixing Properties of Solutions. The mixing properties of solutions can be calculated according to the Lewis−Randall rule that the actual states of the pure components are standard states. As for an ideal ternary solution, the mixing Gibbs energy, mixing enthapy, and mixing entropy can be obtained.28,29

a

AIC = −2 ln L(θ ) + 2k

e((AICmin − AICi )/2)

(27)

Here N is the number of observations; RMSD is the rootmean-square deviation of the observations.

(34)

Table 7. Values of AIC and ωi of the Four Models, Including NRTL Model, Wilson Model, Apelblat Model, and λh Model models

105 RMSD

k

AIC

e((AICmin − AICi)/2)

ωi

NRTL Wilson Apelblat λh

10.72 1.23 0.32 1.55

6 6 3 2

−3937.01 −4873.20 −5453.21 −4778.94

0 1.13 × 10−126 1 3.85 × 10−147

0 1.13 × 10−126 1 3.85 × 10−147

H



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Table 8. Calculated Values for ΔGmix, ΔHmix, and ΔSmix in Binary Mixed Solvents Methanol + Water with Varied Mole Fractions of Water (fc) at the Temperature Ranging from 278.15K to 318.15 K under 101.1 kPaa

Table 9. Calculated Values for ΔGmix, ΔHmix, and ΔSmix in Binary Mixed Solvents Ethanol + Water with Varied Mole Fractions of Water ( fc) at the Temperature Ranging from 278.15K to 318.15 K under 101.1 kPaa

fc

T/K

ΔGmix (J mol−1)

ΔHmix (J mol−1)

ΔSmix (J mol−1 K−1)

fc

T/K

ΔGmix (J· mol−1)

ΔHmix (J mol−1)

ΔSmix (J mol−1· K−1)

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.2002 0.2002 0.2002 0.2002 0.2002 0.2002 0.2002 0.2002 0.2002 0.4000 0.4000 0.4000 0.4000 0.4000 0.4000 0.4000 0.4001 0.4001 0.5999 0.5999 0.5999 0.5999 0.5999 0.5999 0.6000 0.6001 0.6002 0.8001 0.8001 0.8001 0.8001 0.8002 0.8002 0.8002 0.8002 0.8003 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

−403.04 −438.63 −546.18 −665.90 −761.00 −837.89 −939.23 −1042.73 −1145.74 −15728.63 −15708.36 −15689.44 −15671.71 −15655.17 −15639.82 −15625.90 −15613.38 −15601.60 −20269.48 −20245.39 −20221.55 −20197.98 −20174.63 −20151.48 −20128.46 −20105.41 −20082.70 −34068.98 −34082.63 −34096.43 −34110.41 −34124.56 −34139.05 −34153.77 −34168.69 −34183.90 −43506.32 −43488.48 −43470.53 −43452.24 −43433.67 −43414.91 −43395.86 −43376.14 −43354.66 −4.18 −4.82 −5.56 −6.53 −7.63 −9.13 −10.92 −12.89 −15.59

−4230.06 −4495.46 −5390.34 −6320.36 −6987.42 −7474.49 −8109.19 −8717.47 −9283.40 −16911.95 −16844.56 −16777.41 −16710.54 −16644.09 −16578.15 −16512.94 −16448.53 −16384.71 −21608.70 −21592.35 −21575.60 −21558.48 −21540.88 −21522.74 −21503.93 −21483.94 −21463.91 −33319.47 −33311.61 −33303.84 −33296.13 −33288.40 −33280.11 −33271.36 −33261.98 −33250.48 −44480.09 −44473.87 −44467.08 −44459.27 −44450.59 −44441.27 −44431.12 −44419.39 −44404.03 0.87 1.05 1.27 1.56 1.90 2.38 2.97 3.65 4.61

−13.76 −14.33 −16.81 −19.29 −20.88 −21.89 −23.27 −24.51 −25.58 −4.25 −4.01 −3.78 −3.54 −3.32 −3.10 −2.88 −2.67 −2.46 −4.81 −4.76 −4.70 −4.64 −4.58 −4.52 −4.46 −4.40 −4.34 2.69 2.72 2.75 2.78 2.80 2.83 2.86 2.90 2.93 −3.50 −3.48 −3.46 −3.44 −3.41 −3.39 −3.36 −3.33 −3.30 0.02 0.02 0.02 0.03 0.03 0.04 0.05 0.05 0.06

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.2001 0.2001 0.2001 0.2001 0.2001 0.2001 0.2001 0.2001 0.2001 0.3999 0.3999 0.3999 0.3999 0.3999 0.3999 0.4000 0.4000 0.4000 0.5997 0.5997 0.5997 0.5997 0.5997 0.5998 0.5998 0.5998 0.5998 0.8003 0.8003 0.8003 0.8003 0.8003 0.8003 0.8004 0.8004 0.8004 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

−384.91 −352.94 −329.34 −311.33 −277.99 −273.12 −285.34 −292.35 −297.95 −30801.56 −30729.53 −30657.82 −30586.42 −30515.34 −30444.55 −30374.04 −30303.84 −30233.84 −34606.48 −34567.47 −34528.42 −34489.30 −34450.14 −34410.93 −34371.66 −34332.59 −34293.42 −35834.04 −35844.01 −35854.17 −35864.54 −35875.10 −35885.87 −35896.93 −35908.22 −35919.68 −37019.90 −37018.59 −37016.95 −37015.27 −37013.53 −37011.55 −37009.35 −37006.77 −37004.45 −4.18 −4.82 −5.56 −6.53 −7.63 −9.13 −10.92 −12.89 −15.59

−4330.92 −3932.06 −3626.94 −3385.62 −2994.50 −2898.22 −2973.55 −2995.74 −3003.61 −34816.96 −34797.57 −34778.47 −34759.66 −34741.20 −34723.06 −34705.25 −34687.92 −34670.75 −36762.97 −36762.37 −36761.63 −36760.73 −36759.70 −36758.50 −36757.11 −36756.02 −36754.65 −35288.16 −35277.42 −35266.39 −35255.04 −35243.44 −35231.57 −35218.86 −35205.59 −35192.28 −37082.92 −37082.38 −37080.91 −37079.38 −37077.68 −37075.37 −37072.49 −37068.67 −37065.33 0.87 1.05 1.27 1.56 1.90 2.38 2.97 3.65 4.61

−14.19 −12.64 −11.44 −10.49 −9.11 −8.66 −8.72 −8.63 −8.50 −14.44 −14.37 −14.30 −14.24 −14.17 −14.11 −14.06 −14.00 −13.95 −7.75 −7.75 −7.75 −7.75 −7.75 −7.74 −7.74 −7.74 −7.74 1.96 2.00 2.04 2.08 2.12 2.16 2.20 2.24 2.29 −0.23 −0.23 −0.22 −0.22 −0.22 −0.21 −0.20 −0.20 −0.19 0.02 0.02 0.02 0.03 0.03 0.04 0.05 0.05 0.06

a

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Article

Table 10. Calculated Values for ΔGmix, ΔHmix, and ΔSmix in Binary Mixed Solvents Isopropanol + Water with Varied Mole Fractions of Water ( fc) at the Temperature Ranging from 278.15K to 318.15 K under 101.1 kPaa

Table 11. Calculated Values for ΔGmix, ΔHmix, and ΔSmix in Binary Mixed Solvents Acetone + Water with Varied Mole Fractions of Water ( fc) at the Temperature Ranging from 278.15K to 318.15 K under 101.1 kPaa

fc

T/K

ΔGmix (J mol−1)

ΔHmix (J mol−1)


fc

T/K

ΔGmix (J mol−1)

ΔHmix (J mol−1)


0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.2000 0.2000 0.2000 0.2000 0.2000 0.2000 0.2000 0.2000 0.2000 0.3998 0.3998 0.3998 0.3998 0.3998 0.3998 0.3998 0.3998 0.3998 0.6000 0.6000 0.6000 0.6000 0.6000 0.6000 0.6000 0.6000 0.6000 0.8000 0.8000 0.8000 0.8000 0.8001 0.8001 0.8001 0.8001 0.8001 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

−255.65 −221.05 −207.18 −199.29 −194.93 −201.57 −210.27 −222.68 −247.51 −1240.73 −1218.58 −1197.54 −1177.53 −1158.51 −1140.42 −1123.22 −1106.86 −1091.33 −12509.98 −12489.60 −12469.53 −12449.75 −12430.25 −12411.01 −12392.03 −12373.29 −12354.80 −14553.99 −14570.12 −14586.24 −14602.37 −14618.50 −14634.63 −14650.76 −14666.88 −14683.04 −24058.43 −24064.33 −24070.26 −24076.22 −24082.21 −24088.22 −24094.24 −24100.29 −24106.34 −4.18 −4.82 −5.56 −6.53 −7.63 −9.13 −10.92 −12.89 −15.59

−2963.00 −2537.20 −2345.14 −2222.30 −2140.35 −2175.07 −2229.44 −2319.09 −2526.65 −2504.34 −2441.73 −2381.42 −2323.37 −2267.49 −2213.72 −2162.00 −2112.24 −2064.37 −13652.23 −13635.13 −13618.46 −13602.18 −13586.29 −13570.75 −13555.53 −13540.61 −13525.95 −13654.88 −13654.58 −13654.25 −13653.88 −13653.48 −13653.03 −13652.54 −13651.95 −13651.52 −23731.59 −23729.14 −23726.63 −23724.01 −23721.24 −23718.35 −23715.21 −23711.90 −23708.33 0.87 1.05 1.27 1.56 1.90 2.38 2.97 3.65 4.61

−9.73 −8.18 −7.42 −6.90 −6.52 −6.51 −6.55 −6.69 −7.16 −4.54 −4.32 −4.11 −3.91 −3.72 −3.54 −3.37 −3.21 −3.06 −4.11 −4.05 −3.99 −3.93 −3.88 −3.83 −3.78 −3.73 −3.68 3.23 3.23 3.23 3.24 3.24 3.24 3.24 3.24 3.24 1.18 1.18 1.19 1.20 1.21 1.22 1.23 1.24 1.25 0.02 0.02 0.02 0.03 0.03 0.04 0.05 0.05 0.06

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.2001 0.2001 0.2001 0.2001 0.2001 0.2001 0.2001 0.2001 0.2001 0.3992 0.3992 0.3992 0.3992 0.3992 0.3992 0.3992 0.3992 0.3992 0.5998 0.5998 0.5998 0.5998 0.5998 0.5998 0.5998 0.5998 0.5998 0.8000 0.8000 0.8000 0.8000 0.8000 0.8000 0.8000 0.8001 0.8001 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

−446.81 −490.01 −501.32 −573.42 −635.20 −709.37 −761.82 −797.03 −818.61 −1010.23 −994.27 −979.14 −964.82 −951.23 −938.34 −926.12 −914.51 −903.50 −1336.12 −1325.09 −1314.61 −1304.64 −1295.17 −1286.16 −1277.62 −1269.51 −1261.82 −9282.07 −9265.53 −9249.00 −9232.48 −9215.97 −9199.46 −9182.97 −9166.49 −9149.99 −24740.59 −24744.87 −24749.20 −24753.59 −24758.03 −24762.52 −24767.05 −24771.63 −24776.23 −4.18 −4.82 −5.56 −6.53 −7.63 −9.13 −10.92 −12.89 −15.59

−5850.36 −6257.31 −6287.09 −6980.54 −7526.61 −8167.65 −8563.74 −8779.33 −8860.72 −1922.67 −1874.25 −1827.88 −1783.45 −1740.88 −1700.08 −1660.98 −1623.50 −1587.55 −1965.34 −1934.81 −1905.07 −1876.12 −1847.95 −1820.54 −1793.87 −1767.93 −1742.69 −10204.22 −10204.00 −10203.75 −10203.46 −10203.14 −10202.80 −10202.40 −10201.96 −10201.58 −24504.97 −24501.85 −24498.67 −24495.41 −24492.07 −24488.65 −24485.13 −24481.53 −24477.42 0.87 1.05 1.27 1.56 1.90 2.38 2.97 3.65 4.61

−19.43 −20.37 −20.08 −21.86 −23.11 −24.60 −25.32 −25.49 −25.28 −3.28 −3.11 −2.95 −2.79 −2.65 −2.51 −2.38 −2.26 −2.15 −2.26 −2.15 −2.05 −1.95 −1.85 −1.76 −1.68 −1.59 −1.51 −3.32 −3.31 −3.31 −3.31 −3.31 −3.31 −3.31 −3.31 −3.31 0.85 0.86 0.87 0.88 0.89 0.90 0.91 0.93 0.94 0.02 0.02 0.02 0.03 0.03 0.04 0.05 0.05 0.06

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Journal of Chemical & Engineering Data SE =

HE − GE T

Article

(4) Sun, H.; Liu, B. S.; Ren, K.; Li, J. Solubility of D-phenylglycine methyl ester hydrochloride in water and in organic individual or mixed solvents: Experimental data and results of thermodynamic modeling. Fluid Phase Equilib. 2016, 417, 62−69. (5) Liu, B. S.; Sun, H.; Wang, J. K.; Yin, Q. X. Thermodynamic analysis and correlation of solubility disodium 5′-guanylate heptahydrate in aqueous ethanol mixtures. Fluid Phase Equilib. 2014, 370, 58−64. (6) Sun, H.; Liu, P. H.; Xin, Y.; Liu, B. S.; Wu, S. Thermodynamic analysis and correlation of solubility solvents from 278.15 to 313.15K. Fluid Phase Equilib. 2015, 388, 123−127. (7) Sun, H.; Liu, B. S.; Liu, P. H.; Zhang, J. L.; Wang, Y. L. Solubility of Fenofibrate in different Binary Solvents: Experimental Data and Results of Thermodynamic Model. J. Chem. Eng. Data 2016, 61, 3177−3183. (8) Sun, H.; Wang, L.; Liu, B. S. Solubility of α-glycine in water with additives at a temperature range of (293.15−343.15)K: Experimental data and results of thermodynamic modeling. Fluid Phase Equilib. 2017, 434, 167−175. (9) Sun, H.; Jiang, C. Y.; Liu, B. S.; Zhang, J. L. Determination and Correlation of Solubility of Cephradine and Cefprozil Monohydrate in Water As a Function of pH. J. Chem. Eng. Data 2017, 62, 3423− 3430. (10) Duan, E. H.; Wang, K. K.; Li, X.; Chen, Z. D.; Sun, H. Solubility and Thermodynamic Properties of (2S)-Pyrrolidine-2carboxylic Acid in Water, Alcohols, and Water-Alcohol Mixtures. J. Chem. Eng. Data 2015, 60, 653−658. (11) Stanley, M. W. Phase Equilibria in Chemical Engineering; Butterworth, New York, 1985. (12) Delgado, D. R.; Romdhani, A.; Martinez, F. Solubility of sulfamethizole in some propylene glycol + water mixtures at several temperatures. Fluid Phase Equilib. 2012, 322−323, 113−119. (13) Prausnitz, J. M.; Lichtenthaler, R. N.; Azevedo, E. G. Molecular Thermodynamics of Fluid-Phase Equilibria, 3rd ed.; Prentice Hall: New York, 1999. (14) Wilson, G. M. Vapor-liquid equilibrium. XI. A new expression for the excess free energy of mixing. J. Am. Chem. Soc. 1964, 86, 127− 130. (15) Gow, A. S. Calculation of vapor - liquid equilibria from infinite dilution excess enthalpy data using the Wilson or NRTL equation. Ind. Eng. Chem. Res. 1993, 32, 3150−3161. (16) Renon, H.; Prausnitz, J. M. Estimation of parameters for the NRTL equation for excess Gibbs energies of strongly nonideal liquid mixtures. Ind. Eng. Chem. Process Des. Dev. 1969, 8, 413−419. (17) Apelblat, A.; Manzurola, E. Solubilities of o-acetylsalicylic, 4aminosalicylic, 3,5-dinitrosalicylic, and p-toluic acid, and magnesiumDL-aspartate in water from T = (278 to 348) K. J. Chem. Thermodyn. 1999, 31, 85−91. (18) Manzurola, E.; Apelblat, A. Solubilities of L-glutamic acid, 3nitrobenzoic acid, p-toluic acid, calcium-L-lactate, calcium gluconate, magnesium-DL-aspartate, and magnesium-L-lactate in water. J. Chem. Thermodyn. 2002, 34, 1127−1136. (19) Buchowski, H.; Ksiazczak, A.; Pietrzyk, S. Solvent Activity along a Sateration Line and Solubility of Hydrogen-Bonding Solids. J. Phys. Chem. 1980, 84, 975−979. (20) Yao, G. B.; Yao, Q. C.; Xia, Z. X.; Li, Z. H. Solubility determination and correlation for o-phenylenediamine in (methanol, ethanol, acetonitrile and water) and their binary solvents from T=(283.15−318.15)K. J. Chem. Thermodyn. 2017, 105, 179−186. (21) Li, J. Q.; Wang, Z.; Bao, Y.; Wang, J. K. Solid-liquid phase equilibrium and mixing properties of cloxacillinbenzathine in pure and mixed solvents. Ind. Eng. Chem. Res. 2013, 52, 3019−3026. (22) Smallwood, I. M. Handbook of Organic Solvent Properties; Amoled: London, 1996. (23) Rosenbrock, H. H. An automatic method for finding the greatest or least value of a function. Comput. J. 1960, 3, 175−184. (24) Li, X. B.; Wang, M. J.; Cong, Y.; Du, C. B.; Zhao, H. K. Solubility determination and thermodynamic modeling for 2-amino-4chlorobenzoic acid in eleven organic solvents from T = (278.15 to

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The ΔGmix, ΔHmix, and ΔSmix are calculated based on the regressed parameters of Wilson model presented in Table 3 and tabulated in Tables 8−11. The values of ΔGmix are all negative illustrating that the mixing process of PLP in the these mixed solvents is spontaneous, and the values of ΔGmix decrease with increasing mole fraction of water in the solvent except in pure water which has the maximum value of ΔGmix. The values of ΔHmix are negative in organic solvent and binary mixed solvent, which means the mixing process is exothermic, while the values of ΔHmix in water are positive, which means the mixing process is endothermic.

5. CONCLUSIONS From all topics discussed here it can be concluded that the solubility of PLP in four binary mixed solvents methanol + water, ethanol + water, isopropanol + water, and acetone + water depends strongly on temperature and the solvent composition. The solubility of PLP in all the solvents increases with the increasing temperature. The solubility in water is the highest except in the binary mixed solvent methanol + water with mole fraction of water fc = 0.8 when the temperature is higher than 308.15 K. The Wilson model, NRTL model, Modified Apelblat equation, and λh equation are used to correlated the experimental solubility, and the largest value of RMSD is 16.6649 × 10−5. On the whole, all four of the thermodynamic models can be used to correlate the solubility data of PLP in the binary mixed solvents, and the Modified Apelblat equation could best describe the solubility behavior according to the result of AIC analysis. ΔHmix, ΔGmix, and ΔSmix of solutions are calculated. The mixing process of PLP in the these mixed solvents is spontaneous. The mixing process is exothermic in organic solvent and binary mixed solvent, while it is endothermic in water.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax: 0086-311-88632183. ORCID

Hua Sun: 0000-0002-8954-8173 Baoshu Liu: 0000-0002-2725-2801 Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS The authors would like to express gratitude for Hebei Meibang Engineering & Technology Co., Ltd, China, for their support. REFERENCES

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Solubility Determination and Correlation for Pyridoxal 5-Phosphate

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