Solubility Prediction of Anthracene in Non-Aqueous Solvent Mixtures Using Jouyban-Acree Model

Document Type: Research Paper

Authors

1 Faculty of Pharmacy and Drug Applied Research Centre, Tabriz University of Medical Sciences, Tabriz, Iran

2 Kimia Research Institute, Tabriz, Iran

3 Department of Chemistry, University of North Texas, Denton, USA

Abstract

      A quanitative structure property relationship was proposed to calculate the binary interaction terms of the Jouyban-Acree model using solubility parameter, boiling point, vapour pressure and density of solvents. The applicability of the proposed method for reproducing solubility data of anthracene in binary solvents has been evaluated using 116 solubility data sets collected from the literature. The mean percentage deviation (MPD) of experimental and calculated solubilities has been computed as a measure of accuracy and the MPD of the proposed method was ~ 6 %. The accuracy of the method was compared with that of a previously reported method where the MPD was ~ 12 % and the mean differences between proposed and previous methods was statistically significant.

Keywords


1. Introduction

 

     Polycyclic aromatic hydrocarbons (PAHs) are released to the environment from incomplete combustion of organic materials. They are common constituents of complex mixtures such as automobile exhausts, petroleum refining and crude oil. Most of PAHs are considered dangerous substances because of their toxic and mutagenic or carcinogenic potentials [1]. PAHs are hydrophobic compounds, and they persist in ecosystem because of their poor aqueous solubilities and present in contaminated soil, waters and sediments and play a significant role in the environment safety and human health. Anthracene is a low molecular weight, not acutely toxic, carcinogenic or mutagenic members of PAHs. There is evidence that it is absorbed following oral and dermal exposure [2]. We used anthracene data as model system as very large database have been provided by our group, however, the proposed method could be used for modeling solubility data of a drug in mixed solvents.

      Solubility data is one of the key information in chemical/pharmaceutical areas and it is usually determined in water and many organic solvents. Mixing solvents, cosolvency, is the main solubility enhancement method has been employed in practice. In addition to experimental solubility determinations, a number of equations have been proposed for mathematical representation of solubility data. Solubility of anthracene in non-aqueous mixed solvents has been extensively studied by Acree’s group. The experimentally determined data has been correlated using the Jouyban-Acree model. The general form of the model is:

                       

where X is the mole fraction solubility of the solute, f denotes the volume fraction of the solvents 1 and 2 in the solvent mixture, subscripts m, 1 and 2 are the mixed solvent and solvents 1 and 2, respectively, and Bi is the model constants which is calculated using a no intercept least square analysis [3]. Although the model was proposed for modeling of PAHs solubilities in non-aqueous solvent mixtures, it has been shown that the model is applicable for calculating the solubility of polar and/or semi-polar compounds in aqueous solvent mixtures [4- 5].

      It has also been shown that the model is applicable for modeling physicochemical properties other than solubility in solvent mixtures [6].

      The main drawback of the Jouyban-Acree model is that it suffers from the presence of a number of curve-fitting parameters and needs a minimum number of experimental data points for training. In a previous work, a quantitative structure property relationship (QSPR) has been proposed to reduce the number of data points for predicting the solubility of solutes by the Jouyban-Acree model [7]. The model has been evaluated using a limited number of anthracene data sets in binary and ternary solvents and the solubility parameters of the solvents and that of anthracene have been used as independent variables. To continue our previous efforts on solubility prediction methods, the aim of this work is to propose an extended form of QSPR models using a larger number of anthracene solubility data in binary solvents. Anthracene data was choosen as model system, since a large number of its experimental data has been published so far. It is obvious that, this approach could be employed for other solutes in binary solvents.

 

Figure 1. Relative frequency of mean percentage deviation (MPD) values for the previous and proposed methods.

2. Computational methods

 

      The model constants of the Jouyban-Acree model represent the extent of solvent-solvent and solvent-solute interactions in the solution and these interactions could be related to the physico-chemical properties of solvents and solutes in order to establish a quantitative structure property relationship approach. In a previous paper [7], the differences in solubility parameters of the solvents with that of solute and their square values have been used to correlate the binary interaction terms (Bi) of the Jouyban-Acree model as:

 

in which δ1  and δ2  are the solubility parameters of solvents 1 and 2, respectively, δs is the solute’s solubility parameter and the numerical values of the model constants calculated using experimental data of 30 data sets  [7].  As  a  general  rule,  the  more independent variables the more accurate the correlation  and  the  more  accurate  the predictions. In this work, the experimentally obtained Bi  values for 116 data sets of anthracene solubility in non-aqueous binary solvents, were regressed against (δ12)2,(BP1-BP2)2, (VP1-VP2)2 and (ρ1-ρ2)2 in which BP, VP and ρ are boiling point, vapour pressure and density of solvents, respectively and

 subscripts 1 and 2 denote solvents 1 and 2. The back-calculated Bi values, have been used to predict the solubility of anthracene and mean percentage deviation (MPD) have been computed using:

 

 

Where N is the number of data points.

 

 

 

Table 1. List of solvents and the references of solubility data sets and their references

No.

Solvent 1

Solvent 2

Reference

1

1-Butanol

1,4-Dioxane

[8]

2

1-Butanol

1-Pentanol

[9]

3

1-Butanol

2-Butoxyethanol

[10]

4

1-Butanol

2-Ethyl-1-hexanol

[9]

5

1-Butanol

2-Methoxyethanol

[11]

6

1-Butanol

2-Pentanol

[12]

7

1-Butanol

4-Methyl-2-pentanol

[12]

8

1-Butanol

Dibutyl ether

[13]

9

1-Octanol

1,4-Dioxane

[8]

10

1-Octanol

1-Pentanol

[9]

11

1-Octanol

2-Butoxyethanol

[10]

12

1-Octanol

2-Ethyl-1-hexanol

[9]

13

1-Octanol

2-Methoxyethanol

[11]

14

1-Octanol

2-Pentanol

[12]

15

1-Octanol

4-Methyl-2-pentanol

[12]

16

1-Octanol

Dibutyl ether

[13]

17

1-Pentanol

2-Butoxyethanol

[14]

18

1-Pentanol

2-Pentanol

[12]

19

1-Pentanol

4-Methyl-2-pentanol

[12]

20

1-Propanol

1,4-Dioxane

[8]

21

1-Propanol

1-Pentanol

[9]

22

1-Propanol

2-Ethyl-1-hexanol

[9]

23

1-Propanol

2-Methoxyethanol

[11]

24

1-Propanol

2-Pentanol

[12]

25

1-Propanol

4-Methyl-2-pentanol

[12]

26

1-Propanol

Dibutyl ether

[13]

27

2,2,4-Trimethylpentane

1-Butanol

[15]

28

2,2,4-Trimethylpentane

1-Propanol

[15]

29

2,2,4-Trimethylpentane

2-Butoxyethanol

[14]

30

2,2,4-Trimethylpentane

3-Methyl-1-butanol

[16]

31

2-2-4-Trimethylpentane

1,4-Dioxane

[17]

32

2-2-4-Trimethylpentane

2-Butanol

[18]

33

2-Butanol

1,4-Dioxane

[8]

34

2-Butanol

1-Pentanol

[9]

35

2-Butanol

2-Butoxyethanol

[10]

36

2-Butanol

2-Ethyl-1-hexanol

[9]

37

2-Butanol

2-Methoxyethanol

[11]

38

2-Butanol

2-Pentanol

[12]

39

2-Butanol

4-Methyl-2-pentanol

[12]

40

2-Butanol

Dibutyl ether

[13]

41

2-Butoxyethanol

2-Ethoxyethanol

[19]

42

2-Butoxyethanol

2-Methoxyethanol

[19]

43

2-Methyl-1-propanol

1-Pentanol

[9]

44

2-Methyl-1-butanol

1-Pentanol

[9]

45

2-methyl-1-propanol

1,4-Dioxane

[8]

46

2-Methyl-1-propanol

2-Butoxyethanol

[14]

47

2-Methyl-1-Propanol

2-Ethyl-1-hexanol

[9]

48

2-Methyl-1-propanol

2-Methoxyethanol

[11]

49

2-Methyl-1-propanol

2-Pentanol

[12]

50

2-Methyl-1-propanol

4-Methyl-2-pentanol

[12]

51

2-Methyl-1-propanol

Dibutyl ether

[13]

52

2-Propanol

1,4-Dioxane

[8]

53

2-Propanol

1-Pentanol

[9]

54

2-Propanol

2-Butoxyethanol

[10]

55

2-Propanol

2-Ethyl-1-hexanol

[9]

56

2-Propanol

2-Methoxyethanol

[11]

57

2-Propanol

2-Pentanol

[12]

58

2-Propanol

4-Methyl-2-pentanol

[12]

Table 1. continued

 

 

 

 

 

 

 

 

No.

Solvent 1

Solvent 2

Reference

59

2-Propanol

Dibutyl ether

[13]

60

3-Methyl-1-butanol

1,4-Dioxane

[8]

61

3-Methyl-1-butanol

2-Butoxyethanol

[10]

62

3-Methyl-1-butanol

2-Ethyl-1-hexanol

[9]

63

3-Methyl-1-butanol

2-Methoxyethanol

[11]

64

3-Methyl-1-butanol

2-Pentanol

[12]

65

3-Methyl-1-butanol

4-Methyl-2-pentanol

[12]

66

3-Methyl-1-butanol

Dibutyl ether

[13]

67

Benzene

Methylcyclohexane

[20]

68

Benzene

Octane

[20]

69

Cyclohexane

1,4-Dioxane

[17]

70

Cyclohexane

1-Butanol

[15]

71

Cyclohexane

1-Propanol

[15]

72

CycloHexane

2-Butanol

[18]

73

Cyclohexane

2-Butoxyethanol

[14]

74

Cyclohexane

3-Methyl-1-butanol

[16]

75

Dibutyl ether

2,2,4-Trimethylpentane

[21]

76

Dibutyl ether

Cyclohexane

[21]

77

Dibutyl ether

Heptane

[21]

78

Dibutyl ether

Hexane

[21]

79

Dibutyl ether

Methylcyclohexane

[21]

80

Dibutyl ether

Octane

[21]

81

Heptane

1-Butanol

[15]

82

Heptane

1-Propanol

[15]

83

Heptane

2-Butoxyethanol

[14]

84

Heptane

3-Methyl-1-butanol

[16]

85

Hexane

1,4-Dioxane

[17]

86

Hexane

1,4-Dioxane

[17]

87

Hexane

1-Butanol

[15]

88

Hexane

1-Propanol

[15]

89

Hexane

2-Butanol

[18]

90

Hexane

2-Butanol

[18]

91

Hexane

2-Butoxyethanol

[14]

92

Hexane

3-Methyl-1-butanol

[16]

93

Methylcyclohexane

1,4-Dioxane

[17]

94

Methylcyclohexane

1-Butanol

[15]

95

Methylcyclohexane

1-Propanol

[15]

96

Methylcyclohexane

2-Butanol

[18]

97

Methylcyclohexane

2-Butoxyethanol

[14]

98

Methylcyclohexane

3-Methyl-1-butanol

[16]

99

Octane

1,4-Dioxane

[17]

100

Octane

1-Butanol

[15]

101

Octane

1-Propanol

[15]

102

Octane

2-Butanol

[18]

103

Octane

2-Butoxyethanol

[14]

104

Octane

3-Methyl-1-butanol

[16]

105

p-Xylene

2,2,4-Trimethylpentane

[20]

106

p-Xylene

Cyclohexane

[20]

107

p-Xylene

Heptane

[20]

108

p-Xylene

Hexane

[20]

109

p-Xylene

Methylcyclohexane

[20]

110

p-Xylene

Octane

[20]

111

Toluene

2,2,4-Trimethylpentane

[22]

112

Toluene

Cyclohexane

[22]

113

Toluene

Heptane

[22]

114

Toluene

Hexane

[22]

115

Toluene

Methylcyclohexane

[22]

116

Toluene

Octane

[22]

Table 2. Solubility parameter (δ), boiling points (BP), vapour pressure (VP) and density (ρ) of solvents 1 and 2, number of experimental data points in each set (N), and mean percentage deviations (MPD) for the previous [7] and proposed methods.

 

No.a

δ1

δ2

BP1

BP2

VP1

VP2

ρ1

ρ2

N

MPD

MPD

 

(Cal/cm3)1/2

(Cal/cm3)1/2

(°C)

(°C)

(torr)

(torr)

(g/cm3)

(g/cm3)

 

Previous

Proposed

 

 

 

 

 

 

 

 

 

 

method

method

1

11.39

10.02

117.7

101.3

6.180

37.100

0.806

1.028

9

14.4

9.9

2

11.39

11.10

117.7

137.8

6.180

2.350

0.806

0.812

9

9.0

0.3

3

11.39

10.17

117.7

170.2

6.180

0.852

0.806

0.894

9

4.6

4.5

4

11.39

10.17

117.7

184.3

6.180

0.143

0.806

0.829

9

5.2

5.7

5

11.39

12.12

117.7

124.6

6.180

9.700

0.806

0.960

9

4.3

5.3

6

11.39

10.76

117.7

119.0

6.180

5.830

0.806

0.805

9

9.8

0.4

7

11.39

10.31

117.7

131.7

6.180

8.200

0.806

0.804

9

10.2

2.8

8

11.39

7.77

117.7

142.2

6.180

12.500

0.806

0.764

9

28.0

11.4

9

10.32

10.02

195.2

101.3

0.075

37.100

0.822

1.028

9

11.0

7.0

10

10.32

11.10

195.2

137.8

0.075

2.350

0.822

0.812

9

0.5

1.3

11

10.32

10.17

195.2

170.2

0.075

0.852

0.822

0.894

9

1.4

1.2

12

10.32

10.17

195.2

184.3

0.075

0.143

0.822

0.829

9

1.1

0.8

13

10.32

12.12

195.2

124.6

0.075

9.700

0.822

0.960

9

13.1

4.0

14

10.32

10.76

195.2

119.0

0.075

5.830

0.822

0.805

9

4.0

1.9

15

10.32

10.31

195.2

131.7

0.075

8.200

0.822

0.804

9

4.3

1.5

16

10.32

7.77

195.2

142.2

0.075

12.500

0.822

0.764

9

22.4

1.6

17

11.10

10.17

137.8

170.2

2.350

0.852

0.812

0.894

9

3.1

3.8

18

11.10

10.76

137.8

119.0

2.350

5.830

0.812

0.805

9

8.0

0.6

19

11.10

10.31

137.8

131.7

2.350

8.200

0.812

0.804

9

7.9

1.9

20

11.98

10.02

97.2

101.3

20.850

37.100

0.800

1.028

9

16.8

14.4

21

11.98

11.10

97.2

137.8

20.850

2.350

0.800

0.812

9

12.6

0.4

22

11.98

10.17

97.2

184.3

20.850

0.143

0.800

0.829

9

7.5

9.4

23

11.98

12.12

97.2

124.6

20.850

9.700

0.800

0.960

9

2.6

5.0

24

11.98

10.76

97.2

119.0

20.850

5.830

0.800

0.805

9

15.5

1.8

25

11.98

10.31

97.2

131.7

20.850

8.200

0.800

0.804

9

14.9

4.9

26

11.98

7.77

97.2

142.2

20.850

12.500

0.800

0.764

9

29.4

12.6

27

6.84

11.39

99.2

117.7

49.000

6.180

0.688

0.806

9

12.6

14.5

28

6.84

11.98

99.2

97.2

49.000

20.850

0.688

0.800

9

5.6

14.3

29

6.84

10.17

99.2

170.2

49.000

0.852

0.688

0.894

9

6.9

14.1

30

6.84

11.10

99.2

130.5

49.000

2.370

0.688

0.807

9

11.8

11.7

31

6.84

10.02

99.2

101.3

49.000

37.100

0.688

1.028

8

3.6

16.5

32

6.84

10.80

99.2

99.6

49.000

18.290

0.688

0.803

9

5.2

2.0

33

10.80

10.02

99.6

101.3

18.290

37.100

0.803

1.028

9

23.1

16.7

34

10.80

11.10

99.6

137.8

18.290

2.350

0.803

0.812

9

4.3

0.8

35

10.80

10.17

99.6

170.2

18.290

0.852

0.803

0.894

9

12.0

7.4

36

10.80

10.17

99.6

184.3

18.290

0.143

0.803

0.829

9

2.2

4.7

37

10.80

12.12

99.6

124.6

18.290

9.700

0.803

0.960

9

11.3

7.0

38

10.80

10.76

99.6

119.0

18.290

5.830

0.803

0.805

9

5.2

0.8

39

10.80

10.31

99.6

131.7

18.290

8.200

0.803

0.804

9

3.5

0.8

40

10.80

7.77

99.6

142.2

18.290

12.500

0.803

0.764

9

34.6

18.3

41

10.17

11.49

170.2

135.6

0.852

5.300

0.894

0.925

9

1.9

1.1

42

10.17

12.12

170.2

124.6

0.852

9.700

0.894

0.960

9

6.1

1.0

43

11.20

11.10

107.7

137.8

10.220

2.350

0.798

0.812

9

4.0

2.6

44

10.77

11.10

128.7

137.8

3.120

2.350

0.815

0.812

9

4.7

0.6

45

11.20

10.02

107.7

101.3

10.220

37.100

0.798

1.028

9

21.4

16.1

46

11.20

10.17

107.7

170.2

10.220

0.852

0.798

0.894

9

11.6

9.6

47

11.20

10.17

107.7

184.3

10.220

0.143

0.798

0.829

9

3.7

0.6

48

11.20

12.12

107.7

124.6

10.220

9.700

0.798

0.960

9

8.8

7.3

49

11.20

10.76

107.7

119.0

10.220

5.830

0.798

0.805

9

14.1

6.5

50

11.20

10.31

107.7

131.7

10.220

8.200

0.798

0.804

9

6.0

0.7

51

11.20

7.77

107.7

142.2

10.220

12.500

0.798

0.764

9

33.7

18.4

52

11.49

10.02

82.3

101.3

45.160

37.100

0.781

1.028

9

24.3

18.2

53

11.49

11.10

82.3

137.8

45.160

2.350

0.781

0.812

9

3.6

2.3

54

11.49

10.17

82.3

170.2

45.160

0.852

0.781

0.894

9

14.2

8.9


 

 

 

 

 

 

 

 

 

 

 

Tabel 2. continued

 

 

 

 

 

 

 

 

 

 

No.a

δ1

δ2

BP1

BP2

VP1

VP2

ρ1

ρ2

N

MPD

MPD

 

(Cal/cm3)1/2

(Cal/cm3)1/2

(°C)

(°C)

(torr)

(torr)

(g/cm3)

(g/cm3)

 

Previous

Proposed

 

 

 

 

 

 

 

 

 

 

method

method

55

11.49

10.17

82.3

184.3

45.160

0.143

0.781

0.829

9

4.6

5.4

56

11.49

12.12

82.3

124.6

45.160

9.700

0.781

0.960

9

8.9

7.3

57

11.49

10.76

82.3

119.0

45.160

5.830

0.781

0.805

9

6.5

1.7

58

11.49

10.31

82.3

131.7

45.160

8.200

0.781

0.804

9

7.1

2.4

59

11.49

7.77

82.3

142.2

45.160

12.500

0.781

0.764

9

35.0

18.8

60

11.10

10.02

130.5

101.3

2.370

37.100

0.807

1.028

9

17.1

11.0

61

11.10

10.17

130.5

170.2

2.370

0.852

0.807

0.894

9

5.2

6.0

62

11.10

10.17

130.5

184.3

2.370

0.143

0.807

0.829

9

2.4

1.5

63

11.10

12.12

130.5

124.6

2.370

9.700

0.807

0.960

9

6.6

5.2

64

11.10

10.76

130.5

119.0

2.370

5.830

0.807

0.805

9

7.4

0.3

65

11.10

10.31

130.5

131.7

2.370

8.200

0.807

0.804

9

5.9

0.2

66

11.10

7.77

130.5

142.2

2.370

12.500

0.807

0.764

9

29.6

12.8

67

9.19

7.82

80.1

100.9

95.200

46.000

0.874

0.765

7

20.0

1.7

68

9.19

7.58

80.1

125.7

95.200

14.000

0.874

0.699

8

16.6

12.3

69

8.21

10.02

80.7

101.3

98.000

37.100

0.774

1.028

10

24.9

15.8

70

8.21

11.39

80.7

117.7

98.000

6.180

0.774

0.806

9

4.0

3.0

71

8.21

11.98

80.7

97.2

98.000

20.850

0.774

0.800

9

10.2

5.2

72

8.21

10.80

80.7

99.6

98.000

18.290

0.774

0.803

9

9.8

12.1

73

8.21

10.17

80.7

170.2

98.000

0.852

0.774

0.894

9

10.7

3.5

74

8.21

11.10

80.7

130.5

98.000

2.370

0.774

0.807

9

3.6

3.3

75

7.77

6.84

142.2

99.2

12.500

49.000

0.764

0.688

7

24.7

1.1

76

7.77

8.21

142.2

80.7

12.500

98.000

0.764

0.774

7

11.4

5.0

77

7.77

7.38

142.2

98.4

12.500

45.700

0.764

0.680

7

17.2

0.9

78

7.77

7.28

142.2

68.7

12.500

151.300

0.764

0.655

7

19.4

3.0

79

7.77

7.82

142.2

100.9

12.500

46.000

0.764

0.765

7

13.9

3.3

80

7.77

7.58

142.2

125.7

12.500

14.000

0.764

0.699

7

14.0

0.5

81

7.38

11.39

98.4

117.7

45.700

6.180

0.680

0.806

9

2.9

7.7

82

7.38

11.98

98.4

97.2

45.700

20.850

0.680

0.800

9

4.2

5.7

83

7.38

10.17

98.4

170.2

45.700

0.852

0.680

0.894

9

3.0

11.6

84

7.38

11.10

98.4

130.5

45.700

2.370

0.680

0.807

9

2.6

5.9

85

7.28

10.02

68.7

101.3

151.300

37.100

0.655

1.028

12

16.4

7.8

86

7.38

10.02

98.4

101.3

45.700

37.100

0.680

1.028

8

10.9

13.0

87

7.28

11.39

68.7

117.7

151.300

6.180

0.655

0.806

9

4.9

4.9

88

7.28

11.98

68.7

97.2

151.300

20.850

0.655

0.800

9

1.4

4.2

89

7.38

10.80

98.4

99.6

45.700

18.290

0.680

0.803

9

3.4

3.7

90

7.28

10.80

68.7

99.6

151.300

18.290

0.655

0.803

9

1.4

5.9

91

7.28

10.17

68.7

170.2

151.300

0.852

0.655

0.894

9

5.2

8.1

92

7.28

11.10

68.7

130.5

151.300

2.370

0.655

0.807

9

3.5

2.4

93

7.82

10.02

100.9

101.3

46.000

37.100

0.765

1.028

10

19.2

8.9

94

7.82

11.39

100.9

117.7

46.000

6.180

0.765

0.806

9

2.7

1.1

95

7.82

11.98

100.9

97.2

46.000

20.850

0.765

0.800

9

8.9

1.9

96

7.82

10.80

100.9

99.6

46.000

18.290

0.765

0.803

9

9.3

10.6

97

7.82

10.17

100.9

170.2

46.000

0.852

0.765

0.894

9

6.5

2.6

98

7.82

11.10

100.9

130.5

46.000

2.370

0.765

0.807

9

2.1

1.7

99

7.58

10.02

125.7

101.3

14.000

37.100

0.699

1.028

9

10.0

10.8

100

7.58

11.39

125.7

117.7

14.000

6.180

0.699

0.806

9

1.3

3.0

101

7.58

11.98

125.7

97.2

14.000

20.850

0.699

0.800

9

8.1

2.7

102

7.58

10.80

125.7

99.6

14.000

18.290

0.699

0.803

9

8.2

7.2

103

7.58

10.17

125.7

170.2

14.000

0.852

0.699

0.894

9

2.3

6.2

104

7.58

11.10

125.7

130.5

14.000

2.370

0.699

0.807

9

2.1

1.2

105

8.85

6.84

138.4

99.2

8.700

49.000

0.857

0.688

7

29.0

6.3

106

8.85

8.21

138.4

80.7

8.700

98.000

0.857

0.774

7

23.4

11.9

107

8.85

7.38

138.4

98.4

8.700

45.700

0.857

0.680

7

23.4

6.6

108

8.85

7.28

138.4

68.7

8.700

151.300

0.857

0.655

7

29.5

3.3

109

8.85

7.82

138.4

100.9

8.700

46.000

0.857

0.765

7

22.4

5.3

110

8.85

7.58

138.4

125.7

8.700

14.000

0.857

0.699

7

21.0

3.5

111

8.90

6.84

110.6

99.2

28.500

49.000

0.862

0.688

12

31.6

9.2

112

8.90

8.21

110.6

80.7

28.500

98.000

0.862

0.774

7

20.8

9.9

113

8.90

7.38

110.6

98.4

28.500

45.700

0.862

0.680

12

26.1

8.3

114

8.90

7.28

110.6

68.7

28.500

151.300

0.862

0.655

7

26.8

0.3

115

8.90

7.82

110.6

100.9

28.500

46.000

0.862

0.765

12

26.9

8.2

116

8.90

7.58

110.6

125.7

28.500

14.000

0.862

0.699

12

20.9

9.5

 

 

 

 

 

 

 

 

 

 

11.6±9.0

6.1±5.0

a Details of data sets are the same as in Table 1.


3. Results and discussion

      The solubilities of anthracene in 116 different binary solvent mixtures (for details see Table 1) were used to compute Bi terms of each binary solvent and the Bi terms were employed to build up a quanitative structure property relationship (QSPR) model using physico-chemical properties of the solvents. Details of the physico-chemical properties were listed in Table 2. The obtained QSPR models for calculating Bi terms are:


      The back-calculated Bi terms were used to calculate the solubility of anthracene in binary solvent mixtures and MPD values were also listed in Table 2. The lowest and highest MPDs were 0.2 (for solubility of anthracene in 3-methyl-1-butanol + 4-methyl-2-pentanol) and 18.8 (for solubility of anthracene in 2- propanol + dibutyl ether) and the overall MPD  (± SD) was 6.1±5.0. The required information for predicting solubility of anthracene in binary solvents is the numerical values of X1 and X2, i.e. two points for each binary solvent systems. The same calculations were done using equations (2-4) taken from a previous work and MPD values were reported in Table 2. The lowest and highest MPDs were 0.5 (for solubility of anthracene in  1-octanol + 1-pentanol) and 35.0 (for solubility of anthracene in 2-propanol + dibutyl  ether). The  maximum  MPD  of previous and proposed methods belonged to the same data set. The overall MPD (±SD) was 11.6±9.0 and it was significantly different from the proposed  method (paired t-test, p MPD values sorted in four subgroups, i.e. 30 %. All MPD values of the proposed method in this work lied in < 20 % category while it was 78 % for the previous method.

     As general conclusion, the proposed method is able to compute solubility of anthracene in mixed solvent systems using experimental data of the solute in mono- solvent systems and the expected prediction error is ~ 6 % which is acceptable error range for prediction purposes. The corresponding prediction error of the previous method is ~12 %. Employing BP, VP and ρ of the solvents along   with   δ   values   improved   the predictability of the method by a factor of 2. This is expected since employing three more physico-chemical properties provides more information   from  the  solvent-solvent interactions and resulted in more accurate predictions.

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