Henry's Constants of Persistent Organic Pollutants ... - ACS Publications

Subscriber access provided by LAURENTIAN UNIV

Article

Henry’s Constants of Persistent Organic Pollutants by a Group-Contribution Method Based on Scaled-Particle Theory Neil K. Razdan, David M. Koshy, and John M Prausnitz Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.7b03023 • Publication Date (Web): 09 Oct 2017 Downloaded from http://pubs.acs.org on October 13, 2017

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

Environmental Science & Technology is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 23

Environmental Science & Technology

1

Henry’s Constants of Persistent Organic Pollutants

2

by a Group-Contribution Method Based on Scaled-

3

Particle Theory

4

Neil K. Razdan⸹,†,*,‡, David M. Koshy⸹,†, John M. Prausnitz⸹

5

⸹Chemical and Biomolecular Engineering Department, University of California, Berkeley, CA,

6

94720-1462, USA

7

KEYWORDS: Henry’s constant; persistent organic pollutants; polychlorinated biphenyls; van’t

8

Hoff equation; group-contribution; scaled-particle theory

9

ABSTRACT: A group-contribution method based on scaled-particle theory was developed to

10

predict Henry’s constants for six families of persistent organic pollutants: polychlorinated

11

benzenes,

12

dibenzofurans, polychlorinated naphthalenes, and polybrominated diphenyl ethers. The group-

13

contribution model uses limited experimental data to obtain group-interaction parameters for an

14

easy-to-use method to predict Henry’s constants for systems where reliable experimental data are

15

scarce. By using group-interaction parameters obtained from data reduction, scaled-particle theory

16

gives the partial molar Gibbs energy of dissolution, Δ𝑔̅2, allowing calculation of Henry’s constant,

17

H2, for more than 700 organic pollutants. The average deviation between predicted values of log

polychlorinated

biphenyls,

polychlorinated

dibenzodioxins,

polychlorinated

ACS Paragon Plus Environment

1


Page 2 of 23

18

H2 and experiment is 4%. Application of an approximate van’t Hoff equation gives the temperature

19

dependence of Henry’s constants for polychlorinated biphenyls, polychlorinated naphthalenes, and

20

polybrominated diphenyl ethers in the environmentally relevant range 0 to 40oC.

21

1. INTRODUCTION

22

Persistent organic pollutants (POPs) are chemicals that have long environmental lifetimes and

23

provide serious health threats to humans and wildlife.1-10 POPs travel through sediments, bodies

24

of water, and air for decades. They are often lipophilic and accumulate in fatty tissue, thereby

25

persisting in food chains before re-entering a cycle of dissolution and slow evaporation.1-3,6,8-10 In

26

2001, the Stockholm Convention on Persistent Organic Pollutants, an international treaty with 128

27

signatories, was formed to limit the environmental impact of these toxic chemicals.1-3

28

Thermodynamic, chemical and transport properties of POPs are of much interest to track and

29

minimize POPs within the environment.1-10

30

Of primary significance is the Henry’s constant that governs the air-water partition of POPs. In

31

recent years, there has been much work measuring, tabulating, and correlating Henry’s

32

constants.11-29 Shen et al (2005) and Mackay et al (2006) have published large databases for

33

Henry’s constants and other key properties for hundreds of chemicals, including POPs.17,30

34

Bamford et al (2000, 2002), Cetin et al (2005) and Odabasi et al (2016) have measured and

35

correlated temperature-dependent Henry’s constants for some polychlorinated biphenyls,

36

polybrominated diphenyl ethers, and polychlorinated naphthalenes; these pollutants are

37

representative of the most studied families of POPs.11,13,16,20 However, data are not available for

38

many POPs that are of interest for environmental protection.

39

This work concerns Henry’s constants of polychlorinated benzenes (CBs), polychlorinated

40

biphenyls (PCBs), polychlorinated dibenzodioxins (PCDDs), polychlorinated dibenzofurans


2

Page 3 of 23


41

(PCDFs), polychlorinated naphthalenes (PCNs), and polybrominated diphenyl ethers (PBDEs).

42

These six families of POPs contain a total of 706 congeners that provide a major environmental

43

threat.1-3,6-10,31A congener is a variant, or configuration, of a common chemical structure. For

44

example, each of the 209 PCB congeners is a unique configuration of chlorine atoms substituted

45

on a biphenyl backbone. Reliable data for these pollutants are limited, in part, due to experimental

46

difficulty in measuring very small solubilities.

47

UNIFAC has been used extensively to estimate activity coefficients for liquid-mixture

48

components.32 However, for highly dilute aqueous solutions, UNIFAC predictions of Henry’s

49

constant are often in serious error.33-35

50

Several studies have presented models that predict Henry’s constants for solutes in water.18-23

51

Group-contribution models and quantitative structure-property relationships (QSPR) have

52

provided a basis for correlating molecular structure to Henry’s constant for numerous aqueous

53

solutes.24-29 While often reliable, these models are computationally demanding and require specific

54

software packages for implementation. The model we present is arithmetic and uses only

55

rudimentary matrix algebra in the calculation of group-interaction parameters. Further, many

56

published models are applicable only to one family of POPs.

57

In this work, we propose a simple group-contribution model for predicting temperature-

58

dependent Henry’s constants based on molecular structure. We use an additive method to

59

determine solute-solvent interaction energies for constituent functional groups. Using interaction

60

energies, scaled-particle theory (SPT) provides the partial molar Gibbs energy of inserting and

61

solvating a solute molecule in a given solvent.36,37 This Gibbs energy can then be converted to a

62

Henry’s constant.


3


Page 4 of 23

63

To our knowledge, applying the group-contribution method toward the calculation of energetic

64

interaction parameters for Henry’s constant predictions has not been reported in the literature.

65

When pertinent data are available, our novel method can be easily extended by future investigators

66

because it requires only arithmetic operations to arrive at Henry’s constant predictions; the

67

energetic contributions of new functional groups can be determined by basic matrix algebra. Thus,

68

this physically based group-contribution method, applied to several families of POPs, provides a

69

useful advance in group-contribution techniques.

70

2. MATERIALS AND METHODS

71

2.1 Thermodynamic Framework. For a solute 2 in solvent 1, Henry’s constant for the solute,

72

H2, [Pa] is defined as the ratio of the solute’s liquid-phase fugacity, 𝑓2L , to its liquid-phase mole

73

fraction, x2, at high dilution

74

H2 =

𝑓2L for 𝑥2 → 0 𝑥2

(1a)

75

At vapor-liquid equilibrium (e.g. air-water partition), 𝑓2L = 𝑓2V , where 𝑓2V is the solute’s vapor-

76

phase fugacity. At modest pressure, fugacity is replaced by partial pressure. Henry’s constant then

77

relates the solute’s equilibrium partial pressure, y2P, to the liquid-phase mole fraction

78

H2 =

𝑦2 P for 𝑥2 → 0 𝑥2

(1b)

79

where y2 is the vapor-phase mole fraction of the solute and P is pressure. At high dilution, there

80

are very few solute-solute interactions; solute-solvent interactions determine the energetics of

81

solvation, required for SPT.

82

SPT provides a framework to determine H2. In SPT, the partial molar Gibbs energy of

83

dissolution, Δ𝑔̅2, is the sum of two contributions. The first contribution, 𝑔̅c , is the work required

84

to create a cavity in the solvent for inserting one molecule of solute. The second contribution, 𝑔̅i ,


4

Page 5 of 23


85

is the partial molar Gibbs energy of interaction between one molecule of solute and its surrounding

86

solvent molecules. SPT assumes that the dominant entropic contributions to Δ𝑔̅2 are included in

87

𝑔̅c . Strictly, this is not correct; 𝑠̅i is a small negative value because favorable interactions between

88

the solute and solvent restrict motion of the solute. However, the entropic gain from cavity

89

formation, 𝑠̅c, is significantly larger than 𝑠̅i . Neglecting 𝑠̅i greatly simplifies calculation of 𝑔̅i while

90

only negligibly affecting the accuracy of 𝑠̅2 = 𝑠̅i + 𝑠̅c .36,37

91 92

Henry’s constant is given by ln

H2 𝜈1 Δ𝑔̅2 𝑔̅c + 𝑔̅i = = 𝑅𝑇 𝑅𝑇 𝑅𝑇

(2)

93

where 𝜈1 is the liquid-phase molar volume of the solvent, R is the gas constant and T is absolute

94

temperature. Δ𝑔̅2 is the partial molar Gibbs energy change of the solute going from a pure vapor

95

phase to a dissolved solute in aqueous solution.

96

In scaled-particle theory36-39, 𝑔̅c is a function of solvent molecular diameter, 𝜎1 , solute molecular

97

diameter, 𝜎2 , and solvent molecular density, 𝜌1 . From SPT, 𝑔̅c is

98

3 2 𝑔̅c = 𝐾 (0) + 𝐾 (1) σ12 + 𝐾 (2) 𝜎12 + 𝐾 (3) 𝜎12

(3)

99

where 𝜎12 = (𝜎1 + 𝜎2 )/2. 𝐾 (0) , 𝐾 (1) , 𝐾 (2) , and 𝐾 (3) are theoretically-derived functions given in

100

the Supporting Information (SI).36,37 For water at 25oC, 𝜎1 = 0.275 nm, and 𝜌1 = 3.34 ∙ 1028

101

molecules/m3.23

102

𝐾 (0) = 4.767 ∙ 103

103

𝐾 (1) = −8.396 ∙ 1013

104

𝐾 (2) = 4.177 ∙ 1023

105

𝐾 (3) = 2.52 ∙ 1029

106

J mol J m ∙ mol

m2

J ∙ mol

J . m3 ∙ mol

Partial molar Gibbs energy of interaction, 𝑔̅i , is


5


107

Page 6 of 23

𝑔̅i 32 𝜖12 3 = (− ) ( ) (𝜋𝜌1 𝜎12 ) 𝑅𝑇 9 𝑘B 𝑇

(4)

108

where subscript 1 refers to water and subscript 2 refers to solute. Here, 𝜖12 = √𝜖1 𝜖2 is the solute-

109

solvent interaction parameter [J], kB is Boltzmann’s constant [J/K], 𝜌1 is the molecular density of

110

the solvent [molecules/m3]. For dispersion forces in water23, 𝜖1 /𝑘B = 85.3 [K]; for the solutes

111

considered in this work, 𝜖2 is rarely tabulated.

112 113

Bondi (1964) presents a group-contribution method for diameter 𝜎2 based on molecular structure.40

114

We use a group-contribution method for 𝜖2 = ∑j 𝑛j 𝜖j where nj is the number of times group j

115

appears in a solute molecule and 𝜖j represents the energetic contribution of functional group j

116

interacting with water.

117

As shown in Table 1, we consider 15 functional groups contained in six major classes of POPs.

118

Fig 1 shows the 15 functional groups amongst the six families of POPs. Group contributions

119

for 𝜖2 were determined from Henry’s-constant data for 51 POPs. Using group-contributions for 𝜎2

120

reported by Bondi (1964), and group-contributions for 𝜖2 reported in this work, we calculate

121

Henry’s constant for the solute using Eqs (1)-(4).

122

Table 1: Group-contribution 𝜖j and Bondi volume, Vj, for 15 groups Group j

Group Identification

𝝐𝒋 /𝐤 [K]

𝐕𝐣 [cm3/mol]

Aromatic C-H (ACH)

1

88.65

8.06

Aro-Chlorine (Cl)

2

93.82

12

Ortho-Chlorine (ClOrtho)

3

91.18

12

Aro-Bromine (Br)

4

131.78

15.12

Ortho Bromine (BrOrtho)

5

128.16

15.12


6

Page 7 of 23


Group Identification

𝝐𝒋 /𝐤 [K]

𝐕𝐣 [cm3/mol]

Biphenyl

6

-372.9

9.48

𝛼-PCB-Chlorine

7

72.06

12

Ether

8

-435.1

6.4

𝛼-PBDE-Bromine

9

114.82

15.12

Condensed C-H

10

-219.3

4.74

𝛼-PCN-Chlorine

11

124.75

12

Dioxin

12

-83

12.8

𝛼-PCDD-Chlorine

13

94.18

12

Furan

14

-71.83

11.14

𝛼-PCDF Chlorine

15

77.14

12

Group j Polychlorinated Biphenyls (PCBs)

Polybrominated Diphenyl ethers (PBDEs)

Polychlorinated Naphthalenes (PCNs)

Polychlorinated Dibenzodioxins (PCDDs)

Polychlorinated Dibenzofurans (PCDFs)

123 124 125 126 127 128 129

𝛼-halogens are those next to the linkage between two aromatic groups (i.e. biphenyl, ether, condensed C-H, dioxin, and furan). The family-specific aromatic linkages (biphenyl, ether, condensed C-H, dioxin, and furan) are a single group regardless of number of bonds and atoms. Ortho-halogens are substituted halogens that are directly next to another halogen. Ortho-halogens are lower priority than 𝛼-halogens. For example, 2,3 dichlorobiphenyl has one α-Chlorine and one ortho-Chlorine atoms instead of 2 ortho-Chlorine atoms. Examples in Appendix A demonstrate conversion of volume, V2, to σ2 .


7


Page 8 of 23

130 131

Fig 1: 15 functional groups in six families of POPs with group IDs from Table 1.

132

For the temperature range 0 to 40oC, the temperature-dependence of Henry’s constant was

133

determined by application of a simplified van’t Hoff equation using approximate values for partial

134

molar entropy of dissolution, Δ𝑠̅2, shown in Table A-1, in the Appendix.11,13,16

135

136

An approximate form of the van’t Hoff equation (Eq. 5) is H2 𝜈1 d ln ( 𝑅𝑇 ) Δℎ̅2 Δ𝑔̅2 (298K) + 298K ∙ Δ𝑠̅2 = = d(1/𝑇) 𝑅 𝑅

(5a)

137

where T = 298 K is the reference state, Δℎ̅2 and Δ𝑠̅2 are the partial molar enthalpy and partial

138

molar entropy change due to dissolution of the solute from a pure vapor phase to a dissolved solute

139

in aqueous solution. We assume 𝜈1 , Δ𝑠̅2, and Δℎ̅2 are constant in the small temperature range

140

considered here.11,13 The partial molar Gibbs energy change is given by Δ𝑔̅2 = 𝑔̅i + 𝑔̅c , as

141

calculated by Eq’s (1)-(4). Because Δ𝑠̅2, and Δℎ̅2 are constant, Δ𝑔̅2 is linear with respect to

142

temperature, with slope −Δ𝑠̅2.

143

Integrating Eq. 5a,


8

Page 9 of 23

144


ln

H2 (𝑇) 𝑇 Δ𝑔̅2 (298K) + 298K ∙ Δ𝑠̅2 1 1 = ln ( )∙[ ( − )] H2 (298K) 298K 𝑅 𝑇 298K

(5b)

145

Table A-1 gives approximate Δ𝑠̅2 determined by correlating published experimental data to the

146

number of chlorine or bromine substitutions, that is, to the halogenation number.11,13,16 Table SI-1

147

gives Δ𝑔̅2 at 298K for all solutes considered in this work.

148

2.2 Data Reduction. Literature reports on POP Henry’s-constant data often show large

149

disagreement. To ensure the consistency of the data used for data reduction, Henry’s-constant data

150

for each POP family were obtained from a single literature source.11-17 Sources for H2 data were

151

chosen based on the number of solutes studied and on the range of halogenation number. Henry’s

152

constants were obtained from published sources for CBs, PCBs, PCNs, and PBDEs that calculated

153

values using measurements of y2 and x2 and application of Eq. 1a.11,12,16,17 For the remaining

154

solutes, Henry’s constants were calculated from literature data for gas-chromatogram retention

155

index (GC-RI) correlations for solute subcooled liquid vapor pressure and experimentally

156

measured solid-phase solute solubility.14,15 Supplemental information (SI) gives the compiled

157

experimental data used in this study. Data were collected for 72 POPs, where data for 51 were

158

used to determine group-interaction parameters and data for 21 POPs were used to test the model.

159

Data for these 21 solutes were not used to determine group contributions for 𝜖2 .

160

We identified 15 functional groups contained in the six families of POPs investigated; these

161

groups are listed in Table 1 are shown in Fig 1. To account for the large variation in Henry’s

162

constant as a function of halogen location, we distinguish groups for 𝛼-halides (substitutions

163

adjacent to aromatic linkages), adjacent (ortho) halide groups, and isolated halide groups (Aro-

164

halide). All 15 functional groups are represented at least three times in the fitting set and at least

165

once in the validation set. Molecules for the fitting set were also chosen such that the full range of

166

halogenation number is represented within each POP family. We constructed a 51 x 15 matrix to


9


Page 10 of 23

167

represent the linear combination of constituent functional groups for each molecule in the fitting

168

set, reproduced in Fig SI-4, and performed a least-squares regression analysis to determine the

169

energy parameter, 𝜖j , for each functional group.

170

In the fitting set, data for all solutes were used to determine aromatic carbon-hydrogen (ACH),

171

non-ortho chlorine (Cl), ortho chlorine (Clortho), non-ortho bromine (Br), and ortho bromine

172

(Brortho) group-interaction parameters. The remaining functional groups are unique to a family of

173

POPs; they were fitted using only experimental data for that family.

174

Each group’s unique 𝜖j and molecular volume, Vj , are compiled in Table 1. Appendix A

175

demonstrates conversion of Vj to 𝜎2 and provides sample calculations for Henry’s constant, H2.

176

Table SI-2 lists 𝜎2 and 𝜖2 for all solutes considered in this work.

177

3. RESULTS AND DISCUSSION

178

For both fitting and validation sets, Fig 2 and Table SI-1 compare experimental and predicted

179

room-temperature log H2. Both fitting and validation sets show strong agreement with

180

experimental log H2. The average deviation between predicted results for log H2 and experimental

181

results is 4%. The average deviations and root-mean-square-error (RSME) varied slightly for

182

different POP families. Average deviations and RSME amongst CBs, PCBs, PCDDs, PCDFs,

183

PCNs, and PBDEs are 2%, 3%, 5%, 5%, 3%, and 5% and 0.26, 0.26, 0.33, 0.27, 0.19, and 0.29,

184

respectively. The average deviation, RMSE, squared coefficient of determination (r2), and squared

185

Pearson coefficient (p2), between our predicted log H2 and experiment in the fitting set and

186

validation set are 4%, 0.22, 0.89, and 0.91 and 4%, 0.27, 0.88, and 0.91, respectively. Considering

187

experimental uncertainty, these metrics show an excellent fit indicating very good predictive

188

accuracy of our model. It is important to note that errors in H2 are larger than those in log H2.


10

Page 11 of 23


189

For comparison, we calculated log H2 for the validation set of POPs using the EPISuiteTM

190

computational software developed by the US Environmental Protection Agency (US EPA). We

191

obtained an average deviation, RMSE, r2, and p2 of 7%, 0.46, 0.38, and 0.71, respectively. Results

192

from our model are better than those from the EPISuiteTM software provided by the US EPA. The

193

EPISuiteTM software was chosen because it is freely available and is one of the few QSPR models

194

able to calculate H2 for all six families of POPs.

195

Most of the functional groups in Table 1 yield a positive 𝜖j indicating that addition of that

196

functional group parameter increases the energetic term toward higher solubility in water,

197

indicating increased solvation. However, some functional groups (biphenyl, ether, furan, dioxin,

198

and condensed C-H) give a negative 𝜖j , indicating that these linker groups decrease solubility. The

199

negative 𝜖j may arise from a steric effect that limits water-solute interaction.

200

201 202

Fig 2: Experimental and predicted logarithm of Henry’s constants at 25oC in units of Pa. Solid line

203

corresponds to perfect fit. Filled squares are the fitting set. Empty triangles are the validation set.


11


Page 12 of 23

204

There are only four studied POPs with deviation in log H2 greater than 10%: 1, 2, 3, 4, 7-CDD;

205

2, 3, 4, 7, 8-CDF; PBDE-100; and 1, 2, 3, 4, 7-CDD. In each of these four molecules, there is a

206

sequence of at least four consecutively adjacent functional groups that are not Group ACH. The

207

relatively high error in H2 of these POPs suggests that higher-order effects are needed to account

208

for the effect of four or more consecutively adjacent halogen substitutions and benzene linkages

209

(e.g biphenyl).

210

Using suggested values for Δ𝑠̅2, given in Table A-1, and an approximate van’t Hoff equation,

211

we extended the model to the environmentally relevant temperature range 0 to 40oC and compared

212

results to experimental data for 39 solutes.

213

214 215

Fig 3: Logarithm of Henry’s constants in units of Pa versus temperature for a selection of PCBs,

216

PBDEs, and PCNs. Squares are experimental data.11,13,16 Lines are predicted using SPT and the

217

approximate van’t Hoff equation.


12

Page 13 of 23


218

Fig 3 compares temperature-dependent experimental and predicted log H2 for 9 of the 39 solutes

219

studied. Figs SI-1, SI-2, and SI-3 compare temperature-dependent log H2 for all PCBs, PCNs, and

220

PBDEs, respectively, for those solutes where data are available. The average deviation of predicted

221

results for log H2 over the temperature range 0 to 40oC is within 5% for PCBs, PCNs, and PBDEs

222

and the RMSE for each family is 0.32, 0.29, and 0.26, respectively. No meaningful correlation was

223

found between temperature and any of the reported evaluation metrics.

224

The slopes of the curves in Fig. 3 are primarily determined by Δ𝑠̅2, since, at constant pressure,

225

dΔ𝑔̅2/dT = −Δ𝑠̅2. The ordinate intercepts of the curves in Fig. 3 are primarily determined by the

226

predicted H2 at 298K, as shown in Eq. 5b. Thus, any systematic overestimation or underestimation

227

of H2, such as in PCB-195, result from inaccuracy in predicted H2 at 298K. In cases, such as PCB-

228

170, where there is both overestimation and underestimation, prediction of H2 at 25oC is accurate

229

but the suggested Δ𝑠̅2 deviates from the experimental entropy change.

230

The proposed group-contribution method is accurate for calculation of Henry’s constants and

231

validates the use of scaled-particle theory to calculate energetic-interaction parameters for

232

prediction of Henry’s constant. As a predictive tool, this method addresses the lack of reliable

233

experimental data for many congeners of POPs. Environmental scientists and engineers can

234

implement this model to calculate Henry’s constants that will aid in assessment of air-water

235

partitioning of POPs in the environment. In addition, because this SPT method is general, future

236

work can apply the method to additional classes of molecules with repeating functional groups.

237

For example, Henry’s constants for highly toxic bromo/chloro-POPs could be correlated by the

238

methods of our work.41,42 We anticipate that our SPT model will be a useful advance in group-

239

contribution models for Henry’s constant predictions.

240


13


241

APPENDIX A

242

We present some examples for calculating Henry’s constants.

Page 14 of 23

243

Example 1. To illustrate the use of our model, we show a sample calculation for Henry’s

244

constant for 1-chlorodibenzo-p-dioxin. This molecule contains 7 aromatic CH groups, one dioxin

245

linkage, and one 𝛼 − PCDD chlorine group.

246

Using the 𝜖j values in Table 1 and Eq’s (1)-(4) we find:

247

𝜖2 = 𝑘B ∙ (7 ∙ [88.65] + [−83.00] + [94.18]) = 630.9 ∙ 𝑘B 𝜖12

248

𝑘B

𝜖 𝜖2

= √ 𝑘1

B

𝜖

= 232.0K , with 𝑘1 = 85.3K. B

249

We use Bondi’s method for estimation of van der Waals diameter to calculate 𝜎2 . A molecule

250

of 1-chlorodibenzo-p-dioxin contains 7 aromatic CH (ACH groups), one dioxin linkage, and one

251

aromatic Cl (AroC-Cl) group. 1

252

3 107 nm 6 ∙ [7 ∙ V ACH + VDioxin + VCl ] 1 mol 𝜎2 = ( ∙ ) ∙ = 0.636 nm 𝜋 6.02 ∙ 1023 molecules 1 cm

253 254

𝜎12 =

𝜎1 +𝜎2 2

= 0.456 nm, with 𝜎1 = 0.275 nm.

At 298K, we calculate 𝑔̅c using values for 𝐾 (0) , 𝐾 (1) , 𝐾 (2) , and 𝐾 (3) and Eq. 3, found in the body

255

of the paper

256

3 2 𝑔̅c = 𝐾 (0) + 𝐾 (1) σ12 + 𝐾 (2) 𝜎12 + 𝐾 (3) 𝜎12 = 53.2

257 258

261

(3)

Using 𝜎12 and 𝜖12 and substituting into Eq. 4, found in the body of the paper 𝑔̅i = 𝑅𝑇 (−

32 𝜖12 kJ 3 )( ) (𝜋𝜌1 𝜎12 ) = −68.0 9 𝑘B T mol

259 260

kJ mol

Δ𝑔̅2 = 𝑔̅i + 𝑔̅c = −14.8

(4) kJ mol

Finally, rearranging Eq. 2 from the body of the paper, H2 (298K) =

𝑅𝑇 Δ𝑔̅2 ∙ exp ( ) = 3.5 ∙ 105 Pa 𝜈1 𝑅𝑇


14

Page 15 of 23


262

This calculated result matches the experimental value 3.5 ∙ 105 Pa.15

263

Example 2. We also show a sample calculation for Henry’s constant for PCB-87. This molecule

264

contains 5 aromatic CH groups, one biphenyl linkage, 2 𝛼 − PCB chlorine groups, one non-ortho

265

chlorine, and 2 ortho chlorines.

266 267

Using the 𝜖j in Table 1 and Eq’s (1)-(4) we find: 𝜖2 = 𝑘B ∙ (5 ∙ [88.648] + [−372.9] + 2 ∙ [72.05] + [93.82] + 2 ∙ [91.18]) = 490.3 ∙ 𝑘B 𝜖12

268

𝑘B

𝜖 𝜖2

= √ 𝑘1

B

ϵ

= 204.6K, with k1 = 85.3K B

269

We use Bondi’s method for estimation of van der Waals diameter to calculate 𝜎2 . A molecule

270

of PCB-87 contains 5 aromatic CH (ACH groups), 1 biphenyl linkage, and 5 aromatic Cl (AroC-

271

Cl) groups. 1

272

3 6 ∙ [5 ∙ V ACH + VBiphenyl + 5 ∙ VCl ] 1 mol 107 nm 𝜎2 = ( ∙ ) ∙ = 0.704 nm 𝜋 6.02 ∙ 1023 molecules 1 cm

273 274

𝜎12 =

𝜎1 +𝜎2 2

= 0.439 nm, with 𝜎1 = 0.275 nm.

At 298K, we calculate 𝑔̅c using values for 𝐾 (0) , 𝐾 (1) , 𝐾 (2) , and 𝐾 (3) and Eq. 3, found in the body

275

of the paper

276

3 2 𝑔̅c = 𝐾 (0) + 𝐾 (1) σ12 + 𝐾 (2) 𝜎12 + 𝐾 (3) 𝜎12 = 63.8

277 278

(3)

Using 𝜎12 and 𝜖12 and substituting into Eq. 4, found in the body of the paper 𝑔̅i = 𝑅𝑇 (−

32 𝜖12 kJ 3 )( ) (𝜋𝜌1 𝜎12 ) = −74.4 9 𝑘B T mol

279 280

kJ mol

Δ𝑔̅2 = 𝑔̅i + 𝑔̅c = −10.6

(4) kJ mol

Finally, rearranging Eq. 2 from the body of the paper, 𝑅𝑇 Δ𝑔̅2 ∙ exp ( ) = 1.90 ∙ 106 Pa 𝜈1 𝑅𝑇

281

H2 (298K) =

282

This calculated result compares favorably to experiment 2.11 ∙ 106 Pa.11


15


Page 16 of 23

283

To illustrate the temperature dependence of Henry’s constant, we use an approximate van’t Hoff

284

equation (Eq. 5b). PCB 87 has 5 chlorine substituents, so an averaged entropy of −156 K∙mol is

285

chosen (Table A-1).

286 287 288 289

J

For T = 304K, rearrangement of Eq. 5b yields: H2 (𝑇) = H2 (298K) ∙ (

[Δ𝑔̅2 (298K) + 298K ∙ Δ𝑠̅2 ] 1 𝑇 1 ) ∙ exp ( ∙( − )) = 2.99 ∙ 106 Pa 298K 𝑅 𝑇 298K

This calculated result is comparable to the experimental value 2.77 ∙ 106 Pa.11 Table A-1: Suggested Δs̅ 2 for PCBs, PBDEs, and PCNs Halogenation number

Suggested 𝚫𝐬̅𝟐 [J/mol/K] PCBs11

1

-104

2

-110

3

-78

4

-67

5

-156

6

-234

7

-358

8

-488

9

--

10

-PBDEs13

1

--

2

--

3

-150

4

-130


16

Page 17 of 23


Halogenation number

Suggested 𝚫𝐬̅𝟐 [J/mol/K]

5

-140

6

-115

7

--

8

--

9

--

10

-120 PCNs16

1

--

2

--

3

-175

4

-175

5

-262

6

-334

7

-280

8

-210

290 291 292 293

Suggested partial molar entropies, Δs̅ 2 , for PCBs, PBDEs, and PCNs are determined from averaging experimental results for a given number of chlorines or bromines on the hydrocarbon molecule.

294

ASSOCIATED CONTENT

295

Supporting Information. The following files are available free of charge.

296

Full expressions for constants 𝐾 (0) , 𝐾 (1) , 𝐾 (2) , and 𝐾 (3) , two tables of H2, Δ𝑔̅2, 𝜎2 , and 𝜖2 at

297

25oC for 72 solutes, three figures of temperature-dependent H2 for 39 solutes, and SMILES tags

298

for all 72 solutes. (PDF) 51 x 15 matrix describing constituent functional groups for each

299

molecule in the fitting set. (XLSX)


17


300

AUTHOR INFORMATION

301

Corresponding Author

302

*Phone (408) 772-6293; e-mail [email protected].

303

Present Address

304

‡Department of Chemical Engineering and Materials Science, University of Minnesota,

305

Minneapolis, MN 55455, USA: effective September 1, 2017.

306

Author Contributions

307

†These authors contributed equally.

308

Notes

309

The authors declare no competing financial interest.

310

REFERENCES

311 312

Page 18 of 23

(1) Jones, K.C.; de Voogt, P. Persistent organic pollutants (POPs): state of the science. Environ. Pollut. 1999, 100 (1-3), 209-221.

313

(2) Harrad, S. Persistent organic pollutants; John Wiley & Sons: 2009; pp 1-5; 33-39.

314

(3) Persistent Organic Pollutants; Fielder, H., Eds.; The Handbook of Environmental Chemistry

315 316 317 318 319

3.0; Springer: New York, 2002. (4) Wania, F.; Mackay, D. Tracking the distribution of persistent organic pollutants. Environ. Sci. Technol. 1996, 30 (9), 390A-396A. (5) Beyer, A.; Mackay, D.; Matthies, M.; Wania, F.; Webster, E. Assessing long-range transport potential of persistent organic pollutants. Environ. Sci. Technol. 2000, 34 (4), 699-703.


18

Page 19 of 23


320

(6) Ritter, L.; Solomon, K.; R., Forget, J.; Stemeroff, M.; O’leary, C. A review of selected

321

persistent organic pollutants, Proceedings of the International Programme on Chemical Safety

322

(IPCS). December, 1995.

323

(7) Safe, S. Polychlorinated biphenyls (PCBs), dibenzo-p-dioxins (PCDDs), dibenzofurans

324

(PCDFs), and related compounds: environmental and mechanistic considerations which support

325

the development of toxic equivalency factors (TEFs). Crit. Rev. Toxicol. 1990, 21 (1), 51-88.

326 327 328 329 330 331 332 333

(8) Safe, S. H. Polychlorinated biphenyls (PCBs): environmental impact, biochemical and toxic responses, and implications for risk assessment. Crit. Rev. Toxicol. 1994, 24 (2), 87-149. (9) Safe, S.; Hutzinger, O. Polychlorinated biphenyls (PCBs) and polybrominated biphenyls (PBBs): biochemistry, toxicology, and mechanism of action. Crit. Rev. Toxicol. (10) Risebrough, R. W.; Rieche, P. Polychlorinated biphenyls in the global ecosystem. Nature. 1968, 220, 1098-1102. (11) Bamford, H.A.; Poster, D.L.; Baker, J.E. Henry’s law constants of polychlorinated biphenyl congeners and their variation with temperature. J. Chem. Eng. Data. 2000, 45 (6), 1069–1074.

334

(12) Tittlemier, S. A.; Halldorson, T.; Stern, G. A.; Tomy, G. T. Vapor pressures, aqueous

335

solubilities, and Henry's law constants of some brominated flame retardants. Environ. Toxicol.

336

Chem. 2002, 21 (9), 1804-1810.

337

(13) Cetin, B.; Odabasi, M. Measurement of Henry's law constants of seven polybrominated

338

diphenyl ether (PBDE) congeners as a function of temperature. Atmos. Environ. 2005, 39 (29),

339

5273-5280.


19


Page 20 of 23

340

(14) Wang, Y. H.; Wong, P. K. Mathematical relationships between vapor pressure, water

341

solubility, Henry's law constant, n-octanol/water partition coefficient and gas chromatographic

342

retention index of polychlorinated-dibenzo-dioxins. Water Res. 2002, 36 (1), 350-355.

343 344

(15) Govers, H. A.; Krop, H. B. Partition constants of chlorinated dibenzofurans and dibenzo-pdioxins. Chemosphere. 1998, 37 (9-12), 2139-2152.

345

(16) Odabasi, M.; Adali, M. Determination of temperature dependent Henry's law constants of

346

polychlorinated naphthalenes: Application to air-sea exchange in Izmir Bay, Turkey. Atmos.

347

Environ. 2016, 147, 200-208.

348 349

(17) Shen, L.; Wania, F. Compilation, evaluation, and selection of physical-chemical property data for organochlorine pesticides. J. Chem. Eng. Data. 2005, 50, 742–768.

350

(18) Paasivirta, J.; Sinkkonen, S.; Mikkelson, P.; Rantio, T.; Wania, F. Estimation of vapor

351

pressures, solubilities and Henry's law constants of selected persistent organic pollutants as

352

functions of temperature. Chemosphere. 1999, 39 (5), 811-832.

353 354

(19) Sedlbauer, J.; Bergin, G.; Majer, V. Group contribution method for Henry's law constant of aqueous hydrocarbons. AIChE J. 2002, 48 (12), 2936-2959.

355

(20) Bamford, H. A.; Poster, D. L.; Huie, R. E.; Baker, J. E. Using extrathermodynamic

356

relationships to model the temperature dependence of Henry's law constants of 209 PCB

357

congeners. Environ. Sci. Tech. 2002, 36 (20), 4395-4402.

358 359

(21) Kühne, R.; Ebert, R. U.; Schüürmann, G. Prediction of the temperature dependency of Henry's law constant from chemical structure. Environ. Sci. Tech. 2005, 39 (17), 6705-6711.


20

Page 21 of 23


360

(22) Gharagheizi, F.; Abbasi, R.; Tirandazi, B. Prediction of Henry’s law constant of organic

361

compounds in water from a new group-contribution-based model. Ind. Eng. Chem. Res. 2010, 49

362

(20), 10149-10152.

363 364

(23) Schulze, G.; Prausnitz, J.M. Solubilities of gases in water at high temperatures. Ind. Eng. Chem. Fundamen. 1981, 20 (2), 175-177.

365

(24) Dunnivant, F. M.; Elzerman, A. W.; Jurs, P. C.; Hasan, M. N. Quantitative structure-

366

property relationships for aqueous solubilities and Henry's law constants by polychlorinated

367

biphenyls. Environ. Sci. Tech. 1992, 26 (8), 1567-1573.

368 369 370

(25) O’Loughlin, D. R.; English, N. J. Prediction of Henry’s law constants via group-specific quantitative structure property relationships. Chemosphere. 2015, 127, 1-9. (26) Dunnivant, F. M.; Elzerman, A. W. Aqueous solubility and Henry's law constant data for

371

PCB

congeners

for

evaluation

of

372

(QSPRs). Chemosphere. 1988, 17 (3), 525-541.

quantitative

structure-property

relationships

373

(27) Puzyn, T.; Falandysz, J. QSPR Modeling of partition coefficients and Henry’s law constants

374

for 75 chloronaphthalene congeners by means of six chemometric approaches—a comparative

375

study. J. Phys. Chem. Ref. Data. 2007, 36 (1), 203-214.

376

(28) Katritzky, A. R.; Wang, Y.; Sild, S.; Tamm, T.; Karelson, M. QSPR studies on vapor

377

pressure, aqueous solubility, and the prediction of water− air partition coefficients. J. Chem. Inf.

378

Comput. Sci. 1998, 38 (4), 720-725.


21


Page 22 of 23

379

(29) Modarresi, H.; Modarress, H.; Dearden, J. C. QSPR model of Henry’s law constant for a

380

diverse set of organic chemicals based on genetic algorithm-radial basis function network

381

approach. Chemosphere. 2007, 66 (11), 2067-2076.

382 383 384 385 386 387

(30) Mackay, D.; Shiu, W. Y.; Ma K.; Lee, S. C. Handbook of physical-chemical properties and environmental fate for organic chemicals; CRC Press: 2006. (31) Buccafusco, R.J.; Ells, S.J.; LeBlanc G.A. Acute Toxicity of Priority Pollutants to Bluegill (Lepomis macrochirus). Bull Environ.Contam. Toxicol. 1981, 26, 446-452. (32) Fredenslund, A.; Jones, R.L.; Prausnitz, J.M. Group-contribution estimation of activity coefficients in nonideal liquid mixtures. AIChE J. 1975, 21 (6), 1086-1099.

388

(33) Abildskov, J.; Gani, R.; Rasmussen, P.; O’Connell, J.P. Analysis of infinite dilution activity

389

coefficients of solutes in hydrocarbons from UNIFAC. Fluid Phase Equilibria. 2001, 181 (1-2),

390

163-186.

391 392

(34) Abildskov, J.; Gani, R.; Rasmussen, P.; O’Connell, J.P. Beyond basic UNIFAC. Fluid Phase Equilibria. 1999, 158-160, 349-356.

393

(35) Voustas, E.C.; Tassios, D.P. Analysis of the UNIFAC-Type Group-Contribution Models

394

at the Highly Dilute Region. 1. Limitations of the Combinatorial and Residual Expressions. Ind.

395

Eng. Chem. Res. 1997, 36 (11), 4965-4972.

396 397 398 399

(36) Helfand, E.; Reiss, H.; Frisch, H. L.; Lebowitz, J. L. Scaled particle theory of fluids. J. Chem. Phys. 1960, 33, 1379. (37) Pierotti, R. A. A scaled particle theory of aqueous and nonaqueous solutions. Chem. Rev. 1976, 76 (6), 717-726.


22

Page 23 of 23

400 401 402 403


(38) Yu, Y.; Wu, J. Structures of hard-sphere fluids from a modified fundamental-measure theory. J. Chem. Phys. 2002, 117 (22), 10156-10164. (39) Sharp, K.A.; Nicholls, A.; Fine, R.F.; Honig, B. Reconciling the Magnitude of the Microscopic and Macroscopic Hydrophobic Effects. Science. 1991, 106-109.

404

(40) Bondi, A. van der Waals volumes and radii. J. Phys. Chem. 1964, 68 (3), 441-451.

405

(41) Urbaszek, P.; Gajewicz, A.; Sikorska, C.; Haranczyk, M.; Puzyn, T. Modeling adsorption

406

of brominated, chlorinated and mixed bromo/chloro-dibenzo-p-dioxins on C60 fullerene using

407

Nano-QSPR. Beilstein J Nanotechnol. 2017, 8, 752-761.

408

(42) Zacs, D.; Rjabova, J.; Fernandes, A.; Bartkevics, V. Brominated, chlorinated and mixed

409

brominated/chlorinated persistent organic pollutants in European eels (Anquilla anquilla) from

410

Latvian lakes. Food Addit Contam Part A. 2015, 33 (3), 460-472.

411

FOR TABLE OF CONTENTS ONLY:

412


23

Henry's Constants of Persistent Organic Pollutants ... - ACS Publications

Recommend Documents