Sources and Fates of Aquatic Pollutants - American Chemical Society

1 Methods for Estimating Solubilities of Hydrophobic Organic Compounds: Environmental Modeling Efforts Downloaded by BRANDEIS UNIV on October 9, 2013 | http://pubs.acs.org Publication Date: June 15, 1987 | doi: 10.1021/ba-1987-0216.ch001

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Anders W. Andren, William J. Doucette , and Rebecca M. Dickhut Water Chemistry Program, University of Wisconsin—Madison, Madison, WI 53706

A variety of environmental fate models that integrate physicochemical properties of pollutants with advective and diffusive transport equations are now available. To satisfy the demand for missing input data, scientists have begun to incorporate property estimation techniques as part of their computational procedures. The recent appearance of high quality solubility data for polyhalogenated organic compounds makes it possible to evaluate several predictive schemes for these compounds. In this work, a brief review of the thermodynamics of hydrophobic compound solubility relationships is presented. This review is followed by an examination of the UNIFAC activity coefficient prediction technique. The use of octanol-water partition coefficients, total molecular surface areas, and molecular connectivity indexes to predict aqueous solubilities is then examined, and the resulting correlationsare presented.

MATHEMATICAL

M O D E L I N G O F C H E M I C A L F A T E provides an excellent

framework for sorting massive quantities of environmental data in a logical way. Parameters in a model may be varied to gain an understanding as to what processes are most important in determining the environmental behavior of a chemical. One of the most useful modeling approaches integrates data on physicochemical properties of the compound in question with hydrodynamic or aerodynamic transport models. This approach uses the results of such laboratory measurements or calculations as aque-

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Current address: Environmental Engineering Department, Utah State University, Logan, U T 84322-4110 0065-2393/87/0216-0003$07.00/0 © 1987 American Chemical Society

In Sources and Fates of Aquatic Pollutants; Hites, R., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1987.

Downloaded by BRANDEIS UNIV on October 9, 2013 | http://pubs.acs.org Publication Date: June 15, 1987 | doi: 10.1021/ba-1987-0216.ch001

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SOURCES AND FATES OF AQUATIC POLLUTANTS

ous solubility, saturation vapor pressure, liquid and vapor molecular diffusivity, Henry's law constant, U V absorption, sorption-partition coeffi cient, photolysis rate, chemical oxidation rate, and hydrolysis rate. These data are then incorporated into various steady-state or time-dependent fate models. Some of the models most widely used by aquatic and atmospheric scientists have been reviewed by Dickson et al. (J) and Sheehan et al. (2). In these models, much of the aforementioned data are lacking for hydrophobic organic compounds of environmental interest. The tem perature dependence of these parameters is also lacking, so most present assessments cannot be determined as a function of temperature. Property estimation techniques have been used extensively in the chemical engineering and drug design fields (3, 4). Recently, a hand book of chemical property estimation techniques was published (5). To date, however, most techniques have been evaluated with test data sets of relatively high solubility (>1 Χ 10"6 M ) , and the solubility data of the most hydrophobic compounds have been of uneven quality (6, 7). Very recent work has produced high quality aqueous solubility data for polychlorinated biphenyls (PCBs), polybrominated biphenyls (PBBs), methylated biphenyls, polychlorinated dibenzodioxins (PCDDs), and polychlorinated dibenzofurans (PCDFs) (8-10). Dickhut et al. (II) have also examined temperature effects on solubility for PCBs. In this chapter, we briefly review a few of the most important aqueous solubility predictive methods. This property was chosen because Henry's law constants can be computed by using the approximation Ps = HCS, where P $ is saturation vapor pressure, H is Henry's law constant, and Cs is aqueous solubility. Henry's law constants may then be used to calculate liquid- and gas-phase transfer coefficients for incorporation into atmospheric flux models, for example, those models recently reviewed in Liss and Slinn (12) or presented by Mackay et al. (13). We will first present the thermodynamic background necessary to understand some of the estimation techniques. This review is followed by an examination of the use of four activity coefficient prediction schemes with respect to their ability to predict values for chlorinated aromatic hydrocarbons ranging in solubility from 1 Χ 10"3 to 1 X 10~13 M .

Theory

Aqueous Solubility. The solubility of a substance may be con sidered to be an equilibrium partitioning between the pure chemical and that in solution at a specified temperature. Historically, thermodynamicists first developed the concept of "ideal solubility" that was used as an initial approximation to describe the solution behavior of solutes. How ever, solubility is a function of the various molecular forces that operate


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ANDREN ET AL.

5

Methods for Estimating Solubilities


between solvent and solute molecules. Prausnitz et al. (14) classified intermolecular forces into four somewhat arbitrary types: electrostatic, induction, London dispersion, and specific chemical forces. These forces must also be incorporated into any real model that will accurately de scribe solubility. Hildebrand and Scott (15) give a thermodynamic definition of an ideal solution: one in which the activity (a) equals the mole fraction (X) over the entire composition range and over a nonzero range of tempera ture and pressure. This definition establishes the ideal solution in the sense of Raoult's law. Thus, for an ideal solution: X2 = a

(1)

2

where the subscript 2 refers to the solute. The activity may be viewed as a measure of the difference between the substance's free energy at the state of interest and that at its standard state. Lewis and Randall (16) defined the activity as the ratio of the pure solute fugacity at any temperature and pressure to its fugacity at some standard state: =

°2

u (Γ,Ρ,Χ) h (Τ,ΡΙ,ΧΙ)

=

h ff

m 1

where the superscript ss refers to the standard state, and /, T, and Ρ denote fugacity, temperature, and pressure, respectively. Fugacity may be considered as the escaping tendency of a substance. The standard-state composition ( X ° ) and pressure (P 2 ) are arbitrary, but the temperature must be the same as the state of interest. For organic nonelectrolytes, the standard-state fugacity is usually defined as the fugacity (vapor pres sure) of the pure liquid solute at the solution temperature. Because equilibrium partitioning of a solute between phases is achieved when fugacities or chemical potentials are equal, the equilib rium solution condition for the ideal liquid solute is

/2

72

where the superscript L denotes liquid. This equilibrium condition fol lows because /£, the fugacity of the pure liquid, is equal to the standard state fugacity (ff), which we chose as the pure liquid. The ideal solubility equation for liquids reduces to X | = 1, which indicates solubility for all mole fractions (infinite miscibility) of a liquid in a liquid.


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For a solid, the equation of equilibrium for an ideal solution is

where f| is the fugacity of the pure solid solute, and /fL is the fugacity of the pure supercooled liquid. The supercooled liquid is a hypothetical state in which the solid is considered to be a liquid at a temperature below its melting point. The supercooled liquid is usually chosen as the standard state for solids. Thus, the fugacity ratio for solids is dependent on the free energy necessary to melt the solid and may be calculated from thermodynamic considerations (14) by

where AHf is the enthalpy of fusion (kcal mol" 1 ), Tt is the triple point temperature (K), ACP is the change in solute heat capacity (cal deg" 1 mol - 1 ) when changing from a solid to a liquid at constant pressure, and R is the gas constant. Because the triple point and melting point temper atures are very close, the melting point temperature (Tm) is usually used in equation 5. At the melting point, the phases are in equilibrium and AGf

= AHf - TASf

= 0

(6)

where AGf and ASf are Gibbs free energy of fusion and entropy of fusion, respectively. In this case, AHf

= TASf

(7)

and equation 5, together with equation 4, takes the form:

bXI —

- f - ( i - l )

+

ψ

( i - l )

W

Very few determinations of ACP for hydrophobic organic com pounds have been reported. One of the following three assumptions is generally made. Either (a) the values of ACP are small, and because the terms containing this parameter are of opposite sign, the last two terms on the right side cancel (14); (b) ACP =0 (17); or (c) ACP = ASf, which is a constant (18). At the present time, not enough evidence exists to


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ANDREN ET AL.


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substantiate any one of these assumptions. However, equation 8 reduces to equation 9 by assumption a or b or to equation 10 by assumption c.

The ideal solubility equations have proved to be reliable for estimating solubilities of liquids and solids in solvents of a similar chemical nature. This reliability results from the fact that ideal solubility depends only on the properties of the solute and is independent of the nature of the sol vent (15). Real solutions, especially hydrophobic compounds dissolved in water, do not behave ideally. In contrast to ideal solutions, the mole fraction in a real solution is not equal to, but proportional to, the activity. On the basis of Raoult's law, the solute deviation from ideality is de scribed by an activity coefficient, y 2 (16), so that equations 1 and 2 are modified to

e« = 72X2 = - ^ r

(Π)

When 72 > 1, the fugacity of the solute is greater than in an ideal solu tion of the same concentration. Similarly, when y2 < 1, the fugacity is lower than in an ideal solution of the same concentration (19). In nonpolar solutions, where only dispersion forces are important, 72 is generally larger than unity (i.e., lower solubility than that predicted from ideal solubility). In cases where polar or specific chemical forces are impor tant, 72 may be less than unity. In terms of thermodynamic functions, 72 represents the excess Gibbs free energy (GexceSs) associated with nonideal solutions. From phase-equilibrium thermodynamics (14), Ge x c e s s

Gr e a i

G ideal (12)

G r e a l = RT In / r e a l = RT In f$X2y2 G i d e a l = RT In / i d e a I = RT In / f X 2 Substituting equations 13 and 14 into equation 12 yields

(13) (14) (15)

'-"excess RT

In 72


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The activity coefficient thus gives a quantitative measure of departure from ideal behavior. If no solubility of the solvent in the solute occurs, the solubility model is modified by the addition of this correction term. The expres sion for mole fraction solubility becomes Xt = ( / · / / « (1/72)

(16)


where / * represents the pure solute (liquid or solid) fugacity. For a liq uid, the expression may conveniently be expressed in a logarithmic form: In Xk = - In 72

(17)

This expression is valid because fk = /Is at equilibrium. The model may be similarly expressed for solids by combining equation 16 with equation 9 or 10 to yield equation 18 or 19, respectively. lnXl =

—ASf R

1

Tm Τ

l-ln72

(18)

In 72

(19)

In XI = =j$LIn

Equations 18 and 19 would not be particularly useful because the existence of entropy of fusion values is rather limited in the literature. However, Yalkowsky (20 ) found that rigid aromatic molecules exhibit a fairly constant value for this term of 13.5 eu (Walden's rule). Miller et al. (8) subsequently showed that 16 PCBs exhibited ASf values ranging from 12.6 to 16.4 eu and had an average value of 13.2 eu. A reasonable approximation for the entropy term will likely be achieved with ASf = 13.2 for PCBs, polycyclic aromatic hydrocarbons (PAHs), furans, and dioxins. Also, if fl = 1.987 cal/deg mol, and Τ = 298 Κ, equations 18 and 19 can be further simplified to equations 20 and 21, respectively. In XI = 6.64 - 0.0223 Tm - In 72

(20)

In XI = 37.8 - 6.64 In T

(21)

m

Equations experimentally liquids can be the solid in the equation 20:

- In 72

17, 20, and 21 can be very useful. The value Tm is an accessible parameter, and the solubility of solids and compared. The effect of the energy necessary to melt overall solution process can be visualized by rearranging


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XI 72 = e(6W-00223 T )

(22)


m

The amount of energy necessary for this melting process is zero for a substance that is a liquid at the temperature of interest, and this energy increases exponentially for solids of increasing Tm. Figure 1 shows this effect for solubilities at 25 ° C on solids of varying T m . Thus, the importance of the correction factor can easily be appreciated for a halogenated aromatic hydrocarbon whose Tm = 400 ° C because the solid solubility is reduced approximately 4500 times when compared with the liquid solubility. Our ability to provide a thermodynamic framework to account for the energy required to overcome the crystalline lattice forces inherent in a solid solute is important for attempts to predict aqueous solubilities. This thermodynamic framework is also necessary and must be applied to vapor pressure and Henry's law constant predictive schemes. 5. 00

100

200

300

400

500

T m (°C) Figure 1. Melting point correction factor as a function of T m on solubility at 25 ° C .




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Activity Coefficient Estimation Techniques. Various molecular models and predictive techniques have been devised to calculate solute activity coefficients from the properties of the pure components. Reviews of efforts in this area were written by Hildebrand et al. (21), Ben-Nairn (22), Pierotti (23), Prausnitz et al. (14), and Acree (24). Precise theoretical treatment of the various solution interactions has proven to be too complicated to be feasible for incorporation into our present models. A more practical and attractive approach that has found widespread application is to examine the relationships between aqueous solubility and intrinsic molecular properties that are readily determined either on a computational or experimental basis. Some of the more widely used techniques employed by workers in the field of drug design and environmental science are the following: • universal quasi-chemical functional groups activity coefficient (UNIFAC) (25-27) m experimental log Kow (octanol-water partition coefficient) (9,28) • calculated log K o w (29, 30) m molecular connectivity (9, 3J-33 ) • molar volume (34-36 ) m molecular weight (9, 37) • molecular surface area (7, 9, 38-42) m solvametric parameters (43-45) Although the U N I F A C method and various modifications of the Seatchard-Hildebrand techniques employ sound thermodynamically derived components, several approaches employ only an appropriate amount of chemical intuition in combination with multiregressional analysis. In this review, we summarize some of the efforts that have been applied toward predicting aqueous activity coefficients of halogenated aromatic hydrocarbons of environmental interest. U N I F A C . One of the more thermodynamically sound models for determining the activity coefficient is the U N I F A C group contribution method. This method is based on the concept that, whereas literally millions of organic chemicals are known, the number of functional fragments (groups) that constitute these compounds is limited. The activity coefficient is divided into two parts: the combinatorial contribution, due mostly to differences in molecular size and shape, and the residual contribution, accounting for differences in intermolecular forces of attraction (26, 46). For a molecule i in any solution,


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A N D R E N ET AL.


In 7

i

= In yf + In

11

(23)

7?

where 7 , is the total activity coefficient, yi is the combinatorial part, and yf is the residual part. For a solute in water, the combinatorial part in equation 23 is given by equation 24 (25).


In yî = In

+ f

In

^

+ h - 4r- Μ

+ ΧΛ)

(24)

where ζ is the coordination number; fa is the segment fraction; Θ% is the area fraction; and the subscripts 1 and 2 denote the solvent and solute, respectively. The parameters are defined as follows:

*

= 1 rixi + r x 2

θ 2

h =

(25) 2

Sources and Fates of Aquatic Pollutants - American Chemical Society

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