Atmospheric Environment 37 (2003) 2867–2878

Is vapor pressure or the octanol–air partition coefficient a better descriptor of the partitioning between gas phase and organic matter? Hang Xiao, Frank Wania* Department of Chemical Engineering and Applied Chemistry and Department of Physical and Environmental Sciences, University of Toronto at Scarborough, 1265 Military Trail, Toronto, Ont., Canada M1C 1A4 Received 1 November 2002; received in revised form 24 February 2003; accepted 6 March 2003

Abstract Both the sub-cooled liquid vapor pressure (PL ) and the octanol–air partition coefficient (KOA ) are used to describe the partitioning of non-polar organic compounds between the gas phase and a variety of natural organic substrates in soil, atmospheric particles and foliage. Whether the former is preferable over the latter depends on whether the interaction of the organic compound with the organic matter (OM) resembles more those in the pure liquid than those in liquid octanol. The activity coefficient in octanol (gOct ) is a quantitative measure of the difference between these two interactions. An analysis of PL and KOA values for several sets of non-polar and semi-volatile organic compounds (chlorobenzenes, PCBs, PCNs, PCDD/Fs, PBDEs), and of the gOct values derived from these, reveals that gOct tends to range from 1 to 10 suggesting that PL and KOA are very highly correlated. Furthermore, the estimated standard deviation of gOct tends to be so large that PL and KOA are virtually indistinguishable within the measurement uncertainty. Whether gOct within a group of related compounds increases, decreases or stays the same with increasing molecular mass depends on the specific KOA and PL data set used in the calculation of gOct : This implies that with the current precision of KOA ; PL and partition coefficients involving OM it is impossible to judge one parameter better than the other. r 2003 Elsevier Science Ltd. All rights reserved. Keywords: Activity coefficient in octanol; Octanol–air partition coefficient (KOA ); Sub-cooled liquid vapor pressure (PL ); Environmental phase partitioning

1. Introduction Environmentally relevant phase equilibria of organic contaminants are traditionally generalized using simple linear free energy relationships with basic physical– chemical properties involving the pure substance or the octanol phase. Specifically, equilibrium coefficients between organic matter (OM) and the gas phase KOM=A are commonly regressed with a compound’s *Corresponding author. Tel.: +1-416-287-7225; fax: +1416-287-7279. E-mail address: [email protected] (F. Wania).

liquid state vapor pressure PL : log KOM=A ¼ m log PL þ b

ð1Þ

or, more recently, with the compound’s octanol–air partition coefficient KOA : log KOM=A ¼ m log KOA þ b:

ð2Þ

Specifically, the partitioning between air and OM of atmospheric particles has been described using PL (Pankow, 1994) and KOA (Finizio et al., 1997; Pankow, 1998; Harner and Bidleman, 1998a; Shoeib and Harner, 2002). Eqs. (1) and (2) often use the bulk phase partition coefficient KPA rather than KOM=A ; because the content

1352-2310/03/$ - see front matter r 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S1352-2310(03)00213-9

H. Xiao, F. Wania / Atmospheric Environment 37 (2003) 2867–2878

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Nomenclature gOct gOM fOM

activity coefficient of the chemical in octanol at infinite dilution activity coefficient of the chemical in organic matter (OM) phase mass fraction of OM in the sorbing phase

of OM in the particles is unknown and thus cannot serve to normalize the measured distribution coefficients. KOA has also been used to describe the partitioning between the gas phase and the OM in soils (Hippelein and McLachlan, 1998; Harner and Shoeib, 2002), plants (Tolls and McLachlan, 1994; Hiatt, 1998; Welke et al., 1998), human faeces (Moser and McLachlan, 2002) and urban organic film (Diamond et al., 2000). KOA has even been used to describe the partitioning into nasal and lung tissue (Hau et al., 2000, 2002) and synthetic organic polymers used as sampling medium for gaseous organic contaminants (Muller . et al., 2000; Wilcockson and Gobas, 2001; Shoeib and Harner, 2002). The rationale of such relationships is to predict a compound’s environmentally relevant phase distribution behavior from a knowledge of its basic physical– chemical properties. Such relationships are strictly only applicable within a group of structurally related substances, i.e. the regression coefficients m and b differ for different compound classes (Goss and Schwarzenbach, 1998). They have, however proven useful when restricted to the group of semi-volatile, non-polar organic pollutants that interact with OM predominately by dispersive interactions. That group includes many persistent organic pollutants, in particular a large number of halogenated aromatic compounds. Recently, it has become common practice to regress both PL and KOA against an empirically derived KOM=A or KPA data set for such contaminants, and pass a judgement on the suitability of either parameter to describe the data set by means of the goodness of fit. This is particularly common for data sets involving atmospheric particles (Kaupp and McLachlan, 1999; Lee and Jones, 1999; Lohmann et al., 2000b; Falconer and Harner, 2000; Oh et al., 2001; Hung et al., 2002), but has for example also been used on a data set of the sorption of non-polar VOCs to indoor surface materials (Won et al., 2000, 2001). Some studies reported that KOA was found to explain better than PL the observed variability of KPA within a compound class and between compound classes, whereas other studies found no evidence for such difference in fit. Usually, little or no consideration is given to the quality and uncertainty of the chosen physical–chemical property data sets and the impact these may have on the judgement, although both Lohmann et al. (2000a) and Hung et al. (2002) noted the

KOA KOM=A KPA PS PL R

octanol–air partition coefficient, volume basis OM–air partition coefficient bulk phase–gas partition coefficient solid phase vapor pressure, Pa sub-cooled liquid vapor pressure, Pa gas constant (=8.314 Pa m3 mol1 K1)

impact that the choice of PL data had on predicting the partitioning of PCDD/Fs onto atmospheric particles.

2. Theory If the KOA is defined for an infinitely dilute solution of the chemical in octanol, the two parameters PL and KOA are related through the following equation (Goss and Schwarzenbach, 1998): KOA ¼ RT=ðVOct;N gOct;N PL Þ;

ð3Þ

where R; T and VOct;N are the ideal gas constant, temperature and the molar volume of octanol at infinite dilution, respectively. The expression 1=ðVOct;N gOct;N Þ is the solubility of the chemical in octanol if it were to have the same activity coefficient and molar volume as it does at infinite dilution. At dilute concentrations VOct is the same for all chemicals (0.000158 m3 mol1), and we can write log KOA ¼ log PL  log gOct þ constant:

ð30 Þ

The activity coefficient in octanol, gOct can thus serve as a quantitative expression of the difference between the two partitioning properties PL and KOA : Analogously, a KOM=A that is a ratio of molar concentrations, can be related to PL using KPA =fOM ¼ KOM=A ¼ RT=ðVOM gOM PL Þ:

ð4Þ

Assuming constancy of VOM and using logarithms, we yield log KOM=A ¼ log PL  log gOM þ constant:

ð40 Þ

By combining Eqs. (3) and (4), we can further relate KOM=A to KOA : KPA =fOM ¼ KOM=A ¼ VOct gOct KOA =ðVOM gOM Þ;

ð5Þ

log KOM=A ¼ log KOA þ logðgOct =gOM Þ þ constant;

ð50 Þ

where VOM and gOM are the average molar volume and the activity coefficient in the OM, respectively. A comparison of Eqs. (40 ) and (50 ) led Pankow (1998) to suggest that KOA is more suitable than PL in describing KOM=A ; because the ratio gOct =gOM is more likely to remain constant for different compounds than is gOM : However, Goss and Schwarzenbach (1998) showed that constancy of the term gOM is not required

H. Xiao, F. Wania / Atmospheric Environment 37 (2003) 2867–2878

to achieve linear regressions of type (40 ). A constant gOM is only needed to obtain a slope of 1. Linear regressions with slopes different from 1 could still be obtained when gOM varies proportionally with PL : Equivalently, a constant ratio gOct =gOM is required to obtain a linear regression of type (50 ) with a slope of 1, but linear regression with different slopes can be obtained if gOct =gOM varies proportionally with KOA : Assuming that PL and KOA were known with equal accuracy, the question of whether PL or KOA is a better descriptor of KOM=A for a group of related compounds becomes a question of whether gOM or the ratio gOM =gOct is more likely to vary linearly within that group of compounds. The answer to that question would at least require knowledge of whether gOct increases, decreases or stays the same within that group of related compounds. If gOct stays the same, PL and KOA would be equally suited to describe the variability in KOM=A ; because gOM and gOM =gOct would then vary by the same extent. In this contribution we compiled and evaluated a large data set of PL and KOA data for non-polar substances. Not only can we show that the two parameters are highly correlated and the activity coefficient gOct varies only over a very small range, we further demonstrate that with the currently available data it is impossible to tell whether gOct is increasing, decreasing or staying constant within a group of related compounds. This implies that within the current measurement uncertainty of PL and KOA it is impossible to determine whether one parameter is preferable over the other. Differences in the fit of regression equations observed in various studies are thus largely due to the difference in the quality and consistency of the physical– chemical data sets.

3. Data compilation Data sets for the PL and KOA of different chemicals were gathered from the literature (see Table 1) and adjusted to 298.15 K using the regression equations or thermodynamic properties provided in the publications. The data sets included mostly non-polar semi-volatile compounds, in particular halogenated aromatic hydrocarbons such as the chlorobenzenes (CBs), polychlorinated biphenyls (PCBs), naphthalenes (PCNs), dibenzop-dioxins (PCDDs) and dibenzofurans (PCDFs), and chlorinated and brominated diphenyl ethers (PCDEs and PBDEs). Other compound groups included were the organochlorine pesticides, the polycyclic aromatic hydrocarbons (PAHs), and a number of more volatile substances. Since the liquid vapor pressure of semi-volatile organic chemicals at ambient temperature is not accessible to direct experimental determination, most

2869

of the PL data sets were derived from gas chromatographic retention time measurements (Eitzer and Hites, 1988; Hinckley et al., 1990; Falconer and Bidleman, 1994; Kurz and Ballschmiter, 1999; Lei et al., 1999, 2002; Wong et al., 2001; Tittlemier and Tomy, 2001; Tittlemier et al., 2002). Other PL data sets were converted from directly measured solid phase vapor pressures (Rordorf, 1989; Mader and Pankow, 2003), taken from a recent data compilation (Shiu and Ma, 2000), or theoretically derived (Govers and Krop, 1998). The PL for hydrocarbons and some other chemicals was calculated based on data given in Dean (1992). Most of the KOA values had been determined by Harner and coworkers using the generator column technique (Harner and Mackay, 1995; Harner and Bidleman, 1996, 1998a, b; Harner et al., 2000; Harner and Shoeib, 2002; Shoeib and Harner, 2002). Other KOA data were derived from gas chromatographic retention times (Zhang et al., 1999; Su et al., 2002; Wania et al., 2002), head space analysis (Abraham et al., 2001) or . fugacity meter measurements (Komp and McLachlan, 1997). The KOA values of the PCDEs were calculated as the ratio of the octanol–water partition coefficient KOW and the air–water partition coefficient KAW (Kurz and Ballschmiter, 1999), which may lead to an underestimation of KOA due to the effect of the mutual solubility of octanol and water.

4. Correlation between PL and KOA The log PL of the selected chemicals varied over more than 10 orders of magnitude from 6.05 to 7.20. The log KOA values varied over a similarly large range from 0.95 to 11.89. The most recently reported KOA and PL data (indicated by italics in Table 1) were selected and related to each other in a plot of log KOA vs. log PL (Fig. 1). A very tight correlation spanning the full 10 orders of magnitude is observed. The graph includes two diagonal lines that correspond to the theoretically expected relationship between KOA and PL (Eq. (30 )), if the activity coefficients in octanol gOct for all chemicals had values of 1 or 10, respectively. Remarkably, virtually all data points fall in between these two lines. There are two notable exceptions, which we believe are due to poor data quality. The PL and KOA data pairs for the PCDEs reported by Kurz and Ballschmiter (1999) deviate very strongly from the rest of the data, and yield gOct values in excess of 1000. This is clearly unreasonable and suggests flawed data, presumably due to the use of an inappropriate method for deriving KOA : The other exception involves compounds with very low volatility, i.e. a log KOA above 11 and a log PL of less then 5. We believe this is a result of the limitations of the generator column technique to accurately determine extremely high KOA values. As shown in Fig. 2, the

H. Xiao, F. Wania / Atmospheric Environment 37 (2003) 2867–2878

2870

Table 1 Studies used in the compilation of liquid state vapor pressures PL ; octanol–air partition coefficients KOA and activity coefficients in octanol gOct for several groups of non-polar organic chemicals Group

Reference

PCNs PL KOA

Lei et al. (1999) Su et al. (2002), Wania et al. (2002), Harner and Bidleman (1998b), and Lei et al. (1999)

PCBs PL KOA

Falconer and Bidleman (1994) . Zhang et al. (1999), Harner and Mackay (1995), Harner and Bidleman (1996), and Komp and McLachlan (1997)

Chlorobenzenes PL Shiu and Ma (2000) KOA Harner and Shoeib (2002), Harner and Mackay (1995), and Su et al. (2002) PBDEs PL KOA

Wong et al. (2001), Tittlemier and Tomy (2001), and Tittlemier et al. (2002) Shoeib and Harner (2002)

OC pesticides PL Hinckley et al. (1990) KOA Harner and Shoeib (2002) Hydrocarbons PL Dean (1992) KOA Abraham et al. (2001) gOct Tse and Sandler (1994) PCDD/Fs PL KOA

Mader and Pankow (2003)a, Rordorf (1989)a, Govers and Krop (1998) and Eitzer and Hites (1988 and erratum 1998) Harner et al. (2000)

PAHs PL KOA

Lei et al. (2002) and Hinckley et al. (1990) Abraham et al. (2001) and Harner and Bidleman (1998a)

Others PL KOA gOct

Dean (1992) Abraham et al. (2001) Tse and Sandler (1994)

PCDEs PL KOA

Kurz and Ballschmiter (1999) Kurz and Ballschmiter (1999)

Note: The studies shown in italics were used in Fig. 1. a PL calculated from solid state vapor pressure using melting point temperatures and entropies of fusion reported in Rordorf (1989).

reported measured KOA values of very highly halogenated PCDD/Fs and PBDEs (Harner et al., 2000) do not adhere to the linear relationships between log KOA and molecular weight that is apparent for the less halogenated congeners, suggesting that the KOA values for the heavier congeners tend to be too low. It should be noted that for the heavy congeners of PCDD/Fs, such as 1,2,3,4,6,7,8-H7CDD and 1,2,3,4,7,8-H6CDD, the KOA

was directly measured by the generator column method only at three temperatures (Harner et al., 2000). The KOA values at 298.15 K obtained by a regression with temperature are likely to have a larger error than those that rely on measurements at a larger number of experimental temperatures. Although some error may be eliminated by using gas chromatographic retention times to get the KOA values of the other congeners, a

H. Xiao, F. Wania / Atmospheric Environment 37 (2003) 2867–2878

γOct =1

13

2871

PCNs PCBs CBs PBDEs

11

OC Pesticides Hydrocarbon 9

Others

log KOA

PCDDs PCDFs 7

PAHs PCDEs

γOct =100

5

3

1

γOct =10 -1 -7

-5

-3

-1

1

3

5

7

log (PL / Pa) Fig. 1. Linear relationship and regression equation between the log KOA and log PL of more than 200 non-polar organic chemicals (see Table 1 for source of data). The solid diagonal lines correspond to activity coefficients in octanol gOct of 1, 10 and 100, respectively. The broken line is the linear regression for all chemicals, except the PCDEs and the PCDD/Fs with a log KOA > 11:11:

obtained for the remaining 222 chemicals:

12

Log KOA ¼ ð0:9878470:00584Þlog PL

PCDD/Fs

þ ð6:691470:0171Þ

log KOA

11

ð6Þ

The correlation coefficient of the regression curve is very high, and the slope is very close to 1 (see Eq. (30 )). This means that gOct remains constant or changes only very slightly with PL : A regression of log gOct vs. the corresponding log PL data is drawn in Fig. 3A. The linear regression equation is

PBDEs

10

r2 ¼ 0:9924:

9

log gOct ¼ ð0:012270:0058Þlog PL 8

þ ð0:50370:017Þ 200

300

400

500

600

700

Molecular Weight Fig. 2. The plot of log KOA values of the PCDD/Fs and PBDEs measured by Harner et al. (2000) and Harner and Shoeib (2002) against molecular weight. The highly halogenated congeners have KOA values that are slightly lower than would be expected from a linear extrapolation of the relationships that are apparent for the less halogenated congeners.

noticeable deviation still can be observed for the heavier congeners. When eliminating the data points deemed erroneous from Fig. 1, the following regression equation is

r2 ¼ 0:0195:

ð7Þ

A similar relationship can be obtained between log gOct and log KOA (Fig. 3B): log gOct ¼ ð0:004670:0059Þlog KOA þ ð0:484170:051Þ r2 ¼ 0:0028:

ð8Þ

The slopes of Eqs. (7) and (8) are close to zero, which means that there is very little variation in gOct with volatility among the investigated compounds. For example, a log PL increase from 5 to 7, only results in a decrease in gOct from 3.66 to 2.61. Fig. 4A and B shows histograms of log gOct and of the difference between the measured data and those predicted by regression Eq. (7). The variability of the log gOct values is well described by a normal distribution that has a mean

H. Xiao, F. Wania / Atmospheric Environment 37 (2003) 2867–2878 1.2

1.2

1.0

1.0

0.8

0.8

log γ Oct., rep.

log γ Oct., rep.

2872

0.6 0.4

0.6 0.4

0.2

0.2

0.0

0.0

-0.2

-0.2 -6

-4

-2

0

2

4

6

8

-2

log P L

log γ Oct., rep.

0

2

4

6

8

10

12

log K OA 95% Confidence Limit

95% Prediction Limit

Fig. 3. Relationship between the activity coefficient in octanol gOct and the sub-cooled liquid vapor pressure PL or octanol–air partition coefficient KOA for 222 non-polar organic chemicals, and the confidence and prediction limits of the linear regression between log gOct and log PL or log KOA : Only a few data lie beyond the 95% prediction limit.

50

40 Frequency

40

Frequency

Count

Count

30

20

30

20

10

10

0 -0.2

0.0

0.2

0.4

0.6

0.8

1.0

log γ Oct

0 - 0.8 -0.6 -0.4 -0.2

0.0

0.2

0.4

log γ Oct., rep.−log γ Oct., perd.

0.6

Fig. 4. Histogram of the logarithm of the activity coefficient in octanol log gOct for 222 non-polar organic chemicals and superimposed normal distribution. Also shown is the distribution of predicted deviations between the reported data and the values of log gOct predicted from Eq. (7).

value of 0.522 (corresponding to a mean value of gOct of 3.75) and a standard deviation of 0.220. Further analysis shows that there is no significant difference between the reported data set and their average value (t ¼ 1:3  1014 ). The two-sample paired t-test for the values predicted by Eq. (7) and the measured data also shows that the difference between those two populations is not significant. For Eq. (7), although the r2 is only 0.0195, the t-test and F -test results show that the linear relationship is significant (F ¼ 4:38), and the intercept is a more important parameter (t ¼ 29:36; p ¼ 4:69  1078 ) than the slope (t ¼ 2:09; p ¼ 0:038). All this confirms that the activity coefficient in octanol does not change significantly between the investigated chemicals. The experimental variability of the gOct values

is larger than the change of gOct with volatility over 10 orders of magnitude. The use of the most recent PL and KOA data in Figs. 1, 3 and 4 and Eqs. (6)–(8) does not imply that we judge these data to be better than earlier measurements. It was merely a means of arbitrarily choosing one data set for each compound group. The conclusion above would be identical with any other combination of data sets listed in Table 1. Incidentally, this analysis suggests that for non-polar substances PL and KOA can be predicted from one another within one order of magnitude using either Eq. (6) or Eq. (3) assuming a gOct of 3.75. The tight relationship between PL and KOA can further be used to assess the reasonability of PL and KOA data sets for

H. Xiao, F. Wania / Atmospheric Environment 37 (2003) 2867–2878

non-polar chemicals, as a gOct value can reasonably be expected to lie within the range 1–10.

12

γOct

northo-Cl = 2 n ortho-Cl = 3 n ortho-Cl = 4

6 3

γOct

0 15

Kömp & McLachlan, 1997 Harner & Bidleman, 1996

12

Harner & Mackay, 1995

9 6 3 0 FAV (Li et al., 2003)

γOct

12 9 6 3 0 180

230

280

330

380

430

480

530

-1

molecular mass in g·mol

Fig. 5. Activity coefficients in octanol gOct for polychlorinated biphenyl congeners calculated using Eq. (30 ), vapor pressure data by Falconer and Bidleman (1994), and KOA values from Harner and Mackay (1995), Harner and Bidleman (1996), . Komp and McLachlan (1997), Zhang et al. (1999), and plotted against molar mass. The lower figure shows gOct values and their uncertainty calculated from the final adjusted values (FAV) of PL and KOA recommended by Li et al. (2003).

120 90

γOct

The above analysis has shown that in the whole set of 222 non-polar substances no significant change in gOct with molecular size was apparent. It is still conceivable however that within a group of structurally strongly related substances, the activity coefficient in octanol gOct changes in a consistent manner with either PL or KOA : Such pattern may have been lost in the scatter of the data in Fig. 1. Since the gOct is rarely measured directly, it needs to be derived from PL and KOA using Eq. (30 ). If there are multiple sets of PL or KOA data for a group of compound, multiple and possibly divergent sets of gOct are obtained. In the case of the PCBs, three sets of KOA values have been reported (Harner and Bidleman, 1996; . Komp and McLachlan, 1997; Zhang et al., 1999), which can be combined with the PL data by Falconer and Bidleman (1994) to calculate three sets of gOct : In the case of the PCDD/Fs multiple sets of gOct can be obtained by combining different sets of PL data (Eitzer and Hites, 1988; Rordorf, 1989; Govers and Krop, 1998; Mader and Pankow, 2003) with the KOA values reported by Harner et al. (2000). These gOct have been plotted vs. the molecular weight of the chemicals in Figs. 5 and 6. These graphs reveal that the variation of gOct within a group of structurally related substances is entirely dependent on which data source is being employed in the derivation. Whereas the gOct derived from the KOA . values by Komp and McLachlan (1997) appear to increase with the degree of chlorination, those derived from the KOA by Harner and Bidleman (1996) and Zhang et al. (1999) show no such trend. The KOA values by Zhang et al. (1999) are interpolations of the data by Harner and Bidleman (1996), so the agreement is not surprising. Similarly, the gOct data sets for the PCDD/Fs show very different trends depending on which PL data sets was used in their derivation (Fig. 6). In other words, the uncertainty in the physical chemical properties PL and KOA results in a highly uncertain estimate of gOct : Figs. 5 and 6 suggest that the discrepancy between the properties reported by different studies is too large to tell with confidence whether the gOct increases, decreases or stays the same within a group of structurally related substances. One may argue that such statements regarding gOct could be made if only the ‘‘correct’’ KOA and PL data sets could be identified. Li et al. (2003) used a rigorous and transparent procedure to derive a PCB property data set, that makes use of all available measured data, takes into account their relative reliability, and adheres to thermodynamic constraints (Beyer et al., 2002). The values for the KOA and PL of 16 PCB congeners

Zhang et al., 1999 n ortho-Cl= 0 northo-Cl = 1

9

5. Variability of cOct within a group of related compounds

2873

Rordorf, 1989 Mader & Pankow, 2003 Govers & Krop, 1998 Eitzer & Hites, 1988

60 30 0 200

250

300

350

400

450

molecular mass in g·mol-1 Fig. 6. Activity coefficients in octanol gOct for polychlorinated dibenzo-p-dioxin and dibenzofuran congeners calculated using Eq. (30 ), KOA data by Harner et al. (2000), and PL values from Eitzer and Hites (1988), Rordorf (1989), Govers and Krop (1998), Mader and Pankow (2003), and plotted against molar mass.

recommended by Li et al. (2003) can be regarded as the best estimates for these properties, based on all currently available experimental evidence. gOct values and their uncertainty, derived from the values by Li et al.

H. Xiao, F. Wania / Atmospheric Environment 37 (2003) 2867–2878

12 Harner & Bidleman, 1998

γOct

9 6 3 0

γOct

Su et al., 2002

9 6 3 0 Wania et al., 2002

γOct

(2003), are included in Fig. 5. These gOct values neither show any significant change with increasing molecular mass. If a measure of the uncertainty of the physical– chemical properties PL and KOA is reported, it is possible to be quantitative about the uncertainty in the estimated activity coefficients gOct : Such an analysis was performed for the PCNs and PBDEs, using error propagation rules and the standard deviations reported for the PL and KOA data sets. To derive a standard deviation of the KOA of the PCNs at 298.15 K, it was assumed that the relative standard deviation of the KOA values at 298.15 K is equal to the mean relative standard deviation at the temperatures at which the actual measurements were performed (Harner and Bidleman, 1998a, b). The standard deviations of the KOA values by Su et al. (2002) were calculated from the standard deviations of the internal energies of air–octanol phase transfer, DOA U; and the intercepts, b reported in that study. Wania et al. (2002) directly reported the standard deviation of their KOA values, and we derived such standard deviations for the PL data by Lei et al. (1999). The standard deviation of the gOct for the PBDEs was calculated based on the PL values reported by Wong et al. (2001) and the KOA values reported by Wania et al. (2002). The calculated results are given in Fig. 7 for the PCNs and Fig. 8 for the PBDEs. Fig. 8 also includes gOct data calculated from the PL data by Tittlemier and Tomy (2001) and Tittlemier et al. (2002). It can be seen that the uncertainty of gOct is always substantial, and sufficiently large to preclude unequivocal statements about the trend of the gOct with molecular size within a compound group. Incidentally, the fact that all three KOA data sets for the PCNs suggest a decrease of gOct with molecular size, is due to the fact that they are not independent of each other. The gas chromatographic correlation techniques of Su et al. (2002), Wania et al. (2002) both relied on the data from Harner and Bidleman (1998a, b) for calibration. Figs. 7 and 8 suggest that it would not be sufficient to identify a ‘‘correct’’ PL and KOA data set among a choice of conflicting data sets (assuming that is possible), because even the uncertainty in the gOct from one set of measurements is typically too large to judge whether gOct increases, decreases or stays the same. We finally sought to gain insight in the variability of gOct from group contribution methods aimed at predicting the solubility of organic chemicals in octanol. The group contribution values for aromatic carbon (0.15570.024), H-substituted aromatic carbon (0.07370.012) and chlorine (0.13170.026) in OCTASOL (Li et al., 1995) suggest that the substitution of a hydrogen with a chlorine in an aromatic molecule increases the solubility in octanol by less than one-tenth of an order of magnitude (logðSL =mol L1 Þ increases by 0.09770.037). For example, OCTASOL predicts gOct

9 6 3 0 150

200

250

300

350

400

-1

molecular mass in g·mol

Fig. 7. Activity coefficients in octanol gOct for polychlorinated naphthalene congeners calculated using Eq. (30 ), PL data by Lei et al. (1999), and KOA values from Harner and Bidleman (1998), Su et al. (2002), and Wania et al. (2002), and plotted against molar mass. The standard deviation of gOct was derived by error propagation from the standard deviation of the KOA and PL data. 30 Wong et al., 2001 Tittlemier et al., 2002 Tittlemier et al., 2000

20

γOct

2874

10

0 200

300

400

500

600

700

molecular mass in g·mol-1 Fig. 8. Activity coefficients in octanol gOct for polybrominated diphenyl ether congeners calculated using Eq. (30 ), KOA data by Harner and Shoeib (2002), and PL values from Wong et al. (2001), Tittlemier and Tomy (2001), Tittlemier et al. (2002), and plotted against molar mass. The standard deviation of gOct was derived by error propagation from the standard deviation of the KOA values and the PL data by Wong et al. (2001).

for the PCBs ranging from 3.070.4 for monochlorobiphenyl to 2276 for decachlorobiphenyl. Lee et al. (2000) presented a group contribution method for estimating gOct of mono-aromatic chemicals at 25 C.

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Interestingly, the group contribution value for aromatic chlorine groups was statistically not significant, leading to prediction of a constant gOct of 2.83 for all chlorobenzenes. Although one of the estimation methods suggests increasing gOct with increasing degree of halogenation, the predicted increase is minor and subject to large uncertainty.

6. Conclusions We have shown that with the currently available data sets for PL and KOA it is impossible to judge whether the activity coefficient in octanol gOct differs for different organic chemicals. Regression equations between log gOct and log PL or log KOA for a varied set of 222 nonpolar chemicals revealed that gOct remains constant within a large range of PL or KOA values. Statistic analysis showed that there is no significant difference between reported gOct values and their average value. Comparison between gOct derived from different KOA and PL data sets as well as estimations of the standard deviation of activity coefficient in octanol further showed that the uncertainty of estimated gOct is very large. The selection of ‘‘best’’ data sets neither resolves the issue. The incapability to detect consistent changes of gOct is a result of the relatively high measurement uncertainty for KOA and PL and the relatively small range of gOct for non-polar chemicals, which covers only about one order of magnitude (1–10). This in turn precludes a judgement of whether gOM or the ratio gOM =gOct is more likely to vary linearly within a group of compounds. If gOct is indeed more or less constant for the group of investigated compounds, the variation in gOM and gOM =gOct is identical. This implies that within the current measurement uncertainty of PL and KOA it is impossible to determine whether one parameter is preferable over the other for describing environmentally relevant phase equilibria between the gas phase and OM. Indeed, it is largely meaningless to compare PL and KOA in terms of their capability to predict the environmental phase partitioning of non-polar organic chemicals as long as the uncertainty of the physical–chemical descriptor is not taken into account. Differences in the fit of regression equations observed in various studies are largely due to differences in the quality and consistency of the physical–chemical data sets. Notably, the existing set of KOA data is highly consistent because the bulk of it has either been measured by Harner and co-workers using the same direct method or has been derived from the data by Harner et al. by correlation with gas chromatographic retention data (Zhang et al., 1999; Su et al., 2002; Wania et al., 2002). Not surprisingly, KOA data derived independently, such . as those by Komp and McLachlan (1997), are less

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consistent with those from, or based on, the work by Harner and co-workers. Similarly, vapor pressure data sets tend to be less homogeneous because of the multitude of methods and investigators involved in their generation. It should be stressed that despite the significant uncertainties, the quality of the existing PL and KOA data for semi-volatile organic compounds is quite good, especially considering the immense experimental difficulty associated with measuring partition coefficients on the order of 1010 or higher. Without reasonable data quality, the correlation between KOA and PL would not be as tight or show a slope very close to 1 (Fig. 1). To allow a more rigorous assessment of the utility of various physico-chemical descriptors in predicting environmentally relevant phase equilibria, it is however imperative that studies reporting measured correlated or predicted physical–chemical property data provide quantitative information about the uncertainty of these data. Pankow (1998) highlighted the analogy between using KOA instead of PL to describe phase partitioning between the gas phase and OM and using the octanol– water partition coefficient KOW instead of the water solubility of the liquid SL to describe the distribution between the aqueous phase and OM. Although we have not explicitly investigated this, we suspect that the uncertainty of log KOW and SL measurements for hydrophobic substances (Pontolillo and Eganhouse, 2001) is at least as high as the uncertainty of KOA and PL measurements for semi-volatile substances. The statements above concerning the activity coefficient in pure octanol are thus likely also applicable to the activity coefficient in water-saturated octanol. Incidentally, the textbook by Schwarzenbach et al. (1992) includes a figure regressing log SL vs. log KOW which has remarkable similarities with Fig. 1. Even though we can presently not use the goodness of fit with empirically derived partitioning data to judge whether KOA or PL is more suitable in describing such data, it is of course possible to argue for one or the other based on other considerations. Pankow (1998) made a convincing, theoretically based case for KOA ; even though we could not find experimental evidence for his assertion that ‘‘it is far more likely that different compounds will exhibit similar values of the ratio gOct =gOM than it is that they will exhibit similar values of gOM ’’—at least not for non-polar chemicals. The key theoretical argument is that the use of PL implies the use of a different reference state for each chemical (namely that of its pure liquid), whereas the use of KOA makes octanol the common reference phase for all chemicals. Another obvious advantage of the KOA is the possibility of direct experimental determination. The experimentally inaccessible sub-cooled liquid vapor pressure of semi-volatile substances has to be derived from measured solid vapor pressure data. These conversions

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introduce additional uncertainty and in the case of compounds with a high melting point can lead to very substantial errors. Although sub-cooled liquid vapor pressures can also be derived indirectly from gas chromatographic retention times, this technique requires directly measured vapor pressure data for calibration. In conclusion, PL and KOA can be used interchangeably to describe the partitioning of non-polar organic contaminants between the gas phase and a variety of OM. It should be cautioned however that these relationships are unlikely to be suitable for describing the phase partitioning behavior of more polar substances and we thus agree with Goss and Schwarzenbach (2001) in suggesting that future research in the field of environmental partition processes should focus on developing more widely applicable poly parameter linear free energy relationships rather than trying to refine the existing one-parameter relationships represented by Eqs. (1) and (2).

Acknowledgements The authors are grateful to the Natural Sciences and Engineering Research Council (NSERC) of Canada for financial support, and B. Mader and J. Pankow for providing a copy of an unpublished manuscript.

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