Hydrophobicity and Octanol−Water Partitioning of Trace Metals in

The hydrophobicities of dissolved Al, Cu, Mn, and Pb have been determined in various contaminated natural water samples by 1-octanol extraction and C1...
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Environ. Sci. Technol. 2004, 38, 3081-3091

Hydrophobicity and Octanol-Water Partitioning of Trace Metals in Natural Waters ANDREW TURNER* AND EDWARD MAWJI School of Earth, Ocean and Environmental Sciences, University of Plymouth, Drake Circus, Plymouth PL4 8AA, UK

The hydrophobicities of dissolved Al, Cu, Mn, and Pb have been determined in various contaminated natural water samples by 1-octanol extraction and C18 column retention. Octanol extraction varied among the metals studied and between the environments sampled but, in general, was greatest for Pb, whose conditional octanolwater partition coefficient, Dow, exceeded unit value in some samples. In most cases, metal partition into octanol either increased with increasing pH or exhibited a maximum under near-neutral conditions. Although the order and pH-dependence of metal retention by the C18 columns was consistent with these observations, the extent of retention was generally greater than the extent of metal extraction by octanol, possibly because of interferences effected by the C18 column matrix. Speciation calculations and results of controlled experiments employing metals in the presence of model ligands suggest that metals may become hydrophobic either by neutralizing relatively hydrophilic ligands or by combining with ligands that are intrinsically hydrophobic themselves. Given that octanol solubility affords an upper estimate of lipophilicity, the results of this investigation may have important implications regarding our understanding of metal bioavailability and toxicity in natural waters.

Introduction It is widely accepted that the most chemically reactive and biologically available form of many trace metals in the natural environment is the free ion (1). This form of metal may interact with passive and active surface sites on the cell wall and subsequently cross the cell membrane and enter the cytosol where it may combine with intracellular ligands. The presence of dissolved organic ligands (including humic substances) in the bulk solution generally reduces the potential for metal interactions with the cell surface because these ligands form soluble complexes with the free metal ion (2, 3). Significantly, the stability constants of these complexes are such that, for many metals, organic complexes dominate metal speciation in natural waters, and the free ion comprises a relatively small fraction of total dissolved metal (4, 5). Complexes of trace metals are, however, of concern when they are sufficiently small and hydrophobic (or lipophilic) to cross the cell membrane directly. Accordingly, several studies have demonstrated enhanced metal assimilation by and toxicity to various aquatic organisms in the presence of model, anthropogenic ligands, like xanthogenates, dithiocarbamates, phenanthrolines, and oxine (6-8), because of their ability to * Corresponding author phone: +44 1752 233041; fax: +44 1752 233035; e-mail: [email protected]. 10.1021/es030151c CCC: $27.50 Published on Web 05/05/2004

 2004 American Chemical Society

form stable, neutral (or near-neutral) complexes. Extrapolation of these results to the environment is, however, difficult because (i) such ligands typically occur at very low concentrations in contaminated natural waters (9), and (ii) stability constants of their complexes with many metals are unknown (6, 7). An alternative, empirical means of assessing the combined environmental significance of these and other neutral metal complexes and compounds would be to determine the overall hydrophobicity of a metal in a natural sample. An operational measure of this characteristic may be achieved by isolating and preconcentrating metal complexes on a silica column capped with carbon-18 moieties (10, 11). The weak polar forces involved in this separation allow elution with a suitable solvent (commonly methanol) and chromatographic characterization of the metal complexes (12). The main problems with this approach, however, relate to the nature of the metal species isolated or eluted. For example, it has been shown that some charged species adsorb to uncapped silanol groups of the column (13) and that the most hydrophobic species of certain metals are resistant to elution by methanol (14) or dilute acid (15). More significantly, the environmental or toxicological significance of the hydrophobic fraction isolated in this way has not been demonstrated (16). A more appropriate means of assessing the hydrophobicity of metal species in natural waters would be to determine the metal partitioning between the water sample and an organic solvent whose physicochemical properties (for example, electric permittivity) are similar to those of lipid material. A limited amount of information exists on metal partitioning in the presence of hexanol (17), hexane-butanol (18), and olive oil (19), but 1-octanol is a more appropriate solvent in environmental and biological studies (20, 21). Given that the determination of octanol-water partitioning is reasonably straightforward, it is perhaps surprising that this approach has only been applied to a single study involving Cu complexes formed in landfill leachate (22). To this end, therefore, we undertake a detailed and systematic study of the octanol-water partitioning of dissolved trace metals in a variety of contaminated fresh and brackish water environments in order to evaluate the significance of hydrophobic metals in natural waters. Although the ability of a chemical to penetrate the lipid bilayer is also dependent on factors other than octanol solubility, such as molecular size, this approach affords a first-order, upper estimation of a lipophilic fraction of metal. Concurrently, we also measure the hydrophobicity of metals in these samples by solid phase extraction using C18 columns in order to assess the environmental and biological significance of the fraction of metals isolated by a more widely recognized technique.

Experimental Section Sampling and Sample Sites. Four contrasting surface water environments were sampled for this study. The River Carnon rises on granitic moorland of south west England and its catchment is highly mineralized. A long history of sulfidic ore mining has resulted in a water-course that is highly contaminated by trace metals but little affected by organic contaminants (23). The geology of the lower reaches of the River Tamar catchment, southwest England, is similar to that of the Carnon, and the river is contaminated by metals issuing from adits of abandoned mines (24). Currently, arable farming is the most important industry in the catchment. The River Clyde and Manchester Ship Canal (MSC) have received domestic and trade waste from densely populated and industrialized catchments in southwest Scotland and northVOL. 38, NO. 11, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 1. Recovery of Metals from a Filtered River Water Sample (Mersey, UK) that Had Been Spiked with Ionic Metal Standards, Equilibrated, and Extracted with 1-Octanola natural sample spiked sample aqueous phase after octanol extraction back-extract of octanol recovery, % a

Al

Cu

Mn

Pb

341 ( 62 2030 ( 103 1630 ( 4.0 441 ( 137 102

136 ( 7.0 520 ( 50 516 ( 22 33 ( 28 106

3610 ( 558 11100 ( 956 11400 ( 145 191 ( 120 104

1.6 ( 0.02 78 ( 0.97 70 ( 4.8 4.1 ( 2.4 95

Concentrations (in nM) represent the mean ( one standard deviation of three separate experimental determinations.

west England, respectively, for over a century. Despite recent improvements in water quality legislation and water treatment technology these environments remain contaminated by both trace metals and a variety of organic chemicals (25, 26), partly because of chemical inputs from organic-rich, reducing sediments. Carnon and Tamar samples were collected from the shore in 2 L high density polyethylene (HDPE) bottles that had previously been soaked in 10% HNO3 (AnalaR, BDH, Poole, UK) for at least 24 h. The Tamar was sampled on two occasions, following periods of low rainfall (sample I; May 03) and high rainfall (sample II; July 03). Each sample was transported cool and in the dark back to the laboratory where it was vacuum filtered (within 16 h of collection) through two or three 47 mm diameter 0.45 µm pore size Millipore membrane filters using an acid-cleaned 500 mL Nalgene polysulfone filtration unit. The MSC was sampled as above during April 03, and filtration was undertaken within 24 h of collection. The River Clyde sample was collected by the Scottish Environment Protection Agency during June 03 as part of their routine monitoring program and was stored at 4 °C and in the dark before being sent by courier to Plymouth where it was filtered as above within 120 h of collection. The pH, conductivity, and salinity of an aliquot of each filtrate were measured at room temperature using calibrated YSI or Hanna electrodes. The remaining filtrate was stored in an acid-cleaned 1.5 L HDPE bottle at 4 °C and in the dark and was processed and analyzed within 2 weeks of collection. Filters were air-dried and reweighed for the determination of suspended particle concentration. Meanwhile, an additional 100 mL aliquot of sample that had been filtered through a 0.7 µm Whatman GF/F filter (Maidstone, UK) was acidified by addition of 100 µL of 50% HCl and stored frozen in a glass vial for subsequent determination of dissolved organic carbon (DOC) concentration. Experimental. All experiments and preparation of samples, solutions, and standards were undertaken in a Class-100 laminar flow hood using appropriate “clean” techniques (27) and using Milli-Q water (resistivity ) 18 MΩ cm; pH ) 5.56.5) and analytical grade reagents. The hydrophobicity of the dissolved trace metals selected for this study (namely, Al, Cu, Mn, and Pb) was evaluated by (i) solid-phase extraction using C18 columns and (ii) partition into 1-octanol. Column Approach. Six 10 mL aliquots of filtrate were pipetted into individual 50 mL, acid-cleaned (10% HNO3 for 24 h), screw-capped, HDPE centrifuge tubes (Fisher Scientific, Loughborough, UK) using a gravimetrically calibrated micropipet and allowed to reach room temperature (20 ( 2 °C). Three aliquots of each filtrate were passed through methanolconditioned (HPLC-grade, Fisher Scientific) and acid-rinsed (0.3 M HNO3; AnalaR, BDH) reverse-phase C18 columns (“Sep-Pak”-type; BondElut LRC, Fontenay, France) under gravity at a flow rate of about 20 mL h-1 and collected in clean centrifuge tubes. All sample aliquots were analyzed within a few hours of processing or were stored at 4 °C after acidification to pH 2 using 1 M HNO3 (AristaR, BDH) and analyzed within a few days. An additional 10 mL aliquot of filtrate sample that had passed through a column was stored 3082

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frozen in a 10 mL glass vial for subsequent DOC analysis. In early experiments the metal retained by the columns was eluted using either methanol or dilute acid, but this gave rise to contamination for some metals and poor reproducibility for others. The hydrophobic fraction of metal was, therefore, derived from the difference between the mean metal concentration in the original sample aliquots, and the mean metal concentration in the sample aliquots that had passed through the columns. This approach may be affected by the adsorption of some charged metal species onto uncapped silanol groups of the columns (13), and so our definition of hydrophobicity likely represents an upper estimate of this characteristic. Fractional retention of metal was not affected by the age or usage of the column, and so columns were reused (following acid-cleaning and methanol conditioning) up to four times before being discarded. Octanol Approach. A shake-flask method was employed to determine the octanol-water partition of dissolved metals (28-30). For each filtered sample, six 5 mL aliquots were pipetted into individual 50 mL HDPE centrifuge tubes that had been soaked successively in detergent and HNO3 for 24 h each. Three aliquots were left for 16 h at room temperature, while 5 mL of 1-octanol (Aldrich, HPLC-grade; water content 0.45 µm) concentration was less than 20 mg L-1. DOC concentrations

TABLE 2. Chemical Characteristics of the Samples Used in the Experimentsa river

Λ,b µS cm-1

pHb

Sb

I, M

DOC, µM

SPM, mg L-1

Carnon Tamar I Tamar II MSC Clyde

180 35.1 170 8740 280

6.4 7.5 7.6 8.0 7.6

0.2 0.1 0.1 5.8 0.3

0.004 0.002 0.002 0.116 0.006

77c 285 300 1070 260

0.45 µm. b Measured in filtered sample aliquots at room temperature. c DOC was not measured in this sample, but a value of 77 µM was determined by Turner and Rawling (32) in an earlier sampling.

TABLE 3. Total Dissolved Trace Metal Concentrations in the Filtered Samplesa river

Al

Cu

Mn

Carnon 14800 ( 810 535 ( 38.0 5670 ( 73.9 Tamar I 1180 ( 108 212 ( 4.7 435 ( 78.1 Tamar II 2470 ( 159 220 ( 37.7 1430 ( 1.1 MSC 166 ( 54 86.2 ( 3.1 1330 ( 14.9 Clyde 580 ( 63 112 ( 13.1 84.9 ( 8.2 world 1900c 24c 130c average

Pb 7.54 ( 0.56 ndb 1.26 ( 0.24 2.51 ( 0.17 0.96 ( 0.13 0.5c

a Given in nM as the mean ( one standard deviation of three determinations. bnd ) not detected. c Reference 34.

ranged from less than 100 µM in the Carnon to in excess of 1000 µM in the MSC, and the fraction of DOC retained by a C18 column was between about 10 and 20% in all cases. Salinities were between 0.1 and 0.3 (i.e., “fresh” water), with the exception of the MSC. Here, “brackish” water conditions occur because of occasional, controlled incursions of saline water from the adjacent Mersey Estuary (33). Ionic strength (I) was calculated by extrapolating the ratio of ionic strength to salinity of average seawater (0.020 M) to the measured salinities of the samples. Ionic strengths are only approximate since salinities were measured near to the detection limit of the salinometer (0.1) in many cases, and the relative abundances of the major ions in river water and seawater are very different. The concentrations of dissolved trace metals in the samples are given in Table 3. Compared with world average concentrations (also shown), dissolved Cu and Pb are enriched in all cases, where detected. Data for the River Tamar also indicate significant seasonal (or rainfall-induced) differences in metal concentrations, although it should be pointed out that detection of Pb in the first series of Tamar experiments was hampered by the performance of the ICPMS on this occasion. Equilibrium Metal Speciation. A first-order evaluation of the equilibrium speciation of dissolved trace metals in our samples was undertaken using the Windermere Humic Aqueous Model (WHAM), version 6 (35). River water was modeled under two sets of conditions. In the first case we used major solute concentrations reported by Tang and Johannesson (5) (I ∼ 10-3 M) and concentrations of dissolved trace metals and dissolved organic matter (DOM; assumed to be equal to twice the concentration of DOC) representative of those encountered in the Clyde and Tamar. In the second case we employed major solutes in the same ratio, but at double strength (I ∼ 2 × 10-3 M), and concentrations of dissolved trace metals and DOM representative of those encountered in the Carnon. For brackish water we used major solute concentrations equivalent to a salinity of 5.8, and concentrations of dissolved trace metals and DOM representative of those encountered in the MSC. In all cases “default-mode” humic and fulvic material were employed in VOL. 38, NO. 11, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 1. Speciation of dissolved trace metals in river water representative (in terms of chemical concentrations) of the Clyde and Tamar as a function of pH, calculated according to the Windermere Humic Aqueous Model (35). Major solutes were set at concentrations given by Tang and Johannesson (5) and are equivalent to I ∼ 10-3 M. [Al] ) 1 µM; [Cu] ) 100 nM; [Mn] ) 500 nM; [Pb] ) 1 nM; [DOM] ) 7 mg L-1, equivalent to [DOC] ∼ 300 µM; pCO2 ) 3.5 × 10-4 atm; T ) 293 K. The organic fraction is the sum of the fulvic and humic fractions. Inorganic species comprising < 1% of total metal are not shown. a ratio of 1:4 (5), activity coefficients were calculated with the extended Debye-Hu ¨ ckel equation, and equilibrium with the atmosphere was assumed (pCO2 ) 3.5 × 10-4 atm). A general description of the speciation calculations is given below, and results derived from conditions representative of the Clyde and Tamar are shown as a function of pH in Figure 1. In all sets of computations the organically bound (humic plus fulvic) fraction of Cu and Pb increased with increasing pH, in accordance with the occupation of acidic sites on organic substances and at the expense of the free ion (and chloride and sulfate complexes in the case of Pb in brackish water). As a result, greater than 40% Cu and Pb was organically bound above neutral conditions in the simulation of the River Carnon, and nearly 100% was organically complexed under equivalent conditions in the remaining simulations. The magnitudes of both Al and Mn complexation by organic ligands reflected the concentration of DOM in each simulation. In all cases the organic fraction of Mn increased with increasing pH to about pH 8-9 as the proportion of the free ion diminished, and thereafter the organic fraction decreased as carbonate complexes assumed greater importance. With respect to Al, the organic fraction increased with increasing pH under acidic conditions at the expense of the free ion and sulfate complexes. Above pH ∼6 in freshwater and pH ∼8 in brackish water, the proportion of organically complexed Al diminished with increasing pH as hydroxides became increasingly important. Clearly, the precise ionic and organic characteristics of our samples are variable, and speciation cannot be accurately simulated using generic humic and fulvic materials in a fixed ratio, especially given that poorly defined anthropogenic organic chemicals are present in the Clyde and MSC. Nevertheless, the results of the computations afford a qualitative insight into the species that are present in our samples and serve as a framework for assessing the chemical factors that are likely to affect the hydrophobicity of metals in natural waters. 3084

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TABLE 4. Fraction of Total Dissolved Metal in Each Sample that Was Retained by C18a river

Al

Cu

Carnon 82.4 ( 0.27 24.8 ( 1.4 Tamar I 81.9 ( 5.1 32.1 ( 4.5 Tamar II 54.5 ( 2.7 57.6 ( 11.0 MSC 35.0 ( 11.3 Al, Mn) is consistent with that of metals complexed with salicylate, and the magnitude of Dows for Cu and Pb for the second Tamar sampling are similar to those reported for protonated natural and synthetic humic substances (44; Table 6). This suggests that hydrophobic complexes in this environment are formed via interactions of metals with natural organic ligands and that temporal differences in metal hydrophobicity are the result of temporal variations in the composition of dissolved organic matter, in response to variations in hydraulic residence time, for instance. Alternatively, an additional source of hydrophobic ligands may exist that is activated or enhanced during periods of high rainfall. Given the agricultural nature of the Tamar catchment, it is also possible that metal hydrophobicity is augmented by the presence of pesticides or fungicides, including dithiocarbamates, which are washed out from the soil during periods of heavy rainfall. The application of such agro-chemicals could account for both seasonal and rainfallinduced variations in the hydrophobicity of metals and, in particular, Cu and Pb, in the recipient water-course (49). An array of anthropogenic ligands and surfactants is likely to occur in the River Clyde, which receives domestic and industrial wastes throughout its watershed (26), and this may explain why all metals studied in this environment exhibit measurable extraction by octanol at natural pH. The same types of anthropogenic ligands are likely to occur in the MSC (50), and they may account for the observed octanol solubility of Al and Pb in this environment. However, that no hydrophobic Cu or Mn was detectable in the MSC suggests that the precise binding properties of anthropogenic ligands are both site- and metal-specific. A significant, more general observation is the clear difference in octanol-solubility (and C18 retention; Table 4) between Pb and Cu in the Clyde and MSC. Given that both metals exhibit strong complexation by organic ligands (see Figure 1), we surmise that, in environments impacted by anthropogenic organic matter, Pb has a considerably greater affinity for the hydrophobic fraction of ligands than Cu.

TABLE 7. Reactions and Thermodynamic Constants (as log K and at 293 K) Used for Calculating Metal Speciation in the Model Solutions (Figure 5) salicylate (Sal) reaction H+

HSal-

+ H+ + HSal- h H2Sal0 Al3+ + Sal2- h AlSal+ AlSal+ + Sal2- h Al(Sal)2Al(Sal)2- + Sal2- h Al(Sal)33Cu2+ + Sal2- h CuSal0 CuSal0 + Sal2- h Cu(Sal)22Mn2+ + Sal2- h MnSal0 MnSal0 + Sal2- h Mn(Sal)22Sal2- h

oxine (Ox) log K 13.40 3.00 14.22 10.74 6.16 12.03 8.67 7.00 3.90

reaction H+

Ox- h

+ H+ + HOx0 h H2Ox+ Cu2+ + Ox- h CuOx+ CuOx+ + Ox- h Cu(Ox)20 Mn2+ + Ox- h MnOx+ MnOx+ + Ox- h Mn(Ox)20 Pb2+ + Ox- h PbOx+ PbOx+ + Ox- h Pb(Ox)20 HOx0

log K 9.81 4.91 12.10 10.90 7.30 6.19 10.03 7.31

FIGURE 5. Speciation of Al, Cu, and Mn in the presence of salicylic acid (Al-Sal, Cu-Sal, and Mn-Sal, respectively; left-hand panels) and Pb, Cu, and Mn in the presence of oxine (Pb-Ox, Cu-Ox, and Mn-Ox, respectively; right-hand panels) as a function of pH. The fractional speciation of each complex was calculated using MINEQL+, version 3.01b (45), and stability constants given in its database and in refs 46 and 47 (see Table 7). For the salicylate system: [Al] ) 2 µM; [Cu] ) 1 µM; [Mn] ) 1 µM; [Sal] ) 100 µM; [Na] ) 100 µM; pCO2 ) 3.1 × 10-4 atm; T ) 293 K. For the oxine system: [Cu] ) 1 µM; [Mn] ) 1 µM; [Pb] ) 0.5 µM; [Ox] ) 100 µM; pCO2 ) 3.1 × 10-4 atm; T ) 293 K. The bold lines represent the summed fraction of complexes in each case, and the filled squares represent the fraction of metal extracted by octanol in the corresponding experiments (fo; Figure 4). Where octanol extraction was not detected (fo < 5%), data are shown on the x-axis. Note, remaining species in the Cu-Sal calculations above pH 7 (not shown for clarity) were complexes with OH- and CO32-/HCO3-. Neutral alkyl-Pb compounds may also be present in our samples. Thus, while the use of tetra-alkyl Pb as a gasoline additive has declined over the past two decades, laboratory experiments suggest that environmental (chemical and biological) alkylation of Pb in water and sediment may be an important, contemporary source (51, 52). However, it is unlikely that they contribute significantly to the overall hydrophobicity of dissolved Pb, since the more hydrophobic

tetra-alkyl Pb compounds rapidly disappear from the water column by evaporation or hydrolysis, and the relatively persistent di- and trialkyl compounds are insufficiently hydrophobic for detection by the octanol approach. Relationship between Dow and Kow. Previous discussion and our speciation modeling of the metal-ligand systems (Figure 5) have highlighted the conceptual differences between the true octanol-water partitioning of a single VOL. 38, NO. 11, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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complex or compound, Kow, and the overall, apparent partitioning of the combined species of a metal, Dow. To evaluate the significance of a single, well-defined hydrophobic metal complex or compound on the overall octanol-water partitioning of a metal in a natural sample or model system, we require a relationship between Dow and Kow that involves the fractional concentration of the metal in the sample as that particular complex or compound, [MeL]/[Me]. Thus, for a single, hydrophobic metal species among a number of hydrophilic (octanol-insoluble) metal species we may write

Dow )

[(MeL)o] [Me] - [(MeL)o]

(6)

where the numerator represents the concentration of the hydrophobic species in octanol, and the denominator represents the summed concentrations of all hydrophilic species. Dividing by [(MeL)w] we obtain a relationship between Dow and Kow:

Dow )

Kow [Me]/[(MeL)w] - Kow

(7)

Assuming that the hydrophobic species is conserved during octanol extraction (that is, none is formed as a result of potential changes in aqueous metal speciation incurred by the presence of the solvent)

[MeL] ) [(MeL)w] + [(MeL)o]

(8)

or in terms of Kow:

[MeL] ) (Kow + 1)[(MeL)w]

(9)

Combining eqs 7 and 9 yields

Dow )

Kow [Me] ((Kow + 1)/[MeL]) - Kow

(10)

which, after rearrangement, becomes

Dow )

([MeL]/[Me]) (1 + 1/Kow) - ([MeL]/[Me])

(11)

or with Kow as the subject:

Kow )

1 ([MeL]/[Me])(1 + 1/Dow) - 1

(12)

The relationship between Dow and [MeL]/[Me] for different values of Kow, representative of many complexes given in Table 6, is shown in Figure 6; Kow was not extended above 102 as predictions using higher values converged at [MeL]/ [Me] below about 0.9. Although in natural samples and model systems there exists an array of complexes and compounds of differing hydrophobicity, we may extrapolate the predictions to the results obtained by experiment by assuming the existence of a single (or single type of) hydrophobic complex or compound. With respect to the model experiments shown in Figure 5, we may assume that, for a given system, either (i) only the neutral complex is soluble in octanol or (ii) all organic complexes are equally soluble in octanol. Thus, for the CuOx system above pH 5, Dow is about 40, and [MeL]/[Me] ) 0.99 for Cu(Ox)20, resulting in a Kow of about 70 for the neutral complex according to eq 12. Likewise, for the Cu-Sal system at pH ∼ 7, Dow is 0.7 and [MeL]/[Me] ) 0.9 for CuSal0, and a Kow of about 0.8 is calculated for this complex. In the remaining cases, we estimate Kows for the combined organic 3090

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FIGURE 6. Overall octanol-water partition coefficient, Dow, calculated as a function of the fractional concentration of a single hydrophobic metal complex or compound, [MeL]/[Me], and for different values of Kow for the hydrophobic complex (see eqs 6-12 and accompanying text for further details). complexes of about 1 for Al-Sal (at pH 5.5), between about 0.6 and 3 for Mn-Ox (above pH 6), and between about 0.7 and 2 for Pb-Ox (above pH 4). Regarding the natural samples, and with respect to Figure 6, the observed hydrophobicities of dissolved Cu and Al in the River Clyde at natural pH (Dow ∼ 0.2) can be accounted for by the existence of