EPA/600/R-05/077
August 2005
Empirical Models of Pb and Cd Partitioning
Using Data from 13 Soils, Sediments, and
Aquifer Materials
by
Nicholas T. Loux, Sayed M. Hassan+ and Claudia R. Chafin+
U.S. EPA
National Exposure Research Laboratory
Ecosystems Research Division
960 College Station Road
Athens, GA 30605-2700
+Dept. of Crop and Soil Sciences
University of Georgia
Athens, GA.
formerly with Technology Applications Inc.
Athens, GA.
U.S. Environmental Protection Agency
Office of Research and Development
Washington, DC 20460
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NOTICE
The information in this document has been funded wholly by the United States
Environmental Protection Agency. Although it has been subjected to the Agency's peer and
administrative review process and approved for publication as an EPA document, it does not
necessarily constitute official agency policy. Mention of trade names or commercial products
does not constitute endorsement or recommendation for use by the U.S. Environmental
Protection Agency.
n
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FOREWORD
The Ecosystems Assessment Branch of the Ecosystems Research Division, National
Exposure Research Laboratory, Office of Research and Development, U.S. Environmental
Protection Agency conducts research that is designed to meet the agency's needs in areas related
to assessing the ecological health of diverse biological communities. As part of this mission, a
significant amount of research is devoted to improving tools to assess low level, ecological
exposures to toxicants of national concern.
Lead (Pb) and cadmium (Cd) are two of the most commonly found contaminants of
concern at Superfund National Priorities List (NPL) sites. Because these contaminants are
elements, they do not degrade and hence when present at elevated concentrations in soils,
sediments and aquifer materials, may pose a risk to the biological community over geological
time periods. The risk posed by an environmental toxicant is dependent upon its fate in the
environment. Among the properties governing the environmental fate of a metal toxicant, the
solid/water partition coefficient (K^) is perhaps the most significant. Unfortunately, in common
with many other toxicants existing as ions in aqueous solution, theoretical models for predicting
Kds for Pb and Cd that are applicable to all environmental systems do not exist. This document
develops improved, default, empirical partitioning models for Pb and Cd that assist in achieving
this objective.
Eric J. Weber, Ph.D.
Acting Division Director
Ecosystems Research Division
National Exposure Research Laboratory
Athens, Georgia
in
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ABSTRACT
Lead (Pb) and cadmium (Cd) are two of the most common toxicants found in
contaminated environments. Because solubilization of these metallic elements from the solid
phase can influence their fate, transport and bioavailability, the partitioning coefficient (K^) for
these metals between environmental solids and natural waters is a key parameter needed for
assessing the risks posed by these two elements when present in environmental solids at elevated
concentrations.
In common with other ionizable contaminants, theoretical models applicable to all
environments for assessing the partitioning behavior of Pb and Cd do not exist. Consequently,
empirical partitioning models have been developed by the international technical research
community. Using large datasets of Pb and Cd partitioning obtained from 13 aquifer materials,
soils and sediments, two improved, commonly applicable, empirical models of extended
accuracy and applicability were developed in this work:
log10KdPb = -1.66596 + 0.54782*pHsoln - 0.0125584*sand + 0.585286*log10OC
(adj. r2 = 0.757; SEE = 0.484; n = 432; P < 0.01)
log10KdCd = -2.87671 + 0.495043*pHsoln - 0.00500349*sand + 0.55245*log10OC
(adj. r2 = 0.780; SEE = 0.534; n = 676; P < 0.01)
where OC is the sediment organic carbon content in mg/Kg, sand is the % sand content of the
sediment, adj. r2 designates the r2 value of the model adjusted for the degrees of freedom, and
SEE represents the standard error of the estimate of the model.
IV
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TABLE OF CONTENTS
NOTICE ii
FOREWORD iii
ABSTRACT iv
FIGURES vii
TABLES viii
ACKNOWLEDGMENTS xix
CHAPTER 1. INTRODUCTION 1
CHAPTER 2. METHODS 3
2.1 Inductively Coupled Plasma Atomic Emission Analyses 3
2.2 Aqueous pH Measurements 3
2.3 Sediment/Aquifer Material Samples 3
2.4 Equipment and Stock Solutions for Lead Partitioning Studies 6
2.5 Lead Partitioning Procedures with air-dried EPA Sediments 6
2.6 Lead Partitioning Procedures with Aquifer Material Samples 6
2.7 Equipment and Stock Solutions for Cadmium Partitioning Studies 6
2.8 Cadmium Partitioning with air-dried EPA Sediments 7
2.9 Cadmium Partitioning with Aquifer Material Samples 7
2.10 Regression Analysis of Data 7
CHAPTER 3. RESULTS 8
3.1 Lead Partitioning 8
3.2 Cadmium Partitioning 8
3.3 Empirical Partitioning Models 8
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CHAPTER 4. DISCUSSION 17
REFERENCES 26
APPENDIX A. Detailed Statistics of Empirical Lead Partitioning Models A-l
APPENDIX B. Detailed Statistics of Empirical Cadmium Partitioning Models B-l
VI
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FIGURES
Number
la-Id
le-lh
li -11
2a-2d
2e-2h
2i -21
3
4
Partitioning data for lead obtained with aquifer materials from
Utah (a), Texas (b), New Jersey (c) and Wisconsin (d)
Partitioning data for lead obtained with aquifer materials from Florida
(e) and Oregon (f) and with EPA sediments 1 (g) and 7 (h)
Partitioning data for lead obtained with EPA sediments 9 (i), 13 (j),
17 (k) and 18 (1)
Partitioning data for cadmium obtained using aquifer materials from
Georgia (a), Texas (b), New Jersey (c) and Wisconsin (d)
Partitioning data for cadmium obtained with aquifer materials from
Florida (e) and Oregon (f) and with EPA sediments 1 (g) and 7 (h)
Partitioning data for cadmium obtained with EPA sediments 9 (i),
13 G), 17 (k) and 18 (1)
Comparison of simple pH-dependent K^ relationships for lead in the
literature with those obtained in the present study
Comparison of simple pH-dependent K^ relationships for cadmium re-
Dorted in the literature with those obtained in the nresent studv
Page
9
10
11
12
13
14
22
23
Vll
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TABLES
Number Page
1 Literature-reported sediment/water partitioning models for Pb and
Cd with diverse soils and sediments 2
Physical/chemical properties of aquifer material/soil/sediment samples
used in the study 4
Geochemical interpretation of high initial Pb concentration partitioning
data for the Utah aquifer material/groundwater samples 15
Adjusted r2 values (in percentages) for 1 parameter least squares analy-
ses between log10KdPb and sediment/system properties (n = 432) 16
Regression equations relating log10KdPb to various sediment/system
properties 18
Adjusted r2 values (in percentages) for 1 parameter least squares analy-
ses between log10Kd Cd and sediment/system properties (n = 676) 19
Regression equations relating log10Kd Cd to various sediment/system
properties 20
Vlll
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ACKNOWLEDGMENTS
The authors wish to acknowledge the resources provided by the U.S. EPA for conducting
this work. The authors also acknowledge analytical support provided to this effort by Drs.
Everett Jenne and coworkers, Kim Tan and coworkers, Don Macalady and coworkers, and Mike
Perdue and coworkers. The authors also wish to acknowledge the constructive criticisms of this
manuscript provided by Drs. Bill Miller, Robert R. Swank, and John Washington, in addition to
those generated by reviewers of earlier work in this area.
xix
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CHAPTER 1
INTRODUCTION
Lead (Pb) and cadmium (Cd) have been identified as contaminants of concern at 1,026
and 582 active Superfund sites, respectively, in the United States of America (U.S. EPA, 2004).
Neither element is considered to be essential and when present at soil/sediment/aquifer solids
concentrations in excess of guideline values, both elements are considered to pose an
unacceptable risk to human health and the environment.
Current risk assessment methodologies consider numerous potential exposure pathways
when evaluating the risks posed by environmental contaminants. Among these, direct aqueous
exposure to aquatic biota and human exposures occurring through ingestion of contaminated
drinking water are two significant pathways of concern (Salhotra et al., 1990; U.S. EPA, 1992;
Hill et al., 1993). Hence, the environmental solids/water partitioning behavior of lead and
cadmium is a key consideration in conducting exposure assessments at contaminated sites.
Porewater concentrations of dissolved Pb and Cd in soil/water systems can be limited by
a variety of natural biogeochemical processes. For example, in porewaters with elevated sulfide
ion concentration, aqueous Pb and Cd concentrations can be limited by the formation of galena
(PbS) and greenockite (CdS) minerals. In porewaters without significant, reactive sulfide ion
concentrations, aqueous Pb concentrations can be controlled by the precipitation of Pb5(PO4)3OH
(pyromorphite), Pb4O(PO4)2, Pb3(PO4)2, PbSO4 (anglesite), and PbCO3 (cerrusite) phases (Nriagu,
1974; Santillan et al., 1975; Lindsay, 1979). Similarly, Cd porewater concentrations can be
limited by the formation of CdCO3 (otavite), Cd3(PO4)2, and mixed hydroxy carbonate minerals
(Santillan et al., 1975; Lindsay, 1979; Bank et al., 1989). At the lower porewater Pb andCd
concentrations more commonly encountered by the environmental research community, the
solubilities of these two metals can be limited by both solid solution formation with background
phases including oxide, phosphate and carbonate minerals, and by adsorptive phenomena with
reactive, ionizable sites present on particulate organic carbon, aluminosilicates, and the oxide
minerals of iron, manganese, aluminum and silicon.
Although there have been successful applications of both adsorptive and solid solution
mechanistic models for describing the low-porewater-concentration pH-dependent partitioning
behavior of metal contaminants with natural soils and sediments (e.g., Rai and Zachara, 1986;
Loux et al., 1989; Smith et al., 1993), the lack of general, rigorous mechanistic models applicable
to all environmental solids has prompted the development of numerous empirical models
(Hassett, 1974; Gerritse and Van Driel, 1984; Christensen et al., 1989; Rai et al., 1986; Loux et
al., 1990; Basta and Tabatai, 1992; Boekhold and Van Der Zee, 1992; U.S. EPA, 1999; Sauve et
al., 2000; Tipping et al., 2003). Table 1 illustrates a number of the empirical models described in
the technical literature. Generally speaking, empirical models have related the dependent
variable metal K^ (partition coefficient) to the independent variables aqueous pH, sediment
organic carbon content (LOI or loss on ignition is a surrogate for sediment organic carbon
content) and sediment total metals content. Other work (U.S. EPA, 1996 and references cited
within) also has demonstrated that metals tend to have a greater affinity for the smaller grained
particulate matter contained within the sediments. Some of the r2 values for the models listed in
Table 1 appear to be quite impressive (i.e., r2 > 0.9); however, it should be noted that these high
r2 value models appear to either be based on very limited datasets or result from a partial
interpretation of the data with geochemical speciation models.
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Table 1. Literature-reported sediment/water partitioning models for Pb and Cd with diverse
soils and sediments.
Relationship
Reference.
log,0(Kd,Pb) = 0.055*pH + 0.24
loglo(Kd>Pb)= 0.0768*pH+1.55
Kdpb = 1,639 - 902.4*pH + 150.4*pH2
log10(KdPb) = 0.29287*pH + 0.37806
loglo(Kd;Pb) = 0.60*loglo(LOI) + 1.13*pH
-4.36
(r2 = 0.02; n = 33 temperate soils) Gerritse
and Van Driel (1984).
(r2 = 0.17; n = 146; 6 aquifer material
samples) Loux et al. (1990).
(r2 = 0.94; n = 5 ?) Rhoades et al. (1992).
(n = 5; 5 sandy sediments). Hassan et al.
(1996).
(r2 = 0.94; n = 98 English soils). Tipping
et al. (2003).
log10(Kd;Cd) = 0.39*pH-2.5
loglo(Kd;Cd) = 0.529*pH- 0.738
loglo(Kd;Cd)= 0.397*pH - 0.943
logio(KdiCd) = 0.29287*pH - 0.20276
loglo(Kd>Cd)= 0.45*pH-0.55
loglo(KdCd) = - 0.23*loglo(tot Cd)
0.54*pH - 0.23
loglo(KdCd) = 0.
-2.93
0.43*pH
(r2 = 0.6; n = 33 temperate soils). Gerritse
and Van Driel (1984)
(r2 = 0.72; n = 78 ; 21 Danish soils at three
depths). Christiansen, (1989).
(r2 = 0.55; n = 146; six aquifer materials).
Loux etal. (1990).
(n = 5; 5 sandy sediments). Hassan et al.
(1996).
(r2 = 0.56; n= 174). U.S EPA (1999)
(r2 = 0.76; n = 64 contaminated soils).
Sauve et al. (2000).
(r2 = 0.73; n = 98 English soils)
Tipping et al. (2003).
1- LOI designates loss on ignition.
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The empirical models listed in Table 1, while not necessarily accounting for all of the
variables responsible for partitioning, nevertheless provide the most robust relationships
currently available to the technical exposure assessment community. The present work was
designed to expand the applicability of these empirical models through increasing the operational
ranges of the more commonly encountered variables associated with metals partitioning .
CHAPTER 2
METHODS
2.1 Inductively Coupled Plasma Atomic Emission Analyses
Unless otherwise noted, all metals analyses in this work were performed using a Perkin
Elmer Plasma II Inductively Coupled Plasma (ICP) Atomic Emission Spectrometer. Analyses
were generally conducted as per the manufacturer's instructions. All ICP analyses were reported
after averaging three emission intensity readings. In addition, QA/QC standards were placed
after every fifth sample in the sample train, and analytical results of the preceding samples were
discarded if the concentration of the subsequent QA standard deviated by more than 5% from the
true value. Pb analyses were conducted using either the 220.353 nm or 216.999 nm emission
lines. Cd analyses were conducted using the 214.435 emission line. The nebulizer was typically
set at a flow rate of 1 mL/min and all Pb and Cd analyses were conducted using the Myers-Tracy
scandium internal standard methodology (Myers and Tracy, 1983).
2.2 Aqueous pH Measurements
Because soluble phase pH has been identified as a master variable associated with metals
partitioning on natural soils and sediments, great care was taken in making the pH measurements
in this study. Generally speaking, pH meters (and electrodes) were calibrated with commercially
available pH buffers before and after pH determinations were made on each set of samples. All
pH measurements were performed using commercially available pH meters and an Orion RossR
high flow pH electrode. Previous experience indicated that the Ross pH electrode displays
superior stability in low ionic strength media. The accuracy of pH measurements using our
procedure is generally considered to be within the range of 0.05 to 0.10 pH units (APHA,
AWWA, and WEF, 1995).
2.3 Sediment/Aquifer Material Samples
The seven aquifer material samples used in this study were obtained from Florida, New
Jersey, Oregon, Texas, Utah, Wisconsin and Georgia. Paired aquifer material/groundwater
samples were collected and stored at 4°C until used in this work. The EPA soil/sediment
samples 1, 7, 9, 13, 17 and 18 used in this study were described by Means et al. (1978). These
samples were air-dried, sieved through a 2 mm mesh and stored in closed containers at room
temperature until use. A summary of the properties of the aquifer material/sediment/soil samples
is given in Table 2.
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Table 2. Physical/chemical properties of aquifer material/soil/sediment samples used in the study.
Site OC1 pHsed2 extCa3 extMg3 extFe4 extMn4 extAl4
mg/kg mg/kg mg/kg mg/kg mg/kg mg/kg
TX 200 6.16 31000 152 64 19.8 66.9
UT 1340 7.58 15300 1847 688 63.8 339
FL 8350 5.94 12.4 9.14 70.9 0.52 106
NJ 11100 6.01 73.4 0.01 1690 48.2 317
OR 1620 7.81 8330 1610 6070 657 662
WI 810 7.54 492 213 130 15.2 14.5
EPA1 2200 7.30 2410 193 665 37 98
EPA7 20900 8.34 5200 1477 3010 582 827
EPA9 1100 8.55 14500 2405 589 151 342
EPA13 30400 6.74 1100 295 334 331 779
EPA17 8900 7.21 1270 180 4010 1000 1530
EPA18 6600 7.79 2710 676 4810 842 1460
GA 700 5.8 57.4 46.8 645 278 610
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Table 2. (continued).
Site extP5 CEC6 Sand7 Silt7 Clay7 AVS8
mg/kg cM/kg % % % mg/kg
TX 5.3 2.6 79.6 13.8 6.6 0.012
UT 4.5 10.5 21.2 33.8 45 3.58
FL 15.2 11.7 90.3 1.6 8.1 0.002
NJ 9 9.8 34.6 14.4 51 0.013
OR 5.5 88.9 40.6 28.9 30.5 0.007
WI 6.4 7.10 99.3 0.6 0.1 0.004
EPA1 13.5 1.07 93.9 6.1 0
EPA7 225 19.6 12.8 29.1 58
EPA9 21.7 12.4 7.1 17.4 75.6
EPA13 5.8 11.9 20.3 52.6 27.1
EPA17 477 10.6 18.1 35.7 46.2
EPA18 36.5 15.4 34.6 39.5 25.8
GA 3.6 2.3 70 22 8
1- OC analyses for aquifer materials performed courtesy of Dr. Everett Jenne, Battelle Laboratories,
Pacific Northwest; OC analyses for EPA sediments reported in Means et al. (1978).
2- Sediment pH = groundwater pH for aquifer materials; sediment pH (1:2) for EPA sediments
given by Means et al. (1978).
3- Extractable Ca and Mg represents the extractable Ca and Mg at pH = 4.5; analyses performed by
the authors.
4- Extractable Fe, Mn and Al determined using the method of Jenne and Crecelius (1988) (1 hr
extraction at 50 °C with a 0.25 M NH2OH/HC1 solution).
5- Extractable P determined using the method of Burke et al. (1989) (0.001 M H2SO4).
6,7- Cation Exchange Capacity and size distribution determinations on aquifer material samples
performed by Dr. Kim Tan, University of Georgia (ammonium acetate CEC method); EPA
sediment CEC and size distribution values reported by Means et al. (1978). cM/kg designates
centimoles per kilogram.
8- Acid Volatile Sulfides determined by the distillation method of U.S. EPA (1969).
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The study aquifer material, soil and sediment samples were generally from
uncontaminated sites. Nitric/perchloric acid extractions of all our study solid samples (except for
the Georgia aquifer material sample) yielded undetectable quantities of both extractable Pb (ICP
method limit of detection = 7.8 mg/kg) and Cd (ICP method limit of detection = 0.93 mg/kg).
Hence "background" concentrations of Pb and Cd were ignored in calculating the subsequent
experimentally determined K^ values.
2.4 Equipment and Stock Solutions for Lead Partitioning Studies
Lead partitioning was conducted using 50-mL teflon centrifuge tubes cleaned by soaking
for 24 hours in 5% nitric acid solution and rinsed several times with deionized water prior to use.
Stock Pb solutions (1000 mg/L) were prepared by dissolving 1.6 g of analytical reagent grade
Pb(NO3)2 in 1 L of deionized water; 2 drops of 5% nitric acid solution were added to stabilize
each stock solution. Lead concentrations in the stock solution were verified by comparison with
commercial standards for atomic absorption/inductively coupled plasma spectroscopy. A 1:10
dilution of the 1000 mg/L stock solution with distilled-deionized water produced the 100 mg/L
Pb solutions used in some portions of the study.
2.5 Lead Partitioning Procedures with air-dried EPA Sediments
Three grams each of the air-dried EPA sediment/soil samples were hydrated with 15 mL
of distilled-deionized water for 48 hours in 50-mL-capacity teflon centrifuge tubes held at 4 °C
(samples were stored in darkness and were "vortexed" initially and after 24 hours of storage).
Subsequently, fifteen mL of distilled-deionized water acidified with measured quantities of
Ultrex grade nitric acid were added to each sample. Lastly, sequential volumes of 100 or 1000
mg/L Pb were added to each sample to produce the desired initial Pb concentration. Samples
were "vortexed", equilibrated for 24 hours at 20-25 °C in darkness and again "vortexed" and
equilibrated for an additional 24 hours. After equilibration, samples were centrifuged at 10000
relative centrifugal force for 46 minutes; this procedure is designed to remove from solution all
particles with a radius greater than 50 nm and a density equal to or greater than 2.5 g/cm3.
Approximately three 10-mL aliquots were decanted from each sample— one was analyzed for pH,
one was acidified and analyzed via inductively coupled plasma spectroscopy, and the last aliquot
was saved in the event dilutions were necessary.
2.6 Lead Partitioning Procedures with Aquifer Material Samples
Five grams each of groundwater-saturated aquifer material were placed in the 50 mL
teflon centrifuge tubes. 30 mL of the groundwater collected at the same time and location as the
aquifer material samples was acidified with measured sequential volumes of UltrexR grade nitric
acid and added to each sample. Subsequently, measured sequential volumes of 100 or 1000
mg/L stock Pb solution were added to each sample to reach the desired initial Pb concentration.
Samples were equilibrated for 48 hours and analyzed via the methods described previously.
2.7 Equipment and Stock Solutions for Cadmium Partitioning Studies
The Cd partitioning work was performed using 50-mL teflon centrifuge tubes that were
cleaned by soaking for 24 hours in a 5% nitric acid solution and rinsed four times with deionized
water prior to use. Stock solutions of Cd (1000 mg/L) were prepared by dissolving analytical
reagent grade Cd(NO3)2 in deionized water; 0. ImL of a 0.5% nitric acid solution was added to
stabilize the solutions. Commercially prepared Cd standard solutions were used to verify stock
solution concentrations.
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2.8 Cadmium Partitioning with air-dried EPA Sediments
Three grams of air-dried EPA sediments were hydrated with 15 mL of distilled-deionized
water for 48 hours. As with the lead studies, samples were refrigerated at 4°C in darkness and
vortexed at 0 and 24 hours. After hydration, an additional 15 mL of distilled-deionized water
acidified by the addition of metals grade nitric acid was added to each sample to obtain the
desired pH. Measured, sequential volumes of the 1000 mg/L Cd2+ stock solution were then
added to each sample to produce the desired initial Cd concentration. Centrifuge tube caps were
loosened to permit exchange of atmospheric gases. Samples were "vortexed", placed in darkness
for 24 hours at room temperature (20-25 °C), "vortexed" again and equilibrated for an additional
24 hours. Samples were centrifuged at 10000 relative centrifugal force for 46 minutes and three
aliquots were obtained from each sample and analyzed as described previously.
2.9 Cadmium Partitioning with Aquifer Material Samples
Five grams of groundwater-saturated aquifer material were placed in the precleaned teflon
centrifuge tubes. Due to limited quantities of groundwater, the Florida, Wisconsin, Texas and
Utah groundwater samples were mixed 50:50 with distilled-deionized water and allowed to
equilibrate for at least one week prior to being added to the aquifer material. Subsequently, 25
mL of the groundwater solution acidified with measured, sequential volumes of metals grade
nitric acid were added to the centrifuge tubes. Measured sequential volumes of the 1000 mg/L
stock Cd solution were then added to each sample to reach the desired initial Cd concentration.
Samples were equilibrated for 48 hours at room temperature, centrifuged, and analyzed using the
methods described in the previous section.
2.10 Regression Analysis of Data
All regression analyses were performed using Statgraphics Plus Version 5.1R
(Manugistics, 2001). Models were developed by first generating simple least squares analyses
between log10Kd values for Pb and Cd with sediment/system properties. Sediment/system
properties yielding adjusted r2 values in excess of 5% were then used to create multiple
regression expressions. Because some of the sediment/system properties were collinear,
variables were deleted from the more complex equations if the variable probability was not
significant at the 90th percentile in a previous run. Lastly, simpler expressions also were
generated for both the purpose of comparing our results with earlier models and to provide
exposure assessors the ability to estimate metal K^ values using commonly available sediment
properties.
As will be demonstrated in the results section, the high initial solution phase Pb
concentration partitioning results with the Utah aquifer material samples could plausibly be
interpreted within the context of a possible precipitation of solid phase PbSO4. Because the
second pK for bisulfate is well below the typical pH conditions examined in this work, the
precipitation of PbSO4 is unlikely to be pH-dependent (at least within the conditions of this
study) and consequently the high initial Pb concentration data obtained with the Utah aquifer
material was not included in the regression analyses. Finally, unlike the procedure utilized by
Loux et al. (1990), K^s were calculated from data only when the final equilibrated porewater
dissolved metal concentrations were above the ICP method detection limit.
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CHAPTER 3
RESULTS
3.1 Lead Partitioning
Figures la through 11 display the raw Pb partitioning data (i.e., percent Pb remaining in
solution as a function of pH) obtained with six aquifer materials and six EPA sediments. Inset
numbers designate initial soluble lead concentrations. The individual points in these figures
represent experimental data and the lines are "eyeball" and/or cubic spline fits to the data; the
lines were added to assist the reader. Although error bars are not depicted in these figures, the
pH values should be considered to be within ±0.1 pH units and the percent remaining in solution
values should be considered to be the depicted value ± 5 percent. Three major points can be
easily discerned from figures la-11: 1) pH has a major influence on lead partitioning to natural
soils/sediments, 2) the nature of the solid phase has a major impact on lead-sediment/soil pH-
dependent partitioning, and 3) with the exception of the Utah aquifer material sample, virtually
all of the other solid phases displayed an increased affinity for Pb as initial Pb solution
concentration decreased. This third observation supports the contention that binding sites of
variable energies exist in natural soils and sediments, and that the highest energy sites are the
first to sequester lead.
Table 3 depicts the results from geochemical speciation model simulations (MINTEQA2;
Allison et al., 1990) of the high initial lead solution concentration data obtained with the Utah
groundwater/aquifer material. Using either the Davies or extended Debye-Huckel activity coef-
ficient algorithms, these simulated results suggest that PbSO4 was supersaturated under the high
initial Pb solution concentration conditions (i.e., the simulated Ion Activity Product [IAP] was
greater than the literature-reported solubility product). Hence, the inconsistent excess removal of
Pb from solution with the high initial lead solution concentration samples is believed to have
resulted from PbSO4 precipitation. The relative pH independency of the low-pH, high initial lead
solution concentration data also indirectly supports this hypothesis. Because of this presumptive
PbSO4 precipitation, these data were excluded from the subsequent regression analyses.
3.2 Cadmium Partitioning
Figures 2a through 21 display the raw Cd partitioning results (as with the Pb data, these
results are presented as percent Cd remaining in solution as a function of pH). Because there
were insufficient quantities of the paired Utah aquifer material/groundwater samples to conduct
Cd partitioning work, paired aquifer material/groundwater samples obtained in Georgia were
used instead. As with the Pb results displayed in figures la - 11, the nature of the soil/sediment
had a major impact on partitioning results. Also as with the Pb results, the lowest initial Cd
solution concentrations generally displayed the greatest affinity for the solids. Compared with
the Pb partitioning results, Cd does appear to have a lesser affinity for these test aquifer
materials, soils and sediments.
3.3 Empirical Partitioning Models
Table 4 illustrates the adjusted r2 values obtained between log10KdPb and the various
sediment system properties given in Table 2. Generally speaking, the following adjusted r2
values between log10KdPb and system properties exceeded 5 percent: percent sand, pHsoln, log10Al,
log10P, log10Fe, log10Mn, and log10OC. Because percent sand, percent silt and percent clay sum to
100 percent, these variables are collinear and for this reason, only one is used in the subsequent
statistical analyses.
-------
100 _
90 .
181 mg/L
136mg/L
59.5 mg/L
30.7 mg/L
15.6 mg/L
3.07 mg/L
100 _
90 .
70 .
10 .
0
Texas Aquifer Material
50 .
40 . y
30. "
1
184 mg/L
139 mg/L
60.4 mg/L
20 - » 31.2 mg/L
15.8 mg/L
3.10 mg/L
pH
PH
100
New Jersey Aquifer Material
v 182 mg/L
« 137 mg/L
59.7 mg/L
« 30.7 mg/L
15.6 mg/L
• 3.16 mg/L
100
Wisconsin Aquifer Material
v 185 mg/L
x 140 mg/L
61.0 mg/L
» 31.4 mg/L
16.0 mg/L
. 3.24 mg/L
PH
(id)
Figures la-Id.
Percent lead remaining in solution as a function of pH obtained with
aquifer materials from Utah (a), Texas (b), New Jersey (c) and Wisconsin
(d). Inset numbers depict initial Pb concentrations. Note that although
error bars are not given in these figures, the error bars for the pH
measurement technique is approximately ± 0.1 pH units and error bars for
Pb concentrations represent ± 5% of the measured values.
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Florida Aquifer Material
183 mg/L
138 mg/L
60.0 mg/L
30.9 mg/L
15.7 mg/L
(1e)
100
80 .
70 .
Oregon Aquifer Material
178 mg/L
134 mg/L
58.3 mg/L
30.0 mg/L
15.2 mg/L
2.97 mg/L
(10
100 _
90 .
80 .
70 .
60 .
50 .
40 .
30 .
20 .
10 .
0 .
2
EPA Sediment #1
189 mg/L
143 mg/L
62.5 mg/L
32.2 mg/L
16.4 mg/L
dg>
50 ,
40 .
30 .
20 .
10 .
EPA Sediment #7
r 189 mg/L
» 143 mg/L
62.5 mg/L
» 32.3 mg/L
16.4 mg/L
PH
PH
Figures le-lh.
Percent lead remaining in solution as a function of pH obtained with
aquifer materials from Florida (e) and Oregon (f) and with EPA sediments
1 (g) and 7 (h). Inset numbers depict initial lead concentrations. pH
measurements are within ±0.1 pH units and lead concentrations are
within ± 5% of the measured values.
-10-
-------
50
40 .
30 .
20 .
10 .
EPA Sediment #9
189mg/L
143mg/L
62.5 mg/L
32.3 mg/L
16.4 mg/L
50
40 .
30 .
20 .
10 .
EPA Sediment* 13
189 mg/L
143 mg/L
62.5 mg/L
32.3 mg/L
16.4 mg/L
di)
PH
PH
189 mg/L
143 mg/L
62.5 mg/L
32.3 mg/L
16.4 mg/L
50 .
EPA Sediment #16
10 .
40 .
30 .
20 .
10 .
189 mg/L
143 mg/L
62.5 mg/L
32.3 mg/L
16.4 mg/L
3.32 mg/L
Figures li-11. Percent lead remaining in solution as a function of pH obtained with EPA
sediments 9 (i), 13 (j), 17 (k) and 18 (1). Inset numbers depict initial lead
concentrations. pH measurements are within ±0.1 pH units and lead
concentrations are within ± 5% of the measured value.
-11-
-------
100
90
80
70
60
50
40
30
20
10
0
100
90
80
70
60
50
40
30
20
10
0
210 mg/L
159mg/L
70.4 mg/L
36.5 mg/L
18.6 mg/L
3.77 mg/l
T
PH
New Jersey aquifer material
209 mg/L
159 mg/L
70.1 mg/L
36.3 mg/L
18.5 mg/L
3.76 mg/L
(2c)
T
I
PH
100
90
80
70
60
50
40
30
20
10
0
100
90
80
70
60
50
40
30
20
10
0
212 mg/L
161 mg/L
71.2 mg/L Texas aquifer material
36.9 mg/L
18.8 mg/L
3.82 mg/L (
T
PH
Wisconsin aquifer materiao
251 mg/L
190 mg/L
84.1 mg/L
43.6 mg/L
22.2 mg/L
4.51 mg/L
Figures 2a-2d.
Percent cadmium remaining in solution as a function of pH obtained with
aquifer materials from Georgia (a), Texas (b), New Jersey (c) and
Wisconsin (d). Inset numbers depict initial cadmium concentrations. pH
measurements are within ±0.1 pH units and dissolved cadmium
concentrations are within ± 5% of the measured value.
-12-
-------
100
90
80
70
60
50
40
30
20
10
0
Florida aquifer material
210 mg/L
160mg/L
70.6 mg/L
36.6 mg/L
18.6 mg/L
3.78 mg/L
T
(2e)
100
90
80
70
60
50
40
30
20
10
0
Oregon aquifer material
204 mg/L
155 mg/L
68.2 mg/L
35.3 mg/L
18.0 mg/L
3.65 mg/L
(20
T
PH
100
90
80
70
60
50
40
30
20
10
0
EPA sediment #1
189 mg/L
143 mg/L
62.5 mg/L
32.3 mg/L
16.4 mg/L
3.32 mg/L
T
100
90
80
70
60
50
40
30
20
10
0
EPA Sediment #7
189 mg/L
143 mg/L
62.5 mg/L
32.3 mg/L
16.4 mg/L
3.32 mg/L
PH
T
PH
Figures 2e-2h.
Percent cadmium remaining in solution as a function of pH obtained with
aquifer materials from Florida (e) and Oregon (f) and with EPA
sediments 1 (g) and 7 (h). Inset numbers depict initial cadmium
concentrations. pH measurements are within ±0.1 pH units and dissolved
cadmium concentrations are within ± 5% of the measured value.
-13-
-------
100
90
80
70
60
50
40
30
20
10
0
100
90
80
70
60
50
40
30
20
10
0
EPA Sediment #9
189 mg/L
143 mg/L
62.5 mg/L
32.3 mg/L
16.4 mg/L
3.32 mg/L
T
I
PH
EPA Sediment #17
* 189.2 mg/L
« 142.9 mg/L
62.5 mg/L
« 32.3 mg/L
16.4 mg/L
• 3.32 mg/L
T
I
PH
(2k)
100
90
80
70
60
50
40
30
20
10
0
100
90
80
70
60
50
40
30
20
10
0
EPA Sediment #13
, 189.2 mg/L
» 142.9 mg/L
62.5 mg/L
» 32.3 mg/L
16.4 mg/L
B 3.32 mg/L
PH
EPA Sediment #18
189 mg/L
143 mg/L
62.5 mg/L
32.3 mg/L
16.4 mg/L
3.32 mg/L
(21)
Figures 21-21. Percent cadmium remaining in solution as a function of pH obtained with EPA
sediments 9 (i), 13 (j), 17 (k) and 18 (1). Inset numbers depict initial cadmium
concentrations. pH measurements are within ±0.1 pH units and dissolved
cadmium concentrations are within ± 5% of the measured value.
-14-
-------
Table 3. Geochemical interpretation of high initial Pb concentration
partitioning data for the Utah aquifer material/groundwater
samples (unless otherwise designated, all concentrations
in units of molarity).
Given:
pH = 3.0 (fixed activity) [Pb]total = 6.564xlQ-4
Temp. = 25 °C [Pb]dissolved = 2.037xlQ-4
[Na]total = 1.756X10-1 [Cl]total = 1.461X10'1
[Ca]total = 1.180xlO-3 [Mg]total = 1.560xlO-3
[K]total = 4.420xlO-3 [S04]total = 1.856xlO-2
pCO2 = 3.5E-4atm.
ax = [X]*Yx
= -Iog10(apb(2+)*aso4(2.))
MINTEQA2 (Allison et al, 1990) simulated results:
Computed Ionic Strength = 0.196M
Computed difference in charge balance =1.5%
Y?b2+ = Y so42- = 0.2948 (Davies extension)
YPb2+ = 0.2946 (Extended Debye-Huckel)
Yso42- = 0.2633 (Extended Debye-Huckel)
Therefore:
-loglo(IAPPbS04) = 7. 18 to 7.20
^erature = 7.79 (MINTEQA2, Smith and Martell, 1 976)
-15-
-------
Table 4. Adjusted r2 values (in percentages) for 1 parameter least
squares analyses between log10KdPb and sediment/system
properties (n = 432).
Property Adj. r2 Property Adj. r2
extAl
ext Ca
ext Fe
ext Mg
ext Mn
extP
OC
Pb l
CEC
clay
sand
silt
pHsed
pHsoln
18.9
6.06
14.2
4.08
15.1
12.0
18.5
0.64
1.61
19.0
24.7
16.6
4.61
25.9
log10Al
log10Ca
log10Fe
log10Mg
log10Mn
log,0P
Io2 OC
lojj Po
27.4
0.33
21.1
0.00
17.3
17.5
23.2
1.45
1- Total metals concentrations were normalized to mg/kg.
-16-
-------
Two other observations are apparent in Table 4: a) neither Pbtotal nor log10Pbtotal yield adjusted r2
values in excess of 5 percent, and b) Iog10 transformation of the extractable Al, P, Fe, and Mn
variables improved the adjusted r2 values for the relationships between system properties and
logi0Kd>Pb.
Table 5 presents the various empirical models developed during the study to account for the
432 Pb partitioning data points displayed in Figures la-11. Equation (1), relating log10K,Pb to
pHsoln, log10Al, log10P, log10Fe, log10Mn, log10OC and percent sand, yielded an adjusted r value of
79.4 percent. This is the "best" empirical model developed for Pb in the study. However, as
noted in Appendix A, the P value for the log10P variable exceeds 10 percent. Hence this variable
was removed to generate equation (2) in Table 5. Note that both the adjusted r2 values and
standard errors of the estimate (SEE) for both models (1) and (2) are identical. Note also that
both models (1) and (2) are significant at the 99th percentile. Equations (3-5) were developed for
use by exposure assessors with limited available datasets. Decreasing the number of "indepen-
dent" variables in these models results in a degradation of both the model adjusted r2 values and
the standard errors of the estimate (although not severely).
Tables 6 and 7 illustrate a similar analysis performed on the Cd data depicted in Figures
2a-21. From Table 6, in contrast to the Pb data, the adjusted r2 for simple models between
log10KdCd and sediment system properties exceeded 5 percent only for the variables pHsoln,
log10OC, log10Fe, log10P, percent clay and percent sand content. Again, because percent sand and
percent clay are collinear, only one of these two variable was exclusively used to develop
Equations (1) and (2) in Table 7. However, the P values for the log10P and log10Fe variables used
in Equations (1) and (2) exceeded 10 percent (see detailed statistics in Appendix B), hence these
two variables were removed to develop Equations (3) and (4). Note the minimal impact of
removing these variables on model adjusted r2 and SEE values. Lastly, to enable a comparison
between the present findings and those reported in the literature, a simple log10KdCd vs. pH
relationship was developed as Equation (5) in Table 7.
CHAPTER 4
DISCUSSION
The relatively high adjusted r2 values associated with our "best" models depicted in
Tables 5 and 7 are somewhat surprising in light of the fact that the partitioning results were
obtained using a variety of soils/sediments/aquifer materials subjected to different collection,
preservation and equilibration procedures. This observation suggests that these empirical models
do have a considerable degree of robustness.
Our findings both agree and disagree with the technical literature. For example, the y-
axes intercepts for the simple pH models document that Pb has a significantly greater affinity for
soils and sediments than does cadmium. Secondly, solution pH and sediment organic carbon
content both appear to impact Pb and Cd partitioning behavior. However, adding a pH2 term to
the regression equations did not greatly improve Pb partitioning model adjusted r values (Table
5). Similarly, neither total metal nor Iog10(total metal) variables greatly improved the empirical
partitioning models.
The technical literature suggests that labile phosphorus may play a role in Pb partitioning
(Nriagu, 1974; Hassett, 1974; Lindsay, 1979)). At first glance, our findings suggest that log10P
can be a significant variable in the regression equations. However, subsequent analyses led to
-17-
-------
Table 5. Regression equations relating log10KdPb to various sediment/system properties.
1- log10KdPb = -0.670728 + 0.776537*log10Al - 0.455826*log10Fe +
0.117675*log10Mn + 0.607061*log10OC +
0.0000416702*log10P - 0.00518428*sand + 0.561895*pHsoln
(adj. r2 = 0.794; SEE1 = 0.446, P < 0.01)
2- log10KdPb = -0.670967 + 0.776562*log10Al - 0.455873*log10Fe +
0.117702*log10Mn + 0.607089*log10OC - 0.00518412*sand +
0.561896*pHsoln
(adj. r2 = 0.794; SEE = 0.446, P < 0.01)
3- log10KdPb = -1.66596 + 0.54782*pHsoln - 0.0125584*sand +
0.585286*log10OC
(adj. r2 = 0.757; SEE = 0.484, P < 0.01)
4- log10KdPb = 0.821913 - 0.0194336*sand + 0.50909*pHsoln
(adj. r2 = 0.646; SEE = 0.585, P < 0.01)
5- log10KdPb = -3.27603 + 0.909033 *log10OC + 0.520959*pHsoln
(adj. r2 = 0.645; SEE = 0.586, P < 0.01)
6- log10Kd;Pb = -0.903834 + 1.09284*pHsoln - 0.0887548*pHsoln2
(adj. r2 = 0.277; SEE = 0.836, P < 0.01)
7- log10Kd;Pb = 0.302684 + 0.401918*pHsoln
(adj. r2 = 0.259; SEE = 0.847, P < 0.01)
1- SEE designates standard error of the estimate.
-18-
-------
Table 6. Adjusted r2 values (in percentages) for 1 parameter
least squares analyses between log10Kd Cd and sedi-
ment/system properties (n = 676)
Property
Adjusted
R-Squared
Property
Adjusted
R-Squared
extAl
ext Ca
ext Fe
ext Mg
ext Mn
extP
OC
CEC
% clay
% sand
% silt
pHsed
pHsoln
3.07
4.88
6.81
1.58
2.02
4.05
9.31
0.62
3.54
7.80
7.10
1.93
2.08
60.7
log10Al
log10Ca
log10Fe
logmMg
log10Mn
2.59
0.43
5.13
0.15
0.06
7.57
18.3
0.98
-19-
-------
Table 7. Regression equations relating log10KdCd to various sediment/system properties.
1) log10KdCd = -2.72079 + 0.57592*log10OC - 0.00594147*sand +
0.495213*pHsoln - 0.0383169*log10P - 0.049595l*log10Fe
(adj. r2 = 0.780; SEE = 0.534, P < 0.01)
2) log10KdCd =-3.45769 +0.49161 l*pHsoln + 0.00697647*clay +
0.589151*log10OC + 0.0375007*log10Fe - 0.0678679*log10P
(adj. r2 = 0.781; SEE = 0.532, P < 0.01)
3) log10KdCd = -2.87671 + 0.495043*pHsoln - 0.00500349*sand +
0.55245*log10OC
(adj. r2 = 0.780; SEE = 0.534, P < 0.01)
4) log10KdCd =-3.38864+ 0.489278*pHsoln + 0.00665484*clay +
0.583745*log10OC
(adj. r2 = 0.781; SEE = 0.534, P < 0.01)
5) log10KdiCd= -1.24069 + 0.497497*pHsoln
(adj. r2 = 0.608; SEE = 0.714, P < 0.01)
-20-
-------
this variable being removed from the equations. This finding suggests that the log10P variable
was probably collinear with one or more of the other significant variables. Given that both log10P
and log10Al were significantly related to Pb partitioning and only log10P was significantly related
to Cd partitioning, this could be interpreted within the context of possible plumbogummite
mineral (PbAl3(PO4)2(OH)5-H2O) formation with the Pb partitioning data.
As indicated previously, the high initial soluble Pb concentration partitioning data with
the Utah aquifer material/groundwater samples was consistent with a PbSO4 precipitation
mechanism (the Utah groundwater was apparently in contact with the Great Salt Lake and had a
relatively high sulfate content) . Conversely, sediment organic carbon content appeared to be
more heavily involved in the loss of Cd from solution than in Pb partitioning. The role of
organic carbon in cadmium partitioning has been discussed elsewhere in the technical literature
(Christensen, 1989; Holm et al., 2003). Lastly, a negative correlation term with the sediment per
cent sand content suggests that soil/sediment/aquifer material sand content is a particularly good
variable to account for the composite metal affinities displayed by the combined silt and clay
sediment particulate fractions.
Figure 3 compares the simple pH-dependent partitioning models for Pb developed in this
work with models in Table 1 generated by Gerritse and Van Driel, (1984), Loux et al. (1990),
Rhoades et al. (1992), and Hassan et al. (1996). Generally speaking, the models from the present
work and those developed by Loux et al. (1990) and Hassan et al. (1996) tended to cluster
together. The model from Hassan et al. (1996) was derived from partitioning data obtained using
5 sandy solid phases and was selected to be conservative in nature (i.e., to err on the side of
underestimating the Kd). The curve developed by Loux et al. (1990) was generated under
competitive conditions (with other cations). In addition, the equilibrium porewater Pb
concentrations were below the method detection limit for many of the higher pH data points used
by Loux et al. (1990) (-0.165 mg/L Pb); hence, K^ values for these data points were estimated
by assuming that the porewater Pb concentration equaled the method detection limit. This curve
likely underestimates Pb partitioning at high pH conditions and overestimates Pb partitioning at
low pH values. The shape of the polynomial curve obtained in this work does not compare
favorably with that obtained by Rhoades et al. (1992). Lastly, none of the curves compare
favorably with the results obtained by Gerritse and Van Driel (1984).
Figure 4 illustrates various simple pH-dependent Cd K^ relationships published in the
technical literature (in Table 1) and the findings from this work. The curves derived by
Christiansen (1989), Loux et al. (1990), Hassan et al. (1996), USEPA (1999) and the present
work also tend to cluster together. The slopes of the curves from the present work and the model
developed by Christiansen (1989) also tend to be comparable. As with the Pb data, differences
between the present findings and the expression developed by Loux et al. (1990) can be
attributed to the fact that the data used by Loux et al. (1990) were developed under competitive
cationic partitioning conditions and that a number of data points at higher pH conditions had
porewater Cd concentrations below the method detection limit (-.013 mg/L); K^ values for these
data points were calculated assuming that the porewater Cd concentration equaled the method
detection limit. Hence, the slope of the Cd expression generated by Loux et al. (1990) is likely to
be less than the true value.
There are several limitations associated with the empirical models developed in this
work. Numerous authors have described a solids concentration effect (SCE) on measured
-21-
-------
4
3.5
3
2.5
2
1.5
1
0.5
0
Rhoadesetal.(1992)
!*
Present study
Hassan etal. (1996)
Present (polynomial)
pH
Figure 3. Comparison of simple pH-dependent K^ relationships for lead in the literature
with those obtained in the present study. A second order polynomial did not
greatly improve the adjusted r-squared value with our data.
-------
I 5 1
8s
-1
-2
Christiansen (1989)
U.S. EPA
(1999)
Present
study
Gerritse and Van Driel (1984)
pH
Figure 4. Comparison of simple pH-dependent K^ relationships for cadmium reported in the
literature with those obtained in the present study.
-23-
-------
experimental Kds for both metals and organic toxicants (e.g., see Benoit, 1995 and references
cited therein). Generally speaking, the inverse relationships between metal K^s and solids
concentrations are either considered to be "real" or are attributed to experimental artifact. Even
if one accepts the hypothesis that the SCE is the result of including colloid-associated metals in
the "dissolved" metal concentration measurement (e.g., Benoit, 1995), the ramifications are such
that these colloid-associated metals also may be mobile and hence, the SCE may well be "real" to
the exposure assessment technical community regardless of whether or not the SCE is an
experimental artifact (e.g., Puls et al., 1990). The experimental conditions utilized in this work
produced sediment concentrations ranging from 0.08 to 0.13 kg/L. The findings from Gerritse
and Van Driel (1984) were obtained using a solids concentration of ~0.2 kg/L; this difference in
solids concentration might explain some of the disparities between the findings from the two
works.
Our procedure of ignoring extractable concentrations of background Pb and Cd is
supportable from a quantitative perspective. For example, the weak nitric acid extract method
limit of detection for extractable Pb was determined to be 7.8 mg/kg. Given that the typical
solids concentration used in the study was -0.1 kg/L, then the maximum extractable background
Pb concentration in the centrifuge tubes can be estimated to be 0.78 mg/L. Only for the initial
added concentrations of -3 mg/L would this quantity be a significant contribution (26%). At an
initial added Pb concentration of -15 mg/L, the maximum possible background extractable Pb
would be approximately 5.2% of the added spike. Similarly, the background extractable Cd
method limit of detection was estimated to be -0.93 mg/kg. At a solids concentration of-0.1
kg/L the maximum background Cd contribution would be -0.1 mg/L. Hence even at initial
added Cd concentrations of-3 mg/L, a background Cd contribution of circa 3.3% is well with
the limits of precision for atomic emission inductively coupled plasma spectrometry.
As noted in Table 2, the Utah aquifer material sample contained a significant quantity of
acid volatile sulfides. Hence, it is possible that PbS precipitation also may have occurred during
experimentation involving the Utah samples. Given a solids concentration of 0.1 kg/L, possible
PbS production could have precipitated as much as -2 mg/L of Pb with the Utah samples. Even
if PbS precipitation occurred, it would have been most significant only for the two lowest initial
Pb concentration sets of runs. Given that the second pIC, for H2S is approximately 7, PbS
precipitation would likely display a pH dependency within the conditions of the study (unlike the
probable PbSO4 precipitation).
One source of error in this work is the result of mineral phase dissolution under the
conditions of our study. Adjusting the system pH may lead to the significant dissolution of
calcareous minerals (at pH values less than 5) and aluminosilicate minerals (at pH values less
than 4). For those low pH datapoints where more solid has dissolved than precipitated (on a
weight basis), our methodology may lead to an underestimation of the true Kd value. This error,
if it occurred, would be conservative in the sense that it underestimates metals partitioning and
hence also overestimates potential metals solubilization, transport and bioavailability.
Alternatively, from Table 2, the maximum pH 4.5 extractable sedimentary Ca content is given as
31,000 ppm (or 3.1 % of the sediment). Assuming that this Ca was present as CaCO3, then the
maximum estimated CaCO3 content of the sediment is 7.74 %. Consequently, the maximum
estimated error in estimated K^ values as the result carbonate mineral dissolution at pH
conditions less than 5 is 7.74 %.
A question also has arisen as to the significance of mineral phase dissolution and/or
precipitation under the conditions of our study. An objective for conducting this study was to
study phenomena as they occur in the environment. Given that mineral phase dissolution and/or
precipitation probably occurred in our work, these processes also occur in the environment. The
significance of these processes has been previously addressed.
-24-
-------
Another limitation in this work is that while the EPA sediment samples were composited
and relatively homogeneous, the aquifer material samples were not. A visual inspection of the
aquifer material solids illustrated "patchiness" in these samples. Hence, background variation in
aquifer material properties presumably contributed to the unexplained variation in the results
from the derived empirical models.
There is evidence in the technical literature suggesting that carbonate mineral formation
may be involved in both environmental Pb and Cd partitioning (Rai et al., 1986; Bank et al.,
1989; Rhoades et al., 1992). Although there was no effort in this work to identify the actual
mechanisms leading to Pb or Cd partitioning, carbonate mineral formation may have been
significant. If so, then this effect must be taken into account when the results from this work are
applied to groundwater systems because the partial pressure of carbon dioxide in aquifers is
generally much greater than the atmospheric value (e.g., Loux et al., 1991 and references cited
therein).
The empirical models for Pb and Cd presented in Tables 5 and 7 represent the most
robust empirical models available to the technical community. Expressions developed herein
yield estimated K^ values less than corresponding values actually measured by some other
researchers; however, this likely results from the lesser organic carbon content sediments and
higher initial porewater Pb and Cd concentrations used in our study to develop our models.
Therefore, our models may have more general applicability for assessments related to
contaminated sites with low organic carbon content surficial soils. Lastly, our expressions yield
more conservative results in risk assessments containing a significant drinking water exposure
pathway of concern.
-25-
-------
REFERENCES
Allison, J.D., Brown, D.S. and Novo-Gradoc, K. 1991. MINTEQA2 PRODEFA2,
Version 3.0 User's Manual. U.S. Environmental Protection Agency, Athens,
Georgia, USA. EPA/600/3-91/021.
APHA, AWWA, and WEF. 1995. Standard Methods for the Analyses of Water
and Wastewater, 19th Edition. American Public Health Association, Washington,
DC, USA.
Bank, S., Bank, J.F., Marchetti, P.S., and Ellis, P.O. 1989. Solid-state cadmium-
113 NMR study of cadmium speciation in environmentally contaminated
sediments. J. Environ. Qual. 18:25-30.
Basta, N.T. and Tabatabai, M.A. 1992. Effect of cropping systems on adsorption
of metals by soils: H, Effect of pH. Soil Sci. 153:195-204.
Benoit, G. 1995. Evidence of the particle concentration effect for lead and other
metals in fresh waters based on ultraclean technique analyses", Geochim.
Cosmochim. Acta 59:2677-2687.
Boekhold, A.E. and Van Der Zee, S.E.A. 1992. A scaled sorption model validated
at the column scale to predict cadmium contents in a spatially variable field soil.
Soil Sci. 154:105-112.
Burke, A. J., Waller, P. H., and Pickering, W. F.: 1989. The evaluation of inorganic
phosphate species in salt water lake sediments. Chem. Spec. Bioavail. 1:47-57.
Christensen, T.H. 1989. Cadmium soil sorption at low concentrations: VIE.
Correlation with soil parameters. Water Air Soil Pollut. 44:71 -82.
Gerritse, R.G. and Van Driel, W. 1984. The relationship between adsorption of
trace metals, organic matter, and pH in temperate soils. J. Environ. Qual. 13:197-
204.
Hassan, S.M., Garrison, A.W., Allen, H.E., DiToro, D.M., and Ankley, G.T. 1996.
Estimation of partition coefficients for five trace metals in sandy sediments and
application to sediment quality criteria. Environ. Tox. Chem., 15:2198-2208.
Hassett, J.J. 1974. Capacity of selected Illinois soils to remove lead from aqueous
solution. Comm. Soil Sci. Plant Anal., 5:499-505.
Hill, I.R., Matthiessen, P., and Heimbach, F. 1993. Guidance Document on
Sediment Toxicity Tests and Bioassays for Freshwater and Marine
Environments, From the Workshop on Sediment Toxicity Assessment held at Slot
Moermond Congrescentrum Renesse, the Netherlands, 8-10 November, 1993.
SETAC Press, Pensacola, Florida, USA.
Holm, P.E., Rootzen, H., Borggard, O.K., Moberg, J.P., and Christensen, T.H.
2003. Correlation of cadmium distribution coefficients to soil characteristics. J.
Environ. Qual. 32:138-145.
-26-
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Jenne, E.A., and Crecelius, E.A. 1988. Determination of Sorbed Metals, Amorphic
Fe, Oxidic Mn and Reactive Particulate Organic Carbon in Sediments and Soils.
Proceedings 3rd International Conference on Environmental Contamination,
Venice, September 26-29, 1988.
Lindsay, W.L. 1979. Chemical Equilibria in Soils. John Wiley and Sons, New
York, USA.
Loux, N.T., Brown, D.S., Chafin, C.R, Allison, J.D., and Hassan, S.M. 1989.
Chemical speciation and competitive cationic partitioning on a sandy aquifer
material. Chem. Spec. Bioavail. 1:111-126.
Loux, N.T., Chafin, C.R., and Hassan, S.M. 1990. "Statistics of Aquifer Material
Properties and Empirical, pH-Dependent Partitioning Relationships for As(ni),
As(V), Ba(II), Be(H), Cd(H), Cr(VI), Cu(II), Hg(II), Ni(II), Pb(II), Sb(V), Se(IV),
Se(VI), T1(I), and Zn(II). U.S. Environmental Protection Agency internal report
submitted to the EPA Office of Solid Waste, February, 1990.
Loux, N.T., Allison, J.D., Chafin, C.R. and Hassan, S.M. 1991. Carbonate
equilibria and groundwater sample collection: Implications for estimated average
subsurface properties in continental North America. Intern. J. Environ. Anal.
Chem. 44:41-53.
Manugistics, 2001. Statgraphics Plus version 5.1, Rockville, Maryland, USA.
Means, J.C., Hassett, J.J., Banwart, W.L., Wood, S.G. and Khan, A. 1978.
Sorption Properties of Sediments and Energy-Related Pollutants. Progress
Report, USEPA Contract No. 68-03-2555.
Myers, S.A. and Tracy, D.H. 1983. "Improved performance using internal
standardization in ICP plasma emission spectroscopy". Spectrochim. Acta Part B,
38:1227-1253.
Nriagu, J.O. 1974. Lead orthophosphate—IV Formation and stability in the
environment. Geochim. Cosmochim. Acta 38:887-898.
Puls, R.N., Eychaner, J.H., and Powell, R.M. 1990. Colloidal-Facilitated
Transport of Inorganic Contaminants in Groundwater: Part 1 Sampling
Considerations. U.S. Environmental Protection Agency Robert S. Kerr
Environmental Research Laboratory, Ada, Oklahoma, USA. December, 1990.
EPA/600/M-90/023.
Rai, D. and Zachara, J.M. 1986. Geochemical Behavior of Chromium
Species, EPRI Report EA-4544, Electric Power Research Institute, Palo Alto,
California, USA.
Rai, D., Zachara, J.M. Schwab, A.P., Schmidt, R.L., Girvin, D.C. and Rogers, J.E.
1986. Chemical Attenuation Rates, Coefficients, and Constants in Leachate
Migration. Volume 1: A critical review. Electric Power Research Institute Report
number EA-3356, Volume 1. Palo Alto, California, USA.
-27-
-------
Rhoads, K., Bjornstad, B.N. Lewis, R.E., Teel, S.S., Cantrell, K.J., Serne, R.J.,
Smoot, J.L., Kincaid, C.T., and Wurstner, S.K. 1992. Estimation of the release
and migration of lead through soils and groundwater at the Hanford Site 218-E-
128 Burial Ground, Volume 1, Final report. Battelle Pacific Northwest National
Laboratory report number PNL-8356-Vol. 1, Richland, Washington.
Salhotra, A.M., Mineart, P., Sharp-Hansen, S. and Allison, T. 1990. Multimedia
Exposure Assessment Model (MULTIMED) for Evaluating the Land Disposal of
Wastes-Model Theory. U.S. EPA Office of Research and Development, Athens,
Georgia, USA.
Santillan-Medrano, J. and Jurinak, J.J. 1975. The chemistry of lead and cadmium
in soil: solid phase formation. Soil Sci. Soc. Am. Proc. 39:851-856.
Sauve, S., Norvell, W.A., McBride, M., and Hendershot, W. 2000. "Speciation
and complexation of Cadmium in extracted soil solutions", Env. Sci. Technol.,
34:291-296.
Smith, R.M. and Martell, A.E. 1976. Critical Stability Constants: Volume 4,
Inorganic Complexes. Plenum Press, New York.
Smith, K.S., Ranville, J.F., and Macalady, D.L. Influence of fulvic acid on trace
metal sorption onto ferric oxyhydoxysulfate particles in acidic systems. Abstracts
of papers of the Am. Chem. Soc. 205:96-GEOC, Part 1, March 28, 1993.
Tipping, E., Rieuwerts, J., Pan, G., Ashmore, M.R., Lofts, S., Hill, M.T.R., Farago,
M.E., and Thornton, I. 2003. "The solid-solution partitioning of heavy metals
(Cu, Zn, Cd, Pb) in upland soils of England and Wales. Environmental Pollution,
125:213-225.
U.S. EPA. 1969. Chemistry Laboratory Manual, Bottom Sediments, Compiled by
Great Lakes Region Committee on Analytical Methods, U.S. EPA, F.W.Q.A.,
December, 1969.
U.S. EPA. 1992. Sediment Classification Methods Compendium. U.S.
Environmental Protection Agency, Office of Water, Washington, DC. EPA 823-
R-92-006.
U.S. EPA. 1996. Soil Screening Guidance: User's Guide; Attachment C:
Chemical Properties for SSL Development. U.S. Environmental Protection
Agency, Washington, DC. EPA 540/R-96/018.
U.S. EPA. 1999. Understanding variation in partition coefficient, Kd, values,
Volume I: The Kd model, methods of measurement, and application of chemical
reaction codes. U.S. Environmental Protection Agency, Office of Air and
Radiation, Washington, DC.EPA 402-R-99-004A.
U.S. EPA. 2004. Http://oaspub.epa.gov/oerrpage/advquery
-28-
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Appendix A
Summary of statistics used to generate regression equations for Pb listed in Table 5.
A-l
-------
Regression equation (1).
Equation
log10KdPb = -0.670728 + 0.776537*log10Al - 0.455826*log10Fe + 0.117675*log10Mn
+ 0.607061 *log10OC + 0.0000416702*log10P - 0.00518428*sand +
0.561895*pHsoln
Multiple Regression Analysis
Dependent variable: log10KdPb
Parameter
CONSTANT
log10Al
log10Fe
log10Mn
lOgjnOC
log,0P
sand
pHsoln
Estimate
-0.670728
0.776537
-0.455826
0.117675
0.607061
0.0000416702
-0.00518428
0.561895
Standard T
Error Statistic
0.471192 -1.42347
0.0982006 7.90767
0.10453 -4.36071
0.0603468 1.94997
0.0631243 9.61692
0.0597063 0.000697919
0.00155686 -3.32996
0.0179919 31.2305
P-Value
0.1553
0.0000
0.0000
0.0518
0.0000
0.9994
0.0009
0.0000
Analysis of Variance
Sum of Squares Df
Source
Mean Square
F-Ratio
P-Value
Model
Residual
Total (Coir.)
332.305
84.4677
416.772
7
424
431
47.4721 238.29
0.199216
0.0000
R-squared = 79.7329 percent
R-squared (adjusted for d.f.) = 79.3983 percent
Standard Error of Est. = 0.446337
Mean absolute error = 0.355951
Durbin-Watson statistic = 1.69009 (P=0.0006)
Lag 1 residual autocorrelation = 0.147307
1-
Df designates degrees of freedom
A-2
-------
Regression equation (2).
Equation
log10Kd;Pb =-0.670967
0.776562*log10Al - 0.455873*log10Fe + 0.117702*log10Mn
0.607089*log10OC - 0.00518412*sand + 0.561896*pHsoln
Multiple Regression Analysis
Dependent variable: log10KdPb
Parameter
CONSTANT
log10Al
log10Fe
log10Mn
log10OC
sand
Estimate
-0.670967
0.776562
-0.455873
0.117702
0.607089
-0.00518412
Standard
Error
0.323513
0.0915385
0.0804758
0.045402
0.0481764
0.00153934
T
Statistic P-Value
-2.074 0.0387
8.48345 0.0000
-5.66472 0.0000
2.59245 0.0099
12.6014 0.0000
-3.36775 0.0008
0.561896 0.017966
31.2755
0.0000
Analysis of Variance
Source
Model
Residual
Sum of Squares
332.305
84.4677
Df
6
425
Mean Square
55.3841
0.198748
F-Ratio
278.67
P-Value
0.0000
Total (Coir.)
416.772
431
R-squared = 79.7329 percent
R-squared (adjusted for d.f.) = 79.4468 percent
Standard Error of Est. = 0.445811
Mean absolute error = 0.355951
Durbin-Watson statistic = 1.69009 (P=0.0006)
Lag 1 residual autocorrelation = 0.147303
A-3
-------
Regression equation (3).
Equation
log10KdPb = -1.66596 + 0.54782*pHsoln - 0.0125584*sand + 0.585286*log10OC
Multiple Regression Analysis
Dependent variable: log10KdPb
Parameter
CONSTANT
pHsoin
sand
log10OC
Estimate
-1.66596
0.54782
-0.0125584
0.585286
Standard
Error
0.193836
0.0193298
0.0008877
0.0415855
T
Statistic
-8.59467
28.3406
-14.1471
14.0743
P-Value
0.0000
0.0000
0.0000
0.0000
Analysis of Variance
Sum of Squares Df Mean Square F-Ratio
Source
P-Value
0.0000
Model
Residual
316.329
100.444
3 105.443
428 0.234682
449.30
Total (Corr.)
416.772
431
R-squared = 75.8996 percent
R-squared (adjusted for d.f.) = 75.7307 percent
Standard Error of Est. = 0.48444
Mean absolute error = 0.388245
Durbin-Watson statistic = 1.5065 (P=0.0000)
Lag 1 residual autocorrelation = 0.239135
A-4
-------
Regression equation (4).
Equation
log10KdPb = 0.821913 - 0.0194336*sand + 0.50909*pHsoln
Multiple Regression Analysis
Dependent variable: log10KdPb
Parameter
CONSTANT
sand
pHsoin
Estimate
0.821913
-0.0194336
0.50909
Standard T
Error Statistic
0.0960819 8.55429
0.000895416 -21.7035
0.0231137 22.0255
P-Value
0.0000
0.0000
0.0000
Analysis of Variance
Source Sum
Model
Residual
of Squares
269.842
146.931
Df Mean Square
2 134.921
429 0.342496
F-Ratio
393.93
P-Value
0.0000
Total (Corr.)
416.772
431
R-squared = 64.7456 percent
R-squared (adjusted for d.f.) = 64.5812 percent
Standard Error of Est. = 0.585231
Mean absolute error = 0.463089
Durbin-Watson statistic = 1.73709 (P=0.0031)
Lag 1 residual autocorrelation = 0.129666
A-5
-------
Regression equation (5).
Equation:
log10KdPb = -3.27603 + 0.909033 *log10OC + 0.520959*pHsoln
Multiple Regression Analysis
Dependent variable: log10KdPb
Parameter
CONSTANT
log10OC
pHsoin
Estimate
-3.27603
0.909033
0.520959
Standard
Error
0.189863
0.0420158
0.0232767
T
Statistic
-17.2547
21.6355
22.3811
P-Value
0.0000
0.0000
0.0000
Analysis of Variance
Source
Model
Residual
Sum of Squares
269.359
147.413
Df Mean Square
2
429
134.68
0.34362
F-Ratio
391.94
P-Value
0.0000
Total (Corr.)
416.772
431
R-squared = 64.6299 percent
R-squared (adjusted for d.f.) = 64.465 percent
Standard Error of Est. = 0.586191
Mean absolute error = 0.467002
Durbin-Watson statistic = 1.66961 (P=0.0003)
Lag 1 residual autocorrelation = 0.159717
A-6
-------
Regression equation (6).
Equation
log10KdiPb = -0.903834 + 1.09284*pHsoln - 0.0887548*pHsoln2
Polynomial Regression Analysis
Dependent variable: log10KdPb
Parameter
CONSTANT
pHsoin
pHsolnA2
Estimate
-0.903834
1.09284
-0.0887548
Standard
Error
0.374977
0.203356
0.025792
T
Statistic
-2.41037
5.37402
-3.44118
P-Value
0.0164
0.0000
0.0006
Analysis of Variance
Source
Model
Residual
Sum of Squares
116.793
299.979
Df
2
429
Mean Square
58.3964
0.699253
F-Ratio
83.51
P-Value
0.0000
Total (Corr.)
416.772
431
R-squared = 28.0232 percent
R-squared (adjusted for d.f.) = 27.6876 percent
Standard Error of Est. = 0.836213
Mean absolute error = 0.657179
Durbin-Watson statistic = 1.66392 (P=0.0002)
Lag 1 residual autocorrelation = 0.165565
A-7
-------
Regression equation (7).
Equation:
log10KdiPb = 0.302684 + 0.401918*pHsoln
Regression Analysis - Linear model: Y = a + b*X
Dependent variable: loglOKd
Independent variable: solnpH
Parameter
Intercept
Slope
Estimate
0.302684
0.401918
Standard
Error
0.134629
0.032668
T
Statistic P- Value
2.24827
12.3031
0.0251
0.0000
Analysis of Variance
Source
Model
Residual
Sum of Squares
108.512
308.26
Df
1
430
Mean Square
108.512
0.716883
F-Ratio
151.37
P-Value
0.0000
Total (Corr.)
416.772
431
Correlation Coefficient = 0.510259
R-squared = 26.0364 percent
R-squared (adjusted for d.f.) = 25.8644 percent
Standard Error of Est. = 0.84669
Mean absolute error = 0.68069
Durbin-Watson statistic = 1.61928 (P=0.0000)
Lag 1 residual autocorrelation = 0.189019
A-8
-------
Appendix B
Summary of statistics used to generate regression equations for Cd listed in Table 7.
B-l
-------
Regression equation (1).
Equation:
log10KdCd = -2.72079 + 0.57592*log10OC - 0.00594147*Sand +
0.495213*pHsoln - 0.0383169*log10P - 0.049595l*log10Fe
Statistics:
Dependent variable: log10Kd
,Cd
Parameter
CONSTANT
log10OC
sand
pH !
log,0P
log10Fe
Estimate
-2.72079
0.57592
-0.00594147
0.495213
-0.0383169
-0.0495951
Standard
Error
0.216514
0.0411699
0.00106336
0.0116394
0.0418937
0.0483949
T
Statistic P-Value
-12.5664 0.0000
13.9889 0.0000
-5.58745 0.0000
42.5463 0.0000
-0.914622 0.3604
-1.0248 0.3055
Analysis of Variance
Sum of Squares Df
Source
Mean Square F-Ratio
P-Value
Model
Residual
685.427
191.306
5
670
137.085 480.11
0.285532
0.0000
Total (Corr.)
876.734
675
R-squared = 78.1796 percent
R-squared (adjusted for d.f.) = 78.0168 percent
Standard Error of Est. = 0.534352
Mean absolute error = 0.405888
Durbin-Watson statistic = 0.730478 (P=0.0000)
Lag 1 residual autocorrelation = 0.629705
B-2
-------
Regression equation (2).
Equation:
log10KdCd =-3.45769 +0.49161 l*pHsoln +0.00697647*Clay +
0.589151*log10OC + 0.0375007*log10Fe -
0.0678679*log10P
Statistics
Dependent variable: log10KdCd
Parameter
CONSTANT
pHsoln
clay
log10OC
log10Fe
log,0P
Estimate
-3.45769
0.491611
0.00697647
0.589151
0.0375007
-0.0678679
Standard
Error
0.138702
0.0115897
0.00118019
0.0409778
0.0395088
0.0433684
T
Statistic
-24.9288
42.4178
5.9113
14.3773
0.949173
-1.56492
P-Value
0.0000
0.0000
0.0000
0.0000
0.3425
0.1176
Analysis of Variance
Source
Model
Residual
Sum of Squares
686.438
190.296
Df Mean Square
5
670
137.288
0.284024
F-Ratio
483.37
P-Value
0.0000
Total (Corr.)
876.734
675
R-squared = 78.2949 percent
R-squared (adjusted for d.f.) = 78.1329 percent
Standard Error of Est. = 0.532939
Mean absolute error = 0.402332
Durbin-Watson statistic = 0.734254 (P=0.0000)
Lag 1 residual autocorrelation = 0.627921
B-3
-------
Regression equation (3).
Equation:
log10KdCd = -2.7463 + 0.494383*pHsoln - 0.00562497*Sand +
0.562986*log10OC - 0.044992*log10Fe
Statistics
Dependent variable: log10Kd Cd
Standard T
Parameter Estimate Error Statistic P-Value
CONSTANT
sand
log10OC
log10Fe
-2.7463
0.494383
-0.00562497
0.562986
-0.044992
0.214683 -12.7923 0.0000
0.0116026 42.6098 0.0000
0.00100536 -5.595 0.0000
0.0386603 14.5624 0.0000
0.0481267 -0.934867 0.3499
Analysis of Variance
Source
Model
Residual
Sum of Squares
685.188
191.545
Df
4
671
Mean Square F-Ratio
171.297 600.07 0,
0.285463
P-Val
.0000
Total (Corr.) 876.734 675
R-squared = 78.1524 percent
R-squared (adjusted for d.f.) = 78.0222 percent
Standard Error of Est. = 0.534287
Mean absolute error = 0.406058
Durbin-Watson statistic = 0.729923 (P=0.0000)
Lag 1 residual autocorrelation = 0.63002
B-4
-------
Regression equation (4).
Equation:
log10KdCd = -2.87671 + 0.495043*pHsoln - 0.00500349*Sand +
0.55245*log10OC
Statistics
Dependent variable: log10Kd Cd
Standard T
Parameter Estimate Error Statistic P-Value
CONSTANT
pHsoln
sand
log10OC
-2.87671
0.495043
-0.00500349
0.55245
0.163175
0.01158
0.000754123
0.0369777
-17.6295
42.7498
-6.63484
14.9401
0.0000
0.0000
0.0000
0.0000
Analysis of Variance
Source
Model
Residual
Sum of Squares
684.939
191.795
Df Mean Square
3
672
228.313
F-Ratio
799.95
0.285409
P-Value
0.0000
Total (Corr.) 876.734 675
R-squared = 78.1239 percent
R-squared (adjusted for d.f.) = 78.0263 percent
Standard Error of Est. = 0.534237
Mean absolute error = 0.406539
Durbin-Watson statistic = 0.729352 (P=0.0000)
Lag 1 residual autocorrelation = 0.630415
B-5
-------
Regression equation (5).
Equation:
log10KdCd = -3.38864 + 0.489278*solnpH + 0.00665484*Clay
0.583745*log10OC
Statistics
Dependent
Parameter
variable: log10KdCd
Estimate
CONSTANT -3.38864
pHsoln 0.489278
clay 0.00665484
log10OC 0.583745
Standard
Error
T
Statistic
0.128545 -26.3615
0.011511 42.5052
0.000981515 6.78017
0.0344532 16.9431
P-Value
0
0
0
0
.0000
.0000
.0000
.0000
Analysis of Variance
Source
Model
Residual
Sum of Squares
685.46
191.274
Df Mean Square F-Ratio
3 228
672 0
.487 802
.284634
.74
P-Value
0.
.0000
Total (Corr.)
876.734
675
R-squared = 78.1833 percent
R-squared (adjusted for d.f.) = 78.0859 percent
Standard Error of Est. = 0.533511
Mean absolute error = 0.402237
Durbin-Watson statistic = 0.731466 (P=0.0000)
Lag 1 residual autocorrelation = 0.629254
B-6
-------
Regression equation (6).
Equation:
log10Kd;Cd = -1.24069 + 0.497497*pHsoln
Statistics
Dependent variable: log10Kd Cd
Independent variable: pHsoln
Parameter
Intercept
Slope
Estimate
-1.24069
0.497497
Standard
Error
0.0932551
0.0153971
T
Statistic
-13.3042
32.3112
P-Value
0.0000
0.0000
Analysis of Variance
Source
Model
Residual
Sum of Squares
532.779
343.955
Df
1
674 0.
Mean Square
532.779
510318
F-Ratio
1044.01
P-Value
0.0000
Total (Coir.) 876.734
675
Correlation Coefficient = 0.779542
R-squared = 60.7686 percent
R-squared (adjusted for d.f.) = 60.7104 percent
Standard Error of Est. = 0.714366
Mean absolute error = 0.582519
Durbin-Watson statistic = 0.412912 (P=0.0000)
Lag 1 residual autocorrelation = 0.792533
B-7
------- |