METHODS FOR SCALING AND COMPARING ADSORPTION DATASETS 
 
 
 
 
 
 
 
Except where reference is made to the work of others, the work described in this thesis is 
my own or was done in collaboration with my advisory committee.  This thesis does not 
include proprietary or classified information. 
 
 
__________________________________ 
Owen Kent Hartzog 
 
 
 
 
 
Certificate of Approval: 
 
 
 
 
_________________________             _________________________ 
T. Prabhakar Clement               Mark O. Barnett, Chair 
Professor                         Associate Professor 
Civil Engineering               Civil Engineering 
 
 
 
 
 
_________________________                                            _________________________ 
Dongye Zhao                George T. Flowers 
Associate Professor               Interim Dean 
Civil Engineering               Graduate School 
 
 
 
METHODS FOR SCALING AND COMPARING ADSORPTION DATASETS 
 
 
 
Owen Kent Hartzog 
 
 
 
 
 
A Thesis 
 
Submitted to 
 
the Graduate Faculty of 
 
Auburn University 
 
in Partial Fulfillment of the 
 
Requirements for the 
 
Degree of 
 
Master of Science 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Auburn, Alabama 
August 9, 2008 
 iii 
METHODS FOR SCALING AND COMPARING ADSORPTION DATASETS 
 
 
 
 
 
Owen Kent Hartzog 
 
 
Permission is granted to Auburn University to make copies of this thesis at its discretion, 
upon request of individuals or institutions and at their expense. The author reserves all 
publication rights. 
 
 
 
 
______________________________ 
Signature of Author 
 
 
 
______________________________ 
Date of Graduation 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 iv 
THESIS ABSTRACT 
 
METHODS FOR SCALING AND COMPARING ADSORPTION DATASETS 
 
 
 
 
 
Owen Kent Hartzog 
 
Master of Science, August 9, 2008 
(B.S., University of Mississippi, 2006) 
 
65 Typed Pages 
 
Directed by Mark O. Barnett 
 
The presence of reactive groundwater contaminants are a great concern to many 
government agencies and private entities.  The fate and transport of these contaminants is 
determined by their interactions with subsurface solids and hence a thorough 
understanding of these processes is necessary for the remediation of contaminated sites.  
There is an abundance of adsorption literature; however, these studies vary in their goals 
and methods.  Some studies are general in nature, dealing with the general chemistry of 
adsorption in a well-controlled laboratory setting while others examine a specific 
problem at a contaminated site, using the soils and conditions at the site.   This inherent 
difference, along with inadequate reporting of experimental conditions, makes it difficult 
to take information from one study and compare it confidently to others.   Proper 
comparisons are an important part of studying these systems.  Furthermore, developing 
 v 
predictive reactive-transport models requires the ability to scale the reactions to various 
systems. 
As models capable of predicting the fate and transport of groundwater 
contaminants are developed, the need to compare adsorption data in a reliable manner is 
important.  In this thesis, various approaches for comparing adsorption data were 
examined to determine the best method for designing and analyzing the results of 
adsorption experiments.  The interactions of arsenate and goethite were examined as a 
representative system although results can be extended to other systems.  A study of 
model-generated data was first executed to examine the basic theoretical principles of 
dataset comparison.  These principles were then tested on a suite of experimental data 
from our laboratory and from the literature.   
The results indicated that the most important factor in the comparison of sorption 
datasets is the total adsorbate-adsorbent ratio (e.g. mol As/mol Fe).  If this value is too 
low, the system will be limited only by the amount of adsorbate present and accurate 
comparisons between datasets cannot be made.  Additionally, it was found that 
normalization techniques can have a marked effect on comparisons, especially between 
systems with differing adsorbent types (i.e. natural and synthetic goethite).  It is nearly 
always better to use the specific surface area of the adsorbent as a scaling parameter 
rather than the reactive mass of the adsorbent (in this case, Fe content).  The 
incorporation of these techniques will improve the methods for scaling and comparing 
adsorption data in future studies. 
 
 
 vi 
ACKNOWLEDGEMENTS 
 
The author would like to acknowledge the excellent instruction, support, and 
guidance of his advisor, Dr. Mark Barnett. Additional thanks to Dr. Dongye Zhao and Dr. 
T. Prabhakar Clement for their knowledge and support during the author?s term at 
Auburn University. The author would like to thank Jinling Zhuang for his technical 
assistance and training in the environmental laboratory at Auburn University. This work 
was supported by an ERSP research project from the Office of Science (BER), U.S. 
Department of Energy Grant no. DE-FG02-06ER64213. 
 
 
 
 
 
 
 
 
 
 
 vii 
Style manual or journal followed: Auburn University Graduate School: Guide to 
Preparation and Submission of Theses and Dissertations. 
Computer software used: Microsoft Office 2003: Excel, Word; EndNote; VisualMINTEQ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 viii 
TABLE OF CONTENTS 
LIST OF TABLES...............................................................................................................x  
LIST OF FIGURES .......................................................................................................... xi 
CHAPTER I. INTRODUCTION.........................................................................................1 
1.1 Problem Statement.............................................................................................1 
1.2 Objectives ..........................................................................................................2 
1.3 Organization.......................................................................................................2 
CHAPTER II. LITERATURE REVIEW ............................................................................4 
            2.1 Background Information....................................................................................4 
                        2.1.1 Sources of Contamination...................................................................4 
                        2.1.2 Health Concerns..................................................................................5 
                        2.1.3 Treatment Technologies and Methods................................................5 
            2.2 Iron Oxide Interactions in the Subsurface .........................................................6 
                        2.2.1 Presence of Iron Oxides in the Subsurface .........................................6 
                        2.2.2 Arsenic Interactions with Iron Oxides ................................................7 
            2.3 Status of the Adsorption-Scaling Literature ....................................................13 
                        2.3.1 Typical Study Details........................................................................14 
                        2.3.2 Normalization and Plotting Techniques............................................15 
            2.4 Importance for the Development of Reactive Transport Models ....................16 
 ix 
CHAPTER III. METHODS FOR SCALING AND COMPARING ADSORPTION 
DATASETS .......................................................................................................................17 
3.1 Abstract............................................................................................................17 
            3.2 Introduction......................................................................................................18 
            3.3 Methods............................................................................................................21 
                        3.3.1 Modeling...........................................................................................22 
                        3.3.2 Literature Comparison ......................................................................23 
                        3.3.3 Experimental.....................................................................................23 
3.4 Results and Discussion ....................................................................................25 
                        3.4.1 Modeling...........................................................................................25 
                        3.4.2 Literature Comparison ......................................................................28 
                        3.4.3 Normalization Technique..................................................................35 
            3.5 Conclusions......................................................................................................37 
CHAPTER IV. CONCLUSIONS AND RECOMMENDATIONS...................................39 
REFERENCES ..................................................................................................................41 
APPENDICES ...................................................................................................................49 
 
 
 
 
 
 
 
 x 
LIST OF TABLES 
 
Table 2.1. Reactions and equilibrium constants for the aqueous species of arsenate, As 
(V), and arsenite, As (III).....................................................................................................9 
Table 2.2. Reactions and constants for surface complexation reactions involving arsenic 
and goethite........................................................................................................................11 
Table 3.1. Summary of experimental conditions and sorbent properties for the 
experiments in this study and from literature sources .......................................................23 
 
 
 
 
 
 
 
 
 
 
 
 
 xi 
LIST OF FIGURES 
 
Figure 2.1. Eh-pH diagram for aqueous As species in the system As- O2- H2O at 25?C  
and 1 bar total pressure ........................................................................................................9 
Figure 2.2  Model-generated adsorption edges for the adsorption of arsenic on goethite 
using the constants given in Tables 1 & 2 .........................................................................13 
Figure 3.1A. Results from the model system. A) log Kd (L/g Fe) vs. pH for four (As/Fe)T  
values. ...............................................................................................................................26 
Figure 3.1B. Results from the model system. B) qe (mol As/ mol Fe) vs. pH for four 
(As/Fe)T values ..................................................................................................................27 
Figure 3.2. Results from the theoretical adsorption study.  log Kd (L/g Fe) vs. pH for four  
solid- solution ratios with a constant (As/Fe)T of 100 mmol As/mol Fe...........................28 
Figure 3.3A. Comparison of literature and experimental results normalized to Fe-content 
and plotted as A) log Kd (L/g Fe) vs pH for data with various (As/Fe)T values ..............31 
Figure 3.3B. Comparison of literature and experimental results normalized to Fe-content 
and plotted as B) qe (mol As/ mol Fe) vs. pH for data with various (As/Fe)T values .......32 
Figure 3.4A. Comparison of literature and experimental results normalized to surface 
area and plotted as A) log Ka (L/m2) vs. pH for data with various (As/Fe)T values ........34 
Figure 3.4B. Comparison of literature and experimental results normalized to surface area 
and plotted as B) qe (mol As/ m2) vs. pH for data with various (As/Fe)T values ..............35 
 xii 
Figure 3.5A. Comparison of adsorption isotherms normalized to A) Fe content .............36 
Figure 3.5B. Comparison of adsorption isotherms normalized to B) surface area for three 
laboratory- synthesized Fe- coated sands ..........................................................................37 
 1 
CHAPTER ONE 
INTRODUCTION 
 
1.1 Problem Statement
The Department of Energy, along with many other public and private entities, are 
interested in the fate and transport of groundwater contaminants including metals, radio-
nuclides, and chlorinated solvents.  The interactions of these groundwater contaminants 
with subsurface solids are complex and as such are the subject of a wide variety of 
studies.  Many research projects have studied and reported these interactions and 
processes in the laboratory.  However, extrapolating these results to the field scale in 
order to predict the fate of the contaminants has been met with only moderate success.  
The ability to make reliable predictions regarding reactive contaminants will be 
beneficial in making remediation decisions and assessing risks to the public. 
One of the first and most basic steps in improving the ability to scale subsurface 
interactions is establishing a method to compare experimental datasets.  The work that 
has been completed to study groundwater contaminant reactions has utilized a variety of 
experimental conditions, soils, sediments, and overall approaches to their work.  These 
differences create a need for a method that enables researchers and practitioners to 
normalize their data and compare them with other data from other experiments.  The 
ability to compare data is dependent on the ability to identify the most important 
 2 
governing factors in the reactions, the parameters on which the reaction scale, and the 
experimental conditions which affect the reactions.  Previous researchers have attempted 
this as needed for their work.  However, no consensus has been reached and no standard 
set for the method one should follow to properly normalize and compare these subsurface 
reactions.  
 
1.2 Objective 
The primary objective of this work is to improve the ability to make reliable 
predictions of the fate and reactive transport of groundwater contaminants in field-scale 
applications.  A highly toxic oxyanion, arsenate [As (V)], is used throughout this research 
as a representative contaminant.  Its adsorption reactions with iron oxyhydroxides, 
specifically goethite, will be used as a means to thoroughly study the scaling of 
subsurface interactions. These scaling behaviors were investigated through a series of 
theoretical calculations, a review of previous literature, and new experiments.  The results 
of adsorption studies were normalized and compared in many different manners in order 
to get to the root of the scaling issues. 
 
1.3 Organization 
This report is organized according to the guidelines for a publication-style thesis 
as outlined in the Guide to Preparation and Submission of Theses and Dissertations by 
the Auburn University Graduate School.  Chapter 2 contains a review of the relevant 
literature, Chapter 3 is a draft manuscript fully covering the research completed for this 
thesis, and Chapter 4 contains conclusions drawn from this research.  Additionally, 
 3 
samples of each of the calculations performed in this research were also completed and 
are attached as Appendix A.   
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 4 
CHAPTER TWO 
LITERATURE REVIEW 
 
2.1 Background Information
The presence of reactive groundwater contaminants is a great concern to many 
government agencies and private entities.  These contaminants include: solvents, heavy 
metals, organic compounds, radio-nuclides, and many more.  The metalloid oxyanions 
arsenate, As(V), and arsenite, As(III), have received special attention due to their 
worldwide presence and highly toxic nature.  Arsenic-contaminated sites present a danger 
to the environment and to the public that access the groundwater contained there.  
2.1.1 Sources of Contamination 
Arsenic is present in many parts of the world, most notably, in West Bengal, 
Bangladesh, and the western United States, but also in South America and other locations 
worldwide (Smedley and Kinniburgh 2002).  Many of these locations are affected due to 
the presence of natural arsenic minerals and the conditions that trigger their release into 
groundwater.  The development of high pH (<8.5) conditions and reducing conditions at 
near-neutral pH?s have been shown to mobilize As even in locations with modest 
amounts of As in aquifer materials (Smedley and Kinniburgh 2002).  The presence of 
competitive ions can also affect the interactions between As and subsurface minerals 
significantly and either prevent the uptake of As or trigger its release into the 
 5 
groundwater.  There are also many anthropogenic sources of arsenic such as industrial 
processes located around the globe (Han, Su et al. 2003).  Arsenic finds it way into 
groundwater through its use in metal mining, processing, and smelting operations (Smith, 
Naidu et al. 1998) and its use as a pesticide for both wood preservation and agricultural 
applications (Welch, Westjohn et al. 2000).   
2.1.2 Health Concerns 
The primary means of arsenic exposure to humans is through the ingestion of 
water, food, and, for children, contaminated soil.  A typical exposure rate is 50 ?g/day of 
total arsenic and 3.5 ?g of that is inorganic arsenic species which is considerably more 
toxic (ATSDR 2007).  The effects of an acute exposure to arsenic can range from minor 
pain, stomach irritation, fatigue, shortness of breath and nerve damage for low level 
exposure (300-30,000 ?g/L in water) to death for higher level exposures (60,000 ?g/L in 
water) (ATSDR 2007).  The damage from chronic exposure to arsenic at low levels is 
also a major concern.  Characteristics of long-term toxic exposure to arsenic include skin 
lesions, warts on the hands and feet, skin cancer, and blood vessel changes.  The 
prolonged exposure to arsenic can also increase the risk for cancer of the liver, bladder, 
and lungs (ATSDR 2007). 
2.1.3 Treatment Technology and Methods 
The EPA has recognized several technologies for the treatment of As-
contaminated water and they are summarized here (USEPA 2000).  Similar to traditional 
water treatment processes, coagulation with ferric or aluminum salts is often utilized to 
remove dissolved and suspended arsenic.  These processes have been studied extensively 
and are well understood.  This technology is often paired with an oxidation step when 
 6 
treating water containing arsenite, As(III), due to the enhanced coagulation removal of 
the oxidized form, arsenate [As(V)].  Coagulation is followed by a settling step or 
microfiltration to remove the flocs which have formed (USEPA 2000).   
 Ion exchange is another, more expensive, treatment method for arsenic- 
contaminated waters.  This technology employs a synthetic resin containing an initial ion 
which is removed and replaced with the arsenate or arsenite ion.  The resins can be 
regenerated for repeated use, however, their capacity wanes and fouling occurs reducing 
the resins? effectiveness.  Also, the regenerate solution must be disposed of, which adds 
more expense.  Selective membrane technology is also employed for arsenic removal but 
faces the same expense and fouling issues as ion exchange resins.  These technologies 
include reverse osmosis (RO) and electrodialysis reversal (EDR) (USEPA 2000).   
 Other important technologies aim to exploit the interactions of arsenic and iron 
oxides as a means of water treatment.  This includes the study of arsenic removal by 
adsorption with iron oxide-coated sand, goethite-coated sand, and granular ferric oxide in 
a fixed bed apparatus. 
 
2.2 Iron Oxide Interactions in the Subsurface 
2.2.1 Presence of Iron Oxides in the Subsurface 
The focus on iron oxides, an important factor that controls the mobility of As in 
the subsurface, is due to its high sorption capacity and its presence in soils around the 
world.  In fact, much of the motivation for present modeling work is the recognition that 
amorphous iron oxides are universally prevalent in clays, soils and sediments; thus their 
interaction with groundwater constituents must be well understood for reactive transport 
 7 
to be modeled effectively (Jenne 1968; Pierce and Moore 1982).  The presence of 
amorphous iron oxides, including hydrous ferric oxide (HFO) and ferrihydrite, as discrete 
minerals and as coatings on soil and sediment has been thoroughly noted in the literature 
(Buffle 1990; Wilkie and Hering 1996; Dixit and Hering 2003).  Iron oxide-coated sand 
has been recognized as a significant presence in the subsurface environment and has been 
labeled as a dominant factor controlling As adsorption behavior (Edwards and Benjamin 
1989; Scheidegger, Borkovec et al. 1993; Hiemstra and Van Riemsdijk 1999; Lombi, 
Wenzel et al. 1999; O'Reilly, Strawn et al. 2001; Cheng, Barnett et al. 2004; Swartz, 
Blute et al. 2004; Ying and Axe 2005).  The formation and transformation of iron oxides 
has also been a focus of some attention.  In addition to amorphous forms, crystalline 
forms of iron oxide, including hematite and goethite, are common in soil (Buffle 1990).  
Iron oxide minerals often precipitate at oxic-anoxic boundaries and form amorphous 
ferrihydrite; over time these minerals transform into crystalline structures such as 
goethite (Dixit and Hering 2003).  Due to the fact that goethite is widespread in the 
subsurface (Schwertmann and Cornell 1991), much work has been devoted towards the 
study of its interactions with groundwater contaminants (Grossl and Sparks 1995; Zhao 
and Stanforth 2001; Dixit and Hering 2003; Lakshmipathiraj, Narasimhan et al. 2006; 
Gimenez, Martinez et al. 2007). 
2.2.2 Arsenic Interactions with Iron Oxides 
 The work that has been done to elucidate the interactions of arsenic and iron 
oxides in the subsurface is spread out over many decades and many areas of focus.  There 
are studies that describe arsenic?s interactions with amorphous iron oxide forms (Pierce 
and Moore 1980; Pierce and Moore 1982; Fuller, Davis et al. 1993; Waychunas, Rea et al. 
 8 
1993; Waychunas, Fuller et al. 1996; Wilkie and Hering 1996; Raven, Jain et al. 1998; 
Goldberg and Johnston 2001; Goldberg 2002; Dixit and Hering 2003; Zeng, Fisher et al. 
2008) as well as crystalline forms (Hingston, Posner et al. 1971; Lumsdon, Fraser et al. 
1984; Fendorf, Eick et al. 1997; Matis, Zouboulis et al. 1997; Hiemstra and Van 
Riemsdijk 1999; Grafe, Eick et al. 2001; Zhao and Stanforth 2001; Dixit and Hering 
2003; Lakshmipathiraj, Narasimhan et al. 2006; Gimenez, Martinez et al. 2007; Manasse 
and Viti 2007; Stachowicz, Hiemstra et al. 2007).  In addition, much of this work has 
been well reviewed and summarized by Smith et al. (1998) and Sadiq (1997).   
 Arsenic is present primarily as the oxyanions arsenate, As (V), and arsenite, 
As(III), in groundwater.  Table 2.1 shows reactions and constants for the aqueous species 
of arsenate and arsenite (Dixit and Hering 2003).  These are multiprotic acids with pKa?s 
of 2.3, 6.8, and 11.6 for arsenate species H3AsO4, H2AsO4-, and HAsO42-, respectively.  
The pKa?s for the arsenite species H3AsO3 and H2AsO3- are 9.2 and 12.7, respectively 
(Goldberg and Johnston 2001).  Arsenic is present as arsenate, As (V), in oxidizing 
conditions and as arsenite, As (III), in reducing conditions.  Figure 2.1 shows the redox 
potential and dominant species at various pH?s (Smedley and Kinniburgh 2002).  Much 
of the focus on arsenic chemistry is placed on its inorganic complexes due to the higher 
toxicity of the inorganic species and the low propensity for arsenic to form organic 
complexes in soil (Sadiq 1997).  Instead, the focus concerning arsenic complexation is on 
the reactions with iron oxides. 
 
 
 9 
TABLE 2.1: Reactions and constants for the aqueous species of arsenate, As (V), and 
arsenite, As (III). (Dixit and Hering 2003) 
 
As (V) Protonation and Complexation log K
AsO43- + 3H+ = H3AsO4 20.60
AsO43- + 2H+ = H2AsO4- 18.35
AsO43- + H+ = HAsO42- 11.60
As (III) Protonation and Complexation
AsO33- + 3H+ = H3AsO3 34.74
AsO33- + 2H+ = H2AsO3- 25.52
AsO33- + H+ = HAsO32- 13.41  
 
FIGURE 2.1: Eh-pH diagram for aqueous As species in the system As- O2- H2O at 25?C 
and 1 bar total pressure. (Smedley and Kinniburgh 2002) 
 10 
Iron oxides, amorphous and crystalline, have a high affinity for arsenic and are 
able to bind the oxyanions in large quantities.  Studies have shown that adsorption  is the 
primary means of arsenic uptake over coprecipitation (Lumsdon, Fraser et al. 1984; 
Fuller, Davis et al. 1993; Waychunas, Rea et al. 1993; Sadiq 1997) and that arsenate is 
adsorbed more strongly than arsenite (Wilkie and Hering 1996).  Arsenate has been 
shown to form inner-sphere complexes on amorphous and crystalline iron oxides 
(Fendorf, Eick et al. 1997; Goldberg and Johnston 2001).  These complexes are 
monodentate at low arsenic loadings and bidentate at high arsenic loadings (Waychunas, 
Rea et al. 1993).  Arsenite forms both inner and outer-sphere complexes (Goldberg and 
Johnston 2001).  The formation of these complexes has been confirmed by numerous 
spectroscopic studies using various techniques, including wide angle X-ray scattering 
(WAXS), extended X-ray absorption fine structure (EXAFS), and infrared spectroscopy 
(Lumsdon, Fraser et al. 1984; Waychunas, Rea et al. 1993; Waychunas, Fuller et al. 
1996; Fendorf, Eick et al. 1997).  The reactions and constants shown in Table 2.2 have 
been used to model the interactions of arsenate and arsenite with goethite using a surface 
complexation model (Liger, Charlet et al. 1999; Dixit and Hering 2003). 
 
 
 
 
 
 
 11 
TABLE 2.2: Reactions and constants for surface complexation reactions involving 
arsenic and goethite. (Liger, Charlet et al. 1999; Dixit and Hering 2003) 
 
Surface Hydroxyl Protonation log K
>FeOH + H+ = >FeOH2+  7.47?
>FeOH - H+ = >FeO-  -9.51?
? Liger et al. (1999)
As (V) Protonation and Complexation
>FeOH + AsO43- + 3H+ - H2O = >FeH2AsO4 31.00
>FeOH + AsO43- + 2H+ - H2O = >FeHAsO4- 26.81
>FeOH + AsO43- + H+ - H2O = >FeAsO42- 20.22
As (III) Protonation and Complexation
>FeOH + AsO33- + 3H+ - H2O = >FeH2AsO3 39.93
>FeOH + AsO33- + 2H+ - H2O = >FeH2AsO3- 32.40  
 
The widespread presence of goethite in the subsurface environment 
(Schwertmann and Cornell 1991; Dixit and Hering 2003) and its particular promise as an 
adsorbent (Lakshmipathiraj, Narasimhan et al. 2006) has led many to study what governs 
its interactions with arsenic.  Arsenic surface complexes on crystalline oxides have been 
shown to be more ordered than their counterparts on amorphous surfaces (Waychunas, 
Rea et al. 1993).  The adsorption of arsenic is affected to various degrees by ionic 
strength, pH, and coexisting ions.  McBride (1997) studied the ionic strength effect and 
found that the type of complex is an important factor in ionic strength dependence.  
Inner-sphere complex formation increases with or is unaffected by ionic strength, while 
outer-sphere complex formation decreases with increases in ionic strength (McBride 
1997).  The pH dependence of arsenic adsorption varies based on the oxidation state of 
the adsorbing ion.  Figure 2.2 shows how the adorption of arsenate and arsenite onto 
 12 
goethite varies with pH.  Arsenate adsorbs significantly across a wide range of pH values 
but reaches maximum adsorption at low pH, 4-5 (Manning and Goldberg 1996; Dixit and 
Hering 2003; Lakshmipathiraj, Narasimhan et al. 2006).   Arsenite adsorption is at a 
maximum and fairly constant in the range of pH values from 5-9 (Wilkie and Hering 
1996; Dixit and Hering 2003; Lakshmipathiraj, Narasimhan et al. 2006).  Arsenic 
adsorption can also be affected significantly by the presence of ions that compete for 
surface sites.  Phosphate is chemically very similar to arsenate and has a large effect on 
its interactions with goethite and other iron oxides.  Thus there have been many studies to 
elucidate this effect (Hingston, Posner et al. 1971; Jain and Loeppert 2000; Zhao and 
Stanforth 2001; Dixit and Hering 2003; Zeng, Fisher et al. 2008).  Competition from 
phosphate will decrease the adsorption of arsenate and arsenite, with arsenite being 
affected to a greater extent (Jain and Loeppert 2000; Dixit and Hering 2003).  However, 
the order and duration of the anions? exposure to the surface affects the adsorption 
behavior.  Hongshao and Stansford (2001) found that arsenate and phosphate adsorb 
equally when added simultaneously, but differently when the addition was staggered one 
way or the other. 
 
 
 
 
 
 
 
 13 
 
0
20
40
60
80
100
120
140
3 4 5 6 7 8 9 10 11
pH
qe (
?m
ol/
g)
As (V)
As (III)
 
FIGURE 2.2: Model-generated adsorption edges for the adsorption of arsenic on goethite 
using the constants given in Tables 1 & 2. I=0.01M; CT(As)=100?M; 0.5 g L-1 goethite. 
(Dixit and Hering 2003) 
 
2.3 Status of Adsorption-Scaling Literature 
There is an abundance of literature concerning the adsorption of groundwater 
contaminants onto iron oxides.  These studies vary in their goals, determined by the 
funding agency, and this affects the way the study is completed.  The differences and 
deficiencies in adsorption experimentation has been well summarized by E.A. Jenne 
(Jenne 1998).  Some studies are general in nature, dealing with the chemistry in a well-
controlled laboratory setting while others attack a specific problem at a contaminated site, 
using the soils and conditions at the site in their work.   This inherent difference, along 
with inadequate reporting of experimental conditions, has led to a situation in which it is 
 14 
difficult to take information from one study and apply it confidently to others.  
Developing predictive reactive-transport models requires the ability to scale the reactions 
to various systems.  The first step in identifying scaling parameters is being able to 
compare adsorption data from different systems. 
2.3.1 Typical Study Details 
   Designing experiments for the laboratory that reflect field conditions can be 
difficult.  Therefore, many adsorption studies have adjusted parameters such as solid-
solution ratio to facilitate their laboratory limitations.  In the field, there are often high 
solid-solution ratios and low adsorbate-adsorbent ratios (Wilkie and Hering 1996).  These 
conditions make analysis in the laboratory and comparisons in the literature difficult due 
to the small amount of solution and low level of contaminants.   Additionally, care must 
be taken when deviating from field conditions because some deviations may affect the 
mechanisms of the reactions being studied.  Reports in the literature have indicated that 
different complexes are formed at low adsorbate-adsorbent ratios than at high ratios.  For 
example, monodentate complexes are formed at low arsenic loadings while bidentate 
complexes are formed at higher arsenic loadings (Waychunas, Rea et al. 1993; Wilkie 
and Hering 1996).  Despite its importance, the adsorbate-adsorbent ratio has been used as 
a key parameter for comparison in very few studies.  Dixit and Hering (2003) used the 
ratio as a basis for comparing pH edges and determining crossover pH.  Similarly, Wilkie 
and Hering (1996) compared data with identical chemical conditions recognizing the 
importance of having similar adsorbate-adsorbent ratios when adsorption is near 100%.  
Wilkie and Hering (1996) also noted the inadequacy of pH control and parameter 
reporting in previously published work. 
 15 
2.3.2 Normalization and Plotting Techniques 
 As is the case with the scaling of experimental conditions between laboratory and 
field settings, little effort has been directed at properly normalizing the results of 
adsorption experiments for comparison.  Most studies that use comparisons do not 
normalize the results at all or normalize only to the mass of the adsorbent.  This 
technique often produces results that appear sufficient and prevents further examination 
to determine a more accurate technique. However, the mass of adsorbent is not 
necessarily directly related to the reactive capacity.  Some published results employ a 
different technique and indicate that surface area may be a better parameter with which to 
normalize adsorption data (Pablan, Turner et al. 1998; Gimenez, Martinez et al. 2007).  
Normalization to the surface area is not common in the literature.  Success with this 
normalization technique indicates that the amount of sorption sites on a particular 
adsorbent surface is more related to the surface area than the mass of the sorbent.  Pablan 
et al. (1998) suggests that an effective surface area, a portion of the overall surface area, 
exists and could be a useful parameter in predicting sorption in various surfaces.  
Furthermore, a recent study of uranium adsorption to iron oxide-coated sand has 
concluded that surface area may be a better normalization parameter than iron content 
(Logananthan 2008, to be submitted).  Proper normalization along with proper plotting 
techniques could aid significantly in comparisons between systems with different 
adsorbents. 
 Proper plotting technique can make comparisons between adsorption datasets 
easier.  Plots of log KD have been shown to be less sensitive to the solids concentration 
and thus relatively independent of solid-solution ratio (Jenne 1998; Pablan, Turner et al. 
 16 
1998).  Still, most comparisons are made using the traditional sigmoidal plots of % 
adsorbed and qe (normalized or not).  Jenne (1998) noted the difficulty in comparing data 
plotted this way due to the sensitivity to metal and solids concentration.  If data are 
compared in sigmoidal plots, the experimental systems must be identical which is very 
tough to achieve.  Thus, the literature contains comparisons which are accompanied by 
rationalizations and explanations to account for the differences that exist.   
 
2.4 Importance for the Development of Predictive Models 
 The lack of the ability to adequately scale adsorption reactions from laboratory to 
field-scale is a major concern to reactive transport modelers and must be overcome.  The 
ability to predict the fate and transport of harmful groundwater contaminants with 
minimal laboratory experiments, scaling the results to the field conditions, and plugging 
those parameters into model is a primary aim of many industries and government 
agencies who confront groundwater contamination.  A reliable model will save time, 
money, and human resources enabling a much more efficient cleanup of the world?s 
contaminated sites.  The literature contains abundant information on the chemistry of 
groundwater contaminant interactions with subsurface solids, yet very little useful 
information on how to apply the chemistry to solve problems.  The first step in being able 
to extrapolate adsorption data is to identify the factors which govern the scaling of these 
reactions and processes.  This step is crucial and is largely missing in previous work. 
 17 
CHAPTER THREE 
METHODS FOR SCALING AND COMPARING ADSORPTION DATASETS 
 
3.1 Abstract 
As models capable of predicting the fate and transport of groundwater 
contaminants are constructed, the need to compare adsorption data in a reliable manner is 
important.  In this work, various approaches for comparing adsorption data were studied 
to determine the best method for designing and analyzing the results of adsorption 
experiments.  The interactions of arsenate and goethite were examined as a representative 
system.  A study of simulated data was first executed to examine the basic principles of 
dataset comparison.  These principles were then tested on a suite of experimental data, 
both new and from the literature.  The most important factor in the comparison of 
sorption datasets was found to be the total adsorbate-adsorbent ratio.  If this value is too 
low, the system will be limited only by the amount of adsorbate present and accurate 
comparisons cannot be made.  Additionally, it was found that normalization techniques 
can have a marked effect on comparisons, especially between systems with differing 
adsorbent types (i.e. natural and synthetic goethite).  It is nearly always better to use the 
specific surface area of the adsorbent as a scaling parameter rather than the reactive mass 
of the adsorbent (in this case, Fe content).  The incorporation of these methods and 
techniques will improve the methods of comparing adsorption data in future studies.
 18 
3.2 Introduction 
The presence of reactive groundwater contaminants is a great concern to many 
government agencies and private entities.  These contaminants include solvents, heavy 
metals, organic compounds, and radionuclides.  The metalloid oxyanions arsenate, As(V), 
and arsenite, As(III), have received special attention due to their worldwide presence and 
highly toxic nature.  Arsenic-contaminated sites present a danger to the public and the 
environment. 
Arsenic is present in many parts of the world including, most notably, West 
Bengal, Bangladesh, and the western United States, but also South America and other 
locations worldwide (Smedley and Kinniburgh 2002).  Many of these locations are 
affected due to the elevated presence of naturally occuring arsenic and the conditions that 
trigger their release into groundwater.  The development of high pH (<8.5) conditions 
and reducing conditions at near-neutral pH?s have been shown to mobilize As, even in 
locations with modest amounts of As in aquifer materials (Smedley and Kinniburgh 
2002).  Modeling the reactive transport of arsenic is of utmost importance and relies on 
the ability to predict the interactions of arsenic with major subsurface constituents. 
The focus on iron oxides as an important factor in the mobility of As and other 
contaminants in the subsurface is due both to its abundant presence in soils and sediments 
around the world and its natural affinity for As.  In fact, much of the motivation for the 
present modeling work is the recognition that amorphous and crystalline iron oxides are 
universally prevalent in clays, soils and sediments; thus their interaction with 
groundwater constituents must be well understood (Jenne 1968; Pierce and Moore 1982).  
The presence of amorphous iron oxides, including hydrous ferric oxide (HFO) or 
 19 
ferrihyrdite, as discrete minerals and as coatings on soil and sediment has been widely 
reported in the literature (Buffle 1990; Wilkie and Hering 1996; Dixit and Hering 2003).  
Iron oxide coating on host minerals have also been recognized as a significant presence in 
the subsurface environment and labeled as a dominant factor controlling As adsorption 
(Edwards and Benjamin 1989; Scheidegger, Borkovec et al. 1993; Hiemstra and Van 
Riemsdijk 1999; Lombi, Wenzel et al. 1999; O'Reilly, Strawn et al. 2001; Cheng, Barnett 
et al. 2004; Swartz, Blute et al. 2004; Ying and Axe 2005)  In addition to amorphous 
forms, crystalline forms of iron oxide, including hematite and goethite, are common in 
soil (Buffle 1990).  Iron oxide minerals often precipitate at oxic-anoxic boundaries and 
form amorphous ferrihydrite; over time these minerals transform into crystalline 
structures such as goethite (Dixit and Hering 2003).  Due to the fact that goethite is 
widespread in the subsurface (Schwertmann and Cornell 1991), much work has been 
devoted towards the study of its interactions with As (Grossl and Sparks 1995; Zhao and 
Stanforth 2001; Dixit and Hering 2003; Lakshmipathiraj, Narasimhan et al. 2006; 
Gimenez, Martinez et al. 2007).  The complex mixtures and transformations of iron 
oxides in the subsurface necessitates the creation of a reliable means of scaling to predict 
the interactions between iron oxides and groundwater contaminants such as arsenic. 
The interactions of arsenate and arsenite with iron oxides, amorphous and 
crystalline, have been studied extensively to elucidate the effect of pH, competitive ions, 
and oxidation/reduction conditions on the sorption processes as well as the mechanism 
and form of the resulting complexes (Hingston, Posner et al. 1971; Pierce and Moore 
1980; Pierce and Moore 1982; Fuller, Davis et al. 1993; Waychunas, Rea et al. 1993; 
Wilkie and Hering 1996; Fendorf, Eick et al. 1997; Raven, Jain et al. 1998; Lombi, 
 20 
Wenzel et al. 1999; Grafe, Eick et al. 2001; Zhao and Stanforth 2001; Goldberg 2002; 
Yang, Barnett et al. 2002; Dixit and Hering 2003; Williams, Barnett et al. 2003; Gupta, 
Saini et al. 2005; Yang, Barnett et al. 2005; Lakshmipathiraj, Narasimhan et al. 2006; 
Gimenez, Martinez et al. 2007; Manasse and Viti 2007).  The literature has also been 
reviewed and summarized to consolidate the work thus far (Sadiq 1997; Smith, Naidu et 
al. 1998).  These studies found that iron oxides have a high capacity to adsorb arsenic and 
that this adsorption is highly dependent on pH.  Arsenate adsorbs most effectively at low 
pH (~4), while arsenite adsorbs optimally at near-neutral pH (Pierce and Moore 1982).  
Both monodentate and bidentate inner-sphere complexes are formed on the iron oxide 
surface as confirmed by wide angle X-ray scattering (WAXS), extended X-ray absorption 
fine structure (EXAFS), and infrared spectroscopy (Lumsdon, Fraser et al. 1984; 
Waychunas, Rea et al. 1993; Waychunas, Fuller et al. 1996; Fendorf, Eick et al. 1997).  
The competition for surface sites between arsenic and other ions, particularly phosphate, 
is also an important point of interest in the study of arsenic?s subsurface interactions with 
iron oxides.  Several studies have shown that the presence of phosphate as a co-solute 
increases arsenic?s mobility and competes with arsenic for adsorption sites (Hingston, 
Posner et al. 1971; Woolson, Axley et al. 1973; Peryea 1991; Jain and Loeppert 2000).   
Alongside the supply of arsenic adsorption data has grown an inclination and need 
to compare the results of the numerous studies.  The work completed thus far has 
contained many different sets of experimental conditions and surface types, leading to a 
wide range of methods being employed for comparing the data.  Some researchers have 
noted the importance of selecting appropriate datasets for comparisons, using adsorbate-
adsorbent ratios as a basis (Wilkie and Hering 1996; Dixit and Hering 2003).  However, 
 21 
for all comparisons, the researcher often has limited access to vital information 
concerning the previous study.  It has been noted previously that data is often collected in 
a range of adsorbate-adsorbent ratios that make comparisons between data sets difficult 
or of little use (Wilkie and Hering 1996; Dixit and Hering 2003).  Much of the published 
literature contains data collected near 100% adsorption or far away from field conditions.  
These characteristics of the published data restrict their use for comparison to systems 
which are exactly the same.  The present state of the literature data lacks a means to 
reliably compare adsorption data. 
The main objective of this work is to examine the different methods employed for 
the comparison of adsorption data, using both theoretical (i.e., model) and experimental 
data by: 1) Generating theoretical adsorption curves and making comparisons to extract 
relevant principles such as the best graphical method, experimental design considerations, 
and normalization techniques; 2) Testing these principles through comparisons of 
datasets from the literature and our laboratory; and 3) Drawing conclusions regarding the 
best methods for designing experiments used for comparison, processing adsorption data, 
and comparing with previously published results. 
 
3.3 Methods 
 These objectives were accomplished through a series of model and experimental 
studies.  First, theoretical equilibrium isotherms were generated through the use of a 
published surface complexation model.  Using these equations, theoretical adsorption 
edges were produced for various conditions and plotted using several common methods.  
The model adsorption edges were compared in order to examine how varying conditions 
 22 
affect the graphical presentation of the data.  Next, these principles were tested by 
plotting actual experimental data, from our laboratory and the literature, to see if the 
theoretical results are mirrored in existing data.   
3.3.1 Modeling 
 The theoretical comparison study was completed by calculating adsorption curves 
and comparing the results in various manners.  For the model, the three plane model 
(TPM) was applied through Visual Minteq (ver. 2.52) with the existing goethite database 
(goethite021.mdb) for low and high affinity sites (Weng, Temminghoff et al. 2001).  A 
set of isotherms was generated for a range of pH values (3-10).  At 25?C and I= 0.01M, 
Freundlich constants were fit to the isotherm for each pH value to determine an 
equilibrium isotherm (qe=KfCen) for each pH value.  These equations were then used for 
all the calculations at the corresponding pH values. The theoretical work was performed 
in this manner to simplify the extraction of relevant principles by eliminating 
uncontrolled factors associated with laboratory experiments and to enable us to assess a 
much wider range of solid-solution ratios.  The equations were applied for a range of 
solid-solution ratios from traditional laboratory-scale to full field-scale values.  This 
included varying the total adsorbate-adsorbent ratio from 1-1000 mmol As/ mol Fe.  
Adsorption data were normalized and plotted both as Kd (L/g Fe) and qe (mmol As/ mol 
Fe), where Kd is the distribution coefficient and qe is the amount of As adsorbed at 
equilibrium.  These are two common plotting methods when comparing adsorption data.  
Plots of % adsorbed are not useful for comparison due to differences in arsenic 
concentrations, solid-solution ratios, and adsorbent properties which require the data to 
be normalized in some manner. 
 23 
3.3.2 Literature Comparison 
Experimental conditions for the datasets used in this comparison study are given 
in the respective publications (Dixit and Hering 2003; Gimenez, Martinez et al. 2007; 
Stachowicz, Hiemstra et al. 2007).  These data were chosen due to their quality, the range 
of experimental conditions, the type of surface (e.g., natural goethite, synthetic goethite, 
coated sand), and/or the similarity of the experimental conditions to the ones used here.  
The literature data were normalized both on the basis of the theoretical iron content of 
goethite of 0.6285 g iron/g goethite and the surface area reported in each study.  The 
adsorbent properties and pertinent experimental conditions are given in Table 3.1. 
 
TABLE 3.1: Summary of experimental conditions and sorbent properties for the 
experiments in this study and from literature sources.  M1, M2, DH1-4, S, & G are pH 
edge datasets for testing comparison techniques.  M1-low, M1-med, and M1-high are 
experimental datasets used to study normalization techniques.  
Dataset Reference Media
Surface Area 
(m2/ g FeOOH)
Fe Content 
(mol Fe/ g)
         As:FeT             
(mmol As/mol Fe)T
Synthesis Method 1 ? M1 (?) Coated Sand 178 6.83E-05 19.5
Synthesis Method 2 ? M2 (?) Coated Sand 104 8.56E-06 15.6
Dixit & Hering (10 ?mol/L) DH1 (?) Synthetic Goethite 54 1.13E-02 1.8
Dixit & Hering (25 ?mol/L) DH2 (?) Synthetic Goethite 54 1.13E-02 4.4
Dixit & Hering (50 ?mol/L) DH3 (?) Synthetic Goethite 54 1.13E-02 8.9
Dixit & Hering (100 ?mol/L) DH4 (?) Synthetic Goethite 54 1.13E-02 17.8
Stachowicz et al. S (+) Synthetic Goethite 98 1.13E-02 14.8
Giminez et al. G (?) Natural Goethite 2 1.13E-02 17.8
Low Iron Sand M1-low (?) Coated Sand 279 7.15E-06 Varied
Medium Iron Sand M1-med (?) Coated Sand 148 3.26E-06 Varied
High Iron Sand M1-high (?) Coated Sand 113 5.69E-05 Varied  
? This study 
 
3.3.3 Experimental 
For comparison, additional experimental data were also measured.  The chemicals 
used in this work were reagent grade and all solutions were prepared fresh using 
deionized water (DIW) (18M?cm) from a Milli-Q water system.  The coated sands used 
here were prepared according to previously published protocols (Schwertmann and 
 24 
Cornell 1991; Scheidegger, Borkovec et al. 1993; Cheng, Barnett et al. 2004; Cheng, 
Barnett et al. 2006) .  The sand produced using a homogeneous suspension method, 
abbreviated here as ?M1?, had an iron content of 68.3 ?mol Fe/ g sand and a surface area 
of 283 m2/g Fe (178 m2/g FeOOH).  The sand produced using a heterogeneous 
suspension method, abbreviated here as ?M2?, had a lower iron content of 8.56 ?mol Fe/g 
sand and a surface area of 165 m2/g Fe (104 m2/g FeOOH).  The specific surface area of 
the sands was measured by BET surface area analysis (ASAP 2020, Micrometrics). 
As(V) stock solutions were prepared by dissolving Na2HAsO4.7H2O (s) in DIW.  
All reaction solutions contained 0.01 M NaNO3 to control the ionic strength.  The As(V) 
concentrations of the solutions used in pH edge experiments with the homogeneous and 
heterogeneous suspension system sands were 13.3 ?M and 1.33 ?M, respectively.  The 
pH of the reaction solutions for the adsorption edges was adjusted by the addition of 
HNO3 or NaOH as required to achieve the desired pH.  The batch experiments were 
conducted in 50 mL polypropylene centrifuge tubes (Corning), at room temperature 
(~22 ?C), and were shaken for 24 hours to equilibrate.  This reaction time was determined 
to be sufficient by preliminary kinetic tests (not shown). 
To further study normalization methods, three goethite-coated sands of varying Fe 
content and surface area were produced using the homogeneous suspension method (M1-
low, M1-med, M1-high).  The sands had iron contents of 7.15, 32.6, and 56.9 ?mol Fe/ g 
sand and specific surface areas of 444, 235, and 178 m2/g Fe (279, 148, 113 m2/g 
FeOOH), respectively (shown in Table 3.1).  Adsorption isotherm experiments were 
performed with As(V) concentrations from 0-100 ?M for each sand.  The solution pH 
 25 
was maintained at 7?0.2, the temperature was 22 ? 2?C, and the ionic strength was 
maintained by adding 0.01M NaNO3. 
 After reaction, the solution equilibrium pH was measured using an Orion model 
(410A+) pH meter and filtered through a 0.45 ?m syringe filter (Whatman). Analysis of 
the filtrate was performed within 24 hours using a Graphite Furnace Atomic Absorption 
Spectrophotometer (GFAAS; Perkin-Elmer 3110 PC).  
 
3.4 Results and Discussion 
3.4.1 Modeling 
Figures 3.1A and 3.1B illustrate the difficulties that arise when performing batch 
adsorption experiments at one condition and trying to extrapolate the results to 
significantly different conditions.  Here the systems have the same total As but widely 
varying solid-solution ratios, which results in large differences in (As/Fe)T.  The 
distribution coefficients from systems with the same As(V) concentration but different 
(As/Fe)T can vary by several orders of magnitude as seen in Figure 3.1A.  This variability 
is also seen when plotting qe (As adsorbed/mass of sorbent) vs. pH (Figure 3.1B), but to a 
much lesser extent.  Problems arise particularly when comparing adsorbate-limited 
systems (low As:Fe, ~1 mmol As/mol Fe), which is often the case in porous media, 
where As is low relative to iron.  The differences in the results largely disappear when the 
systems are no longer limited by the amount of adsorbate present, as shown by the 100 
and 1000 mmol As/mol Fe curves.  These issues are critical when modeling in the field 
using the constant-KD approach and could be a major reason for the trouble in reliably 
predicting field-scale reactive transport (Bethke and Brady 2000). 
 26 
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
2 3 4 5 6 7 8 9 10 11
pH
log
 K
D 
(L
/g 
Fe
)
~ 1000 mmol As/mol Fe
~ 100 mmol As/mol Fe
~ 10 mmol As/mol Fe
~ 1 mmol As/mol FeA
 
FIGURE 3.1A: Results from the model system. A) log KD (L/g Fe) vs. pH for four 
(As/Fe)T values. (Typical field value: ~1mmol As/mol Fe; Typical laboratory value: 1-
100 mmol As/mol Fe) 
 
 
 
 
 27 
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
2 3 4 5 6 7 8 9 10 11
pH
qe
 (m
ol 
As
/ m
ol 
Fe
)
~ 1 mmol As/mol Fe
~ 10 mmol As/mol Fe
~ 100 mmol As/mol Fe
~ 1000 mmol As/mol FeB 
 
FIGURE 3.1B: Results from the model system. B) qe (mol As/ mol Fe) vs. pH for four 
(As/Fe)T values.  (Typical field value: ~1mmol As/mol Fe; Typical laboratory value: 1-
100 mmol As/mol Fe) 
 
Accounting for these factors by keeping the ratio of adsorbate to adsorbent 
constant and varying just the solid-solution ratio, the variability greatly declines.  Figure 
3.2 shows four systems with the same (As/Fe)T of 100 mmol As/ mol Fe but with 
different solid-solution ratios.  These curves are more similar than those in Figure 3.1A 
with a difference of less than 1 log KD unit per order of magnitude difference in solid-
solution ratio.  A slight difference in KD with respect to solid-solution ratio is observed 
due to non-linear isotherms.  Slight variances in the equilibrium point along the 
Freundlich isotherm curve produces differences in the slope between the four systems.  
Figure 3.2 shows that the difference in the systems is lower in the low pH range, when 
 28 
the isotherm is more linear, and increases in the upper pH range, where the isotherms are 
highly non-linear.  The same calculations were performed assuming a linear isotherm and 
the pH edges were equal for all ratios (not shown).   
 
-4
-3
-2
-1
0
1
2
3
4
5
6
2 3 4 5 6 7 8 9 10 11
pH
log
 K
D 
(L
/g 
Fe
) 1 g/L
10 g/L
100 g/L
1000 g/L
 
FIGURE 3.2: Results from the theoretical adsorption study.  log KD (L/g Fe) vs. pH for 
four different solid- solution ratios with a constant (As/Fe)T of 100 mmol As/mol Fe.  
Adsorbate-adsorbent ratio was maintained by varying AsT; 1, 10, 100 , and 1000 g/L 
contained 0.00667, 0.0667, 0.667, and 6.67 mM As, respectively. 
 
3.4.2 Literature Comparison 
A survey of the literature produced many studies of arsenate adsorption onto 
goethite or goethite-containing solids.  These ranged from leaching studies in natural 
minerals to adsorption studies on laboratory-synthesized goethite.  Three datasets were 
chosen for this comparison study: Dixit and Hering?s (2003) study of adsorption onto 
 29 
laboratory-synthesized goethite; the Stachowicz et al. (2007) study of arsenate adsorption 
on synthetic goethite with a high specific surface area (98 m2/g); and the Giminez et al. 
(2007) study that used a natural goethite mineral with low specific surface area (2 m2/g).  
These studies, along with our experiments on iron-coated sand, provided the needed 
range of data to test the results of the modeling study.  The conditions of these 
experimental datasets, given in Table 3.1, show that these data have a range of (As/Fe)T 
from 1.8-19.5 mmol As/ mol Fe, approximately 1 order of magnitude.  The range of 
conditions found in the literature illustrates the reality that laboratory data is not 
necessarily collected under the same conditions that are present in the field.  Assuming a 
typical field solid-solution ratio of 3750 g/L (Phillippi, Loganathan et al. 2007), a soil Fe 
content of 0.1-50 g/kg (Goldberg, Lesch et al. 2005), a background arsenate soil 
concentration of 10 mg As/kg soil, and a groundwater arsenate concentration of 10-500 
?g/L; yields the range of (As/Fe)T of 0.15? 84 mmol As/ mol Fe.  The range of laboratory 
values is a small section of the possible field conditions. 
Figure 3.3 shows the literature data normalized to Fe-content and plotted in two 
different ways corresponding to Figures 3.1A and 3.1B.  To quantify the spread between 
the collected data, a line was fitted to each group of data and statistical values were 
extracted.  The linear, least-squares fit was based on all the datasets combined (M1, M2, 
DH1-4, S, G).  Likewise, the standard deviation was calculated for the combined datasets 
of each system (Fe normalized & surface area normalized).  Figure 3.3A shows the data 
plotted as log KD vs. pH.  Most of the data is reasonably comparable (?1 standard 
deviation) when plotted this way, including datasets M1, M2, DH1-4 and S.  There is, 
however, a larger difference between these datasets and the natural material, dataset G.  
 30 
The difference between most of the data is about an order of magnitude in log KD, but this 
set of data drops far below the rest of the data, over an order of magnitude lower than the 
next lowest data set. The difference in the top groups (M1, M2, DH1-4 and S) is expected 
based on the spread of data in a similar range of Figure 3.1A, however, the discrepancy 
between those groups and the natural material could not be predicted with the simulated 
data.  Figure 3.3B shows the data plotted in a different manner (qe vs. pH) and the results 
are as expected after looking at the model-predicted results in Figure 3.1B with respect to 
the absolute value and relative spread of the data.  The adsorbate-limited datasets, DH1 
and DH2, have values that are different from the rest of the datasets due to their lower 
(As/Fe)T values of 1.8 and 4.4 mmol As/ mol Fe, respectively.  The adsorption in these 
datasets is ~ 100%, which inhibits their comparability with the other datasets.  The group 
of datasets which are not adsorbate-limited are in a fairly tight group.  However, if the 
data is inspected closely, it shows that there is a single difference of note amongst the 
non-adsorbate limited datasets.  Again, this difference lies between the synthetic 
materials and the natural material.  Datasets M1, M2, DH3, DH4, & S (synthetic) are 
closely grouped while dataset G (natural) is separated. 
 31 
-3.0
-2.0
-1.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
2 3 4 5 6 7 8 9 10 11
pH
log
 K
D 
(L
/g 
Fe
)
M1 M2
DH1 DH2
DH3 DH4
S G
A
 
FIGURE 3.3A: Comparison of literature and experimental results normalized to Fe-
content and plotted as A) log KD (L/g Fe) vs. pH for data with various (As/Fe)T values.  
Dotted lines are ?1 standard deviation of the mean for the combined data. 
 
 
 
 
 32 
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
2 3 4 5 6 7 8 9 10 11
pH
q e 
(m
ol 
As
/ m
ol 
Fe
)
M1
M2
DH1
DH2
DH3
DH4
S
G0.00
0.01
0.02
2 3 4 5 6 7 8 9 10 11
FIGURE 3.3B: Comparison of literature and experimental results normalized to Fe-
content and plotted as B) qe (mol As/ mol Fe) vs. pH for data with various (As/Fe)T 
values. The main scale in 3.3B matches the scale in Figure 3.1B; an inset is provided for 
clarity.  Normalization factors are given in Table 3.1. 
 
Figure 3.4 shows the literature data normalized to surface area and plotted in the 
same ways as in Figure 3.3.  As far as data comparisons go, the data show the same 
principles as the model study.  Figure 3.4A shows that all of the datasets, including the 
natural material, are more closely grouped than in Figure 3.3A.  Figure 3.4B shows that 
the data may be more sensitive to adsorbate-limitation when normalized to specific 
surface area as there are larger differences between the datasets DH1, DH2, DH3, & DH4 
in Figure 3.4B than in 3.3B.  Looking at the data in Figure 3.4B and ignoring the 
adsorbate-limited datasets, DH1 and DH2, the difference in the non-limited sets is 
slightly larger than in Figure 3.3B (Fe-normalized).  This has been seen in one previous 
 33 
study (Davis, Meece et al. 2004), where a drastic difference between the spread of the Fe-
normalized data and the surface area-normalized data was not found.  However, the 
exception in Figure 3.4B lies with the natural material which is not comparable when 
normalized to Fe but matches well with the other data when surface area is taken into 
account.  This is an important consideration in the field where you can have widely 
varying specific surface area conditions. 
A quantitative look at the spread of the data in Figures 3.3A and 3.4A showed a 
preference for surface area normalization.  The standard deviation of the distribution 
coefficient for the Fe normalized data was 1.1 orders of magnitude compared to 0.87 for 
the surface area normalized data.  These values show that the data is more consistent 
when normalized to surface area.  The figures have lines that represent ? 1 standard 
deviation from the mean of the respective data to illustrate these results. 
Figures 3.3 and 3.4 show that even for systems that have very similar 
experimental conditions and that are not adsorbate-limited, there will be some variance in 
the sorption edges.  This variance may be due to many factors including adsorbent 
heterogeneities, unaccounted for competitive ions, and experimental error.  These have 
been noted in previous studies when comparing datasets (Wilkie and Hering 1996; 
Hiemstra and Van Riemsdijk 1999; Dixit and Hering 2003; Ponthieu, Juillot et al. 2006; 
Gimenez, Martinez et al. 2007).  This system, arsenate and goethite, illustrates many of 
the problems encountered when comparing data near the saturation of the adsorbent.  
Details and specific values such as adsorbent capacity, adsorption affinity, etc. will vary 
for other systems, but the basic considerations for comparing data still apply to all 
 34 
systems.  Accounting for these issues is necessary when performing adsorption studies, 
and is best accomplished during the experimental design phase of the study. 
-3.0
-2.0
-1.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
2 3 4 5 6 7 8 9 10 11
pH
log
  K
A 
(L
/m
2 )
M1 M2
DH1 DH2
DH3 DH4
S G
A
 
FIGURE 3.4A: Comparison of literature and experimental results normalized to surface 
area and plotted as A) log KA (L/m2) vs. pH for data with various (As/Fe)T values.  
Dotted lines are ?1 standard deviation of the mean for the combined data. 
 
 
 
 
 35 
0.0E+00
1.0E-06
2.0E-06
3.0E-06
4.0E-06
5.0E-06
2 3 4 5 6 7 8 9 10 11
pH
q e 
(m
ol 
As
/m
2 )
M1 M2
DH1 DH2
DH3 DH4
S G
B
 
FIGURE 3.4B: Comparison of literature and experimental results normalized to surface 
area and plotted as B) qe (mol As/ m2) vs. pH for data with various (As/Fe)T values.  The 
scale in 3.4B matches the scale in Figure 3.3B.  Normalization factors are given in Table 
3.1. 
 
3.4.3 Normalization Technique 
 To further examine the factors governing the most appropriate technique used to 
normalize adsorption data, adsorption isotherms were constructed and normalized using 
the two different methods.  Figures 3.5A and 3.5B show the isotherms normalized to Fe 
content and surface area, respectively.  The maximum adsorption values range from 0.01 
to 0.03 mol As/ mol Fe for the Fe-normalized isotherms.  The highest specific adsorption 
belonged to the sand with the lowest Fe content while the medium and high Fe adsorbed 
at a similar level.  Figure 3.5B, however, shows that when the isotherms are normalized 
 36 
to the specific surface area, the adsorption maximum is about the same for all three sands, 
~1.1 ?mol/ m2.  Our study of the literature data indicated that this is more often the case 
and that normalizing adsorption data to surface area is a more appropriate method when 
compared to normalization based on Fe content.  In some cases there will not be a 
significant difference between the two methods, but most often the surface area method 
will be as good as or better than other methods.  This advantage is particularly evident 
when one of the systems being compared contains natural materials with low specific 
surface area. 
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0 20 40 60 80 100
Ce (?mol/L)
q e 
(m
ol 
As
/ m
ol 
Fe
)
M1- low
M1- med
M1- high
A
 
FIGURE 3.5A: Comparison of adsorption isotherms normalized to A) Fe content for 
three laboratory- synthesized Fe- coated sands.  Experimental conditions: pH= 7?0.2; 
I=0.01M; T=~22?C.  Normalization factors are given in Table 3.1. 
 
 
 37 
FIGURE 3.5B: Comparison of adsorption isotherms normalized to B) surface area for 
three laboratory- synthesized Fe- coated sands.  Experimental conditions: pH= 7?0.2; 
I=0.01M; T=~22?C.  Normalization factors are given in Table 3.1. 
 
3.5 Conclusions 
 Model calculations were used to investigate the issues that arise when comparing 
adsorption data with various goethite adsorbents, experimental conditions, and on 
different scales.  The majority of problems arise when systems are at or near their 
adsorption capacity.  This condition often means that the system is limited by the amount 
of adsorbate present and experimental data may be of little use for comparisons.  A 
survey and comparison of literature data shows that these problems frequently come into 
play even in well-controlled laboratory studies.  Datasets should meet the following 
0.0E+00
1.0E-06
2.0E-06
3.0E-06
4.0E-06
5.0E-06
0 20 40 60 80 100
Ce (?mol/L)
q e 
(m
ol 
As
/m
2 )
M1- low
M1- med
M1- high
B
 38 
major criteria in order to make a valuable comparison with each other:  1) the systems 
should not be limited by the amount of adsorbate present.  This makes presenting data 
as % adsorbed useful for isolated studies, but not appropriate for interstudy comparisons.  
2) The datasets should have a similar adsorbate-adsorbent ratio; which will minimize the 
variance in the data due to non-linear isotherms.  3) The data should be normalized to the 
specific surface area of the adsorbent.   In some cases normalization based on Fe content 
is acceptable, but rarely is this method more successful than the surface area method as a 
scaling parameter. 4) The literature survey also highlights the fact that laboratory data are 
frequently taken under conditions fairly dissimilar to those seen in the field.  This 
discrepancy will make appropriate scaling, comparison, and normalization techniques of 
utmost importance in the future.   
 
 
 
 
 
 
 
 39 
CHAPTER FOUR 
CONCLUSIONS 
 
 The objective of the research described here was to examine the methods of 
comparing adsorption datasets for the purpose of scaling reactive transport models.  The 
need for this work becomes evident when reviewing literature and noting the relative 
inability to meaningfully compare multiple adsorption studies.  There are many harmful 
groundwater contaminants across the globe and much effort is devoted to the modeling 
and remediation of contaminated sites.  The reactive transport of the groundwater 
contaminants is governed by the interaction of these contaminants with subsurface media 
and, often the specific presence of iron oxides in the soil.  For this reason, the reactions 
between goethite and arsenic were used as a model system to study adsorption and the 
scaling behaviors of subsurface reactions.  However, these results are applicable to other 
systems containing different media and contaminants. 
 Model-generated data were first used to identify the relevant theoretical 
parameters necessary to accurately compare adsorption datasets.  The range of conditions 
at which these data were generated spans the gap from traditional laboratory-scale to 
typical field-scale conditions.  The principles developed in this theoretical study were 
then applied to experimental data from the published literature and our laboratory.  The 
results show that the majority of problems arise when systems are at or near their 
 40 
adsorption capacity.  This condition often means that the system is limited by the amount 
of adsorbate present and experimental data may be of little use for comparisons.  Specific 
conclusions are as follows: 1) experimental systems should not be limited by the amount 
of adsorbate present as this may be useful for isolated studies, but not for interstudy 
comparisons.  2) The datasets should have a similar adsorbate-adsorbent ratio, which will 
minimize the variance in the data due to non-linear isotherms.  3) The data should be 
normalized to the specific surface area of the adsorbent.   In some cases normalization 
based on Fe content is acceptable, but rarely is this method more successful than the 
surface area method as a scaling parameter. 4) The literature survey also highlights the 
fact that laboratory data are frequently taken under conditions fairly dissimilar to those 
seen in the field.  This discrepancy is of particular note and makes appropriate scaling, 
comparison, and normalization techniques of utmost importance.  It is recommended that 
the preceding principles be noted and applied in future comparisons and noted when 
scaling parameters for use in reactive transport models. 
 
 
 
 
 
 
 
 41 
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 49 
APPENDICES 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 50 
APPENDIX A. 
SAMPLE CALCULATIONS 
Example 1 
Example calculations to determine amount of arsenic (As) adsorbed per mass of 
adsorbent (iron oxide-coated sand, IOCS) from analytical data. 
Given: 
5
2
10 /
6.83 10 /
1.08 /
gIOCS L
molFe gIOCS
m gIOCS
??  
From analytical measurements: 
1 /
0.267 /
o
e
C mgAs L
C mgAs L
=
=  
Solution: 
Amount of arsenic adsorbed per gram of IOCS 
( )
10 /
o e
e
C Cq
gIOCS L
?=  
(1 0.267) / 0.0733 /
10 /e
mgAs Lq mgAs gIOCS
gIOCS L
?= =  
Amount of Arsenic adsorbed per m2 of adsorbent 
7 2
2
0.0733 / 9.06 10 /
(1.08 / )(74921.6 / )e
mgAs gIOCSq molAs m
m gIOCS mgAs molAs
?= = ?  
Amount of Arsenic adsorbed per mole of Fe 
5
0.0733 / 0.0143 /
(6.83 10 / )(74921.6 / )e
mgAs gIOCSq molAs molFe
molFe gIOCS mgAs molAs?= =?  
 
 51 
Example 2 
Example calculation for determining the distribution coefficient (Kd) from analytical data. 
Given: 
5
2
6.83 10 /
1.08 /
molFe gIOCS
m gIOCS
??
 
From analytical measurements: 
0.0733 /eq mgAs gIOCS=  
0.267 /eC mgAs L=  
Solution: 
/
0.0733 / 0.275 /
0.267 /
d e e
d
K q C
mgAs gIOCSK L gIOCS
mgAs L
=
= =  
Distribution coefficient normalized to surface area. 
2
2
0.275 / 0.254 /
1.08 /d
L gIOCSK L m
m gIOCS= =  
Distribution coefficient normalized to mass of adsorbent. 
0.275 / 72.1 /
(6.83 10 5 / )(55.84 / )d
L gIOCSK L gFe
molFe gIOCS gFe molFe= =? ?  
 
 
 
 
 
 
 52 
Example 3 
Example determination of Freundlich constants from isotherm data. 
Isotherm data plotted traditionally: 
0
0.005
0.01
0.015
0.02
0.025
0 2E-05 4E-05 6E-05 8E-05 0.0001 0.0001 0.0001
Ce (mol As/L)
qe
 (m
ol 
As
/ m
ol 
Fe
)
 
Freundlich equation: ne F eq K C=  
Linearized Freundlich equation: log log loge F eq K n C= +  
Isotherm data plotted as log qe vs. log Ce: 
y = 0.192x - 0.8625
R2 = 0.9803
-3
-2.8
-2.6
-2.4
-2.2
-2
-1.8
-1.6
-1.4
-1.2
-1
-12 -10 -8 -6 -4 -2
log Ce (mol As/L)
log
 qe
 (m
ol 
As
/ m
ol 
Fe
)
 
Determination of Freundlich parameters: 
0.863
0.192
10 0.137 /F
n
K L molFe?
=
= =
 
 53 
Example 4 
Finding KD using the Freundlich equation for a given set of conditions. 
Using the predermined constants, a Freundlich equation can be written for this system at 
equilibrium: 
0.1920.137
e eq C=  
This equation, a set solids concentration, and a set value for the total amount of 
contaminant in the system allow us to calculate equilibrium concentrations in the aqueous 
and solid phases. 
4.17 510 6.67 10 /
TC molAs L
? ?= = ?  
46.43 10 /
SC molFe L
?= ?  
Two equations: 
0.1920.137
e eq C=  
4 5(6.43 10 / ) 6.67 10 /
e eq molFe L C molAs L
? ?? + = ?  
Solve for the two unknowns: 
0.0207 /eq molAs molFe=  
55.33 10 /
eC molAs L
?= ?  
Calculate KD from qe and Ce: 
5
0.0207 / 388 /
5.33 10 /
e
D
e
q molAs molFeK L molFe
C molAs L?= = =?