Arsenite Depletion by Manganese Oxides: A Case Study on the Limitations of Observed First Order Rate Constants

Arsenic (As) contamination of drinking water is a threat to global health. Manganese(III/IV) (Mn) oxides control As in groundwater by oxidizing more mobile AsIII to less mobile AsV. Both As species sorb to the Mn oxide. The rates and mechanisms of this process are the subject of extensive research; however, as a group, study results are inconclusive and often contradictory. Here, the existing body of literature describing AsIII oxidation by Mn oxides is examined, and several potential reasons for inconsistent kinetic data are discussed. The oxidation of AsIII by Mn(III/IV) oxides is generally biphasic, with reported first order rate constants ranging seven orders of magnitude. Reanalysis of existing datasets from batch reactions of AsIII with δ-MnO2 reveal that the first order rate constants reported for As depletion are time-dependent, and are not well described by pure kinetic rate models. This finding emphasizes the importance of mechanistic modeling that accounts for differences in reactivity between MnIII and MnIV, and the sorption and desorption of AsIII, AsV, and MnII. A thorough understanding of the reaction is crucial to predicting As fate in groundwater and removing As via water treatment with Mn oxides, thus ensuring worldwide access to safe drinking water.


Introduction
Drinking water contamination by inorganic contaminants, such as carcinogenic arsenic (As), is a major threat to global health [1]. The ability to predict the fate of contaminants in groundwater is crucial for ensuring continued access to safe drinking water. To achieve this goal, it is necessary to develop a thorough understanding of the interaction of trace minerals phases with common groundwater contaminants. Minerals, such as manganese (Mn) (hydr)oxides, present in the aquifer, have the capacity to sorb and/or react with many common contaminants, thereby altering their environmental fate [2][3][4]. Manganese is the second-most abundant transition metal in the Earth's crust, making up approximately 0.1% of the total mass [5]. In oxidizing subsurface environments, dissolved Mn frequently precipitates as Mn (hydr)oxides. For simplicity, we will refer to all Mn (hydr)oxides as Mn oxides. Over 30 of these minerals have been identified throughout the natural environment, and are found in diverse locations, from salt-and fresh-water bodies to the desert [5]. Mn oxides play a significant role in controlling aqueous contaminant fate, due in part to their ubiquitous appearance as coatings on mineral surfaces and in places with water, like in bedrock fractures [5].
Mn oxides are considered one of the strongest naturally-occurring oxidizing agents, and have large sorption capacities [6][7][8]. The environmentally relevant oxidation states of Mn are +II, +III, and +IV. The standard reduction potential for MnO 2(s) to Mn II (aq) is 1.23 V, compared to less than 0.7 V for reduction of colloidal Fe oxides, making Mn IV oxide reduction more thermodynamically favorable [9]. Additionally, Mn oxides exhibit high sorption capacities, with specific surface areas (SSAs) up to the order of 100 m 2 /g [10,11]. These traits allow Mn oxides to have an impact on the biogeochemical cycling of many environmental contaminants, including organic contaminants [4], selenium (Se) [12][13][14], chromium (Cr) [15,16], uranium (U) [17,18], and arsenic. Arsenic (As) groundwater contamination is a major health threat to 140 million people worldwide [1]. Exposure to As, a known carcinogen, causes pulmonary, epidermal, liver, and kidney problems [19][20][21][22]. The fate of As in the subsurface is controlled, in part, by Mn oxides and aqueous Mn(II), due to the redox chemistry of As [23][24][25]. The mobile As III oxidation state is more toxic than the relatively immobile As V state [26]. The oxidation of As III to As V by Mn oxides can be described by the general reaction given in Equation (1).
Mn III,IV oxides + As III → Mn II,III + As V (1) Elevated As and Mn concentrations are frequently correlated in groundwater [22,[27][28][29][30][31][32]. Concentrations of As and Mn in these studies were as high as 1340 µg/L [28] and 4000 µg/L [27], respectively. An aggregation of many studies shows that Mn contamination (>400 µg/L) typically occurs in more shallow groundwater than As contamination (>10 µg/L) [25]. Furthermore, As depletion from solution can be predicted by sediment Mn oxide concentration [33]. Observational field studies must be used in conjunction with laboratory experiments to quantitatively and mechanistically understand the interactions of As and Mn in the subsurface.
Careful experimental design and consistent results are required for the successful application of the results of laboratory data to field systems. Previous experimental research on As III oxidation and sorption with Mn oxides describes a wide range of reaction rates and multiple plausible reaction schemes [34][35][36][37]. The oxidation of As III by Mn oxides is characterized by biphasic kinetics, with a fast initial phase followed by a slower phase [37,38]. In this review, we first examine possible causes of inconsistent kinetic data. Then, we describe the current understanding of the reaction mechanism that dictates the second phase of the reaction. For simplicity, the kinetics and reaction mechanism are first explained using data collected at ambient temperature (25 • F) and circumneutral pH (6)(7)(8). The effects of pH, temperature, other metal oxides, competitive ions, and additional environmental factors are considered separately. Finally, we explore the next steps in applying the information gained by decades of research on As(III) removal by Mn oxides. A thorough understanding of As III oxidation by Mn oxides presents a critical opportunity for reducing the impact of As on human health, by predicting and controlling As in drinking and irrigation water.

Mn Oxide Structure
In environmental settings, Mn oxides commonly occur in a wide range of structures, average Mn oxidation numbers (AMONs), and particle sizes, and therefore, have variable reactivities. The basic unit of Mn oxide minerals is the MnO 6 octahedra, which primarily forms tunnel and/or layered structures ( Figure 1). Tunnel structure Mn oxides contain a sequence of edge-sharing MnO 6 octahedra, with either rectangular or square cross sections. Cations (e.g., sodium (Na) or potassium (K)) and/or water partially fill the larger tunnels [5]. Layered Mn oxide minerals (phyllomanganates), consist of sheets of edge-sharing MnO 6 octahedra with cations and water molecules in the interlayers [5]. The Mn oxide structure formed is a function of many environmental conditions (e.g., temperature, pressure, presence of oxygen, presence of Mn-oxidizing microorganisms) during the mineral's formation [5,[39][40][41]. To further complicate the comparison of rate data across studies, the nomenclature used to describe synthetic minerals is inconsistent. For example, acid birnessite has been used to describe both triclinic and hexagonal birnessite [4,50]. The commonly used δ-MnO 2 is also referred to by more general terms, including hydrated Mn oxide (HMO) and birnessite [63,64]. Remucal and Ginder-Vogel (2014) delineate several Mn oxides commonly used in experimental studies [4]. There is significant room for improvement regarding consistency in mineral synthesis and nomenclature across studies.

As III Depletion Rate Law
Advances in analytical techniques have greatly increased the availability of reliable kinetic data, resulting in a better understanding of the initial reaction rate [65]. For example,  reported a decrease in reaction rate after 30 min, but were unable to collect quantitative data from earlier timepoints [38]. In contrast, Ginder-Vogel et al. (2009) determined rate constants for a similar system with sub-second resolution by using quick X-ray absorption spectroscopy (Q-XAS) [63]. Despite these developments, the current understanding of the factors impacting the rate of As oxidation by Mn oxides remains limited. Observed first order rate constants for aqueous As III depletion, in the presence of different Mn oxides, span several orders of magnitude (5.3 × 10 −1 to 4.9 × 10 3 h −1 for δ-MnO 2 , 1.2 × 10 −4 to 4.9 × 10 3 h −1 , for all Mn oxides) ( Figure 2, Table S1). We aggregated reported rate constants and the corresponding experimental conditions, including pH, temperature, initial As III concentration, initial Mn oxide concentration, SSA when reported, and AMON when reported. Statistical analyses show no significant trend (α = 0.05) between the rate constants and experimental conditions across studies.
The As III depletion rate is critical for obtaining order of magnitude estimates of As III removal rate from solution. Since As V is less mobile and toxic than As III , an As III depletion rate law is essential for predicting As mobility in subsurface systems. In order to evaluate the validity of the observed first order approximation commonly used, we must first consider the entire reaction mechanism. Observed rate constants for first order depletion of As III for experiments at pH values between 6 and 8 at 25 • C. (a) Reported rate constants vs initial Mn oxide concentration. Closed symbols represent points where the Mn oxide concentration in molarity was reported. Open symbols represent points where we calculated the Mn oxide concentration by assuming pure MnO 2 . (b) Reported rate constants vs initial As III concentration [34,38,50,55,[66][67][68][69][70][71][72][73].
The depletion of As III from solution is a multistep mechanism, and includes sorption, electron transfer, and desorption ( Figure 3) [74]. The overall rate of As III removal from solution is dependent on several factors, including the As concentration, density, and types of reactive sites on the Mn oxide (>Mn), and proton activity [4,50,74]. Thus, an equation describing the depletion rate of As III in the presence of Mn oxides should take the form of Equation (1), where α, β, γ, and ε represent the reaction order with respect to a given component.
r As III = −k obs As III α In general, when an observed first order rate constant, with respect to As III depletion, is reported, it incorporates the effect of the other possible reactants into the rate constant (Equation (3), α = 1). In a well buffered solution at high [Mn]/[As] this is an acceptable approach to determining pseudo first order rate constants [75,76]. This method assumes that the proton activity and Mn surface site concentrations remain constant over the time period being analyzed and can thus be incorporated into an observed, first order rate constant. This approach yields two fitting parameters for the experimental data: rate constant (k obs ) and the reaction order (α) with respect to As III concentration (Equation (3)). Existing work generally fits the kinetic data with integer reaction orders leading to a first [38,50] or second order reaction [77,78]. However, the multistep nature of the reaction mechanism indicates that the overall rate law is likely much more complicated than an integer reaction order. The oxidation of As III on Mn oxides can be considered a surface catalyzed reaction, which are typically modeled with non-integer overall reaction orders. For example, the general Langmuir-Hinshelwood model for the reaction of two molecules on a catalyst has non-integer reaction orders for both reactants, and is second order for reactive site concentration [79]. . Proposed overall mechanism for As III depletion by Mn III,IV oxides. Reaction stoichiometries are not shown, because the ratios between different electron transfer pathways (e.g., the relative magnitudes of k ox,1 , k ox,2 , and k ox,3 ) are unknown. Mn comproportionation and disproportionation are also not shown, but are important to understanding the overall electron balance [56].
Consideration of the changes in surface site concentration throughout the reaction is necessary for the derivation of a mechanistic model. The relative concentrations of Mn IV and Mn III surface sites are expected to change throughout the reaction, as Mn III is produced as a reaction intermediate [35]. Reaction order with respect to reactive site concentration is more difficult to determine than that of As III concentration. An easy approximation is to use the concentration of Mn oxides as a proxy for reactive site concentration. Studies on organic compounds and Mn oxides resulted in reaction orders with respect to [MnO 2 ] ranging from 0.04 to 1.37 [4]. The reliability of this proxy is dependent on the mineral composition and structure. For crystalline phyllomanganates, we expect the reactive site concentration to be roughly proportional to mineral concentration, due to the simple stoichiometry between As and Mn. As mineral structure becomes less crystalline, the correlation should weaken because defects increase.
Reactive site concentration is typically approximated by number of sites per unit area (12 sites/nm 2 for δ-MnO 2 and acid birnessite) [55]. This can be converted to a mass basis by multiplying by the specific surface area (SSA) of the mineral. However, SSA determined by Brunauer-Emmett-Teller (BET) theory is correlated with suspension pH and Na/Mn content during synthesis, and is not related to crystallite size, as previously believed [51]. Further work is needed to understand the relationship between mineral crystallinity, surface area, and reactivity specifically within the context of As III oxidation.
It is also important to consider how the mineral composition affects reactivity. Synthesis methods yield minerals with a variety of Mn III concentrations and cation (K + , Na + ) substitutions [10,38,51,[80][81][82]. The reactivity of a Mn surface site is dependent on its oxidation state because Mn III may be less reactive than Mn IV [48]. As a result, the Mn reactive site concentrations are split into Mn III and Mn IV in Equation (2). Additionally, the interlayer cations impact the aggregate structure of the Mn oxide, presumably altering its reactivity [51]. Without accounting for this variability, kinetic data are not comparable across studies, or even across solids from different syntheses, due to the sensitivity of the synthesis method.
The reaction rate is expected to depend on proton activity, due to the pH dependency of the redox half reactions. While kinetic experiments show a change in observed first order rate constant at different pHs [50,73], one study determined the reaction order with respect to proton activity to be zero [77]. In experiments examining organic compounds reaction with Mn oxides, the {H + } reaction order increases with increasing pH [4]. This implies that the reaction mechanism changes with changing pH. While it cannot be assumed that this correlation translates to the reaction of As III on Mn oxides, this finding does indicate that pH may be an important consideration. In As III and Mn oxide equilibrium experiments, the pH increased during the reaction when the solution was initially acidic; however, when the solution was initially basic, the pH decreased from the start of the reaction to the end [49]. This suggests a pH-dependent reaction mechanism is present. This change could be described quantitatively by a full rate law describing As III depletion by Mn oxides for each mechanism. To move beyond first order approximations and better understand the kinetics of this reaction, the reaction orders, with respect to As concentration, Mn III and Mn IV site concentration, and proton activity, are required.

Data Analysis
Despite the ubiquitous usage of observed first order rate constants in mineral surface reactions, there is no standard method to calculate these constants. As a result, values can vary considerably within a single dataset and across studies, making comparison difficult. To demonstrate this, we have re-analyzed data from two experiments performed in Ginder-Vogel et al. (2009) that examined As III oxidation by δ-MnO 2 [63]. In one experiment, 80 mL of reaction buffer (5 mM MOPS, 10 mM NaCl at pH 7), with 10 mL of 10 g/L δ-MnO 2 and 10 mL of 50 mM As III in reaction buffer, were mixed in a batch reactor. Samples were taken every 15 s for 5 min, and analyzed by liquid chromatography inductively coupled plasma mass spectrometry (LC-ICP-MS). A second experiment using Q-XAS was performed using the same relative concentrations as the batch experiments. The resulting data has one-second resolution for 294 s. The experiment analyzed by LC-ICP-MS measures the aqueous As III , while the experiment analyzed by Q-XAS measures the fraction of total (aqueous plus sorbed) As present as As III , which is then multiplied by the total initial As concentration from ICP-MS to yield the total As III concentration. Both experiments were performed in triplicate, and the resulting As III concentrations are shown in Figure 4a   Rate constants calculated using one-parameter (blue squares) and two-parameter (red circles) model; (c) Rate constants calculated from start of reaction to cut-off time compared with r 2 for that rate constant; (d) Rate constants calculated from 60 s prior to cut-off time to cut-off time compared with r 2 for that rate constant.
First order rate constants are typically fit by using a linearized first order rate law (Equation (4)). The line of best fit can be forced through the origin so that there is only one fitting parameter, k. However, some choose not to force the line of best fit through the origin in pursuit of a better model fit. This effectively creates an error term, or a two-parameter fit (Equation (5)). Figure 4b displays the rate constants calculated using both the one-parameter and two-parameter fit. These rate constants were calculated by using the data from the initial timepoint to the given cut-off time. The rate constant from the first 60 s of the Q-XAS dataset is 3.90 × 10 −3 s −1 with the one-parameter fit, and 3.12 × 10 −3 s −1 with the two-parameter fit ( Table 1). The corresponding r 2 (not shown) indicate that the two-parameter model has a better fit. In fact, the r 2 is negative beyond 255 s for the LC-ICP-MS dataset and 80 s for the Q-XAS dataset. This represents a model fit that is worse than predicting that the As III concentration at any timepoint is equal to the average As III concentration throughout the reaction. The better fit of the two-parameter model indicates that As III depletion over the entire reaction period is not adequately described by a first order model. This poor fit is a result of the combination of multiple sorption and electron transfer rates that factor into As III disappearance from solution, as well as a Mn oxide surface that changes throughout reductive dissolution. The two-parameter model may be used to describe how the reaction progresses with time, but this model would not yield information about the reaction mechanism. The error term has no physical meaning, and thus only indicates if the reaction is well described by a kinetic rate, shown by an error of 0. Since the two models give us different information about the reaction, it is important to report which fitting method is used, so that the rate constants can be compared across studies. The rate constants determined in the analyses described below use the two-parameter fit.
When reporting rate constants for As III depletion by Mn oxides, the time range that the rate constants were calculated from is frequently reported [50,63]. To investigate the effect of the timepoint where the data is cut off, observed first order rate constants were determined by using the data presented in Ginder-Vogel et al. (2009) from the start of the reaction to a given cut-off time. For example, the rate constant determined using a cut-off time of 60 s is calculated using all the data points from 0 to 60 s. The resulting rate constants and fit, as measured by r 2 , are shown in Figure 4c. The rate constant is shown as a function of cut-off time. Both data sets indicate that the rate constant has multiple orders of magnitude variability (10 −2 -10 −4 s −1 ) on relatively small timescales, demonstrating the importance of reporting the time range used. This order of magnitude variability in rate constant was also observed with sequential additions of bisphenol A to Mn oxide [57]. Reductive dissolution of Mn oxides by As III is characterized by structural changes, rather than simply reducing Mn IV to aqueous Mn II [56]. As the mineral structure changes, the oxidation affinity of the Mn atoms changes. Primarily, Mn III builds up in δ-MnO 2 during As III oxidation, causing increased Jahn-Teller distortion in the mineral [56]. The Mn III centers are less reactive than Mn IV centers [48]. This results in a decreasing rate constant throughout the experiment, as indicated in Figure 4c. Despite a poor model fit, the observed first order rate constant is helpful in comparing rates within an experiment when used carefully. The value of achieving the best fit rate law must be weighed with the loss in comparability when comparing two rate constants fit with different time intervals.
In other words, consider if the quality of information gained by having a perfectly fit rate law justifies comparing a rate constant fit from 0 to 15 min, to one fit from 5 to 30 min. If the goal of the work is to compare rate constant across a single study, it makes sense to aim for consistent time intervals. On the other hand, if the rate constant is going to be used as a model input parameter, the best fit may be more important.
To this end, first order rate constants for the two datasets were calculated using a rolling 60 s time window (Figure 4d). For example, the rate constant for the 200 s cut-off time was calculated using the data from 140 s to 200 s. The Q-XAS data fits the first order model better at the beginning of the reaction, but as the reaction slows and the As III concentration levels off, the fit becomes worse. The rate constants associated with the best fits are given in Table 1. The best fit was within the first 60 s of reaction for all the rate constants except the LC-ICP-MS experiment calculated with the 60 s window.
Alternate measures of reaction progression may be better suited to comparing different trials. For example, the slope of the plot of [As III ] vs time for the first 30 s (m 30s ) has the benefit of fitting the reaction for a standard amount of time. If the system is well suited for this measure, the first 30 s would encompass just the first phase of the reaction. However, m 30s is based on a linear fit of the data. The reliability of this metric is also dependent on having accurate, frequent data collection, so that the value is resistant to outliers, and is not skewed by mixing time at the start of the reaction. Instead, the time until the As III concentration in solution is half of the initial value (t 1/2 ) could be used. The benefit of this approach is that a model fit is not assumed. The data is not fit to a rate law that implicitly assumes that As III removal is kinetically limited. As a result, t 1/2 would not yield mechanistic information, but would give a basis for comparison between experimental conditions. Additionally, the metric can be estimated from existing rate constants if the rate law was fit well. For example, if the first order model fits the data well without an error term, t 1/2 is equivalent to the half-life, ln(2)/k. Using multiple metrics to describe the data is a good way to begin to develop an overall picture of the reaction, without calculating sorption and desorption rates. Alternatively, an understanding of the full reaction mechanism could yield meaningful kinetic information by allowing for determination of the rates in Figure 3.

Reaction Mechanism
Hypotheses about the reaction mechanism have evolved over the past four decades, keeping pace with new experimental and analytical methods. Early speculation attributed the formation of a passivating Mn II -As V complex to the second, slower reaction rate, and the lack of Mn II release into solution [36,71]. Moore et al. (1990) observed the formation of a gel after 4 hours of reaction. The gel is reported to have an As/Mn ratio between 0.9 and 1, which would be expected of krautite, a Mn II -As V mineral [71]. However, the distance between As and Mn atoms on reacted Mn oxide is about 8% shorter than the theoretical distance for Mn 2 (OH) 8 (AsO 4 ) 7− , the proposed Mn II -As V complex [70]. Even if krautite was precipitating in experimental conditions, the formation requires As concentrations much higher than would be found in most natural systems. The solubility constant (K sp ) for krautite is 0.63 [36]. For a system at pH 7, with the World Health Organization (WHO) limit of 10 ppb As, the Mn II concentration in solution would be 1.2 M at equilibrium. Since this Mn concentration is significantly higher than typical environmental values (~10 −5 M), it is unlikely that a significant amount of krautite forms, other than in concentrated experimental conditions [83].
The next attempts at defining the reaction scheme focused on the role of Mn III . Nesbitt et al. (1997) proposed that the oxidation of As occurs in two steps, with Mn III as an intermediate [35]. Mn III is thought to create a film on the solid surface as MnOOH*. The Mn III concentration reaches a maximum, then decreases as it oxidizes additional As III . This mechanism is theoretically supported by X-ray photoelectron spectroscopy (XPS) and by reanalysis of batch experiments using δ-MnO 2 performed by Scott and Morgan (1995) [34]. Mn III concentrations from the batch experiments were calculated by closing the charge balance in the aqueous phase using Mn III , rather than measuring the proposed intermediate directly. This approach assumes that all the Mn II formed is released into solution, not sorbed to the solid surface. However, advances in solid state characterization have shown that Mn II sorbs to the solid, both on edge and vacancy sites [36]. This disconnect implies that although two one-electron transfers by Mn III may play a role in the overall reaction mechanism, desorption is another rate-limiting step.
The predominant redox reactions can be determined by the aqueous Mn II /As V ratio for various reaction conditions. If As III oxidation occurs by two one-electron transfers (e.g., from 2 Mn III to 2 Mn II ), the ratio would be 2. If Mn IV is reduced directly to Mn II , one Mn II atom is produced per atom of As V product, and the ratio would be 1. Theoretically, this ratio must be between 1 and 2, assuming all reaction products are in solution. The Mn II /As V ratio can be predicted as a function of initial AMON. Pure MnO 2 would have a ratio of 1, and Mn oxides with Mn III substitutions would have higher ratios. Assuming a Mn oxide is made of only Mn III and Mn IV , and the presence of Mn II does not affect the reaction, the Mn II /As V ratio is given by Equation (6).
However, under most reaction conditions, the ratio ranges from 0 to 2 because transport of Mn away from the solid surface is slower than transport of As V [34]. Nesbitt et al. (1997) refers to Mn II /As V ratios significantly greater than 1, reported in Scott and Morgan (1995), as evidence for the Mn III intermediate [35]. Strangely, the ratios reported in Scott and Morgan (1995) reached a maximum of 0.93, and not above 1 [34]. In stirred-flow experiments with δ-MnO 2 , the Mn II /As V ratio is 1.15 during the slower phase of the reaction [37]. A higher ratio in stirred-flow experiments than in batch experiments is expected because the reaction products are removed from the system as they form. As a result, Mn II remains in the aqueous phase, rather than sorbed to the solid surface. According to Equation (6), ratios of 0.93 and 1.15 correspond to AMONs of 4.15 and 3.74, respectively, rather than 3.95, as expected [37]. Thus, the mechanism is more complicated than the mechanism represented by Equation (6).
The mechanism is likely a combination of several different electron transfer and sorption steps. Equations (7)-(10) describe the potential rate limiting steps, where Mn III,IV O x represents a general Mn oxide and ≡ represents sorption to the Mn oxide. The reactions describe As III sorption and desorption on the Mn oxide, electron transfer, As V sorption and desorption, and Mn II sorption and desorption, in the order presented below.
Mn III, These reactions happen in conjunction with both comproportionation, where Mn II and Mn IV form two Mn III , and disproportionation, where two Mn III form Mn II and Mn IV [37,44,[84][85][86]. As discussed above, the electron transfer rate is time-dependent, likely due to differences in reactivity between Mn IV and Mn III . Thus, k 2 changes throughout the reaction, and the electron transfer could be described by two separate reactions, as is done in Figure 3.
The conceptual basis for the sorption steps can be understood by considering the electrostatic forces involved. As the Mn oxide is reductively dissolved, Mn II and Mn III are produced. Vacancy sites have a strong negative charge, so they sorb positively charged Mn II,III . Meanwhile, the oxyanion formed by As V sorbs to edge sites. Once the vacancy sites are filled, Mn II competes with As V for edge sites. The electron transfer happens at edge sites, so sorbed reaction products passivate the solid surface, slowing the As III depletion rate [36]. The reaction rate also decreases as comproportionation forms Mn III , which is less reactive than Mn IV [48]. In experimental systems, As III oxidation by Mn oxides is complicated by sorption, desorption, and electron transfer between Mn species. In environmental systems, the pH, temperature, presence of other oxides and other ions, and various other factors further complicate our understanding of As III depletion in solution.

Environmental Factors Affecting As Oxidation by Mn Oxides
The study of several environmental factors in isolated controlled laboratory experiments has led to a clear understanding of the potential impact of these factors in the subsurface. Figure 5 depicts the expected effect of pH, temperature, presence of competitive ions, and presence of Fe oxides on As III depletion by Mn oxides.

pH
The system pH affects the Mn oxide surface properties and As protonation state, changing the relative impact of different steps in the reaction mechanism and altering the kinetic rate [50,87]. Synthetic Mn oxides encompass a wide range of average PZCs. The reported range for the PZC of the birnessite group is 1.5-3.5, 2.8-4.6 for minerals in the hollandite group, and 6.4-7.3 for pyrolusite ( Figure 6) [88]. Biogenic Mn oxides typically have higher PZCs than synthetic birnessite [39]. A high temperature synthesis method can be used to create birnessite nanosheets with a PZC less than 0.36 [72]. As the pH of the system increases, the surface of the Mn oxide becomes more negative, resulting in increased sorption of Mn II and Mn III to the solid surface (Figure 5b,c) [50]. The PZC of edge sites is expected to be higher than that of vacancies [89]. As a result, there is less electrostatic repulsion at edge sites by negatively charged As oxyanions, compared to at vacancies. This confirms previous work indicating that As sorption occurs at edge sites, while Mn II,III sorption occurs at vacancies [36].
Both inorganic As species are triprotic oxyanions. The fractions of each As species in a given protonation state are shown in Figure 5. Pentavalent As has pK a values of 2.2, 6.9, and 11.5, therefore, H 2 AsO 4 − or HAsO 4 2− predominate in neutral pH natural waters [90]. Trivalent As has pK a values of 9.2, 12.1, and 13.4, and H 3 AsO 3 predominates at circumneutral pH [90]. The lack of charge allows As III to diffuse faster than As V to the negatively-charged Mn oxide surface. Since As III is oxidized at this surface, the negative charge of As V and the Mn oxide do not repel as they would if As V was added to solution directly [38]. This may contribute to the greater sorption capacity of As V on Mn oxides when added as As III than when added as As V [38]. More recently, the difference in sorption capacities has been associated with a surface alteration during the electron transfer [70]. In the case of birnessite and cryptomelane, the As III depletion rate of birnessite is greater than that of cryptomelane, despite the larger surface area of cryptomelane [38]. This is attributed to the higher average PZC of cryptomelane, which sorbs As V to a larger extent than birnessite [38]. At circumneutral pH, the cryptomelane surface has an overall less negative charge than birnessite, and can thus sorb more As. Sorbed As V competes with As III for edge sites, preventing As III oxidation. Figure 5. Expected impact of environmental factors on As oxidation by Mn oxides (a) relative to the reaction of a pure As, Mn oxide system at 25 • C, and circumneutral pH (b), as projected from above a phyllomanganate layer. As III,V adsorb to edge sites while Mn II sorbs above vacancies. Mn III replaces Mn IV in the reacted oxide. Low pH (c) and temperature (e) inhibit Mn II sorption; high pH (d) and temperature (f) enhance Mn II sorption. The oxidation rate is lower at lower temperatures. Anions (e.g., PO 4 3− ) (g) and surface cations (e.g., Pb II , Co II ) (f) sorb to edge and above vacancy sites, respectively, impeding sorption and oxidation of As III . As III,V preferentially adsorb to Fe oxides, while As III is oxidized on the Mn oxide surface (i).

Figure 6.
Protonation state of As III and As V as a function of pH compared to the average PZC of δ-MnO 2 . As pH increases, the Mn oxide surface and the As III and As V oxyanions have a more negative charge.
The electron transfer process between Mn and As is also affected by solution pH. The pH-dependent redox potentials of the As III and Mn IV reaction indicate that the As III oxidation capacity of Mn oxides is not constant with respect to pH (Figure 7). However, analysis of the redox potentials indicates that essentially all As III is oxidized at equilibrium. In extremely acidic conditions (below pH 2), the redox reaction is given by Equation (11).  Assuming the activities of solids and liquids are in unity, and making use of the redox half reactions that make up Equation (11), with the Nernst equation, gives the equilibrium constant in Equation (12).
[H 3 AsO 3 ] H + 2 = 10 22.0 (12) This large K value demonstrates that even at low pH, if equilibrium is established, almost all of the As exists as As V . A similar theoretical analysis in basic conditions leads to the same conclusion. However, experimental results determining the oxidation capacity of different Mn oxides indicate that this may not always be the case. Solutions of As III and suspended Mn oxides were allowed to reach presumed chemical equilibrium [49]. Birnessite exhibits a minimum amount of As III oxidized at pH 6.3, while cryptomelane and hausmannite appear to oxidize increasing amounts of As III as the pH increases from 2 to 11.5 [49]. However, none of the reactions oxidize all of the As III , even though the thermodynamic calculations above dictate that they should [49]. From these experiments and calculations, it is evident that As III oxidation by Mn oxides may be kinetically limited and not thermodynamically limited.
Since thermodynamic trends do not always translate to kinetic trends, the kinetics of the oxidation reaction require experimental investigation.  performed batch reactions of acid birnessite with As III , and calculated observed first order rate constants [50]. Experiments at pH 4.2, 7.2, and 9.0 result in rate constants of 0.433, 0.133, and 0.246 s −1 , respectively. This suggests that the kinetics of the reaction may exhibit a minimum rate constant at circumneutral pH because the rate constant at pH 7.2 is lower than that of the higher and lower pH values. Kinetic modeling using the reactions and rate constants presented in Equations (7)- (10) indicate that as pH increases from 4 to 8.2, so do the rates of As V adsorption (5 × 10 6 -8 × 10 9 M −2 s −1 ), Mn II desorption (2.5 × 10 6 -1.5 × 10 10 M −2 s −1 ), and Mn II adsorption (5-12 M −1 s −1 ), while other rates remain the same [87]. This seems inconsistent with our understanding of pH, and could possibly be explained by an underspecified system with too many fitting parameters. Further experiments at intermediate pH values are needed to more accurately determine the relationship between pH and reaction rate.

Temperature
As with pH, the impact of temperature has been studied over a small range, but the results are somewhat inconclusive. Existing investigations into the kinetics of As oxidation by Mn oxides are limited to 25 ± 20 • C [38,50,87].  reports first order observed rate constants of 0.0026 s −1 (10 • C), 0.0027 s −1 (25 • C), and 0.0037 s −1 (40 • C) for As III oxidation by δ-MnO 2 [50]. Scott (1991) modeled the overall As III removal reaction using rate constants as described by Equations (7)-(10). As temperature increases from 15 to 35 • C, the rate constants for As III adsorption (2.5-7.5 M −1 s −1 ), Mn II adsorption (2.5 × 10 6 -9 × 10 6 M −2 s −1 ), and Mn II desorption (2.5-35 M −1 s −1 ) increases. The As to Mn electron transfer decreases (0.03-0.015 s −1 ) as temperature increases, contrary to what is expected in chemical reactions [87]. Enhanced Mn II adsorption is attributed to the decrease of the Mn oxide PZC with increasing temperature [91]. As a result, the solid surface's negative charge increases as temperature increases, resulting in increased Mn II sorption. While PZC does decrease with increasing temperature, we do not expect the change over a small temperature range to greatly effect sorption, because an increase of 15 • C is associated with a PZC decrease of only up to 0.45 pH units [92,93]. At higher temperatures, the combination of a decrease in removal capacity due to enhanced Mn II sorption, and an increase in reaction rate due to increased internal energy, results in a net increase in overall reaction rate (Figure 5e,f) [50].

Other Oxides
Mn oxides are just one component of the soil or sediment matrix that impact contaminant fate. Iron and aluminum (Al) oxides, as well as clays and organic matter, are known to have high sorption capacities for As [94][95][96]. Numerous studies have reinforced our understanding of the impact of combinations of Fe and Al oxides in both natural and synthetic systems. Due to their high sorption capacities and environmental abundance, the impact of Fe oxides has been especially well investigated. Goethite, α-FeOOH, is commonly used as the synthetic analogue of environmentally relevant Fe oxides, and has a PZC of 9.4 [97,98]. In systems with As, Fe oxides, and Al oxides, As V adsorbs to both metal oxides, while As III preferentially adsorbs to Fe oxides [99]. This trend exists in systems of mixed Fe oxides and Al oxides as well as coprecipitated Al, Fe oxides [99,100]. However, As III binds to Fe oxides in weak complexes (outer-sphere, bi-nuclear bidentate, and monodentate) that are easily desorbed when environmental conditions change [101][102][103][104][105][106][107][108][109]. Weak tridentate complexes are possible when As III sorbs to magnetite, a type of Fe oxide [110]. As III adsorbs on Fe oxides to a greater extent than As V [111][112][113][114][115].
The As III depletion capacity of a Mn and Fe oxide system is higher than that of either oxide alone [49,74,[116][117][118]. This phenomenon is the product of two opposing mechanisms. In one, As III is oxidized to As V by the Mn oxides. Some of the As V is released by the Mn oxide then sorbs to the Fe oxide, decreasing passivation of the Mn oxide surface, resulting in further As III oxidation (Figure 5i). At the same time, the Fe oxides also sorb As III , preventing As III oxidation on the Mn oxide surface [74]. Ying et al. (2012) confirmed this using a reactor with birnessite and goethite separated by a 0.1 µm polycarbonate filter that allowed for As transport [114].
Kinetic analysis of As removal in multiple oxide systems is inconclusive.  calculated lower observed first order rate constant for Fe and Al oxide coated Mn oxides than for pure Mn oxides [119]. More recently, Parikh et al. (2010) found little impact of α-FeOOH on the initial oxidation rate of δ-MnO 2 in As III batch reactions [74]. The depletion rate of aqueous As III is expected to change for different metal oxide surface site concentrations according to Equation (13). As with Mn reactive sites, Fe and Al oxides have different reaction orders due to differences in sorption affinities.
Studying combined Fe and Mn oxide systems allows for exploitation of the natural heterogeneity of soils and provides opportunities to engineer solids for As removal. Samples with natural Fe and Mn oxide mixtures have demonstrated high As removal capacity, confirming the trends observed with synthetic Mn oxides [120][121][122]. Recent work on engineered Fe-Mn binary oxides have been successful in removing As from solution [115,123]. These strategies include pure Fe-Mn binary oxides, magnetic nanoparticles (Mag-Fe-Mn), and Fe-Mn binary oxide impregnated chitosan [124,125]. Engineered particles have also proved effective in removing aromatic organoarsenic compounds [126].

Competitive Ions
For a comprehensive understanding of As III oxidation by Mn oxides, it is important to incorporate the role of aqueous cations and anions. Ions may co-precipitate with Mn oxides or interact with existing Mn oxides. These interactions can be further divided into systems where the ions are present before the As enters (e.g., in allogenic or anthropogenic As contamination) or systems where As and other ions are added simultaneously to Mn oxides (e.g., in water treatment applications). The fate of As in systems with other ions depends on the source of the solutes.
Phosphate is prevalent in environmental systems because of its use as a fertilizer that can leach into groundwater [127]. The phosphate ion (PO 4 3− ) has a similar structure to arsenate. Furthermore, the pK a s of phosphoric acid are similar to those of H 3 AsO 4 . They are 2.2, 7.2, 12.3 for phosphoric acid (H 3 PO 4 ) compared with 2.2, 6.9, and 11.5 for H 3 AsO 4 . As a result, phosphate competes for reactive sites with As V , reducing As V production, as well as total As sorption (Figure 5g). In systems with lower phosphate concentrations than As concentrations, the initial As III depletion rate is not impacted by the presence of sulfate or phosphate [74,77]. In a reaction where the phosphate concentration was equal to As concentration, the slope of the initial reaction rate (m 30s ) was 0.02 with phosphate, compared to 0.10 without phosphate [74]. Divalent cations are of interest in As oxidation by Mn oxides, due to their similarity to Mn II . The presence of Mn II , Fe(II), calcium (Ca(II)), cobalt (Co.(II)), nickel (Ni(II)), zinc (Zn(II)), and lead (Pb(II)) decrease the oxidation rate of As III by Mn oxides [34,55,64,67,77,116,128]. With the exception of Pb, these metals are all in the fourth row of the periodic table, so they have similar electron configurations and atomic radii. Additionally, all but Ca and Pb have metal-oxygen bond distances between 2.06 and 2.20 Å [129]. As with the addition of metal oxides, a reaction rate with a factor for competitive ions can be added to the rate law. For example, Ca affects As oxidation by Mn oxides with a reaction order of −0.2 [77]. In the study of Pb(II) and Zn(II), the addition of metals decreased the initial As III depletion rate, but resulted in equal or greater extents of As III removal. The initial rate decrease is attributed to site blockage, while the increase in oxidation capacity can be explained by decreased overall electrostatic repulsion from the metal cations, enhancing oxyanion As sorption [55].
In batch experiments with biogenic Mn oxides, the As III oxidation rate decreased when metal ions were added. The reduction of oxidation rate was dependent on the ion and followed the order Mn 2+ > Co 2+ ≈ Ni 2+ > Zn 2+ , with first order rate constants 0.071 h −1 , 0.091 h −1 , 0.128 h −1 , 0.215 h −1 , respectively. The addition of metal ions increased the total As adsorbed significantly by suppressing the charge repulsion between the negatively charged mineral surface and As oxyanions. The adsorption was highest for Zn 2+ (99.5%), then Ni 2+ and Co 2+ (38.3% and 39.5%, respectively), then Mn 2+ (25.9%), compared to 4.3% for no metal ion addition [69]. However, different Mn oxide minerals have different affinities for different ions. A biogenic Mn oxide produced by Mn oxidizing fungus KR21-2 had sorption affinities ranking Co 2+ > Zn 2+ > Ni 2+ , while that of synthetic γ-MnO 2 was Zn 2+ > Co 2+ > Ni 2+ [130]. It is clear that divalent cations decrease the rate of As oxidation by Mn oxides, but the extent of the decrease is dependent on the specific mineral and cation (Figure 5h).

Other Factors
Investigations into the impact of bacteria, sunlight, and reactive oxygen species round out the existing literature on environmental factors in As III oxidation by Mn oxides. Microorganisms can aid in As III oxidation by either oxidizing Mn to produce Mn oxides, that in turn, oxidize As III , or oxidize As III directly [39]. These microorganisms can use As III as the sole electron donor (chemolithoautotrophic metabolism) or as one of multiple electron donors [131][132][133][134]. An As oxidase with associated genes has been identified in A. faecalis, but others may exist [135]. To investigate the effect of As III oxidizing microbes in the presence of Mn oxides, Parikh et al. (2010) mixed P. fluorescens and A. faecalis with As III and δ-MnO 2 . In both pretreated experiments and simultaneous additions, the bacteria enhanced passivation, decreasing As III oxidation and initial reaction rates. This suggests As III diffusion through the biofilm formed in pretreatment is the rate limiting step [74]. In a similar study with P. fluorescens and A. tumefaciens, Jones et al. (2012) found an additive increase in initial reaction rate with both bacteria and δ-MnO 2 , relative to bacteria or δ-MnO 2 alone. The combined bacteria and δ-MnO 2 system has decreased As sorption and increased desorption, implying that the As is sorbed in weak complexes. In batch reactions with only bacteria, the bacteria oxidized As III with an observed zero order reaction, and cells did not retain As [66]. The microbial community of an environmental system may greatly impact As oxidation either by inhibiting oxidation due to biofilm formation or by directly enhancing oxidation [136].
The presence of light and oxygen may also impact As III oxidation by Mn oxides. Shumlas et al. (2016) found that at pH 5, the oxidation reaction is faster in simulated sunlight than in the dark, but the trend did not hold for pH 7 and pH 9. The effect on overall oxidation capacity is unclear because the reactions were not run until the As V concentrations leveled off. The impact of light was consistent for both oxic and anoxic experiments, indicating that elemental oxygen may not play a role in As III oxidation by Mn oxides on short timescales [137]. While the primary concern of As contamination is in groundwater, where light and oxygen are approximately constant, it is important to consider the laboratory conditions that may impact the environmental relevance of an experiment.
While Mn II is oxidized to Mn III,IV in the presence of O 2 [138], the impact of O 2 on As oxidation by Mn oxides has not been studied systematically. As a result, some studies on As oxidation by Mn oxides are performed in an anoxic chambers, but others are not [50,67]. In oxic environments, there may be artificially high oxidation capacities due to the regeneration of Mn oxides throughout the experiment. However, the oxidation rate of Mn II in solution is expected to be slower than the oxidation rate of As III by Mn oxides [137]. Additionally, the relative concentration of O 2 in the lab compared to in oxic sediment is either the same or slightly higher, whereas As and Mn oxide concentrations may be orders of magnitude larger than what is environmentally relevant. As a result, the inconveniences associated with performing experiments on synthetic Mn oxides in anaerobic chambers likely provide little added information concerning As(III) oxidation mechanisms. However, bacteria and other metal oxides are also affected by the presence of O 2 , so anaerobic natural samples should be kept anaerobic during experiments.

Conclusions
Studies on As III oxidation by Mn oxides cite the potential of Mn oxides to remove As from drinking water and predict subsurface As mobility. This can only happen if the knowledge generated by these studies is carefully parsed to elucidate mechanisms, then applied to in situ remediation methods or ex situ engineered systems. Both of these applications require more rigorous kinetic modeling and solids characterization.
A critical step in developing a comprehensive model As III depletion by Mn oxides is determining the rate constants involved in the full reaction mechanism ( Figure 3). However, this requires on a complete understanding of the individual reaction steps including sorption, desorption, electron transfer between As and Mn, and electron transfer between Mn species. Completing this model is numerically difficult, due in part to rates spanning many orders of magnitude. The model developed by Feng et al. (2018) takes a reductionist approach, and does not incorporate the role of Mn III in determining depletion rates [139]. While this approach can predict As(III) oxidation rates in a limited set of conditions, the resulting model parameters lose physical significance, as it does not incorporate steps in the known reaction mechanism. Other modeling approaches use non-kinetic parameters to describe the sorption processes involved. Various surface complexation models (SCM) fit As sorption to Fe oxides [112,[140][141][142] and several divalent cations on Mn oxides [143][144][145][146][147][148]. For systems that SCMs do not fit well, the CD-MUSIC model has been used [149,150]. Reactive transport modeling is also valuable in separating the transport effects from kinetic effects, and fits this system well [114,143,151]. More thorough reporting of solid characteristics, specifically PZC and interlayer cations, would greatly improve the quality of experimental data.
Beyond modeling, a better understanding of the impact of temperature and light on As III oxidation could greatly improve water treatment capabilities. For example, if a certain wavelength of light dramatically increases the As III oxidation rate by Mn oxides, it could be used to enhance As immobilization in engineered water treatment. In many cases, robust data sets that consider a wide range of conditions (e.g., at many pH values) are more valuable than studies that briefly consider several unrelated factors. Additionally, frequent sampling and careful data interpretation are critical for a reliable experiment. Our current library of computational methods and both solid and aqueous phase characterization techniques is strong enough to accurately and completely understand As III depletion by Mn oxides, and move toward applying the information to reduce human exposure to As-contaminated drinking water.