# «THERMODYNAMIC MODELING OF METAL ADSORPTION AND MINERAL SOLUBILITY IN GEOCHEMICAL SYSTEMS A Dissertation Submitted to the Graduate School of the ...»

concentrations of the bacterial surface species, and aH, is the activity of aqueous protons in the bulk solution. The four protonation constant (pKa) values used to describe proton binding onto the cell wall in the Fein et al. (2005) model are 3.3, 4.7, 6.8, and 8.9.

We describe Cd adsorption onto deprotonated functional groups on the bacterial

**surface according to:**

The equilibrium constant (Kj.cd) for complexation reaction (3) involving Site / is defined

**by:**

where [R-A,~] represents the concentration of deprotonated cell wall functional group A,, [R-Ai(Cdf] represents the concentration of cell wall functional group A; that is complexed with Cd2+, and acd2t is the activity of Cd2+ in solution after equilibrium is attained.

The objective of the Cd-bacteria experiments is to constrain values of Kt.cd that can be used to model Cd-bacterial adsorption in the more complex systems. In systems with low metal:sorbent concentration ratios, Cd binding onto only one cell wall functional group is required to describe Cd adsorption (e.g., Fein et al., 1997, Yee and Fein, 2001, Fein et al., 2001). However, systems having higher metahsorbent ratios may involve more than one Cd-binding site to obtain the best-fit (Yee and Fein, 2001; Borrok and Fein, 2004).

We use the computer program FITEQL 2.0 (Westall 1982) to solve for the stability constants for all metal-sorbent surface complexes. This program accounts for the aqueous speciation of Cd, and all Cd-surface complexes. We include aqueous cation hydrolysis reactions, using the constants reported by Baes and Mesmer (1976). We test a range of models that invoke Cd binding onto between one and four bacterial sites. The relative goodness of fit of each model is determined by comparing the overall variance parameter, V(Y), calculated by FITEQL. In both the 10 and 1 ppm bacteria-only systems (Figure 4.1), a model involving Cd adsorption onto bacterial Sites 2, 3, and 4 yields the lowest V(Y) value. For the 10 ppm Cd experiments (Figure 4.1 A), the calculated stability constants log Ki-cd, log ATj-cd and log K4.cd are 3.3,4.3, and 4.9, respectively. The log stability constant values calculated using the 1 ppm Cd experimental data (Figure 4.IB) are similar: 3.4,4.7, and 4.8. Borrok et al. (2004) invoked Sites 2 and 3 to describe the adsorption of 10 ppm Cd onto 1 g l"1 of B. subtilis, yielding similar calculated values for log K.2-cd and log Ksjca of 3.4 and 4.6, respectively, despite the different Cd: bacterial site ratio of their experiment. We use the equilibrium * constants calculated from our data to describe Cd adsorption to B. subtilis in systems containing two- and three-sorbent mixtures.

4.3.2.2 Kaolinite proton and metal adsorption model Schroth and Sposito (1997; 1998) described the surface charge properties of KGa-2, and developed a NEM to describe proton and metal adsorption to the surface of the kaolinite. This model accounts for proton activity with a single amphoteric surface

**site, XOH, according to the reactions:**

The log equilibrium constant values for reactions 5 and 6 are 3.5 and -7.2, respectively (Schroth and Sposito, 1998). In this approach, Cd adsorption is described by complexation both with the amphoteric site and an additional permanent negatively

**charged surface site, YO', according to:**

We use values for the equilibrium constants for reactions (5) and (6) and for site concentrations from Schroth and Sposito (1998), and we use the measured Cd adsorption behavior of kaolinite as a function of pH to solve for the equilibrium constants for reactions (7) and (8). We calculate log Kj and log K& values of-2.8 and 3.9 from the 10 ppmCd adsorption data, and -2.4 and 3.9 from the 1 ppm Cd experimental data, respectively. The best-fit model for the 10 ppm data is depicted in Figure 4.1 A, and that for the 1 ppm data in Figure 4.IB. Our 10 ppm data sets can be adequately described by Cd adsorption at the XOH site only (Equation 7), where a low percentage of free Cd is adsorbed below pH 5. However, it is necessary to invoke the YO~ site to describe the significant adsorption observed below pH 5 in 1 ppm experiments. The best-fit, as quantified by the V(Y) parameter, is achieved when both XOH and YO ~ sites are invoked for both the 10 ppm and 1 ppm data sets, so both models utilize these two sites.

Schroth and Sposito (1998) calculated log K? and log Kg values of-1.45 and 3.65, respectively. Our equilibrium constant values, particularly that of Kj, are significantly different. Were we to use the log A value given by Schroth and Sposito (1998) to model our 10 ppm and 1 ppm data, the models would predict significantly more Cd adsorption than we observe below pH 5, where the structural YO ~ site dominates adsorption. For example, in the 10 ppm experiments we never observe more than 15% of the Cd adsorbed to the kaolinite surface at any pH. Using the Schroth and Sposito (1998) constants to model our data yields predictions of more than 30% adsorption between pH 5 and 7. Schroth and Sposito (1998) conducted their experiments with 10 g l"1 kaolinite and 8.9 x 10"7 M Cd (0.1 ppm), and observed a range of 30% to 90% Cd removal from solution across the pH range 2 to 8. Our systems contain 10 or 100 times the initial Cd concentration, and only 1 g l'1 kaolinite. Because their data describe a greater range of adsorption behavior, the equilibrium constants calculated by Schroth and Sposito (1998) are likely applicable to a wider range of conditions than ours.

Differences in the calculated log Kj value could be attributed to differences in equilibration time between our study and that of Schroth and Sposito (1998), or the large difference in Cd:kaolinite ratios. However, because the other adsorption measurements in our study are conducted under the same conditions as these, and the constants are reasonably similar, we use our Cd-kaolinite stability constants calculated from 1 ppm and 10 ppm adsorption data (Table 4.1) in the multi-sorbent predictive models of the same Cd concentrations.

4.3.2.3 HFO proton and metal adsorption model Dzombak and Morel (1990) described the reactive sites on the surface of HFO using two types of amphoteric sites with the same acidity constants, but with different site concentrations. The strong site, =FesOH, represents a subset of low concentration sites with a high affinity to adsorb metal cations. The weak site, =FewOH, is a high concentration site with lower cation affinity, useful for describing cation adsorption behavior in systems with higher sorbent-sorbate ratios. Both sites react with protons

**according to:**

account for the electrostatic effects on surface free energies (Bethke, 2007), where Az is the change in surface charge due to cation adsorption, W is the surface potential, F is Faraday's constant, R is the ideal gas constant, and TK is the temperature, in Kelvin.

Incorporating this factor into the mass law equations for the reactions in (9) and (10)

**yields:**

Log A / and log Ku values are given as 7.29 and -8.93, respectively (Dzombak and ^y Morel, 1990). Adsorption of aqueous Cd2+ onto both the strong and weak HFO surface

**sites can be represented as:**

At low sorbate:sorbent concentrations, where there are abundant surface sites available, metal adsorption can be described by adsorption to the strong site, =FesOH, only. By modeling 24 sets of pH-dependent Cd adsorption data, Dzombak and Morel (1990) calculated an average stability constant, log KnFO-cd, of 0.47 for the strong site.

Using one set of pH dependent adsorption data in which the sorbate:sorbent ratio is high, they calculated a log KHFO-CH value of -2.90 for the weak site. In this same data set, Dzombak and Morel (1990) calculated the log KnFO-cd of the strong adsorption site to be

-0.51, significantly below the value of 0.5 calculated from the low sorbate:sorbent ratio data. Our 10 ppm Cd experiments have a high sorbate:sorbent ratio, and it is necessary to invoke binding onto both the strong and the weak sites to fit our data. For these data, we calculate values for the strong and weak sites to be -0.3 and -3.6, respectively. To describe adsorption of 1 ppm Cd to 1 g l"1 HFO, a lower sorbate:sorbent ratio, it is only necessary to invoke the strong site, consistent with similar datasets in Dzombak and Morel (1990). The log Kmo-cd value that we calculate for the strong site from the 1 ppm Cd data is 0.4. The best-fit to the 10 ppm Cd experiments closely match the observed, adsorption behavior (Figure 4.1 A). However, the best-fit model of the 1 ppm Cd data exhibits a steeper adsorption edge than is observed in the experimental data, so that the model fails to account for significant adsorption observed below pH 5.5. Several best-fit • models to sets of Cd adsorption data in Dzombak and Morel (1990) exhibit a similar trend. To account for Cd adsorption at lower pH, a model would need to incorporate a site that deprotonates at lower pH.

4.3.3 Cd adsorption to two-component mixtures Figures 4.2,4.3, and 4.4 compare the measured extents of Cd adsorption onto 2component sorbent mixtures to the CA model predictions of the Cd adsorption behaviors. The graphs also depict the same model fits to the 1 component end-member systems that are shown in Figure 1 for reference. Models of the two-sorbent mixtures use the acidity and equilibrium constants calculated in the SCMs described in Section 4.3.2 and compiled in Table 4.1 to independently predict the extent of Cd adsorption in each two-sorbent system. Molal ratios of site concentrations for each mixture are listed in Table 4.2.

The Cd adsorption behaviors for mixtures of HFO and B. subtilis cells are depicted in Figure 4.2. Experiments containing 75% HFO and 25% B. subtilis (by mass) exhibit Cd adsorption behavior similar to that of the corresponding 100% HFO systems.

In this system, B. subtilis cells contribute 54% of the potential Cd adsorption sites on a molal basis, and HFO the remaining 46%. Clearly, Cd preferably binds to the HFO surface relative to the sites on the B. subtilis cell walls. Mixtures of 25% HFO and 75%

mixtures of HFO and B. subtilis cells. Dashed lines represent best-fit models to 1 g l"1 HFO and B. subtilis end members from Figure 1. Darkened symbols and lines represent adsorption data and predicted adsorption behavior for two-sorbent mixtures, including

0.75 g 1_1 HFO + 0.25 g 1"' B. subtilis cells (A, thin line), and 0.25 g f1 HFO + 0.75 g l"1 B. subtilis cells ( •, thick line).

B. subtilis adsorb significantly less Cd than the 100% HFO experiments, but more than was observed in systems containing 100% B. subtilis cells. HFO has significantly lower site concentrations compared to B. subtilis, contributing less than 46% of the surface sites when it is 75% of the mass of the mixture, and approximately 8% of the sites when " it is 25% of the mixture by mass. The predictive models (solid lines) describe the 10 ppm data reasonably well, but exhibit similar misfits to the 1 ppm data to those observed between the model and the 100% HFO data. Lund et al. (2008) observed that discrepancies in fitting metal adsorption to the pure phases caused discrepancies in the predicted fits of multi-component systems using the CA approach, and we observe the same phenomenon. Thus, the difference between the model predictions and experimental data in the two-component 1 ppm experiments is likely caused by the relatively poor fit of the one-component 1 ppm Cd + HFO model.

** Figure 4.3 illustrates Cd adsorption behavior onto mixtures of B.**

subtilis and kaolinite. These data show Cd adsorption decreasing systematically with increasing kaolinite in the mixture; 100% B. subtilis adsorbs the greatest portion of free Cd, followed by the 75% B. subtilis + 25% kaolinite mixture, the 25% B. subtilis + 75% kaolinite mixture, and the 100% kaolinite adsorption experiments. In experiments containing 75% B. subtilis and 25% kaolinite by mass, the bacteria represent more than 92% of the surface sites on a molal basis, and in mixtures of 25% B. subtilis and 75% kaolinite by mass, B. subtilis contributes nearly 58% of the reactive sites. However, the majority of Cd adsorption below pH 4 is predicted to occur onto the permanent structural site, YO ~, of kaolinite. In both the 10 ppm and 1 ppm Cd experiments, the predictive models provide excellent fits to the measured extents of adsorption in the B. subtiliskaolinite systems.

mixtures of kaolinite and B. subtilis cells. Dashed lines represent best-fit models to 1 g 1 kaolinite and B. subtilis end members from Figure 1. Darkened symbols and lines represent adsorption data and predicted adsorption for two-sorbent mixtures, including

0.75 g l"1 B. subtilis cells + 0.25 g l"1 kaolinite (A, thin line), and 0.25 g 1"' B. subtilis cells + 0.25 g l"1 kaolinite ( •, thick line).

Cd adsorption onto mixtures of HFO and kaolinite is depicted in Figure 4.4. A mixture of 75% HFO + 25% kaolinite adsorbs free Cd to a similar extent as the 100% HFO experiments, with only slightly less adsorption above pH 7. The 25% HFO + 75% kaolinite mixture adsorbs substantially more Cd than experiments conducted with 100% kaolinite, but less than those with 100% HFO. These results suggest that HFO dominates the adsorption behavior of Cd in experiments where it is 75% of the total sorbent mass, and strongly influences Cd adsorption even as a minor component of 25% of the sorbent mass. HFO has nearly identical site concentrations as kaolinite, contributing approximately 77% of the surface sites when it is 75% of the mixture, and 27% of the sites when it is 25% of the mixture. The HFO-like adsorption behavior of both mixtures attests to the higher affinity of HFO for adsorption of Cd compared to that of kaolinite and B. subtilis. Predictive models of the mixtures containing 10 ppm Cd fit.

the experimental data well, but the models deviate from the 1 ppm data significantly.

This difference can be attributed again to the poor fit of the one-component 1 ppm Cd + HFO model.