# Modeling of Adsorption by Soils Constant Capacitance Model

The constant capacitance model is a chemical surface complexation model that was developed to describe ion adsorption at the oxide-solution interface (Schindler et al ., 1976; Stumm, Kummert, and Sigg, 1980) . As is characteristic of surface complexation models, this chemical model explicitly defines surface species, chemical reactions, equilibrium constants, mass balances, charge balance, and electrostatic potentials The reactive surface site is defined as SOH, an average reactive surface hydroxyl ion bound to a metal, S, in the oxide mineral . The constant capacitance model has been extended to describe the adsorption of trace element anions on soil surfaces The applications of the model to predict arsenate and selenite adsorption by soils will be presented (Goldberg et al , 2005, Goldberg, Lesch, and Suarez, 2007)

The constant capacitance model contains the following assumptions: (1) all surface complexes are inner-sphere; (2) anion adsorption occurs via ligand exchange with reactive surface hydroxyl groups; (3) no surface complexes are formed with background electrolyte ions; (4) the relationship between surface charge, o (molc .L-1), and surface potential, y (V), is linear and is given by

where C (F. m-2) is the capacitance, S (m2 . g-1) is the surface area, a (g.L-1) is the solid concentration, and F (C . molc-1) is the Faraday constant. The structure of the solid-solution interface for the constant capacitance model is depicted in Figure 3 . 1 .

In the constant capacitance model, the protonation and dissociation reactions of the reactive surface site are

Charge

Surface Species a

figure 3.1

Structure of the solid-solution interface for the constant capacitance model .

For soils, the SOH reactive site is generic, representing reactive hydroxyl groups including aluminol and silanol groups on the edges of clay mineral particles The surface complexation reactions for the adsorption of arsenate and selenite are

SOH + H3AsO4 o SH2AsO4 + H2O (3 . 7)

SOH + H3AsO4 o SHAsO- + H + + H2O

SOH + H3AsO4 o SAsOt + 2H + + H2O (3 9)

The equilibrium constants for the above reactions are

K- (int) = [SP ][H+] exp(-FV / RT )

K finrt = [SH2^^ As( ' [S0H][H3ÄS04] (3.13)

ka (int)=[smHA0]exp{-F^ 'RT ) (3 .14)

K (int) = ttAsOf ][H +] eXp(_2F¥ / RT) * [SOH][H3 AsO4] y (3 .15)

(int) = [S^H][H2Se03]eXp("F¥ ' RT) (3 .16)

In the constant capacitance model, charged surface complexes create an average electric potential field at the solid surface. These coulombic forces provide the dominant contribution to the solid-phase activity coefficients because the contribution from other forces is considered equal for all surface complexes In this manner, the exponential terms can be considered solidphase activity coefficients that correct for the charges on the surface complexes (Sposito, 1983). The mass balance of the surface reactive site for arsenate adsorption is

[SOH]r = [SOH] + [SOH2+ ] + [SO-] + [SH2 AsO4]

+ [SHASO4- ] + [SAO42- ] (3 17)

and for selenite adsorption is

[SOH]t = [SOH] + [SOH2+ ] + [SO-] + [SSeO3-] (3 .18)

where SOHT is the total number of reactive sites . Charge balance for arsenate adsorption is a = [SOH2+ ] - [SO-] - [SHAsOf ] - 2[SAsO42- ] (3 . 19)

and for selenite adsorption it is o = [SOH2+] - [SO- ] - [SSeOa- ] (3 . 20)

The above systems of equations can be solved using a mathematical approach. The computer program FITEQL 3 .2 (Herbelin and Westall, 1996) is an iterative nonlinear least squares optimization program that was used to fit equilibrium constants to experimental adsorption data using the constant capacitance model The FITEQL 3 2 program was also used to predict chemical surface speciation using previously determined equilibrium constant values The stoichiometry of the equilibrium problem for the application of the constant capacitance model to arsenate and selenite adsorption is shown in Table 3 .1 . The assumption that arsenate and selenite adsorptions take place on only one set of reactive surface sites is clearly a gross simplification because soils are complex multisite mixtures of a variety of reactive sites Therefore, the surface complexation constants determined for soils will

TABLE 3.1

Stoichiometry of the Equilibrium Problem for the Constant Capacitance Model

TABLE 3.1

Stoichiometry of the Equilibrium Problem for the Constant Capacitance Model

Species |
Components | |||

SOH |
eFy/RT |
HXA- |
H+ | |

H+ |
0 |
0 |
0 |
1 |

OH- |
0 |
0 |
0 |
-1 |

soh2+ |
1 |
1 |
0 |
1 |

SOH |
1 |
0 |
0 |
0 |

SO- |
1 |
-1 |
0 |
-1 |

H3AsO4 |
0 |
0 |
1 |
0 |

H2AsO4- |
0 |
0 |
1 |
-1 |

HAsO42- |
0 |
0 |
1 |
-2 |

AsO43- |
0 |
0 |
1 |
-3 |

H2SeO3 |
0 |
0 |
1 |
0 |

HSeO3- |
0 |
0 |
1 |
-1 |

SeO32- |
0 |
0 |
1 |
-2 |

SH2AsO4 |
1 |
0 |
1 |
0 |

SHAsO4- |
1 |
-1 |
1 |
-1 |

SAsO42- |
1 |
-2 |
1 |
-2 |

SSeO3- |
1 |
-1 |
1 |
-1 |

a A is an anion and x is the number of protons in the undissociated form of the acid.

a A is an anion and x is the number of protons in the undissociated form of the acid.

be average composite values that include soil mineralogical characteristics and competing ion effects

The total number of reactive surface sites, SOHT (mol .L-1), is an important input parameter in the constant capacitance model It is related to the reactive surface site density, Ns (sites .nm-2):

where NA is Avogadro's number. Values of surface site density can be determined using a wide variety of experimental methods, including potentio-metric titration and maximum ion adsorption Site density results can vary by an order of magnitude between methods The ability of the constant capacitance model to describe anion adsorption is dependent on the reactive site density (Goldberg, 1991) A surface site density value of 2 31 sites per nm-2 was recommended for natural materials by Davis and Kent (1990) This value has been used in the constant capacitance model to describe selenite adsorption by soils . A reactive surface site number of 21 . 0 ]mol .L-1 was used to describe arsenate adsorption by soils

For application of the constant capacitance model to soils, the capacitance value was chosen from the literature To describe arsenate and selenite adsorption, the capacitance was set at 1 06 F m-2, considered optimum for aluminum oxide by Westall and Hohl (1980) . For the development of self-consistent parameter databases, a constant value of capacitance is necessary

Protonation and dissociation constant values were obtained from the literature for arsenate adsorption and by computer optimization for selenite adsorption. To describe arsenate adsorption, the protonation constant, log K+, was set to 7.35 and the dissociation constant, log K, was set to -8 .95 . These values are averages of a literature compilation of protonation-dissociation constants for aluminum and iron oxides obtained by Goldberg and Sposito (1984)

Surface complexation constants for arsenate and selenite adsorption by soils were obtained using computer optimization . An evaluation of the goodness of model fit can be obtained from the overall variance V in Y:

where SOS is the weighted sum of squares of the residuals and DF represents the degrees of freedom

Recently, general prediction models have been developed to obtain anion surface complexation constants from easily measured soil chemical properties—cation exchange capacity, surface area, organic carbon, inorganic carbon, Fe oxide, and Al oxide content—that correlate with soil adsorption capacity for trace element anions This approach has been successfully applied to predict adsorption of arsenate (Goldberg et al , 2005) and selenite (Goldberg, Lesch, and Suarez, 2007) adsorption by soils In this approach, arsenate and selenite adsorption behavior by soils is predicted independently of experimental adsorption measurements using the general prediction models

Trace element adsorption was investigated using 53 surface and subsurface samples from soils belonging to 6 different soil orders chosen to provide a wide range of soil chemical properties . Soil chemical characteristics are listed in Table 3. 2 . Soils Altamont to Yolo constitute a set of 21 soil series from the southwestern Unites States, primarily California This set of soils consists mainly of alfisols and entisols Soils Bernow to Teller constitute a set of 17 soil series from the midwestern United States, primarily Oklahoma This set of soils consists mainly of mollisols

Soil pH values were measured in 1:5 soil:deionized water extracts (Thomas, 1996) Cation exchange capacities were obtained by sodium saturation and magnesium extraction (Rhoades, 1982) Ethylene glycol monoethyl ether adsorption was used to determine surface areas (Cihacek and Bremner, 1979) . Free Fe and Al oxides were extracted with citrate buffer and hydrosulfite (Coffin, 1963); Al and Fe concentrations were measured using inductively coupled plasma optical emission spectrometry (ICP-OES) Carbon contents were obtained using a carbon coulometer Organic C was calculated as the difference between total C measured by combustion at 950°C and inorganic C determined by acidification and heating (Goldberg et al ., 2005, Goldberg, Lesch, and Suarez, 2007)

Adsorption experiments were carried out in batch systems to determine adsorption envelopes, the amount of ion adsorbed as a function of solution pH at fixed total ion mass One-gram samples of soil were equilibrated with 25 mL of 0 . 1 M NaCl background electrolyte solution on a shaker for 2 hours . The equilibrating solution contained 20 ]mol . L-1 of As(V) or Se(IV) and had been adjusted to the desired pH range of 2 to 10 using 1 M HCl or 1 M NaOH . After reaction, the samples were centrifuged, decanted, analyzed for pH, filtered, and analyzed for As or Se concentration using ICP-OES Additional experimental details are provided in Goldberg et al (2005) for As(V) and in Goldberg, Lesch, and Suarez (2007) for Se(IV) adsorption

Arsenate adsorption envelopes were determined for 27 southwestern and 22 midwestern soil samples Arsenate adsorption increased with increasing solution pH, exhibited an adsorption maximum in the pH range 6 to 7, and decreased with further increases in solution pH, as can be seen in Figure 3 . 2 . Selenite adsorption envelopes were determined for 23 southwestern and 22 midwestern soil samples Selenite adsorption decreased with increasing solution pH over the pH range 2 to 10, as can be seen in Figure 3 . 3 .

The constant capacitance model was fit to the As(V) adsorption envelopes by optimizing the three As(V) surface complexation constants( log K1As, log K2As, and log K3As) simultaneously. The protonation constant was fixed at log

TABLE 3.2

Chemical Characteristics of Soils

TABLE 3.2

Chemical Characteristics of Soils

Depth |
mmolc |
S |
IOC |
OC |
Fe |
Al | ||

Soil Series |
cm |
pH |
kg-1 |
m2.g-1 |
g.kg-1 |
g.kg-1 |
g.kg-1 |
g.kg-1 |

Altamont |
0-25 |
5.90 |
152 |
103 |
0.0099 |
9.6 |
7.7 |
0.58 |

25-51 |
5.65 |
160 |
114 |
0.011 |
6.7 |
8.2. |
0.64. | |

0-23 |
6.20 |
179 |
109 |
0.12 |
30.8 |
9.2 |
0.88 | |

Arlington |
0-25 |
8.17 |
107 |
61.1 |
0.30 |
4.7 |
8.2 |
0.48 |

25-51 |
7.80 |
190 |
103 |
0.16 |
2.8 |
10.1 |
0.60 | |

Avon |
0-15 |
6.91 |
183 |
60.1 |
0.083 |
30.8 |
4.3 |
0.78 |

Bonsall |
0-25 |
5.88 |
54 |
15.7 |
0.13 |
4.9 |
9.3 |
0.45 |

25-51 |
5.86 |
122 |
32.9 |
0.07 |
2.1 |
16.8 |
0.91 | |

Chino |
0-15 |
10.2 |
304 |
159 |
6.4 |
6.2 |
4.7 |
1.64 |

Diablo |
0-15 |
7.58 |
301 |
190 |
0.26 |
19.8 |
7.1 |
1.02 |

0-15 |
7.42 |
234 |
130 |
2.2 |
28.3 |
5.8 |
0.84 | |

Fallbrook |
0-25 |
6.79 |
112. |
68.3 |
0.023 |
3.5 |
6.9. |
0.36 |

25-51 |
6.35 |
78 |
28.5 |
0.24 |
3.1 |
4.9 |
0.21 | |

Fiander |
0-15 |
9.60 |
248 |
92.5 |
6.9 |
4.0 |
9.2 |
1.06 |

Haines |
20 |
9.05 |
80 |
59.5 |
15.8 |
14.9 |
1.7 |
0.18 |

Hanford |
0-10 |
8.40 |
111 |
28.9 |
10.1 |
28.7 |
6.6 |
0.35 |

Holtville |
61-76 |
8.93 |
58 |
43.0 |
16.4 |
2.1 |
4.9 |
0.27 |

Imperial |
15-46 |
8.58 |
198 |
106 |
17.9 |
4.5 |
7.0 |
0.53 |

Nohili |
0-23 |
8.03 |
467 |
286 |
2.7 |
21.3 |
49.0 |
3.7 |

Pachappa |
0-25 |
6.78 |
39. |
15.1 |
0.026 |
3.8 |
7.6 |
0.67 |

25-51 |
7.02 |
52 |
41.0 |
0.014 |
1.1 |
7.2. |
0.35 | |

0-20 |
8.98 |
122 |
85.8 |
0.87 |
3.5 |
5.6 |
0.86 | |

Porterville |
0-7.6 |
6.83 |
203 |
137 |
0.039 |
9.4 |
10.7 |
0.90 |

Ramona |
0-25 |
5.89 |
66 |
27.9 |
0.02 |
4.4 |
4.5 |
0.42 |

25-51 |
6.33 |
29 |
38.8 |
0.018 |
2.2 |
5.9 |
0.40 | |

Reagan |
Surface |
8.39 |
98 |
58.8 |
18.3 |
10.1 |
4.6 |
0.45 |

Ryepatch |
0-15 |
7.98 |
385 |
213 |
2.5 |
32.4 |
2.6 |
0.92 |

Sebree |
0-13 |
5.99 |
27 |
21.2 |
0.0063 |
2.2 |
6.0 |
0.46 |

Wasco |
0-5.1 |
5.01 |
71 |
30.9 |
0.009 |
4.7 |
2.4 |
0.42 |

Wyo |
6.26 |
155 |
53.9 |
0.014 |
19.9 |
9.5 |
0.89 | |

Yolo |
0-15 |
8.43 |
177 |
73.0 |
0.23 |
11.5 |
15.6 |
1.13 |

Bernow |
B |
4.15 |
77.6 |
46.4 |
0.0028 |
3.8 |
8.1 |
1.1 |

Canisteo |
A |
8.06 |
195 |
152 |
14.8 |
34.3 |
1.7 |
0.44 |

Dennis |
A |
5.27 |
85.5 |
40.3 |
0.0014 |
18.6 |
12.9 |
1.7 |

B |
5.43 |
63.1 |
72.4 |
0.0010 |
5.2 |
30.0 |
4.1 | |

Dougherty |
A |
4.98 |
3.67 |
241 |
0.0010 |
7.0 |
1.7 |
0.28 |

Hanlon |
A |
7.41 |
142 |
58.7 |
2.6 |
15.1 |
3.7 |
0.45 |

Kirkland |
A |
5.05 |
154 |
42.1 |
0.014 |
12.3 |
5.6 |
0.80 |

Luton |
A |
6.92 |
317 |
169 |
0.099 |
21.1 |
9.1 |
0.99 |

Mansic |
A. |
8.32 |
142 |
42.2 |
16.7 |
10.1 |
2.7 |
0.40 |

B |
8.58 |
88.1 |
35.5 |
63.4 |
9.0 |
1.1 |
0.23 |

TABLE 3.2 (Continued)

Chemical Characteristics of Soils

Depth mmolc S IOC OC Fe Al

Soil Series cm pH kg-1 m2.g-1 g.kg-1 g.kg-1 g.kg-1 g.kg-1

TABLE 3.2 (Continued)

Chemical Characteristics of Soils

Depth mmolc S IOC OC Fe Al

Soil Series cm pH kg-1 m2.g-1 g.kg-1 g.kg-1 g.kg-1 g.kg-1

Norge |
A |
3.86 |
62.1 |
21.9 |
0.0010 |
11. 6 |
6.1 |
0.75 |

Osage |
A |
6.84 |
377 |
134 |
0 59 |
29 2 |
15 9 |
1 4 |

B |
6.24 |
384 |
143 |
0 0100 |
18 9 |
16 5 |
1 3 | |

Pond Creek |
A |
4.94 |
141 |
35 4 |
0 0023 |
16 6 |
5 2 |
0 70 |

B |
6.78 |
106 |
59 6 |
0 016 |
5 0 |
5 1 |
0 81 | |

Pratt |
A |
5.94 |
23 9 |
12 3 |
0 0026 |
4 2 |
1 2 |
0 18 |

B |
5.66 |
23 3 |
117 |
0 0007 |
2 1 |
0 92 |
0 13 | |

Richfield |
B |
7.12 |
275 |
82 0 |
0 040 |
8 0 |
5 4 |
0 76 |

Summit |
A |
7.03 |
374 |
218 |
0 25 |
26 7 |
16 2 |
2 3 |

B |
6 23 |
384 |
169 |
0 0079 |
10 3 |
17 8 |
2 5 | |

Taloka |
A |
4 88 |
47 4 |
87 0 |
0 0021 |
9 3 |
3 6 |
0 62 |

Teller |
A |
4.02 |
43.1 |
227 |
0.0008 |
6.8 |
3.2 |
0.53 |

Source: Adapted from Goldberg, S ., S .M . Lesch, D. L . Suarez, and N . T. Basta. 2005. Soil Sci. Soc.

Am. J. 69: 1389-1398; Goldberg, S., S.M . Lesch, and D. L. Suarez . 2007. Geochim.

Cosmochim. Acta 71: 5750-5762.

Source: Adapted from Goldberg, S ., S .M . Lesch, D. L . Suarez, and N . T. Basta. 2005. Soil Sci. Soc.

Am. J. 69: 1389-1398; Goldberg, S., S.M . Lesch, and D. L. Suarez . 2007. Geochim.

Cosmochim. Acta 71: 5750-5762.

K+ = 7. 35 and the dissociation constant was fixed at log K = -8 .95 . The ability of the model to describe the As(V) adsorption data was very good . Figure 3 . 2 shows some model fits for surface horizons . Values of the optimized As(V) surface complexation constants are provided in Table 3.3 . For the Bernow, Canisteo, Summit B, and Nohili soils, only two surface complexation constants were optimized because log K2As did not converge .

The constant capacitance model was fit to the Se(IV) adsorption envelopes by optimizing the Se(IV) surface complexation constant (log K2Se) because log K1 Se converged for only five of the soils . Subsequently, to improve the model fit, the protonation constant (log K+) and the dissociation constant (log K-) were simultaneously optimized with log K2Se . Because initial optimizations indicated that the deprotonated surface species was present in only trace amounts (log K- < -39), it was omitted from the final optimizations . The ability of the model to describe the Se(IV) adsorption data was very good . Figure 3 .3 shows some model fits for surface horizons . Values of the optimized Se(IV) surface complexation constants are provided in Table 3 .4 . Optimized constants are not listed for soils having >1% inorganic C because the model could not converge log K2Se and log K+ simultaneously.

A general regression modeling approach was used to relate the constant capacitance model As(V) and Se(IV) surface complexation constants to the following soil chemical properties: cation exchange capacity, surface area, inorganic carbon content, organic carbon content, iron oxide content, and aluminum oxide content An exploratory data analysis revealed that the As(V) and Se(IV) surface complexation constants were linearly related to

figure 3.2

Fit of the constant capacitance model to As(V) adsorption on southwestern soils (a, c) and midwestern soils (b, d): (a) Altamont soil, (b) Dennis soil, (c) Pachappa soil, and (d) Pond Creek soil . Circles represent experimental data . Model fits are represented by solid lines . (Source: Adapted from Goldberg, S., S.M . Lesch, D. L . Suarez, and N .T. Basta. 2005. Soil Sci. Soc. Am. J. 69: 1389-1398.)

figure 3.2

Fit of the constant capacitance model to As(V) adsorption on southwestern soils (a, c) and midwestern soils (b, d): (a) Altamont soil, (b) Dennis soil, (c) Pachappa soil, and (d) Pond Creek soil . Circles represent experimental data . Model fits are represented by solid lines . (Source: Adapted from Goldberg, S., S.M . Lesch, D. L . Suarez, and N .T. Basta. 2005. Soil Sci. Soc. Am. J. 69: 1389-1398.)

each of the log transformed chemical properties . Therefore, the following initial regression model was specified for each of the As(V) and Se(IV) surface complexation constants:

LogKj = po j + Pi j (ln CEC) + p2 j (ln SA) + pa j (ln(iOC)

+ p4 j (ln OC) + p5 j (ln Fe) + p6 j (ln Al) + e (3 . 23)

where the P^ represent regression coefficients, e represents the residual error component, and j = 1, 2 for southwestern and midwestern soils, respectively.

For As(IV) and Se(IV), an initial analysis of the regression model presented by Equation (3 . 23) yielded rather poor results when the two sets of soils were considered together. Additional statistical analyses revealed that the midwestern and southwestern soils represented two distinct populations exhibiting different soil property and surface complexation constant relationships . A multivariate analysis of covariance established a common intercept and common ln(CEC) term for the general regression prediction equations for As(V) adsorption For Se(IV) adsorption, a multivariate analysis of covari-ance established a common ln(SA) term for log K2Se and a common ln(Fe) term for log K+ .

Chemical Equilibrium and Reaction Modeling of Arsenic and Selenium in Soils 81 TABLE 3.3

Constant Capacitance Model Surface Complexation Constants for As(V) Adsorption Depth Optimized Optimized Optimized Predicted Predicted Predicted

Chemical Equilibrium and Reaction Modeling of Arsenic and Selenium in Soils 81 TABLE 3.3

Constant Capacitance Model Surface Complexation Constants for As(V) Adsorption Depth Optimized Optimized Optimized Predicted Predicted Predicted

Soil Series |
(cm) |
LogK!A8 |
LogK2A8 |
LogK3A8 |
LogK^A, |
LogK2A, |
LogK3A, |

Altamont |
0-25 |
9.99 |
3.92 |
-3.89 |
9.88 |
3.56 |
-4.10 |

25-51 |
10.09 |
4 41 |
-3.69 |
9 98 |
3 56 |
-4 08 | |

Arlington |
0-25 |
9.57 |
2 04 |
-4.59 |
9 99 |
3 20 |
-4 15 |

25-51 |
9.95 |
2 92 |
-4.24 |
10 20 |
3 33 |
-4 10 | |

Avon |
0-15 |
9.29 |
3 02 |
-4 52 |
9 38 |
3 22 |
-4 42 |

Bonsall |
0-25 |
9 50 |
2 77 |
-4 64 |
9 92 |
3 20 |
-4 15 |

25-51 |
10 90 |
3 64 |
-3 27 |
10 47 |
3 56 |
-3 82 | |

Diablo |
0-15 |
9 26 |
3 14 |
-4 45 |
9 90 |
3 51 |
-3 96 |

Fallbrook |
0-25 |
10 02 |
3 00 |
-4 20 |
9 93 |
3 30 |
-4 27 |

25-51 |
9 56 |
2 84 |
-4 62 |
9 68 |
2 85 |
-4 57 | |

Fiander |
0-15 |
10.08 |
2 10 |
-4.76 |
10 14 |
3 06 |
-4 14 |

Haines |
20 |
9 43 |
2 39 |
-4 01 |
9 33 |
2 60 |
-4 45 |

Hanford |
0-10 |
9 83 |
3 04 |
-4 16 |
9 53 |
2 92 |
-4 28 |

Holtville |
61-76 |
10 32 |
3 66 |
-3 88 |
9 97 |
2 67 |
-4 26 |

Imperial |
15-46 |
10 23 |
3 77 |
-3 77 |
10 10 |
2 98 |
-4 08 |

Nohili |
0-23 |
12 82 |
-2 21 |
10 74 |
4 04 |
-3 17 | |

Pachappa |
0-25 |
9 67 |
3 55 |
-4 15 |
9 91 |
3 26 |
-4 15 |

25-51 |
10 03 |
3 06 |
-4 44 |
10 05 |
3 16 |
-4 33 | |

Porterville |
0-7 6 |
10 36 |
3 89 |
-3 60 |
10 14 |
3 68 |
-3 84 |

Ramona |
0-25 |
9 58 |
2 79 |
-4 37 |
9 55 |
3 02 |
-4 59 |

25-51 |
9 96 |
2 99 |
-4 46 |
9 93 |
3 19 |
-4 18 | |

Reagan |
Surface |
9 66 |
2 94 |
-4 07 |
9 74 |
2 84 |
-4 18 |

Ryepatch |
0-15 |
9 40 |
3 07 |
-4 70 |
9 50 |
3 11 |
-4 26 |

Sebree |
0-13 |
9 64 |
3 28 |
-4 70 |
9 76 |
3 11 |
-4 41 |

Wasco |
0-5 1 |
9 65 |
3 31 |
-4 45 |
9 46 |
3 04 |
-4 59 |

Wyo |
10 36 |
3 67 |
-3 80 |
9 79 |
3 62 |
-4 06 | |

Yolo |
0-15 |
10 00 |
3 96 |
-3 86 |
10 09 |
3 51 |
-3 93 |

Bernow |
B |
12 84 |
-1 78 |
11 21 |
5 29 |
-2 40 | |

Canisteo |
A |
10 54 |
-3 70 |
9 39 |
2 21 |
-5 11 | |

Dennis |
A |
10 99 |
5 02 |
-2 57 |
11 06 |
5 28 |
-2 77 |

B |
12 51 |
6 93 |
-0 73 |
12 50 |
6 97 |
-0 83 | |

Dougherty |
A |
9.49 |
3 23 |
-4 21 |
9.69 |
3 21 |
-4 13 |

Hanlon |
A |
10 11 |
3 18 |
-4 17 |
10 35 |
3 61 |
-3 66 |

Kirkland |
A |
10 44 |
5 25 |
-3 14 |
10 42 |
4 26 |
-3 60 |

Luton |
A |
10 46 |
4 46 |
-3 31 |
10 96 |
4 66 |
-3 23 |

Mansic |
A |
9 71 |
3 05 |
-4 24 |
10 26 |
3 34 |
-3 65 |

B |
10 21 |
2 58 |
-3 65 |
9 47 |
2 19 |
-4 53 | |

Norge |
A |
10 31 |
3 90 |
-3 99 |
10 37 |
4 46 |
-3 47 |

Osage |
A |
11 75 |
5 08 |
-2 63 |
11 55 |
5 27 |
-2 49 |

B |
12 26 |
5 97 |
-1 86 |
11 43 |
5 50 |
-2 66 | |

—continued |

TABLE 3.3 (Continued)

Constant Capacitance Model Surface Complexation Constants for As(V) Adsorption

TABLE 3.3 (Continued)

Constant Capacitance Model Surface Complexation Constants for As(V) Adsorption

Soil Series |
Depth (cm) |
Optimized Optimized Optimized L°gK1As LogK2A8 LogK3A8 |
Predicted LogK1As |
Predicted LogK2As |
Predicted LogK3As | ||

Pond |
A |
10.02 |
4.44 |
-3.86 |
10.09 |
4.04 |
-4.05 |

Creek |
B |
10 85 |
4 98 |
-3.01 |
10 73 |
4 53 |
-3 09 |

Pratt |
A |
9 14 |
2 56 |
-4.78 |
9 09 |
2 73 |
-4 75 |

B |
9 26 |
2 55 |
-4.64 |
9 17 |
2 69 |
-4 87 | |

Richfield |
B |
10 00 |
3 85 |
-4 17 |
10 62 |
4 34 |
-3 45 |

Summit |
A |
11 65 |
-2 57 |
11 58 |
5 34 |
-2 51 | |

B |
13 14 |
-1 61 |
11 73 |
5 85 |
-2 24 | ||

Taloka |
A |
10 25 |
4 11 |
-3 89 |
10 09 |
3 88 |
-3 92 |

Teller |
A |
10 20 |
3 61 |
-4 34 |
10 10 |
3 87 |
-3 99 |

Source: Adapted from Goldberg, S ., S .M . Lesch, D . L . Suarez, and N . T. Basta. 2005. Soil Sci. Soc. Am. J. 69: 1389-1398.

figure 3.3

Fit of the constant capacitance model to Se(IV) adsorption on southwestern soils (a, c) and midwestern soils (b, d): (a) Bonsall soil; (b) Pond Creek soil; (c) Pachappa soil; (d) Summit soil. Circles represent experimental data. Model fits are represented by solid lines . (Source: Adapted from Goldberg, S., S.M . Lesch, and D. L . Suarez . 2007. Geochim. Cosmochim. Acta 71: 5750-5762.)

TABLE 3.4

Constant Capacitance Model Surface Complexation Constants for Se(IV) Adsorption

TABLE 3.4

Constant Capacitance Model Surface Complexation Constants for Se(IV) Adsorption

Depth |
Optimized |
Optimized |
Predicted |
Predicted | |

Soil Series |
(cm) |
LogK2Se |
LogK+ |
LogK2Se |
LogK+ |

Altamont |
0-20 |
-1.42 |
2.72 |
-1.23 |
2.79 |

Arlington |
0-25 |
-1. 04 |
2 82 |
-0 88 |
2 81 |

Avon |
0-15 |
-1 24 |
2 27 |
-1 21 |
2 16 |

Bonsall |
0-25 |
-0.90 |
2 80 |
-0 62 |
2 81 |

Chino |
0-15 |
-1 57 |
2 96 |
-1 42 |
2 72 |

Diablo |
0-15 |
-1 57 |
2 11 |
-1 47 |
2 68 |

0-15 |
-1 75 |
2 85 |
-1 41 |
2 77 | |

Fallbrook |
25-51 |
-0 73 |
2 53 |
-0 70 |
2 38 |

Fiander |
0-15 |
-1 01 |
3 20 |
-0 99 |
3 25 |

Haines |
20 |
-1 40 |
2 04 | ||

Hanford |
0-10 |
-0 53 |
2 68 |
-0 81 |
3 04 |

Holtville |
61-76 |
-0 82 |
2 87 | ||

Imperial |
15-46 |
-1 13 |
3 15 | ||

Nohili |
0-23 |
-1 10 |
4 44 | ||

Pachappa |
0-25 |
2 17 |
-0 69 |
2 47 | |

25-51 |
-0.53 |
2 50 |
-0 65 |
2.35 | |

0-20 |
-1 22 |
3 10 |
-1 09 |
2 63 | |

Porterville |
0-7 6 |
-1 04 |
2 86 |
-1 26 |
2 78 |

Reagan |
Surface |
-1 09 |
2 83 | ||

Sebree |
0-13 |
-0 47 |
2 11 |
-0 53 |
2 12 |

Wasco |
0-5 1 |
-0 93 |
1 28 |
-1 19 |
1 45 |

Wyo |
-0.58 |
2 79 |
-1 05 |
2 57 | |

Yolo |
0-15 |
-0 79 |
3 28 |
-0 85 |
3 27 |

Bernow |
B |
0 62 |
2 85 |
0 59 |
2 24 |

Canisteo |
A |
1 77 |
1 77 | ||

Dennis |
A |
0 31 |
2 36 |
0 38 |
2 25 |

B |
1 63 |
2 19 | |||

Dougherty |
A |
-1 77 |
2 11 |
-1 94 |
2 14 |

Hanlon |
A |
-0 92 |
2 50 |
-0 96 |
2 37 |

Kirkland |
A |
-0 06 |
1 76 |
-0 31 |
2 21 |

Luton |
A |
-0 79 |
2 33 |
-0 59 |
2 41 |

Mansic |
A |
-0 97 |
2 21 | ||

B |
-1 78 |
1 96 | |||

Norge |
A |
-0 24 |
2 08 |
0 06 |
2 33 |

Osage |
A |
0 15 |
2 13 |
-0 08 |
2 57 |

B |
0.22 |
3 24 |
0 14 |
2 65 | |

Pond Creek |
A |
-0.44 |
2 07 |
-0 46 |
2 26 |

B |
0 03 |
1 89 |
-0 11 |
2 13 | |

Pratt |
A |
-0 99 |
2 56 |
-0 92 |
2 23 |

B |
-1.59 |
2 00 |
-1 73 |
2 29 | |

Richfield |
B |
-0 77 |
2 22 |
-0 40 |
2 23 |

Summit |
A |
-0 14 |
2 66 |
-0 20 |
2 18 |

B |
0 49 |
1 54 |
0 44 |
2 18 | |

Taloka |
A |
-0 88 |
2 38 |
-0 91 |
2 08 |

Teller |
A |
-1.46 |
2.15 |
-1.25 |
2.11 |

Source: Adapted from Goldberg, S ., S .M . Lesch, and D . L . Suarez . 2007. Geochim. Cosmochim. Acta 71: 5750-5762.

The prediction equations for obtaining As(V) surface complexation constants to describe As(V) adsorption with the constant capacitance model are

LogK^ = 10.64 - 0.107 ln(CEC) + 0.094 ln(SA) + 0.078 ln( IOC)

- 0.365 ln(OC) + 1.09ln(Fe) (3 . 24)

LogKAs = 3.39 - 0.083 ln(CEC) + 0.018 ln(SA) - 0.002 ln(iOC)

- 0.400 ln(OC) +1.36ln(Fe) (3 . 25)

LogKA = -2.58 - 0.296 ln(CEC) - 0.004 ln(SA) + 0.115 ln(iOC)

- 0.570 ln(OC) + 1.38ln(Fe) (3 . 26)

for midwestern soils,

LogKA = 10.65 - 0.107ln(CEC) + 0.256 ln(SA) + 0.022 ln(iOC)

- 0.143 ln(OC) + 0.385 ln(Fe) (3 . 27)

LogKA = 3.39 - 0.083 ln(CEC) + 0.247 ln(SA) - 0.061 ln(iOC)

- 0.104 ln(OC) + 0.313 ln(Fe) (3 . 28)

LogKA = -2.58 - 0.296 ln(CEC) - 0.376 ln(SA) + 0.024 ln(iOC)

- 0.085 ln(OC) + 0.363 ln(Fe) (3 . 29)

and for southwestern soils

The prediction equations for obtaining Se(IV) surface complexation constants to describe Se(IV) adsorption with the constant capacitance model are

LogK2Se = 0.675 - 0.380 ln(SA) - 0.083 ln(OC) + 0.274 ln(Fe) (3 . 30)

LogK+ = 3.36 + 0.115 ln( IOC) + 0.774ln(Fe) (3 31)

for midwestern soils

LogKi = 1.18 - 0.380 ln(SA) - 0.470 ln(OC) + 1.03ln(Fe)

LogK+ = 0.613 + 0.774 ln(Fe) - 0.811 ln( Al) (3 33)

for southwestern soils .

Surface complexation constants obtained with the prediction equations are provided in Table 3 .3 for As(V) and Table 3 .4 for Se(IV). A "jack-knifing" procedure was performed on Equations (3 . 24) to (3 .33) to assess their predictive ability. Jack-knifing is a technique where each observation is sequentially set aside, the equation is reestimated without this observation, and the set-aside observation is then predicted from the remaining data using the reestimated equation . A jack-knifing procedure indicated good general agreement between ordinary predictions and jack-knife estimates for both As(V) and Se(IV) surface complexation constants, suggesting predictive capabilities Additional details on statistical analyses are provided in Goldberg et al . (2005) for As(V) and Goldberg, Lesch, and Suarez (2007) for Se(IV)

The As(V) surface complexation constants were predicted using the prediction Equations (3 . 24) to (3 . 26) for midwestern soils and Equations (3 . 27) to (3 . 29) for southwestern soils . These surface complexation constants were then used in the constant capacitance model to predict As(V) adsorption on the soils The ability of the model to predict As(V) adsorption is shown in Figure 3 .4 for two soils not used to obtain the prediction equations . Prediction of As(V) adsorption by the Summit soil was good . Prediction of As(V) adsorption by the Nohili soil deviated from the experimental adsorption data by 30% or less, a reasonable result considering that the prediction was obtained without optimization of any adjustable parameters

The Se(IV) surface complexation constants were predicted using the prediction Equations (3 .30) and (3.31) for midwestern soils and Equations (3 .32) and (3 33) for southwestern soils These surface complexation constants were then used in the constant capacitance model to predict Se(IV) adsorption on the soils The ability of the model to predict Se(IV) adsorption is shown in Figure 3.5 for four soils . For the Pond Creek and Summit soils, the prediction equations provide descriptions of the experimental data that are comparable in quality to the optimized fits (compare Figures 3 .3b with 3 . 5b and 3 . 3d with 3 . 5d) . For the Bonsall and Pachappa soils, the prediction equations describe the experimental data less closely than the optimized fits (compare Figure 3 . 3a with 3 .5a and Figure 3 . 3c with 3 .5c) . However, the model always correctly predicts the shape of the adsorption envelope as a function of solution pH

figure 3.4

Constant capacitance model prediction of As(V) adsorption by soils not used to obtain the prediction equations: (a) Nohili soil and (b) Summit soil . Experimental data are represented by circles . Model predictions are represented by solid lines . (Source: Adapted from Goldberg, S., S.M. Lesch, D. L . Suarez, and N.T. Basta. 2005. Soil Sci. Soc. Am. J. 69: 1389-1398.)

Predictions of As(V) and Se(IV) adsorption were reasonable for most of the soils . These predictions were obtained independently of any experimental measurement of As(V) or Se(IV) adsorption on these soils, that is, solely from values of a few easily measured chemical properties . Incorporation of these prediction equations into chemical speciation transport models should allow simulation of As(V) and Se(IV) concentrations in soil solution under diverse environmental conditions

figure 3.4

Constant capacitance model prediction of As(V) adsorption by soils not used to obtain the prediction equations: (a) Nohili soil and (b) Summit soil . Experimental data are represented by circles . Model predictions are represented by solid lines . (Source: Adapted from Goldberg, S., S.M. Lesch, D. L . Suarez, and N.T. Basta. 2005. Soil Sci. Soc. Am. J. 69: 1389-1398.)

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