Soil adsorption, equation

An example of using one predicted property to predict another is predicting the adsorption of chemicals in soil. This is usually done by first predicting an octanol water partition coelficient and then using an equation that relates this to soil adsorption. This type of property-property relationship is most reliable for monofunctional compounds. Structure-property relationships, and to a lesser extent group additivity methods, are more reliable for multifunctional compounds than this type of relationship. 

After an extensive study of the adsorption of arsenious oxide by metallic hydroxides,3 Sen concluded that this type of adsorption resembles that of cations by manganese dioxide, and that the chemical affinity between the adsorbent and the substance adsorbed plays an important part, thus differing from adsorption by charcoal. It has been observed that soils having a high absorption capacity for bases also absorb the arsenite ion from solutions of 0-001 to 0-01X concentration.4 The absorption increases with time, without reaching an end-point, and the process follows the normal adsorption equation C1=kC1Jn. The addition of ferric oxide or calcium carbonate to the soil considerably increases the capacity for absorption, but such salts as calcium sulphate or copper sulphate have no effect. 

In the geological and soil science literature, ion exchange and precipitation are frequently considered as adsorption and thermodynamically described by adsorption equations, or isotherms. This is not correct because, as shown previously, the processes are principally different adsorption is directed by the decrease of surface energy, and it takes place on the free surface sites ion exchange is just a competitive process on an already covered surface, determined by the ionic composition of the liquid phase. Precipitation, including colloid formation, is governed by the composition of the liquid phase, the crystal structure (coprecipitation), or primary chemical forces. 

The numerical solution to the advection-dispersion equation and associated adsorption equations can be performed using finite difference schemes, either in their implicit and/or explicit form. In the one-dimensional MRTM model (Selim et al., 1990), the Crank-Nicholson algorithm was applied to solve the governing equations of the chemical transport and retention in soils. The web-based simulation system for the one-dimensional MRTM model is detailed in Zeng et al. (2002). The alternating direction-implicit (ADI) method is used here to solve the three-dimensional models. 

If BCF is not available from experimental measurements, it can be estimated via correlation equations from water solubility (S), octanol-water partition coefficient (KQw) or soil adsorption coefficient (Koc). Of the three, correlations from Kow are considered the most reliable because they are currently based on the largest body of bioassay data and because measurements involve a water-lipophilic phase partitioning which bears obvious similarity to water-to-fish partitioning. One recommended correlation equation is (11) ... 

Nonionics have been shown also to be more effective than ionics in the removal of oily soil from relatively nonpolar substrates (polyester, nylon). On cotton, however, a relatively hydrophilic fiber, anionics can outperform nonionics in detergency, and both of these are superior to cationics (Fort, 1968). The effects here may be due to differences in the orientation of adsorption of the different types of surfactants on the different substrates. On nonpolar substrates and soils, POE nonionics are adsorbed (Chapter 2) from aqueous solution via dispersion forces or hydrophobic bonding with their hydrophobic POE groups oriented toward the adsorbent and their hydrophilic POE groups toward the bath. Adsorption of the surfactant in this fashion on the substrate lowers the substrate-bath interfacial tension jSB and facilitates soil removal (equation 10.3) adsorption in this fashion on both substrate and soil produces a steric barrier that inhibits soil redeposition. 

The important assumptions for the pesticide model are instantaneous, linear, reversible adsorption described by an adsorption partition coefficient, K, and first-order decay described by an overall decay rate, k. Parameters for the pesticide model include universal soil loss equation parameters (if erosion loss is to be modeled), pesticide application information (rate, date, and method of application), K, k, and a dispersion coefficient. 

Phosphate behavior is also described by Langmuir and Freundlich adsorption equations, although these models may be too simple to accurately explain soil phosphate behavior. Kinetic models of phosphate retention by soils are also being employed. Although kinetics can suggest retention mechanisms, the complexity of soil-phosphate behavior makes this prospect difficult to achieve. 

The rates of soil adsorption reactions may also depend on the exponential of the amount already adsorbed. Phosphate adsorption by soils, for example, sometimes follows the Elovich equation ... 

Colloid chemists commonly measure surface area by the adsorption of N2 gas. The adsorption is conducted in vacuum and at temperatures near the boiling point of liquid nitrogen (—196° C). The approach is based on the Brunauer-Emmett-Teller (BET) adsorption equation, and has been adapted to a commercially available instrument. Unfortunately, the technique does not give reliable values for expansible soil colloids such as vermiculite or montmorillonite. Nonpolar N2 molecules penetrate little of the interlayer regions between adjacent mineral platelets of expansible layer silicates where 80 to 90% of the total surface area is located. Several workers have used a similar approach with polar H2O vapor and have reported complete saturation of both internal (interlayer) and external surfaces. The approach, however, has not been popular as an experimental technique. 

The frequent good fit of adsorption data to the Freundlich equation is influenced by the insensitivity of log-log plots and by the flexibility afforded curve fitting by the two empirical constants K and n. This flexibility does not guarantee accuracy, however, if the data are extrapolated beyond the experimental range. The Freundlich equation has the further limitation that it does not predict a maximum adsorption capacity, however mythical the adsorption maximum may be. Despite its shortcomings, the Freundlich equation is a common adsorption equation and is included in several models for predicting pesticide behavior in soil. 

Methods using regression equations with soil adsorption coefficients or bioconcentration factors (Nos. 4 and 5 in Table 1-1) are not recommended because of the relatively large method errors that would be involved. 

Additional sources include the references cited in Table 1-2 of this chapter. Appropriate references in Chapters 2, 4, and 5 may also be helpful these chapters describe regression equations between Kow and (1) solubility, (2) soil adsorption coefficients, and (3) bioconcentration factors. 

Regarding the quantity of boron adsorbed, adsorption maxima calculated with the Langmuir adsorption equation 16,17, 25-27) vary from approximately 10 up to 100 figrams of B/gram of soil. Soils derived from volcanic ash deposits adsorb unusually large amounts of boron 16, 18) because of their enriched contents of amorphous materials with affinity for anions. 

Several mathematical models have been proposed for representing the overall adsorption of pesticides by soils. The most comprehensive one appears to be that of Lambert et al. (9), in which the partition of pesticides between soil water and soil is represented by a linear adsorption equation similar to the Langmuir equation. In this model they have assumed that the active adsorbent for pesticides in soils is the soil organic matter. This approach has been successful in modeling the adsorption of nonionic pesticides on soils (12), Lambert (13) has introduced an index of soil adsorption of pesticides which is intended to indicate the amount of active organic matter in a soil and therefore may be used to compare the adsorption capacity of one soil with that of another. Lambert states that the index is independent of the pesticide being adsorbed. 

The equilibrium between water and sediments can be described by the equation C = Kf.Cy where Cj = concentration of PCBs in sediments, CjY = concentration of PCBs in water and fCp = equilibrium constant that reflects the character of sediments. To calculate the Kf value, tabulated values of Kqq (soil adsorption coefficient) can be used and Kf values calculated using the equation Kf =Kfy,.TOC (total organic carbon). For a description of the behaviour (or distribution) of individual PCB congeners between water and sediments a linear relationship between K( and tabulated Kq values can be used logfr = 0.85 log Q y -F 0.13. The relationship is valid within the range of values of log Kq = 4.S-7.7. 

Many attempts have been made to devise an equation which will mathematically fit soil adsorption isotherms, but because of the complexity of soil surfaces, none have been found to be particularly successful. In the simplest case, the quantity adsorbed per unit weight, x/m, increases in direct proportion to the concentration in solution, C, and a constant called the distribution coefficient, K, relates the two terms ... 

Adsorption — An important physico-chemical phenomenon used in treatment of hazardous wastes or in predicting the behavior of hazardous materials in natural systems is adsorption. Adsorption is the concentration or accumulation of substances at a surface or interface between media. Hazardous materials are often removed from water or air by adsorption onto activated carbon. Adsorption of organic hazardous materials onto soils or sediments is an important factor affecting their mobility in the environment. Adsorption may be predicted by use of a number of equations most commonly relating the concentration of a chemical at the surface or interface to the concentration in air or in solution, at equilibrium. These equations may be solved graphically using laboratory data to plot "isotherms." The most common application of adsorption is for the removal of organic compounds from water by activated carbon. 

In the presence of NAPL, the concentration of contaminants in the soil moisture (Cw) can be calculated simply from the solubility of the compounds (equation 3 in Table 14.3). Adsorption of contaminants to the soil particles is a much more complex phenomenon, which depends both on contaminant properties and on soil characteristics. The simplest model for describing adsorption is based on the observation that organic compounds are preferentially bound to the organic matter of soil, and the following linear equation is proposed for calculating the adsorbed concentration (Cs) ... 

This equation is widely used to describe adsorption in soil and near-surface aquatic environments. Another widely used linear coefficient is the organic-carbon partition coefficient Koc, which is equal to the distribution coefficient divided by the percentage of organic carbon present in the system as proposed by Flamaker and Thompson.131... 

The TDE solute module is formulated with one equation describing pollutant mass balance of the species in a representative soil volume dV = dxdydz. The solute module is frequently known as the dispersive, convective differential mass transport equation, in porous media, because of the wide employment of this equation, that may also contain an adsorptive, a decay and a source or sink term. The one dimensional formulation of the module is ... 

From the pollutant and biological cycles the processes of advection, diffusion, volatilization (diffusion at the soil-air interface), adsorption or desorption (equilibrium), and degradation or decay, which are also the most important chemical processes in the soil zone. All other processes can be lumped together under the source or sink term of equation (3). 

PESTAN (12) is a dynamic TDE soil solute (only) model, requiring the steady-state moisture behavior components as user input. The model is based on the analytic solution of equation (3), and is very easy to use, but has also a limited applicability, unless model coefficients (e.g., adsorption rate) can be well estimated from monitoring studies. Moisture module requirements can be obtained by any model of the literature. 

The last two assumptions are the most critical and are probably violated under field conditions. Smith et al. (3) found that at least a half-hour was required to achieve adsorption equilibrium between a chemical in the soil water and on the soil solids. Solution of the diffusion equation has shown that many volatile compounds have theoretical diffusion half-lives in the soil of several hours. Under actual field conditions, the time required to achieve adsorption equilibrium will retard diffusion, and diffusion half-lives in the soil will be longer than predicted. Numerous studies have reported material bound irreversibly to soils, which would cause apparent diffusion half-lives in the field to be longer than predicted. 

Where AG is free energy, R is gas constant (1.987 cal/deg K mole-1), T is degrees Kelvin, and AS is entropy. Kd is the distribution constant of the herbicide between the solution phase and the adsorbed phase (equation 4). Thus, least squares linear regression analysis of ln(Kd) vs. 1/T yielded values for heats of adsorption (AH) for the herbicides in Keeton soil. 

Results of adsorption experiments for butylate, alachlor, and metolachlor in Keeton soil at 10, 19, and 30°C were plotted using the Freundlich equation. A summary of the coefficients obtained from the Freundlich equation for these experiments is presented in TABLE IV. Excellent correlation using the Freundlich equation over the concentration ranges studied (four orders of magnitude) is indicated by the r values of 0.99. The n exponent from the Freundlich equation indicates the extent of linearity of the adsorption isotherm in the concentration range studied. If n = 1 then adsorption is constant at all concentrations studied (the adsorption isotherm is linear) and K is equivalent to the distribution coefficient between the soil and water (Kd), which is the ratio of the soil concentration (mole/kg) to the solution concentration (mole/L). A value of n > 1 indicates that as the solution concentration increases the sorption sites become saturated, resulting in a disproportionate amount of chemical being dissolved. Since n is nearly equal to 1 in these studies, the adsorption isotherms are nearly linear and the values for Kd (shown in TABLE IV) correspond closely to K. These Kd values were used to calculate heats of adsorption (AH). 

TABLE IV. Adsorption Coefficients for Butylate, Alachlor, and Metolachlor in Keeton Soil at Various Temperatures Obtained Using the Freundlich Equation. ... 

Heats of Adsorption. Temperature effects were determined by measuring adsorption at three temperatures. As seen from TABLE IV, the K values vary with temperature such that for butylate, K increases with temperature, while for alachlor and metolachlor, K decreases with temperature. These results indicate that butylate becomes more adsorbed to Keeton soil as the temperature increases while alachlor and metolachlor become less adsorbed as temperature increases. In order to obtain a quantitative measure of these effects, heats of adsorption (AH) were calculated as described previously in the Materials and Methods section (equation 3). TABLE IV contains values for the average molar distribution constants (Kd) for butylate, alachlor, and metolachlor which were plotted vs the inverse temperatures (1/°K) to obtain the AH s shown in Figure 3. 

Pigna M, Colombo C, Violante A (2003) Competitive sorption of arsenate and phosphate on synthetic hematites (in Italian). Proceedings XXI Congress of Societa Italiana Chimica Agraria SICA (Ancona), pp 70-76 Quirk JP (1955) Significance of surface area calculated from water vapour sorption isotherms by use of the B. E. T. equation. Soil Sci 80 423-430 Rancourt DG, Fortin D, Pichler T, Lamarche G (2001) Mineralogical characterization of a natural As-rich hydrous ferric oxide coprecipitate formed by mining hydrothermal fluids and seawater. Am Mineral 86 834-851 Raven K, Jain A, Loeppert, RH (1998) Arsenite and arsenate adsorption on ferrihydrite kinetics, equilibrium, and adsorption envelopes. Environ Sci Technol 32 344-349... 

Loukidou et al. (2005) fitted the data for the equilibrium sorption of Cd from aqueous solutions by Aeromonas caviae to the Langmuir and Freundlich isotherms. They also conducted, a detailed analysis of sorption rates to validate several kinetic models. A suitable kinetic equation was derived, assuming that biosorption is chemically controlled. The so-called pseudo second-order rate expression could satisfactorily describe the experimental data. The adsorption data of Zn on soil bacterium Pseudomonas putida were fit with the van Bemmelen-Freundlich model (Toner et al. 2005). 

The adsorption and desorption of pyrethroids to and from soil and sediment are usually described either by the linear or Freundlich isotherm by using the following equations [9] ... 

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