Method/Model

Methods

Adsorption isotherms

Linear distribution coefficient Langmuir

Freundlich

Models

Clay ion-exchange model

Triple-layer model

Relatively easy to measure. The main disadvantage is that the empirical coefficients may change with changing environmental conditions, requiring measurement.

Applicable only at very dilute concentrations of organic compounds and where >0.1% organic matter is present. Usefulness is uncertain.

Underlying assumptions for the derivation of the equation typically will not apply.

Limited available data on adsorption under simulated deep-well conditions are best described by the formula; however, the disadvantage of all adsorption isotherms applies.

May be useful for predicting adsorption of heavy metals. Aqueous-phase-activity solid-solution model coefficients can be obtained from distribution-of-species models. Estimating clay-phase activity coefficients is more problematic.

Of limited value because of the complexity of adsorption sites, unpredictable interactions among adsorbents, and complications introduced by high salinities.

Source: U.S. EPA, Assessing the Geochemical Fate of Deep-Well-Injected Hazardous Waste: A Reference Guide, EPA/625/6-89/025a, U.S. EPA, Cincinnati, OH, June 1990.

The amount of adsorption at concentrations other than those that were measured can then be predicted using the empirical constants in an appropriate formula. The correct application of this method requires acknowledging such effects as matrix and temperature.

Three types of adsorption isotherms are discussed in this section:

1. The linear distribution coefficient

2. The Langmuir adsorption isotherm

The distribution coefficient assumes that adsorption is linear (i.e., the amount of adsorption is directly proportional to the concentration of the compound in solution) and is actually a special case of the Langmuir and Freundlich isotherms, which are nonlinear.31,32

The simplest type of isotherm is the linear-distribution coefficient, Kd.121 It is also called the partition coefficient, Kp.58 The equation for calculating adsorption at different concentrations is

where S = amount adsorbed (|g/g solid), C = concentration of adsorbed substance in solution (|g/mL), and Kd = linear distribution coefficient = partition coefficient = Kp.

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 Hamaker and Thompson.131

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