Freundlich constants

The Langmuir and Freundlich equations have often been employed to model the sorption of metal ions by bacteria. Mullen et al. (1989) used the Freundlich isotherm to describe the sorption of Cd and Cu by B. cereus, B. subtilis, E. coli and P. aeruginosa over the concentration range of 0.001-lmM. The respective values of the Freundlich constant (Kf) indicated that E. coli was most efficient at sorbing Cd2+ and Cu2+. 

Chlorofluorocarbon (CFC) replacements have recently been used for their lower stability and because they have carbon-hydrogen bonds, which means that their atmospheric lifetime is expected to be much shorter than those of CFCs. The adsorption properties of l,l,2-trichloro-l,2,2-trifluoroethane (CFC 113) and its replacement compounds, l,l-dichloro-2,2,2-trifluoroethane (HCFC123), 1,1-dichloro-l-fluoroethane (HCFC141b), and l,l-dichloro-l,2,2,3,3-pentafluoropropane (HCFC225ca) on four kinds of activated carbons were investigated. The adsorption isotherms of inhalational anesthetics (halothane, chloroform, enflurane, isoflurane, and methoxyflurane) on the activated carbon were measured to evaluate the action mechanism of inhalational anesthesia. The anesthesia of CFC replacements can be estimated by the Freundlich constant N of the adsorption isotherms (Tanada et al., 1997). 

The Langmuir and Freundlich constants for several systems are presented in Table 1.23 and Table 1.24, respectively. 

Freundlich constants for several carbons and benzene (USACE, 2001) ... 

Freundlich constant, typically range between 0.75 and 0.95 = concentration of the organic chemical sorbed by the solid phase (mg/Kg)... 

The calculation of Kd shown above assumes a linear relationship between the concentration sorbed and the concentration of the chemical in the aqueous phase (i.e., a linear isotherm). If sorption was known to be non-linear, the Freundlich constant, N, would need to be known or an estimate of it would need to be made. Generally values of N range from 0.7 to 1.2. 

Freundlich constants and ranges of Kd values for radionuclide sorption on the Rattlesnake Ridge sandstone are given in Table III. The constants K and N were calculated using linear regression. Linear sorption isotherms (N = 1.0) are observed only for strontium, selenium, and radium. 

Table III. Freundlich Constants for Radionuclide Sorption (Molar Basis) on Sandstone...

Tin and americium were so extensively sorbed under all conditions that isotherm data could not be obtained. These elements are not significantly mobile in the Mabton Interbed aquifer. Values of Freundlich constants for technetium, radium, uranium, neptunium, and plutonium are given in Table IV. The Freundlich equation did not fit the selenium sorption data very well probably because of slow sorption kinetics or precipitation. Precipitation was also observed for technetium at 23°C for concentrations above 10 7M. This is about the same solubility observed for technetium in the sandstone isotherm measurements. Linear isotherms were observed only in the case of radium sorption. In general, sorption on the Mabton Interbed was greater than on the Rattlesnake Ridge sandstone. This is probably due to the greater clay content of the Mabton standard. 

Table IV. Freundlich Constants (Molar Basis) for Radionuclide Sorption on Mabton Interbed Solids...

Bacterial sorption of some metals can be described by the linearized Freundlich adsorption equation log S = log K+n log C, where S is the amount of metal absorbed in pmol g, C is the equilibrium solution concentration in pmol L, and K and n are the Freundlich constants. 

Using the techniques of analytic geometry, let us derive the Freundlich constants in a little more detail than used in the derivation of the constants in the discussion of reverse osmosis treated previously. As mentioned, the straight-line form of the equation requires only two experimental data points however, experiments are normally conducted to produce not just two pair of values but more. Thus, the experimental resnlts must be reduced to just the two pairs of values required for the determination of the parameters therefore, assuming there are m pairs of values, these m pairs must be reduced to just two pairs. Once the reduction to two pairs has been done, the isotherm equation may be then be written to just the two pairs of derived values as follows ... 

As was done with the Freundlich constants, the Langmnir equation may be manipnlated in order to solve the Langmnir constants. From the m pairs of experimental data... 

In this review we concentrate on the studies that attempt to elucidate the importance of carbon surface properties in controlling the equilibrium uptakes of aromatic and aliphatic adsorbates. Rather than comparing model parameters, such as Langmuir or Freundlich constants, we examine the uptakes at comparable equilibrium concentrations and attempt to rationalize the differences observed under different conditions and on different adsorbents. 

The Freundlich equation is often written in these two (equivalent) forms. F or Q is the quantity of (ad)sorbate associated with the (ad)sorbent, usually expressed as mol kg while [A] or Q, is the total chemical concentration of the (ad)sorbate in solution (e.g., in mol liter" ) m is referred to as the Freundlich constant and n is the measure of the nonlinearity involved. 

Sorption of Mo(VI) in these experiments can be described by the Freundlich isotherm. Freundlich constants for sorption from sewage-contaminated ground water were calculated from a linear plot of the concentration of Mo(VI) sorbed by sediment in each column compared to input concentration (Figure 1) using the following equation ... 

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