Showing papers on "Freundlich equation published in 1981"
354 citations
TL;DR: In this article, a multicomponent isotherm is derived based on the assumption that an exponential distribution of adsorption energies exists for each component in a k-component system.
318 citations
TL;DR: In this paper, the authors proposed a simplified method for multi-solute adoption prediction based on the ideal adsorbed solution (IAS) theory and Freundlich adsorption isotherms.
205 citations
TL;DR: A strong negative correlation was found between poliovirus adsorption and both the contents of organic matter and the available negative surface charge on the substrates as determined by their capacities for adsorbing the cationic polyelectrolyte, polydiallyldimethylammonium chloride.
Abstract: The adsorption of radiolabeled infectious poliovirus type 2 by 34 well-defined soils and mineral substrates was analyzed in a synthetic freshwater medium containing 1 mM CaCl2 and 1.25 mM NaHCO3 at pH 7. In a model system, adsorption of poliovirus by Ottawa sand was rapid and reached equilibrium within 1 h at 4°C. Near saturation, the adsorption could be described by the Langmuir equation; the apparent surface saturation was 2.5 × 106 plaque-forming units of poliovirus per mg of Ottawa sand. At low surface coverage, adsorption was described by the Freundlich equation. The soils and minerals used ranged from acidic to basic and from high in organic content to organic free. The available negative surface charge on each substrate was measured by the adsorption of a cationic polyelectrolyte, polydiallyldimethylammonium chloride. Most of the substrates adsorbed more than 95% of the virus. In general, soils, in comparison with minerals, were weak adsorbents. Among the soils, muck and Genesee silt loam were the poorest adsorbents; among the minerals, montmorillonite, glauconite, and bituminous shale were the least effective. The most effective adsorbents were magnetite sand and hematite, which are predominantly oxides of iron. Correlation coefficients for substrate properties and virus adsorption revealed that the elemental composition of the adsorbents had little effect on poliovirus uptake. Substrate surface area and pH, by themselves, were not significantly correlated with poliovirus uptake. A strong negative correlation was found between poliovirus adsorption and both the contents of organic matter and the available negative surface charge on the substrates as determined by their capacities for adsorbing the cationic polyelectrolyte, polydiallyldimethylammonium chloride.
150 citations
TL;DR: In this article, four adsorption equations were fitted to phosphate isotherm data for 38 soils from northern New South Wales, and the two-surface Langmuir equation provided the best fit to the data.
Abstract: Four adsorption equations were fitted to phosphate isotherm data for 38 soils from northern New South Wales. The two-surface Langmuir equation provided the best fit to the data. The Freundlich equation, however, was almost as effective, provided that an estimate of native adsorbed phosphate was included. It required fewer adsorption points because the transformed data produced a straight line. A regression constant, a, from the Freundlich equation although underestimating adsorption capacity, calculated from the Langmuir II equation, was highly correlated with this parameter (r = 0.984) and a buffering index (r = 0.986), calculated from the Langmuir I equation. The other Freundlich regression constant, n, was significantly correlated (P <1%) with the intensive parameters of adsorption from the one- and two-surface Langmuir equations. Since only two adsorption points are required for fitting the Freundlich equation and the parameters are easier to derive, it is suggested that this equation may be more suitable for commercial soil-testing laboratories than the Langmuir one- and two-surface equations for routine determination of phosphate adsorption characteristics of soils.
97 citations
TL;DR: In this paper, the problem of diffusion controlled adsorption kinetics is solved by application of an implicite difference method, which can be used for all forms of adorption isotherms.
Abstract: The problem of diffusion controlled adsorption kinetics is solved by application of an implicite difference method. Thereby all forms of adsorption isotherms can be used in the calculations. Computation examples are given concerning Langmuir, Freundlich, Volmer, Frumkin, and van der Waals isotherms.
96 citations
TL;DR: In this paper, the uptake of UO 2+ 2 and its hydroxo complexes has been determined at 20°C and pH 6.0 for fine-grained kaolinite, illite and montmorillonite.
93 citations
TL;DR: In this article, two empirical three-parameter equations, an extended Freundlich and an extended Langmuir equation, are proposed and compared with other equations, such as the Langmuirus, the Freundlic, the Fitter-Sutton, the modified Langmuirs, the double-Langmuir, the Gunarys, the Langmires, and finally the Langmusir equation.
Abstract: Summary
Phosphate sorption was studied on surface and subsurface soils sampled from the old field experiments at Askov, Denmark. Two empirical three-parameter equations, an extended Freundlich and an extended Langmuir equation are proposed and compared with the Langmuir, the Freundlich, the ‘double’ Langmuir, the Gunary, and the Fitter-Sutton equations.
In the proposed equations the affinity parameter of the Langmuir equation and the exponent of the Freundlich equation are replaced by the term Bc −D the value of which decreases with increasing phosphate concentration, c. On average the Freundlich equation thus modified yielded the closest fit to the sorption data. This was followed by the Fitter-Sutton, the modified Langmuir, the ‘double’ Langmuir, the Gunary, the Freundlich, and finally the Langmuir equation. Out of the three equations that yielded the closest fit to the sorption data the correlation between the parameters within the equations, furthermore, was least for the proposed extended Freundlich equation. Therefore, this equation may be generally suitable for describing phosphate sorption by soils.
84 citations
TL;DR: In this article, the uniform interpretation of gas/solid physical adsorption means that the different types of isotherms can be described by means of a single isotherm equation derived from the dynamical character of adorption.
84 citations
01 Jun 1981
TL;DR: In this paper, the distribution of adsorption potential for various organic compounds in aqueous solutions on the activated carbons were calculated from the modified Freundlich expression, logarithmic relationship of molar adsorbed amount and reduced concentration.
Abstract: Studies on adsorption isotherms for 16 organic compounds such as benzene mono- or disubstitutes, fatty acids, and aliphatic alcohols in aqueous solutions on five commercial granular activated carbons were carried out at 25°C. It was elucidated that the Polanyi potential theory could only be applied to the adsorptions of sparingly soluble compounds from solutions, and the Freundlich equation could, theoretically, be applied to the adsorptions of sparingly soluble compounds from solutions when the distribution functions of adsorption potential could be approximated by exponential functions. The distributions of adsorption potential for various organic compounds in aqueous solutions on the activated carbons were calculated from the modified Freundlich expression, logarithmic relationship of molar adsorbed amount and reduced concentration. Further, applicability of the Traube's rule and influence of surface oxides of activated carbon on the adsorption potentials of organic compounds were also discussed.
80 citations
TL;DR: In this article, the effect of soil and sediment properties on sorption of Naphthol was examined by using the Freundlich equation, and the role of both sorbate and sorbent properties as well as the solute-solvent interaction in determining the degree of hydrophobic or nonpolar sorption was examined.
Abstract: The effect of soil and sediment properties on sorption of ..cap alpha..-naphthol was examined. Batch equilibrium sorption isotherms were determined for sorption of ..cap alpha..-naphthol by soil and sediment samples collected from the Ohio, Missouri, Mississippi, and Illinois rivers and their watersheds. The sorption isotherms were represented by the Freundlich equation, Soil thin-layer chromatography was used in combination with the sorption studies to examine the role of both sorbate and sorbent properties as well as the solute-solvent interaction in determining the degree of hydrophobic or nonpolar sorption.
TL;DR: In this article, the adsorption and movement of metolachlor were determined in three commonly occurring soils of the Texas High Plains, and the results indicated that organic matter was the predominant adsorbent for metolACHlor in the soils studied.
Abstract: Metolachlor [2-chloro-N-(2-ethyl-6-methylphenyl)-N-(2-methoxy-1-methylethyl)acetamide] has considerable potential for yellow nutsedge (Cyperus esculentus L.) control in crops commonly produced in the Texas High Plains. Little information is available, however, concerning adsorption characteristics of metolachlor in soils of this region. Adsorption and movement of metolachlor were determined in three commonly occurring soils of the Texas High Plains. Organic carbon contents of the soils by weight varied from 0.3 to 0.5%, and the clay fraction ranged from 16 to 33%. Freundlich adsorption isotherms exhibited two linear regions for each soil, suggesting the possibility of multilayer adsorption. K′oc values and coefficients of determination for organic carbon and clay content vs. Freundlich K values indicated that organic matter was the predominant adsorbent for metolachlor in the soils studied. Desorption, soil column leaching, and thin-layer plate studies demonstrated metolachlor to be sufficiently mobile in scils low in organic matter to cause possible crop injury or loss of efficacy.
TL;DR: In this paper, the shape of the isotherms is affected by the time of adsorption and the adsorbent content, and the effect of the surface area to solution volume ratio is eliminated when the adaption is plotted as a function of the polymer concentration times the ratio solution volume/adsorbent area.
TL;DR: In this paper, the authors considered the problem of contaminant transport in the groundwater environment with adsorption and ion exchange reactions and formulated the solution for any adorption isotherm and an arbitrary number of exchanging cations.
Abstract: Contaminant transport in the groundwater environment with adsorption and ion exchange reactions is considered. For the case where the influence of dispersion is negligible, the method of characteristics is used to formulate the solution for any adsorption isotherm and an arbitrary number of exchanging cations. The approach applies equally well to linear flow systems and to nonlinear systems along streamlines in a nonuniform flow field. Transport problems related to the emerging technologies of in situ gasification of lignite and in situ leach mining of uranium are discussed. The first example considers migration of organics using the nonlinear Freundlich isotherm for adsorption of organics on lignite. Other examples consider ammonia migration and site restoration using the mass action law of ion exchange chemistry in in situ leach mining of uranium.
TL;DR: In this article, the Freundlich adsorption isotherm was measured in 14 agricultural soils from England and Wales with a wide range of properties, and the effect of pH adjustment on sorption varied between the 5 soils examined although, in general, there was increasing sorption with increasing pH.
Abstract: Summary
Copper sorption was measured in 14 agricultural soils from England and Wales with a wide range of properties. Sorption from 0.01 M CaCl2 was described by the Freundlich adsorption isotherm when Cu in solution was initially at 200 HM and greater, but at lower initial concentrations (i. e. 100 fiM and less) there was a steep rise in the gradients of the isotherms. At initial concentrations of 100 JIM and less, sorption was linearly correlated to the concentration of Cu remaining in solution; the gradients of these relationships varied considerably amongst the soils and were highly correlated to soil pH. There was no correlation between either the gradients or the extrapolated values of final solution concentration at which there was no sorption of added Cu by the soils (an ‘equilibrium’ concentration), and other determined soil properties.
The effect of pH adjustment on sorption varied between the 5 soils examined although, in general, there was increasing sorption with increasing pH. Extrapolated values for ‘equilibrium’ concentrations for an individual soil were higher at pH 6.0 or greater, than at pH 5.5. A large proportion of the Cu in the final solutions was apparently complexed but this varied between soils and was dependent on both pH and total concentration. There was little effect of varying pH of the final solution on these proportions in most soils.
Neither extractable Cu in the soils, nor the sorption characteristics were related to availability as measured by uptake by perennial ryegrass.
TL;DR: In this article, the spectra of CO2 on perovskite-type oxide LaCoCoCO3 were given, showing that CO2 and CO adsorb on the same sites while O2 adsorbs on a different type of site.
Abstract: Adsorption isotherms and i.r. spectra of CO2 on the perovskite-type oxide LaCoCO3 are given. Coverages at 50 mmHg are above half a monolayer. At 195 K the B.E.T. multilayer adsorption isotherm fits the data satisfactorily while at 623–673 K the Freundlich isotherm is obeyed. At lower temperatures (195–373 K) mainly physical adsorption, with a constant isosteric heat of 18.8 kJ mol–1, takes place. Entropy calculations show this adsorbed species to be in a supermobile state with a vibration perpendicular to the surface at a frequency of 4.2 × 1011 s–1. At higher temperatures (373–673 K) chemisorption occurs; the heat of adsorption of the adsorbed species at 623–673 K was found to be 33.5 kJ mol–1 for a coverage of 0.5. At 298 K i.r. bands at 1110, 1070 and 840 cm–1 were observed. At 423, 573 and 773 K bands were found at 1770, 1635, 1465, 1355, 1105, 1060 and 850 cm–1, attributed to carbonate species. Coadsorption data show that CO2 and CO adsorb on the same sites while O2 adsorbs on a different type of site. It is concluded that CO2 adsorbs on O2– ions and O2 adsorbs on surface metal ions.
TL;DR: In this article, the adsorption of micro amounts of cobalt (II) from aqueous solutions on manganese dioxide has been investigated and optimised as a function of equilibrium time, hydrogen ion, sorbate and sorbent concentrations.
TL;DR: In this article, a bisolute system of dissolved organics on activated carbon is measured in fixed beds and three different models with different assumptions about diffusion in the liquid filled pores and diffusion on the surface in series with external film diffusion.
TL;DR: In this article, the heat capacities of the adsorbed phase were derived for monolayer localized adsorption of monoatomic gases on heterogeneous solid surfaces, assuming that the sites having various adorption energies are distributed on the adsorbent surface completely at random.
Abstract: Equations for low-temperature adsorption isotherms, isosteric heats of adsorption, and heat capacities of the adsorbed phase are developed for monolayer localized adsorption of monoatomic gases on heterogeneous solid surfaces. The model assumes that adsorption sites having various adsorption energies are distributed on the adsorbent surface completely at random. The interactions between adsorbed molecules are treated in the quasichemical approximation. The equations are illustrated by numerous model calculations.
TL;DR: In this paper, an appropriate isotherm for the adsorption of benzotriazole on to copper surfaces from ammonium chloride solutions is presented, which has taken into account the relative size factor.
Abstract: An appropriate adsorption isotherm for the adsorption of benzotriazole on to copper surfaces from ammonium chloride solutions is presented. The analysis, which has taken into account the relative size factor, leads to the appropriate isotherm being that due to Frumkin. Some thermodynamic parameters of the adsorption isotherm are thus evaluated.
TL;DR: In this paper, the metal concentrations of four English rivers were extracted by extractants used to predict plant uptake of these elements from soils, and EDTA (0·1 n ) was the most efficient extractant, followed by ammonium acetate, while distilled water proved inefficient.
01 Jan 1981-Journal of Environmental Science and Health Part B-pesticides Food Contaminants and Agricultural Wastes
TL;DR: Dimensional analysis of the Freundlich equation shows the units of K to be moles(1-N) L(N)g-1, instead of the commonly used units, moles/g, and it is recommended that mole fraction be used to express equilibrium concentration.
Abstract: Freundlich K values cannot be directly converted from one set of units to another unless the slope, N, is unity. Dimensional analysis of the Freundlich equation shows the units of K to be moles(1‐N) LN g‐1, instead of the commonly used units, moles/g. A mathematical relationship exists between the ratio of K values in two different sets of units, and N. The magnitude of K does not change by the same factor as the adsorption data (x/m, C) from which it was calculated, when units are changed, unless N = 1.0. To avoid problems associated with units of K, it is recommended that mole fraction (a unitless quantity) be used to express equilibrium concentration, and that K no longer be used as an indicator of relative adsorption. An alternate means of assessing relative adsorption among pesticides is proposed.
TL;DR: In this paper, the sorption of Cd(II) on illite was studied at initial Cd concentrations from 1 to 1000 μg 1−1, with a constant solid phase concentration of 0.5 g 1 −1.
Abstract: The sorption of Cd(II) on illite was studied at initial Cd concentrations from 1 to 1000 μg 1−1, with a constant solid phase concentration of 0.5 g 1−1. Percentage sorbed at equilibrium increased sharply from pH 6.5 to 9.0, with a shift toward increased adsorption at lower initial concentrations, indicating specific, non-equivalent sites. Freundlich log-log plots were linear with a slope of 0.83. Susquehanna River sediments (silt/clay fraction) showed similar behavior, sorbing Cd somewhat more strongly than illite, as did mont-morillonite, while kaolinite sorbed Cd less strongly. Sorption on illite was not altered appreciably by removing the Fe- or Mn-oxide coating with dithionite, by removing organic matter with H2O2, or by using a carbonate-free medium. Equilibration time, desorption at lower pH's, and the effect of citrate in shifting the sorption to higher pH's were also studied. The data are discussed in terms of Cd speciation equilibria and possible sorption mechanisms.
TL;DR: In this paper, the Gibbs adsorption equation strongly overestimates the surface concentration, in agreement with the findings of others, but this does not necessarily mean that the equation cannot be applied to polymer solutions, as supposed previously.
TL;DR: In this paper, the authors analyzed the breakout behavior of axial diffusion in deep beds with adaption, assuming that a constant pattern wave has developed upstream of the bed outlet, and showed that breakout curves are much sharper than corresponding constant pattern profiles, especially for very favorable isotherms.
01 Jan 1981
TL;DR: In this paper, the power exchange model is used to predict heavy metal levels in the subsurface controlled by adsorption processes, and the results show that the results can accurately describe a wide range of competing sorbate concentrations and ratios.
Abstract: The empirical data on adsorption of metal cations by naturally occurring soil materials can be systematized in terms of power exchange functions. For example, given the reaction PbX + Ca2+ = CaX + Pb2+, the exchange function is: Kex = ([Pb2+]/[Ca2+]) (CaX/PbX)n where Kex and n are constants, the brackets denote activities of the ions, and CaX and PbX are their mole fractions on sorbent X. This approach is mathematically equivalent to regular solution exchange when the mole fractions of two competing cations sorbed lie between 0.25 and 0.75, and to Freundlich isotherm-type behavior when the mole fraction of the minor cation is < 0.05. Combined literature review and laboratory study show that the exchange behavior of H+, Na+, K+, Ca2+, Mg2+, Cd2+, Co2+, Ni2+, Pb2+, UO 2 2+ and Zn2+ and their hydroxy-complexes on a variety of adsorbents (montmorillonites, beidellite, illite, ferric oxyhydroxides, zeolites, soils and humic materials) can be accurately described for a wide range of competing sorbate concentrations and ratios using from one to three power exchange expressions. The adsorption of the alkali metal and alkaline earth cations on pure clays at about 10−2 to 10−4 M often follows the power exchange function with n = 1, corresponding to simple ion exchange. Adsorption of heavy metals (between 10−3 and 10−7 M) is usually more complex, and fits power exchange functions with n = 0.8 to 2.0. Log-linearization of power exchange expressions yields lines with correlation coefficients usually in the range from 0.98 to 1.00. The power exchange model is a potentially useful predictor of heavy metal levels in the subsurface controlled by adsorption processes.
TL;DR: In this article, an adorption equation was proposed for predicting the adsorption isotherms of organic compounds from water on activated carbons, and the equation was applied to predict the adaption of water-on-activated carbons.
Abstract: An adsorption equation is postulated for predicting the adsorption isotherms of organic compounds from water on activated carbons.
TL;DR: In this paper, a bench scale system was used to measure the equilibrium adsorption isotherms of n-heptane, n-butanol, and methyl isobutyl ketone at a concentration range of 50 to 900 ppm on a Columbia JXC activated carbon.
Abstract: A bench scale system to measure adsorption of organic vapors on activated carbon is described in this report. The system was used to measure the equilibrium adsorption isotherms of n-heptane, n-butanol, and methyl isobutyl ketone at a concentration range of 50 to 900 ppm on a Columbia JXC activated carbon and the adsorption capacity of eleven additional solvents at a concentration of 365 ppm. It is found that the Polyani–Dubinin correlation describes the results well. Using n-heptane as a reference solvent, the mean error in the prediction of equilibrium adsorption capacity is 1.9% and the maximum error 7.2%.
TL;DR: In this paper, the surface heterogeneity effects of the solids were taken into account, leading to an improvement due to agreement between theory and experiment and providing a new picture of the nonideality of the adsorbed phase.
Abstract: Equations for the excess adsorption isotherms and the heats of immersion are developed, taking the surface heterogeneity effects of the solids into account. It is shown that taking the heterogeneity effects into account leads to an improvement due to agreement between theory and experiment and provides a new picture of the non-ideality of the adsorbed phase.