Langmuir Sorption Isotherm Research Articles

Sorption of hafnium on hydrous titanium oxide using radiotracer technique

The sorption of hafnium on hydrous titanium oxide (TiO2·1.94 H2O) has been studied in detail. Maximum sorption of hafnium can be achieved from a pH 7 buffer solution containing boric acid and sodium hydroxide using 50 mg of the oxide after 30 minutes shaking. The value ofkd, the rate constant of intraparticle transport for hafnium sorption, from 0.01M hydrochloric and perchloric acid and pH 7 buffer solutions has been found to be 17 mmole·g−1·min−2. The kinetics of hafnium sorption follows Lagergren equation in 0.01M HCl solution only. The values of the overall rate constantK′=6.33·10−2 min−1 and of the rate constant for sorptionk1=6.32·10−2 min−1 and desorptionk2=2.28·10−5 min−1 have been evaluated using linear regression analysis. The value of correlation factor(γ) is 0.9824. The influence of hafnium concentration on its sorption has been examined from 4.55·10−5 to 9.01·10−4 M from pH 7 buffer solution. The sorption data followed only the Langmuir sorption isotherm. The saturation capacity of 9.52 mmole·g−1 and of a constant related to sorption energy have been estimated to be 2917 dm3·mole−1. Among all the additional anions and cations tested only citrate ions reduce the sorption significantly. Under optimal experimental conditions selected for hafnium sorption, As(III), Sn(V), Co(II), Se(IV) and Eu(III) have shown higher sorption whereas Mn(II), Ag(I) and Sc(III) are sorbed to a lesser extent. It can be concluded that a titanium oxide bed can be used for the preconcentration and removal of hafnium and other metal ions showing higher sorption from their very dilute solutions. The oxide can also be employed for the decontamination of radioactive liquid waste and for pollution abatement studies.

Sorption of nitrogen, methane, carbon dioxide and their mixtures on bituminous coals at in-situ conditions

Sorption data are presented for N 2, CH 4, CO 2 and their mixtures on several bituminous coals. The data are used to interpret the application of the Langmuir sorption isotherm to coals. The Langmuir constants show variations consistent with sorbate molecular properties and changes in coal rank; differences in limiting sorption values amongst sorbates are interpreted with the Gurvitsch rule. Deviations from the Lewis rule are used to infer the usefulness of the mixture formulation of the Langmuir isotherm.

The synthesis of tertiary amyl methyl ether (TAME): Microkinetics of the reactions

The microkinetics of the liquid-phase synthesis of tertiary amyl methyl ether (TAME) from methanol and a mixture of isoamylenes, namely 2-methyl-1-butene and 2-methyl-2-butene, using a macroporous sulphonic acid ion exchange resin as catalyst (Lewatit SPC 118) was determined in a continuous-flow recycle reactor in the temperature range 323–343 K at 1.6 MPa. The reaction proceeds within the gel phase of the microspheres overlapped by a multiple sorption equilibrium between components in the macropore liquid and the gel phase. A kinetic model was developed using the microkinetic data from experiments, where Langmuir sorption isotherms in liquid-phase activities from a modified UNIFAC method were assumed to describe the sorption behaviour of the components. The rate-controlling step, the chemical reaction of sorbed molecules, was formulated according to the homogeneous catalysis as first order in all species. The forward reaction is proportional to the activity ratio of isoamylenes to methanol and the activation energy was determined to be 89.5 kJ/mol.

Sorption Isotherm‐Sequential Extraction Analysis of Heavy Metal Retention in Landfill Liners

AbstractThe chemical partitioning of heavy metals in soil materials is of great importance in risk assessment, landfill bottom liner design, and remedial investigation. The sorption characteristics of clayey calcareous sediments used to construct landfill bottom liners at four sites in southeastern Michigan were studied using a new method: combined sequential extraction‐sorption isotherm analysis (CSSA). After spiking to simulate high levels of contamination, the sediments sorbed large quantities of Pb (∼1480–145 000 mg kg‐1), Ni (∼750–8100 mg kg‐1), and Cd (∼980–5070 mg kg‐1). Sequential extraction data indicated that Pb and Ni were principally in a carbonate‐occluded form, whereas Cd was mainly in an exchangeable form at high levels (>1000 mg kg‐1) of contamination. these results suggest that Pb and Ni will be immobilized by the liner materials but Cd will probably be highly mobile. By applying sequential extraction analysis after spiking, Langmuir sorption isotherms were constructed successfully for most of the individually targeted phases. Thus, CSSA appears to be a promising method for predicting the attenuation capabilities of soils and sediments because it allows the sorption capacities of individual phases to be determined while together in a natural system.

Concentration-Dependent Diffusion Coefficients and Sorption Isotherms. Application to Ion Exchange Processes As an Example

The physical significance of concentration-dependent diffusion coefficients is examined. It is shown that such concentration dependences cogently follow from typical sorption isotherms. As an example, NMR images of the progress of isovalent competitive ion exchange processes in alginate gels are compared with the predictions of diffusion models assuming Henry or Langmuir sorption isotherms. It is shown that the model on the basis of the Langmuir isotherm provides a much better correspondence with the experimental data than the linear absorption model based on the Henry isotherm. The better correspondence of the Langmuir model is due to the fact that saturation effects are taken into account in this model, which is based on the law of mass action.

Equilibrium and kinetic sorption behaviors of cesium and strontium in soils

The equilibrium and kinetic sorption of cesium and strontium was studied in some varieties of important-crude soil in Taiwan using the batch method. Cesium and strontium sorption data at 20 C were fitted to the Freundlich and Langmuir sorption isotherms. Nonlinear isotherms were found, and the Freundlich isotherm provided a better fit of the ion equilibrium sorption than the Langmuir isotherm did for both soils. The linear sorption isotherm was feasible for Sr 2+ sorption on both soils with an initial concentration <10 4N; however, Cs + was not. Both nuclides sorptions on chosen soils indicated two mechanisms at least, and the sorption process is diffusion-controlled. The sorption rate coefficients of Cs + and Sr 2+ of chosen soils at 25 C were determined in this study. The free energy of Cs + and Sr 2+ sorption at dilute solution on given soils was calculated from Freundlich isotherm constant.

Effects of laboratory‐scale variability upon batch and column determinations of nonlinearly sorptive behavior in porous media

Porous media are considered to be composed of spatial distributions of particles, which individually follow Langmuir sorption isotherms (with their own distinct, randomly sampled sorption capacities and selectivity coefficients). Analyses of batch and column methods for determining the sorptive parameters of these porous media reveal that batch‐derived estimates of retardation based upon Langmuir and Freundlich isotherms systematically underestimate and overestimate that observed at low concentrations, respectively, when local equilibrium conditions are met in the columns. These results, derived by stochastically analyzing the sorptive behavior expected during batch and column experiments, follow from the failure of the homogeneous‐based Langmuir and Freundlich models to properly describe sorptive behavior in the ensembles of particles composing the media. As the variability in the underlying sorptive properties increases, the Langmuir isotherm ceases to describe well the behavior of the aggregate of (individually Langmuir) particles both under static (batch) and dynamic (column) conditions. In such composite porous media there tends to be an inherent uncertainty involved with characterizing sorptive behavior at lower concentrations.

Influence of electrolyte composition and pH on cadmium sorption by an acid sandy soil

SUMMARYExtraction of soil with CaCl2, has been recommended as a measure of bioavailability of heavy metals. Interpretation of soil extraction data in terms of plant uptake potential may improve when the chemical behaviour of heavy metals in these extracts is ascertained. The effect of pH, Cd complexation by Cl, and competition between Cd and Ca on Cd sorption was studied at an ionic strength of 0.03 m. Sorption of cadmium was measured in 0.01 m CaCl2, in 0.01 m Ca(NO3)2, in a mixture of 0.02 m NaCl and 0.01 m NaNO3, and in 0.03 m NaNO3, at different values of pH ranging from 3.8 to 4.9. Adsorption isotherms were all linear, with a negative intercept on the y‐axis. This intercept indicated (linear) desorption of only part of the initial soil Cd content. About 50% of the Cd in solution was complexed in the presence of 0.02 m Cl at ionic strength of 0.03. Due to competition between Cd and Ca, sorption of Cd was reduced by 80% in the Ca‐electrolytes as compared with the Na‐electrolytes. Sorption was highly sensitive to pH as each 0.5 unit increase in pH resulted in twice as much sorption of Cd. An empirical factor in the sorption equation that accounts for this effect of pH showed a similar response to changes in pH as a mechanistic factor. This mechanistic factor was developed by assuming that Cd and protons sorb onto the same sites and that a two‐site Langmuir sorption isotherm for protons was able to describe the titration curve of the soil. This similarity may explain the successful application of the empirical factor in this and previous studies.

Kinetics of the hydroisomerization and hydrocracking of paraffins on a platinum containing bifunctional Y-zeolite

The kinetics of hydroisomerization and hydrocracking of n-octane, n-decane and n-dodecane were studied on a Pt/US-Y zeolite at 130 – 250°C, 5 – 100 bar total pressure and molar hydrogen to hydrocarbon ratios from 10 to 150. In first instance modeling was based on the lumping of the components and the reaction network. The obtained Hougen-Watson rate equations are independent of the carbon number of the feed and correspond to a mechanism with a rate-determining step on the acid function and with a Langmuir sorption isotherm. Next, kinetic equations based upon elementary reaction steps were derived. The corresponding network was generated by an algorithm. The merits of such a fundamental approach are discussed. Estimates of the kinetic parameters obtained by non linear regression are presented.

Mathematical analysis of transport properties of polymer films for food packaging. VI. Coupling of moisture and oxygen transport using langmuir sorption isotherms

AbstractDeterioration of food products stored in flexible packaging materials can be attributed to the presence of both water and oxygen in the environment surrounding the food. Mathematical models for the simultaneous permeation of moisture and oxygen through the packaging polymeric film and subsequent adsorption on the food surface are presented for the case of competitive adsorption of the two diffusing species. These models are then used to predict internal packaging conditions over time for selected food products. Oxygen and moisture permeation are treated as independent phenomena, and the competition is regarded as occuring on a surface described by the Langmuir adsorption isotherm. It is found that for certain polymer physical properties and relative surface coverages, water and oxygen molecules can dislodge each other from the food surface and, even for situations where the initial partial pressure of oxygen is less than the external partial pressure, can cause an outward flow of the more weakly adsorbed material. This theory is then extended to incorporate varying external conditions of storage.

Solute Retention in Column Liquid Chromatography. IV. Extension of the Langmuir Sorption-Isotherm Function to Include Stepped Variation of Retentions with Composition of Multicomponent Mobile Phases

Abstract Retentions are reported for substituted phenol solutes with a reverse-phase silica sorbent and acidified aqueous mobile phases containing 0-100% v/v tetrahydrofuran over the temperature range 10[ddot]-35[ddot]C. Curvature in plots of 1/k'(M) against ⊘ is substantial, although monotone, while those of 1/V'R(M) against ⊘ exhibit points of inflexion. All are shown to be described to well within experimental error by expansion of the Langmuir monolayer sorption isotherm relation presented and discussed previously in Parts I-III of this Series. Account is thereby taken of multilayer formation of sorbed mobile-phase constituents; the relation is then shown to describe all six BET isotherm Types of isocratic retention data, as well as retentions under conditions of gradient elution. Fully parabolic curve shapes for retentions derived from the literature are identified in addition that are not forecast or described by any other model heretofore put forth in column liquid chromatography, yet which are sho...

Sorption of Cadmium by the Green Microalgae Chlorella vulgaris, Ankistrodesmus braunii and Eremosphaera viridis

Summary Sorption of cadmium ions by three unicellular green algae generally shows a fast and a slow phase. The fast sorption of cadmium, completed after less than 5 minutes, is described as a Freundlich or Langmuir Sorption Isotherm. Values for binding constants of cadmium for these algae range between 2 × 10 -6 mol l -1 and 2 × 10 -5 mol l -1 . The maximal amount of cadmium which can be sorbed by cells of Chlorella and Ankistrodesmus is 10 15 mol/cell and by the larger cells of Eremosphaera up to 5 × 10 -12 mol/cell. At a cadmium concentration of 10 -7 mol l -1 in the medium the concentration in the cell wall for all three species is approximately 0.5 mmol l -1 . The main portion (about 80%) of cadmium is sorbed during the fast sorption phase. Only in case of Eremosphaera a slow sorption component has a marked influence on the amount of cadmium sorbed. Experiments revealed that cadmium is mainly sorbed in the cell wall. The binding sites seem to be acid groups in the cell wall structure.

Phosphorus sorption by some coconut‐growing acid soils of Sri Lanka and its relationship to selected soil properties

AbstractPhosphorus (P) sorption in the presence of 10−2M calcium chloride by ten coconut‐growing acid soil samples of Sri Lanka belonging to the Ultisol, Alfisol and Entisol orders was evaluated using the Langmuir sorption isotherm. The data for all samples fitted the single‐site Langmuir sorption isotherm when equilibrium P was less than 1 μg ml−1, but showed some deviations at larger concentrations of P. A two‐site Langmuir sorption isotherm was successfully used to describe the sorption data of three samples at these high concentrations. The single‐site Langmuir sorption maxima were greater for Ultisols (349–825 μg g−1) than for the other soils (136–345 μg g−1). These sorption maxima were significantly correlated with %‐clay, %‐silt, dithionite‐extractable iron, and 1M ammonium acetate (pH 4.8)‐extractable aluminium. Regression analysis of P sorption on different forms of iron (Fe) and aluminium (Al) indicated that crystalline ‘free Fe oxides’ (dithionite‐extractable Fe minus 0.3M oxalate‐extractable Fe) and ‘active Al’ which consists of hydroxy Al monomers and polymers [1M ammonium acetates, (pH 4.8)‐extractable Al minus 1M potassium chloride extractable Al] were the important factors contributing towards P sorption.

Motion of a multicomponent sorbed mixture in a porous medium when the medium is preliminarily saturated with certain components of the mixture

The numerical and invariant solutions of a system of quasilinear equations in partial derivatives, describing the motion of a multicomponent sorbed gas (or liquid) mixture through a porous medium previously saturated by certain sorbed components of the mixture, are analyzed; in the presence of Langmuir sorption isotherms, invariant solutions are obtained in the form of Riemann invariants.