Langmuir Equilibrium Constant Research Articles

Competitive sorption of CH₄ and CO₂ on coals: Implications for carbon geo-storage

Geological carbon storage, particularly within coal seams, is recognized as a viable strategy for achieving net-zero emissions. However, following CO₂ injection into the coal seam, limited studies have addressed the competitive sorption dynamics of CH₄ and CO₂ on coal, despite the natural presence of CH₄ in these formations. In this work, sorption experiments were conducted using two types of coal: sub-bituminous coal and anthracite. Initially, pure CH4 and CO2 gases were employed to conduct individual sorption tests. Subsequently, the competitive sorption of CH4 and CO2 was evaluated using pre-mixed binary gas mixtures with varying CH4/CO2 ratios. Further, the displacement effect of CO2 on CH4 was investigated by injecting CO2 into coal samples that had been pre-adsorbed with CH4. The data reveal that, for both coals, the ideal selectivity calculated from pure gas measurements underestimates the corresponding values from real multicomponent systems. Anthracite demonstrates a higher selectivity for CO₂ over CH₄ during both adsorption and desorption processes when compared to the ideal selectivity calculated from pure gas sorption data. Conversely, the sub-bituminous coal initially shows lower selectivity for CO₂ than for CH₄ during adsorption, but this trend reverses and intensifies during desorption. If competitive sorption effects are neglected, coal selectivity for CO₂ over CH₄ under the examined conditions would be underestimated by a factor of 1.5 to 2.5. Due to the competitive sorption effects between CH₄ and CO₂, the Langmuir equilibrium constants for gas mixtures are influenced by compositional changes, leading to dynamic deviations from those observed under pure gas conditions. This finding contrasts with the traditional extended Langmuir model, which presumes that the equilibrium constants remain unchanged regardless of gas composition. In addition, the displacement study underscores the efficacy of CO2 in displacing CH4, with higher CO2 ratios intensifying displacement effects. The study highlights the substantial impact of real multicomponent scenarios on coal selectivity for CO₂ and CH₄, offering deeper insights into predicting competitive sorption behavior between CO₂ and CH₄ during CO₂-enhanced coalbed methane recovery and carbon storage processes.

Advanced thermodynamic approach to adsorption of charged adsorbates from aqueous electrolyte solutions

This study present estimation of the thermodynamic parameters and the influence of ionic activity coefficient on the thermodynamic equilibrium constant of adsorption of phosphates on fly ash. The adsorption was conducted over a wide range of initial phosphate concentrations at different pH values pH = (3; 7; 10). The adsorption results were treated using the Langmuir, Freundlich and Sips adsorption isotherms, which provide information about the maximum adsorption capacity. The Langmuir and Sips isotherms were a satisfactory fit to the adsorption data, especially at pH = 3, with an acceptable regression coefficient over the entire concentration range, Langmuir (r2 = 0.9737) and Sips (r2 = 0.9969). The estimated maximum phosphate sorption capacity of fly ash was 6.21 ± 0.68 (mmol·g−1) according to Langmuir and 4.19 ± 0.16 (mmol·g−1) according to the Sips model, at pH = 3.0. However, there is no data in the published literature for estimating the thermodynamic parameters of the phosphate adsorption process using thermodynamic models for activity coefficients. Novel approach of this paper was determination of the thermodynamic equilibrium constant and Gibbs free energy, using the Pitzer ion-interaction model to predict the nature of adsorption. The Pitzer-ion interaction model was used for the mixed ionic systems, taking into consideration the effect of other present ions besides phosphates in the equilibrium solution resulting from fly ash desorption. The procedure for comprehensive estimation of the ion activity coefficient at maximum adsorption capacity and the dimensionless thermodynamic equilibrium constant using Langmuir's and Sips’s constants was presented. The calculated value of the phosphate activity coefficient in the equilibrium solution was γH2PO4,e = 0.7003 ± 0.0027 and the converted molar activity coefficient was γH2PO4,e = 0.6903 ± 0.0027. The estimated values of Gibbs free energy were: ΔGL = −6.788 ± 0.521 kJ·mol−1 based on Langmuir equilibrium constant and ΔGa = −7.707 ± 0.527 kJ·mol−1 based on activity and thermodynamic equilibrium constant. According to Sips model, the adsorption process is even more spontaneous, with the Gibbs free energy calculated using the phosphate activity coefficient and the thermodynamic equilibrium constant, ΔGa = −9.707 ± 0.617 kJ·mol−1. Consideration of the ionic activity coefficient is particularly important for large, charged adsorbates at higher concentrations, as the absolute difference in free energy for adsorption is app. 12 %. The scientific contribution is reflected in obtaining the necessary and more accurate information for the improvement of adsorption processes and possibly for the upgrading of fly ash in overall wastewater treatment technology.

How to avoid mistakes in treating adsorption isotherm data (liquid and solid phases): Some comments about correctly using Radke-Prausnitz nonlinear model and Langmuir equilibrium constant

Two flaws in concepts were identified and discussed in the paper (“Removal of Pb(II) from contaminated waters using cellulose sulfate/chitosan aerogel: Equilibrium, kinetics, and thermodynamic studies”. J. Environ. Manag. 286, 112167; https://doi.org/10.1016/j.jenvman.2021.112167). In the literature, the Radke–Prausnitz model is expressed in different forms, but some of them are incorrect. The first flaw is related to the nonlinear form of the Radke–Prausnitz model. The nonlinear form of this three parameters model is expressed correctly as qe=ARPBRPCeβARP+BRPCeβ–1. The units of two parameters are ARP (L/kg) and BRP [(mol/kg)/(mol/L)β] by considering qe (mol/kg) and Ce (mol/L). The limitation for its exponent is 0≤ β ≤ 1. This model is developed by two authors (Radke and Prausnitz). The correct paper (DOI: 10.1021/i160044a003) cited as reference of this model is “Radke, C.J., Prausnitz, J.M., 1972. Adsorption of organic solutes from dilute aqueous solution of activated carbon. Ind. Eng. Chem. 11, 445–451”. The second is the misconception about the unit of the Langmuir constant (KL; L/mg). The correct unit of KL is litre per milligram of adsorbate (i.e., Pb ions), not litre per milligram of adsorbent (the cellulose sulfate/chitosan aerogel material as reported by Najaflou and co-workers. They proposed a new equation [KL (L/mg) × m/V (mg/L)] to convert the Langmuir constant and then applied it to calculate the thermodynamic parameters of the adsorption process. The m/V is a solid/liquid ratio (g/L or kg/L). However, this conversion and application are mistakes that were thoroughly discussed in this paper. The correction is KEqo=1γAdsorbate×KLLmol×ComolL, with C° (1 mol/L by definition) being the standard state of solute and γAdsorbate (dimensionless) being the activity coefficient of adsorbate in solution. To avoid unexpected mistakes, the present authors suggest that researchers should have a correct citation (citing the original reference instead of using secondary references) and check the consistency of units (i.e., the constants of adsorption models) carefully.

Adsorption of Methylene Blue on Chestnut Shell-Based Activated Carbon: Calculation of Thermodynamic Parameters for Solid–Liquid Interface Adsorption

Chestnut shell-based activated carbon was prepared with chestnut shell as the raw material and ZnCl2 as the activating agent. Based on thermodynamic parameters, the adsorption behavior of methylene blue (MB) on chestnut shell-based activated carbon was studied, and the effect of temperature on the thermodynamic parameters and adsorption behavior was investigated. The Langmuir equilibrium constant (KL) and the standard equilibrium constant (K0) were used to calculate the thermodynamic parameters, respectively. Comparative analysis showed that spontaneous adsorption (ΔG0 < 0) was more compatible with the standard equilibrium constant (K0). Furthermore, the thermodynamic parameters at 30, 40 and 50 °C were measured, and the adsorption potential was investigated and calculated. Eventually, the mechanism of the adsorption process was determined. It was concluded that the adsorption process mainly involved chemical adsorption, which indicated that MB adsorption was caused by the force of the chemical bond.

Preparation of activated carbon from the residues of the mushroom (Agaricus bisporus) production chain for the adsorption of the 2,4-dichlorophenoxyacetic herbicide

The production of the edible mushroom Agaricus bisporus occurs on a world scale, where tons are constantly produced. At the same time, this production generates a large amount of waste that needs to be adequately conditioned. Therefore, mushroom residues were used to develop activated carbon for the removal of 2,4-D—the developed adsorbent showed a microporous structure with several spaces on the surface. The FTIR analysis showed that the activated carbon has functional groups such as aromatic rings, carboxylate, hydroxyl. It was found that the optimum adsorption of the 2,4-D occurs at pH 4 and adsorbent dosage of 0.4 g L−1; The equilibrium data were better fitted to the Freundlich model. However, for calculating the thermodynamic parameters, it was considered the Langmuir equilibrium constant (KL). The value of Langmuir Qmax was 241.7 mg g−1 at 298 K. The thermodynamic behavior indicated a spontaneous and favorable, and exothermic. The magnitude of the adsorption enthalpy is in agreement with physical adsorption. System equilibrium was attained before 30 min regardless of 2,4-D concentration. The kinetic curves showed good statistical adjustment to the linear driving force (LDF) model, with capacity values close to the experimental ones (qexp = 194.6 mg g−1; qpred = 187.3 mg g−1), at 100 mg L−1 of 2,4-D. The adsorbent removed up to 70% of the simulated effluent when using the Jacuí river as the sample. Regeneration studies showed that the activated carbon could be used up to 9 times without losing significant efficiency. Last, the process cost production was estimated to be 2.39 USD kg−1 of activated carbon. Therefore, it can be concluded that activated carbon developed from edible mushroom residues is a promising alternative as an adsorbent for the treatment of actual effluents containing 2,4-D herbicide.

The adsorption of organic dyes using Diatomite from Phu Yen

The prevalence of organic dyes contamination in water has driven widespread research on developing effective treatment systems including adsorption using various sorbents. The aim of this study is to investigate the methylene Blue (MB) adsorption of Diatomite Phu Yen and the influence of Fe loading into adsorption capacity. The prepared samples were characterized by XRD, TEM, EDX and BET methods to examine their structural, morphological properties, elemental composition and surface characteristics. Bath adsorption isotherms are conducted at several temperatures (283, 293, 303 and 313K).The data sets are analyzed with Langmuir and Freundlich models which produce Langmuir and Freundlich equilibrium constants (KL, KF), of adsorption for each process. Adsorption kinetics are followed closely the pseudo-second order model. The obtained results show that Diatomite could be an efficient adsorpbent for the removel of organic dyes from polluted environment. The presence of Fe results in negative MB adsorption behavior.

Patterns of protein adsorption in ion-exchange particles and columns: Evolution of protein concentration profiles during load, hold, and wash steps predicted for pore and solid diffusion mechanisms

Elucidation of protein transport mechanism in ion exchanges is essential to model separation performance. In this work we simulate intraparticle adsorption profiles during batch adsorption assuming typical process conditions for pore, solid and parallel diffusion. Artificial confocal laser scanning microscopy images are created to identify apparent differences between the different transport mechanisms. Typical sharp fronts for pore diffusion are characteristic for Langmuir equilibrium constants of KL ≥1. Only at KL = 0.1 and lower, the profiles are smooth and practically indistinguishable from a solid diffusion mechanism. During hold and wash steps, at which the interstitial buffer is removed or exchanged, continuation of diffusion of protein molecules is significant for solid diffusion due to the adsorbed phase concentration driving force. For pore diffusion, protein mobility is considerable at low and moderate binding strength. Only when pore diffusion if completely dominant, and the binding strength is very high, protein mobility is low enough to restrict diffusion out of the particles. Simulation of column operation reveals substantial protein loss when operating conditions are not adjusted appropriately.

Adsorption of Pd(II) and Au(III) Ions by Commercial Tris(2-Aminoethyl) Amine Polystyrene Polymer Beads

Adsorption of gold and palladium species containing chlorine ion species onto commercial N-(2-[bis(2-aminoethyl)amino)ethyl]aminomethyl–polystyrene polymer beads (TRIS) was investigated. The influence of the pH, initial metal ion concentration, and contact time on the adsorption performance was examined in a batch adsorption experiment. To examine and discuss both the theoretical character of the metal ion adsorptions, Langmuir, modified Langmuir, Freundlich, Tempkin, Dubinin–Radushkevich, and nonlinear solutions of modified Langmuir and Redlich–Peterson isotherm models variables are calculated. The modified Langmuir monolayer adsorption capacities of the Pd(II) and Au(III) chlorine ions species were found to be 206.93 and 173.18 mg/g, respectively. The two metal adsorption kinetics fit the pseudo-second-order kinetic models. In thermodynamic calculations, the choice of different equilibrium constants with having a dimension is an important problem in the field. To overcome these problems, the modified Langmuir isotherm equilibrium constant was used for determination of thermodynamic parameters. Adsorption mechanism steps were characterized using Fourier transform infrared (FTIR), scanning electron microscopy (SEM), and energy-dispersive X-ray spectroscopy (EDS). The adsorbent is made to interact with each metal ion in the HCl solution electrostatic interaction and surface complex formation between the amine groups. The calculation of the thermodynamic parameters using the dimensionless modified Langmuir equilibrium constant was found to be more satisfying and reliable. Adsorptions of Pd(II) and Au(III) on TRIS beads were exothermic and endothermic spontaneous processes, respectively.

Utilization of Polypyrrole/ZnO Nanocomposite in the Adsorptive Removal of Cu2+, Pb2+ and Cd2+ Ions from Wastewater

The present study was demonstrated the synthesis, characterization, and utilization of Polypyrrole/ZnO (Polypy/ZnO) nanocomposite in the removal of divalent copper, lead, and cadmium ions from aqueous solutions. Leaves extract of Mangifera indica has been used to synthesize zinc oxide nanoparticles (ZnO NPs) and green synthesized ZnO NPs incorporated in the polypyrrole system for enhancing metal loading capacity. Synthesized Polypy/ZnO was characterized using FT-IR, P-XRD, FE-SEM, and EDX methods. Maximum adsorption of copper, lead, and cadmium ions have been found at contact time 50 minutes, dosage 1 g, and pH 6, respectively. The Langmuir equilibrium constants were 6.75, 7.19, and 7.59 L/g for Cu2+, Pb2+, and Cd2+ ions. The desorption constants for the adsorptive removal of Cu2+, Pb2+, and Cd2+ ions by using Polypy/ZnO were evaluated from the Elovich model as 1.96, 1.68, and 1.17 g/mg, respectively.

Synthesis, Characterisations, Adsorptive Performances and Photo-catalytic Activity of Fe3O4-SiO2 Based Nanosorbent (Fe3O4-SiO2 BN)

In the present study, we have synthesised and characterised Fe3O4-SiO2 based nanosorbent (Fe3O4-SiO2 BN) using FESEM, EDX, FTIR and powder XRD methods. Synthesised Fe3O4-SiO2 BN was utilised in the adsorption of methylene blue (MB) from aqueous solutions. Optimum conditions for the adsorption of MB by the nanosorbent were found to be 60 min, pH 8 and 1 g dosage of the Fe3O4-SiO2 BN. The equilibrium data of adsorption have been tested with different isotherm and kinetic models and their parameters evaluated. Langmuir isotherm model was best fitted to equilibrium data of adsorption of MB onto Fe3O4-SiO2 BN as compared to Freundlich and Temkin isotherm models. Langmuir equilibrium constant and theoretical mono saturation capacity have been evaluated as 10.277 L/g and 0.0482, respectively. The rate constant (k2) of adsorption of MB on Fe3O4-SiO2 BN was found as to be 11.049 g/mg min from pseudo second order kinetic model. The photo-catalytic activity of magnetised Fe3O4-SiO2 BN has also been carried out in the presence of electromagnetic radiation and maximum MB degraded as 97.35% after irradiation time 140 min.

Adsorptive performances and characterisations of biologically synthesised zinc oxide based nanosorbent (ZOBN)

In the present study, we have synthesised zinc oxide based nanosorbent (ZOBN) by using the leaves extract of Shorea robusta (Sal) and removed Pb2+ and Cd2+ ions from waste water. Biologically synthesised ZOBN has been characterised by using different analytical methods such as UV–Visible spectroscopy, FTIR, powder XRD, FESEM and EDX. Adsorption study of Pb2+ and Cd2+ ions onto ZOBN from waste water was performed under the batch adsorption experiments and maximum adsorption of Pb2+ and Cd2+ ions found at optimized conditions such as higher contact time, higher acidic pH and moderate temperature. The adsorption efficiencies of Pb2+ and Cd2+ ions have been recorded as 52.5% and 35.5% at contact time 60 min, 92.9% and 89.9% at pH 6 and 45.1% and 39.9% at temperature 60OC, respectively. Regression values indicated that the Pseudo first order kinetic model was best fitted to the adsorption of Pb2+ and intra particle diffusion model for Cd2+ ions onto ZOBN. The diffusion constant (kd) for Pb2+ and Cd2+ ions have been evaluated as 0.41 and 0.28 mg/g min1/2. Langmuir isotherm model was found highly suitable for the equilibrium data of adsorption as compared to Freundlich, Temkin and Dubbin-Radushkevich isotherm models. The values of Langmuir equilibrium constant (L/g) and theoretical monolayer saturation capacity have been evaluated for Pb2+ ions as 7.19 L/g and 0.092 and for Cd2+ ions as 12.01 L/g and 0.03, respectively.

Synthesis of Porous Octahedral ZnO/CuO Composites from Zn/Cu-Based MOF-199 and Their Applications in Visible-Light-Driven Photocatalytic Degradation of Dyes

In the present paper, a porous octahedral (ZnO/CuO) composite is synthesized from zinc/copper-based metal-organic framework-199, and its applications in visible-light-driven photocatalytic degradation of dyes are demonstrated. The precursors of Zn-BTC, Cu-BTC, and Zn/Cu-BTC (BTC: benzene-1,3,5-tricarboxylate) were synthesized using a microwave-assisted method. Benzene-1,3,5-tricarboxylate acts as a sacrificial template and was removed from the precursors via thermal decomposition to form CuO, ZnO, and ZnO/CuO. ZnO/CuO with a large specific surface area of 32.5 m2·g–1 is composed of porous octahedral particles of 5–10 μm in diameter. Methylene blue (MB) was utilized as the dye model for photocatalytic degradation reactions. The porous octahedral ZnO/CuO exhibits superior visible-light-driven photocatalytic degradation of MB compared with single CuO or ZnO. The kinetic model of photocatalytic degradation was proposed as 1/KL×lnC+C=−krt+1/KL×lnCe+Ce, where KL is the Langmuir equilibrium constant and Ce is the MB concentration at equilibrium. The model significantly fits the kinetic data. In addition, the acquired catalyst manifests excellent photocatalytic degradation for several other dyes including phenol red, methyl orange, and Congo red.

Comparison the New Kinetics Equation of Non-competitive Sorption Cd(II) and Zn(II) onto Green Sorbent Horse Dung Humic Acid (HD-HA)

The new kinetics equation has been proposed and applied to the sorption of Cd(II) and Zn(II) onto green sorbent horse dung humic acid (HD-HA). This work aims to study the new kinetics equation and to compare its parameters with Lagergren and Ho kinetics equation in the same system. HD-HA was extracted and purified by Stevenson’s methods and then characterized by detection of its functional group, UV-Vis spectra, and total acidity. The sorption study of this work was investigated by batch experiment in pH optimum 5. Langmuir’s monolayer sorption capacity (b) of Cd(II) and Zn(II) onto HD-HA was 1.329×10-3 and 1.070×10-3 mole.g-1, respectively. Langmuir equilibrium constant (KL) of Cd(II) and Zn(II) sorption was 5,651 and 6,399 (mole/L)-1, respectively. The kinetics parameters were determined by Lagergren, Ho, and the new kinetics equation. The best linearity (R2) and the most fitted sorbed metal ion in equilibrium (xe) with the experimental data was the Ho kinetics equation. However, the correct value of sorption rate constant (ka) was not really known, because the ka resulted from Ho and Lagergren kinetics equation can not be compared with another parameter and there is no scale to measure the correctness of this value of ka. In this work, the correctness value of ka of the new kinetics equation can be measured by ka/kd equal to K, and this K should be equal to KL. The values of K of Cd(II) (3,452 (mole/L)-1) and and Zn(II) (10,898 (mole/L)-1) were quite similar with KL. Additionally, the value of intercept from linear regression of this new kinetics equation (Cd(II) = 6.8517; Zn(II) = 6.0408) was highly similar with the manually calculation of -ln(xe/ab) (Cd(II) = 7.0638; Zn(II) = 6.9838). These new kinetics equations also reveal that Lagergren sorption rate constant (kLag) is the complex function of ka(ab-xe2)/xe).

Re-evaluation of the century-old Langmuir isotherm for modeling adsorption phenomena in solution

One of the first reported equations to describe adsorption at equilibrium is the Langmuir model (J. Am. Chem. Soc. 1918, 40, 1361–1403). Initially, the model was used to describe adsorption from the gas phase, along with adsorption from the liquid phase. Herein, the shortcomings of the Langmuir model for adsorption processes from liquid phase are revealed. This study reports a revised form of the Langmuir isotherm model that provides further insight on the nature of adsorption and desorption processes in condensed phases. This approach is anticipated to provide a theoretical background for universal calculation of the adsorption thermodynamic parameters. We also provide an overview of the methods that use the Langmuir equilibrium constant for calculation of thermodynamic parameters of adsorption and source of their limitations are highlighted.

Analytical solution of the Langmuir-based linear driving force model and its application to the adsorption kinetics of boscalid onto granular activated carbon

The application of intraparticle diffusion models is generally difficult because of complex mathematical structure. The linear driving force (LDF) approach reduces the mathematical effort and provides a reasonable approximation of the intraparticle diffusion theory. In this work, an exact analytical solution of a LDF equation based on the Langmuir equilibrium model (LLDF) was derived. The LLDF model depends on three unknown parameters, namely the adsorbed amount at equilibrium, the maximum adsorbent capacity and the mass transfer coefficient. The LLDF model was used for analyzing the adsorption kinetics of boscalid onto granular activated carbon. The experimental results at equilibrium showed that the maximum adsorption capacity of activated carbon for boscalid and the Langmuir equilibrium constant of the process were 167 mg g−1 and 0.53 L mg−1, respectively. The LLDF equation was successfully applied to the kinetic data, allowing the evaluation of the mass transfer coefficient of boscalid (8.4 × 10−3 h−1). The LLDF model has general validity for describing intraparticle diffusion-adsorption onto porous media and its reliability can be assessed by a simple graphical method.

Adsorption modeling of CO2 in fluidized bed reactor

A model was proposed for studying the adsorption of CO2 in fluidized bed reactor based on combination of two-phase fluidization with tanks-in-series model. Logical combinations of ideal reactors can be of critical importance in gaining insights into the nature of FBRs and might better be further utilized in process simulation software. Implementation of the tanks-in-series model, in addition, is more consistent with hydrodynamics of the bed compared to one-phase and two-phase models. Considering this model, the fluidized bed was divided into 4 equal-volume stages, in which gas flows as completely mixed flow in emulsion phase and in bubble phase as plug flow. Using experimental data, the number of sections was found as a function of Hata number, superficial gas velocity and minimum fluidization velocity. The experimental results in a laboratory scale fluidized bed reactor with two particle sizes (335 and 605μm) at different superficial gas velocities (0.47, 0.62, 0.79, 0.94 and 1.25m/s) and aspect ratios were used for model validation. Obtained breakthrough curves from modeling were compared against experimental data to verify the validity of the model and acceptable agreement was observed. By fitting the results of the proposed model with experimental data, the reaction constant and Langmuir equilibrium constant were determined to be 0.041/s and 0.019m3/mol, respectively. Increasing the superficial gas velocity and better mixing of adsorbent result in greater adsorption capacity. Moreover, it was observed that smaller particles have higher adsorption capacity due to higher specific surface area and mass transfer coefficient than larger particles. It has also been found that the optimum superficial gas velocity was in the range of 0.62 and 0.79m/s for both particles sizes.

Equilibrium, Thermodynamic, and Kinetic Studies of the Adsorption of 2,4-Dichlorophenoxyacetic Acid from Aqueous Solution by MIEX Resin

The study investigated the performance of 2,4-D adsorption on MIEX resin. The different temperatures affecting the adsorption performance were specifically evaluated. Equilibrium data followed the Freundlich and Langmuir isotherm model for all investigated temperatures (283 K to 333 K). The Langmuir model was slightly better than the Freundlich model at a lower temperature (283 K); however, with the increase of temperature the Freundlich model could well describe the isotherm data. The solute coefficient of distribution (Kd) could be better used to estimate the thermodynamic parameters compared with the Langmuir equilibrium constant (KL). The thermodynamic parameters (ΔH0, ΔS0, and ΔG0) showed that the adsorption of 2,4-D was feasible, endothermic, and spontaneous at 283 K to 313 K. The activation energy (Ea, 47.70 kJ·mol–1) determined by using the rate constant k2 of pseudo-second order model (the suitable kinetic model) and the mean free energy value (Efe, 6.0348 kJ·mol–1) evaluated by using the Dubinin–Radushkevich (D–R) model indicated that chemical ion-exchange was the predominant mechanism of 2,4-D adsorption. The calculated film diffusion coefficient value (Df) suggested film diffusion was the kinetic rate-limiting step. The adsorbent displayed excellent reusability with 0.1 mol·kg–1 NaCl as the regeneration agent.

Isolation of bovine serum albumin from whey using affinity chromatography

The adsorption of bovine serum albumin (BSA) to a chromatography resin with immobilised llama antibody fragments as affinity ligands was investigated. The maximum adsorption capacity of the affinity resin was 21.6 mg mL−1 with a Langmuir equilibrium constant of 20.4 mg mg−1. Using packed bed chromatography, BSA was adsorbed from pure BSA solutions. Recovery was achieved by desorption at pH 3. In experiments with initial BSA concentrations of 1 mg mL−1 and 0.1 mg mL−1, BSA could be concentrated to 6.9 and 7.7 mg mL−1, respectively. BSA was also isolated from filtered bovine cheese whey containing less than 0.1 mg mL−1 BSA. The purified BSA was in this case concentrated to 7.4 mg mL−1 BSA. The presence of other components in the feedstock did not alter the adsorption capacity of the affinity resin. The results show that high recovery combined with high purity can be obtained using affinity chromatography.

Kinetics and Thermodynamics of the Adsorption of Lead (II) on a Activated Carbon from Coconut Shells

The effect of temperature on the adsorption of lead by an activated carbon from coconut shells is investigated. The pseudo second order equation is applied to the kinetic data obtained at different temperatures in order to determine the adsorption rate constants at these temperatures. Then, the Arrhenius equation is applied to the rate constants to determine the activation energy of the sorption reaction and the pre-exponential factor. By applying the Eyring equation to the rate constants, the standard thermodynamic activation parameters of the sorption reaction can also be calculated. In addition, the isotherms of lead adsorption on the activated carbon from coconut shells, at different temperatures, are determined and fitted by the Langmuir equation. The Van’t Hoff equation is applied to the Langmuir equilibrium constants in order to determine the standard enthalpy of the sorption reaction. The other standard thermodynamic parameters<br />(Gibbs standard enthalpy and standard entropy) are deduced. The isosteric standard sorption enthalpy is also determined by using both the classical approach and an adapted Clausius Clapeyron equation. The results are identical. The value obtained is higher, but more correct than that of Langmuir. On the basis of these<br />thermokinetic parameters, the activated carbon from Coconut shells can be considered as a very efficient carbon for the sorption of lead and its sorption efficiency (rate and quantity) increase with the temperature.

Graphical Evaluation of the Favorability of Adsorption Processes by Using Conditional Langmuir Constant

A graphical method for evaluating the Langmuir favorable adsorption is proposed in this work. The conditional Langmuir constant (KLN), a new parameter related to the Langmuir equilibrium constant (KL), can be used to predict the shapes of Langmuir favorable adsorption isotherms. On the dimensionless Langmuir isotherm diagram, all the Langmuir favorable adsorptions (0 < RL < 1) are further divided into three subgroups: favorable adsorption, very favorable adsorption, and highly favorable or pseudoirreversible adsorption, with two critical Langmuir constants (KLN1 and KLN2) as the demarcation point. The feasibility of the method is demonstrated by analyzing 14 adsorption systems. The graphical method is effective and intuitional, and can be used for the favorable evaluation of any Langmuir isotherms. This method shows the advantage that the parameter KLN does not depend on the initial adsorbate concentration (co) over RL method.