Peterson Equation Research Articles

Copper sorption onto dried red alga Pterocladia capillacea and its activated carbon

Sorption of Cu(II) ions on dried red alga Pterocladia capillacea and its activated carbon have been studied. The sorption equilibrium was determined as a function of contact time at several Cu(II) ion concentrations and the effect of adsorbent concentration was also investigated. The pseudo second-order kinetic model provided the best correlation for the experimental data in compared to the pseudo-first order kinetic. Ion exchange was occurred in the initial reaction period. The experimental results were fitted to the Langmuir, Freundlich and Redlich–Petrson isotherms to obtain the characteristic parameters of each model. Both the Langmuir and Redlich–Peterson equations were significantly better for dried red alga biomass. On the other hand, Freundlich and Redlich–Peterson equation were significantly better than Langmuir for the activated carbon prepared from dried red alga. Error functions have been used to determine the alternative single component parameters by non-linear regression analysis. The error function method provided the best parameters for the isotherm equation in this system and is demonstrated for error comparison purposes. Red alga biomass and its activated carbon may be evaluated as an environmentally friendly and extra economic treatment.

Studies on the Adsorption of 2-Naphthalenesulfonic Acid on Basic Resin from Effluents

The adsorption reaction of 2-naphthalenesulfonic acid with the strong basic resin N201 was investigated experimentally with varying parameters (viz., the effects of pH, temperature, contact time, sodium sulfate, and fixed-bed column runs) and compared with the weakly basic resin D301. Results showed that the optimum initial pH for 2-naphthalenesulfonic acid adsorption by N201 was 2.4, and the equilibration time required was 2.5 h. The three single-component isotherms were analyzed with the Langmuir, Freundlich, and Redlich−Peterson equations. The Redlich−Peterson equation gave the lowest errors by use of the sum of the squares of the errors. The thermodynamic parameters (ΔG, ΔH, and ΔS) were also determined, and the adsorption process is more favored at low temperatures. The kinetics followed a pseudo-second-order rate equation very well. However, a dramatic decrease in adsorption capacity was observed for both resins upon addition of Na2SO4 into the 2-naphthalenesulfonic acid solution. The adsorption and...

Equilibrium and kinetics of adsorption of fluoride onto zirconium impregnated cashew nut shell carbon

Zirconium impregnated cashew nut shell carbon was studied to assess its capacity for the adsorption of fluoride from aqueous solutions. The dependence of the adsorption of fluoride on the pH of the solution has been studied to achieve the optimum pH value and a better understanding of the adsorption mechanism. The influence of addition of the co-existing ions on the adsorption of fluoride was also studied. Adsorption isotherms have been modeled by Langmuir, Freundlich and Redlich–Peterson equations and their constants were determined. Pseudo-first- and second-order equations were used to describe the adsorption rate of fluoride and adsorption rate constant was calculated. A mechanism involving three stages, viz.; external surface adsorption, intra-particle diffusion and final equilibrium has been proposed for the adsorption of fluoride onto adsorbent material. Thermodynamic parameters such as Δ G°, Δ H° and Δ S° were calculated in order to understand the nature of sorption. Field studies were carried out with the fluoride containing water sample collected from a fluoride-endemic area in order to test the suitability of the sorbent at field conditions.

Adsorption isotherm, kinetic and mechanism studies of some substituted phenols on activated carbon fibers

Activated carbon fibers (ACFs) were used for the adsorption of phenol, 2-chlorophenol (2-CP), 4-chlorophenol (4-CP), 2,4-dichlorophenol (DCP), 2,4,6-trichlorophenol (TCP), 4-nitrophenol (4-NP) and 2,4-dinitrophenol (DNP) from aqueous solutions, and the adsorption capacities followed the order of TCP > DNP ≈ DCP > 4-NP > 4-CP > 2-CP > phenol. Adsorption isotherms at different temperatures were determined and modeled with Langmuir, Freundlich and Redlich–Peterson equations. Thermodynamic parameters were calculated and correlated with the adsorption behaviors. The effects of solution pH on the adsorption were also studied. The adsorption mechanism was discussed based on the experimental results, and the π–π interactions, solvent effects, hydrophobic interactions and molecular dimensions were considered to be important in the adsorption. Kinetic studies showed rapid adsorption kinetics of the phenols, due to the open pore structure of the ACFs. The kinetics was fitted with the pseudo-first-order, pseudo-second-order and intraparticle diffusion models. Steric effects on adsorption kinetics were observed for TCP, 4-NP and DNP, but serious impact on the ultimate uptake was only found for DNP. The relationship between the steric effects and the molecular dimension was also proposed.

Biosorption of chromium (III) by orange ( Citrus cinensis) waste: Batch and continuous studies

The present study explores the ability of orange waste biomass to remove Cr (III) from aqueous solutions. Batch kinetic and isotherm studies were carried out on a laboratory scale to evaluate the adsorption capacity of orange waste. The effects of particle size, adsorbent dose and solution pH on Cr (III) removal were also studied. The results showed that the higher the adsorbent dosage and the pH, the higher the percentage of metal removal. No significant influence of particle size on sorption capacity was observed in the experimental conditions studied. A kinetic study revealed that the adsorption of Cr (III) onto orange waste was a gradual process and equilibrium was reached within 3 days. A pseudo-second order model was the most appropriate to describe the kinetic experimental data. Equilibrium assays displayed a maximum sorption capacity ranging from 0.57 mmol/g to 1.44 mmol/g when the pH increased from 3 to 5, according to the Sips model, which along with the Redlich–Peterson equation, is very suitable for correlating equilibrium data. The use of the studied adsorbent in the removal of chromium in continuous mode was successful and the breakthrough curves were adequately represented by BDST model. Due to the slow kinetics of chromium sorption onto orange waste, the sorption capacity in batch assays was higher than that in continuous assays.

Nanostructured hydrous titanium(IV) oxide: Synthesis, characterization and Ni(II) adsorption behavior

The synthetic oxide was characterized as hydrated and agglomerated nanocrystallite (11–13 nm) titanium(IV) oxide (NHTO), which was used for Ni(II) adsorption from aqueous solution. The variable parameters investigated were the effects of pH, contact time, metal concentration and temperature on reaction. The optimum pH fixed was 5.0 (±0.1) for Ni(II) adsorption. The kinetic data described the pseudo-first order equation well and, film diffusion governed the reaction. The Redlich–Peterson equation described well the equilibrium isotherm data of all temperatures. The Fe(III) showed negative influence on Ni(II) adsorption. The negative Gibbs free energy (−Δ G° = 13.90–16.30 kJ mol −1) and positive enthalpy change (+Δ H° = 6.15 kJ mol −1) indicated spontaneous and endothermic nature of the reaction, respectively, and took place with increasing entropy (Δ S° = +0.07 kJ mol −1 K −1). The mean energy of adsorption ( E DR = 13.25–16.35 kJ mol −1 at T = 288–328 K) predicted physisorption nature of Ni(II) on NHTO. The dilute (0.1 M) mineral acids desorbed 95–98% of adsorbed metal from the NHTO surface.

Adsorption studies of methylene blue and phenol onto vetiver roots activated carbon prepared by chemical activation

Vetiver roots have been utilized for the preparation of activated carbon (AC) by chemical activation with different impregnation ratios of phosphoric acid, X P (g H 3PO 4/g precursor): 0.5:1; 1:1 and 1.5:1. Textural characterization, determined by nitrogen adsorption at 77 K shows that mixed microporous and mesoporous structures activated carbons (ACs) with high surface area (>1000 m 2/g) and high pore volume (up to 1.19 cm 3/g) can be obtained. The surface chemical properties of these ACs were investigated by X-ray photoelectron spectroscopy (XPS) and Boehm titration. Their textural and chemical characteristics were compared to those of an AC sample obtained by steam activation of vetiver roots. Classical molecules used for characterizing liquid phase adsorption, phenol and methylene blue (MB), were used. Adsorption kinetics of MB and phenol have been studied using commonly used kinetic models, i.e., the pseudo-first-order model, the pseudo-second-order model, the intraparticle diffusion model and as well the fractal, BWS ( Brouers, Weron and Sotolongo) kinetic equation. The correlation coefficients ( R 2) and the normalized standard deviation Δ q (%) were determined showing globally, that the recently derived fractal kinetic equation could best describe the adsorption kinetics for the adsorbates tested here, indicating a complex adsorption mechanism. The experimental adsorption isotherms of these molecules on the activated carbon were as well analysed using four isotherms: the classical Freundlich, Langmuir, Redlich–Peterson equations, but as well the newly published deformed Weibull Brouers–Sotolongo isotherm. The results obtained from the application of the equations show that the best fits were achieved with the Brouers–Sotolongo equation and with the Redlich–Peterson equation. Influence of surface functional groups towards MB adsorption is as well studied using various ACs prepared from vetiver roots and sugar cane bagasse. Opposite effects governing MB and phenol adsorption mechanism on ACs are demonstrated. The various effects involved in adsorption mechanisms of each molecule are demonstrated.

Kinetics of zinc ions removal from effluents using ion exchange resin

Abstract The ability of a new ion exchange resin to remove zinc ions from effluent has been studied. The equilibrium exchange capacity has been determined as 2.7 mmol/g resin and analysed using the Langmuir, Freundlich and Redlich–Peterson equations. The Redlich–Peterson gave the best-fit to the experimental data. A series of kinetic studies were carried out in an agitated batch reactor. Three variables were studied, initial zinc ion concentration, resin mass and resin particle size. The results were analysed using three kinetic models, pseudo-first order, pseudo-second order and the Elovich model. The results were compared on the basis of SSE values and the best-fit correlation of the experimental data was obtained using the Elovich model which suggests a chemisorption process.

Study of equilibrium, kinetic and thermodynamic parameters about methylene blue adsorption onto natural zeolite

Adsorption equilibrium and kinetic of methylene blue (MB) onto natural zeolite was studied in a batch system. Variables of the system include contact time, pH, salt concentration, temperature, and initial MB concentration. The increase in temperature resulted in a higher MB loading per unit weight of the zeolite. Langmuir, Freundlich, Redlich–Peterson, Koble–Corrigan and Temkin isotherm models were applied to experimental equilibrium data of MB adsorption depending on temperature. The effect of contact time at different temperatures and initial concentration were fitted to pseudo-second-order kinetic model. Linear regressive method and nonlinear regressive method were used to obtain the relative parameters. The error analysis was conducted to find whether linear method or nonlinear method was better to predict the experimental results and which model was better to fit the experimental data. Both methods were suitable to obtain the parameters. The Redlich–Peterson equation was best to fit the equilibrium data. The pseudo-second-order kinetic model can be used to describe the adsorption behavior. The nonlinear method may be better with the absolute error as limited condition. The adsorption process was spontaneous and endothermic.

Comparison of 5 anthropometric skinfold formulas to air displacement plethysmography (ADP) when predicting body fat composition in female adolescents with phenylketonuria (PKU)

Objective: To analyze the precision of five anthropometric skinfold formulas at predicting percent body fat (% BF) in female PKU adolescents when compared with standard results from ADP. Design: Skinfold and ADP measurements were recorded from a cross-section of female PKU patients, aged 10–19 years. ADP was chosen as the comparative standard. Anthropometric values were used to calculate % BF with formulas created by Slaughter, Peterson, Wilmore, Durnin, and Jackson. Bland-Altman agreement analysis determined the efficacy of formulas versus ADP at predicting % BF. Results: Formulas by Peterson and Durnin had the smallest estimation errors (7% and 3%); Slaughter's had the greatest estimation error (19%). Peterson's formula had the smallest mean difference from ADP and the smallest standard deviation (0.76±4.8), whereas Slaughter's had the largest (−7.7±7.4). All formulas, except for Peterson's (P=0.23), showed a statistically significant difference (P<0.05) from ADP. Conclusions: This investigation revealed Peterson's equation to have superior precision in calculating % BF within the female adolescent PKU population. Slaughter's equation was the least reliable at accurately determining %BF. Therefore, Peterson's formula is recommended when performing anthropometric analysis of body composition in the female PKU adolescent population. Funded by: Emory Hospital General Clinical Research Center

The effects of pH and ionic strength on fulvic acid uptake by chitosan hydrogel beads

The objective of this work is to investigate the effects of pH and ionic strength on the adsorption capacity for fulvic acid (FA) by chitosan hydrogel beads. The results indicated that the sorption amount increased with decreasing pH and increasing ionic strength concentration. The sorption isotherms were well described by using non-linear Langmuir, Freundlich and Redliche–Peterson equation. The adsorption kinetics of FA onto chitosan hydrogel beads could be described by pseudo-second-order rate model. The extent of FA removal in the presence of other ions decreases in the order Ca 2+ > Mg 2+ > Na + ≈ K + and Cl − > NO 3 − > CO 3 2−. FTIR along with XPS analyses revealed the amine groups on the beads were involved in the sorption of FA and the organic complex between the protonated amino groups and FA was formed after FA uptake. Sorption mechanisms including electrostatic interaction and surface complexation were found to be involved in the complex sorption of FA on the chitosan hydrogel beads.

Removal of direct blue-86 from aqueous solution by new activated carbon developed from orange peel

The use of low-cost, easy obtained, high efficiency and eco-friendly adsorbents has been investigated as an ideal alternative to the current expensive methods of removing dyes from wastewater. This study investigates the potential use of activated carbon prepared from orange peel for the removal of direct blue-86 (DB-86) (Direct Fast Turquoise Blue GL) dye from simulated wastewater. The effects of different system variables, adsorbent dosage, initial dye concentration, pH and contact time were studied. The results showed that as the amount of the adsorbent increased, the percentage of dye removal increased accordingly. Optimum pH value for dye adsorption was determined as ∼2.0. Maximum dye was sequestered within 30 min after the beginning for every experiment. The adsorption of direct blue-86 followed a pseudo-second-order rate equation and fit well Langmuir, Tempkin and Dubinin–Radushkevich (D–R) equations better than Freundlich and Redlich–Peterson equations. The maximum removal of direct blue-86 was obtained at pH 2 as 92% for adsorbent dose of 6 g L −1 and 100 mg L −1 initial dye concentration at room temperature. The maximum adsorption capacity obtained from Langmuir equation was 33.78 mg g −1. Furthermore, adsorption kinetics of DB-86 was studied and the rate of adsorption was found to conform to pseudo-second-order kinetics with a good correlation ( R 2 > 0.99) with intraparticle diffusion as one of the rate determining steps. Activated carbon developed from orange peel can be attractive options for dye removal from diluted industrial effluents since test reaction made on simulated dyeing wastewater show better removal percentage of DB-86.

Comparative adsorption isotherms and modeling of nickel and cobalt citrate complexes onto chelating resins

The sorption characteristics of nickel and cobalt-organic acid complexes on two commercial chelating resins (Purolite S930 and S950) were compared. Purolite S390 is based on an iminodiacetic funtional group and S950 is an aminophosphonic acid resin. Batch equilibrium adsorption tests of these resins were examined and compared using various metal citrate concentrations (15–2000 mg/L) and solution pH. The solution pH of complex solutions was varied by preparing metal solutions in 0.01, 0.1, 0.5 and 1.0 M of citric acid. Equilibrium adsorption data were fitted to empirical isotherm models; linear, Langmuir, Freundlich and Redlich–Peterson (R–P) equations to establish the mechanism for the uptake of the metal complexes onto the resins. Our study showed that nickel-citrate complex adsorption exhibited both monolayer and multilayer adsorption; the mechanism on both resins varying with acid concentration, whereas cobalt complex adsorption was independent of acid concentration but the mechanism of metal loading was found to be influenced by the nature of the resins.

Arsenic removal from an aqueous solution by modified A. niger biomass: Batch kinetic and isotherm studies

Batch studies were conducted to examine the adsorption kinetics and adsorption capacity of iron oxide-coated biomass (IOCB) for As(III) and As(V). The optimum pH for As(V) and As(III) removal was found to be 6. The equilibrium time for removal of arsenic was found to be approximately 7 h. The adsorption of As(V) on IOCB was rapid compared to that of As(III) adsorption. An increase in temperature (from 5 to 30 °C) was found to increase As(III) removal, whereas in the case of As(V), the removal increased with temperature from 5 to 10 °C, but remained relatively constant thereafter up to 30 °C. The pseudo-second order rate equation was found to describe better the kinetics of arsenic adsorption than other equations. The isotherm data for As(V) removal fitted better with the Langmuir equation compared with other tested models and the isotherm data for As(III) removal fitted better with Redlich–Peterson equation than other tested models. Iron oxide-coated fungal biomass ( A. niger) was found to be efficient in removing arsenic from an aqueous solution.

Equilibrium studies of the sorption of Hg(II) ions onto chitosan

Abstract Chitosan is a biopolymer found in the body of the shellfish, crustaceans and some fungi. The free amino groups of this biopolymer show different properties such as anti-microbial, anti-acid and chelating of metal ions. Chitosan has been used as an adsorbent for the removal of the metal ions from industrial effluents. In this paper, the sorption of mercuric ions from solution onto chitosan particles with sizes of 0.177, 0.5 and 1.19 mm at three initial pH 3.00, 4.50, 6.00 ± 0.1 has been investigated. The experimental data were analyzed using the Langmuir, Freundlich and Redlich–Peterson equations. Error function and correlation coefficients were determined for each isotherm analysis. The results showed that increasing of pH increased the extent of Hg(II) ions uptake and decreasing of adsorbent particle sizes increased the amount of mercury removals. The study of equilibrium isotherm shows that the best model for analysis of experimental data is Langmuir model with correlation coefficient higher than 0.982. Maximum Hg(II) ions uptake with chitosan in our experiments (from Langmuir equation) is 1127.1 (mg Hg2+/g chitosan).

Equilibrium and kinetic studies on sorption of basic dyes by a natural biopolymer poly(γ-glutamic acid)

A bacteria-derived biodegradable and non-toxic biopolymer poly(γ-glutamic acid) (γ-PGA) was evaluated as an adsorbent for removal of basic dyes from aqueous solution. Sorption experiments were carried out with three basic dyes Auramine O (Au–O), Rhodamine B (Rh–B) and Safranin O (Sa–O) by a batch mode at different initial dye concentrations, agitation times, γ-PGA doses, temperatures, pH and added salts. Sorption isotherms were well described by the Redlich–Peterson equation, closely followed by Sips, when compared to Freundich and Langmuir models. The maximum sorption capacity derived from Langmuir model at 301 K was 277.29, 390.25 and 502.83 mg/g for Au–O, Rh–B and Sa–O dyes, respectively. The kinetics of dyes sorption on γ-PGA followed a pseudo second order equation and the rate was controlled by chemical sorption. An ion-exchange model assuming adsorption to be a chemical phenomenon also predicted the kinetic data precisely. Thermodynamic parameters (Δ H°, Δ S° and Δ G°) obtained revealed dye sorption to be an exothermic and spontaneous process with decreasing randomness of dyes at the solid/solution interface. Dye sorption increased with increase in solution pH and reached a plateau at pH 5, while desorption of about 98% of dyes from spent γ-PGA occurred at pH 1. The incorporation of salts decreased the dye sorption, suggesting the binding of dyes on γ-PGA may involve ion-exchange mechanism.

Application of different equations to adsorption isotherms of phenolic compounds on activated carbons prepared from cork

Activated carbons were prepared from solid cork wastes by physical activation with carbon dioxide or steam, and chemical activation by impregnation with phosphoric acid. In this work we show the possibility of using these activated carbons for the adsorption of phenolic compounds from the aqueous phase. The materials present a different response to the adsorptives used ( p-nitrophenol, p-chlorophenol, p-cresol and phenol), depending on the type of activation and the parameters (burn-off, absolute concentration) used in each case. All the samples were capable of retaining the contaminants, with the best result being reached by the sample with higher burn-off and the worst with the carbonised, while intermediate values were reached with the remaining samples. The experimental isotherms were analysed with two and three parameters equations (Freundlich, Langmuir, Dubinin–Radushkevich–Kaganer and Redlich–Peterson). The results obtained from the application of the equations are similar in some aspects, but the degree of confidence is quite different. The best fit was achieved with the Redlich–Peterson equation, which can be explained by the fact that this has three adjustable parameters. However, overall the Freundlich and DRK equations appear to be more useful and provide parameters which can be correlated with the structural characteristics of the solids obtained from N 2 adsorption measurements.

Characterization and Properties of Manganese Oxide Coated Zeolite as Adsorbent for Removal of Copper(II) and Lead(II) Ions from Solution

A new adsorbent, manganese oxide coated zeolite (MOCZ), was characterized and employed for the removal of Cu(II) and Pb(II) from aqueous solution using batch equilibrium experiments. Scanning electron microscope (SEM), X-ray photoelectron spectroscopy (XPS), and BET analyses were used to observe the surface properties of the coated layer. Binding of Cu(II) and Pb(II) ions by MOCZ was clearly pH-dependent, and the loading capacities increased with increasing pH. Adsorption behavior of Cu(II) and Pb(II) ions can be approximately described with the Langmuir and Redlich−Peterson equation. The thermodynamic parameters (ΔG°, ΔH°, and ΔS°) were also determined, and the adsorption process is more favored at higher temperatures.

Removal of Orange-G and Methyl Violet dyes by adsorption onto bagasse fly ash—kinetic study and equilibrium isotherm analyses

In the study, bagasse fly ash (BFA) (generated as waste material from sugar mill), was used as an adsorbent for the removal of Orange-G (OG), and Methyl Violet (MV), from aqueous solution. Batch studies were performed to address various experimental parameters like pH, contact time, adsorbent dose and initial concentration for the removal of these dyes. Effective pH for OG and MV removal were 4 and 9, respectively. Greater percentage of dye was removed with decrease in the initial concentration of dyes, and increase in amount of adsorbent used. Kinetic study showed that the adsorption of dyes on BFA was a gradual process. Quasi-equilibrium reached in 4 h. Pseudo-first-order, pseudo-second-order, Bangham and intra-particle particle diffusion models were used to fit the experimental data. Pseudo-second-order rate equation was able to provide realistic description of adsorption kinetics. Equilibrium isotherms were analysed by Freundlich, Langmuir, Redlich–Peterson, Dubnin–Radushkevich, and Tempkin isotherm equations using correlation coefficients and five different error functions. Freundlich equation is found to best represent the equilibrium data for OG-BFA system while Redlich–Peterson equation better fits the data for MV-BFA system. Thermodynamic study showed that adsorption of MV on BFA (with a more negative Gibbs free energy value) is more favoured among the dyes studied. BFA which was used without any pretreatment showed high surface area, pore volume and pore size exhibiting its potential to be used as an adsorbent for the removal of OG and MV.

Nickel and cobalt sorption on anaerobic granular sludges: kinetic and equilibrium studies

AbstractThe kinetics and equilibria of sorption of the divalent metal ions cobalt and nickel onto anaerobic granular sludge are described. Single component and binary equimolar systems were studied at different pH values (pH 6, 7 and 8). The kinetic modelling of metal sorption by anaerobic granular sludge has been carried out using Lagergren equations. On fitting the experimental kinetic data both in first‐ and pseudo‐second‐order equations, the regression analysis of a pseudo‐second‐order equation gave a higher r2 value, indicating that both external mass transfer and intra‐particle diffusion are involved in the sorption process. The experimental isotherm data were analysed using the Langmuir, Freundlich and Redlich–Peterson equations. The Redlich isotherm, a combination of the Langmuir and Freundlich equations, was found to have the highest regression correlation coefficients at pH 7. At pH 8, the Langmuir mechanism dominated for cobalt and nickel adsorption. In contrast, at pH 6, the Freundlich equation gave a better correlation coefficient which suggests a more heterogeneous adsorption at that pH. The maximal adsorption capacity of the granular sludge, as determined by the Langmuir equation, for cobalt or nickel in single systems (8.92 mg g−1 Co TSS; 9.41 mg g−1 Ni TSS, pH 7) compared with binary systems (8.06 mg g−1 Co TSS; 8.43 mg g−1 Ni TSS, pH 7) showed no great difference in the accumulation of these metals onto granular sludge. Copyright © 2004 Society of Chemical Industry