Mass Action Law Model Research Articles

A mathematical model for ammonium removal and recovery from real municipal wastewater using a natural zeolite

A study was carried out to remove/recover ammonium (NH4+) from residual effluents in tertiary treatment by sorption/desorption processes onto a natural clinoptilolite zeolite (NZ) in batch and fixed-bed column systems. Batch equilibrium and kinetic experiments were performed at different loading of NZ and contact time intervals, respectively. The results obtained in batch were fitted by the Freundlich and Langmuir isotherms and mass action law model. The Freundlich isotherm showed better agreement with experimental data than the Langmuir model. The isotherm studies revealed a type III with a maximum capacity of 2.8 ± 0.2 mg/g at 40 mgNH4+/L. Moreover, the data from the fixed-bed column studies was well fitted by a mass transfer model, considering the intraparticle diffusion resistance given by the linear driving force model (LDF). Finally, the capacity of NH4+ recovery of activated zeolite was measured experimentally and by a robust dynamic desorption model. The column desorption results demonstrated that higher recoveries (92–99.99%) were observed when increasing the flow rate to 0.12 mL/min. The uniqueness of this study is its capability to simulate both the sorption and desorption processes of the naturally derived sorbent for the effective removal and recovery of NH4+-N from real wastewater stream.

Perspective of reactive separation of levulinic acid in conceptual mixer settler reactor.

Levulinic acid is a carboxylic acid present in industrial downstream. It is an important chemical and can be transformed into various important chemicals such as 1,4-pentanediol, aminolevulinic acid, succinic acid, gamma valarolactone, hydoxyvaleric acid, and diphenolic acid. It is considered one of the top ten most important building block chemicals and bio-derived acids. Levulinic acid can be directly produced using biomass, chemical synthesis, and fermentation processes at industrial and laboratory scales. The biomass process produces the char, whereas the fermentation process generates waste during the production of levulinic acid, leading to an increase in the production cost and waste streams. The separation of levulinic acid from the waste is expensive and challenging. In the present study, reactive extraction was employed using trioctylamine in i-octanol for the separation of levulinic acid. The experimental results were expressed in terms of performance parameters like distribution coefficient (0.099-6.14), extraction efficiency (9-86%), loading ratio (0.09-0.7), and equilibrium complexation constant (11.34-1.05). The mass action law model was also applied and found the predicted values were in close agreement with the experimental results. The mixer settler extraction in series was used to achieve more than 98% separations of acid. Furthermore, the conceptual approach for separation of levulinic acid using a mixer settler reactor scheme was discussed and presented various design parameters including extraction efficiency, diffusion coefficient, equilibrium complexation constant, and loading ratio. The study is helpful in recovering the valuable chemicals present in industrial downstream and reducing their environmental impacts if any.

Reactive extraction of cis,cis-muconic acid from aqueous solution using phosphorus-bonded extractants, tri-n-octylphosphineoxide and tri-n-butyl phosphate: Equilibrium and thermodynamic study

• The muconic acid extraction by TOPO and TBP have been done firstly in the literature. • Different solvents used to solve TOPO and TBP. • Kinetic studies of the extraction mucconic acid was studied firstly in the literature. cis,cis- Muconic acid falls under the category of carboxylic acids and finds application mostly in biodegradable polymers, agrochemicals, and the food industry. Owing to the high thermal reactivity based upon the two-terminal carboxylic groups present in their structure, the chemical industry has widely used carboxylic acids. The major obstacle encountered during the production of carboxylic acids is their recovery from aqueous solutions and fermentation media. Therefore, the recovery of HccMA by reactive extraction as a particular product capture method, using tri- n -octylphosphine oxide (TOPO) and tri- n -butyl phosphate (TBP) in organic diluents such as 1-butanol, isoamyl alcohol, methyl ethyl ketone (MEK), methyl isobutyl ketone (MIBK), diisobutyl ketone, isobutanol, n -hexane, dimethyl glutarate, ethyl propionate, and diethyl carbonate (DEC) was executed in this study. This method was experimentally conducted to explore the most proper extractant and diluent combination. Extraction experiments were also conducted with pure diluents alone to examine the extractant effect on the extraction system. The important extraction parameters like distribution coefficient ( K D ), extraction efficiency ( E %), loading ratio ( Z ), dimerization constant ( D ), partition coefficient ( P ), and complexation constant ( K E 11 ) were determined. Mass action law model interpreted the obtained results. For HccMA/TOPO extraction system, the maximum extraction efficiency was found 93.19% in the presence of n -hexane as a diluent. For HccMA/TBP extraction system, the maximum extraction efficiency was found 90.37% in the presence of ethyl propionate as a diluent. Thermodynamic studies at variable temperatures were also carried out to estimate ΔH, ΔS, and ΔG of the process. To investigate the feasibility of designing a counter-current liquid–liquid extraction column, the number of theoretical stages (NTS) were assessed by theodified Kremser equation and found between 3 and 5 to et the desired extraction efficiency.

Modeling and optimization of reactive extraction equilibria and kinetic study of gallic acid using tributyl phosphate in isoamyl alcohol

ABSTRACT Equilibrium and kinetic experiments were performed for gallic acid recovery using tributyl phosphate dissolved in isoamyl alcohol as a diluent. Employing an extractive-reaction system results in significantly higher acid recovery in comparison to physical extraction. Overall equilibrium extraction complexation constant KE was found to be in the range 4.325–6.896. 1:1 acid: extractant complexes are proposed from the results obtained from mass action law model. Adsorption isotherm models (Langmuir, Freundlich, Temkin) and Response Surface Methodology was used, Mass transfer coefficient (kL ) and diffusivity coefficient were also calculated. Extraction kinetics was observed to be very slow based on the Hatta number.

Equilibrium Treatment for Highly Selective Sulfonated Microcapsules Containing Di(2-ethylhexyl)phosphoric Acid

Microcapsules containing di(2-ethylhexyl)phosphoric acid (DEHPA) within a sulfonated poly(styrene-co-divinylbenzene) shell (SMC-DEHPA), were characterized by different analytical techniques including the stepwise isothermal analysis and FT-IR, which indicated the presence of DEHPA, sulfonic groups, and sulfone cross-linking in the material. The separation of copper from aqueous solutions was investigated by equilibrium studies. According to the ideal mass action law model, the useful capacity of this material was 1.782 ± 0.013 equiv kg–1, where DEHPA represents half of this value (in agreement with its content). On the other hand, nonsulfonated microcapsules or those without DEHPA presented lower useful capacities. Furthermore, sulfonated material exhibited an enhancement of the selectivity for copper, as confirmed by the equilibrium constants (Ksulfonated > 104Knonsulfonated). Thus, the incorporation of sulfonic groups into the polymeric shell favors the mobility of the counterions in the microcapsule, m...

Drug solubilization mechanism of α-glucosyl stevia by NMR spectroscopy

We investigated the drug solubilization mechanism of α-glucosyl stevia (Stevia-G) which was synthesized from stevia (rebaudioside-A) by transglycosylation. (1)H and (13)C NMR peaks of Stevia-G in water were assigned by two-dimensional (2D) NMR experiments including (1)H-(1)H correlation, (1)H-(13)C heteronuclear multiple bond correlation, and (1)H-(13)C heteronuclear multiple quantum coherence spectroscopies. The (1)H and (13)C peaks clearly showed the incorporation of two glucose units into rebaudioside-A to produce Stevia-G, supported by steviol glycoside and glucosyl residue assays. The concentration-dependent chemical shifts of Stevia-G protons correlated well with a mass-action law model, indicating the self-association of Stevia-G molecules in water. The critical micelle concentration (CMC) was 12.0 mg/mL at 37°C. The aggregation number was 2 below the CMC and 12 above the CMC. Dynamic light scattering and 2D (1)H-(1)H nuclear Overhauser effect spectroscopy (NOESY) NMR experiments demonstrated that Stevia-G self-associated into micelles of a few nanometers in size with a core-shell structure, containing a kaurane diterpenoid-based hydrophobic core and a glucose-based shell. 2D (1)H-(1)H NOESY NMR measurements also revealed that a poorly water-soluble drug, naringenin, was incorporated into the hydrophobic core of the Stevia-G micelle. The Stevia-G self-assembly behavior and micellar drug inclusion capacity can achieve significant enhancement in drug solubility.

Reactive Extraction of Phenylacetic Acid with Tri-n-butyl Phosphate in Benzene, Hexanol, and Rice Bran Oil at 298 K

Phenylacetic acid extraction from an aqueous system gets consideration because of its extensive uses in the production of β-lactam antibiotics. In the present paper, reactive extraction has been investigated for the removal of phenylacetic acid by tri-n-butyl phosphate from the aqueous phase in benzene, hexanol, and rice bran oil as diluents. Reactive extraction data were discussed in terms of overall distribution coefficients (Do), loading ratio (ϕ), degree of extraction (η %), and equilibrium complexation constants (Eαβ). The mass action law model was used to represent equilibrium of reactive extraction of phenylacetic acid–tri-n-butyl phosphate. Also the results on water coextraction have been presented. A further extensive discussion on toxicity, back extraction, and regeneration was given. It is a first kind of study for the removal of phenylacetic acid from the aqueous phase by reactive extraction using tri-n-butyl phosphate in benzene, hexanol, and rice bran oil.

NMR investigation of a novel excipient, α‐glucosylhesperidin, as a suitable solubilizing agent for poorly water‐soluble drugs

α-Glucosylhesperidin (Hsp-G), a functional food additive, significantly enhances the solubility and bioavailability of poorly water-soluble drugs despite little surface activity. Herein, we present investigations into the underlying mechanism by nuclear magnetic resonance techniques. A concentration dependence of the chemical shift of Hsp-G protons correlated well with a mass-action law model, indicating self-association of Hsp-G molecules. The critical micelle concentration was 5.0 mg/mL (6.5 mM) at 37°C. The gradual rather than abrupt chemical shift variation upon Hsp-G aggregation would be different mode to conventional surfactants. Dynamic light scattering and two-dimensional nuclear Overhauser effect spectroscopy measurements demonstrated that Hsp-G molecules self-associated into particular small micelles, with the flavanone skeleton forming a hydrophobic core, and surrounding sugar groups working as a shell. The packing of the hydrophobic portion is not strictly oriented and the intermolecular arrangement of micelle shell is loose. Solubility enhancement was due to the incorporation of drugs into Hsp-G micelle, with naringenin being more soluble than flurbiprofen. This difference is possibly related to the structural similarities between the hydrophobic portion and the micelle core. Hsp-G micellization process with little loss of surface tension is a unique observation in surface and interface science. © 2011 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 100:4421–4431, 2011

Modeling of the three-phase equilibrium in systems of the type water + nonionic surfactant + alkane

Liquid–liquid equilibria of systems water (A) + C i E j surfactant (B) + n-alkane (C) have been modeled by a mass-action law model previously developed and so far successfully applied to a series of binary water + C i E j systems and to the ternary system water + C 4E 1 + n-dodecane. These calculations provide the basis for the presented modeling. The aqueous systems give information about the association constants and the χ AB-parameter of the Flory–Huggins theory and the ternary C 4E 1-system provides universal temperature functions for the χ AC- and the χ BC-parameter. The three-phase equilibrium for seven ternary C i E j systems ( i = 6–12, j = 3–6) has been calculated by fitting one additional parameter for each of both temperature functions to the characteristic “fish-tail” point. The agreement with the experimental data is reasonably well. For systems with very small three-phase areas the results can considerably be improved by individual temperature functions that incorporate the experimental temperature maximum of the “fish” into the parameter fit. Based on the parameters of the system water + C 8E 4 + n-C 8H 18 the “fish-shaped” phase diagram of the system water + C 8E 4 + n-C 14H 30 was predicted reasonably well.

Purification of glycerol/water solutions from biodiesel synthesis by ion exchange: sodium and chloride removal. Part II

AbstractBACKGROUND: Equilibrium studies were carried out with the aim of finding the basic design parameters for ion exchange plants using a glycerol phase obtained from biodiesel production. The uptake of sodium and potassium ions on a strongly acidic ion exchanger, Amberlite IR‐120, in the proton form from glycerol/water mixtures has been studied. The effect on the selectivity towards sodium of the percentage of water in glycerine/water mixtures on the macroporous resin Amberlite 252 has been analyzed. Finally, chloride removal by a strongly basic anionic‐exchange resin Amberlite IRA‐420 at three different temperatures has been studied.RESULTS: The strongly acidic ion exchanger Amberlite IR‐120 exhibits higher selectivity for potassium versus sodium ions. The ideal mass action law model was able to fit the experimental equilibrium data. The equilibrium data obtained at different percentages of water in the glycerine/water mixture indicate that as the water content increased the resin selectivity for sodium uptake is reduced. The selectivity of the anion exchange resin Amberlite IRA‐420 for chloride ions decreases with temperature. The ideal mass action law was accurate enough to fit the equilibrium data of the three systems and allowed the equilibrium thermodynamic properties to be obtained.CONCLUSIONS: These results confirm that macroporous resin Amberlite 252 could be a good choice to remove sodium ions from glycerol/water solutions with a high salt concentration and also that a strongly basic anionic‐exchange resin could be used for chloride removal. Copyright © 2009 Society of Chemical Industry

Purification of glycerol/water solutions from biodiesel synthesis by ion exchange: sodium removal Part I

AbstractBACKGROUND: In this study, equilibrium and kinetic data of the ion exchange of sodium from glycerol–water mixtures on the strong acid resin Amberlite‐252 were obtained. Basic parameters for the design of ion exchange units for the purification of the crude glycerol phase from biodiesel production have been determined.RESULTS: Equilibrium uptake of sodium ions with the strong acid ion exchanger Amberlite‐252 was studied at three temperatures. The Langmuir equation and the mass action law model were used to fit the experimental equilibrium data. Equilibrium constants and thermodynamic parameters were obtained at each temperature. Kinetic experiments were carried out to evaluate the effective diffusion coefficients of sodium on the resin Amberlite‐252 in glycerine–water media.CONCLUSIONS: Equilibrium results indicate that this process is favourable and also that its selectivity decreases with temperature increase from 303 to 333 K. Both models were able to fit the experimental equilibrium data. Kinetic experiments showed that the rate of mass transfer in this binary system is high. An Arrhenius type equation allowed the correlation of effective diffusion coefficients and temperature. The results indicate that the macroporous resin Amberlite‐252 could be useful for removal of sodium ions from glycerine/water solutions with a high salt concentration. Copyright © 2008 Society of Chemical Industry

Liquid–liquid equilibrium calculation in binary water + nonionic surfactant C iE j systems with a new mass-action law model based on continuous thermodynamics

A systematic study of the LLE for a number of aqueous solutions of n-alkyl polyglycol ethers (C i E j ) with tail length i from 4 to 12 and head length j from 1 to 6 is presented. For calculation a new thermodynamic model was developed basing on the mass-action law and continuous thermodynamics. Besides the micellization the self association of water is taken into account. The resulting polydisperse mixture of micelles and water associates is described by two continuous aggregation-size distribution functions depending on temperature and surfactant concentration. The Gibbs energy of the mixture is calculated by the Flory-Huggins theory with a temparature dependent parameter χ. The model is applied to 13 water + C i E j systems with LCST behavior and to the three systems water + C 4E 1, water + C 10E 4 and water + C 10E 5 with closed-loop miscibility gaps. For the former 13 systems four parameters were fitted to the experimental equilibrium data. For the systems with closed-loop miscibility gaps two additional parameters were necessary, due two the more extended temperature range. The agreement between calculated and experimental data is very good for nearly all systems of both types.

Equilibrium Data for the Exchange of Cu2+, Cd2+, and Zn2+ Ions for H+ on the Cationic Exchanger Amberlite IR-120

Equilibrium ion-exchange isotherms of H+/Cu2+, H+/Cd2+, and H+/Zn2+ on a strong acid resin, Amberlite IR-120, in an aqueous medium at (283 and 303) K have been determined in order to assess the possibility of using ion exchange to eliminate heavy-metal ions from industrial aqueous liquid streams. The experimental equilibrium data have been satisfactorily correlated using the homogeneous mass action law model (LAM). This model assumes nonideal behavior for both the solution and solid phases. Wilson and Pitzer equations have been used to calculate activity coefficients in the resin and liquid phases, respectively. The values of the thermodynamic equilibrium constants show a temperature dependence.

Ion-Exchange Equilibria of Cu2+, Cd2+, Zn2+, and Na+ Ions on the Cationic Exchanger Amberlite IR-120

Equilibrium ion-exchange isotherms of Na+/Cu2+, Na+/Cd2+, and Na+/Zn2+ on a strong acid resin, Amberlite IR-120, in aqueous medium at (283 and 303) K have been determined in order to assess the possibility of using ion exchange to eliminate heavy metal ions from industrial aqueous liquid streams. The experimental equilibrium data have been satisfactorily correlated using the homogeneous mass action law model (LAM). This model assumes nonideal behavior for both the solution and the solid phase. Wilson and Pitzer equations have been used to calculate activity coefficients in the solid and liquid phases, respectively. The values of the thermodynamic equilibrium constant demonstrate temperature dependence.

Ion Exhange Equilibria in Nonaqueous and Mixed Solvents on the Cationic Exchanger Amberlite IR-120

Na+/K+ equilibrium ion exchange isotherms on Amberlite IR-120 (known as a strong acid resin) in pure methanol, ethanol, 2-propanol, 1-butanol, and 1-penthanol and in mixtures of methanol + water, ethanol + water, 2-propanol + water, 1-butanol + methanol, and 1-penthanol + methanol at 313 K have been determined. Experimental equilibrium data have been satisfactorily correlated using the homogeneous mass action law model (LAM). This model assumes nonideal behavior for both the solution and the solid phase. Wilson and Debye−Huckel equations have been used to calculate activity coefficients in the solid and liquid phase, respectively. It has been observed that the dielectric constant of the solvent or the mixture exerts a strong influence not only on the useful capacity of the resin but also on the equilibrium behavior of the system.

NMR Investigation on the Various Aggregates Formed by a Gemini Chiral Surfactant

In this paper we report an NMR investigation on the chiral gemini surfactant (2S,3S)-2,3-dimethoxy-1,4-bis(N-hexadecyl-N,N-dimethylammonium)butane dibromide (1), carried out to study the aggregation in various solvents. If the aggregation equilibrium of 1 can be described by the mass action law model, by observing the variation of chemical shift with respect to [1], we can obtain the aggregation number n. In CDCl3 the values are n = 2 and 19 ± 3, at low and high [1], respectively, indicating that 1 is present in dimeric assemblies and as reversed micelles. In CD3OD, despite evidence that 1 is under aggregating conditions, the model does not hold; 1 should form a relatively flexible structure, because in the 13C NMR spectra 1J(13C,14N) coupling is observed (1J = 3.4 Hz). 1 is scarcely soluble in D2O; in the 1H NMR spectrum of 1 × 10-3 M 1, the signals relative to the tails and to one of the NCH3 groups disappear, while the other head group signals are well resolved, indicating the presence of large assembl...

Apparent molar volumes and heat capacities of aqueousn-dodecylpyridinium chloride at molalities from 0.003 mol·kg−1to 0.15 mol·kg−1, at temperatures from 283.15 K to 393.15 K, and at the pressure 0.35MPa

Apparent molar volumes of aqueous solutions ofn-dodecylpyridinium chloride (DDPC) were measured atT=(298.15, 313.15, 328.15, 343.15, 358.15, and 372.05) K atp=0.35MPa. A mass-action model was used to describe the results and to obtain densities of DDPC solutions at 5 K intervals fromT=283.15 K toT=393.15 K. Apparent molar heat capacities of aqueous solutions of DDPC were determined at 5 K intervals fromT=283.15 K toT=393.15 K atp=0.35MPa using a fixed-cell, power-compensation, differential-output, temperature-scanning calorimeter. Measurements were made from molalities 0.003 mol·kg−1to 0.15 mol·kg−1for both densities and heat capacities. The same mass-action law model was used to try to describe all the apparent molar heat capacity results simultaneously.

Enthalpies of mixing a non-ionic surfactant with water at 303.15 K studied by calorimetry

The enthalpy of mixing n-octyl penta(oxyethylene glycol)(C8E5) with water has been studied at 303.15 K by titration and mixing calorimetry. In the region of the critical micelle concentration (c.m.c.), when liquid surfactant is added to water, a sudden endothermic shift is observed in the differential enthalpy of mixing of C8E5. The variation of the differential enthalpy with composition in this region gives information on the average size of the non-ionic micelles. Using the mass-action law model, an aggregation number of 41 was obtained for the micelles. The value is lower than those obtained from recent spectroscopic studies. The thermodynamic quantities of micelle formation of C8E5, and of C8E4, in water have been obtained. For binary mixtures the enthalpy of mixing was exothermic for all compositions. The apparent and partial molar enthalpies of mixing of the surfactant and the partial molar enthalpies of the water have been calculated. Beyond the c.m.c. the partial molar enthalpies of the two components vary regularly with the composition.

A Model for the Effect of Estrogen Antagonists on Cooperative Estradiol Binding

Partial agonists such as estriol and estrone have been reported to diminish or even eliminate the upward convexity of the Scatchard plot of the binding of labeled estradiol to estrogen receptor. This has been interpreted as agonist interference with the receptor dimerization induced by estradiol. In order to investigate how a partial agonist or antagonist might interfere with dimerization we have developed a theoretical mass-action law model, where soluble receptors can dimerize and bind to two different ligands. Special attention was devoted to manifestations of positive cooperativity to determine whether they could be modified by competition with a second ligand. This was done using a computer program that evaluated a large set of combinations of affinity constants in an effort to explore all possible situations. The model could reproduce the effect of a second ligand on the cooperative binding of estradiol to the estrogen receptor but only if the second ligand was anticooperative, which is not the case of estriol, estrone and tamoxifen. Furthermore, even when the Scatchard plot was linear, the model still required dimerization of the receptor in most of the cases, showing that the addition of an antagonist may eliminate the upward curvature of the Scatchard without truly eliminating dimerization or cooperativity. We conclude that the effect of a second ligand on the binding of labeled estradiol to estrogen receptor is not necessarily due to interference with dimerization and/or cooperativity. The inability of this model to fully explain the published data for estriol, estrone, clomiphene, and tamoxifen suggests that a more complex mechanism is involved.

Interaction of poly(ethylene oxide) with sodium dodecyl sulfate micelles: a fast kinetic study by temperature jump

The modification of sodium dodecyl sulfate (SDS) micelle dissolution-formation relaxation time tau2 (and relaxation amplitude) brought about by the addition of poly(ethylene oxides) (PEO) is investigated by using the temperature-jump technique with a spectroscopic probe (acridine orange). Whereas small molecular weight additives (dioxane, PEO 1000) have no special effect on these quantities, a very particular behavior is observed with PEO 10,000. It is shown that this behavior is in relation with the formation of the stoichiometric polymer-surfactant complex, which has been previously observed by means of different static methods. The influence of different parameters on tau2 is examined: polymer concentration, surfactant concentration, added salt concentration, temperature. The results are interpreted, with the aid of a mass action law model for polymer-surfactant complex formation, as supporting the idea that the complex is constituted of a micelle wrapped up by the polymer chain rather than by a polymer saturated by a linear adsorption of surfactant molecules. The observed features agree with the picture of a polymer-surfactant complex entity having between 0.5 and 1 chain of PEO 10,000 per micelle. 25 references, 9 figures.