Thermodynamic Equilibrium Constants Research Articles

An insight into thermodynamics of adsorptive removal of fluoride by calcined Ca–Al–(NO3) layered double hydroxide

A framework for determination of thermodynamic equilibrium constant and Gibbs free surface energy change was presented. The interactive effect of temperature on adsorption process was addressed by RSM. Endothermic, spontaneous reaction was observed.

Thermodynamic description of the ion exchange and superequivalent sorption of phenylalanine by KU-2-8 cationite

The coefficients and thermodynamic equilibrium constants, activity coefficients of the sorbent phase, and integral and differential Gibbs energies of the ion-exchange and superequivalent sorption of phenylalanine by strongly acidic KU-2-8 cationites in the H form are calculated using a new thermodynamic approach that allows us to describe the simultaneous exchange and superequivalent sorption of substances by ionites.

Spectrophotometric and electrochemical quantification of the host–guest interaction of tenoxicam and β-CD in aqueous solution at different pH values

This work dealt with the spectrophotometric and electrochemical determination of the thermodynamic formation constants, Kf, of the host–guest inclusion complex between diverse tenoxicam species in aqueous solution, Tenox́, and β-cyclodextrin (β-CD) namely: β-CD-H2Tenox+, β-CD-HTenox(z) and β-CD-Tenox−. It was found that it is possible to form the said inclusion complex regardless of the nature of the tenoxicam chemical species and that for each case, similar values of Kf were found from both experimental techniques. Moreover, the values of the Tenox’s acidity constants are also reported. From all these estimated thermodynamic equilibrium constants, the 3D distribution diagram for the different species of the Tenox in the space molar fraction-[β-CD]-pH was constructed.

Temperature-Dependent Model for the Prediction of Binary Ion Exchange Equilibria Involving Na+, K+, Ca2+ and Mg2+ Ions

The effect of temperature on the ion exchange equilibrium behavior of binary systems is studied experimentally and modeled. The study considers the exchange between binary systems involving Na+, K+, Ca2+ and Mg2+ ions with Cl– as a nonexchanging anion on Rohm and Hass gel-type Amberjet 1200H resin as the ion exchange medium. Experimental equilibrium data is obtained for the six constitutive binary systems at 4.0, 25.0 and 60.0 °C with a total solution concentration of 0.10 N. The nonidealities in the solution and exchanger phases are modeled by applying the Pitzer and Wilson models, respectively. Thermodynamic equilibrium constant and Wilson interaction parameters are modeled with respect to temperature. The model proposed allows the influence of temperature on the ion exchange equilibrium behavior to be predicted well.

The reaction enthalpy of hydrogen dissociation calculated with the Small System Method from simulation of molecular fluctuations.

We show how we can find the enthalpy of a chemical reaction under non-ideal conditions using the Small System Method to sample molecular dynamics simulation data for fluctuating variables. This method, created with Hill's thermodynamic analysis, is used to find properties in the thermodynamic limit, such as thermodynamic correction factors, partial enthalpies, volumes, heat capacities and compressibility. The values in the thermodynamic limit at (T,V, μj) are then easily transformed into other ensembles, (T,V,Nj) and (T,P,Nj), where the last ensemble gives the partial molar properties which are of interest to chemists. The dissociation of hydrogen from molecules to atoms was used as a convenient model system. Molecular dynamics simulations were performed with three densities; ρ = 0.0052 g cm(-3) (gas), ρ = 0.0191 g cm(-3) (compressed gas) and ρ = 0.0695 g cm(-3) (liquid), and temperatures in the range; T = 3640-20,800 K. The enthalpy of reaction was observed to follow a quadratic trend as a function of temperature for all densities. The enthalpy of reaction was observed to only have a small pressure dependence. With a reference point close to an ideal state (T = 3640 K and ρ = 0.0052 g cm(-3)), we were able to calculate the thermodynamic equilibrium constant, and thus the deviation from ideal conditions for the lowest density. We found the thermodynamic equilibrium constant to increase with increasing temperature, and to have a negligible pressure dependence. Taking the enthalpy variation into account in the calculation of the thermodynamic equilibrium constant, we found the ratio of activity coefficients to be in the order of 0.7-1.0 for the lowest density, indicating repulsive forces between H and H2. This study shows that the compressed gas- and liquid density values at higher temperatures are far from those calculated under ideal conditions. It is important to have a method that can give access to partial molar properties, independent of the ideality of the reacting mixture. Our results show how this can be achieved with the use of the Small System Method.

Electrochemical quantification of the thermodynamic equilibrium constant of the tenoxicam-β-cyclodextrin inclusion complex formed on the surface of a poly-β cyclodextrin-modified carbon paste electrode

In this work it is shown that when a carbon paste electrode, CPE, is modified with a β-cyclodextrin polymer, the tenoxicam oxidation becomes an adsorption controlled process due to formation of a surface inclusion complex with the β-CD molecules comprising the surface of the polymer. It was found that such surface inclusion complex can be formed independently of the tenoxicam predominant species, Tenox’, in the aqueous solution namely: H2Tenox+, HTenox or Tenox−, depending on the solution pH. The electrochemical quantification of the thermodynamic constant of the equilibrium Tenox’+β-CD (polymer)=Tenox’-β-CD (polymer) was estimated as log Kincl.=4.26±0.01. Furthermore, from the analyses of the experimental voltammograms according with Laviron's equation for an irreversible surface reaction [E. Laviron, J. Electroanal. Chem. 52 (1974) 355-393] it is shown that the surface concentration, ΓR, of tenoxicam increases as its concentration in solution does, reaching a maximum value of 1.51×10−10molcm−2 at 64μM.

Thermodynamic model for tungstic acid extraction from sodium tungstate in sulfuric acid medium by primary amine N1923 diluted in toluene

A thermodynamic model for the extraction of tungstic acid from sodium tungstate in sulfuric acid using the primary amine N1923 diluted in toluene has been developed. The liquid–liquid extraction equilibrium data were determined by performing a series of experiments at 293.15K. The activity coefficients of the ions and molecules in the aqueous and organic phases were calculated using the Pitzer equations. Nonlinear regression, based on the balance equations of chemical, mass and charge equilibria and the experimental data, was used as the optimization method. Next, the thermodynamic equilibrium constant and the new Pitzer parameters for sodium tungstate electrolytes in the aqueous phase and the binary interactions between the species in the organic phase were obtained. The new model was used to predict the extraction efficiency from different initial conditions. Experiments were performed to verify the new model. The results indicated that the model could moderately predict this extraction system. Furthermore, the extraction reaction mechanism was investigated using the new model, and the scope of the new model is discussed.

Quantum-Chemical Modeling of Equilibrium State of Systems Cyclotri-, Tetra-, Penta-and Hexaphosphates with di-and Trivalent Cations of p-and d-elements

The thermodynamic properties and equilibrium constants of cyclotri-, tetra-, penta-and hexaphosphates systems with di-and trivalent cations, p-and d-elements for different cyclophosphate / metal molar ratios equal 2:1, 1:1, 1:2 and 1:3 were calculated by using PM3 quantum-chemical semi-empirical method. It was shown that the state of systems equilibrium determines their strength and formation patterns.

Adsorption Parameters Studies for the Removal of Mercury from Aqueous Solutions Using Hybrid Sorbent

ABSTRACTThe aim of this research work is to investigate adsorption of mercury ions from an aqueous solution on a biocompatible polymeric polypyrrole‐chitosan (PPy/CTN) nanocomposite. The PPy/CTN nanocomposite was prepared in aqueous media by chemical polymerization of pyrrole in the presence of ferric chloride as an oxidant. Langmuir, Freundlich, and Temkin adsorption isotherms were applicable to the adsorption process, and their constants were evaluated. The thermodynamic equilibrium constant and the Gibbs free energy were determined. Results indicated that the Langmuir model gave a better fit to the experimental data than the other two equations. The adsorption capacity (qmax) of PPy/CTN for Hg(II) ions in terms of monolayer adsorption was 40 mg/g. The negative value of Gibbs free energy (ΔGo) indicates feasible and spontaneous adsorption of Hg(II) on the PPy/CTN nanocomposite. Also the change in entropy (ΔSo) and enthalpy (ΔHo) were estimated to be –0.21 KJ (mol K)−1 and –18.183 kJ mol−1, respectively.

Study on Halide Ions Selectivity of Industrial Grade Anion Exchange Resin Auchlite A-378

The thermodynamic approach was applied to predict the trend selectivity of industrial grade anion exchange resin Auchlite A-378 in chloride form towards iodide and bromide ions in the solution. The study was conducted by performing the Clˉ/Iˉ and Clˉ/Brˉ uni-univalent ion exchange reactions under gradually increasing temperature conditions. The thermodynamic equilibrium constants K values were used to calculate the enthalpies of the two uni-univalent ion exchange reactions. It was observed that the K values for Clˉ/Iˉ ion exchange reaction were higher than Clˉ/Brˉ exchange reaction under identical experimental conditions. Also the enthalpy values for the two uni-univalent ion exchange reactions were calculated as -39.51 and -18.38 kJ/mol respectively. The high K and low enthalpy values obtained for Clˉ/Iˉ ion exchange reaction is responsible for higher selectivity of the resin towards iodide ions as compared to that towards bromide ions, when both the ions are present in the same solution.

Zinc Chloride and Hydrochloric Acid Coextraction from Galvanizing Pickling Waste in the Presence of Iron(II). Results with Hollow Fiber Membrane Contactors

Spent pickling acid from the industrial galvanizing process currently requires specialist disposal, yet there is the potential to recover the zinc as a valuable metal. In this work, we compare the extraction of zinc using tributyl phosphate from real galvanizing effluent and laboratory prepared solutions. Both commercial and handmade hollow fiber membrane contactors are used for this purpose. While the zinc is effectively extracted, care must be taken to prefilter the solution upstream of the membrane contactor to minimize crud formation and interfacial effects. The extraction of both zinc and HCl from the effluent is satisfactorily described using mathematical models for both the multicomponent equilibria and mass transfer balances. In development of the multicomponent equilibrium model, the thermodynamic equilibrium constants obtained from the ZnCl2–NaCl–HCl aqueous system were found to be applicable to the ZnCl2–FeCl2–HCl system.

Study on Halide Ions Selectivity of Industrial Grade Anion Exchange Resin Auchlite A-378

The thermodynamic approach was applied to predict the trend selectivity of industrial grade anion exchange resin Auchlite A-378 in chloride form towards iodide and bromide ions in the solution. The study was conducted by performing the Clˉ/Iˉ and Clˉ/Brˉ uni-univalent ion exchange reactions under gradually increasing temperature conditions. The thermodynamic equilibrium constants K values were used to calculate the enthalpies of the two uni-univalent ion exchange reactions. It was observed that the K values for Clˉ/Iˉ ion exchange reaction were higher than Clˉ/Brˉ exchange reaction under identical experimental conditions. Also the enthalpy values for the two uni-univalent ion exchange reactions were calculated as -39.51 and -18.38 kJ/mol respectively. The high K and low enthalpy values obtained for Clˉ/Iˉ ion exchange reaction is responsible for higher selectivity of the resin towards iodide ions as compared to that towards bromide ions, when both the ions are present in the same solution.

Experimental determination of the silica solubility and of the H4SiO 4 0 activity ratio in standard and desalinated seawater

The solubility of amorphous silica was studied in mixtures of riverine and marine waters simulating the water composition at the river-sea geochemical barrier. The value of the thermodynamical equilibrium constant was determined for the reaction of silicon solubility as Kr0 = (1.71 ± 0.01) × 10−3 at 22°C. A near-linear dependence was found for the activity ratio of the H4SiO40 and the salinity with the increase of this ratio from 1.00 in the riverine to 1.15 in the standard seawater.

Removal of uranium(VI) from aqueous solutions using nanoporous ZnO prepared with microwave-assisted combustion synthesis

The adsorption of the uranyl ions from aqueous solutions on the nanoporous ZnO powders has been investigated under different experimental conditions. The adsorption of uranyl on nanoporous ZnO powders were examined as a function of the contact times, pH of the solution, concentration of uranium(VI) and temperature. The ability of this material to remove U(VI) from aqueous solution was followed by a series of Langmuir and Freunlinch adsorption isotherms. The adsorption percent and distribution coefficient for nanoporous ZnO powders were 98.65 % ± 1.05 and 7,304 mL g−1, respectively. The optimum conditions were found as at pH 5.0, contact time 1 h, at 1/5 Zn2+/urea ratio, 50 ppm U(VI) concentration and 303 K. The monomolecular adsorption capacity of nanoporous ZnO powders for U(VI) was found to be 1,111 mg g−1 at 303 K. Using the thermodynamic equilibrium constants obtained at different temperatures, various thermodynamic parameters, such as ΔG°, ΔH° and ΔS°, have been calculated. Thermodynamic parameters (ΔH° = 28.1 kJ mol −1, ΔS° = 160.30 J mol−1 K−1, ΔG° = −48.54 kJ mol−1) showed the endothermic and spontaneous of the process. The results suggested that nanoporous ZnO powders was suitable as sorbent material for recovery and adsorption of U(VI) ions from aqueous solutions.

Ion-Exchange Reaction Thermodynamics to Study the Selectivity Behaviour of Nuclear and Non-Nuclear Grade Anion Exchange Resins

In the present investigation, attempts were made to understand the difference in bromide ion selectivity of the two closely related anion exchange resins Auchlite ARA-9366 and Auchlite A-378 in chloride form. The selectivity difference was predicted based on the thermodynamic equilibrium constants and enthalpy values of Clˉ/Brˉ ion exchange reactions performed by using the two resins. During Clˉ/Brˉ exchange reactions, with rise in temperature from 30.0°C to 45.0 °C, the equilibrium constant (K) values were observed to decreases from 8.15x10-2 to 6.06x10-2 for Auchlite ARA-9366 resins and from 2.16x10-2 to 1.10x10-2 for Auchlite A-378 resins. The decrease in K values with rise in temperature, indicate exothermic ion exchange reactions having enthalpy values of -36.14 and -18.38 kJ/mol respectively. The high K and low enthalpy values obtained for Auchlite ARA-9366 resins indicate their greater selectivity for the bromide ions in the solution as compared to Auchlite A-378 resins.

Ion-Exchange Reaction Thermodynamics to Study the Selectivity Behaviour of Nuclear and Non-Nuclear Grade Anion Exchange Resins

In the present investigation, attempts were made to understand the difference in bromide ion selectivity of the two closely related anion exchange resins Auchlite ARA-9366 and Auchlite A-378 in chloride form. The selectivity difference was predicted based on the thermodynamic equilibrium constants and enthalpy values of Clˉ/Brˉ ion exchange reactions performed by using the two resins. During Clˉ/Brˉ exchange reactions, with rise in temperature from 30.0°C to 45.0 °C, the equilibrium constant (K) values were observed to decreases from 8.15x10-2 to 6.06x10-2 for Auchlite ARA-9366 resins and from 2.16x10-2 to 1.10x10-2 for Auchlite A-378 resins. The decrease in K values with rise in temperature, indicate exothermic ion exchange reactions having enthalpy values of -36.14 and -18.38 kJ/mol respectively. The high K and low enthalpy values obtained for Auchlite ARA-9366 resins indicate their greater selectivity for the bromide ions in the solution as compared to Auchlite A-378 resins.

Confusing Quantitative Descriptions of BrønstedLowry AcidBase Equilibria in Chemistry Textbooks – A Critical Review and Clarifications for Chemical Educators

AbstractIn chemistry textbooks, the pK value of water in the solvent water at 25 °C is sometimes given as 14.0, sometimes as 15.7. This is confusing. The particular chemical reaction considered is the one in which water as BrønstedLowry acid reacts with water as BrønstedLowry base in water as solvent to yield equal concentrations of hydrated oxonium and hydroxide ions, H3O+(aq) and HO−(aq), respectively. This reaction is also known as the ‘self‐ionization’ of water for which the equilibrium constant is abbreviated as Kw with its known value of 10−14.0 at 25 °C, i.e., pKw(25 °C)=14.0. Identical values for pK and pKw at a fixed temperature appear reasonable, since K and Kw refer to one and the same reaction. Therefore, reasons for the apparent disagreement between the ‘thermodynamically correct’ pKa value for water (14.0 at 25 °C) and the value reported in most organic chemistry textbooks (15.7) should be discussed when teaching acidbase chemistry. There are good arguments for introducing, from the very beginning, the concepts of activity and thermodynamic standard states when teaching quantitative aspects of chemical equilibria. This also explains in a straightforward way why all thermodynamic equilibrium constants, including Kw, are dimensionless, and why pK(25 °C)=0.

Affinity of a Drug for and Residence Time at its Target

A major problem in drug designing and development is the difficulty in predicting efficacy in humans from in vitro data. For a long time, it was thought that an important contributor to the efficacy of a drug is its affinity for the target. This traditional view was challenged by accumulative evidence suggesting that thermodynamic equilibrium constants, such as Kd or Ki, in most cases do not reflect potency in vivo. A new concept was, therefore, introduced in 2006; the drug-residence time (tR) concept [1]. This has arisen from the fact that a drug can elicit its action as long as it remains bound to its target. The drug-residence time, which is the reciprocal of the rate constant for dissociation of the binary drug-target complex (koff), was suggested as an alternative perspective on drug optimization, with superior predictability for the duration of pharmacological effect and target selectivity. Nevertheless, recent studies revealed that long tR has predictability value only when koff is slower than the elimination rate of the drug from the target vicinity [2]. Therefore, pharmacokinetics as well as other factors, such as selectivity of targeting, biodynamics of the target, and endogenous ligands and signaling should be taken into account.

Thermodynamic Studies of Aqueous Solutions of 2,2,2-Cryptand at 298.15 K: Enthalpy–Entropy Compensation, Partial Entropies, and Complexation with K+ Ions

The osmotic coefficient measurements for binary aqueous solutions of 2,2,2-cryptand (4,7,13,16,21,24-hexaoxa-1,10-diazabicyclo[8.8.8] hexacosane) in the concentration range of ~0.009 to ~0.24 mol·kg(-1) and in ternary aqueous solutions containing a fixed concentration of 2,2,2-cryptand of ~0.1 mol·kg(-1) with varying concentration of KBr (~0.06 to ~0.16 mol·kg(-1)) have been reported at 298.15 K. The diamine gets hydrolyzed in aqueous solutions and needs proper approach to obtain meaningful thermodynamic properties. The measured osmotic coefficient values are corrected for hydrolysis and are used to determine the solvent activity and mean ionic activity coefficients of solute as a function of concentration. Strong ion-pair formation is observed, and the ion-pair dissociation constant for the species [CrptH](+)[OH(-)] is reported. The excess and mixing thermodynamic properties (Gibbs free energy, enthalpy, and entropy changes) have been obtained using the activity data from this study and the heat data reported in the literature. Further, the data are utilized to compute the partial molal entropies of solvent and solute at finite as well as infinite dilution of 2,2,2-cryptand in water. The concentration dependent non-linear enthalpy-entropy compensation effect has been observed for the studied system, and the compensation temperature along with entropic parameter are reported. Using solute activity coefficient data in ternary solutions, the transfer Gibbs free energies for transfer of the cryptand from water to aqueous KBr as well as transfer of KBr from water to aqueous cryptand were obtained and utilized to obtain the salting constant (ks) and thermodynamic equilibrium constant (log K) values for the complex (2,2,2-cryptand:K(+)) at 298.15 K. The value of log K = 5.8 ± 0.1 obtained in this work is found to be in good agreement with that reported by Lehn and Sauvage. The standard molar entropy for complexation is also estimated for the 2,2,2-cryptand-KBr complex in aqueous medium.

Thermodynamics of CuInO2Preparation by Cation Exchange Reaction

Abstract To investigate the optimum conditions of the CuInO2 (CIO) preparation by cation exchange reaction method, the standard entropy, thermal capacity at constant pressure, standard enthalpy and standard Gibbs free energy of formation were estimated. The relations of temperature (T) and thermodynamic equilibrium constants (K), the conditions for three independent reactions were analyzed in CuInO2 preparation. The curves of Gibbs free energy-T, K − T and PCuCl − T for those reactions have been plotted. The results showed that the CIO powder could be synthesized by cation exchange reaction. There were two main reactions through the way of NaInO2 reacting with CuCl. One was NaInO2(s) reacting with CuCl(s) at T ≥ 1698 K. The cost was higher in the way. The other was NaInO2(s) reacting with CuCl(g) at T < 1698 K. However, the yield of CIO would be decreased because CuInO2 powder decomposed into Cu2O(s) and In2O3(s) with the temperature reduced, especially when T ≤ 573 K. And the higher vapor pressure of CuCl(g) was necessary for the process, which needs the higher temperature since the vapor pressure of CuCl(g) increases with increasing temperature, especially when T > 973 K. It was recommended that NaInO2(s) react with CuCl(g) for preparing CIO under conditions of 973 < T ≤ 1698 K and the vacuum in the reactor.