Thermodynamic Equilibrium Constants Research Articles

The thermodynamic characteristics of ion exchange in a sulfonated polymer based on cis-tetraphenylcalix[4]resorcinarene

The selectivity and thermodynamic characteristics of exchange of protons in SO3H groups of a sulfonated network polymer based on cis-tetraphenylcalix[4]resorcinarene for Na+, Cu2+, and In3+ cations from aqueous solutions are considered. Semiempirical quantum-chemical calculations of molecular ensembles modeling the structure of the elementary polymer unit in the H and Na forms were performed. The experimental data on the equilibrium phase compositions and the heat of exchange were used to calculate the thermodynamic equilibrium constants, Gibbs energy, enthalpy, and entropy of ion exchange.

Adsorption, kinetics and equilibrium studies on removal of Cr(VI) from aqueous solutions using different low-cost adsorbents

Abstract The removal of Cr(VI) from aqueous solution by batch adsorption technique using different low-cost adsorbents was investigated. Adsorbents such as clarified sludge—a steel industry waste material, rice husk ash, activated alumina, fuller's earth, fly ash, saw dust and neem bark were used to determine the adsorption efficiency. The influence of pH, adsorbent type and concentration, initial Cr(VI) concentration and contact time on the selectivity and sensitivity of the removal process were investigated. Adsorption process was found to be highly pH dependent. The optimum pH range for adsorption of Cr(VI) was found to be between 2 and 3. Kinetics studies were performed to understand the mechanistic steps of the adsorption process and the rate kinetics for the adsorption of Cr(VI) was best fitted with the pseudo-2nd-order kinetic model. Langmuir and Freundlich adsorption isotherms were applicable to the adsorption process and their constants were evaluated. The thermodynamic equilibrium constant and the Gibbs free energy were determined for each system. The adsorption capacity (qmax) calculated from Langmuir isotherm and the Gibbs free energy (ΔGo) value obtained for the different adsorbents showed that clarified sludge was the most effective among the selected adsorbents for the removal of Cr(VI) from aqueous solution. The adsorption efficiencies of rice husk ash and activated alumina were also equally comparable with that of clarified sludge.

Numerical study of hydrogen permeation flux in SrCe 0.95Yb 0.05O 3-α and SrCe 0.95Tm 0.05O 3-α

The separation of hydrogen from gas mixtures may be achieved using perovskite membranes doped with rare earth oxides. The separation flux has been studied in such membranes and is based on a model of the proton transfer mechanism. The thermodynamic equilibrium constants ( K w, K i, K ox, K s) and charge carrier mobilities ( μ OH, μ Vo, μ h, μ e) for SrCe 0.95Yb 0.05O 3-α and SrCe 0.95Tm 0.05O 3-α may be estimated by fitting the hydrogen permeation flux model to the actual experimental data for SrCe 0.95Yb 0.05O 3-α and SrCe 0.95Tm 0.05O 3-α. The results indicate that the thermodynamic equilibrium constants K H and K w and the mobility of proton and electrons in SrCe 0.95Tm 0.05O 3-α may be higher than for SrCe 0.95Yb 0.05O 3-α, leading to the higher hydrogen permeation flux in SrCe 0.95Tm 0.05O 3-α. A parametric sensitivity analysis has been performed by using the New Morris Method to investigate the influence of the thermodynamic equilibrium constants and the charge carrier mobilities on the hydrogen permeation flux model. The results indicate that the hydrogen permeation flux model utilised in this study was most sensitive to the internal electronic equilibrium constant ( K i) value and least sensitive to the hole mobility ( μ h).

Thermodynamics of adsorption of binary aqueous organic liquid mixtures on a RPLC adsorbent

The surface excess adsorption isotherms of organic solvents commonly used in RPLC with water as co-eluent or organic modifiers (methanol, ethanol, 2-propanol, acetonitrile and tetrahydrofuran) were measured on a porous silica surface derivatized with chlorotrimethylsilane (C 1-silica with 3.92 μ mol C 1 groups per m 2 of SiO 2), using the dynamic minor disturbance method. The 5 μ m diameter particles were packed in a 150 mm × 4.6 mm column. The isotherm data were derived from signals resulting from small perturbations of the equilibrium between the aqueous–organic solutions and the adsorbent surface. The partial molar surface area of the adsorbed components were assumed to be the same as those of the pure components. The difference σ − σ i ∗ between the surface tensions of the adsorbed mixtures and that of the pure liquids was measured as a function of the organic modifier molar fraction. A simple and unique convention for the position of the Gibbs dividing surface was proposed to delimit the Gibbs’s adsorbed phase and the bulk liquid phase. The activity coefficients of the organic modifiers and of water and their thermodynamic equilibrium constants between the two phases were measured. The strong non-ideal behavior of the adsorbed phase is mostly accounted for by the surface heterogeneity. Some regions of the surface (bonded –Si(CH 3) 3 moieties) preferentially adsorb the organic compound while the regions close to unreacted silanols preferentially adsorb water.

Thermodynamic properties of vapor complex Na 2ZrCl 6

Thermodynamic studies were carried out for the vapor complex of sodium chloride with zirconium tetrachloride at 718–778 K and 0.5–2.5 kPa by using high temperature phase equilibrium-quenching experiments, taking closed Pyrex glass ampoules as the reaction containers. The results show that the sole predominant vapor complex is Na 2ZrCl 6 for the ZrCl 4-NaCl system under the experimental conditions. The thermodynamic equilibrium constants and other thermodynamic functions of the reaction 2NaCl( s)+ZrCl 4(g)=Na 2ZrCl 6(g) have been derived from the measurements. The results for the changes in enthalpy and entropy are Δ H 0=(−70.1±1.5) kJ/mol and Δ S 0=(−105.9±2.0) J/(mol·K) in the temperature range.

Thermodynamic Properties of Vapor Complex Na2HfCl6

Thermodynamic studies were carried out for the vapor complex of sodium chloride with hafnium tetrachloride at 712-778 K and 0.5-3.1 kPa by using high temperature phase equilibrium-quenching experiments, with closed Pyrex glass ampoules as the reaction containers. The results show that the sole predominant vapor complex is Na2HfCl6 for the HfCl4-NaCl system under the experimental conditions. The thermodynamic equilibrium constants and other thermodynamic functions of the reaction 2NaCl(s)+HfCl4(g)=Na2HfCl6(g) have been derived from the measurements. The results for the changes in enthalpy and entropy are -65.51.5 kJ/mol and 99.62.0 J/(mol K) in the temperature range.

Theoretical prediction of thermodynamic equilibrium constants of chemical reactions in water

In this work we characterize the thermodynamics of two simple chemical reactions in water. Applying the quasi-gaussian entropy theory to the molecular dynamics calculations, we model the equilibrium constant and its temperature dependence along the typical water isochore. Such a theoretical–computational approach could be useful to predict the optimal condition for chemical reactions in condensed phase at a very low computational cost.

Equilibrium Constant Studies for Complexation between Ammonium Ions and 18-Crown-6 in Aqueous Solutions at 298.15 K

Osmotic vapor pressure and density measurements have been carried out for bi- nary aqueous and ternary aqueous solutions containing a fixed concentration of 18-crown-6 (0.2 mol·kg −1 ) and ammonium chloride or ammonium bromide at 298.15 K. The concentra- tion of the ammonium salts was varied between 0.02 to 0.5 mol·kg −1 . The measured water activities were used to obtain the activity coefficient of water and the mean molal activity coefficient of the ions in binary as well as ternary solutions. Using the method developed by Patil and Dagade reported earlier in this journal and the McMillan-Meyer pair and triplet Gibbs energy interaction parameters, the thermodynamic equilibrium constant (K )f or the 18-crown-6:NH + complexes were determined. It is observed that the nature and polariz- ability of anions play important roles in imparting stability to the complexed species. The log10 K values for the 18-crown-6:NH + complexed species are lower than for the complexes involving alkali metal ions such as K + . The volume of complexation for the studied systems obtained from the apparent molar volumes of ammonium halides in ternary solutions are positive and of smaller magnitude than those reported for complexation with alkali ions. The results are further discussed in terms of water structural effects, complex formation, the role of counter anions and hydrophobic interactions.

Removal of uranium(VI) from aqueous solutions by manganese oxide coated zeolite: discussion of adsorption isotherms and pH effect

This paper discusses the adsorption properties for uranium(VI) by manganese oxide coated zeolite (MOCZ). The removal of uranium(VI) from aqueous solution by adsorption onto MOCZ in a single-component system with various contact times, pH, competitive ions, temperatures and initial concentrations of uranium(VI) was investigated. The experimental results were fitted to the Langmuir, Freundlich and the three-parameter Redlich–Peterson model isotherms to obtain the characteristic parameters of each model. Both the Langmuir and Redlich–Peterson isotherms were found to best represent the measured adsorption data. According to the evaluation using the Langmuir equation, the maximum adsorption capacity of uranium(VI) ions onto MOCZ was 15.1 mg g −1 at 293 K and pH 4.0. Using the thermodynamic equilibrium constants obtained at different temperatures, various thermodynamic parameters, such as Δ G 0, Δ H 0 and Δ S 0, have been calculated. The thermodynamics of uranium(VI) ion/MOCZ system indicates the spontaneous and endothermic nature of the process. It was noted that an increase in temperature resulted in a higher uranium loading per unit weight of the adsorbent.

Thermodynamic parameters of adsorption of 1,10-phenanthroline and 2,2′-bipyridyl on hematite, kaolinite and montmorillonites

The thermodynamic equilibrium constant ( K), free energy (Δ G), enthalpy (Δ H), entropy (Δ S), isosteric heat ( q st) of adsorption, and the constant ( k L) of the Langmuir adsorption equation using the adsorption isotherms (pH 6) of 1,10-phenanthroline (OP) and 2,2′-bipyridyl (BP) on hematite, sodium kaolinite (Na-K), sodium montmorillonite (Na-Mt) and hydroxy-aluminium montmorillonite (HAM) were obtained. The magnitude of enthalpy and isosteric heat established that adsorption on these minerals is a physical phenomenon. The equilibrium reaction constant ( K) was used to calculate the enthalpy (Δ H) and free energy (Δ G) for OP adsorption, parameters which could not be obtained by applying the constant ( k L) of the Langmuir equation of adsorption. The isosteric heat for hematite, Na-K, Na-Mt and HAM in kJ mol −1 was: 10.8–0.66, 13.4–28.6, 9.12–16.0 and 13.5–6.35, respectively. The equilibrium reaction constant ( K) was similarly used to obtain the enthalpy (Δ H) and free energy (Δ G) for BP adsorption on hematite, Na-K and Na-Mt, but this was not possible in the case of HAM. The k L constant did not behave as K in the adsorption of BP; it was only possible to obtain Δ G with values close to the order of magnitude of those obtained with K, but not Δ H. Isosteric heat in kJ mol −1 was −28.2 to −17.1 for hematite, 0.388–7.43 for Na-K, 3.55–7.47 for Na-Mt, and −0.363 to 2.30 for HAM. The adsorption of OP on hematite, Na-K, Na-Mt and HAM is an exothermic process, as is BP adsorption on Na-K and Na-Mt. BP adsorption on HAM, however, is endothermic at low surface cover and exothermic at a surface cover greater than 0.5 mol kg −1. The negative Δ S values obtained for both systems of adsorption are likely due to the displacement of solvent molecules on the surface by OP and BP solutes. In the case of OP adsorption hematite presents a heterogeneous surface and the other minerals a homogeneous surface. In the case of BP, all the minerals present heterogeneous surfaces.

Adsorption of organic acids on metal oxides: Application of the surface potential measurements

Simultaneous interpretation of surface potential, electrokinetic and adsorption data for salicylic acid on hematite surface was introduced. The interpretation on the basis of the surface complexation model using both 2-p K and 1-p K models suggested that salicylate ion is bound to one metal ion at the solid surface by two oxygen bonds. The equilibrium parameters describing the interfacial equilibrium were obtained as follows: for the 2-p K model the thermodynamic equilibrium constant for protonation and deprotonation of surface sites are lg K p 0 = 4.1 ± 0.2 and lg K d 0 = − 8.2 ± 0.2 , respectively, while the thermodynamic equilibrium constant of adsorption of salicylic acid is lg K a 1 0 = 1.6 ± 0.1 . For 1-p K model the thermodynamic equilibrium constant of adsorption of salicylic acid was obtained as lg K a 3 0 = 2.3 ± 0.2 . The inner layer capacitance increases with pH from 1.8 to 3 F m −2. It was shown that the surface potential measurement by single crystal electrodes is a helpful tool in elucidation of the complex equilibrium at the interface.

Study of pH-dependent charges of soils by surface acid–base properties

The pH-dependent charges of Hungarian soils have been studied via surface acid–base properties. The intrinsic stability constants of protonation and deprotonation processes, as well as the concentration of surface sites, have been determined by surface complexation modeling. The protonation and deprotonation constants have been nearly the same for most soils. There is a relation between the concentration of surface sites and composition, expect for the freshly deposited soils with high primary silicate content. The results show that the concentrations of silanol and aluminol sites are different for each soil, the intrinsic stability constants of protonation and deprotonation processes, however, are nearly the same within experimental error. This can only be explained if these stability constants are real thermodynamic equilibrium constants. The fact that these constants are nearly the same supports the conclusion that we succeeded in excluding all processes that would disturb the measurements. The parameters characteristic of the edge sites of the soils are of two types: (a) the parameters depending on the quality and composition of the soils, (i.e.), the concentration of surface sites; (b) the parameters depending on the thermodynamically well-defined acid–base processes, independent of soil composition.

Theoretical Investigations on Thermal Rearrangement Reactions of (Aminomethyl)silane

Thermal rearrangement reactions of (aminomethyl)silane H(3)SiCH(2)NH(2) were studied by ab initio calculations at the G3 level. The results show that two dyotropic reactions could happen when H(3)SiCH(2)NH(2) is heated. In one reaction, the silyl group migrates from the carbon to the nitrogen atom while a hydrogen atom shifts from the nitrogen to the carbon atom, forming (methylamino)silane CH(3)NHSiH(3) (reaction A). This reaction can proceed via three paths: a path involving two consecutive steps with two transition states and one intermediate metastable carbene species (A-1); and two concerted paths (A-2 and A-3). In the other reaction, the amino group migrates from the carbon to the silicon atom while a hydrogen atom shifts from the silicon to the carbon atom, via a double three-membered ring transition state, forming aminomethylsilane CH(3)SiH(2)NH(2) (reaction B). Reaction rate constants, changes (DeltaS(#), DeltaH, and DeltaG) in thermodynamic functions and equilibrium constants of the reactions were calculated with the MP2(full)/6-311G(d,p) optimized geometries, harmonic vibrational frequencies and G3 energies of reactants, transition states, intermediates and products with statistical mechanical methods and the conventional transition-state theory (TST) with Wigner tunneling approximation over a temperature range 400-1800 K.

Evaluation of equilibrium parameters of the anatase/aqueous electrolyte solution interface by introducing surface potential data

The single crystal anatase electrode (SCrE) was used to measure the inner surface potential ( φ 0) at the anatase/aqueous electrolyte interface as a function of pH. Measurements were performed in sodium perchlorate and sodium chloride aqueous solutions. Absolute values of the surface potential were calculated from electrode potentials using the electrokinetic isoelectric point as the point of zero potential. The slope of φ 0 (pH) function, with respect to pH, was found to be lower than the Nernstian. These results were accompanied with surface charge density and electrokinetic potential data and were interpreted simultaneously on the basis of the Surface Complexation Model. Both 1-pK and 2-pK mechanisms were employed. Data in the acidic region were interpreted since they were more reliable. Simultaneous interpretation of three sets of data enabled calculation of surface concentrations of all species, and thus thermodynamic equilibrium constants and the inner layer capacitance for each pH value separately. It was found that the equilibrium constants of surface protonation did not depend on the pH and the nature of the counterions, supporting the applicability of both 1-pK and 2-pK models. Thermodynamic equilibrium constants for association of perchlorate ions with positively charged surface groups did not change with pH, as expected, but the inner layer capacitance changed from 0.5 to 1.5 F m −2 by increasing the pH. Chloride ions showed an increase in the association equilibrium constant with pH and a less pronounced increase of capacitance. The advantage of the applied procedure lies in the possibility of avoiding the model assumptions of the constancy of parameters describing the interfacial equilibrium. It was shown that the thermodynamic equilibrium constants of surface protonation are real constants as defined by the Surface Complexation Model. The capacitance, however, changes with pH and surface potential and its constancy is just an approximation introduced by necessity when only one set of experimental data, such as surface charge density is quantitatively interpreted.

Mathermatical modeling of equilibria and the state of holmium heteropoly tungstate ions

The interaction in the HoW10O369−-H+-OH−-H2O system is studied using pH titration at cH0W10O369− = 10−3 mol/l in various base electrolytes (NaNO3, NaCl, Na2SO4). The pH titration data are used to simulate the processes in the solution in ranges of zH+ = 0−6.5 and zOH+ = (−4)-0. The concentration and thermodynamic equilibrium constants are calculated, and heteropolytungstate anion (HPTA) distribution diagrams are plotted. Thallium salts are synthesized in the regions of dominant existence of heteropoly anions HnHoW10O36(9−n)− (n = 2−4). The compounds are identified using chemical analysis and IR spectroscopy.

Studies of Thermodynamic Properties of Binary and Ternary Methanolic Solutions Containing KBr and 18-Crown-6 at 298.15 K

Experimental measurements of the speed of sound, density and osmotic vapour pressure are reported for binary 18-Crown-6 (18C6) + CH3OH, KBr + CH3OH and ternary KBr + 18C6 + CH3OH solutions at 298.15 K. The density and compressibility data were processed to obtain the apparent molar volume (o V ) and apparent molar isentropic compressibility (\(\phi _{K_S } \)) of the solutes in methanol. Expansivity data were obtained for the 18C6 + CH3OH system from density data at different temperatures and were used for calculation of the isothermal compressibility values at 298.15 K. The isothermal compressibility and expansivity data are further used to obtain the apparent molar isothermal compressibility (\(\phi _{K_T } \)) and apparent molar expansivity (o E ) of 18C6 in methanolic solutions and as well as the energy-volume coefficient parameter (∂ U/∂ V) T in methanol solutions. The volume and compressibility changes due to complexation of KBr with 18C6 are obtained at infinite dilution for o V and o K . The results are compared with the similar data obtained by us previously for aqueous and CCl4 solutions. The osmotic coefficient data were used to calculate activities and activity coefficients of each component at 298.15 K as a function of the concentration of binary and ternary methanolic solutions containing KBr and 18C6. The activity and activity coefficient data are used to evaluate the pair and triplet interaction parameters by making appropriate use of the McMillan-Meyer theory of solutions. The calculation of the thermodynamic equilibrium constant (K) is made using the pair interaction parameter, g NE (non-electrolyte – electrolyte pair interaction), for the complexation equilibria. The nature of interactions present in the CH3OH solutions is discussed.

Adsorption of Zn(II) from aqueous solution by using different adsorbents

Abstract The removal of Zn(II) from aqueous solution by different adsorbents was investigated. Clarified sludge (a steel industry waste material), rice husk ash, neem bark and a chemical adsorbent activated alumina were used for the adsorption studies. The influence of pH, contact time, initial metal concentration, adsorbent nature and concentration on the selectivity and sensitivity of the removal process was investigated. The adsorption of Zn(II) increased with increased concentration of the adsorbents and reached maximum uptake at 10 g/L and pH between 5 and 7. The equilibrium time was achieved after 1 h for clarified sludge, 3 h for rice husk ash and 4 h for activated alumina and neem bark, respectively. The adsorption process was found to follow a first-order rate mechanism and rate constant was evaluated at 30 °C. The rate constant was highest in case of clarified sludge (6.90 × 10−2 min−1) and the activated alumina gave the lowest value (1.86 × 10−2 min−1). Langmuir and Freundlich adsorption isotherms fit well in the experimental data and their constants were evaluated. The thermodynamic equilibrium constant and the Gibbs free energy were calculated for each system. The adsorption capacity (qmax) calculated from Langmuir isotherm and the values of Gibbs free energy obtained showed that clarified sludge has the largest capacity and affinity for the removal of Zn(II) compared to the other adsorbents used in the study.

Partition Equilibria for Alcohols in Reverse Micellar AOT-Oil-Water Systems Studied by PGSE-FT NMR. A Comparison Between AOT-containing and the Corresponding AOT-free Systems

Microemulsions of the reverse micellar type were investigated by determining the self-diffusion coefficients of the components using the Pulsed Field Gradient Spin Echo – Fourier Transform NMR method (PGSE-FT NMR). The microemulsions were composed of the surfactant AOT, water and an oil (either benzene or cyclohexane), forming a water core in an oil continuum. The primary alcohols ranging from methanol to 1-decanol were added to the microemulsions as a fourth component. The degree of binding, p, of the alcohol to the micelles was determined from the measured self-diffusion coefficients for this component. Partition equilibrium constants were calculated from the values of p. Thermodynamic partition equilibrium constants, Kc, calculated from the partition coefficients are presented and compared with values based on literature data for AOT-free systems. Similarities and differences between these cases are revealed and interpreted.

A thermodynamic study of the binding of human serum albumin onto N,N′‐diethylaminoethyl dextran microbeads

AbstractAdsorption of proteins on solid surfaces is widely studied because of its importance in various biotechnological, medical, and technical applications, e.g., biosensors, cardiovascular implants, and chromatography. Adsorption thermodynamics has been studied on the microbeads of N,N′‐diethylaminoethyl (DEAE) Dextran anion exchanger for the human serum albumin (HSA) at 25, 30, 35, 40, and 45°C. As a result, some thermodynamic parameters like Freundlich constants, thermodynamic equilibrium constant (KD), standard free energy changes (ΔGassoc), standard entropy changes (ΔSassoc), and standard enthalpy change (ΔHassoc) have been evaluated. Using the linear Van't Hoff plot, ΔHassoc value of the system for the interaction of bovine serum albumin (BSA)‐adsorbed crosslinked DEAE dextran microbeads was determined as 20.650 kJ/mol. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 101: 3942–3947, 2006

Synthesis, characterization, and application of new low‐cost ion exchangers

AbstractThis paper represents a simple method for preparing and characterizing of low‐cost ion exchangers of sulfonated carbon prepared from Terminalia Chebula‐Retz., (family–combretaceae) as a source of cheap plant material blended with phenol‐formaldehyde as a crosslinking agent. The prepared ion exchange resins (IERs) are characterized by infrared (IR) spectral and thermal studies. All the important physicochemical properties of the ion exchangers have been determined. The synthesized resins have cation exchange capacity upto 1.84 mmol g−1. The rational thermodynamic equilibrium constant (ln K) are calculated for H+ and Zn2+ exchanges on the resin having various amount of sulfonated Terminalia Chebula Retz. carbon (STCC). The thermodynamic parameters were calculated, and suitable explanations are given. It is concluded from the present study that PFR sample could be blended with 20% (w/w) of STCC, without affecting its physicochemical, spectral, and thermal properties. Hence blending with STCC will definitely lower the cost of the ion exchange resin. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 101: 4104–4113, 2006