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Layered double hydroxide (LDH) phases that form during cement hydration can incorporate a variety of interlayer anions in their interlayer positions. Here, a range of phases of general formula [MII(1−x)MIII(x)(OH)2][An−]x/n·zH2O were synthesized, where MII = Mg2+ (hydrotalcite) or Ca2+ (AFm), MIII = Al3+ such that [MII/Al] = 2 (Ca and Mg, atomic units) or 3 (Mg only), and A = Cl−, Br−, or I−. All the synthesized phases were characterized to assess their composition, density, and crystal structure. By approach from undersaturation, the solubility data of these compounds was measured at 5, 25, and 60°C. This thermochemical data was used to successfully model their formation using thermodynamic modeling and to infer the fields of stability of these compounds for conditions of relevance to cementitious systems. It is seen that halide-containing hydrotalcite phases strongly compete with hydroxide-containing hydrotalcite, with the latter prevailing at high pH. In contrast, halide-containing AFm compounds are more stable compared with hydroxide-containing AFm compositions.

Background: It is known that the adenosine triphosphate (ATP) hydrolysis in a number of ATPases is reversible. Radioactive methods are standard in measuring ATPase reversibility. We used myosin as a well-studied model enzyme to develop a luciferase-based assay to quantify the reversibility of ATP hydrolysis. In myosin, ATP bound to the active site is hydrolyzed into adenosine diphosphate (ADP) and inorganic phosphate (Pi) and recombined back into ATP multiple times before products of hydrolysis are released. The reversibility of ATP hydrolysis by skeletal myosin was previously confirmed using radioactively labeled isotopes. Transient kinetics studies indicated that the ATP hydrolysis step is temperature-sensitive, with a dissociation equilibrium constant of 1.6 at 3 °C. Consequently, the association equilibrium constant at this temperature is 0.63. The goal of our work was two-fold, (a) to develop a luciferase-based assay to measure the equilibrium constant of enzymatic ATP hydrolysis, eliminating the need for radioactively labeled Pi, and (b) refine the value of the association equilibrium constant of the myosin ATPase hydrolysis step. Methods: In this assay, a reaction mixture containing myosin and saturating levels of ADP and Pi was incubated to reach equilibrium, then the reaction was terminated, and the amount of ATP produced by myosin was quantified using the luciferase assay. The equilibrium constant of ATP hydrolysis was defined as the ratio of ATP to ADP bound to myosin. Results: We obtained a value of 0.78 ± 0.14 for the association equilibrium constant of ATP hydrolysis at 0 °C. 50 μM ADP bound to myosin is turned into 21.9 ± 3.0 μM ATP. Our result is in excellent agreement with the literature data, supporting the viability of the new methodology. Discussion: This methodology allows a more accessible and safe option to measure ATP production and reversibility of ATPase enzymes. Standard laboratory equipment is utilized in the assay, and the number of steps in the developed assay is reduced significantly compared to the radioactive method. [ABSTRACT FROM AUTHOR]

The affinity constant, also known as the equilibrium constant, binding constant, equilibrium association constant, or the reciprocal value, the equilibrium dissociation constant (Kd), can be considered as one of the most important characteristics for any antibody–antigen pair. Many methods based on different technologies have been proposed and used to determine this value. However, since a very large number of publications and commercial datasheets do not include this information, significant obstacles in performing such measurements seem to exist. In other cases where such data are reported, the results have often proved to be unreliable. This situation may indicate that most of the technologies available today require a high level of expertise and effort that does not seem to be available in many laboratories. In this paper, we present a simple approach based on standard immunoassay technology that is easy and quick to perform. It relies on the effect that the molar IC50 approaches the Kd value in the case of infinitely small concentrations of the reagent concentrations. A two-dimensional dilution of the reagents leads to an asymptotic convergence to Kd. The approach has some similarity to the well-known checkerboard titration used for the optimization of immunoassays. A well-known antibody against the FLAG peptide, clone M2, was used as a model system and the results were compared with other methods. This approach could be used in any case where a competitive assay is available or can be developed. The determination of an affinity constant should belong to the crucial parameters in any quality control of antibody-related products and assays and should be mandatory in papers using immunochemical protocols. [ABSTRACT FROM AUTHOR]

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Layered double hydroxide (LDH) phases that form during cement hydration can incorporate a variety of interlayer anions in their interlayer positions. Here, a range of phases of general formula [MII(1−x)MIII(x)(OH)2][An−]x/n·zH2O were synthesized, where MII = Mg2+ (hydrotalcite) or Ca2+ (AFm), MIII = Al3+ such that [MII/Al] = 2 (Ca and Mg, atomic units) or 3 (Mg only), and A = Cl−, Br−, or I−. All the synthesized phases were characterized to assess their composition, density, and crystal structure. By approach from undersaturation, the solubility data of these compounds was measured at 5, 25, and 60°C. This thermochemical data was used to successfully model their formation using thermodynamic modeling and to infer the fields of stability of these compounds for conditions of relevance to cementitious systems. It is seen that halide‐containing hydrotalcite phases strongly compete with hydroxide‐containing hydrotalcite, with the latter prevailing at high pH. In contrast, halide‐containing AFm compounds are more stable compared with hydroxide‐containing AFm compositions. [ABSTRACT FROM AUTHOR]

Avenanthramides (AVs) are the phytochemicals found in cereals exclusively in oats. These are widely known natural substances that have antioxidant properties. The free radical deactivation potential of the eight AVs against five reactive species has been studied in physiological pH. At physiological pH, the radical quenching processes were studied using the sequential proton loss followed by electron transfer (SPLET) from the phenolic hydroxyl groups. Using density functional theory (DFT) computations, theoretical studies have been carried out in the gas phase and aqueous solution at M06-2X/6-31 + G (d,p) level of theory. The free radical scavenging ability of the studied AVs was analyzed by using conceptual density functional theory-based parameters and electrostatic potential analysis. By examining the hydrogen atom and electron affinities of each reactive species, the relative destructive potential of each has been compared. The electron transfer capabilities between the studied compound and reactive species were identified by utilizing the ionization energy and electron affinity plots. Additionally, by calculating the redox potentials and equilibrium constants for the entire process in the aqueous solution, the viability of scavenging the free radical species by selected AVs (both in neutral and mono-deprotonated) has been investigated. From the analysis, the neutral as well as the mono-deprotonated form of AVs are found to scavenge •OH and •OOH, and •NO2 radicals effectively, while they are inefficacious toward the O2•‾ and •NO radicals. [ABSTRACT FROM AUTHOR]

Obtaining and production of metals from natural raw materials causes a large amount of liquid, solid, and gaseous wastes of various hazard classes that have a negative impact on the environment. In the production of titanium dioxide from ilmenite concentrate, hydrolytic sulphuric acid is formed, which includes various metal cations, their main part is iron (III) and titanium (IV) cations. Hydrolytic acid waste is sent to acid storage facilities, which have a high environmental load. The article describes the technology of ion exchange wastewater treatment of acid storage facility from iron (III) and titanium (IV) cations, which form compounds with sulphate ions and components of organic waste in acidic environments. These compounds are subjected to dispersion and dust loss during the evaporation of a water technogenic facility, especially in summer season. Sorption of complex iron (III) cations [FeSO4]+ and titanyl cations TiO2+ from sulphuric acid solutions on cation exchange resins KU-2-8, Puromet MTS9580, and Puromet MTS9560 was studied. Sorption isotherms were obtained both for individual [FeSO4]+ and TiO2+ cations and in the joint presence. The values of the equilibrium constants at a temperature of 298 K and the changes in the Gibbs energy are estimated. The capacitive characteristics of the sorbent were determined for individual cations and in the joint presence.

AbstractSorption treatment of wastewater from chromium compounds is a current and actively developing area of research. However, there is a lack of sorbents combining high efficiency and economic affordability with the possibility of application in industrial conditions. In this work, the sorption properties of biochar material “EcoChar,” obtained as a result of fast pyrolysis of agricultural poultry waste, were studied in relation to the removal of trivalent chromium ions, and the basic thermodynamic parameters of the process, which is the type of strong chemisorption, were determined. Based on the IR spectra of the sorbent material, the formation of chelate complexes by hydrolyzed chromium ions with the involvement of carboxylic groups and simple ether bonds is suggested. Using the Langmuir model, the values of sorption capacity of sorbent were found as, 68.8 ± 0,2 mg Cr(III)/g and 87.5 ± 0,3 mg Cr(III)/g at 298 and 318 K, respectively. These values, which are much higher than those of their corresponding waste material counterparts, make the use of this biochar as an adsorbent advantageous for the removal of Cr(III) containing compounds from acidic wastewater.

To investigate the isomerization transition of cluster ConMoS (n = 1–5), we employ density functional theory and transition state theory methods in this study. The cluster is optimized at the B3LYP/def2tzvp quantum chemical level. The results reveal eight isomerization reactions for the clusters ConMoS (n = 3, 5). Analyzing the activation energies shows a greater propensity for the isomerization transformation in the forward reaction compared to the reverse reaction. At room temperature, six isomerization transformation processes exhibit rapid conversion to the product configurations. Investigation of the equilibrium constants and application of the Arrhenius formula demonstrate that the cluster isomerization reactions are primarily driven by the forward reactions, with four reactions displaying efficient reactant to product conversion rates. Furthermore, there exists a consistent relationship between the structural complexity of the cluster and the change in entropy value. This study provides theoretical insights into reaction rates and optimization of reaction pathways, facilitating mutual validation and development between experimental and theoretical approaches. [ABSTRACT FROM AUTHOR]

The problem of environmental pollution is global and has multilateral consequences. One of them is the ingestion of toxicants into the human body with drinking water and food. Chronic intoxication with heavy metals poses an extreme danger to human health. In this regard, the development and search for ways to remove toxicants from the body and neutralize their adverse effects on the body does not lose relevance. Currently, based on numerous studies and practice, it can be argued that most of the plant raw materials and their waste is a source for obtaining various products, for example, dietary fibers, which are used as sorbents. Our study was aimed to evaluation of the sorption properties in katran Kochiana and bunia orientalis roots' meals on lead and cadmium salts. Studies have shown that the dietary fibers from the roots of these plants have sorption activity in relation to lead and cadmium ions. The roots of both plants had a greater affinity for cadmium ions, and it was also revealed that the sorption potential of the bunias roots' meals was slightly higher than that of katran Kochiana, although when examining samples for the presence of dietary fibers in the roots of bunia orientalis, their lower content was found. [ABSTRACT FROM AUTHOR]

The thermodynamic analysis of the composition of the vapor phase of the Cd-I2 system in the temperature range of 298-2000 K at the values of the total pressure in the system from 0.1 kPa to 100 kPa was assessed. The calculations assumed that the Cd-I2 system in the vapor phase contains the following components: I, I2, Cd, CdI, and CdI2. The results show that the dominant component of the vapor phase is cadmium diiodide (CdI2). In the temperature range of 298-950 K, Cd, and I2 predominate among the dissociation products, and the equilibrium in the vapor phase is described by the reaction CdI2(g) ↔ Cd(g) + I2(g). The optimal temperature conditions for growing cadmium diiodide crystals from the vapor phase are proposed. Single crystals of CdI2 have been grown at the temperature of the source zone – 890-900 K, and crystallization zone – 500-530 K. [ABSTRACT FROM AUTHOR]

To analyze the features of catalysis of the Schiff condensation with an iodonium salt as halogen bond donor, the equilibrium constants and reaction rate constants have been determined for the formation of the Schiff bases from various para-substituted aldehydes and aniline. The correlation has been found between the logarithms of calculated constants and Hammett σ-constants. Based on the obtained data, assumptions about the influence of the catalyst on the progress of the studied reaction have been made. [ABSTRACT FROM AUTHOR]

Sorption treatment of wastewater from chromium compounds is a current and actively developing area of research. However, there is a lack of sorbents combining high efficiency and economic affordability with the possibility of application in industrial conditions. In this work, the sorption properties of biochar material "EcoChar," obtained as a result of fast pyrolysis of agricultural poultry waste, were studied in relation to the removal of trivalent chromium ions, and the basic thermodynamic parameters of the process, which is the type of strong chemisorption, were determined. Based on the IR spectra of the sorbent material, the formation of chelate complexes by hydrolyzed chromium ions with the involvement of carboxylic groups and simple ether bonds is suggested. Using the Langmuir model, the values of sorption capacity of sorbent were found as, 68.8 ± 0,2 mg Cr(III)/g and 87.5 ± 0,3 mg Cr(III)/g at 298 and 318 K, respectively. These values, which are much higher than those of their corresponding waste material counterparts, make the use of this biochar as an adsorbent advantageous for the removal of Cr(III) containing compounds from acidic wastewater. [ABSTRACT FROM AUTHOR]

Quantum-chemical calculations of the structure of the molecular forms of glycine and glycylglycine and conjugate ionic forms have been performed. Our own and published data on the thermodynamic characteristics of the reactions of acid–base interactions of glycine and glycylglycine in aqueous organic solutions are summarized, and the influence of the composition of mixed solvents on the acid dissociation constant of the amide group in the copper(II) peptide complex is considered. [ABSTRACT FROM AUTHOR]

The affinity constant, also known as the equilibrium constant, binding constant, equilibrium association constant, or the reciprocal value, the equilibrium dissociation constant (Kd), can be considered as one of the most important characteristics for any antibody–antigen pair. Many methods based on different technologies have been proposed and used to determine this value. However, since a very large number of publications and commercial datasheets do not include this information, significant obstacles in performing such measurements seem to exist. In other cases where such data are reported, the results have often proved to be unreliable. This situation may indicate that most of the technologies available today require a high level of expertise and effort that does not seem to be available in many laboratories. In this paper, we present a simple approach based on standard immunoassay technology that is easy and quick to perform. It relies on the effect that the molar IC50 approaches the Kd value in the case of infinitely small concentrations of the reagent concentrations. A two-dimensional dilution of the reagents leads to an asymptotic convergence to Kd. The approach has some similarity to the well-known checkerboard titration used for the optimization of immunoassays. A well-known antibody against the FLAG peptide, clone M2, was used as a model system and the results were compared with other methods. This approach could be used in any case where a competitive assay is available or can be developed. The determination of an affinity constant should belong to the crucial parameters in any quality control of antibody-related products and assays and should be mandatory in papers using immunochemical protocols.

Supersaturation occurs in many industrial applications promoting reactive crystallisation between the reactants to form solutes. These solutes accumulate during precipitation, leading to the formation of scales on the inner walls of the reactor and particularly around the stirrer, causing modifications in the hydrodynamics. This encrustation is responsible for process shutdowns in continuous crystallisation processes. Supersaturation control is essential for industrial processes aimed at controlling or inhibiting the formation of these solids. Knowledge of mineral solubility and chemical speciation is required to account for the composition of the complexes in the system in their various solid or aqueous forms. This speciation is obtained by considering the thermodynamic equilibrium constants of the dissociation/complexation reactions involved in the system, the pressure, and the activity coefficients of the chemical species in their molecular or electrolyte form. From these thermodynamic quantities and the state of the system, we can predict the direction of the reaction. This study highlights the risk of the lack of experimental information on equilibrium constants at high temperatures and moderate pressures. Our goal is to evaluate the accuracy of existing models classically used to predict the equilibrium constant in such very hard conditions encountered in hydrometallurgical processes. Furthermore, we demonstrate the influences of equilibrium constants estimation and activity coefficient models on the speciation of H2SO4-Al2(SO4)3-MgSO4 systems, forming hydronium alunite and kieserite in the laterite liquor of hydrometallurgical processes. [ABSTRACT FROM AUTHOR]

In semi-steelmaking, the bottom-blown O2–CaO process is employed to achieve high efficiency dephosphorization. However, there is little research on the requirements for smelting parameters. In this paper, the mechanism changes of temperature effect on dephosphorization are studied by the industrial tests in a 300 t dephosphorization converter. Firstly, the influences of temperature on the equilibrium constant (KP), CaO melting ratio (K) and slag viscosity (ƞ) were analyzed. KP decreases, K increases and ƞ decreases to stability with increasing temperature. The dephosphorization effect is better than the conventional process' even at higher ƞ, because the CaO powder has melted and P is mostly removed during the process of fire-spot zone upward floatation. Hence, the requirements for slagging with good fluidity are reduced. Then, the relationships between the three factors and phosphorus partition between slag and hot metal (LP) were investigated by the correlation analysis. The importance order in the bottom-blown O2–CaO process is: lgKP＞η, it demonstrates that the melting of CaO powder doesn't affect dephosphorization. While the influence order in the conventional process is: K＞η＞lgKP. Finally, we summarize the dephosphorization reaction in the bottom-blown O2–CaO process includes transient reaction accounts for approximately 86% and continuous reaction with about 14%. The process of CaO upward floatation plays major roles in dephosphorization. Based on above results, the temperature requirement of molten steel for dephosphorization becomes lower. The industrial tests show the optimum temperature range for dephosphorization decreases from 1593-1603 K to 1573–1583 K, which validate the conclusion.

The measurement of values of apparent equilibrium constants K′ for enzyme-catalyzed reactions involve a substantial number of critical details, neglect of which could lead to systematic errors. Here, interferences, impurities in the substances used, and failure to achieve equilibrium are matters of substantial consequence. Careful reporting of results is of great importance if the results are to have archival value. Thus, attention must be paid to the identification of the substances, specification of the reaction(s), the conditions of reaction, the definition of the equilibrium constant(s) and standard states, the use of standard nomenclature, symbols, and units, and uncertainties. This document contains a general discussion of various aspects of these equilibrium measurements as well as STRENDA (Standards for Reporting Enzymology Data) recommendations regarding the measurements and the reporting of results.

Encrustation occurs in many processing fluids where high levels of dissolved solids are present, especially in processes that use heat transfer equipment. The deposition of these scales in the interior surfaces of an autoclave can cause major issues in the operation of industrial processes such as hydrometallurgy. The knowledge of the minerals' chemistry, distribution of the chemical forms of these minerals in the autoclave, and their solubility product can assist to inhibit these solid deposits. To model such systems, it is necessary to know the reactions involved and by extension their equilibrium constants. These electrolytic systems being strongly non-ideal, models of activity coefficients are necessary to deduce the concentration of each species. This review presents and compares various models for the calculation of activity coefficients and the thermodynamic equilibrium constants at temperatures above 25 °C. For model validity and comparison purposes, a case study on the speciation of the aqueous binary systems of H2SO4-Al2(SO4)3 and H2SO4−MgSO4 is presented and compared with experimental data. From the results obtained and in the framework presented above, the Density equilibrium constant model coupled with the Truesdell-Jones activity coefficient model gave the best fit with experimental data at the studied temperatures of 235, 250, 270, and 300 °C.

The B3LYP/6-311g++(d,p), G3, and CBS-QB3 methods (DFT) have been used to calculate the free energy and equilibrium constants of the "chair"–"boat" conformational transition of cyclohexanone in the temperature range 298.15–428.15 K. The equilibrium composition of the chair and boat conformers of cyclohexanone has been calculated. It has been shown that with an increase in the proportion of the boat conformation, the selectivity of the process of cyclohexane oxidation to cyclohexanone decreases. The transition states of addition reactions of cyclohexyl hydroperoxide at the carbonyl group of cyclohexanone for chair and boat conformations have been found by the QST2 method. The energy profiles of these reactions have been calculated. It has been established that the addition of hydroperoxide to the carbonyl group of the boat conformation of the ketone is accompanied by a transition to the chair conformation. [ABSTRACT FROM AUTHOR]

Diethylenetriaminecobalt(II), [Co(DETA)2]2+, formed by diethylenetriamine (DETA) coordinating with Co(II) ion, can be used to remove NO from flue gas. Diethylenetriaminecobalt(II) is capable of binding NO to form metal nitroso complexes. The determination of the equilibrium constant of the reaction between [Co(DETA)2]2+ and NO is important to the development of the technology for the elimination of NO from exhausted gas streams with diethylenetriaminecobalt solution. In this paper, the equilibrium constants of this reaction have been determined by a series of experiments in a bubble reactor at the range of 30–70°C under atmospheric pressure in the [Co(DETA)2]2+ solution of pH 7.5. All experimental data are in good agreement with the following equation: KT=1.8619×10−6exp4677.52TL⋅mol−1, where the changes in enthalpy and entropy are ΔH0 = −38.89 kJ ⋅ mol−1 and ΔS0 = −109.7 J ⋅ K−1 ⋅ mol−1, respectively. [ABSTRACT FROM AUTHOR]

Introduction: Peracetic acid (PAA) is a highly effective disinfectant against a wide range of viruses and bacteria. Its versatility, cost‐effectiveness, and ability to quickly decontaminate large areas make it an ideal choice. PAA is also environmentally friendly and safe, as it does not produce any harmful by‐products. However, to ensure its efficacy, it is crucial to maintain the optimal concentration of PAA in the solution. Objective: The objective of the study is to investigate the use of attenuated total reflection Fourier transform infrared (ATR‐FTIR) spectroscopy as a method for quantifying the concentration of peracetic acid (PAA), which comes in quaternary equilibrium mixture in commercial formulation. The study also aims to determine the rate constants and equilibrium constant for the production of PAA in various conditions, including the presence of catalyst and stabilizer. Methods: The spectra of all chemicals in PAA solution obtained in FT‐IR Spectrometer were compared to identify the characteristic peaks of PAA, which were then computed using normal mode analysis at B3LYP/6‐31G(d) level by Gaussian 09. The ATR‐FTIR was used to measure time‐dependent PAA signals until they reached equilibrium in three different conditions: (1) Acetic acid (10 to 17.4 M) and hydrogen peroxide (5 M), (2) with sulfuric acid as catalyst, and (3) with phosphoric acid as stabilizer. The collected data was analyzed through regression analysis, in which curves and rate law formulas were fitted to obtain the rate constants for peracetic acid synthesis and hydrolysis. Results: This study shows that ATR‐FTIR spectroscopy can detect and quantify peracetic acid with a characteristic peak at 1753 cm−1. The proposed method is applicable to all peracetic acid solutions, including those with stabilizers and catalysts. The ATR‐FTIR method offers advantages such as short detection time, simple operation, small sampling volume, and accurate measurement. Moreover, the accuracy of this quantitative method is confirmed by the fact that the reaction rate constants deduced from the fitted curves are more consistent with the actual reaction rate constants than those of the reference data based on KI titration method. [ABSTRACT FROM AUTHOR]

In the present study, the inclusion complex of neoandrographolide and β-cyclodextrin (β-CD) was studied by experimental and theoretical methods. The inclusion complex of neoandrographolide/β-CD was prepared by the saturated solution method. The equilibrium constant of the inclusion complex was determined by UV -vis spectra. The structure of the complex was characterized by DTA, FT-IR, and molecular modeling techniques. All these results indicated that neoandrographolide could enter the cavity of β-CD to form an inclusion complex, and the neoandrographolide/β-CD inclusion complex exhibited different spectroscopic features and properties from neoandrographolide. The molar rate of the inclusion complex was 1:1. The five-membered lactone ring of the neoandrographolide molecule was inserted into the cavities of β-CD from the wider edge. The calculated equilibrium constant of the complex was 489.9918 mol/L. The in-vitro antiproliferative activity of neoandrographolide was significantly improved through the inclusion complexation process. Taken together, the inclusion complexation process was a successful method that could be used in the pharmaceutical industry. [ABSTRACT FROM AUTHOR]

Atom transfer radical polymerization (ATRP) is a versatile & famous technique for the synthesis of well defined molecular architectures. In ATRP, there is a dynamic equilibrium exists between active & dormant species. Therefore, ATRP progress through a sequence of activation & deactivation cycles, ending upon complete monomer consumption & termination reactions are minimized. This paper presents a systematic computational study on kinetics & thermodynamics associates in the ATRP of itaconimide monomers & methyl methacrylate (MMA). For this, the copolymerization system is modeled as a unimer, dimer & trimer of various itaconimides & MMA monomer. The density functional theory with B3LYP functional & 6–31 + G(d)/LanL2DZ basis sets is used in the prediction of geometries & energetics associated with the dissociation of terminal R–X bond present in the unimer, dimer & trimer. The relative equilibrium constant (KATRP) for the ATRP activation/deactivation steps is calculated from the free energy values associated with dissociation of R–X bond. The relative KATRP values of dimer & trimer of selected monomers is compared with their respective unimer. From the transition state geometries of the dimeric propagating radical, activation energy is calculated. The gas phase rate coefficients for propagation (kp) (of itaconimides & MMA copolymerization) are calculated using the standard transition state theory. The effect of system parameters such as solvent, temperature & substituent on KATRP & kp values of dimer is investigated systematically. The change in the initiating system & temperature has significant effect on kp values as compared to solvent & various substituent. The KATRP values of dimer & trimer dormant species are higher as compared to their respective monomeric species. The neighboring monomer & penultimate monomer plays vital role in kinetics & thermodynamics associated with copolymerization. The obtained initial results show that the mechanism of copolymerization of itaconimide monomers & MMA follows penultimate model. [ABSTRACT FROM AUTHOR]

An equilibrium constant is an important parameter in regard to determining the backward reaction rate constant in chemical kinetics modeling for a hypersonic flow. Three common approaches for the equilibrium constant determination are based on the partition function, Gibbs free energy, and the experimental reaction rate measurement. The present study conducted a computational fluid dynamics (CFD) analysis with different equilibrium constant formulations in a thermochemical nonequilibrium hypersonic flow in order to study the influence of the equilibrium constant in carbon dioxide flow during the Martian entry. The equilibrium constant for the carbon dioxide molecule dissociation differs from one method to another among the reactions that are considered in the carbon dioxide flow. Three different flow conditions, which are based on the experimental data that is provided in the literature, are considered in the detailed comparison analysis using CFD. The variation of the flow properties in terms of pressure, temperature, and mass fraction along the stagnation line is compared for different cases of the equilibrium constant computation. The results that are obtained from the present study confirm that the equilibrium constant influences the numerical computation in the thermochemical nonequilibrium flow especially for the non-catalytic wall boundary condition.

An algorithm is described for calculating the equilibrium constants and changes in the enthalpy of chemical reactions according to data from a calorimetric experiment performed on instruments of different types. Freeware is developed that executes the described algorithm. Differences from existing computer programs with similar functionality are briefly discussed, along with different statistical criteria of maximum likelihood. [ABSTRACT FROM AUTHOR]

BACKGROUND: The adsorption equilibrium constant of the Langmuir model (KL; L mol−1) has been applied as the standard thermodynamic equilibrium constant, KEqo, for calculating the thermodynamic parameters (∆G°, ∆S°, and ∆H°) of an adsorption processes by using the van't Hoff equation. Some authors have (directly and indirectly) applied the constant KRP (L kg−1) of the Redlich–Peterson model for such calculations. However, this is an incorrect application because the unit of KRP is not suitable (it is not an equilibrium constant). Its new adsorption equilibrium constant, Ke(RP) (L mol−1), was revisited based on aRP (L mol−1)g. In the literature, there is still uncertainty regarding the application of aRP as KEqo for calculating the thermodynamic parameters. Therefore, the present study aimed to evaluate the feasibility of applying Ke(RP) to calculate thermodynamic parameters using available literature data. The thermodynamic parameters obtained from Ke(RP) were compared to those from KL. A case study using a biosorbent for adsorbing methylene blue dye at different temperatures was carried out to re‐verify the feasibility. RESULTS: The Redlich–Peterson model is only valid when its exponent is in a strict range (0 ≤ g ≤ 1). The Redlich–Peterson model (68%; 227 observations collected from 52 published papers) describes adsorption equilibrium datasets better than the Langmuir model. The negative ΔG° values obtained based on Ke(RP) (11.7–47.6 kJ mol−1) were significantly different (p = 2.98 × 10−12) from those on KL (12.2–40.8 kJ mol−1). The magnitudes of ΔH° obtained based on Ke(RP) were significantly different (P < 0.05) to those on KL; however, such differences did not affect conclusions drawn on dominant mechanism adsorption (physical or chemical). The magnitude of ΔH° for chemisorption (involved in covalent bonds) is higher than 200 kJ mol−1. For the case study, the ∆H° (kJ mol−1) and ∆S° [J mol−1 × K−1] values calculated based on Ke(RP) (11.65 and 111.5) were like those on KL (11.34 and 110.4, respectively). CONCLUSION: A new equilibrium constant, Ke(RP) (L mol−1), of the Redlich–Peterson model can be applied as KEqo for calculating the thermodynamic parameters (∆G°, ∆S°, and ∆H°) of an adsorption processes under specific cases (i.e., F, H, and L‐shaped adsorption isotherms). Most of the adsorption processes (98%) involve physical adsorption. © 2022 Society of Chemical Industry (SCI). [ABSTRACT FROM AUTHOR]

In the present paper, a simple method for analyzing the self-aggregation of dyes in a solution by a UV-visible absorption measurements is proposed. The concept of excess absorbance is introduced to determine an equation whose coefficients determine the parameters of the aggregation equilibrium. The computational peculiarities of the model are first discussed theoretically and then applied to sodium fluorescein in polar protic and aprotic solvents, as well as in aqueous solutions of methylene blue, which is a cationic dye. Although the experimental responses are very different, the model appears to work equally well in both cases. The model reveals that the trimer is the most likely configuration in both solvents. Furthermore, aggregation is strongly favored for the protic solvent. Interestingly, the model establishes that in aqueous solutions of methylene blue, the tetramer is the predominant form, which has long been assumed and recently demonstrated with sophisticated computational techniques. [ABSTRACT FROM AUTHOR]

In this study, we have carried out to modeling by mathematical equations the environment of the combustion chamber under some conditions using the software MATLAB in order to make an adequate algorithm of resolution and get solution of the different equations that taken part in the phenomenon of combustion, so the first was to identifies the kind of the fuel to use in that model (taking Methane as fuel combustion) and minimizing the reduction of novice gas burned is in priority, for this, we want to establish the optimal values to take to preserve the environment, especially from CO2 and CO emissions, secondly, its nature according to the equivalent ratio (lean, stoichiometric or rich mixture), all variations of equivalent ratio, the third idea is to retrace the ways of a different product of the reaction and see their variations compared to the equivalent ratio, once traced, we can improvise which exact place in the reaction, a product will be finished either in the form of a gas or to decompose in order to bind to another and form another component. We also discussed the percentage of O2 and H2O emissions for an interesting viewpoint of the environmental aspect of hydrocarbon's chemical reaction. Another additional part will be dedicated to the process of flameless combustion to write its mathematical equation, compare it with the so-called traditional one, and see the variations in the temperature according to the equivalent ratio. [ABSTRACT FROM AUTHOR]

[Display omitted] • Relation between Gibbs energies and enthalpies of hydrogen bonding at 298.15 K was derived. • Its validity was checked on 293 proton acceptor – proton donor pairs of various structures. • Hydrogen bonding enthalpy can be calculated from only binding constant at 298.15 K. Thermodynamics of hydrogen bonding has long been the central object of study in the solution chemistry of organic non-electrolytes. Correlations between the entropies and enthalpies of hydrogen bonding in a series of similar chemicals were first noted more than 50 years ago but have never been considered a general phenomenon. In this work, the relationship between hydrogen bonding enthalpies (Δ HB H) and Gibbs energies (Δ HB G) was obtained based on the previous studies of the compensation relationship in the thermodynamics of solvation of molecular compounds: Δ HB G /(kJ·mol−1) = 0.66·Δ HB H /(kJ·mol−1) + 2.5 n , where n characterizes acid-base complex stoichiometry. The relationship derived was shown to cover a wide range of proton acceptors and proton donors of various structures, basicities and acidities. It enables to predict the hydrogen bonding enthalpy from only the complexation constant measured at a single temperature. For 293 proton acceptor – proton donor pairs, the root-mean-square deviation between the predicted and literature hydrogen bonding enthalpies was 1.2 kJ·mol−1. Furthermore, the Gibbs energies and enthalpies of hydrogen bonding, i.e., localized donor–acceptor interactions, were shown to obey the linear relationship with the same slope as the thermodynamic functions of non-specific solvation caused by van der Waals interactions. It may be considered a signature of their common nature. Compared to the thermodynamic functions of non-specific solvation, the dependence between Gibbs energies and enthalpies of hydrogen bonding has an additional intercept, which apparently has an entropic origin. [ABSTRACT FROM AUTHOR]

[Display omitted] • A novel chemical equilibrium constant formulation regarding the reaction of nitrogen and oxygen is developed. • The proposed formulation representation only correlates experimental values of four molecular constants of the reactants and product. • The predicted equilibrium constant values are in good agreement with the experimentally measured data. Nitrogen (N 2) and oxygen (O 2) are the two main components in the air. Here, we report a novel formulation representation concerning the chemical equilibrium constant regarding the reaction of N 2 and O 2. It depends only on the standard experimental data subject to four molecular constants of N 2 , O 2 and NO, while the conventional calculation schemes involve application of multiple experimental spectroscopic data or calorimetric data. Comparing two sets of experimentally measured data respecting the equilibrium constant with the theoretical prediction results obtained from the developed formulation and provided in the previous literature, we validate the reliability of the proposed prediction model. The mean absolute deviations between two experimental data sets and the predicted results from the proposed formulation are 2.983 % and 4.047 %, respectively, and the corresponding deviations of the same experimental measurements from the previous theoretical values reported in the literature are 11.07 % and 33.53 %, respectively. [ABSTRACT FROM AUTHOR]

The object of research is the synthesis of methanol under medium pressure, and the subject of research is the calculation of the equilibrium composition. A method and an algorithm for calculating the equilibrium composition of products are proposed. Calculations have been carried out using two mechanisms of methanol synthesis. First of all, the first approach to the mechanism of methanol synthesis was applied, which provides for the formation of methanol from a mixture of carbon oxides and hydrogen by the simultaneous reaction of methanol synthesis from carbon monoxide (IV) and steam reforming of carbon monoxide (II). The poor convergence of the system of two equations on the basis of this interaction mechanism is established, which complicates the selection of initial approximations and the choice of a real solution. At the second stage, the mechanism of the formation of methanol from carbon monoxide (II) with the simultaneous flow of steam reforming of CO in the opposite direction is considered. The degree of the equation describing the dependence of the equilibrium constant on the partial pressures of the reactants decreases in comparison with the first approach and causes much better convergence when solving the system of two equations. The use of a coefficient that takes into account the effect of pressure on the value of the equilibrium constant is proposed, and its dependence on temperature is approximated. The developed algorithm is implemented in MathCAD, while the relative maximum deviation for methanol is 8.53 %. The third approach is to use two coefficients that adjust the equilibrium constant depending on pressure. In this case, the relative maximum deviation of methanol is 16.25 %. The program according to the proposed algorithm takes into account the multiplicity of the initial data, namely the possibility of varying the composition of the initial mixture, pressure and temperature. The calculation was carried out according to the initial data of industrial implementation of methanol synthesis. Comparison of the equilibrium concentration of methanol with the real one at the outlet of the synthesis column established the degree of equilibrium reaching 39.4 %, which indicates the presence of a reserve of methanol synthesis and the possibility of increasing the practical yield of methanol. [ABSTRACT FROM AUTHOR]

A comparative evaluation of the results of an experimental study and thermodynamic analysis of the chemical equilibrium in a heterophase heterogeneous catalytic reaction of cyclohexanone hydrogenation is reported. It is shown that when calculating the thermodynamic equilibrium constant of heterophase hydrogenation reactions in gas–liquid systems it is necessary to take into account the change in the enthalpy and entropy of the initial chemical system caused by hydrogen absorption. The value of the enthalpy of hydrogen absorption not only reflects the endothermic physical process of gas dissolution, but also characterizes the state of the reagents in the exothermic chemical reaction of hydrogenation. Therefore, the thermal simulation of the apparatus, in which gas absorption and chemical reaction with its participation occur simultaneously, should be performed without taking into account the heat of gas dissolution. [ABSTRACT FROM AUTHOR]

Current methods for determining equilibrium constants often operate in three-dimensional environments, which may not accurately reflect interactions with membrane-bound proteins. With our technique, based on single-molecule localization microscopy (SMLM), we directly determine protein-protein association ( K a ) and dissociation ( K d ) constants in cellular environments by quantifying associated and isolated molecules and their interaction area. We introduce Kernel Surface Density (ks-density,) a novel method for determining the accessible area for interacting molecules, eliminating the need for user-defined parameters. Simulation studies validate our method's accuracy across various density and affinity conditions. Applying this technique to T cell signaling proteins, we determine the 2D association constant of T cell receptors (TCRs) in resting cells and the pseudo-3D dissociation constant of pZAP70 molecules from phosphorylated intracellular tyrosine-based activation motifs on the TCR-CD3 complex. We address challenges of multiple detection and molecular labeling efficiency. This method enhances our understanding of protein interactions in cellular environments, advancing our knowledge of complex biological processes.

The sorption of 2-pyridinecarboxylic, 3-pyridinecarboxylic, and 4-pyridinecarboxylic acids by polystyrene sulfonic acid type cation exchange resin Dowex 50W-X8 and Dowex 50W-X4 from aqueous solutions was studied. Based on the analysis of the FT-IR spectra of acids, sulfates of their protonated forms, and an acid-saturated cation exchange resin, it was shown that pyridinecarboxylic acid is in the protonated form in the cation exchange phase. The equilibrium constants of sorption proceeding with participation of pyridinecarboxylic acid, sulfonic cation exchange resin, and proton were calculated according to experimental data on the equilibrium distribution of acids in the aqueous solution–cation exchange resin system. The values of the equilibrium constant of the cation exchange of the sulfonic ion-exchange resin proton by the pyridinecarboxylic acid cation from solution lie in the range 3.2–4.4. The equilibrium constants of sorption of 2-pyridinecarboxylic acid molecules are 25 dm3 mol–1, they increase to 195–220 dm3 mol–1 for 4-pyridinecarboxylic acid, and reach 320–330 dm3 mol–1 for 3-pyridinecarboxylic acid. Changing the amount of the cross-linking agent (from 4 to 8% divinylbenzene) in the polystyrene sulfonic acid type cation exchange resin does not significantly affect its sorption activity toward pyridinecarboxylic acids. [ABSTRACT FROM AUTHOR]

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

Self-recovery ability after over thermal fault decomposition is a fundamental factor determining the stability of environmentally friendly insulation medium C5F10O in engineering applications. This article proposes 42 possible reaction pathways for the decomposition products of C5F10O to reform C5F10O after overheating fault based on its thermal decomposition and industrial synthesis pathways. Dominant reaction paths and reactants in the recovery process at temperature of 298–1000 K are theoretically analyzed according to the chemical equilibrium constant and rate constant, which were calculated based on the density functional theory using the thermodynamics properties of the reactions such as activation energy and enthalpy. According to the results, at low temperatures, 26 of the 42 proposed reactions have the equilibrium constants greater than 1, and the rate constants of them are much higher than that of the decomposition reactions, proving that decomposed C5F10O can be partly recovered after the overheating fault is removed. Among the recovery pathways, reactions with primary or secondary decomposition products of C5F10O as the reactants hold higher equilibrium constants and are the dominant reactions for the recovery process. R11, R8, and R5 hold the largest rate constants in similar reactions and contribute the most to the restoration of C5F10O, that is, (CF3)2CFCO $\cdot $ , (CF3)2CFCOF $\cdot $ , and CF3OCCF(CF3)2 are the dominant reactants for the formation of C5F10O. And the synthesis reactions R22, R17, R7, and R15 of these reactants are also necessary for the self-recovery process of C5F10O. [ABSTRACT FROM AUTHOR]

The equilibrium (association) constant, KA, for the first protonation of the sulfate ion in aqueous solution: [H+(aq) + SO 4 2 - (aq) ⇌ HSO 4 - (aq)] has been measured at 298.15 K in NaCl and NaClO4 media using glass-electrode potentiometry at five ionic strengths in the range 0.5 ≤ I/(mol·dm−3) ≤ 5.0. The present KA values vary smoothly with I and are in good agreement with reliable literature data but indicate that the previously reported value of KA at I = 5 mol·dm−3 in NaClO4 media is in error. [ABSTRACT FROM AUTHOR]

In order to meet prominent disagreement for the water gas shift reaction (WGSR) equilibrium constant values obtained from various conventional empirical correlations and mitigate the strong dependence on plenty of experimental data points, here, we report a novel WGSR equilibrium constant formulation representation approach with direct algebraic operation, which only involves experimental data of 3–6 molecular constants for each reactants and products and does not contain the fitting of any experimental equilibrium constant data. The reliability of the developed approach is demonstrated by comparing the predicted values with experimentally measured data and the calculated results with other previous WGSR equilibrium constant correlations. The average absolute deviations between the theoretical values predicted from the developed technique and the directly measured data reported in the literature are 3.993%, 5.970%, 2.418%, 2.083%, 8.659%, 3.733%, and 3.755% for 7 experimental data sets, respectively. [Display omitted] • We report a novel WGSR equilibrium constant formulation representation approach. • This approach only involves 6–3 molecular constants of the reactants and products. • Practical applications of this method are verified from comparing the deviations. • The developed approach provides direct algebraic operation and high accuracy. [ABSTRACT FROM AUTHOR]

Alkyl bromides are used as initiators in most of the atom transfer radical polymerization (ATRP) process and play an important role for controlling the ATRP equilibrium. In this work, the effect of solvent on equilibrium constant of ATRP (KATRP) and rate constant of activation (kact) of three isomeric alkyl bromides [namely, N-phenyl(3-bromo-3-methyl)succinimide, N-phenyl(3-bromo-4-methyl)succinimide, and N-phenyl(3-bromomethyl)succinimide] is reported. The kact and KATRP values of alkyl bromide are determined experimentally using UV–Vis-NIR spectrometry. The termination rate constant for model compound is calculated using DOSY NMR spectroscopy. The kact and KATRP values for the mentioned alkyl bromides are determined in five different polar solvent and the effect of polarity is observed. The obtained values of kact and KATRP of N-phenyl(3-bromo-3-methyl)succinimide in acetonitrile at 25 °C is 6.60 × 10−2 L mol−1 s−1 and 1.42 × 10−9, respectively. These values are quite comparable with the experimentally determined reported kact and KATRP of values of acrylates and benzyls initiators. Alternatively, the investigation of possible chain initiation activity for the ATRP process for the mentioned alkyl bromides is carried out theoretically using density functional theory (DFT) method [B3LYP/6-31+G(d) level]. A good correlation is obtained between the experimentally determined and theoretically calculated KATRP values of studied alkyl bromides in chosen solvents. Significantly, it is found that the values of kact and KATRP of alkyl bromides is solvent dependent and the magnitude values of the kact and KATRP increases with increasing the solvent polarity. The proposed bromo substituted succinimides can be used as the initiator for the polymerization of acrylates, benzyls, maleimides, and itaconimides monomer under the selected solvent system. [ABSTRACT FROM AUTHOR]