The regularities of reversible chain reactions in the equilibrium state

The characteristics of dynamic equilibrium states in the experimentally studied reversible chain reactions of quinoneimines with hydroquinones and in some reversible chain reactions with similar mechanisms are discussed. The concentrations of radicals and non-radical participants were calculated. The equilibrium concentrations of the same reaction participants depend only on the initial reactant concentrations, being independent of the number of chain initiation-chain termination steps in the reaction mechanism. The results of mathematical modeling of reversible chain reactions using the experimentally determined rate constants for elementary steps of a reaction in the quinoneimine-hydroquinone system are presented. Expressions relating the equilibrium constants of elementary steps to each other and to the equilibrium constant of the total stoichiometric reaction are derived. Examples of other actual reversible chain reactions are presented, indicating that such reactions are widespread.     

Cyclization in reversible and irreversible step-growth polymerizations

Several aspects of cyclization reactions in step-growth polymerizations are considered. The Jacobson–Stockmayer ring-chain equilibrium theory provides the basis for understanding these systems, but there are circumstances where some modifications to the theory are needed. In particular, for ring expansion polymerizations, i.e. those for which there is never a significant fraction of open chains, the statistics are a bit different from those appropriate for ring-chain equilibrium. Also, if the reactions are irreversible the occurrence of rings is significantly different from the reversible case. Rings are more prevalent in irreversible reactions. The implications of these observations for the processing of polymers are briefly considered.     

Multiple rate-determining steps for nonideal and fractal kinetics

We show that the kinetic model of a single rate-determining step in a reaction mechanism can be extended to systems with multiple overall reactions for which the elementary reactions obey nonideal or fractal kinetics. The following assumptions are necessary: (1) The system studied is either closed or open, but no constraints exist preventing the evolution toward equilibrium. (2) Elementary reactions occur in pairs of forward and backward steps. (3) The kinetics of the elementary steps are either nonideal or fractal and are compatible with equilibrium thermodynamics. (4) The number of reaction routes is identical with the number of rate-determining steps. If these hypotheses are valid, then the overall reaction rates can be explicitly evaluated: they have a form similar to the kinetic equations for the elementary reactions and the apparent reaction orders and fractal coefficients can be expressed analytically in terms of the kinetic parameters of the elementary reactions. We derive a set of relationships which connect the equilibrium constants of the reaction routes, the corresponding overall rate coefficients, and the stoichiometric numbers of the rate-determining steps. We also derive a set of generalized Boreskov relations among the apparent activation energies of the forward and backward overall processes, the corresponding reaction enthalpies, and the stoichiometric coefficients of the rate-determining steps. If the elementary reactions obey fractal kinetics, the same is true for the rate-determining steps. The fractal exponents of the forward and backward overall reactions are linear combinations of the fractal exponents of the fractal elementary reactions. Similar to the theory of single rate-determining steps, our approach can be used for selecting suitable reaction mechanisms from experimental data.     

An outline of new calculation methods for the determination of both thermodynamic and kinetic parameters from isothermal heat conduction microcalorimetry

An outline of equations allowing calculation, from calorimetric data, of both thermodynamic and kinetic parameters for reactions which proceed to completion is given. In addition equilibrium constants are calculable for reactions which proceed to an equilibrium position. Advantages of the methods for solid state kinetic and stability studies are briefly discussed.     

Kinetics and thermodynamics of the exchange reactions of peroxy radicals with hydroperoxides

The enthalpies and equilibrium constants of the exchange reactions of peroxy radicals with hydroperoxides of various structures are calculated. The experimental data on the reactions of hydrogen atom abstraction by the peroxy radicals from the hydroperoxides are analyzed, and the kinetic parameters characterizing these reactions are calculated using the intersecting parabolas method. The activation energies and rate constants for nine reactions of H atom abstraction by a peroxy radical from the OOH group of a peroxide are calculated using the above parameters. The geometric parameters of the transition states for the reactions are calculated. The low triplet repulsion plays an important role in the fast occurrence of the reactions. The polar interaction in the transition state is manifested in the reactions of the peroxy radicals with hydroperoxides containing a polar group.     

Rate and Equilibrium of Acetyl Group Exchange between Pyridines and Pyridine N-Oxides

22 Acetyl group exchange reactions between N-acetoxypyridinium salts and 4-dimethylaminopyridine, 4-morpholinopyridine, and N-methylimidazole in acetonitrile at 298 K have been studied. The rate constants varied from 10⁵ to 10^–4 L/mol·s, and the equilibrium constants ranged from 10⁹ to 10^–9. The rates and equilibrium constants of these reactions did not comply with the Brönsted equation. The kinetics of the acetyl exchange reactions are well described by a correlation equation containing squared terms.     

Response reactions: equilibrium coupling

It is pointed out and illustrated in the present paper that if a homogeneous multiple equilibrium system containing k components and q species is composed of the reactants actually taken and their reactions contain only k + 1 species, then we have a unique representation with (q - k) stoichiometrically independent reactions (SIRs). We define these as coupling reactions. All the other possible combinations with k + 1 species are the coupled reactions that are in equilibrium when the (q - k) SIRs are in equilibrium. The response of the equilibrium state for perturbation is determined by the coupling and coupled equilibria. Depending on the circumstances and the actual thermodynamic data, the effect of coupled equilibria may overtake the effect of the coupling ones, leading to phenomena that are in apparent contradiction with Le Chatelier's principle.     

Chemical reactions in microdroplets and microbubbles. Thermodynamic approach

In small dispersed systems, the standard chemical potential of the components present in the curved phases is different from the one in phases with a flat interface. Thermodynamic properties of reactions in such systems, at mechanical equilibrium, may be different from those for the same reactions at the same temperature, in a phase with zero curvature. Among these properties, we study here the dependence of the equilibrium constant on the curvature, on the surface tension and on the stoichiometry of the process. Reactions in an electric field are also discussed.     

时间参量法(Ⅳ)──对峙反应的热动力学研究

根据热动力学基本理论和对峙反应的通用微分动力学方程,将时间作为已知参量,建立了对峙反应热动力学时间参量法的数学模型,并利用该法分别研究了硝基乙烷与氨和三(羟甲基)氨基甲烷反应的热动力学.     

Terephthalic acid esterification kinetics: 2-(2-methoxyethoxy)ethyl terephthalates

The process of esterification of terephthalic acid is characterized by a mechanism that involves three equilibrium reactions. Two are esterification-hydrolysis equilibria entailing the reactions of the two terephthalic acid carboxyl groups with alcoholic hydroxyl groups, whereas the third one is a transesterification-acidolysis equilibrium that is concerned with the reaction between two terminal terephthalic acid moieties. The products of these three interrelated equilibria are terephthalic acid, its monoester and diester, the particular alcohol, and water. The alcohol used in the present study was 2-(2-methoxyethoxy)ethanol. Equilibrium constants and rate constants were developed from experimental data obtained at 230°C. The esterification-hydrolysis reactions were found to be catalyzed by carboxyl groups, and the rate of transesterification was found to be a function of the terephthalic acid concentration. With the constants developed, the system of nonlinear differential equations, as derived from the mechanism postulated, was integrated numerically using the Runge-Kutta method. Good agreement between calculated and experimental values was observed.     

Chemical equilibrium of glycerol carbonate synthesis from glycerol

In this paper, the chemical equilibrium for the glycerol carbonate preparation from glycerol was investigated. The chemical equilibrium constants were calculated for the reactions to produce glycerol carbonate from glycerol. The theoretical calculation was compared with the experimental results for the transesterification of glycerol with dimethyl carbonate. Transesterification of glycerol with cyclic carbonates or alkyl carbonates is thermodynamically favourable for producing glycerol carbonate from glycerol according to the equilibrium constant. Increasing temperature can increase the chemical equilibrium constant for the reaction of glycerol with dimethyl carbonate. For the reaction of glycerol with ethylene carbonate, increasing temperature can decrease the chemical equilibrium constant. The reaction of glycerol with carbon dioxide is thermodynamically limited. High temperature and low pressure are favourable to the reaction of glycerol and urea.     

Note Concerning the Concepts of Reaction Numbers,Independent Reactions and Resistant Groups in Chemical Thermodynamics and Kinetics

A linear algebraic characterization for sets of independent reactions, independent reaction numbers, conservation laws and resistant groups for both equilibrium and kinetic systems is suggested. Basing on the ranks of two stochiometric matrices N and M, these concepts are discussed and formulas given for setting up of independent sets of equilibrium and kinetic equations. The difference in the definition of independent reaction numbers for these two types of systems is pointed out. A brief consideration is devoted to the transformations of equilibrium and kinetic equations induced by transformation from one set of linearly independent reactions to another. Finally the conservation laws are formulated as chemical invariants within the N, M framework.     

Pairwise exchanges of oxo and imido groups in rhenium(VII) compounds

The kinetic and thermodynamic parameters for the oxo and imido exchange reactions among MeReO(3), MeReO(2)(NR), MeReO(NR)(2), and MeRe(NR)(3) (R = 1-adamantyl, Ad; or 2,6-diisopropylphenyl, Ar) have been measured. The rate constant for the NAr series decreases from 0.27 to 0.0024 L mol(-1) s(-1) at 25 degrees C in benzene as the total number of participating imido groups increases from 2 to 4, indicating that steric effects play an important role in the kinetics of the ligand exchange reactions. But, with NAd, the values of k/L mol(-1) s(-1) are 0.2 (4 NAd), 100 (3 NAd), and 0.74 (2 NAd). The equilibrium constants, also subject to steric effects, are much larger than those predicted by ligand combination statistics and greatly favor the mixed oxo-imido compounds. The different steric demands by imido and oxo ligands are believed to be the main factor for the larger equilibrium constants because the equilibrium constant shows minimal dependence on temperature. The large negative activation entropies for the ligand exchange reactions are consistent with a metathesis mechanism featuring nearly concurrent interchange of oxo and imido groups.     

Determination of equilibrium constants by titration calorimetry : Part II. Data reduction and calculation techniques

Techniques of data reduction and methods of calculation have been given for the determination of equilibrium constants by titration calorimetry. It has been shown how, starting with typical titration calorimetry data, the apparent heat liberated in the reaction vessel can be calculated, corrected for extraneous heat effects, and used to solve for the equilibrium constant and enthalpy change value(s) for the reaction(s) under investigation. Equations are given for calculating the energy contributed to the overall heat effects measured in the reaction vessel by processes other than chemical reactions such as heat of stirring, heat losses, heat of dilution, etc., and by chemical reactions other than the one(s) for which equilibrium constant(s) are sought. Mathematical techniques and equations are presented for calculating equilibrium constants and enthalpy change values from titration data by least squares analysis.     

Reversed-phase ion-pair liquid chromatographic method for determination of reaction equilibria involving ionic species: exemplification of the method using ligand substitution reactions of ethylenediaminetetraacetatochromium(III) ion with acetate and phosphate ions

A reversed-phase ion-pair liquid chromatographic method is presented for the determination of reaction equilibria involving ionic species of the same charge sign as reactant and product compounds. It has been demonstrated that ion-exchange chromatography or reversed-phase ion-pair chromatography is a useful tool for the determination of equilibrium constants of chemical reactions involving ionic species such as metal complexation reactions. Previous work with these methods has been based on the assumption that the limiting retention factors of the reactant and product species are constant independent of concentration of the chemical species (X) in the mobile phase, which reacts with the analyte compound. However, when all the reactant and product species are ions of the same charge sign as that of the species X, it is virtually impossible to apply these methods to the equilibrium constant determination because the retention factors of both the reactant and product species may depend on the concentration of X. In this study, an alternative approach was developed that estimates the limiting retention factors of ionic species from the dependence of the retention factor on the ionic strength of the mobile phase. Ligand substitution reactions of ethylenediaminetetraacetatochromium(III) ion with acetate and phosphate ions were used as model reactions to test this method. The equilibrium constants determined by this method are in good agreement with those obtained by a UV-visible spectrophotometric method.     

Place exchange reactions of alkyl thiols on gold nanoparticles

The kinetics and equilibrium position of place exchange (alkylthiol-for-alkylthiol) reactions of gold nanoparticles are reported. These reactions were monitored via a gas chromatography analysis of structurally similar incoming and outgoing alkylthiols, as a function of time. The place exchange reactions described here proceed to an equilibrium position, where Keq approximately 1. The product-time data follow Langmuir diffusion kinetics.     

可逆反应的热静力学研究法

本文建立了一种新的可逆反应的热静力学研究方法, 并利用本法研究了18-冠-6与钾离子、钡离子在水中的配位反应。实验测得的这两种反应的平衡常数和焓变与文献值很好吻合。本法适用于平衡常数大于1而小于10^4的反应体系。     

化学平衡的本质——浅谈混合熵对化学平衡的贡献

化学平衡是物理化学的重要内容之一。化学反应的等温方程式,给出了平衡常数与标准摩尔反应Gibbs自由能的关系。然而,仅从化学反应等温方程式还很难理解混合熵对化学平衡贡献的本质。本文建立了理想气体体系Gibbs自由能与反应进度的关系,给出了三个理想气体反应体系Gibbs自由能与反应进度的具体关系,分析了混合熵对化学平衡的本质贡献。     

Study of nitration equilibrium in the glycerin-aqueous nitric acid system. 1. Dependence of the equilibrium constants of nitration reactions on the temperature,acidity of the medium,and structure of the nitrated compound

The equilibrium constants of seven sequential-parallel reactions of conversion of glycerin into glycerin trinitrate in aqueous HNO₃ were measured. The effect of the acidity of the medium on the equilibrium nitration constants is correlated with processes of protonation of glycerin and its nitrates. The equilibrium nitration constants are higher for primary hydroxides than for secondary hydroxides, and they decrease in both series in going from glycerin to its dinitrates.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 8, pp. 1723–1729, August, 1990.