Effects of nonequilibrium on velocity and plate height in reactive capillary electrophoresis

Models for velocity and plate height for reactive CE are developed under the formalism of generalized nonequilibrium theory, as described by Giddings. The resultant equations are consistent with chromatographic theory and validated with an independent stochastic simulation. Moreover, unlike prior methods for CE, this model allows calculation of thermodynamic equilibrium constants and kinetic rate constants from a single, undistorted peak. The theoretical development shows that velocity is directly dependent on the equilibrium constant and is independent of the rate constant. On the other hand, plate height varies little with equilibrium constant and is inversely proportional to rate constant. The ability to evaluate equilibrium constants from velocity and rate constants from plate height is most greatly influenced by electric field strength and mobility difference. The accuracy in calculated equilibrium constants is limited by mobility difference; however, the accuracy in rate constants is limited by plate height and equilibrium constant.     

A rapid and precise computer-aided method for the spectrophotometric determination of substances in solution

The Newton—Raphson iteration method for the solution of mass-balance equations is used. Given accurate spectrophotometric data (absorbances, absorptivities) and equilibrium constants, this procedure permits rapid determination of substances in solution. The program is convenient to use and gives satisfactory results on a number of systems. The pyridoxal hydrochloride system was selected for evaluation of equilibrium constants and molar absorptivities from spectrophotometric and potentiometric data and was then used as the main test of the SPEDEAD program (SPEctrophotometric DEtermination by Absorbance Data).     

Dynamics of hydrogen bond complexes in polymer melts

The dynamics of hydrogen bond complex formation between functional groups which are attached to a polymer chain, is studied in the molten state. The concentration of complexes in the thermodynamic equilibrium is distorted by the application of a large oscillatory strain in the nonlinear viscoelastic regime. The relaxation back to the thermodynamic equilibrium is studied as a function of the temperature in the linear viscoelastic regime. From the mechanical response the kinetic analysis can be performed using a modified Doi-Edwards theory. Using the equilibrium constants obtained from IR-spectroscopy, the rate constants for complex formation and decomplexation are obtained. The temperature dependence is equivalent to the temperature dependence of the zero shear viscosity which implies that complex formation is a diffusion-controlled process.     

Comparison of the experimental, semi-experimental and ab initio equilibrium structures of acetylene: influence of relativisitic effects and of the diagonal Born-Oppenheimer corrections

The equilibrium structure of acetylene (also named ethyne) has been reinvestigated to resolve the small discrepancies noted between different determinations. The size of the system as well as the large amount of available experimental data provides the quite unique opportunity to check the magnitude and relevance of various contributions to equilibrium structure as well as to verify the accuracy of experimental results. With respect to pure theoretical investigation, quantum-chemical calculations at the coupled-cluster level have been employed together with extrapolation to the basis set limit, consideration of higher excitations in the cluster operator, inclusion of core correlation effects as well as relativistic and diagonal Born-Oppenheimer corrections. In particular, it is found that the extrapolation to the complete basis set limit, the inclusion of higher excitations in the electronic-correlation treatment and the relativistic corrections are of the same order of magnitude. It also appears that a basis set as large as a core-valence quintuple-zeta set is required for accurately accounting for the inner-shell correlation contribution. From a pure experimental point of view, the equilibrium structure has been determined using very accurate rotational constants recently obtained by a "global analysis" (that is to say that all non-negligible interactions are explicitly included in the Hamiltonian matrix) of rovibrational spectra. Finally, a semi-experimental equilibrium structure (where the equilibrium rotational constants are obtained from the experimental ground state rotational constants and computed rovibrational corrections) has been obtained from the available experimental ground-state rotational constants for ten isotopic species corrected for computed vibrational corrections. Such a determination led to the revision of the ground-state rotational constants of two isotopologues, thus showing that structural determination is a good method to identify errors in experimental rotational constants. The three structures are found in a very good agreement, and our recommended values are r(CC) = 120.2958(7) pm and r(CH) = 106.164(1) pm.     

Computer calculation of equilibrium concentrations in mixtures of metal ions and complexing species

A method is described for calculating equilibrium concentrations of all species in multi-metal-multi-ligand mixtures from the pH of the solution, the total concentration of each metal and each complexing agent, and the relevant equilibrium constants (pK(a) values and stability constants). No restriction is imposed on types of possible complexes, which can include mixed, hydrolysed, protonated and polynuclear species. Two examples are given. One of these comprises a 10-metal-10-ligand system (195 equilibrium constants). In the second system, mixed complex formation is important. The computer program is given.     

The extrapolation of experimental equilibrium constant data to zero ionic strength: Critical review and new approach

Different Debye-Hückel expressions for the activity coefficients of species in aqueous solution in the ionic strength range I = 0-3.5m (3M) are used for the extrapolation of equilibrium constants data to I = 0 and the interpolation to unknown I values. This may be accomplished using four or more values of the equilibrium constants that are equally well distributed on the I scale. The interpolated and extrapolated equilibrium constant values obtained are quite satisfactory and within the experimental error of the corresponding equilibrium constants. The values at I 0.1 are very important as they can particularly influence the equilibrium constant value calculated at I = 0 and for which the error can reach 0.1 log unit or more. The values at I 1.5 can also influence the extrapolated value at I = 0 and the interpolated value at a given I when an inadequate extrapolation model is selected. Among the expressions used, only those with two or more unknown parameters are suitable for such calculations.     

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.     

Detailing hydrogen bonding and deprotonation equilibria between anions and urea/thiourea derivatives

Spectrophotometric and 1H NMR titrations of N-methoxyethyl-N'-(4-nitrophenyl)thiourea (3) by Bu(4-)NOAc show that in DMSO deprotonation of the receptor and formation of a hydrogen-bonded complex with anion proceed simultaneously but in MeCN deprotonation requires the participation of the second acetate anion. The formation constants of hydrogen-bonded complexes were determined from titrations in the presence of added acetic acid, which suppressed deprotonation. These constants together with independently measured stability constants of (AcO)(2)H(-) complexes were employed for a rigorous numerical analysis of titration results in the absence of added acid, which allowed us to determine the equilibrium deprotonation constants as well as pKa values for 3 in both solvents. Although 3 appeared to be a weaker acid than AcOH in both solvents, it can be deprotonated by acetate in dilute solutions when the concentration of liberated acetic acid is low enough. With disubstituted N,N-bis(methoxyethyl)-N'-(4-nitrophenyl)thiourea 4 only deprotonation equilibrium is observed. In contrast, both parent urea derivatives 1 and 2 cannot be deprotonated by acetate anions. Independent of the real type of equilibrium, whether it is a deprotonation or a hydrogen bonding, titration plots always can be satisfactorily fitted to a formal 1:1 binding isotherm. A relationship between apparent "binding constants" and real equilibrium constants of hydrogen bonding association and deprotonation processes is discussed.     

Determination of equilibrium constants of alkaline earth metal ion chelates with Dowex A-1 chelating resin

A complexation chemistry model is applied to chelating ion-exchange systems and a method is presented for the determination of equilibrium constants for metal ion chelates with these resins. Protonation constants for the iminodiacetic based chelating resin Dowex A-1 were determined from potentiometric pH-data. Equilibrium constants were determined for 1:1 beryllium, magnesium, calcium, strontium and barium chelates with the resin in a wide pH range by measuring the concentrations of respective metal ions in the aqueous phase with direct current plasma atomic emission spectrometry (DCP-AES). A batch technique was used for the equilibrium experiments. At pH below 7 protonated 1:1 species were also found to be formed with the resin. From the obtained equilibrium constants, theoretical distribution coefficients were calculated as function of pH for respective metal ion resin system.     

Effect of pH on concentration of species present in aqueous solutions of carbonyl compounds affected by hydration-dehydration and keto-enol equilibria

Equations have been derived for hydration-dehydration and keto-enol equilibria of carbonyl compounds, showing the changes, with pH, of individual species present in aqueous solutions. An Egtran computer program has been constructed, so that the pH-variation of individual species for widely varying values of equilibrium constants can be evaluated. The treatment enables isolation of individual equilibrium constants from experimental data and identification of the system involved. The ratios of hydrated and non-hydrated, as well as of keto and enol forms, are pH-independent.     

Hydrogen bonding of organic bases with trifluoroacetic acid in chloroform: A method of calculating association constants of multi-equilibria systems

¹³ C NMR chemical shifts of sixteen organic bases, hydrogen-bonded with trifluoroacetic acid in deuteriochloroform, are used to calculate equilibrium constants for self-association of acid and for hydrogen bonding of base with various acid n-mers. In this treatment each hydrogen bond of the species in equilibrium is assigned a free energy. The equilibrium constants then correspond to changes in these energies. Thermodynamic models are proposed which differ in the extent to which a given hydrogen bond perturbs the free energies of neighboring bonds in the molecular aggregates. Each furnishes a minimum set of independent, freely variable equilibrium constants, the values of which are then determined through a least squares fitting of the experimental data by an iterative procedure.     

Combined use of NMR relaxation measurements and hydrodynamic calculations to study protein association. Evidence for tetramers of low molecular weight protein tyrosine phosphatase in solution

We describe a novel method for determining weak association constants of oligomeric protein complexes formed transiently under equilibrium conditions. This type of equilibrium process is recognized as being biologically important, but generally hard to study. Heteronuclear spin relaxation rates measured at multiple protein concentrations are analyzed using relaxation rates predicted from hydrodynamic calculations, yielding equilibrium constants and structural characterization of the protein complexes. The method was used to study the oligomerization equilibrium of bovine low molecular weight protein tyrosine phosphatase. X-ray structures of monomeric and dimeric forms of the protein have been reported previously. Using longitudinal and transverse (15)N relaxation rates measured at four different protein concentrations, we detected the monomer, dimer, and a previously unknown tetramer and measured the dissociation constants of the equilibria involving these species. A comparison of experimental and predicted relaxation rates for individual backbone amide (15)N spins enabled delineation of the tetramerization interface. The results suggest a novel concept for substrate modulation of enzymatic activity based on a "supramolecular proenzyme". The fast and reversible switching of the "supramolecular proenzyme" would have obvious advantages for the regulation of enzymes involved in cell signaling pathways.     

Thermodynamics of ionization of water over wide ranges of temperature and pressure

We have summarized results of many experimental investigations of the thermodynamics of ionization of H₂O(liq.) from 0–300°C and from 1.0 atm to nearly 8000 atm. Results of these investigations (equilibrium constants, enthalpies of ionization, heat capacities, partial molal volumes, and compressibilities) have been used for a number of thermodynamic calculations. It is particularly noteworthy that it is possible to use thermal data from 0–145°C with an equilibrium constant for 25°C in calculating reasonably accurate equilibrium constants for temperatures as high as 300°C. Similarly, it is possible to use volumetric data that refer to 1.0 atm in calculating useful equilibrium constants that apply for pressures as high as 2000 atm.Much of the work reported here was done while the author was on leave at the University of Lethbridge.     

Hydrogen bond structural group constants

The ability of functional groups to act as hydrogen bond acids and bases can be obtained from either equilibrium constants for 1:1 hydrogen bonding or overall hydrogen bond constants. Either method leads to structural constants for hydrogen bonding that in some way are analogous to substituent constants. Extensive lists of these functional group constants are reported. It is shown that those derived from overall hydrogen bond constants are the more useful in analyses of physicochemical and biochemical properties.     

The determination of equilibrium constants for simple reaction systems from temperature-dependent physicochemical data

This paper provides a pragmatic approach for calculation of equilibrium constants that have been determined from systems at equilibrium by measuring a component of the equilibrium at several (minimum of three) different temperatures. The paper builds on previous work that has shown by selecting appropriate temperatures so that the van’t Hoff isochore could be written in terms of the total amount of a measured analyte (A_total) associated with the equilibrium, equilibrium constants could be determined. This paper describes a mathematical method that uses the linearity of the van’t Hoff plot, ln K versus 1/T as the basis to systematically test for an appropriate A_total value and derive the best values of equilibrium constants. It will also show that this method is freed from constraints in choosing the study temperatures.     

AB initio studies of chemical equilibria. III. SCF and CEPA calculations of the equilibrium constants of the reactions C2H2 + OH− ⇌C2H− + H2O and Li + H2O⇌LiOH + H

Theoretical prediction is made for the equilibrium constants of the two title reactions. A standard statistical-thermodynamic treatment was performed for which the necessary molecular constants were generated by the ab initio SCF and CEPA calculations. Comparison is made with experiment, and origin of errors in the computed equilibrium constants is discussed.     

Understanding atom transfer radical polymerization: effect of ligand and initiator structures on the equilibrium constants

Equilibrium constants in Cu-based atom transfer radical polymerization (ATRP) were determined for a wide range of ligands and initiators in acetonitrile at 22 degrees C. The ATRP equilibrium constants obtained vary over 7 orders of magnitude and strongly depend on the ligand and initiator structures. The activities of the Cu(I)/ligand complexes are highest for tetradentate ligands, lower for tridentate ligands, and lowest for bidentate ligands. Complexes with tripodal and bridged ligands (Me6TREN and bridged cyclam) tend to be more active than those with the corresponding linear ligands. The equilibrium constants are largest for tertiary alkyl halides and smallest for primary alkyl halides. The activities of alkyl bromides are several times larger than those of the analogous alkyl chlorides. The equilibrium constants are largest for the nitrile derivatives, followed by those for the benzyl derivatives and the corresponding esters. Other equilibrium constants that are not readily measurable were extrapolated from the values for the reference ligands and initiators. Excellent correlations of the equilibrium constants with the Cu(II/I) redox potentials and the carbon-halogen bond dissociation energies were observed.     

甲酰氯异构化和光解的理论研究——从头算水平上的反应热力学、动力学分析

由于对化学反应体系解核运动Schrdinger方程困难,化学界常常求解参加反应粒子的电子运动Schrdinger方程,得到其电荷密度分布、自由价和键级等静态物理量,作为反应性指标;这虽有简明的优点,但往往缺乏传递性和统一性。如用电荷密度分布分析亲电反应,仅在同系物中有定性比较其反应性相对大小的意义,无定量价值。此外,用反应的势垒大小判断反应的难易,忽略了鞍点处曲率的影响,就动力学的Arrhenius速度常数公式看,     

Equilibrium Constant Units Revisited

The problem of the units associated with equilibrium constants is revisited. A brief survey of the arguments for and against using units with equilibrium constants is presented and the compromise solution that we have adopted in our teaching, both at the university and school level, is presented and justified.     

Effect of the reactants molar ratio on the kinetics of cycloaddition of 2,3-dimethylbuta-1,3-diene to allyl methacrylate

The cycloaddition reaction between 2,3-dimethylbuta-1,3-diene and allyl methacrylate proceeds by the second order kinetics. The rate constants increase with the increase in the excess of one of the reactants. The change in the effective rate constants is described by the Michaelis-Menten equation indicating that the reaction proceeds through the initial equilibrium stage of formation of an intermediate complex which then transforms into the product. The effective rate constants, the equilibrium constants of formation of the intermediate complex, and the rate constant of its transformation into the reaction product were determined, as well as the thermodynamic parameters of the formation of the intermediate complex and the activation parameters of the transformation of the intermediate complex into the product. The limiting stage of the reaction is established and its mechanism is suggested.