Relative Equilibrium Constants Research Articles

Effect of preferential solvation on reactivity of a free radical in binary solvent mixtures

The absorption maxima of p-NH2C6H4S˙ and the rate constants and relative equilibrium constants for the reversible addition reaction of p-NH2C6H4S˙ with α-methylstyrene have been measured by a flash photolysis method in binary solvent mixtures with different compositions. In a polar–non-polar mixture, preferential solvation of p-NH2C6H4S˙ by the polar solvent was observed via the effect on the absorption maximum and the rate parameters. The linear free-energy relationship between the reaction rate constants and the relative equilibrium constants revealed that solvation of the reactant is more important that solvation of the transition state.

Spectroabsorptiometric investigations of complexing reactions of polyhydroxylic flavylium compounds

The anhydrobasic form of delphinidin forms with Al(III) at pH 5.85 a complex,Dp:Al=3:1, with the relative equilibrium constant of 14.38±0.07, at room temperature and at ionicstrengh I=0.2 mol/L. Complexation in acetate buffer has a positive effect on delphinidin stabilization, the decomposition rate constant of which is k=0.052 min -1 , at pH 5.85 and room temperature, and which decreases to k=0.0025 min -1 in the presence of Al(III) because of complexation

Adsorption of cadmium by an aquent New Zealand soil and Its components

Cadmium adsorption by a New Zealand soil, three of its particle size fractions, the soil with organic matter removed, and the soil with iron and manganese oxides removed, was studied at the soil's natural pH (5.70) and at cadmium concentrations (0.01 to 0.23 �g mL-1) typical of those found in the environment. Under these conditions, the whole soil had a strong affinity for trace amounts of cadmium, adsorbing about nine-tenths of that added. Relative conditional equilibrium constants for cadmium adsorption by the soil's components decrease in the following order: clay (1.59) > [whole soil (1.00)] > soil without iron and manganese oxides (0.55) > silt (0.54) > sand (0.52) > soil without organic material (0.08) > silica sand (0.001). It is estimated that the <3.9 �m particle size fraction (22% of the soil) and the 3-9-563 pm particle size fraction (78% of the soil), contributed about 45% and 55%, respectively, to the overall capacity of the soil to adsorb cadmium. Most data obtained gives good fits to both linear and Freundlich adsorption isotherms, but is not consistent with the Langmuir adsorption model. Thus it is likely that, under the conditions studied, the soil and its components supply a range of cadmium adsorption sites with varying adsorption energies.

A new dual‐parameter for reactivities of vinyl monomers toward free‐radicals

AbstractA new dual‐parameter of vinyl monomers for the reactivities toward free‐radicals has been evaluated on the basis of kinetic data obtained by the flash photolysis method. As a model reaction system, the reversible addition reactions of the substituted phenylthiyl radicals to vinyl monomers are selected. The absolute rate constants and the relative equilibrium constants for these reactions have been determined. The Hammett reaction constants (ρ) for the addition reaction rates were evaluated by the variation of the substituents at the para‐position of the arylthiyl radicals. From the values, the polar parameters (P‐ values) have been evaluated. The P values of various vinyl monomers correlate with the e values of the Q‐e scheme proposed by Alfrey and Price. The resonance stabilization terms of the propagating radicals were evaluated from the equilibrium constants (K) which correlate with the Q values. The K‐P dual‐parameter can be used in order to predict the reactivities of vinyl monomers for the primary radicals (initiation step). The monomer reactivities from the copolymerization data are also correlated with the dual parameter. There are some advantages in the new dual‐parameter compared with the Q‐e scheme; the separation of the resonance term from the polar term is complete and the steric factor is not included in the polar term.

ChemInform Abstract: Comparative Reactivities of Hydrocarbon C‐H Bonds with a Transition‐Metal Complex

Alkanes are among the most abundant and unreactive of all organic compounds. Industrial use of these resources often relies upon free-radical activation of carbon-hydrogen bonds, often at high temperatures, thereby limiting the selectivities that can be achieved in any functionalization reaction. Consequently, the selective activation of C-H bonds by homogeneous transition-metal compounds has been a topic that has been of great interest to the organometallic community for many years. In this Account, mechanistic studies with a series of homogeneous rhodium organometallic complexes are summarized that provide for the first time a comparative evaluation of the relative equilibrium constants and rates of reaction for both alkane and arene hydrocarbon activation.

Comparative reactivities of hydrocarbon carbon-hydrogen bonds with a transition-metal complex

Alkanes are among the most abundant and unreactive of all organic compounds. Industrial use of these resources often relies upon free-radical activation of carbon-hydrogen bonds, often at high temperatures, thereby limiting the selectivities that can be achieved in any functionalization reaction. Consequently, the selective activation of C-H bonds by homogeneous transition-metal compounds has been a topic that has been of great interest to the organometallic community for many years. In this Account, mechanistic studies with a series of homogeneous rhodium organometallic complexes are summarized that provide for the first time a comparative evaluation of the relative equilibrium constants and rates of reaction for both alkane and arene hydrocarbon activation.

A receptor model for binary mixtures applied to the sweetness of fructose and glucose: De Graaf and Frijters revisited

Assuming that two substances (e.g. tastants or odorants) share a common type of receptor, a binary mixture model is derived from the equations for the equilibrium constants for the separate and combined reactions of the substances and the hypothesized receptor(s). It is assumed that a multimolecular interaction between stimulant molecules and a receptor or between a stimulant molecule and several receptors may occur forming a stimulant–receptor complex. This model provides a significantly superior fit to the sweetness data of De Graaf and Frijters (1986) on mixtures of fructose and glucose than an alternative model based on Beidler's (1962) theory of taste stimulation applied to mixtures. (In Beidler's model a unimolecular interaction is assumed between a stimulant molecule and a receptor.) Estimates of the parameters of the model provide information on the relative stoichiometric coefficients of the reactants and the relative equilibrium constants for the reactions between the receptor and the substances alone. The derived model should have a broad domain of application in studying the interaction between ligands and receptors, and is not limited to applications in the chemical senses or to psychophysical experiments in particular.

Reactivities of sulfur‐centered radical toward polyisoprenes and polybutadienes studied by flash photolysis method

AbstractThe kinetic behavior of the thiyl radical in the solution containing polyisoprenes and polybutadienes has been studied by the flash photolysis method. For benzothiazole‐2‐thiyl radical, the addition rate constants toward these polymers and the model compounds of the polymers were evaluated. The relative reverse rate constants and equilibrium constants were also estimated. The addition rate constants decrease with an increase in the degree of polymerization; the ratio of the addition rate constant for polyisoprene (3.1 × 104 M−1 s−1 (in monomer unit); Mv = 674,000) to that for 2‐methyl‐2‐butene (1.5 × 105 M−1 s−1) is about 1/5. This indicates that the polymer chain effect appears in the free‐radical addition reaction. The relative reverse rate constants for the polymers are also smaller than those for 2‐methyl‐2‐butene, suggesting a kind of polymer effects; i.e., it can be presumed that the bonded‐thiyl radicals migrate very rapidly to the neighboring double bonds in the polymer. Significant differences in the rate parameters were observed between polyisoprene and polybutadiene, between cis‐ and trans‐polyisoprenes, and between 1,4‐ and 1,2‐polybutadienes.

Kinetic study of addition of substituted and unsubstituted phenylthiyl radicals to aromatic olefins: Steric effect on reactivities of monomers containing bulky groups

AbstractFor olefins containing aromatic groups such as naphthyl, monomer reactivities have been evaluated on the basis of the absolute rate constants and relative equilibrium constants which were determined by the flash photolysis method using phenylthiyl radicals as attacking radicals. The rate constant for addition of α‐methyl‐1‐vinylnaphthalene is lower than that of α‐methyl‐2‐vinylnaphthalene. This suggests that the aromatic π‐orbital; of the 1‐naphthalene derivative are twisted away from the olefinic π‐orbital; in the transition state, the delocalization of the unpaired electron on the olefinic carbon into the naphthyl group is reduced by the angular structure. For such twisted monomers, the dihedral angles between the aromatic π‐orbitals and the olefinic π‐orbital have been estimated by comparing the observed rate constants with the reactivity indexes calculated by the molecular orbital method. In the case of α,β‐disubstituted olefins, the rate constants are lower than those of α,α‐disubstituted ones; this suggests that the approach of the phenylthiyl radical is impeded. New reactivity parameters were evaluated for the monomers with bulky groups.

Zur Anwendung der NMR‐Verschiebungsreagenztechnik bei Substanzen mit zwei unterschiedlichen Assoziationszentren

On the Application of the N.M.R. Shift Reagent Technique to Substances with Two Different Association SitesThe competition of two potential association sites of the same substrate molecule for the shift reagent is described by a simple association model. The relative equilibrium constants are determined by the dependence of the induced shifts observed on the amount of the added shift reagent. An example of 3.17‐bifunctionalized steroids demonstrates the applicability of the method.

Autoradiographic Investigations of Endogenic Non-Metallic Inclusions

The quantitative autoradiography of “point” sources, i.e. the sources of diameters between 5 … 100 μm, has enabled investigations of insulated non-metallic inclusions. Several heats were made in an induction furnace. ST-5 steel samples were deoxidated by use of complex deoxidizers Al + Ce contained various amounts of cerium with the radioisotopes 141-Ce and 143-Ce. On the base of autoradiographs the cerium contents in the insulated from steel samples non-metallic inclusions were determined. It was found that the inclusions compositions were variable and depended on the inclusions size and time of their origin. It was determined also the relative equilibrium constant of cerium for the Al-Ce-O system.

Zur Anwendung von Lanthanoid‐Verschiebungsreagenzien bei der NMR‐spektroskopischen Untersuchung von Gemischen monofunktioneller Kohlenwasserstoffe

Application of Lanthanide Shift Reagents in 1H‐N.M.R.‐Spectroscopic Investigations of Mixtures of Monofunctional HydrocarbonsThe influence of n.m.r. shift reagents on the 1H‐n.m.r.‐spectra of mixtures has been investigated. Hydrocarbons of the type CH3(CH2)nX (X = OH, CHO, COR, COOCH3, COOH, OR with R = Methyl‐, Ethyl‐, n‐Propyl‐, n‐Butyl‐ and n = 1,2) served as model substances. The components of the mixtures compete with the shift reagent. Relative equilibrium constants have been calculated to describe this behavior in mixtures. Several equations have been deduced and tested to describe the induced shifts of the protons in mixtures. These equations are applicable to qualitative and quantitative analysis of unknown mixtures.

AlPO4-supported rhodium catalysts: IV. Individual and competitive hydrogenation of styrene and α-methylstyrene

Hydrogenation rates of the olefinic double bond of styrene (S) and α-methylstyrene (MS) have been measured using methanol as the solvent in the temperature range 293–323 K over RhAlPO4 catalysts of different rhodium loading. Both organic reactants exhibited nearly identical areal rates and apparent activation energies independent of the rhodium loading (0.25 to 1 wt%) of the catalyst. The hydrogenation reaction involves a Horiuti-Polanyi mechanism modified by an irreversible adsorption of alkene. Styrene hydrogenation was also studied using other alcohols as solvents. The initial rate of hydrogenation was dependent on the polarity of the solvent. The competitive hydrogenation of both S and MS provides unambiguous evidence that the relative reactivity, RMS,S, and the relative adsorption equilibrium constant, KMS,S, are independent of the reaction temperature, initial hydrogen pressure, and rhodium loading. Thus, the adsorption heat and the activation energy are nearly identical for two organic reactants.

Immersionskalorimetrische Einschätzung der Adsorptionsfähigkeit von Aktivkohlen gegenüber organischen Stoffen aus wäßrigen Lösungen

AbstractIn comparison with the conventional methods for testing the adsorptive capacity of active charcoals, the author presents a new technique. The measuring possibilities of the immersion calorimetry are used. This measuring technique is based on the determination of the interaction of active charcoal with liquid adsorptives. The immersion heat referred to one mol adsorptive is used as the measure. Due to simplifying assumptions and a micropore volume of active charcoal measured with water vapour, immersion‐calorimetrically relative equilibrium constants can be determined. By the example of phenol and indol, the adsorptive capacity of several domestic and foreign samples of active charcoal is assessed on the basis of the difference of the immersion heats in benzene and water.

Kinetic study for addition of the phenylthio radicals to vinylpyridines

AbstractThe absolute rate constants for reversible addition of the substituted phenylthio radicals to vinylpyridines in solution at 23°C have been determined by flash photolysis method. For each phenylthio radical, the reactivities of vinylpyridines is 3–5 times lower than that of styrene. The relative equilibrium constants estimated with flash photolysis indicate that the stabilities of the adduct carbon‐centered radicals generated from vinylpyridines are similar to that from styrene. The Hammett plots suggest that the difference in the reactivities originates in the polar transition state; the nitrogen atom in 4‐vinylpyridine withdraws the electrons of vinylic double bond.

Synthesis of methyl tertiary butyl ether catalyzed by ion-exchange resin. Influence of methanol concentration and temperature

Synthesis and decomposition of methyl t-butyl ether (MTBE) have been carried out in the temperature range of 50–95 °C and in the presence of a sulfonic acid resin. A Langmuir-Hinshelwood model rate expression has been selected to interpret results. Relative rate constants and equilibrium constants are given as a function of temperature and the activation energy and reaction enthalpy have been determined. The results are particularly discussed in terms of the effect of methanol concentration. The catalytic activity of the resin is sensitive to the concentration of methanol, and at a given temperature, the variation in the apparent equilibrium constant is mainly due to the variation of methanol activity coefficient as a function of its molar fraction.

The isomerization and metathesis of n-butenes : II. Acid catalysis on the fully oxidized catalyst

The mechanism of n-butene isomerization was studied over a freshly oxidized molybdena-alumina catalyst using the microcatalytic pulse technique. A 2-butyl carbonium ion common intermediate was invoked to interpret the results. A model was derived which was built upon statistical and energetic arguments and based on the experimental energy profile; it accounted for the selectivities and their temperature dependencies. In particular it was shown that temperature-dependent cis/trans ratios very different than unity are possible and sometimes found for acid-catalyzed reactions. The model also correctly described the relative reactivities and equilibrium constants for the three isomers.

Zur Beschreibung der Wechselwirkung zwischen p‐substituierten Benzaldehyden und NMR‐Verschiebungsreagenzien

Investigations to the Interaction between p‐Substituted Benzaldehydes and N.M.R.‐Shift ReagencesThe influence of n.m.r. shift reagents (Eu(fod)3 and Pr(fod)3) on the chemical shifts of p‐dimethylaminobenzaldehyde has been investigated at 13C and 1H‐n.m.r. spectroscopy. The induced shifts of the protons are quantitatively explained on the basis of pseudocontact interaction. In 13C‐n.m.r. spectra significant contact interactions have also been noted. The 13C induced shifts have been separated into pseudocontact and contact contributions by two different methods. Calculations of relative equilibrium constants in mixtures have been carried out for p‐dimethylaminobenzaldehyde, p‐nitrobenzaldehyde, anisaldehyde and benzaldehyde. The relative equilibrium constants show a good correlation with the Hammett substituent constants.

Studies of exchange equilibria of palladium(II) tertiary phosphine complexes

The reactions of tertiary phosphine complexes of Pd(II) with phosphine !igand: have been investigated by NMR and conductivity measurements. Depending on the nature of the phosphine ligand either ligand exchange or the formation of cationic complexes can occur. Relative equilibrium constants for these reactions have been obtained. NMR line broadening experiments have enabled the relative rates of ligand exchange between the neutral and cationic complexes and between the cationic complex and free ligand to be obtained. A mechanism for the former process is suggested. The equilibrium constant data suggest that optimum stability for the complexes is achieved with ligands of intermediate donor ability. The significance of this observation is discusssed.

Relative affinities of bilirubin for serum albumins from different species

Relative equilibrium constants (”affinity ratios“) of complexes of bilirubin with a molar excess of charcoal-treated serum albumins from different species (human, bovine, rabbit and chicken) in aqueous solution, were estimated by circular dichroism measurements in the visible region at 26–27 °C, pH 7.4, and in the presence of 0.1 M NaCl. By variation of the mol ratios of the components of pairs of different bilirubin•serum albumin complexes showing circular dichroic bands of opposite sign, the apparent association constants of complexes of bilirubin with either human or chicken albumin were found to be greater by factors between 6 and 17 than those of bovine or rabbit albumins. The usefulness in the determination of affinity ratios is illustrated by the evaluation of single equilibrium constants of systems of high-ligand affinity from those of relatively lower affinity, the latter of which are more readily amenable to direct experimental measurement.