Reversible Second-order Reaction Research Articles

Sulfonated poly(styrene-divinylbenzene) catalysts: II. Diffusion and the influence of macroporous polymer physical properties on the rate of reesterification

Macroporous polymer catalysts consist of aggregates of gelular microparticles interspersed with macropores. A set of macroporous, sulfonated, crosslinked polystyrene catalysts has been prepared, the crosslinking, surface area, and average macropore diameter having been varied independently. The catalysts were tested in a reaction involving molecules of intermediate size and polarity, the reesteriflcation of ethyl acetate with n-propanol. Reaction rate data, measured at 106 °C and 1 atm, demonstrate that sites on the surfaces of the gel microparticles are less active than sites within the microparticles. The more highly crosslinked polymers offer greater resistance to diffusion in the microparticles but have the more active catalytic sites within the microparticles. The data are represented by a model accounting for diffusion in macropores, Langmuir adsorption on microparticle surfaces, diffusion/swelling in microparticles, and second-order reversible reaction within microparticles. The model accounts for variations in diffusion coefficients and microparticle volume caused by swelling of the microparticles. The reaction rates were strongly influenced by diffusion in the microparticles, but the effects of macropore diffusion and adsorption on microparticle surfaces were negligible.

Reactions involving electron transfer at semiconductor surfaces. Part 10.—Oxygen isotope equilibration on non-illuminated zinc oxides

Rapid isotopic equilibration, 16O2+18O2⇌ 216O18O, was observed upon contacting an equimolar mixture of (16O2+18O2) at 295 or 77 K with oxygen-deficient surfaces of pure and doped zinc oxides from which light was excluded at all stages. Kinetic expressions for opposing second-order reactions accurately described variations in mole fraction of 16O2, 16O18O and 18O2 in the gas phase during the approach to full isotopic equilibration at 295 or 77 K. Rate constants thereby derived for this R0-type exchange did not correlate with reported concentrations of conduction-band electrons for the zinc oxides, indicating that the rate-determining process for exchange was not collective-electron type charge transfer at the oxygen-deficient surfaces in the absence of illumination. Surfaces could be rendered inactive by extensive preoxidation in 16O2 at 650 K in the dark, but heating for 2 h periods in the dark under continuous evacuation restored activity to a progressively increasing extent at temperatures of 400–650 K. Preadsorption of H2O, H2 or (CH3)2CHOH at 295 K strongly inhibited activity. An explanation of the observed results is developed based on: (i) dissociative chemisorption at e–|Zncus sites on the oxygen-deficient surfaces; (ii) formation of triatomic oxygen surface intermediates; (iii) equilibration by reversible second-order reactions of O2 with these triatomic oxygen intermediates.

On the reaction of plasmin or plasmin-streptokinase complex with aprotinin or α2-antiplasmin

The reaction between plasmin and aprotinin occurs in a two-step reaction: A fast reversible second-order reaction followed by a slower first-order transition. The dissociation constant of the initial complex and the rate constants of the two steps have been determined. It is also demonstrated that plasmin-streptokinase complex is inactivated by aprotinin but about 100-fold slower than plasmin. The rate constant was determined as 1.1 × 10 4 M −1·s −1. There are no significant inhibitors of plasmin-streptokinase complex in plasma. However, after addition of aprotinin (1 μmol/1) to normal plasma a progressive inactivation takes place ( t 1 2 = 250 s ). It is suggested that aprotinin may be used to control bleeding complications during thrombolytic therapy with streptokinase. In contrast to plasmin the streptokinase-plasmin complex reacts very slowly with α 2-antiplasmin (rate constant 0.8 M −1·s −1). This is at least 2 × 10 7 fold slower than the reac tion between plasmin and α 2-antiplasmin, indicating a pronounced stability of the streptokinase-plasmin complex. The reaction rate of the plasmin-streptokinase reaction is demonstrated to be extremely rapid. A value of 4.7 × 10 7 M −1·s −1 is obtained for the rate constant.

Kinetics of Metal Extraction by Chelate Formation: Part I: Mass Transfer with a Fast Reversible Chemical Reaction and Product Extraction

The description of the rate of extraction of a bivalent metal sets out from the assumption that the mass transfer process consists of the diffusion of the active component from the organic into the aqueous phase, accompanied by its instantaneous dissociation, a fast reversible reaction with the metal ion leading to the 1—1 complex, a consecutive instantaneous formation of the extractable 1—2 complex, and the transfer of this complex into the organic phase. This description reduces after the introduction of suitable simplifying assumptions to the model of component transfer with a fast reversible second-order reaction followed by product extraction. An approximate solution has been elaborated for this model based on the film theory of mass transfer, resulting in a dependence of the reaction factor on dimensionless parameters. The approximation suggested becomes the exact solution in the cases of an instantaneous reversible reaction and of a reversible reaction of the pseudo-first order. The accuracy of the approximation has been checked by a numerical solution. A computational algorithm for the extraction rates is given, including diffusion resistances on both sides of the interface.

On the kinetics of the reaction between human antiplasmin and a low-molecular-weight form of plasmin.

The reaction between antiplasmin (A) and a low-molecular-weight form of plasmin (P) proceeds in at least two steps: a fast reversible second-order reaction followed by a slower irreversible first-order transition, and may be represented by: P +A k1 in equilibrium k-1 PA k2 leads to PA'. The low-Mr plasmin, which is obtained by limited elastase digestion, is composed of an intact B chain and a small A chain lacking the lysine-binding sites. The k1 of the reaction is (6.5 +/- 0.5) x 10(5) M-1 s-1 which is 30--60 times smaller than that for normal plasmin and antiplasmin. The dissociation constant of the first step is 1.9 x 10(-9) M which is 10 times higher than for normal plasmin and antiplasmin. The rate constant of the second step is (4.2 +/- 0.2) x 10(-3) s-1 for both normal and low-Mr plasmin. Low Mr plasmin which has substrate bound to its active site does not react or reacts only very slowly with antiplasmin. The reaction rate, however, is only slightly influenced by 6-aminohexanoic acid in concentrations up to 1 mM which decrease the reaction rate of normal plasmin approximately 50-fold. The findings further indicate that the lysine-binding site(s) of plasmin are of great importance for the rate of its reaction with antiplasmin.

On the kinetics of the reaction between human antiplasmin and plasmin.

The reaction between antiplasmin (A) and plasmin (P) proceeds in at least two steps: a very fast reversible second-order reaction followed by a slower irreversible first-order reaction, and may be represented by: . The two forms of plasmin with different affinities for lysine-Sepharose (plasmin I and plasmin II) react at different rates with antiplasmin. The k1 is (3.8±0.3)×107 M−1 s−1, for the reaction between plasmin I and antiplasmin, and (1.8±0.2) × 107 M−1 s−1 for plasmin II and antiplasmin. This reaction rate is one of the fastest so far described for protein-protein interactions. The k1 for trypsin and antiplasmin is (1.8±0.2) × 10−10 M for plasmin II with antiplasmin. The second step has a half-time of approximately 165 s for both types of plasmin, corresponding to a k2 of 4.2×10−3 s−1. Plasmin which has 6-aminohexanoic acid bound to its lysine binding site or the substrate d-valyl-l-lysyl-p-nitroanilide bound to its active site does not react, or reacts very slowly, with antiplasmin. From these findings we postulate that plasmin formed in the circulating blood is rapidly neutralized by antiplasmin, but plasmin bound to fibrin is not. This hypothesis may provide a molecular basis for the mechanism of thrombolysis in vivo.

On the dissolving rate of a solid with chemical reaction

An investigation on dissolving rate of a solid in a liquid flowing between two flat plates, with the contribution of a second-order reversible chemical reaction, has been carried out. The process was analyzed as an isothermal one, taking place within a transition region at a stationary laminar flow. From the differential momentum and mass balances a process model was formulated under suitable initial and boundary conditions and a numerical solution was obtained for the benzoic acid-methanol reaction. According to the proposed model it is possible to calculate concentration profiles for any cross-section of a slit reactor. The presented model has been experimentally proved. Average difference between experimental values and theoretical calculations ranged to ± 5.3%. Longitudinal diffusion has been shown to have a negligible effect on the results. The presented method of calculation was found to be sufficiently accurate for the problem under consideration.

A study of the disproportionate of 3,6-di-tert-butyl-2-hydroxyphenoxyl

1. The disproportionation constants of 3,6-di-tert-butyl-2-hydroxyphenoxyl in various approximations of an equation describing reversible second-order reactions were measured by the rotating sector method. 2. The rate constant of the reaction of quinone and pyrocatechol taking into account the equilibrium constant for disproportionation of the radicals studied was calculated.

Kinetics of redistribution of some tetrahedral nickel(II) chelates

Scrambling of N-t-butylsalicylaldiminonickel(II) or N-isopropyltrifluoroacetyliminonickel(II) with N-isopropylacetyliminonickel(II) has been shown to follow a rate law for second-order reversible reactions in tetrachloroethylene solvent, activation entropies and energies being consistent with a bimolecular associative mechanism.

Approximation Method for Equilibrium Distributions in Second-Order Chemical Reaction Kinetics

The method introduced allows the classical deterministic value to be used to produce approximations to a high order of accuracy for the mean and the fluctuations in reversible second-order chemical reactions. The reaction A+B⇄C+D is examined and the results are encouraging for the use of this approach in other problems of a similar nature.

Stochastic Models for Second-Order Chemical Reaction Kinetics. Time Course of Reactions

A detailed study is given of the time course of a stochastic model for the reversible second-order chemical reaction A+B⇄C+D. The solutions are obtained by perturbation theory for a range of values of the rate constants of the reaction and the techniques developed may be applied to a variety of other reactions. The main conclusion of this study is that fluctuations in the number of molecules of every component present in the system at any time are negligible even for small systems.

Effect of internal diffusion on catalytic reactions. IV. Reversible second-order reaction with Langmuir-Hinshelwood type of rate equation

Effect of internal diffusion on catalytic reactions. IV. Reversible second-order reaction with Langmuir-Hinshelwood type of rate equation