Equilibrium processes, study

An interesting example of a non-equilibrium process studied by maximum information entropy methods was reported by Levine. 

The same structural factors come into play in determining the position of equilibria in reversible additions to carbonyl compoimds. The best studied of such equilibrium processes is probably addition of cyanide to give cyanohydrins. 

Research into the aquatic chemistry of plutonium has produced information showing how this radioelement is mobilized and transported in the environment. Field studies revealed that the sorption of plutonium onto sediments is an equilibrium process which influences the concentration in natural waters. This equilibrium process is modified by the oxidation state of the soluble plutonium and by the presence of dissolved organic carbon (DOC). Higher concentrations of fallout plutonium in natural waters are associated with higher DOC. Laboratory experiments confirm the correlation. In waters low in DOC oxidized plutonium, Pu(V), is the dominant oxidation state while reduced plutonium, Pu(III+IV), is more prevalent where high concentrations of DOC exist. Laboratory and field experiments have provided some information on the possible chemical processes which lead to changes in the oxidation state of plutonium and to its complexation by natural ligands. 

This consists of protonation in a fast pre-equilibrium process followed by ratedetermining reaction of the protonated substrate SH +, equation (30) a typical example is the much-studied acid-catalyzed depolymerization of trioxane, shown in equation (31).144... 

The structure of compounds 183 and 184 was established by X-ray investigation. Equilibrium processes were studied by NMR and IR spectroscopy. 

The first chair of theoretical physics in France was the professorship established for Pierre Duhem in 1894 at the Bordeaux Faculty of Sciences. 1 Duhem was well known in French scientific circles not only as a physicist but as a physicist of exceptional mathematical skills who addressed himself early in his scientific studies to chemical problems. He wrote a controversial doctoral thesis (1886) in which he developed the concept of thermodynamic potential for chemistry and physics, and he later developed a treatment of equilibrium processes formally analogous to the mechanics of Lagrange. The goal was to make mechanics a branch of the more general science of thermodynamics, a science that embraces "every change of qualities, properties, physical state, chemical constitution. "2... 

The kinetic effects of detergency will not be explored in this study, but review articles on this topic can be found elsewhere (1-5). Instead, the agitation will be held constant (see Experimental Section) so that the equilibrium (or near equilibrium) processes can be observed. Equilibrium was achieved for similar soil/substrate systems within 5-10 minutes in previous studies (3). 

In principle, each of the above protodelithiation reactions is in equilibrium. It is clear that, in practice, they are not. The protonating species, HBr, isopropanol and 2-butanol, are simply too acidic for the reaction to be reversible. Although the hydrogen/lithium exchange equilibria cannot be smdied in both directions, halogen/Uthium exchange reactions with aryl substituents evidently are true equilibrium processes. Winkler and Winkler studied reaction 11 (among others), in either diethyl ether or in THF at 25 °C. 

Another application in the first category is for experimentalists investigating equilibrium processes (such as the determination of equilibrium constants) to evaluate whether equilibrium is reached. The experimental duration must be long enough to reach equilibrium. To estimate the required experimental duration to insure that equilibrium is reached, one needs to have a rough idea of the kinetics of the reaction to be studied. Or experiments of various durations can be conducted to evaluate the attainment of equilibrium. 

The carbonyl ylide 1 can undergo an internal cyclization reaction to generate the corresponding epoxide 2, which is in fact an equilibrium process, and epoxides themselves have frequently served as precursors to carbonyl ylides. Other pathways such as concerted rearrangements and internal proton transfers have also been observed to neutralize the charged ylide intermediate and give substituted ethers as represented by 3. Perhaps the best known studies and most synthetically useful... 

In many systems studied the results point out that Eq. (9) is an equilibrium process and that the mechanism of decomposition of the transient complex LmMn + 1-R involves radical processes. 

For example, the standard synergetic approach [52-54] denies the possibility of any self-organization in a system with with two intermediate products if only the mono- and bimolecular reaction stages occur [49] it is known as the Hanusse, Tyson and Light theorem. We will question this conclusion, which in fact comes from the qualitative theory of non-linear differential equations where coefficients (reaction rates) are considered as constant values and show that these simplest reactions turn out to be complex enough to serve as a basic models for future studies of non-equilibrium processes, similar to the famous Ising model in statistical physics. Different kinds of auto-wave processes in the Lotka and Lotka-Volterra models which serve as the two simplest examples of chemical reactions will be analyzed in detail. We demonstrate the universal character of cooperative phenomena in the bimolecular reactions under study and show that it is reaction itself which produces all these effects. 

This article examines the dynamics of spin-equilibrium processes, principally from studies in solutions. The properties of the complexes which are relevant to the dynamics studies are first reviewed. Then the techniques used to observe these rapid processes are described. Some aspects of solid-state dynamics are mentioned. Finally, some implications for the description of intersystem crossing processes in excited states and for spin equilibria in heme proteins are described. 

The Raman laser temperature-jump technique has been used in studies of a variety of spin-equilibrium processes. It was used in the first experiment to measure the relaxation time of an octahedral spin-equilibrium complex in solution (14). Its applications include investigations of cobalt(II), iron(II), iron(III), and nickel(II) equilibria. 

The derivation of a similarly atypical rate expression is required for the simulation of the electrochemical behavior encountered in electrohydrodimerization studies. In these studies, the variation of the bulk concentration of the olefin (e.g., ethyl cinnamate, diethyl furmarate) reveals that there is a concentration dependence to the reaction order associated with the dimerization of the electrogenerated radical ion [33]. This variation in apparent reaction order with concentration can only be attributed to a two-step mechanism [25] involving two independent rate or equilibrium processes. A mechanism that meets this criterion and appears to fit the electrochemical data is the preequilibrium mechanism [36] in which the electrogenerated radical ions first engage in an equilibrium dimerization before the rate-determining ring closure of the dimer takes place. Symbolically, this mechanism may be written ... 

The most extensive and detailed studies of the equilibrium processes are those of Brandts and his colleagues 336, 339, 373). A careful calorimetric study has been reported by Tsong et al. 374)- This work and that of others is discussed by Tanford in a recent review 333). Although the primary data are of very high quality, considerable uncertainty is involved in their interpretation. The problems are perfectly general in protein chemistry. 

Ray Kapral came to Toronto from the United States in 1969. His research interests center on theories of rate processes both in systems close to equilibrium, where the goal is the development of a microscopic theory of condensed phase reaction rates,89 and in systems far from chemical equilibrium, where descriptions of the complex spatial and temporal reactive dynamics that these systems exhibit have been developed.90 He and his collaborators have carried out research on the dynamics of phase transitions and critical phenomena, the dynamics of colloidal suspensions, the kinetic theory of chemical reactions in liquids, nonequilibrium statistical mechanics of liquids and mode coupling theory, mechanisms for the onset of chaos in nonlinear dynamical systems, the stochastic theory of chemical rate processes, studies of pattern formation in chemically reacting systems, and the development of molecular dynamics simulation methods for activated chemical rate processes. His recent research activities center on the theory of quantum and classical rate processes in the condensed phase91 and in clusters, and studies of chemical waves and patterns in reacting systems at both the macroscopic and mesoscopic levels. 

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