Steps, elementary

The following elementary steps can be distinguished in ionic polymerizations. 

In the course of the oxygen storage process, different steps could be distinguished  

Consequently, a better understanding of the oxygen storage process will derive from a better understanding of both oxygen activation and migration on these samples. To tackle theses questions, the study of isotopic exchange reactions has been developed. 

On oxide-supported metals, 0/ 0 exchange occurs through a sequence of well differentiated steps  

finally, every step i is coupled with step -i corresponding to the reverse route for the exchanged species. 

Depending on reaction temperature, two other steps may be involved  

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Gas-phase reactions play a fundamental role in nature, for example atmospheric chemistry [1, 2, 3, 4 and 5] and interstellar chemistry [6], as well as in many teclmical processes, for example combustion and exliaust fiime cleansing [7, 8 and 9], Apart from such practical aspects the study of gas-phase reactions has provided the basis for our understanding of chemical reaction mechanisms on a microscopic level. The typically small particle densities in the gas phase mean that reactions occur in well defined elementary steps, usually not involving more than three particles. 

The system of coupled differential equations that result from a compound reaction mechanism consists of several different (reversible) elementary steps. The kinetics are described by a system of coupled differential equations rather than a single rate law. This system can sometimes be decoupled by assuming that the concentrations of the intennediate species are small and quasi-stationary. The Lindemann mechanism of thermal unimolecular reactions [18,19] affords an instructive example for the application of such approximations. This mechanism is based on the idea that a molecule A has to pick up sufficient energy... 

The resulting rate law agrees with the fonn found experimentally. Of course the postidated mechanism can only be proven by measuring the rate constants of the individual elementary steps separately and comparing calculated rates of equation (A3.4.148) with observed rates of HBr fomiation. 

As with the other surface reactions discussed above, the steps m a catalytic reaction (neglecting diffiision) are as follows the adsorption of reactant molecules or atoms to fomi bound surface species, the reaction of these surface species with gas phase species or other surface species and subsequent product desorption. The global reaction rate is governed by the slowest of these elementary steps, called the rate-detemiming or rate-limiting step. In many cases, it has been found that either the adsorption or desorption steps are rate detemiining. It is not surprising, then, that the surface stmcture of the catalyst, which is a variable that can influence adsorption and desorption rates, can sometimes affect the overall conversion and selectivity. 

ErtI G 1990 Elementary steps in heterogeneous catalysis Agnew. Chem., Int. Ed. Engl. 29 1219... 

The branching cycle involving the radicals FI, OFl and O in the Fl2 + O2 reaction involves the tliree elementary steps... 

In the bromate-iron clock reaction, there is an autocatalytic cycle involvmg the species intennediate species HBrO. This cycle is comprised of the following non-elementary steps ... 

An important point about kinetics of cyclic reactions is tliat if an overall reaction proceeds via a sequence of elementary steps in a cycle (e.g., figure C2.7.2), some of tliese steps may be equilibrium limited so tliat tliey can proceed at most to only minute conversions. Nevertlieless, if a step subsequent to one tliat is so limited is characterized by a large enough rate constant, tlien tire equilibrium-limited step may still be fast enough for tire overall cycle to proceed rapidly. Thus, tire step following an equilibrium-limited step in tire cycle pulls tire cycle along—it drains tire intennediate tliat can fonn in only a low concentration because of an equilibrium limitation and allows tire overall reaction (tire cycle) to proceed rapidly. A good catalyst accelerates tire steps tliat most need a boost. 

Complex chemical mechanisms are written as sequences of elementary steps satisfying detailed balance where tire forward and reverse reaction rates are equal at equilibrium. The laws of mass action kinetics are applied to each reaction step to write tire overall rate law for tire reaction. The fonn of chemical kinetic rate laws constmcted in tliis manner ensures tliat tire system will relax to a unique equilibrium state which can be characterized using tire laws of tliennodynamics. 

As an example for an efficient yet quite accurate approximation, in the first part of our contribution we describe a combination of a structure adapted multipole method with a multiple time step scheme (FAMUSAMM — fast multistep structure adapted multipole method) and evaluate its performance. In the second part we present, as a recent application of this method, an MD study of a ligand-receptor unbinding process enforced by single molecule atomic force microscopy. Through comparison of computed unbinding forces with experimental data we evaluate the quality of the simulations. The third part sketches, as a perspective, one way to drastically extend accessible time scales if one restricts oneself to the study of conformational transitions, which arc ubiquitous in proteins and are the elementary steps of many functional conformational motions. 

Porschke D. Elementary steps of base recognition and helix-coil transitions in nucleic acids. Mol. Biol. Biochem. Biophys. 24 (1977) 191-218... 

The symbol stands here for a succession of elementary steps (heterocydization. first deshydratation, second deshydratation). 

Each equation m Figure 4 6 represents a single elementary step An elementary step IS one that involves only one transition state A particular reaction might proceed by way of a single elementary step m which case it is described as a concerted reaction, or by a series of elementary steps as m Figure 4 6 To be valid a proposed mechanism must meet a number of criteria one of which is that the sum of the equations for the elementary steps must correspond to the equation for the overall reaction Before we examine each step m detail you should verify that the mechanism m Figure 4 6 satisfies this requirement... 

The molecularity of an elementary step is given by the number of species that undergo a chemical change m that step Transfer of a proton from hydrogen chloride to tert butyl alcohol is bimolecular because two molecules [HCl and (CH3)3COH] undergo chemical change... 

Because this is an elementary step it involves a single transition state... 

Inferring the structure of a transition state on the basis of the reactants and prod nets of the elementary step m which it is involved is a time honored practice m organic chemistry Speaking specifically of transition states George S Hammond suggested that... 

For a proposed reaction mechanism to be valid the sum of its elementary steps must equal the equation for the overall reaction and the mechanism must be consistent with all experimental observations The S l mechanism set forth m Figure 4 6 satisfies the first criterion What about the second d... 

Section 4 9 The potential energy diagrams for separate elementary steps can be merged into a diagram for the overall process The diagram for the reac tion of a secondary or tertiary alcohol with a hydrogen halide is charac terized by two intermediates and three transition states The reaction is classified as a ummolecular nucleophilic substitution, abbreviated as SnI... 

The elementary steps (1) through (3) describe a free radical chain mech anism for the reaction of an alkane with a halogen... 

The E2 mechanism is a concerted process m which the carbon-hydrogen and carbon-halogen bonds both break m the same elementary step What if these bonds break m separate steps s... 

Neither bromine nor ethylene is a polar molecule but both are polarizable and an induced dipole/mduced dipole force causes them to be mutually attracted to each other This induced dipole/mduced dipole attraction sets the stage for Br2 to act as an electrophile Electrons flow from the tt system of ethylene to Br2 causing the weak bromine-bromine bond to break By analogy to the customary mechanisms for electrophilic addition we might represent this as the formation of a carbocation m a bimolecular elementary step... 

The mechanism of alkene epoxidation is believed to be a concerted process mvolv mg a single bimolecular elementary step as shown m Figure 6 14... 

Bile acids (Section 26 13) Steroid derivatives biosynthesized in the liver that aid digestion by emulsifying fats Bimolecular (Section 4 8) A process in which two particles re act in the same elementary step Biological isoprene unit (Section 26 8) Isopentenyl pyrophos phate the biological precursor to terpenes and steroids... 

Concerted reaction (Section 4 8) Reaction that occurs m a sm gle elementary step... 

Molecular ion (Section 13 22) In mass spectrometry the species formed by loss of an electron from a molecule Molecular orbital theory (Section 2 4) Theory of chemical bonding in which electrons are assumed to occupy orbitals in molecules much as they occupy orbitals in atoms The molecular orbitals are descnbed as combinations of the or bitals of all of the atoms that make up the molecule Molecularity (Section 4 8) The number of species that react to gether in the same elementary step of a reaction mechanism... 

Propagation steps (Section 4 17) Elementary steps that repeat over and over again in a chain reaction Almost all of the products in a chain reaction arise from the propagation steps... 

Transcription (Section 28 11) Construction of a strand of mRNA complementary to a DNA template Transfer RNA (tRNA) (Section 28 11) A polynucleotide of n hose that is bound at one end to a unique amino acid This ammo acid is incorporated into a growing peptide chain Transition state (Section 3 1) The point of maximum energy in an elementary step of a reaction mechanism Translation (Section 28 12) The reading of mRNA by van ous tRNAs each one of which is unique for a particular ammo acid... 

Figure 2.7 shows a representation of this situation. The ordinate is an energy axis and the abscissa is called the reaction coordinate and represents the progress of the elementary step. In moving from P to H, the particle simply moves from one equilibrium position to another. In the absence of any external forces, the energy of both the initial and final locations should be the same as shown by the solid line in Fig. 2.7. Between the two minima corresponding to the initial and final positions is the energy barrier arising from the dislodging of the particles neighboring the reaction path from their positions of minimum energy.

Mechanisms. Mechanism is a technical term, referring to a detailed, microscopic description of a chemical transformation. Although it falls far short of a complete dynamical description of a reaction at the atomic level, a mechanism has been the most information available. In particular, a mechanism for a reaction is sufficient to predict the macroscopic rate law of the reaction. This deductive process is vaUd only in one direction, ie, an unlimited number of mechanisms are consistent with any measured rate law. A successful kinetic study, therefore, postulates a mechanism, derives the rate law, and demonstrates that the rate law is sufficient to explain experimental data over some range of conditions. New data may be discovered later that prove inconsistent with the assumed rate law and require that a new mechanism be postulated. Mechanisms state, in particular, what molecules actually react in an elementary step and what products these produce. An overall chemical equation may involve a variety of intermediates, and the mechanism specifies those intermediates. For the overall equation... 

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