Rate law generalization

Rate Determining Step the slowest reaction in the reaction mechanism Rate Law general mathematical expression that gives the rate of reaction, depends on rate constant and concentrations of reactants Reactants substances initially present in a chemical reaction... 

Explain why rate laws generally cannot be written from balanced equations. Under what circumstance is the rate law related directly to the balanced equation for a reaction ... 

The Langmuir-Hinshelwood picture is essentially that of Fig. XVIII-14. If the process is unimolecular, the species meanders around on the surface until it receives the activation energy to go over to product(s), which then desorb. If the process is bimolecular, two species diffuse around until a reactive encounter occurs. The reaction will be diffusion controlled if it occurs on every encounter (see Ref. 211) the theory of surface diffusional encounters has been treated (see Ref. 212) the subject may also be approached by means of Monte Carlo/molecular dynamics techniques [213]. In the case of activated bimolecular reactions, however, there will in general be many encounters before the reactive one, and the rate law for the surface reaction is generally written by analogy to the mass action law for solutions. That is, for a bimolecular process, the rate is taken to be proportional to the product of the two surface concentrations. It is interesting, however, that essentially the same rate law is obtained if the adsorption is strictly localized and species react only if they happen to adsorb on adjacent sites (note Ref. 214). (The apparent rate law, that is, the rate law in terms of gas pressures, depends on the form of the adsorption isotherm, as discussed in the next section.)... 

Various specific rate laws and mechanisms are described in the next section the present discussion is in more general terms. For example, why is it that a contact catalyst is able to serve as such, that is, why is it able to provide a reac-... 

A general fonn of the rate law , i.e. the differential equation for the concentrations is given by... 

In the case of bunolecular gas-phase reactions, encounters are simply collisions between two molecules in the framework of the general collision theory of gas-phase reactions (section A3,4,5,2 ). For a random thennal distribution of positions and momenta in an ideal gas reaction, the probabilistic reasoning has an exact foundation. Flowever, as noted in the case of unimolecular reactions, in principle one must allow for deviations from this ideal behaviour and, thus, from the simple rate law, although in practice such deviations are rarely taken into account theoretically or established empirically. 

The paradigmatical binding reaction (equation (C2.l4.22)) is generally analysed as a second order forward reaction and a first order backward reaction, leading to the following rate law ... 

For a closed chemical system witli a mass action rate law satisfying detailed balance tliese kinetic equations have a unique stable (tliennodynamic) equilibrium, In general, however, we shall be concerned witli... 

A rate law describes how the rate of a reaction is affected by the concentration of each species present in the reaction mixture. The rate law for reaction A5.1 takes the general form of... 

The transfer reactions follow second-order kinetics, the general rate law being... 

Homogeneous GopolymeriZation. Nearly all acryhc fibers are made from acrylonitrile copolymers containing one or more additional monomers that modify the properties of the fiber. Thus copolymerization kinetics is a key technical area in the acryhc fiber industry. When carried out in a homogeneous solution, the copolymerization of acrylonitrile foUows the normal kinetic rate laws of copolymerization. Comprehensive treatments of this general subject have been pubhshed (35—39). The more specific subject of acrylonitrile copolymerization has been reviewed (40). The general subject of the reactivity of polymer radicals has been treated in depth (41). 

The acid-catalyzed hydrolysis of 2-alkoxy-2-phenyl-l,3-dioxolanes has been studied. The initial step is rate-determining under eertain eonditions and is deseribed by the rate law given below, whieh reveals general acid catalysis. 

If the decomposition reaction follows the general rate law, the activation energy, heat of decomposition, rate constant and half-life for any given temperature can be obtained on a few milligrams using the ASTM method. Hazard indicators include heats of decomposition in excess of 0.3 kcal/g, short half-lives, low activation energies and low exotherm onset temperatures, especially if heat of decomposition is considerable. 

The frictional properties of TPs, specifically the reinforced and filled types, vary in a way that is unique from metals. In contrast to metals, even the highly reinforced plastics have low modulus values and thus do not behave according to the classic laws of friction. Metal-to-thermoplastic friction is characterized by adhesion and deformation resulting in frictional forces that are not proportional to load, because friction decreases as load increases, but are proportional to speed. The wear rate is generally defined as the volumetric loss of material over a given unit of time. Several mechanisms operate simultaneously to remove material from the wear interface. However, the primary mechanism is adhesive wear, which is characterized by having fine particles of plastic removed from the surface. 

PtL3X + Y — PtLjY + X the rate law is generally found to be of the form... 

In deducing from the resulting kinetic equation the nature of the electrophile and how it is produced it is important to represent all the reagents present in terms of the species which they may produce. In this way it is possible to eliminate many negative or fractional orders in reagent and generally obtain a simpler kinetic equation. For example, the observed rate law in the uncatalyzed iodination of aniline can be written21,22 as... 

Once v, is determined under one set of conditions, the procedure is then repeated, varying the concentrations of reactant, catalyst, buffer, etc. The resulting family of v, values can be used to formulate the rate law. This desirable method is probably deserving of wider use in general chemical reactions, just as it is used in biochemical reactions. The method of initial rates is, however, not without its problems. For one thing, the accurate determination of product in the presence of so much substrate is not always feasible. For another, this approach may conceal important effects that come into play only later in the course of the reaction. If the method of initial rates is used, separate experiments must be performed to check these points. 

Generally, to do this one guesses the rate law or mechanism and tests the data against its predictions. The initial supposition of the mechanism may be made on the basis of precedents in the literature, the results of an earlier trial, or the appearance of the raw data. 

More will be said about jump experiments in Chapter 11, which deals with fast reaction techniques. Very fast equilibration reactions are especially amenable to this method. As developed there, a first-order equation describes the approach to equilibrium irrespective of the actual rate law. The most general case is represented by an elementary reaction of the form... 

In the general case, consider the exchange of AX and X. With no implication as to the rate law or the mechanism, we represent this as... 

If the rate constant is dependent on [BH+] in this way, the reaction is general acid-catalyzed and if similarly dependent on [B], general base-catalyzed. When such terms are present in the rate law, then the corresponding ones for H+ or OH- will invariably contribute as well. 

Specific and general acid catalysis. Formulate the rate law for the acid-catalyzed hydrolysis reaction42... 

Base catalysis. Develop chemical equations and rate laws that illustrate specific and general base catalysis. Equations (10-37)—(10-44) can be used as a model. 

The luminescence of an excited state generally decays spontaneously along one or more separate pathways light emission (fluorescence or phosphorescence) and non-radiative decay. The collective rate constant is designated k° (lifetime r°). The excited state may also react with another entity in the solution. Such a species is called a quencher, Q. Each quencher has a characteristic bimolecular rate constant kq. The scheme and rate law are... 

The order of a reaction cannot in general be predicted from the chemical equation a rate law is an empirical law ... 

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