Mechanistic equations

Mechanistically, equations 45 and 46 involve the formation of a [CI2O2] intermediate ... 

Employing mechanistic equations based on the Rice-Herzfeld postulation yields ... 

In stoichiometric and non-stoichiometric mechanistic equations, a double-headed arrow (— ) indicates that the reaction involves more than one mechanistic step. 

In multi-step mechanistic equations the rate constants for the forward and reverse first step of a reaction are represented by k and Ar j, respectively, those for the second step by k2 and 2, etc. The corresponding equilibrium constants are Kx and K2. 

For mechanisms that are more complex than the above, the task of showing that the net effect of the elementary reactions is the stoichiometric equation may be a difficult problem in algebra whose solution will not contribute to an understanding of the reaction mechanism. Even though it may be a fruitless task to find the exact linear combination of elementary reactions that gives quantitative agreement with the observed product distribution, it is nonetheless imperative that the mechanism qualitatively imply the reaction stoichiometry. Let us now consider a number of examples that illustrate the techniques used in deriving an overall rate expression from a set of mechanistic equations. 

These basic premises go a long way in correlating and tying together the extraordinary complexity of many pyrolysis reactions. In terms of mechanistic equations, they may be... 

Based on the set of mechanistic equations set forth above, the rate of disappearance of reactant M is given by ... 

In order for the overall rate expression to be 3/2 order in reactant for a first-order initiation process, the chain terminating step must involve a second-order reaction between two of the radicals responsible for the second-order propagation reactions. In terms of our generalized Rice-Herzfeld mechanistic equations, this means that reaction (4a) is the dominant chain breaking process. One may proceed as above to show that the mechanism leads to a 3/2 order rate expression. 

Reversible First-Order Parallel Reactions. This section extends the analysis developed in the last section to the case where the reactions are reversible. Consider the case where the forward and reverse reactions are all first-order, as indicated by the following mechanistic equations. 

Since many reactions of this type involve a series of second-order processes, it is instructive to consider how one analyzes systems of this sort in order to determine the kinetic parameters that are necessary for reactor design purposes. We will follow a procedure described previously by Frost and Pearson (11). Consider the following mechanistic equations. 

The following mechanistic equations for chemisorption and reaction are appropriate. 

Although the Michaelis-Menten equation is applicable to a wide variety of enzyme catalyzed reactions, it is not appropriate for reversible reactions and multiple-substrate reactions. However, the generalized steady-state analysis remains applicable. Consider the case of reversible decomposition of the enzyme-substrate complex into a product molecule and enzyme with mechanistic equations. 

The following set of mechanistic equations is consistent with their experimental results ... 

Species A is present in liquid solution at an initial concentration CA0. It may undergo the reactions indicated by the following mechanistic equations ... 

This reaction set may be regarded as parallel reactions with respect to consumption of species B and as a series reaction with respect to species A, V, and W. Common examples include the nitration and halogenation of benzene and other organic compounds to form polysubstituted compounds. To characterize the qualitative behavior of such systems, it is useful to consider reactions 9.3.3 and 9.3.4 as mechanistic equations and to analyze the effects of different contacting patterns on the yield of species V. We shall follow the treatment of Levenspiel (7). 

While we have taken some liberties with the numerical values that we will subsequently employ, the following set of mechanistic equations has been proposed in an effort to explain the observed autocatalytic kinetic behavior (13). 

A sequential isomerization reaction is believed to be characterized by the following mechanistic equations. 

For flat-plate geometry wher only one side of the plate is exposed to reactant gases, one may proceed as in previous subsections to show that for mechanistic equations of the form... 

Independent Parallel Reactions of Different Species on the Same Catalyst. One often requires a catalyst that promotes the reactions of one component of a feedstock but does not promote the reactions of other constituents of the mixture. For example, one might desire to dehydrogenate six-membered rings, but not five-membered rings. This type of selectivity behavior may be represented by mechanistic equations of the form... 

Mechanistic equations describing the apparent radial thermal conductivity (kr>eff) and the wall heat transfer coefficient (hw.eff) of packed beds under non-reactive conditions are presented in Table IV. Given the two separate radial heat transfer resistances -that of the "central core" and of the "wall-region"- the overall radial resistance can be obtained for use in one-dimensional continuum reactor models. The equations are based on the two-phase continuum model of heat transfer (3). 

In both cases we are not specifically dealing with reorganization processes which are more complicated than in the case of liquids and specifically related with the crystal structure.176 177 More precisely the first special case is met, if, for reactions, the difference in the space coordinate does not matter (i.e., if zA x) = zB x )). Hence pure gas phase reactions or neutral surface reactions can be described by Eq. (93), while Eq. (94) refers to pure transport steps (transport within the same structure). The description of typical electrochemical reactions such as charge transfer reactions require the analysis ofEq. (92). (We will see later that mechanistic equations are typically bimolecular, however, owing to the constancy of regular constituents, the consideration ofEq. (92) suffices in most cases of interest.)... 

This is the dilemma—sensory properties should rank very high, but they don t because we lack the tools to measure them effectively. For the most part, these quality measures are subjective rather than objective, and frequently they require direct testing with consumers to determine efficacy of a particular product attribute. So the issue is really a lack of physical measurement tools that directly assess the performance measures important to the consumer of the product. The lack of objective performance measures and unknown mechanistic equations also makes mathematical modeling very difficult for addressing quality problems. 

Producing NHC-metal complexes by C=C scission of an NHC dimer is one method that is fairly general and interesting mechanistically. Equation 10.19 indicates the overall pathway to complex 46.38... 

The equations shown up to now are stoichiometric equations which show what happens in a reaction—what reactants are used up and what products are formed. They are not mechanistic equations which show how a reaction occurred. An understanding of a reaction mechanism usually allows one to better predict the outcome of the reaction. 

The reaction mechanism above can be boiled down to a set of symbolic equations, referred to as mechanistic equations because they reflect the mechanism. 

---