Multiple rate-determining steps

Ihis number v is the mean stoichiometric number of the rate-determining multiple steps. The mean stoichiometric number is thus represented by the energy average (afiiniiy average) of the stoichiometric niunbers v weighed with the step affinity 4gi in the respective rate-determining steps. 

Enzyme Immunosensors. Enzyme immunosensors are enzyme immunoassays coupled with electrochemical sensors. These sensors (qv) require multiple steps for analyte determination, and either sandwich assays or competitive binding assays maybe used. Both of these assays use antibodies for the analyte of interest attached to a membrane on the surface of an electrochemical sensor. In the sandwich assay type, the membrane-bound antibody binds the sample antigen, which in turn binds another antibody that is enzyme-labeled. This immunosensor is then placed in a solution containing the substrate for the labeling enzyme and the rate of product formation is measured electrochemically. The rate of the reaction is proportional to the amount of bound enzyme and thus to the amount of the analyte antigen. The sandwich assay can be used only with antigens capable of binding two different antibodies simultaneously (53). 

Even relatively complex reactions can behave very simply, and 99 percent of the time, understanding simple first-, second-, and zero-order kinetics is more than good enough. With very complicated mechanistic schemes with multiple intermediates and multiple pathways to the products, the kinetic behavior can get very complicated. But more often than not, even complex mechanisms show simple kinetic behavior. In complex mechanisms, one step (called the rate-determining step) is often much slower than all the rest. The kinetics of the slow step then dictates the kinetics of the overall reaction. If the slow step is simple, the overall reaction appears simple. 

It is not always possible to determine intrinsic isotope effects. However, other useful information about the reaction can still be obtained. Above we assumed a single rate determining step sensitive to each isotope substitution. More frequently, however, the isotope sensitivity is found in different steps. Studies with multiple isotope effects can be used to determine the sequence of steps. To illustrate, a more complicated reaction scheme is needed ... 

Such a single rate-determining step scarcely occurs in ordinary reactions usually, the overall reaction affinity is distributed in multiple rate-determining steps rather than localized at a single step as is described in Sec. 7.4. 

Fig. 7-11. Potential energy curves for a mialtistep reaction of (a) single rate-determining step and (b) multiple rate-determining steps v = stoichiometric number of a single rate-determining step v = mean stoichiometric number of multiple rate-determining steps.

For reactions in which the rate is determined not by a single elementary step but by multiple elementary steps, the overall affinity of the reaction is distributed among those multiple steps which determine the reaction rate as shown in Fig. 7-11 (b). The ratio of the forward to the backward reaction rate is then derived from Eqns. 7-40 and 7-43 to give Eqn. 7-60 ... 

The reaction affinity - AG and the ratio v /vj of the forward to the backward rate can be estimated, regardless of whether the reaction rate is determined by a single step or multiple steps. Thus, Eqn. 7-51 can be used to determine the mean stoichiometric number of the multiple rate-determining steps. 

The general mechanism of MeOH on Pt and PtRu is well established. First, MeOH is adsorbed and subjected to multiple dehydrogenation steps to give adsorbed CO. This dehydration step is known to occur at low potentials. The adsorbed CO is then oxidized by active OH species produced by the dissociation of H2O. This is fhe pofenfial-driven rate-determining step because OH formation does not occur on Pt until higher potentials. The addition of Ru pro-mofes fhe reaction because it is able to produce OH species at lower potentials. This promotional effect is known as the "bifunctional" mechanism ... 

Reaction conditions permitting a catalyst to pass through many catalytic rounds. Multiple-turnover conditions are usually obtained by maintaining the substrate concentration in excess over the concentration of active catalyst. This technique usually allows one the opportunity to evaluate the catalytic rate constant ka,t, which is the first-order decay rate constant for the rate-determining step for each cycle of catalysis, and one can evaluate the magnitude of other parameters such as the substrate s dissociation constant or Michaehs constant. 

The electron waiting-line problem is hence clear. In a particular multistep electron-transfer reaction, the step with the lowest servicing rate or conductivity produces the largest queue and, indeed, the total queue is virtually a simple multiple of the queue at the rds. In other words, in the steady state, all n steps proceed at the rate of the rate-determining step ir, [cf. Eq. (9.4)], and the total net current is... 

None of these difficulties arise when hydrosilylation is promoted by metal catalysts. The mechanism of the addition of silicon-hydrogen bond across carbon-carbon multiple bonds proposed by Chalk and Harrod408,409 includes two basic steps the oxidative addition of hydrosilane to the metal center and the cis insertion of the metal-bound alkene into the metal-hydrogen bond to form an alkylmetal complex (Scheme 6.7). Interaction with another alkene molecule induces the formation of the carbon-silicon bond (route a). This rate-determining reductive elimination completes the catalytic cycle. The addition proceeds with retention of configuration.410 An alternative mechanism, the insertion of alkene into the metal-silicon bond (route b), was later suggested to account for some side reactions (alkene reduction, vinyl substitution).411-414... 

The rate-determining step in nucleophilic additions is usually nucleophilic attack on the multiple bond.127 For example, the entropy of activation of a Michael condensation is always a large, negative quantity. This arises from the fact that in the transition state the five atoms, 0=C—C—C=0 of the anion and the four atoms, C=C-—C=0 (or C=C—C=N) of the a,/ -unsaturated carbonyl (or nitrile) system are all restricted to one plane to allow maximum... 

The simplest enzymatic system is the conversion of a single substrate to a single product. Even this straightforward case involves a minimum of three steps binding of the substrate by the enzyme, conversion of the substrate to the product, and release of the product by the enzyme (Scheme 4.6). Each step has its own forward and reverse rate constant. Based on the induced fit hypothesis, the binding step alone can involve multiple distinct steps. The substrate-to-product reaction is also typically a multistep reaction. Kinetically, the most important step is the rate-determining step, which limits the rate of conversion. 

Some emulsions are undesirable when they occur. In process industries chemical demulsification is commonly used to separate water from oil in order to produce a fluid suitable for further processing. The specific kind of emulsion treatment required can be highly variable, even within the same industry. The first step in systematic emulsion breaking is to characterize the emulsion in terms of its nature (O/W, W/O, or multiple emulsion), the number and nature of immiscible phases, the presence of a protective interfacial film around the droplets, and the sensitivity of the emulsifiers [295,408,451], Demulsification then involves two steps. First, there must be agglomeration or coagulation of droplets. Then, the agglomerated droplets must coalesce. Only after these two steps can complete phase separation occur. It should be realized that either step can be rate determining for the demulsification process. 

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