Prior rapid equilibria

When pyridine is present in only slight excess, however, the rate of exchange is dependent on the concentration of excess pyridine and a mechanism is postulated which involves a rate-determining step consisting of attack of a noncomplexed aluminum alkyl, formed in a prior rapid equilibrium, with a complexed aluminum alkyl. 

Prior equilibrium. Consider the net reaction between certain metal halide and alkyl cobalt complexes, RCo + MX = Co+ + RM + X". There is a rapid equilibrium ... 

Only three steps of the proposed mechanism (Fig. 18.20) could not be carried out individually under stoichiometric conditions. At pH 7 and the potential-dependent part of the catalytic wave (>150 mV vs. NHE), the —30 mV/pH dependence of the turnover frequency was observed for both Ee/Cu and Cu-free (Fe-only) forms of catalysts 2, and therefore it requires two reversible electron transfer steps prior to the turnover-determining step (TDS) and one proton transfer step either prior to the TDS or as the TDS. Under these conditions, the resting state of the catalyst was determined to be ferric-aqua/Cu which was in a rapid equilibrium with the fully reduced ferrous-aqua/Cu form (the Fe - and potentials were measured to be within < 20 mV of each other, as they are in cytochrome c oxidase, resulting in a two-electron redox equilibrium). This first redox equilibrium is biased toward the catalytically inactive fully oxidized state at potentials >0.1 V, and therefore it controls the molar fraction of the catalytically active metalloporphyrin. The fully reduced ferrous-aqua/Cu form is also in a rapid equilibrium with the catalytically active 5-coordinate ferrous porphyrin. As a result of these two equilibria, at 150 mV (vs. NHE), only <0.1%... 

STEADY STATE TREATMENT. While the Michaelis-Menten model requires the rapid equilibrium formation of ES complex prior to catalysis, there are many enzymes which do not exhibit such rate behavior. Accordingly, Briggs and Haldane considered the case where the enzyme and substrate obey the steady state assumption, which states that during the course of a reaction there will be a period over which the concentrations of various enzyme species will appear to be time-invariant ie., d[EX]/dr s 0). Such an assumption then provides that... 

This rate equation is identical to that for a rapid equilibrium ordered addition bisubstrate mechanism (/.c., a scheme where substrate A rapidly binds prior to the addition of the second substrate B). Huang has presented the theoretical basis for mechanisms giving rise to... 

The assumption that the consumption of the intermediate in the slow step is insignificant relative to its formation and decomposition in the first step is called a pre-equilibrium condition. A pre-equilibrium arises when an intermediate is formed in a rapid equilibrium reaction prior to a slow step in the mechanism. The slowest elementary step in a sequence of reactions—in our example, the reaction between 02 and N202—is called the rate-determining step of the reaction. The rate-determining step is so much slower than the rest that it governs the rate of the overall reaction (Fig. 13.24). A rate-determining step is like a slow ferry on the route between two cities. The rate at which the traffic arrives at its destination is governed by the rate at which it is ferried across the river, because this part of the journey is much slower than any of the others. 

Does bimolecular substitution on tricoordinate sulfur involve the formation of an intermediate, or is it a one-step process The evidence is somewhat inconclusive. For example, when sulfite ester (14) is hydrolyzed with HO containing 180, 180 is found in the product but no significant amount is present in the recovered unreacted ester.70 Bunton and co-workers interpreted this to mean that the mechanism shown in Reaction 4.37 in which the intermediate 15 is formed in a rapid equilibrium prior to the transition state for the reaction, is ruled out. If 15 were so formed, they reasoned, it would rapidly equilibrate with isoenergetic 16. Then loss of HO- from 16 would result in lsO in recovered... 

Particularly intriguing is the selectivity observed in Eqs. [3] and [4] (Scheme 29). In these cases, an enamine that probably exists as a 1 1 diastereomeric mixture yields products whose diastereomeric and enantiomeric excesses exceed 67%. This suggests that the isomeric enamines exist in a rapid equilibrium prior to the conjugate addition and/or the conjugate addition is at least partially reversible. 

The second-order approach was successfully used for Cr retention and transport predictions by Selim and Amacher (1988) and for Zn retention by Hinz et al. (1992). This model was recently modified such that the total adsorption sites Smax were not partitioned between Sc and Sk phases based on a fraction of sites/(Selim Amacher, 1997 Ma Selim, 1998). Instead it was assumed that the vacant sites are available to both types of Se and Sk. Therefore,/is no longer required and the amount of solute adsorbed on each type of sites is only determined by the rate coefficients associated with each type of sites. As a result, sites associates with equilibrium or instantaneous type reactions will compete for available sites prior to slow or kinetic type sites are filled. Perhaps such mechanism is in line with observations where rapid (equilibrium type) sorption is first encountered and followed by slow types of retention reactions. We are not aware of the use of this second-order approach to describe heavy metal retention kinetics and transport in soils. 

The limiting value, AG kcalmol S had previously been felt to be rather high, and one possible explanation considered was a rapid equilibrium between the two spin states of cobalt(m) tlg t ge prior to the electron transfer. The data from other oxidants have weakened if not altogether removed the necessity for this. It has moreover been argued from ligand-field considerations that for the hexa-aquo-cobalt(iii) ion the spin-change free energy may in any case be quite small. ... 

In the Fe2+-Tl3+ reaction, the limiting form attained when [Fe2+] < A [Fe3+] showed an inverse dependence on [Fe3+], In other words, [Fe3+] was so high that the first step produced so low a [Tl2+] as to make the second step rate-controlling. Under these conditions, the first step is a rapid prior equilibrium. 

Just because a rapid prior equilibrium can be invoked does not mean that one has learned anything about the mechanism of the fast step. That is, an interpretation of Eq. (6-20) is given in Eq. (6-23) the data say nothing, however, about the mechanism by which the constituents of Eq. (6-21) and of Eq. (6-22) are interconverted. 

The first case is one in which the rate constant is strictly a product or quotient of constants. Two cases illustrate this. One features a rapid prior equilibrium,... 

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