Rapid equilibrium steps

In estimating these barriers Richard addresses a problem that so far has been avoided. When discussing the correlation of log h2o with pATR in Fig. 3, it was implied that the rate and equilibrium constants refer to the same reaction step. That is not strictly true, because attack of water on a carbocation yields initially a protonated alcohol which subsequently loses a proton in a rapid equilibrium step. As we are reminded in Equation (26) the equilibrium constant AR refers to the combination of these two steps. To calculate an intrinsic barrier for reaction of the carbocation with water therefore the equilibrium constant KR should be corrected for the lack of stoichiometric protonation of the alcohol. Fortunately, there have been enough measurements of pA,s of protonated alcohols240 (e.g. pAa = -2.05 for CthOHi1") for the required corrections to be made readily. 

Generalization Kinetic Consequences of Rapid-Equilibrium Steps... 

Rapid-equilibrium steps do not contribute a kinetic step the species in rapid equilibrium can be grouped together as a single, kinetic unit. 

K = 9 pmoll cat/- m = 2.5 X 10 mol Ms ) of PNSHH, resulting in a very high enantiopreference for the (i )-enantiomer. The conversion of (ii )-PNSHH follows an ordered Uni—Bi mechanism, and the inhibition pattern of bromide ion as well as the occurrence of burst kinetics suggested that the bromide ion is first released from the enzyme, followed by the epoxide product para-nmostyrene oxide, PNSO). In addition, multiple turnover analyses showed that the binding of (f( )-PNSHH occurs in a rapid equilibrium step and that the rate of... 

The exact nature of base catalysis is still not clear The most probable explanation is that it results from protonation of the leaving group by the conjugate acid of the base, formed in a rapid equilibrium step subsequent to formation of the tetrahedral intermediate (Scheme 8). Protonation wiU improve the leaving tendency of the displaced... 

Chojnowski and coworkers demonstrated that the formation of small siloxanes catalyzed by B(C6F5)3 is a second order process. The complexation of the boron to hydrosilane is a rapid equilibrium step that precedes the rate determining step [31]. They proposed a mechanism in which the boron-hydrosilane complex is attacked by the alkoxysilane nucleophile leading to a zwitterionic oxonium ion (Fig. 5a). 

One common kind of reaction involves proton transfer occurring as a rapid equilibrium preceding the rate-determining step, for example, in the reaction of an alcohol with hydrobromic acid to give an alkyl bromide ... 

Because proton-transfer reactions between oxygen atoms are usually very fast, step 3 can be assumed to be a rapid equilibrium. With the above mechanism assume4 let us examine the rate expression which would result, depending upon which of the steps is rate-determining. 

The details of proton-transfer processes can also be probed by examination of solvent isotope effects, for example, by comparing the rates of a reaction in H2O versus D2O. The solvent isotope effect can be either normal or inverse, depending on the nature of the proton-transfer process in the reaction mechanism. D3O+ is a stronger acid than H3O+. As a result, reactants in D2O solution are somewhat more extensively protonated than in H2O at identical acid concentration. A reaction that involves a rapid equilibrium protonation will proceed faster in D2O than in H2O because of the higher concentration of the protonated reactant. On the other hand, if proton transfer is part of the rate-determining step, the reaction will be faster in H2O than in D2O because of the normal primary kinetic isotope effect of the type considered in Section 4.5. 

The rate law that we have derived is not the same as the experimental one. We have stressed that a reaction mechanism is plausible only if its predictions are in line with experimental results so should we discard our proposal Before doing so, it is always wise to explore whether under certain conditions the predictions do in fact agree with experimental data. In this case, if the rate of step 2 is very slow relative to the rapid equilibrium in step 1—so that N202] 2[N202][02],... 

In summary, therefore, solution and fiber biochemistry have provided some idea about how ATP is used by actomyosin to generate force. Currently, it seems most likely that phosphate release, and also an isomerization between two AM.ADP.Pj states, are closely linked to force generation in muscle. ATP binds rapidly to actomyosin (A.M.) and is subsequently rapidly hydrolyzed by myosin/actomyosin. There is also a rapid equilibrium between M. ADP.Pj and A.M.ADP.Pj (this can also be seen in fibers from mechanical measurements at low ionic strength). The rate limiting step in the ATPase cycle is therefore likely to be release of Pj from A.M.ADP.Pj, in fibers as well as in solution, and this supports the idea that phosphate release is associated with force generation in muscle. 

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%... 

The discussion above of enzyme reactions treated the formation of the initial ES complex as an isolated equilibrium that is followed by slower chemical steps of catalysis. This rapid equilibrium model was first proposed by Henri (1903) and independently by Michaelis and Menten (1913). However, in most laboratory studies of enzyme reactions the rapid equilibrium model does not hold instead, enzyme... 

For the enzyme isomerization mechanism illustrated in scheme C of Figure 6.3, there are two steps involved in formation of the final enzyme-inhibitor complex an initial encounter complex that forms under rapid equilibrium conditions and the slower subsequent isomerization of the enzyme leading to the high-affinity complex. The value of kohs for this mechanism is a saturable function of [/], conforming to the following equation ... 

Many mechanisms involve reversible steps which are rapid (and therefore in virtual equilibrium) followed by the critical rds. In these cases, the equilibrium constant for each of the rapid steps appears as a multiplicative factor in the rate law. The effective activation energy is the sum of the enthalpies of the equilibrium steps and the activation energy of the rds. 

Notably, under catalytic conditions, reaction steps preceding catalyst-substrate-dihydrido formation are shown to be in rapid equilibrium. Therefore, stereoselec-... 

The results of a temperature jump relaxation study of the complexation of metal cations by dibenzo-30-crown-10 [14] in methanol led Chock (1972) to propose a two-step mechanism. The first step (9) comprises a rapid equilibrium... 

The reaction was second order in acid and first order in substrate, so both rearrangements and the disproportionation reaction proceed via the doubly-protonated hydrazobenzene intermediate formed in a rapid pre-equilibrium step. The nitrogen and carbon-13 kinetic isotope effects were measured to learn whether the slow step of each reaction was concerted or stepwise. The nitrogen and carbon-13 kinetic isotope effects were measured using whole-molecule isotope ratio mass spectrometry of the trifluoroacetyl derivatives of the amine products and by isotope ratio mass spectrometry on the nitrogen and carbon dioxide gases produced from the products. The carbon-12/carbon-14 isotope... 

Removal of the proton from an intramolecular hydrogen bond by a base occurs in a two-step mechanism (a rapid equilibrium between H-bonded and non-H-bonded forms followed by base catalyzed proton removal from the non-H-bonded form) rather than by direct attack of the base on the intramolecularly hydrogen bonded species (6). 

Figure 11.1 illustrates the behavior of Equation 11.6. By the assumption of rapid equilibrium the rate determining step is the unimolecular decomposition. At high substrate composition [S] KM and the rate becomes zero-order in substrate, v = Vmax = k3 [E0], the rate depends only on the initial enzyme concentration, and is at its maximum. We are dealing with saturation kinetics. The most convenient way to test mechanism is to invert Equation 11.6... 

The pyridinium chlorochromate (PCC) oxidations of pentaamine cobalt(III)-bound and unbound mandelic and lactic acids have been studied and found to proceed at similar rates.Free-energy relationships in the oxidation of aromatic anils by PCC have been studied. Solvent effects in the oxidation of methionine by PCC and pyridinium bromochromate (PBC) have been investigated the reaction leads to the formation of the corresponding sulfoxide and mechanisms have been proposed. The major product of the acid-catalysed oxidation of a range of diols by PBC is the hydroxyaldehyde. The reaction is first order with respect to the diol and exhibits a substantial primary kinetic isotope effect. Proposed acid-dependent and acid-independent mechanisms involve the rapid formation of a chromate ester in a pre-equilibrium step, followed by rate-determining hydride ion transfer via a cyclic intermediate. PBC oxidation of thio acids has been studied. ... 

Such a mechanism is a form of substrate-induced activation. If all of the binding steps are rapid relative to the ESA-to-EPA interconversion step, the initial-rate rapid-equilibrium equation for this scheme is... 

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