Pre Rate-Determining Steps

In a number of the reactions discussed in the foregoing sections one or more rapid equilibria preceding the rate-determining step have been demonstrated or can be visualized. Where these occur they have characteristic effects on the form of the rate-law, and their detection usually presents no special difficulties, but sometimes such equilibria can give rise to interesting peculiarities, and sometimes they give added insight into the structure of a transition state. 

The ability of Hg(II) to form tri- and tetra-coordinated ions with suitable ligands is well known. With alkylmercuric halides the formation constants are usually too small for such ions to be conventionally demonstrated (Brown et al., 1965a). It is likely, however, that such complexes would cleave more readily than the uncomplexed materials. These expectations have been strongly supported in a study of the cleavage of allylmercuric iodide by acid and iodide ion (Kreevoy et al., 1966a equations (6) to (8)). The rate was of the form shown in equation (23), in which S is the substrate. The terms which are linear in iodide ion 

The general similarity of the iodide ion-catalyzed reactions to those 

Rate constant, k Value Units, sec-1 Maximum % contribution to ky 

The terms in equation (23) which are independent of the acid concentration show little or no solvent isotope effect. This and considerations following from the Bronsted Catalysis Law make it unlikely that these terms represent cleavage of the complexed substrate by water. A ratedetermining, unimolecular rearrangement from the a- to the v-allylic mercurial was suggested. Oxidative cleavage of some sort is another possibility. 

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Kinetic Studies Provide Only Limited Mechanistic Information. While such studies are invaluable and frequently indicate the nature of pre-rate-determining steps, they provide almost no information concerning such vital fast steps as electron transfers and rearrangements. For example, despite extensive studies of the kinetics of acetaldehyde and vinyl acetate syntheses, it is clear only that olefin, nucleophile, and palladium combine in a complex. The nature of the rate-determining step as well as the details of post-rate determining product forming steps remains uncertain (7,94). In some cases—e.g., the metal-catalyzed autoxi-dation of thiols to disulfides—re-oxidation of metal to its catalytically... 

Should a nucleophile (and this includes anions) complex reversibly with the substrate in a pre-rate-determining step, the set of reactions (19) and (20) may take place, where B denotes a nucleophile or Lewis base. 

Kinetically, these reagents become more basic as aggregate size diminishes more reactive species are obtained in ethers, e.g., in Et20 or THF, than in hydrocarbons or on addition of a donor molecule, e.g., TMED triethylenediamine (DABCO), hexamethyl-phosphorictriamide (HMPA) or dimethylsulfoxide (DMSO). Kinetic studies of metalla-tions by RLi in hydrocarbons or ethers reveal fractional orders in RLi. These arise from dissociation of the larger oligomers, (tetramers and hexamers) to smaller and more reactive species (monomers and dimers) in pre-rate-determining steps. Increasing basicity of the solvent should also help to stabilize the transition state. 

It will be noted that properties of the barrier-to-electron transfer do not enter into the determination of b for chemically controlled rate-determining steps provided the quasiequilibrium hypothesis applies adequately to the steps prior to the ratecontrolling one, which may not always be the case. This means practically that the exchange rate in the pre-rate-determining steps must be at least 10 times the net velocity of the rate-controlling step at all overpotentials. 

During the next fifty years the interest in derivatives of divalent carbon was mainly confined to methylene (CHg) and substituted methylenes obtained by decomposition of the corresponding diazo compounds this phase has been fully reviewed by Huisgen. The first convincing evidence for the formation of dichlorocarbene from chloroform was presented by Hine in 1950. Kinetic studies of the basic hydrolysis of chloroform in aqueous dioxane led to the suggestion that the rate-determining step was loss of chloride ion from the tri-chloromethyl anion which is formed in a rapid pre-equilibrium with hydroxide ions ... 

In this solvent the reaction is catalyzed by small amounts of trimethyl-amine and especially pyridine (cf. 9). The same effect occurs in the reaction of iV -methylaniline with 2-iV -methylanilino-4,6-dichloro-s-triazine. In benzene solution, the amine hydrochloride is so insoluble that the reaction could be followed by recovery. of the salt. However, this precluded study mider Bitter and Zollinger s conditions of catalysis by strong mineral acids in the sense of Banks (acid-base pre-equilibrium in solution). Instead, a new catalytic effect was revealed when the influence of organic acids was tested. This was assumed to depend on the bifunctional character of these catalysts, which act as both a proton donor and an acceptor in the transition state. In striking agreement with this conclusion, a-pyridone is very reactive and o-nitrophenol is not. Furthermore, since neither y-pyridone nor -nitrophenol are active, the structure of the catalyst must meet the conformational requirements for a cyclic transition state. Probably a concerted process involving structure 10 in the rate-determining step... 

STRATEGY Construct the rate laws for the elementary reactions and combine them into the overall rate law for the decomposition of the reactant. If necessary, use the steady-state approximation for any intermediates and simplify it by using arguments based on rapid pre-equilibria and the existence of a rate-determining step. 

The detailed decomposition (P-H ehminahon) mechanism of the hydrido(alkoxo) complexes, mer-crs-[lr(H)(OR)Cl(PR 3)3] (R = Me, Et, Pr R = Me, Et H trans to Cl) (56, 58, 60), forming the dihydrides mer-cis-[lr H)2Cl PR )2] (57, 59) along with the corresponding aldehyde or ketone was examined (Scheme 6-8). The hydrido(ethoxo) as well as the hydrido(isopropoxo) complexes 60 could also be prepared by oxidative addition of ethanol and isopropanol to the phosphine complexes 39 [44]. In the initial stage of the P-H elimination, a pre-equiUbrium is assumed in which an unsaturated pentacoordinated product is generated by an alcohol-assisted dissociation of the chloride. From this intermediate the transition state is reached, and the rate-determining step is an irreversible scission of the P-C-H bond. This process has a low... 

The olefin binding site is presumed to be cis to the carbene and trans to one of the chlorides. Subsequent dissociation of a phosphine paves the way for the formation of a 14-electron metallacycle G which upon cycloreversion generates a pro ductive intermediate [ 11 ]. The metallacycle formation is the rate determining step. The observed reactivity pattern of the pre-catalyst outlined above and the kinetic data presently available support this mechanistic picture. The fact that the catalytic activity of ruthenium carbene complexes 1 maybe significantly enhanced on addition of CuCl to the reaction mixture is also very well in line with this dissociative mechanism [11] Cu(I) is known to trap phosphines and its presence may therefore lead to a higher concentration of the catalytically active monophosphine metal fragments F and G in solution. 

In this case, the actual redox step is preceded by the formation of an adduct or a complex between the catalyst, the substrate and dioxygen. The order of these reaction steps is irrelevant as long as the rate determining step is Eq. (8). If Eqs. (6) and (7) are rapidly established pre-equilibria the reaction rate depends on the concentrations of all reactants. In some instances, the rate determining step is the formation of the MS complex and the reaction rate is independent of the concentration of dioxygen. 

Most catalytic cycles are characterized by the fact that, prior to the rate-determining step [18], intermediates are coupled by equilibria in the catalytic cycle. For that reason Michaelis-Menten kinetics, which originally were published in the field of enzyme catalysis at the start of the last century, are of fundamental importance for homogeneous catalysis. As shown in the reaction sequence of Scheme 10.1, the active catalyst first reacts with the substrate in a pre-equilibrium to give the catalyst-substrate complex [20]. In the rate-determining step, this complex finally reacts to form the product, releasing the catalyst... 

If one would be able to derive from the experimental data an accurate rate equation like (12) the number of terms in the denominator gives us the number of reactions involved in forward and backward direction that should be included in the scheme of reactions, including the reagents involved. The use of analytical expressions is limited to schemes of only two reaction steps. In a catalytic sequence usually more than two reactions occur. We can represent the kinetics by an analytical expression only, if a series of fast pre-equilibria occurs (as in the hydroformylation reaction, Chapter 9, or as in the Wacker reaction, Chapter 15) or else if the rate determining step occurs after the resting state of the catalyst, either immediately, or as the second one as shown in Figure 3.1. In the examples above we have seen that often the rate equation takes a simpler form and does not even show all substrates participating in the reaction. 

Br0nsted acid catalysis, the substrate electrophile is reversibly protonated in a pre-equilibrium step, prior to the nucleophilic attack (Scheme 2). In general acid catalysis, however, the proton is (partially or fuUy) transferred in the transition state of the rate-determining step (Scheme 2). Clearly, the formation of a hydrogen bond precedes proton transfer. 

Although these effects are often collectively referred to as salt effects, lUPAC regards that term as too restrictive. If the effect observed is due solely to the influence of ionic strength on the activity coefficients of reactants and transition states, then the effect is referred to as a primary kinetic electrolyte effect or a primary salt effect. If the observed effect arises from the influence of ionic strength on pre-equilibrium concentrations of ionic species prior to any rate-determining step, then the effect is termed a secondary kinetic electrolyte effect or a secondary salt effect. An example of such a phenomenon would be the influence of ionic strength on the dissociation of weak acids and bases. See Ionic Strength... 

The rate of hydroformylation was proportional to the concentration of the acyl complex. The apparent activation parameters were Ai-T = 49.3 kj mol" and AS = 121 J moT K". Both the activation parameters and the reaction order are consistent with the hydrogenolysis reaction being rate determining. The low order of 0.1 in alkene suggests that the rate-determining step is not purely the reaction with hydrogen and that either a pre-equilibrium also contributes or one of the earlier steps in the cycle is also somewhat slower. 

Reaction rates have first-order dependence on both metal and iodide concentrations. The rates increase linearly with increased iodide concentrations up to approximately an I/Pd ratio of 6 where they slope off. The reaction rate is also fractionally dependent on CO and hydrogen partial pressures. The oxidative addition of the alkyl iodide to the reduced metal complex is still likely to be the rate determining step (equation 8). Oxidative addition was also indicated as rate determining by studies of the similar reactions, methyl acetate carbonylation (13) and methanol carbonylation (14). The greater ease of oxidative addition for iodides contributes to the preference of their use rather than other halides. Also, a ratio of phosphorous promoter to palladium of 10 1 was found to provide maximal rates. No doubt, a complex equilibrium occurs with formation of the appropriate catalytic complex with possible coordination of phosphine, CO, iodide, and hydrogen. Such a pre-equilibrium would explain fractional rate dependencies. 

The simple second-order nature of the kinetics in this system leads to immediate conclusions of some consequence. The rate-determining step is clearly not the heterolytic breaking of a metal-sulfur bond to produce the free R-S group, which then might undergo reaction. Further, the fact that there is no evidence suggesting consecutive processes eliminated the possibility that any such scheme could enter into the total rate except essentially as a pre-equilibrium—e.g., Equations 14 and 15. 

The enzyme-product complexes of the yeast enzyme dissociate rapidly so that the chemical steps are rate-determining.31 This permits the measurement of kinetic isotope effects on the chemical steps of this reaction from the steady state kinetics. It is found that the oxidation of deuterated alcohols RCD2OH and the reduction of benzaldehydes by deuterated NADH (i.e., NADD) are significantly slower than the reactions with the normal isotope (kn/kD = 3 to 5).21,31 This shows that hydride (or deuteride) transfer occurs in the rate-determining step of the reaction. The rate constants of the hydride transfer steps for the horse liver enzyme have been measured from pre-steady state kinetics and found to give the same isotope effects.32,33 Kinetic and kinetic isotope effect data are reviewed in reference 34 and the effects of quantum mechanical tunneling in reference 35. 

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. 

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