Precursor equilibrium constant

The foregoing discussion emphasizes the desirability of treating one-electron electrochemical reactions as involving an electron-transfer step occurring within a precursor state previously formed in the interfacial region. It is therefore useful to separate the overall observed rate constant, kob, into a precursor equilibrium constant, Kp (cm) [eqn. (4b)], and a unimolecular rate constant, ket (s-1), for the elementary electron-transfer step, related by [7]... 

This relation will be valid for both inner- and outer-sphere pathways provided that electron transfer, rather than precursor-state formation, is the rate-determining step. The precursor equilibrium constant can be expressed as... 

Rotzinger then evaluated and H t as a function of the distance between the two reactant metal centers. He used the Fuoss equation to calculate the ion-pairing equilibrium constant to form the precursor complex at these internuclear distances. Assembly of these data then allowed the calculation of the self-exchange rate constants as a function of the internuclear distance in the transition state, the maximum rate being taken as the actual rate. 

Most hterature references to pharmaceutical primary process monitoring are for batch processes, where a model of the process is built from calibration experiments [110, 111]. Many of these examples have led to greater understanding of the process monitored and can therefore be a precursor to design of a continuous process. For example, the acid-catalysed esterification of butan-l-ol by acetic acid was monitored through a factorial designed series of experiments in order to establish reaction kinetics, rate constants, end points, yields, equilibrium constants and the influence of initial water. Statistical analysis demonstrated that high temperatures and an excess of acetic acid were the optimal conditions [112]. 

In Eq. (LL), M is the concentration of the condensed-phase organic (in igm 3) available to absorb semivolatile organic products, ( is a constant that relates the concentration of the ith secondary organic aerosol component formed, C, to the amount of parent precursor organic reacted i.e., C, (ng m ) 1000a, A(parent organic in p,g m 3), and Kom i is the gas-particle partioning coefficient for the ith component. As discussed in more detail in Section D, Kim j is in effect an equilibrium constant between the condensed- and gas-phase concentrations. 

In these relations, Ki denotes the equilibrium constant of reaction step i. For the numerical evaluation of the model, it is assumed that the backward reaction of step lb has the same transition state as the transition state for the re-desorption of A2 in Model 1, and that the entropy of the molecular precursor on the surface is negligible. The results are shown in Figure 4.37. It is observed that the model predicts that catalysts of much larger reactivity (more negative AEt) will be optimal for reactions where the diatomic molecule is strongly bound to the surface before the dissociation. 

The kinetics of oxidation of Dess-Martin periodinane (DMP) and its iodoxybenzoic acid (IBX) precursor have been compared to explain their often different selectivities.152 A fast pre-equilibrium produces transient iodic esters, whose axial alkoxy structure for IBX was determined by 1H NMR spectroscopy, which then disproportionate in a rate-limiting maimer to product. As a result, steric effects in alcohol oxidation reflect a balance between opposing effects on equilibrium constants and rate constants for disproportionation. With 1,2-diols DMP gives spirobicyclic... 

Rate and equilibrium constants have been reported for the reactions of butylamine, pyrrolidine, and piperidine with trinitrobenzene, ethyl 2,4,6-trinitrophenyl ether, and phenyl 2,4,6-trinitrophenyl ether in acetonitrile, hi these reactions, leading to cr-adduct formation and/or nucleophilic substitution, proton transfer may be rate limiting. Comparisons with data obtained in DMSO show that, while equilibrium constants for adduct formation are lower in acetonitrile, rate constants for proton transfer are higher. This probably reflects the stronger hydrogen bonding between DMSO and NH+ protons in ammonium ions and in zwitterions.113 Reaction of 1,3,5-trinitrobenzene with indole-3-carboxylate ions in methanol has been shown to yield the re-complex (26), which is the likely precursor of nitrogen- and carbon-bonded cr-adducts expected from the reaction.114 There is evidence for the intermediacy of adducts similar to (27) from the reaction of methyl 3,5-dinitrobenzoate with l,8-diazabicyclo[5.4.0]undec-8-ene (DBU) cyclization eventually yields 2-aminoindole derivatives.115... 

The major disadvantage of the transamination technology is an equilibrium constant K often near unity. As K 1 would limit the net conversion of substrates to around 50%, the key to efficient transamination technology lies in overcoming the problem of incomplete conversion of the 2-keto acid precursor to the desired amino... 

Reaction of Cytochrome cimu with Tris(oxalato)cobalt(III) The cytochrome c protein was also used as reductant in a study of the redox reaction with tris (oxalato)cobalt(III).284 Selection of the anionic cobalt(III) species, [Conl(ox)3]3 was prompted, in part, because it was surmised that it would form a sufficiently stable precursor complex with the positively charged cyt c so that the equilibrium constant for precursor complex formation (K) would be of a magnitude that would permit it to be separated in the kinetic analysis of an intermolecular electron transfer process from the actual electron transfer kinetic step (kET).2S5 The reaction scheme for oxidation of cyt c11 may be outlined ... 

By using the steady state kinetic equations, it is then possible to express k and k3 as a function of the overall turnover frequency for CO-conversion to hydrocarbons (Nco), the overall turnover frequency for methane formation (NCH ), the probability for chain growth (a), the steady state coverage of the precursor A and the value of the equilibrium constant K. In table I the expressions for the kj and k are given. 

Table I. The Reaction Rate Constants for Propagation and Termination Expressed as a Function of Turnover Frequencies, Probability of Chain Growth, Steady-State Surface Coverage of the Precursor A, and the Equilibrium Constant K.

Note that as a first approximation the effect of hydrogen is not taken into account, which implies that the model will hold only for a limited range of hydrogen pressures. As a driving force for the reaction we use the gas-phase concentration, Cq, of the coke precursor Q, is the equilibrium constant of adsorption of Q on the catalyst surface. The rate constant for coke formation, kc, depends on the amount of coke present on the surface ... 

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