Work-corrected rate constant

It is conventional (and useful) to define a "work-corrected" rate constant k that is related to k. at a given elec-trode potential by... 

Expressing eqn. (15) (Sect. 3.2) in terms of work-corrected rate constants yields the well-known relation [15]... 

Experimental estimates of <5r/c , are relatively difficult to obtain. While they can, in principle, be extracted from temperature-dependence studies, this approach is complicated by uncertainties in the entropic term (Sect. 4.3). An alternative method has recently been described for some Cr(III) reductions which involves comparing the work-corrected rate constants, kco , with unimolecular rate constants, ket, for structurally related reactants that reduce via ligand-bridged pathways [30]. Provided that the corresponding outer- and inner-sphere pathways involve the same activation barrier (Sect. 4.6) and the latter also follow adiabatic pathways, we can write [30]... 

The two work-corrected rate constants, k and kj., should be distinguished carefully. The latter quantity arises from the use of the preequilibrium model and describes the rate constant (s ) for electron transfer at a given electrode potential taken wnth respect to the precursor intermediate for the preequilibrium model. The former quantity is an intermolecular (cm s ) rate constant, which can be utilized in conjunction with either the preequilibrium or collisional-rate formulation. In view of Eqs. (a), (n) and (o) ... 

Work-corrected rate constant for reduction at mercury electrode, at electrode potential equal to Ef of reductant [-0.185 V vs SCE for RulNHg) (see ref. 22 for data sources, etc). 

Let us now assume that these matters have been attended to properly. At this stage we can but assume that the reaction orders were correctly identified and correct mathematical procedures followed. During the course of the work, the investigator should make the occasional quick calculation to show the values are roughly correct. (Does the rate constant yield the correct half-time ) Also, one should examine the experimental data fits to see that the data really do conform to the selected rate equation. Deviations signal an incorrect rate law or complications, such as secondary reactions. 

Rate constant for homogeneous self exchange, corrected for electrostatic work terms using Debye-Huckel-Bronsted model. Data taken from sources quoted in ref. 15 unless otherwise stated. 

In both TST and VTST, quantum mechanical tunneling is introduced into the rate constant expression as a correction factor usually referred to as k. A short discussion of k which is used largely with TST is presented in Section 6.3.1. Tunneling has been explored much more thoroughly in connection with VTST and this work will be discussed later. 

The results obtained in this work are summarized in Table I. The rate constants were obtained from good second-order decays in all cases. The absolute values of the rate constants given in Table I are probably correct to within a factor of 2 to 3 in most cases. The ceric results should be somewhat more reliable than the photolytic results because more time was devoted to their study. It seems likely that more accurate rate constants will be obtained by both methods as more experience is gained in the use of the ESR technique. 

Work by Voorhees and Glicksman concludes that the classical theory is correct in the limit of zero volume fraction of the coarsening phase and that both the kinetics and the size distributions are significantly dependent on the precipitate volume fraction,

diffusion-limited coarsening, given by Eq. 15.18, remains valid for all volume fractions, but the rate constant Kp is a monotonically increasing function of , as in Fig. 15.8. 

What is one to make of the 1975 experiments275 277 278 leading to the conclusions that kI2 (k2 + k2 ) = 4 1 and kx kn- 0 They and the 1984 work which reported experimental values for all four mechanistic rate constants and the ratios ka (k2 + /c23) = 0.23 and k, kl2= 1.8 cannot both be correct. One response is to remain objective and quite neutral, and to consider the experimental situation simply unresolved. Another is to try to make an independent assessment of the two sets of experiments by critically evaluating the experimental designs, the synthetic procedures and characterizations of labeled phenylcyclo-propanes, the analytical methodologies employed and the number of experimental rate... 

We used for Table I the rate constants (16), no - = 3.9 X 109, ke+ NO — = 9.0 X 109, ke+ HjO+ = 2.0 X 1010 and acetone = 5.2 X 109 M 1sec.-1 (slightly corrected [e.g. see (45) ] for other parallel reactions, when such corrections had been neglected (17,20, 27, 52)). The values (16), of ke ferricyanide needed no correction of that type. These rate constants have been used in combination with competition work to calculate the rate constants in both columns 4 and 5. In column 5, the results have been calculated for zero ionic strength using the expression M1/2... 

Buehler et al. presented a preliminary study on formation of water from molecular oxygen and hydrogen using a series of atomistic simulations based on ReaxFF MD method.111 They described the dynamics of water formation at a Pt catalyst. By performing this series of studies, we obtain statistically meaningful trajectories that permit to derive the reaction rate constants of water formation. However, the method requires calibrations with either ab initio simulation results in order to correctly evaluate the energetics of OER on Pt. Thus, this method is system specific and less reliable than the ab initio methods and will not replace ab initio methods. Nevertheless, this work demonstrates that atomistic simulation to continuum description can be linked with the ReaxFF MD in a hierarchical multiscale model. 

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