Rate Theory equations

Before progressing to the Rate Theory Equation, an interesting and practical example of the use of the summation of variances is the determination of the maximum sample volume that can be placed on a column. This is important because excessive sample volume broadens the peak and reduces the resolution. It is therefore important to be able to choose a sample volume that is as large as possible to provide maximum sensitivity but, at the same time insufficient, to affect the overall resolution. 

In this equation it is the reaction rate constant, k, which is independent of concentration, that is affected by the temperature the concentration-dependent terms, J[c), usually remain unchanged at different temperatures. The relationship between the rate constant of a reaction and the absolute temperature can be described essentially by three equations. These are the Arrhenius equation, the collision theory equation, and the absolute reaction rate theory equation. This presentation will concern itself only with the first. 

Figure 2.9. Rate theory equation plotted as h versus 1/u. hmin = A +(2BC)1/2. uopt = (B/C)1/2.

Comparing these statistical rate theory equations, with Eqs. (6.283) and (6.284), we obtain the following phenomenological coefficients... 

As evident from the preceding considerations the fit of experimental rate data to a particular rate theory equation does not necessarily prove the rate controlling mechanism. In the absence of previous knowledge of a system it is desirable to seek further mechanism qualifying data. 

An examination of the rate theory equations for film and particle diffusion kinetics reveals an overall dependence of the rate of reaction on 0 and respectively for gel ( homogeneous ) exchangers. For a macroporous exchanger the rate of exchange, under particle diffusion control, may be either independent of particle size or vary as depending upon whether diffusion within the gel microsphere structure or macropores respectively is rate controlling. 

In the early 1990s, in their studies of proton transfer in solution using Marcus rate theory Equation (5), Hynes and coworkers16 17 noticed the following limitation. If Q is the tunneling distance, it can be shown that the tunneling matrix element that appears in Equation (5) has the form A e- e. For typical electron transfer reactions... 

It is this value AG ) which enters into the nucleation rate absolute reaction-rate theory. Equation (5.17),... 

The recent theoretical approaches include a theory of barrierless electronic relaxation which draws on the model of nonradiative excited state decay, and a general treatment of the effect of solvent dielectric relaxation based on the theory of optical line shapes, as well as treatments based on classical and quantum rate theories. Equation(5) does not hold for all solvents and, more generally, may be frequency-dependent. Papers by Hynes, Rips and Jortner, Sumi and Marcus, and Warshel and Hwang " contain good overviews of the theoretical developments. 

The above results for outer-sphere redox reactions were obtained by CHRISTOV /37d/ using an essentially different approach based on the general formulation of reaction rate theory. Equation (63.IV), however, differs from a similar result of DOGONADZE /147,151/ for adiabatic processes, which incorrectly gives the same activation energy as for non-adiabatic processes i.e., it neglects the large resonance interaction. 

FIGURE 2.21 Rate theory equation plotted as H versus 1/m = A +... 

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