Chemically modified first-order

Once the QFH formula for the excess chemical potential is linearized in (11.37), the logarithmic expression can be expanded to first order and all or part of the classical-average term can be integrated by parts to yield the Wigner-Kirkwood correction to the free energy. Then if (11.40) is reorganized, computation of the chemical potential can be viewed as a classical average with a modified interaction potential of the same form as (11.3). 

Various theoretical formalisms have been used to describe chemical exchange lineshapes. The earliest descriptions involved an extension of the Bloch equations to include the effects of exchange [1, 2, 12]. The Bloch equations formalism can be modified to include multi-site cases, and the effects of first-order scalar coupling [3, 13, 24]. As chemical exchange is merely a special case of general relaxation theories, it may be compre-... 

A zero-order reaction thus becomes a half-order reaction, a first-order reaction remains first order, whereas a second-order reaction has an apparent order of 3/2 when strongly influenced by diffusional effects. Because k and n are modified in the diffusion controlled region then, if the rate of the overall process is estimated by multiplying the chemical reaction rate by the effectiveness factor (as in equation 3.8), it is imperative to know the true rate of chemical reaction uninfluenced by diffusion effects. 

Reaction Order. Studies of the reaction of oxygen with carbon at temperatures of interest for AFBC s suggest that it is near zero order in oxygen (62). Most models have been based on an assumed first order reaction but they can be readily modified to accommodate the more realistic lower reaction order (63, 64). The correction for order of reaction will be most important for the prediction of the combustion of recycled fines which are in the size range in which chemical kinetics dominate and for predicting the performance of pressurized fluidized beds. 

The modelling of kinetics at modified electrodes has received much attention over the last 10 years [1-11], mainly due to the interest in the potential uses of chemically modified electrodes in analytical applications. The first treatment published by Andrieux et al. [5] was closely followed by a complimentary treatment by Albery and Hillman [1, 2]. Both deal with the simplest basic case, that is, the coupled effects of diffusion and reaction for a second-order reaction between a species freely diffusing in the bulk solution and a redox mediator species trapped within the film at the modified electrode surface. The results obtained by the two treatments are essentially identical, although the two approaches are slightly different. 

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