Reversible rate equations, structural kinetic

In recent years the Coal Research Laboratory has been investigating the kinetics and isotherm behavior of methanol sorption on coal (6, 7, 10) along with the sorption of other vapors on coal (6) and of polar vapors on swelling gels (9, 10). Methanol sorption was shown to be reversible on coal, and its sorption behavior supports the model of coal as a gel or mixture of gels in its physical structure. All indications (I, 6, 7) are that its interaction is with specific and a fixed number of sites for a particular coal sample. Although the sorption of methanol is reversible, coal exhibits sorption behavior which is interpreted in terms of an irreversible swelling of the coal gel upon initial exposure to methanol vapor. As a result of these studies, an isotherm and experimental rate equation for the sorption and desorption were derived that fit the observed data. The isotherm derived for methanol sorption on coal was ... 

We have examined the effects of concentration, temperature, solvent and added electrolyte on the kinetics of this structural interconversion. In all instances, the kinetics are well described by the rate law for a reversible first-order reaction [Equation 1] ... 

As we mentioned in Section II.C, one of the most important requirements, which is applicable to the overall structure of reaction schemes, is its thermodynamic consistency. In other words, the scheme, as written, must allow the process to proceed asymptotically to its equilibrium state at infinite time. This can be reached only if any elementary step is included into the overall scheme together with its reverse reaction. Let us consider the consequences for the description of the process kinetics. For the sake of simplicity, we assume that the reaction proceeds in the ideal gas mixture. The value of rate constants k( for forward and k( ) for reverse reactions must satisfy the connecting equation... 

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