Rate laws continued definitions

Berthelot and St Giles, in their kinetic study of esterification reactions, showed that the amount of ester formed at each instant was proportional to the product of the active masses of the reactants and inversely proportional to the volume. Rather inexplicably, these authors did not take into account the role of these factors in defining the rate law of the reaction [4,5,15]. A possible explanation for this can be seen in a note on the life and work on Marcelin Berthelot [16]. In this work, indications are given of Berthelot s understanding of the role of mathematics in chemistry the mathematicians make an incoherent block out of physical and chemical phenomena. For better or for worse, they force us to fit our results to their formulae, assuming reversibility and continuity on all sides, which, unfortunately, is contradicted by a large number of chemical phenomena, in particular the law of definite proportions. ... 

In this equation ut should be interpreted as the volumetric flux density (directional flow rate per unit total area). The indexes range from 1 to 3, and repetition of an index indicates summation over that index according to the conventional summation convention for Cartesian tensors. The term superficial velocity is often used, but it is in our opinion that it is misleading because n, is neither equal to the average velocity of the flow front nor to the local velocity in the pores. The permeability Kg is a positive definite tensor quantity and it can be determined both from unidirectional and radial flow experiments [20], Darcy s law has to be supplemented by a continuity equation to form a complete set of equations. In terms of the flux density this becomes ... 

These laws (determined by Michael Faraday over a half century before the discovery of the electron) can now be shown to be simple consequences of the electrical nature of matter. In any electrolysis, an oxidation must occur at the anode to supply the electrons that leave this electrode. Also, a reduction must occur at the cathode removing electrons coming into the system from an outside source (battery or other DC source). By the principle of continuity of current, electrons must be discharged at the cathode at exactly the same rate at which they are supplied to the anode. By definition of the equivalent mass for oxidation-reduction reactions, the number of equivalents of electrode reaction must be proportional to the amount of charge transported into or out of the electrolytic cell. Further, the number of equivalents is equal to the number of moles of electrons transported in the circuit. The Faraday constant (F) is equal to the charge of one mole of electrons, as shown in this equation ... 

The thermodynamics of irreversible processes begins with three basic microscopic transport equations for overall mass (i.e., the equation of continuity), species mass, and linear momentum, and develops a microscopic equation of change for specific entropy. The most important aspects of this development are the terms that represent the rate of generation of entropy and the linear transport laws that result from the fact that entropy generation conforms to a positive-definite quadratic form. The multicomponent mixture contains N components that participate in R independent chemical reactions. Without invoking any approximations, the three basic transport equations are summarized below. 

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