Mass Action and Conservation of Current

Abstract

The law of mass action does not force a series of chemical reactions to have the same current flow everywhere. Interruption of far-away current does not stop current everywhere in a series of chemical reactions (analyzed according to the law of mass action), and so does not obey Maxwell's equations. An additional constraint and equation is needed to enforce global continuity of current. The additional constraint is introduced in this paper in the special case that the chemical reaction describes spatial movement through narrow channels. In that case, a fully consistent treatment is possible using different models of charge movement. The general case must be dealt with by variational methods that enforce consistency of all the physical laws involved. Violations of current continuity arise away from equilibrium, when current flows, and the law of mass action is applied to a nonequilibrium situation, different from the systems considered when the law was originally derived. Device design in the chemical world is difficult because simple laws are not obeyed in that way. Rate constants of the law of mass action are found experimentally to change from one set of conditions to another. The law of mass action is not robust in most cases and cannot serve the same role that circuit models do in our electrical technology. Robust models and device designs in the chemical world will not be possible until continuity of current is embedded in a generalization of the law of mass action using a consistent variational model of energy and dissipation.

PNP what is in a name july 25-1 2019.pdf 10.31224/osf.io/2739d

“…In fact, something important can be said about electrodynamics in general, independent of the properties of matter. Current, as defined by Maxwell, is universally conserved [35][36][37][38][39].…”

“…Conservation of current is in fact a general and exact property of the Maxwell equations, as general as the Maxwell equations themselves, independent of any properties of matter [35][36][37][38][39]. The dielectric constant is not involved in the derivation of conservation of current at all.…”

“…A general statement of conservation of current-eq. (3) below-can be derived [35][36][37][38][39] because the divergence of the curl in eq. (1) is identically zero, independent of any properties of matter, whenever Maxwell's equations can be used.…”

“…Conservation of total current is not an approximation when total current is defined as because includes the ethereal current 0 , as shown in [35][36][37][38][39].…”

“…We show (eq. 4, below) that Kirchhoff's law can be as exact as the Maxwell equations themselves 2 , once current is defined as in the Maxwell equations, independent of the dielectric properties of matter [35][36][37]40]. Current is usually defined as the flux of charge, although that is not the definition used here, see eq.…”