Equilibrium relationships for non-equilibrium chemical dependencies

In contrast to common opinion, it is shown that equilibrium constants determine the time-dependent behavior of particular ratios of concentrations for any system of reversible first-order reactions. Indeed, some special ratios actually coincide with the equilibrium constant at any moment in time. This is established for batch reactors, and similar relations hold for steady-state plug-flow reactors, replacing astronomic time by residence time. Such relationships can be termed time invariants of chemical kinetics

The switching point between kinetic and thermodynamic control

In organic chemistry, the switching point between the kinetic and thermodynamic control regimes of two competitive, parallel reactions is widely studied. A new definition for this switching point is proposed: the time at which the rates of formation of the competing products are equal. According to this definition, the kinetic control regime is present from the beginning of the reaction, and is valid as long as the rate of formation of the kinetic product is larger than the rate of formation of the thermodynamic product. On the switching point, both rates of formation are equal, so, from this switching point the thermodynamic product has a larger rate of formation, and the thermodynamic control remains until the end of the reaction. A closed form expression is given for the proposed time of the switching point, as a function of the direct and inverse kinetic constants of both competing reactions, as well as the initial concentrations of the starting reagent and the competing products. The concept of competing control regimes is extended also to the case where the reactions start from two competitive reagents which decompose to produce a single product. (C) 2016 Elsevier Ltd. All rights reserved

Single-route linear catalytic mechanism : a new, kinetico-thermodynamic form of the complex reaction rate

For a complex catalytic reaction with a single-route linear mechanism, a new, kinetico-thermodynamic form of the steady-state reaction rate is obtained, and we show how its symmetries in terms of the kinetic and thermodynamic parameters allow better discerning their influence on the result. Its reciprocal is equal to the sum of n terms (n is the number of complex reaction steps), each of which is the product of a kinetic factor multiplied by a thermodynamic factor. The kinetic factor is the reciprocal apparent kinetic coefficient of the i-th step. The thermodynamic factor is a function of the apparent equilibrium constants of the i-th equilibrium subsystem, which includes the (n-1) other steps. This kinetico-thermodynamic form separates the kinetic and thermodynamic factors. The result is extended to the case of a buffer substance. It is promising for distinguishing the influence of kinetic and thermodynamic factors in the complex reaction rate. The developed theory is illustrated by examples taken from heterogeneous catalysis

New invariant expressions in chemical kinetics

This paper presents a review of our original results obtained during the last decade. These results have been found theoretically for classical mass-action-law models of chemical kinetics and justified experimentally. In contrast with the traditional invariances, they relate to a special battery of kinetic experiments, not a single experiment. Two types of invariances are distinguished and described in detail: thermodynamic invariants, i.e., special combinations of kinetic dependences that yield the equilibrium constants, or simple functions of the equilibrium constants; and "mixed" kinetico-thermodynamic invariances, functions both of equilibrium constants and non-thermodynamic ratios of kinetic coefficients

Revisiting Maxwell-Smoluchowski theory: low surface roughness in straight channels

The Maxwell-Smoluchowski (MS) theory of gas diffusion is revisited here in the context of gas transport in straight channels in the Knudsen regime of large mean free path. This classical theory is based on a phenomenological model of gas-surface interaction that posits that a fraction $\vartheta$ of molecular collisions with the channel surface consists of diffuse collisions, i.e., the direction of post-collision velocities is distributed according to the Knudsen Cosine Law, and a fraction $1-\vartheta$ undergoes specular reflection. From this assumption one obtains the value $\mathcal{D}=\frac{2-\vartheta}{\vartheta}\mathcal{D}_K$ for the self-diffusivity constant, where $\mathcal{D}_K$ is a reference value corresponding to $\vartheta=1$. In this paper we show that $\vartheta$ can be expressed in terms of micro- and macro-geometric parameters for a model consisting of hard spheres colliding elastically against a rigid surface with prescribed microgeometry. Our refinement of the MS theory is based on the observation that the classical surface scattering operator associated to the microgeometry has a canonical velocity space diffusion approximation by a generalized Legendre differential operator whose spectral theory is known explicitly. More specifically, starting from an explicit description of the effective channel surface microgeometry -- a concept which incorporates both the actual surface microgeometry and the molecular radius -- and using this operator approximation, we show that $\vartheta$ can be resolved into easily obtained geometric parameters.Comment: 19 pages, 5 figure