The form of the rate constant for elementary reactions at equilibrium from MD: framework and proposals for thermokinetics

Abstract

The rates or formation and concentration distributions of a dimer reaction showing hysteresis behavior are examined in an ab initio chemical reaction designed as elementary and where the hysteresis structure precludes the formation of transition states (TS) with pre-equilibrium and internal sub-reactions. It was discovered that the the reactivity coefficients, defined as a measure of departure from the zero density rate constant for the forward and backward steps had a ratio that was equal to the activity coefficient ratio for the product and reactant species. This surprising result, never formally noticed nor incorporated in elementary rate expressions over approximately one and a half centuries of quantitative chemical kinetics measurement and calculation is accepted axiomatically and leads to an outline of a theory for the form of the rate constant, in any one given substrate -here the vacuum state. A major deduction is that the long-standing definition of the rate constant used for over a century and a half for elementary reactions is not complete, where previous works almost always implicitly refer to the zero density limit for strictly irreducible elementary reactions without any any attending concatenation of side-reactions. This is shown directly from MD simulation,where for specially designed elementary reactions without any transition states, density dependence of reactants and products always feature, in contrast to current practice. It is argued that the rate constant expression without reactant and product dependence is due to historical conventions for strictly elementary reactions. From the above observations, a theory is developed with the aid of some proven elementary theorems in thermodynamics, and expressions under different state conditions are derived whereby a feasible experimental and computational method for determining the activity coefficients from the rate constants may be obtained under various approximations and conditions. Elementary relations for subspecies equilibria and its relation to the bulk activity coefficient are discussed. From one choice of reaction conditions, estimates of activity coefficients are given which * on leave from Chemistry Dept., University of Malaya, 50603 Kuala Lumpur, Email:jesu@um.edu.my 1 are in at least semi-quantitative agreement with the data for non-reacting Lennard-Jones (LJ) particles for the atomic component. The theory developed is applied to ionic reactions where the standard Brönsted-Bjerrum rate equation and exceptions to this are rationalized, and by viewing ion association as a n-meric process, ion activity coefficients may in principle be determined under varying applicable assumptions.

One-Particle Representation of Heat Conduction Described within the Scope of the Second Law

“…There were at least 3 different ways in which NE principles and properties were deduced in previous studies [ 3 , 6 , 9 , 81 , 82 ]. Firstly, if the PLE is assumed as a strong principle [ 26 , 28 , 76 ], then thermostatic potentials such as given by [ 70 ] for NE systems and using time comparisons for irreversible and reversible transitions (Eq 33 [ 3 ]) e.g.…”

Numerical reduced variable optimization methods with an application

“…We refer toP i as any variable that is a function of k constructed on physical or mathematical grounds, and not just to the special case defined in (6). Write…”

“…λ ∞ and Y ∞ ) if k, the rate constant is the single optimizing variable in this approximation in a single step, unlike conventional methods. We assume here that the rate laws and rate constants are not slowly varying functions of the reactant or product concentrations, which has recently from simulation studies been shown to be generally not the case [6]. The first order reaction studied here is the methanolysis of ionized phenyl salicylate with data derived from the literature [7, Table 7.1, p.381] which can be represented as…”

Numerical Reduced Variable Optimization Methods via Implicit Functional Dependence with Applications

“…λ ∞ and Y ∞ if k, the rate constant is the single optimizing variable in this approximation. We assume here that the rate laws and rate constants are not slowly varying functions of the reactant or product concentrations, which has recently from simulation been shown to be generally not the case [21]. Under this standard assumption, the rate equations below all obtain.…”