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Chemical and other species reaction theories involving thermodynamical equilibrium states characterized by a temperature parameter invariably utilize statistical mechanical equilibrium density distributions. Here, a definition of heat-work transformation termed thermo mechanical coherence is first made, and it is conjectured that most molecular bonds have the above heat-work transformation property, which models a chemical bond as a "'centrifugal heat engine"' . Expressions are derived for the standard Gibbs free energy, enthalpy, and entropy where the bond coordinates need not conform to a non degenerate Boltzmann state, since bond breakdown and formation are processes that have direction, whereas equilibrium distributions are derived when the Hamiltonian is of fixed form, which is not the case for chemical reactions using localized Hamiltonians. The empirically determined Gibbs free energy from a known molecular dynamics simulation of a dimer reaction 2A ⇋ A 2 , accords rather well with the theoretical estimate. A relation connecting the rate of reaction with the equilibrium constant and other kinetic parameters is derived and could place the commonly observed linear relationship between the logarithms of the rate constant and equilibrium constant on a firmer theoretical footing. These relationships could include analogues of the Hammett correlations used extensively in physical organic chemistry, as well as others which are temperature dependent. One prediction of the principles developed here is that the equilibrium standard reaction free energy is * Correspondence: Christopher G. Jesudason, M019,Chemical Physics Group, Department of Chemistry, University of Malaya, 50603 Kuala Lumpur, Malaysia; Fax:03-79674193; Tel: 03-7967-4270 E-mail: jesu@um.edu.my 1 more dependent on the height of the intermolecular potential than its depth, so that the sign of the ∆G -0 can change for varying barrier height with fixed well depth, which may appear counter-intuitive. All the above developments can be tested directly in simulations and therefore provides a fertile ground for further research with significant implications on how standard states are determined in relation to the direction of chemical reaction.This work treats the molecular bond using standard thermodynamics as if it were a system, and it is anticipated that with the advent of single-molecule science and experiment, that might be one way in which molecular statistical thermodynamics would develop.

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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.

Abstract:Recently, there have appeared interesting correctives or challenges [Entropy 1999, 1, 111-147] to the Second law formulations, especially in the interpretation of the Clausius equivalent transformations, closely related in area to extensions of the Clausius principle to irreversible processes [Chem. Phys. Lett. 1988, 143(1), 65-70]. Since the traditional formulations are central to science, a brief analysis of some of these newer theories along traditional lines is attempted, based on well-attested axioms which have formed the basis of equilibrium thermodynamics. It is deduced that the Clausius analysis leading to the law of increasing entropy does not follow from the given axioms but it can be proved that for irreversible transitions, the total entropy change of the system and thermal reservoirs (the "Universe") is not negative, even for the case when the reservoirs are not at the same temperature as the system during heat transfer. On the basis of two new simple theorems and three corollaries derived for the correlation between irreversible and reversible pathways and the traditional axiomatics, it is shown that a sequence of reversible states can never be used to describe a corresponding sequence of irreversible states for at least closed systems, thereby restricting the principle of local equilibrium. It is further shown that some of the newer irreversible entropy forms given exhibit some paradoxical properties relative to the standard axiomatics. It is deduced that any reconciliation between the traditional approach and novel theories lie in creating a well defined set of axioms to which all theoretical developments should attempt to be based on unless proven not be useful, in which case there should be consensus in removing such axioms from theory. Clausius' theory of equivalent transformations do not contradict the traditional Entropy 2003, 5 253 understanding of heat-work efficiency. It is concluded that the intuitively derived assumptions over the last two centuries seem to be reasonably well grounded, requiring perhaps some minor elaboration to the concepts of (i) system, (ii) the mechanism of heat transfer, and (iii) the environment, which would be expected to evolve with time in any case. If new generalizations at variance with Clausius' concepts are presented, then these ideas could be expected to require a different axiomatic basis than the one for equilibrium theory, and this difference must be stated at the outset of any new development. So far such empirically self-consistent axiomatic developments are not very much in evidence.