TEMPORAL CONCERNS IN THE DETERMINISTIC AND PROBABILISTIC THERMODYNAMICS OF HOMOGENEOUS CHEMICAL REACTIONS


This abstract was compiled from the following published papers

M. Garfinkle, Discrete Dynamics in Nature and Society, 4(2000)145

M. Garfinkle, Journal Physical Chemistry, A106(2002)490


INTRODUCTION

The analytical description of the reaction path transversed by a chemical process proceeding from initiation to equilibrium should be a rather straightforward affair but this has not been the case. In fact there is a surfeit of such descriptions, often mutually exclusive. There is the mechanistic approach and the thermodynamic approach, and these can be either deterministic or probabilistic as shown below.


Mechanistic
............... Mechanistic
Deterministic
...............Probabilistic

Thermodynamic...........Thermodynamic
Deterministic
...............Probabilistic


The mechanistic and thermodynamic approaches are easily distinguished: one investigates the interactions between reacting particles and the other the energy exchange between reaction states, respectively. Either approach can be deterministic or probabilistic.


The temporal thermodynamic approach to chemical reaction kinetics described herein was developed to bridge the considerable gap between the Guldberg and Waage mass action and the De Donder force-flux approach.

A myriad of papers now appear in the literature involving this unique temporal thermodynamic approach. The purpose is to describe chemical reactions without reference to mechanistic considerations. The reaction data are referenced below.


TEMPORAL APPROACH

Homogeneous chemical processes in closed isothermal systems proceed in discrete steps from reaction initiation to equilibrium. Each reaction step i can be explicitly specified by an extent of reaction term zQi defined as

zQi=Qi/K ,

where Qi is the activity ratio at state i and K is the thermodynamic equilibrium constant. Accordingly the range of zQi is limited to 0<zQi<1.

If zQi specifies any reaction step i then zQi-1 designates the previous step and zQi+1 the succeeding step and the dependency of these steps on each other reveals whether the process is deterministic or probabilistic.

 

A process is designated deterministic if the properties of the future step zQi+1 depend on the properties of the present step zQi which in turn depends on the properties of the past step zQi-1. If this dependency is known such a process can be described by an analytical expression.

 

In contrast, a process is designated probabilistic if the properties of the future step zQi+1 does not depend on the properties of the present step zQi which in turn does not depend on the properties of the previous step zQi-1. In this instance no dependency is discernible and the process can only be described by a stochastic algorithm.

 

In this series of studies both deterministic and probabilistic reaction paths were examined and the results checked against the empirical data of 100 stoichiometric chemical reactions proceeding in closed isothermal systems. Their complexity ranged from one-half to fourth order to chain reactions. Both gas-phase and liquid phase reactions were examined.


DETERMINISTIC APPROACH

This study revealed that the chemical affinities for the reactions studied decayed along a specific path that was independent of their reaction mechanisms. The affinity decay rate defined as RTln(dzQi/dt)T,V followed a specific reaction path described by the the expression

µ 1/t

at constant system temperature and volume where t is the elapsed time from reaction initiation. The correlation of the experimental data with the affinity rate expression is excellent as shown in the following six examples and is described in detail in the referenced articles.

Ostensibly the following reaction depends on ternary collisions which are about 100 times as rare as binary collisions but nevertheless the reaction does follow simple third-order kinetics rather than a sequence of bimolecular processes.

Trimolecular Formation of Nitrosyl Chloride

The following electron-transfer reaction is inversely proportional to hydrogen ion concentration and directly proportional to chloride ion concentration.

Electron-Transfer of Fe(II) to Pu(IV) in Perchloric Acid Solution

The following reaction involves an exceedingly complex series of processes including a free-radical chain mechanism.

Dehydrogenation of Isobutane by Iodine

The following process is a chain reaction with a concurring non-chain reaction that has first-order dependency on iodine concentration and a 3/2 order dependency on styrene concentration

Reaction of Styrene by Iodine in Carbon Tetrachloride

The next process is ostensibly a simple isomerization reaction but in fact might be represented also as a bimolecular process.

Isomerization of Ethylidenecyclopropane to 2-Methylmethylenecyclopropane

The next process is ostensibly a simple unimolecular reaction but is heterogeneous.  The present of an inert gas however suppressed the heterogeoneous process.

Decomposition of Hydrogen Peroxide


PROBABILISTIC APPROACH

The study revealed that the chemical affinities for the reactions studied decayed along an expected path that was independent of their reaction mechanisms where the probability for reaction depended only on the extent of reaction zQi

pi,i±1 µ zQi

where pi,i±1 is the probability that the reaction step following step zQi will be forward zQi+1 towards equilibrium as opposed to backwards zQi-1 away from equilibrium. The correlation of the experimental data with the probabilistic path was excellent as shown in the following six plots where A=RTln[zQi] and is described in detail in the referenced articles.

Ostensibly the following reaction depends on ternary collisions which are about 100 times as rare as binary collisions but nevertheless the reaction does follow simple third-order kinetics rather than a sequence of bimolecular processes.

Trimolecular Formation of Nitrosyl Chloride

The following electron-transfer reaction is inversely proportional to hydrogen ion concentration and directly proportional to chloride ion concentration.

Electron-Transfer of Fe(II) to Pu(IV) in Perchloric Acid Solution

 

The following reaction involves an exceedingly complex series of processes including a free-radical chain mechanism.

Dehydrogenation of Isobutane by Iodine

The following process is a chain reaction with a concurring non-chain reaction that has first-order dependency on iodine concentration and a 3/2 order dependency on styrene concentration

Reaction of Styrene by Iodine in Carbon Tetrachloride

The next process is ostensibly a simple isomerization reaction but in fact might be represented also as a bimolecular process.

Isomerization of Ethylidenecyclopropane to 2-Methylmethylenecyclopropane

The next process is ostensibly a simple unimolecular reaction but is heterogeneous.  The present of an inert gas however suppressed the heterogeoneous process.

Decomposition of Hydrogen Peroxide


CONCLUSION

The results of this comprehensive investigation have appeared in a series of articles in which it was demonstrated that for the homogeneous stoichiometric reactions examined the affinity decay can be described independently of mechanistic considerations by either a deterministic equation or a probabilistic algorithm.

 

These two methodologies are contrary to each other. In one case the reaction path is specific and is described by an analytical expression while for the other case the best that can be hope for is a most probable path which results from a stochastic algorithm. Hence many paths are possibly. Most unexpectedly, the probabilistic paths coincided with the deterministic path.

 

This deterministic study showed excellent collelations with kinetic data (Mater. Chem. Phys.; 1982). The kinetic elapsed time does not necessarily coincide with the thermodynamic elapsed time (Mater. Chem. Phys.; 1983). Reaction velocities can be calculated from affinity decay rates (J. Chem. Phys.; 1983). The temperature dependency of the affinity decay rate is analogous to that of the Helmholtz function(J. Chem. Phys.; 1984). Standard Helmholtz functions can be extracted from affinity rate data (Faraday Trans. I; 1985). Chemical reactions proceed along a singular path that can be described independently of reaction mechanism (J. Phys. Chem.; 1989). Chemical reactions attain their equilibrium state in a determinable finite period (J. Non-Equilib. Thermodyn; 1992). This deterministic study has been fully summarized in the literature (Discrete Dynamics in Nature and Society; 2000).

This probabilistic study showed an exceedingly close correlation with kinetic data (J. Phys. Chem. A; 2002).


Moishe Garfinkle, PhD


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