**5. Conclusion**

Two approaches relating thermodynamics and chemical kinetics were discussed in this article. The first one were restrictions put by thermodynamics on the values of rate constants in mass action rate equations. This can be also formulated as a problem of relation, or even equivalence, between the true thermodynamic equilibrium constant and the ratio of forward and reversed rate constants. The second discussed approach was the use of chemical potential as a general driving force for chemical reaction and "directly" in rate equations.

*K c cc* / , cf. (57). The second degree thermodynamic polynomial results in this

that represents the function 1 1 A B AB *J J Tc c c* (, , , ) . Its transformation to the function

1 110 *J k* exp exp exp *RT RT RT* 

This is thermodynamically correct expression (for the supposed thermodynamic model) of

"thermodynamic driving force" for reaction rate is not simple (stoichiometric) difference in molar chemical potentials of products and reactants. The expression in square brackets can be considered as this driving force. Equation (63) also lucidly shows that high molar chemical potential of reactants in combination with low molar chemical potential of products can naturally lead to high reaction rate as could be expected. On the other hand,

stoichiometric coefficients. In contrast to this straightforward approach illustrated in introduction, also kinetic variable (*k*110) is still present in eq. (63), explaining why some "thermodynamically highly forced" reactions may not practically occur due to very low reaction rate. Equation (63) includes also explicit dependence of reaction rate on standard state selection (cf. the presence of standard chemical potentials). This is inevitable consequence of using thermodynamic variables in kinetic equations. Because also the molar chemical potential is dependent on standard state selection, it can be perhaps assumed that

Rational thermodynamics thus provides efficient connection to reaction kinetics. However, even this is not totally universal theory; on the other hand, presumptions are clearly stated. First, the procedure applies to linear fluids only. Second, as presented here it is restricted to mixtures of ideal gases. This restriction can be easily removed, if activities are used instead

unchanged except the symbol *a* replacing the symbol *c*. But then still remains the problem how to find explicit relationship between activities and concentrations valid at non equilibrium conditions. Nevertheless, this method seems to be the most carefully elaborated

Two approaches relating thermodynamics and chemical kinetics were discussed in this article. The first one were restrictions put by thermodynamics on the values of rate constants in mass action rate equations. This can be also formulated as a problem of relation, or even equivalence, between the true thermodynamic equilibrium constant and the ratio of forward and reversed rate constants. The second discussed approach was the use of chemical potential as a general driving force for chemical reaction and "directly" in rate equations.

1

A B A B AB

discussed in Section 3 and in contrast to (1). It is clear that proper

 

 *i i* 

1 110 A B AB *J k cc K c* ( ) (62)

 

are used in place of functions *J* – all equations remain

, due to arbitrary selection of signs of

(63)

AB A B eq

1 1 A B AB *J JT* (, , , ) gives:

the function *J*

case in following rate equation:

of concentrations, i.e. if functions *J*

**5. Conclusion** 

thermodynamic approach to chemical kinetics.

this is achieved in other approaches, based on

these dependences are cancelled in the final value of reaction rate.

Both approaches are closely connected through the question of using activities, that are common in thermodynamics, in place of concentrations in kinetic equations and the problem of expressing activities as function of concentrations.

Thermodynamic equilibrium constant and the ratio of forward and reversed rate constants are conceptually different and cannot be identified. Restrictions following from the former on values of rate constants should be found indirectly as shown in Scheme 1.

Direct introduction of chemical potential into traditional mass action rate equations is incorrect due to incompatibility of concentrations and activities and is problematic even in ideal systems.

Rational thermodynamic treatment of chemically reacting mixtures of fluids with linear transport properties offers some solution to these problems whenever its clearly stated assumptions are met in real reacting systems of interest. No compatibility conditions, no Wegscheider relations (that have been shown to be results of dependence among reactions) are then necessary, thermodynamic equilibrium constants appear in rate equations, thermodynamics and kinetics are connected quite naturally. The role of ("thermodynamically") independent reactions in formulating rate equations and in kinetics in general is clarified.

Future research should focus attention on the applicability of dependences of chemical potential on concentrations known from equilibrium thermodynamics in nonequilibrium states, or on the related problem of consistent use of activities and corresponding standard states in rate equations.

Though practical chemical kinetics has been successfully surviving without special incorporation of thermodynamic requirements, except perhaps equilibrium results, tighter connection of kinetics with thermodynamics is desirable not only from the theoretical point of view but may be of practical importance considering increasing interest in analyzing of complex biochemical network or increasing computational capabilities for correct modeling of complex reaction systems. The latter when combined with proper thermodynamic requirements might contribute to more effective practical, industrial exploitation of chemical processes.
