Abstract

Background: Inter - conversion processes of labile molecules obey similar rules to those of reversible chemical reactions. Solving the corresponding linear differential systems is used along this work, as well as in the preceding version.

Objective: The main purpose of the present mini revue paper is to recall, improve and correct some mathematical methods in determining the optimal values at equilibrium, and remarkable particular rate constants. This part was not proved correctly in my previous work.

Method: In my previous work, the proof of the equality of the concentrations of the main species at equilibrium was not correct. In the current manuscript, we use increasing velocity in order to obtain this first important result. To this aim, one applies Schwarz inequality and the case when equality occurs. In order to determine significant rate constants, we characterize these special values in terms of the norm of the linear operator defined by the matrix of the differential system. In my previous work, the normal probability density function was used. The latter method was not realistic.

Results: Increasing the velocity, one obtains equal optimal values of the concentrations at equilibrium. This method represents a patent in the field. Secondly, characterization of remarkable rate constants (which are also equal) is deduced. The optimal solutions are written explicitly.

Conclusion: Under suitable conditions, the values at equilibrium and the rate constants are equal. The common value at equilibrium equals the common value of the rate constants.

Keywords: Eigenvectors, equilibrium, increasing velocity, inter–conversion, kinematics, labile molecules, mirror image, rate constants.

Graphical Abstract