Rates of Reactions as a Mathematical Consequence of the Permanence of Atoms and the Role of Independent Reactions in the Description of Reaction Kinetics.

Abstract

Linear algebra treatment of the permanence of atoms (mass conservation) naturally leads to the transformation of formation or destruction rates of components of a reaction mixture into rates of reaction steps, which are sufficient to describe the transformations mathematically. These steps form a scheme of independent reactions which can provide a rational basis for elucidating the reaction mechanism (network) while reducing both the component and parametric dimensionality of the description of kinetics. Several particular reaction examples are used to explain the method and show that rates of additional, dependent reactions cannot be unambiguously related to measured component rates. They also illustrate how the rates of dependent reactions can be correctly expressed in terms of the rates of independent reactions. The method starts only with a knowledge of the components of a reaction mixture. It is argued that the design of consistent reaction networks or mechanisms should take into account not only chemistry but also mathematics.Linear algebra treatment of the permanence of atoms (mass conservation) naturally leads to the transformation of formation or destruction rates of components of a reaction mixture into rates of reaction steps, which are sufficient to describe the transformations mathematically. These steps form a scheme of independent reactions which can provide a rational basis for elucidating the reaction mechanism (network) while reducing both the component and parametric dimensionality of the description of kinetics. Several particular reaction examples are used to explain the method and show that rates of additional, dependent reactions cannot be unambiguously related to measured component rates. They also illustrate how the rates of dependent reactions can be correctly expressed in terms of the rates of independent reactions. The method starts only with a knowledge of the components of a reaction mixture. It is argued that the design of consistent reaction networks or mechanisms should take into account not only chemistry but also mathematics.