Statistical Study of Distribution Diagrams for Two-Component Systems: Relationships of Means and Variances of the Discrete Variable Distributions with Average Ligand Number and Intrinsic Buffer Capacity

Abstract

The lack of emphasis on the analogy between mathematical statistical distributions and physicochemical distributions in statistical teaching in chemistry courses may be due to a lack of application examples. This paper demonstrates that what is known as a distribution diagram for a two-component polydonor system (MLn/.../ML/M/L) is the set of molar fraction distributions of M species as functions of stoichiometric coefficients of L, formally defining a molecular isotopy. The correspondence between the set of means of these distributions of a discrete variable with the average ligand number and the equivalence between the set of its variances with the intrinsic buffer capacity of the polydonor system is shown. The particular case of phosphates in water is presented. This view of distribution diagrams could help teachers of mathematical statistics to illustrate the fundamental notions of mathematical distributions of discrete variables with chemical application examples.