“Why Not Stoichiometry” Versus “Stoichiometry—Why Not?” Part II: GATES in Context with Redox Systems

Abstract

Redox equilibria and titration play an important role in chemical analysis, and the formulation of an accurate mathematical description is a challenge. This article is devoted to static and (mainly) dynamic redox systems; the dynamic systems are represented by redox titrations. An overview addresses earlier approaches to static redox systems (redox diagram plots, including Pourbaix diagrams) and to titration redox systems, thereby covering a gap in the literature. After this short review, the generalized approach to electrolytic systems (GATES) is introduced, with generalized electron balance (GEB) as its inherent part within GATES/GEB. Computer simulation, performed according to GATES/GEB, enables following the changes in potential and pH of the solution, together with chemical speciation at each step of a titration, thus providing better insight into this procedure. The undeniable advantages of GATES/GEB over earlier approaches are indicated. Formulation of GEB according to two approaches (I and II) is presented on the respective examples. A general criterion distinguishing between non-redox and redox systems is presented. It is indicated that the formulation of GEB according to Approach II does not need the knowledge of oxidation degrees of particular elements; knowledge of the composition, expressed by chemical formula of the species and its charge, is sufficient for this purpose. Approach I to GEB, known also as the "short" version of GEB, is applicable if oxidation degrees for all elements of the system are known beforehand. The roles of oxidants and reductants are not ascribed to particular components forming a system and to the species thus formed. This is the complete opposite of earlier approaches to redox titrations, based on the stoichiometric redox reaction, formulated for this purpose. GEB, perceived as a law of matter conservation, is fully compatible with other (charge and concentration) balances related to the system in question. The applicability of GATES/GEB in optimization a priori of chemical analyses made with use of redox titration is indicated. The article is illustrated with many examples of static and dynamic redox systems. The related plots are obtained from calculations made according to iterative computer programs. This way, GATES/GEB enables seeing details invisible in real experiments.

Principles of Titrimetric Analyses According to Generalized Approach to Electrolytic Systems (GATES)

“…It can be applied for different types of reactions occurring in batch or dynamic systems, of any degree of complexity. The generalized electron balance (GEB) concept, discovered (1992,2006) by Michałowski [11,13] and obligatory for description of redox systems, is fully compatible with charge and concentration balance(s), and relations for the corresponding equilibrium constants.…”

“…[21]. Other examples of high degree of complexity are shown in the works [9,11,12,[14][15][16]. One of the examples in Ref.…”

“…The detailed considerations in this chapter are based on principles of the generalized approach to electrolytic systems (GATES), formulated by Michałowski [9] and presented recently in a series of papers, related to redox [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] and nonredox systems [27][28][29][30][31][32] in aqueous and in mixed-solvent media [33][34][35][36][37]. The closed system separated from its environment by diathermal walls secure a heat exchange between the system and its environment, and realize dynamic processes in a quasistatic manner under isothermal conditions.…”

“…Nonredox systems are formulated with use of charge (ChB) and concentration balances f(Y g ), for elements/cores Y g 6 ¼ H, O. The description of redox systems is complemented by generalized electron balance (GEB) concept, discovered by Michałowski as the Approach I to GEB (1992) and the Approach II to GEB (2006); GEB is considered as a law of a matter conservation, as the law of nature [7,9,11,13,25].…”

Ruthenium redox equilibria: 2. Thermodynamic analysis of disproportionation and comproportionation conditions

“…Therefore, the Frost diagram is a convenient source of understanding complex redox chemistry of any element in its various oxidation states and sometimes under different reaction conditions like pH etc. Details and the mechanics of constructing Frost diagrams can be found in numerous basic chemistry books [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17].…”