“Why Not Stoichiometry” versus “Stoichiometry—Why Not?” Part III: Extension of GATES/GEB on Complex Dynamic Redox Systems

<div><p>In the third part of a series of articles issued under a common title, some examples of complex dynamic redox systems are presented and considered from analytical and physico-chemical viewpoints; the analysis is a leitmotiv for detailed, physico-chemical considerations. All attainable physico-chemical knowledge is involved in algorithms applied for resolution of the systems, realized with use of iterative computer programs. The first redox system (System I) is related to titration of FeSO₄ + H₂C₂O₄ with KMnO₄ solution in acidic (H₂SO₄) medium, where simultaneous determination of both analytes from a single curve of potentiometric titration is possible. The possibility of the formation of precipitates (<b>FeC₂O₄</b> and/or <b>MnC₂O₄</b>) in this system is taken into considerations. The second system (System II) relates to the complete analytical procedure involved in the iodometric determination of Cu; four consecutive steps of this analysis are considered. As a reasonable tool for explanation of processes occurring during simulated redox titration, speciation diagrams are suggested. This explanation is based on graphical presentation of results obtained from the calculations. The calculations made for this purpose are performed in accordance with principles of the generalized approach to electrolytic systems (GATES) with generalized electron balance (GEB) or GATES/GEB and realized with use of iterative computer programs offered by MATLAB. The reactions proceeding in this system can be formulated, together with their efficiencies, at any stage of the titration. Stoichiometry is considered as the derivative concept when put in context with GATES/GEB. The article illustrates the enormous possibilities and advantages offered by GATES/GEB.</p></div

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

<div><p>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.</p></div