Non-redox Systems Research Articles

Thermodynamic Formulation of Electrolytic Redox Systems According to GATES/ GEB Principles

The Generalized Electron Balance (GEB) completes the set of equations needed for quantitative description of an electrolytic redox system. Two equivalent Approaches (I, II) to GEB were formulated in context with the Generalized Approach to Electrolytic Systems (GATES), as GATES/GEB. The Approach I to GEB is based on an electron balance of components and species formed by electron-active elements, termed as players. The Approach II to GEB is based on the linear combination f12 = 2∙f(O) – f(H) of elemental balances: f1 = f(H) for Y1 = H, and f2 = f(O) for Y2 = O. Linear independency/dependency of f12 from charge (f0 = ChB) and other elemental/core balances fk = f(Yk ) (k=3,…,K) for different elements/cores Yk of the system tested is the general criterion distinguishing between redox and non-redox systems. The GATES / GEB GATES is the best thermodynamic formulation of electrolytic redox systems of any degree of complexity. The GEB is considered as he general law of Nature. Some other/important/basic physicochemical properties inherent in the f21 formulation are also indicated. The principle of GATES/GEB formulation is exemplified by the titration KIO3 ⇨ KI + HCl.

Physicochemical and Analytical Implications of GATES/GEB Principles

The fundamental property of electrolytic systems involved with linear combination f12 = 2∙f(O) – f(H) of elemental balances: f1 = f(H) for Y1 = H, and f2 = f(O) for Y2 = O, is presented. The dependency/independency of the f12 on Charge Balance (f0 = ChB) and other elemental and/or core balances fk = f(Yk) (k = 3,…,K) is the general criterion distinguishing between non-redox and redox systems. The f12 related to a redox system is the primary form of a Generalized Electron Balance (GEB), formulated for redox systems within the Generalized Approach to Electrolytic System (GATES) as GATES/GEB ⊂ GATES. The set of K balances f0,f12,f3,…,fK is necessary/ sufficient/needed to solve an electrolytic redox system, while the K-1 balances f0,f3,…,fK are the set applied to solve an electrolytic non-redox system. The identity (0 = 0) procedure of checking the linear independency/ dependency property of f12 within the set f0,f12,f3,…,fK (i) provides the criterion distinguishing between the redox and non-redox systems and (ii) specifies Oxidation Numbers (ONs) of elements in particular components of the system, and in the species formed in the system. Some chemical concepts, such as oxidant, reductant, oxidation number, equivalent mass, stoichiometry, perceived as derivative within GATES, are indicated. All the information is gained on the basis of the titration Ce(SO4)2 (C) + H2SO4 (C1) + CO2 (C2) ⇨ FeSO4 (C0) + H2SO4 (C01) + CO2 (C02), simulated with use of the iterative computer program MATLAB.

Some Regularities Inherent in the Balance 2∙f(O) – f(H) Formulated for an Electrolytic System with Symproportionation Reactions Involved

The general properties of the balance f12 = 2∙f(O) – f(H), as the linear combination of elemental balances: f1 = f(H) for H and f2 = f(O) for O, formulated for electrolytic systems, are presented. These properties/regularities are inherently related to linear combination (LC) of f12 with charge (f0) and other elemental/core balances fk = f(Yk) (Yk ≠ H, O), expressed by, where the multipliers dk are involved with oxidation numbers (ONs) of the elements in the system in question. The linear dependence or independence of f12 from f0,f3,…, fK, expressed by LC, provides the general criterion distinguishing between non-redox and redox systems. The f12 is the primary form of Generalized electron balance (GEB), completing the set of K independent balances f0,f12,f3,…,fK needed for the solution of a redox system according to GATES/GEB principles. For the solution of a non-redox system, the set of K–1 independent equations f0,f3,…,fK is required. In this formulation, the terms: ONs, oxidant, reductant, and equivalent mass are derivative/redundant concepts. These properties/regularities of f12 are illustrated here by a redox system where symproportionation reactions occur.

Further remarks on the new criterion differentiating between Non-Redox and Redox Electrolytic Systems

The new general criterion, distinguishing between non-redox and redox electrolytic systems, is based on the properties of the linear combination f12 = 2∙f(O) – f(H) of elemental balances: f1 = f(H) for Y1 = H, and f2 = f(O) for Y2 = O. The f12 is the primary form of the Generalized Electron Balance (f12 = prGEB), completing the set of balances needed to formulate a redox system, according to Generalized Approach to Electrolytic Systems (GATES). In the redox system, f12 is linearly independent on charge (f0 = ChB) and other elemental/core balances fk = f(Yk) (k=3,…,K), i.e., f0,f12,f3,…,fK form the set of independent balances needed to formulate the redox system. In a non-redox system, f12 is linearly dependent on the balances f0,f3,…,fK, i.e., f0,f3,…,fK form the set of K – 1 independent balances needed to formulation of the non-redox system. Further properties, resulting from the combination of these equations specified here, are involved with oxidation numbers (ONs) of elements in components forming a non-redox or redox system. In the GEB formulation, made according to Approach II to GEB, the prior knowledge of oxidation numbers for all elements of the system is not needed. Moreover, ‘oxidant’ and ‘reductant’ are derivative/redundant terms. The mathematical knowledge, required to answer the question put in the title, is comprised within the four basic, algebraic operations. These properties are illustrated on a complex (41 species) example of a dynamic D+T redox system, and its static non-redox (T, D) subsystems.

The new paradigm in thermodynamic formulation of electrolytic systems – A review

The general property of electrolytic systems in aqueous media is presented. The linear combination f12 = 2∙f(O) – f(H) of elemental balances: f1 = f(H) for Y1 = H and f2 = f(O) for Y2 = O, is put in context withcharge balance (f0 = ChB) and other elemental and/or core balances fk = f(Yk) (k=3,…,K) related to the system in question It is stated that f12 is (a) linearly independent on f0,f3,…,fK for a redox system, or is (b) linearly dependent on f0,f3,…,fK when related to a non-redox system.

Some Regularities Involved with Oxidation Numbers Stated in Formulation of Redox Systems According to GATES/GEB Principles

Formulation of Generalized Electron Balance (GEB) for redox systems according to Approach II to GEB does not require the prior knowledge of oxidation numbers of all elements in components forming a system, and in the species of the system thus formed. This formulation is involved with linear combination of charge and elemental and/or core balances related to the system in question. The skillful choice of multipliers for the balances on the step of purposeful formulation of this linear combination allows for to find important regularities for electrolytic systems of different degree of complexity. These multipliers are related to the oxidation numbers of the elements; this regularity is important in the context of the fact that the oxidation number is the contractual concept. This property is valid for redox and non-redox systems. In this context, oxidation number is perceived as the derivative/redundant concept. The paper indicates the close relationships between different rules of conservation and indicates huge possibilities inherent in the generalized approach to electrolytic systems (GATES), and GATES/GEB in particular.

Generation of Reactive Oxygen Species via Electroprotic Interaction of H2O2with ZrO2Gel: Ionic Sponge Effect and pH-Switchable Peroxidase- and Catalase-Like Activity

Formation of reactive oxygen species (ROS) is of vital importance in catalytic oxidation chemistry. In this paper we have shown that a nonredox system such as amorphous zirconium dioxide (a-ZrO2) is highly active in ROS formation via H2O2 decomposition. Interaction between a-ZrO2 and H2O2 in aqueous solution was investigated by means of EPR, HYSCORE, Raman, and UV–vis, along with auxiliary FTIR, TG-MS, and XPS techniques, in a broad range of pH values and H2O2 concentrations. Various reaction intermediates such as superoxide (O2•–) and hydroxyl (•OH) radicals as well as peroxide (O22–) species were identified. At pH 5.3 formation of O22– is accompanied by a substantial release of O2 due to the pronounced catalas...

Oxidation Number, Oxidant and Reductant as Derivative Concepts within GATES/GEB Formulation

Formulation of Generalized Electron Balance (GEB) according to Approach II to GEB, based on linear combination f12 = 2∙f(O) – f(H) of elemental balances: f(H) for H and f(O) for O, is illustrated on the titration of NaBr + H2SO4 (as titrand, D) with Ce(SO4)2 + H2SO4 solution (as titrant, T), according to GATES/GEB principles. Some fundamental advantages inherent in linear combination of f12 with other elemental/core balances are indicated. The prior information on oxidation numbers of all elements participating the redox system is not needed. The multipliers needed to obtain the simpler form of the balance resulting from the linear combination are equal to oxidation numbers of the elements participating the related system. This way, the f12 provides the criterion distinguishing between nonredox and redox systems. The f12 is linearly independent on other balances in a redox system, or linearly dependent in non-redox systems; the D and T are considered here as non-redox subsystems of the D+T redox system. All available physicochemical knowledge related to the D+T system can be involved in the iterative computer program used for calculation purposes.

Formulation of Simple Electrolytic Redox Systems According to GATES/GEB Principles

The linear combination f12 = 2∙f(O) – f(H) of elemental balances: f1 = f(H) for H, and f2 = f(O) for O is the basis to formulate the generalized electron balance (GEB) for electrolytic redox systems according to Approach II to GEB, realized within the generalized approach to electrolytic systems (GATES) as GATES/GEB. Together with charge balance (f0 = ChB) and K–2 elemental/core balances: f3,…,fK, the f12 completes the set of K balances needed for resolution of an electrolytic redox system, of any degree of complexity. For a nonredox system, a proper linear combination of f12 with f0, and fk = f(Yk) (Yk ≠ H, O; k=3,…,K) gives the identity, 0 = 0. Consequently, in nonredox systems, f12 is linearly dependent on f0,f3,…,fK, i.e., f12 is not the independent balance. This independency/dependency property of f12 distinguishes between redox and non-redox systems. In a redox system, a proper linear combination of f12+f0 with the balances for electron-non-active elements/cores gives the simpler form of GEB, where the species composed only of electron-non-active elements are not involved. The multipliers applied in the linear combinations are equal to the oxidation numbers for elements participating redox or non-redox system. This regularity is highly important in context of the fact that the ‘oxidation number’ was essentially a contractual concept. Within GATES/GEB, the terms: oxidation number, oxidant and reductant, stoichiometry, and equivalent mass are derivative/redundant concepts only; the roles of oxidants and reductants are not assigned a priori to individual components. All these concepts are illustrated on simple examples of redox D+T systems, with aqueous solutions of (S1) Br2, and (S2) HBrO as titrand D, and NaOH solution as titrant T.

Solubility and Dissolution in Terms of Generalized Approach to Electrolytic Systems Principles

The correct approach, based on the rules of conservation and detailed physicochemical/thermodynamic knowledge on the system considered is opposed to conventional approach to solubility and dissolution, based on stoichiometry of a reaction notation and on the solubility product (Ksp) of a precipitate. The correct approach is realized according to Generalized Approach to Electrolytic Systems (GATES) principles, with use of iterative programs applied for computational purposes. All the qualitative and quantitative knowledge is involved in the balances and independent expressions for the equilibrium constants. Three two-phase electrolytic systems with diversified chemical properties were selected carefully, from the viewpoint of their diversity. The results of calculations are presented graphically and discussed. The advantages of the GATES in resolution of two-phase (static) non-redox systems and one complex (dynamic) redox system are proved.

GATES as the Unique Tool for Simulation of Electrolytic Redox and Non-Redox Systems

The Generalized Approach to Electrolytic Systems (GATES), based on physical (charge conservation), physicochemical (conservation of elements) and chemical (mass action) laws is the best theory applicable for computer simulation of equilibrium, non-equilibrium and metastable, mono- and polyphase electrolytic redox and non-redox systems. The Generalized Electron Balance (GEB) concept, related to electrolytic redox systems, is put in context with the principle of conservation of all elements in electrolytic redox systems, with aqueous, non-aqueous or mixedsolvent media. Two equivalent approaches to GEB are presented, and termed as the Approach I and Approach II to GEB. The GEB, that enters GATES as GATES/GEB, is fully compatible with charge and concentration balances and completes the set of equations necessary for thermodynamic resolution of redox systems. Computer simulation of such systems is based on all attainable physicochemical knowledge involved in the related algorithm, solvable with use of an iterative computer program, and then presented graphically. This paper is referred mainly to dynamic redox systems, realized according to titrimetric mode. The speciation diagrams for dynamic redox systems are perceived as a reasonable alternative to (static) Pourbaix diagrams. The GEB concept, unknown before 1992, is perceived as the law of the matter conservation, as the general law of Nature. From the GATES viewpoint, the stoichiometric reactions are only the basis to formulate the related equilibrium constants. GATES is also the basis for Generalized Equivalence Mass (GEM) concept, formulated with none relevance to the stoichiometry of chemical reaction notation. From the GATES viewpoint, the stoichiometry is a superfluous concept.

Linear Dependence of Balances for Non-Redox Electrolytic Systems

Two complex dynamic non-redox systems are considered as examples, providing interdependent linear equations. A simple and efficient linear combination method that leads the system of equations to the identity, 0 = 0, is used for this purpose. These examples are clear confirmations of the general property differentiating non-redox and redox electrolytic systems. This property is involved with linear dependence or independence of 2·f(O)-f(H) on charge and elemental/core balances for elements/cores ≠H, O, where f(H) and f(O) are elemental balances for H and O, respectively.

Formulation of general criterion distinguishing between non-redox and redox systems

The paper provides a comprehensive, compatible and consistent approach to thermodynamics of electrolytic redox and non-redox systems, referred to aqueous, non-aqueous and mixed-solvent media. It is stated that the linear combination 2·f(O)−f(H) of elemental balances: f(H) for H and f(O) for O is the property distinguishing between redox and non-redox electrolytic systems. Namely, 2·f(O)−f(H) is the linear combination of concentration balances for other components of a non-redox system, of any degree of complexity. It is also proved that 2·f(O)−f(H) is an independent equation when referred to a redox system, of any degree of complexity. The linear combination 2·f(O)−f(H) is a primary form, pr-GEB, of the Generalized Electron Balance (GEB), 2·f(O)−f(H)=pr-GEB, named as the Approach II, and considered as the alternative for the Approach I to GEB, based on the “card game” principle. The equivalency of both approaches to GEB is also proved in this paper. The GEB, considered as a relatively new Law of Nature, is perceived as a turning point in the theory of electrolytic redox systems.

Comparative Balancing of Non-Redox and Redox Electrolytic Systems and Its Consequences

In this paper, it is proved that linear combination 2·f(O) － f(H) of elemental balances: f(O) for O and f(H) for H is linearly independent on charge and elemental/core balances for all redox systems of any degree of complexity; it is the primary form of the Generalized Electron Balance (GEB), , considered as the Approach II to GEB. The Approach II is equivalent to the Approach I based on the principle of common pool of electrons. Both Approaches are illustrated on an example of titration of acidified (H2SO4) solution of H2C2O4 with KMnO4. It is also stated, on an example of titration of the same solution with NaOH, that 2·f(O) － f(H) is a linear combination of charge and elemental/core balances, i.e. it is not an independent balance when related to the non-redox system. These properties of 2·f(O) － f(H) can be extended on redox and non-redox systems, of any degree of complexity, i.e. the linear independency/dependency of 2·f(O) － f(H) on other balances related to a system in question is a criterion distinguishing redox and non-redox systems. The GEB completes the set of (charge and concentration) balances and a set of expressions for independent equilibrium constants needed for modeling the related redox system.