2. Preliminary information

The balances f(Yg) and ChB will be related to some dynamic redox and non-redox systems for comparative purposes. The balances for a given system are combined according to linear combination principles, and some general properties of the resulting balances are indicated.

The components and species in redox systems are involved in GEB, charge (ChB) and elemental balances. All the balances are founded on the well-established physical, physicochemical and chemical rules involved with charge and all elements conservation, and on the so-named mass action law (MAL), with its 'old-fashioned' principles. However, to be fully compatible with the GATES idea, introduced to avoid the stoichiometric reasoning, the equilibrium law (EL), suggested by Michałowski in 2016, was put instead of MAL; the principle of EL formulation is based on the idea of Lagrange multipliers for searching the local extrema of a function that subjects some constraints, expressed by GEB, ChB and concentration balances. The Gibbs free energy G is applied here as a function of the measurable, intensive properties: p and T and the numbers of constituents are convenient in the study of chemical reaction equilibrium. The problem in question is then consistent with the GATES formulation.

The generalized equivalent mass (GEM) concept, suggested by Michałowski in 1979 [11, 19, 47] is also based on the GATES principles, contrary to IUPAC recommendations [48] based on the stoichiometry of chemical reactions. Within GATES, the stoichiometric reaction notations are used only to formulate the expressions for the set of equilibrium constants related to the system in question, not to one 'representative' reaction, selected arbitrarily.

Within GATES, the mass conservation law is not limited only to components/species of one, specified/ 'responsible' chemical reaction equation but relates to all components/species of an electrolytic system. The mass change involved with an (exo- or endothermal) effect is negligible when compared with the total mass of the system. For example, the mass change, Δm, involved with enthalpy ΔH� of the reaction H2(g) + 0.5O2(g) = H2O(l) (ΔH� = – 286 kJ/mol H2O), equal Δm = ΔH�/c <sup>2</sup> = –3.18∙10�<sup>9</sup> g, is negligible (not measurable) when compared with 18 g of H2O; c = 299,792,458 m/s is the speed of light in vacuum. The neutralization or dilution gives much smaller heat effects. The resulting law of mass preservation is then fulfilled, irrespectively on whether stoichiometric or non-stoichiometric chemical reactions occur (or do not occur) in the system.

X I

zi � Ni ¼ 0 (2)

<sup>i</sup> � ¼ 0 (2a)

,…

zi

ðNi;niA<sup>1</sup> ;niA<sup>2</sup> ;…;niAS Þ,

<sup>3</sup> <sup>¼</sup> OH�<sup>1</sup>

zi � ni1ni2…niS, where nis <sup>¼</sup> niAs (≥0) are the mean num-

i¼2

X I

i¼2

where N<sup>i</sup> is a number of entities of these species in the system [25, 27, 28, 44–46].

(Eq. (1a) or (1b)), the charge balance has the form

12 Redox - Principles and Advanced Applications

allow the formation of mixed solvates Xi

2. Preliminary information

bers of A<sup>s</sup> (s = 1,…, S) molecules attached to Xi

<sup>1</sup> <sup>¼</sup> H2O, <sup>z</sup><sup>2</sup> = +1 for <sup>X</sup><sup>z</sup><sup>2</sup>

where z<sup>1</sup> = 0 for Xz<sup>1</sup>

interrelates charged (zi 6¼ 0) species of this system. In terms of molar concentrations [mol/L]

<sup>z</sup><sup>i</sup> � ½Xzi

<sup>2</sup> <sup>¼</sup> <sup>H</sup>þ<sup>1</sup>

In non-aqueous and mixed-solvent media, with amphiprotic (co)solvent(s) involved, we assume/

The balances f(Yg) and ChB will be related to some dynamic redox and non-redox systems for comparative purposes. The balances for a given system are combined according to linear combination principles, and some general properties of the resulting balances are indicated.

The components and species in redox systems are involved in GEB, charge (ChB) and elemental balances. All the balances are founded on the well-established physical, physicochemical and chemical rules involved with charge and all elements conservation, and on the so-named mass action law (MAL), with its 'old-fashioned' principles. However, to be fully compatible with the GATES idea, introduced to avoid the stoichiometric reasoning, the equilibrium law (EL), suggested by Michałowski in 2016, was put instead of MAL; the principle of EL formulation is based on the idea of Lagrange multipliers for searching the local extrema of a function that subjects some constraints, expressed by GEB, ChB and concentration balances. The Gibbs free energy G is applied here as a function of the measurable, intensive properties: p and T and the numbers of constituents are convenient in the study of chemical reaction

equilibrium. The problem in question is then consistent with the GATES formulation.

system in question, not to one 'representative' reaction, selected arbitrarily.

The generalized equivalent mass (GEM) concept, suggested by Michałowski in 1979 [11, 19, 47] is also based on the GATES principles, contrary to IUPAC recommendations [48] based on the stoichiometry of chemical reactions. Within GATES, the stoichiometric reaction notations are used only to formulate the expressions for the set of equilibrium constants related to the

Within GATES, the mass conservation law is not limited only to components/species of one, specified/ 'responsible' chemical reaction equation but relates to all components/species of an

zi

, z<sup>3</sup> = –1 for X<sup>z</sup><sup>3</sup>

. We apply the notation Xi

All considerations made in this chapter refer, in principle, to the systems where the elements are formed by stable/non-radioactive isotopes [2], i.e. where no nuclear (α, β<sup>+</sup> , β, or electron capture) transformations occur [7], with emission of γ and/or X-ray radiation. However, it is possible to extend the description of redox systems on the systems with radioactive elements, in which the concentrations of the respective components are expressed by dependencies, identified as Bateman's system of linear differential equations [49–52], binding quantitatively the radioactive elements with products of their decay. Radioactive elements and their decay products are also included in the balances for other elements and dependencies for the equilibrium constants.
