Motto: “Everything should be made as simple as possible, but not simpler” [1] .

In the previous issues [2] - [8] and in earlier papers cited therein, the concept of Generalized Electron Balance (GEB), completing the set of compatible equations necessary for quantitative/mathematical solution of electrolytic redox systems, was introduced as two alternative options, named as Approach I and Approach II to GEB. In both Approaches it is assumed/admitted, that all the species exist in an electrolytic system in their natural form, i.e., as solvates. In particular, there are hydrates in aqueous (W = H₂O) media, , or in binary-solvent media (W, A), (W, B) or (A, B) [9] -[11] , respectively. The values of n_Wi, n_Ai and n_Bi, considered as mean numbers of W, A and B attached to, are unknown, in principle, and vary with the co-solvent(s) composition, and solute(s) concentration.

In this paper, we refer also to more complex media with the mixture of co-solvents: W, A, B, E and F. We assume that the co-solvents are mutually miscible and at least one of the co-solvents has amphiprotic properties

[5] . Eeach of the co-solvents has potential/real solvating properties, i.e., in the solvated species. Let denotes N_i entities of these species in the related

system. In further part of the paper, we assume W = H₂O, A = CH₃OH, B = C₂H₅OH, E = (CH₃)₂SO, F = CH₃CN;

W, A, B have amphiprotic properties, and E, F―have not. In particular, N₁₅ ions contain: atoms of H, atoms of O, N₁₅

atoms of I, atoms of C, N₁₅n_15E atoms of S, and N₁₅n_15F atoms of N. It is as-

sumed that the solvents do not form―with solvates―the species other than those formed in (known from) aqueous media. In other words, W, A, B, E, F enter (potentially) the solvating sphere of. On this basis, the elemental balances f(E(i)) for particular elements E(i) are formulated. For ordering purposes, we denote: E(1) = H, E(2) = O, E(3) = I, E(4) = C, E(5) = S, E(6) = N. We apply also the balances f(C(Y)) for the cores C(Y), Y = A, B, E, F. The “core” is a cluster of elements of the same composition, structure and charge, that does not undergo a change in the system in question; e.g., CH₃OH, and CH₃O^? contain the cluster CH₃O^?, considered as the core. We denote C(A) = CH₃O^?, C(B) = C₂H₅O^?, C(E) = (CH₃)₂SO = E, C(F) = CH₅CN = F. The species: H₂CO₃, and have as the common core. However, (anion of HClO₂) and ClO₂ (chlorine dioxide) have different cores.

All the balances in this paper will be presented explicitly, to check the validity of the reasoning and accept it without reservations.

Let us consider a system obtained after addition of V mL of titrant (T) containing I₂ (C) + KI (C₁) + CO₂ (C₂) in A + B + E + F into V₀ mL of titrand (D) containing KBrO₃ (C₀) + HCl (C₀₁) + CO₂ (C₀₂) in W + A + E; all concentrations are expressed in mol/L. The volume V₀ mL of D is composed of N₀₁ molecules of KBrO₃, N₀₂ molecules of HCl, N₀₃ molecules of CO₂, N₀₄ molecules of W, N₀₅ molecules of A, and N₀₆ molecules of E; V mL of T is composed of N₀₇ molecules of I₂, N₀₈ molecules of KI, N₀₉ molecules of CO₂ and N₀₁₁ molecules of A, N₀₁₂ molecules of B, N₀₁₃ molecules of E, and N₀₁₄ molecules of F.

We assume that the solutes composing D and T were introduced in single solvents or mixtures of solvents. In ca. V₀ + V mL of a D + T mixture thus obtained, we have the following species (all changes in oxidation degrees are admitted).

where I_2(s)―solid iodine, I₂―soluble iodine. In the above list of species, H₂O (N₁), CH₃OH (N₄₄), C₂H₅OH (N₄₇), (CH₃)₂SO (N₅₁) and CH₃CN (N₅₂) are free molecules of the corresponding solvents, i.e., not involved in the solvates. We prove that the numbers: N₁, N₄₄, N₄₇, N₅₁ and N₅₂ of the free molecules and the numbers: n_iW, n_iA, n_iB, n_iE, n_iF of these molecules in the solvates do not enter the simplest form of the resulting GEB.

The elemental balances: f(H) for H, and f(O) for O are as follows:

・ f(H)

・ f(O)

From (1) and (2) we obtain

・ 2・f(O) ? f(H)

As we see, Equation (3) does not involve the terms N₁, N₀₄, and {n_iW} related to water. To cancel the terms involved with A, B, E and F, we add Equation (3) to the core balances (4) - (7): 2・f(CH₃O) (4), 4・f(C₂H₅O) (5), 4・f((CH₃)₂SO) (6), 3・f(CH₃CN) (7) and charge balance (8). Further simplification gives addition of the balance for K (9), and of the core balance 4・f(CO₃) (10):

・ 2・f(CH₃O)

・ 4・f(C₂H₅O)

・ 4・f((CH₃)₂SO)

・ 3・f(CH₃CN)

・ Charge balance

・ f(K)

・ 4・f(CO₃)

As the result of this addition, considered as a kind of linear combination [4] , we obtain the simplest form of GEB, expressed in terms of numbers of entities:

Applying the relations:

(where N_A―Avogadro’s constant), from Equations (11), (12) we have

Elemental balances for electro-active elements (“players”) are as follows:

f(Br)

f(Cl)

f(I)

Multiplying (14) - (16) by atomic numbers: Z_Br = 35, Z_Cl = 17, Z_I = 53, for Br, Cl and I, respectively, adding them and applying Equation (12), we have:

After subtracting (13) from (17), we get the equation for GEB, identical with one obtained according to Approach I to GEB

The balance (18) is equivalent to the balance (13).

A remark is needed in relation to the charge balance. Rewriting Equation (8) in terms of concentrations (see Equation (12)), we have

As we see, Equation (19) involves the ionic species related to amphiprotic co-solvents. However, in accordance with the remarks presented in [5] , the solvates of pairs of ions: (, CH₃O^?) and (, C₂H₅O^?) can be perceived as pairs of solvates of H⁺ and OH⁻ ions.

The complex redox system in a mixture with five solvents is considered. The discussion can be extended on mixtures with S solvents, , where at least one of the co-solvents has amphiprotic properties. In such

systems, the solvates are considered/admitted, where ; Equation (13) is the simplest/shortest form of GEB obtained for the redox system considered according to Approach II to GEB.

Equation (13) was obtained from linear combination of the related balance 2・f(O) ? f(H) (Equation (3)) with: charge balance (Equation (8)), elemental balances for other “fans” (C, K) (Equations (9), (10)), and core balances (Equations (4) - (7)) related to organic solvents in this system. This GEB does not involve the species composed only of “fans”: H, O, C, K. In particular, it does not contain the components explicitly related to the solvent species. The paper is an illustration of the compact formulation of redox systems according to GATES/ GEB Principles, presented in Ref. [5] .

One can notice that uncharged (neutral) species: I₂, I_2(s), Cl₂, Br₂, ICl, IBr are not present in Equation (13). Note also that Cl⁻, Br⁻, I⁻, Cl₂, Br₂, I₂, I_2(s), , , I₂Cl⁻, ICl, , IBr, and are the species composed only of “players”. In other species, “players” are associated with “fans”, e.g. in HIO₃ (I―“player”; H, O― “fans”).

Note that―at the start―the Approach II does not distinguish between “fans” and “players”; the terms “fans” and “players” are used here only for the needs of the Approach I to GEB. In further parts of this text, the “players” (the electro-active elements) are distinguished later only to indicate the equivalency of the Approaches I and II.