Electrical Charge Method for Balancing, Quantifying, and Defining Redox Reactions

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Procedures for Balancing Ion-Charge Equations
When using the electrical charge method, H + , O, H 2 O, and electrical charges (or charge) are employed as balancing devices. Based on the charge parameters, the balanced method is developed, and its operating procedures are shown as follows: Step 1. Divide the overall redox reaction into two half reactions ( H + , OH -, and H 2 O can be omitted in the half reactions optionally; a molecular chemical equation is converted to an ionic chemical equation when needed) Step 2 Step 3. Determine the net-charges of the two half reactions net-charge = Σ charge (product) ˗ Σ charge (reactant) Step 4. Make the net-charges of the two half reactions equivalent Step 5. Combine the two half reactions Step 6. Simplify the overall chemical equation Step 7. Provide 1 OHfor each H + and simplify the overall chemical equation (This is an optional step for converting an acidic solution to a basic solution.)

Procedures for Dividing an Overall Reaction into Two Half Reactions
The electrical charge method is a half reaction approach. The first and the most critical step is to divide an overall redox reaction into two half reactions by using the "ping-pong" strategy (Yuen & Lau, 2022a). Its working procedures are as follows: (i) choose one of the reactants and identify all its non-H and non-O elements, (ii) link the reactant's element(s) on all products' element(s), (iii) keep linking left (reactants' side)-right (products' side)-left-right…, until a half reaction is attained, (iv) choose another reactant and repeat the steps (i), (ii), and (iii).

Net-charge and Number of Transferred Electrons
The nature of redox reaction is an electron-transfer reaction. An ion-charge equation can be converted to an ion-electron equation by adding electrons to make the number of electrical charges even on both reactants' side and products' side. The quantitative relationship between net-charge and number of transferred electrons (Te -) in a half reaction is demonstrated in the following examples.

Net-charge and Change of Oxidation Numbers
The mathematical equation of Te -= n ∆ON among Te -, number of atoms with oxidation numbers change (n), and change of oxidation numbers (∆ON) for one set of redox couple has been established (Yuen & Lau, 2022b). In this article, the quantitative relationship between net-charge, n, and ∆ON in a half reaction is shown as: net-charge = Σ charge (product) ˗ Σ charge ( When the net charges = +4, it represents an increase of oxidation number of two carbon atoms (∆ON C = +2; n C = 2) from CH 3 CH 2 OH (ON C = ˗2) to CH 3 COOH (ON C = 0) whereas when net-charge = ˗6, it represents a decrease of oxidation number of two chromium atoms (∆ON Cr = ˗3; n Cr = 2) from Cr 2 O 7 2-(ON Cr = +6) to 2Cr 3+ (ON Cr = +3).

Triangular Relationships among Net-charge, Te -, and ∆ON
All half redox reactions in Examples 1 to 3 contain one set of redox couple. The net-charge or Teof a redox couple can be counted by their ON (reactant), ON (product), and n. Their redox natures are shown in Table 1 Table 1 and Figure 1, the selected half reactions in Table 2 can be quantified, classified, and defined. reduction The relationships among the loss/gain of electrons, the increase/decrease of oxidation number, and the increase/decrease of charge are established in a half redox reaction. Regarding their triangular relationships, an example of oxidation is shown in Figure 2.
In the half oxidation reaction, there are two sets of redox couples shown as Pb 2+ /Pb 3 O 4 and N 3 -/NO. The calculations of net-charges for them are shown as follows: For 3Pb  The net-charge, n, and ∆ON for multiple redox couples in Example 4 are summarized in Table 3. The mathematical relationships between a half reaction and multiple redox couples are demonstrated as follows: net-charge (half reaction) = Σ net-charge (redox couple) net-charge (half reaction) = Σ n ∆ON (redox couple) Te -(half reaction) = Σ Te -(redox couple) Te -(half reaction) = Σ n ∆ON (redox couple) With reference to Table 3, the half reduction reaction of "2Cr(MnO 4 ) 2 +10H + →Cr 2 O 3 +4MnO 2 +5H 2 O" is quantified and defined by its net-charge of -10 (reduction), or summation of net-charges of Cr 2 /Cr 2 O 3 (+2; oxidation) and MnO 4 /MnO 2 (-12; reduction).

The Charge Model: A New Redox Model
The establishment of the electrical charge method for balancing redox reactions initiates and generalizes a new charge model. A comparison of the electron (e -) model, the oxidation number (ON) model (IUPAC, 2019), and the charge model is shown in Table 4.  Table 4, all ion-charge equations in Examples 1 -6 can be defined by the charge model and summarized in Table 5.

Conclusion
The misconceptions among oxidation number, transferred electron, and electrical charge can cause difficulties for understanding redox reactions. This article studies the electrical charge method. The significance of this method is that it manifests both chemical and mathematical accuracy. It only requires simple mathematical manipulations for balancing, and then defining redox reactions. Instead of using the oxidation number and electron, it balances ion-charge equations and counts electrical charges. Due to this functionality, it works well for half redox reactions, including complicated cases where oxidation numbers are uncertain and where there are more than two sets of redox couples. Furthermore, the resulting net-charge can be applied to determine the number of transferred electrons in any balanced half redox equation. The electrical charge method also initiates and establishes a new charge model, which complements the conventional electron model and the oxidation number model for defining redox reactions.