Oxidation States and Redox Reactions

The oxidation state (oxidation number, NO) is the formal charge an atom would have if all bonds were ionic, i.e., if electrons were assigned to the more electronegative atom. It is an accounting tool for tracking electron transfers in chemical reactions.

Main rules for assignment:

• Elements in their free state (O₂, Fe, S₈, Cl₂): NO = 0
• Monoatomic ions: NO = ionic charge (e.g. Fe³⁺ → NO = +3)
• Fluorine: always −1 (the most electronegative element)
• Oxygen: usually −2, except in peroxides (H₂O₂, NO = −1), superoxides (KO₂, NO = −½), and OF₂ (NO = +2)
• Hydrogen: +1 except in metal hydrides (NaH, CaH₂) where NO = −1
• The algebraic sum of NOs in a neutral compound = 0; in a polyatomic ion = the ion charge

Real-world applications: NO is essential for balancing redox reactions, identifying oxidizing/reducing agents, and understanding processes like metal corrosion, battery operation, and photosynthesis.

A redox (reduction-oxidation) reaction involves the transfer of electrons between two chemical species. The fundamental concepts are complementary and inseparable:

• Oxidation: loss of electrons → the oxidation number increases (e.g. $\mathrm{Fe^{2+} \to Fe^{3+} + e^-}$: NO from +2 to +3). The species that is oxidized is a reducing agent (donates electrons).
• Reduction: gain of electrons → the oxidation number decreases (e.g. $\mathrm{MnO_4^- + 5e^- \to Mn^{2+}}$: NO of Mn from +7 to +2). The species that is reduced is an oxidizing agent (accepts electrons).

The two half-reactions form a conjugate redox pair, written as: $$\text{Red} \rightleftharpoons \text{Ox} + n\,e^-$$ A useful mnemonic: "OIL RIG" (Oxidation Is Loss, Reduction Is Gain of electrons).

The activity series of metals ranks metals by their tendency to be oxidized (lose electrons). A metal higher in the series can reduce the ion of a metal lower in the series (e.g. Zn + Cu²⁺ → Zn²⁺ + Cu).

Real-world applications: iron corrosion (rust) is a redox process: $\mathrm{Fe \to Fe^{2+} + 2e^-}$ (oxidation) and $\mathrm{O_2 + 2H_2O + 4e^- \to 4OH^-}$ (reduction). Photosynthesis converts CO₂ to glucose (carbon reduction) using solar energy.

The electron method (half-reaction method) for acidic medium follows systematic steps:

• 1. Assign oxidation numbers to all atoms and identify the two half-reactions (oxidation and reduction)
• 2. Balance atoms other than H and O in each half-reaction
• 3. Add H₂O to balance oxygen atoms, then H⁺ to balance hydrogen atoms
• 4. Add electrons (e⁻) to the appropriate side to balance charge in each half-reaction
• 5. Multiply the half-reactions by the least common multiple (LCM) of the electrons exchanged, so that electrons lost in oxidation equal those gained in reduction
• 6. Sum the two half-reactions, canceling species that appear on both sides

In basic medium, follow the same procedure, then add as many OH⁻ ions as there are H⁺ ions to both sides, combining H⁺ + OH⁻ → H₂O and simplifying water molecules.

For complex reactions (e.g. with polyatomic ions), the ion-electron method can be more convenient, directly balancing the species as they appear in solution.

Real-world applications: redox balancing is essential for analytical chemistry titrations (permanganometry), designing industrial electrochemical processes (chlor-alkali production, metal electrorefining), and understanding biological electron transport chains (mitochondria).

An element's tendency to be oxidized (lose electrons) or reduced (gain electrons) is closely related to its position in the periodic table and its electronegativity:

• Alkali metals (group 1) and alkaline earth metals (group 2): very low electronegativity, easily donate valence electrons → strong reducing agents (e.g. Na → Na⁺ + e⁻, Mg → Mg²⁺ + 2e⁻). They oxidize spontaneously in air.
• Halogens (group 17): high electronegativity, easily accept electrons → strong oxidizing agents (e.g. Cl₂ + 2e⁻ → 2Cl⁻). Fluorine is the most powerful oxidizer.
• Transition metals: can assume multiple oxidation states thanks to partially filled d orbitals. Examples: Mn (from +2 to +7 in MnO₄⁻), Cr (from +2 to +6 in Cr₂O₇²⁻), Fe (+2 and +3). This versatility makes them widely used redox catalysts in industry and biochemistry.
• Noble gases (group 18): stable filled-shell configuration, neither oxidized nor reduced under normal conditions.

The standard reduction potential $E^\circ$ (measured against the standard hydrogen electrode, SHE) quantifies a species' tendency to be reduced. More positive $E^\circ$ values indicate a stronger oxidizing agent; more negative values indicate a stronger reducing agent. The cell potential difference predicts reaction spontaneity: $$E^{\circ}_{\text{cell}} = E^{\circ}_{\text{cathode}} - E^{\circ}_{\text{anode}}$$ If $E^{\circ}_{\text{cell}} > 0$, the reaction is spontaneous (∆G° < 0) under standard conditions.

Real-world applications: the electrochemical series predicts metal corrosion, enables battery design (e.g. Daniell cell: $E^\circ = +1.10$ V), and helps choose oxidizing/reducing agents for chemical synthesis.