Redox Chemistry & Electrochemistry

In K₂Cr₂O₇: K is +1, O is −2. Let Cr = x. Then 2(+1) + 2x + 7(−2) = 0, giving 2x = 12, so x = +6. In KMnO₄: (+1) + x + 4(−2) = 0, giving x = +7. These high oxidation states are characteristic of early transition metals with many d electrons available for bonding to highly electronegative oxygen.

Mn goes from +7 to +2 (gains 5 electrons), while Fe goes from +2 to +3 (loses 1 electron). To balance electrons: 5 Fe²⁺ are needed per MnO₄⁻. The balanced equation in acidic solution is: MnO₄⁻ + 5 Fe²⁺ + 8 H⁺ → Mn²⁺ + 5 Fe³⁺ + 4 H₂O. The 8 H⁺ and 4 H₂O balance both charge and oxygen atoms.

Disproportionation is a reaction in which one species is simultaneously oxidized and reduced — the same element in the same oxidation state produces products in both a higher and a lower oxidation state. The classic example is Cu⁺ in aqueous solution: 2 Cu⁺(aq) → Cu(s) + Cu²⁺(aq), where Cu(+1) is both reduced to Cu(0) and oxidized to Cu(+2). This occurs because Cu⁺ is thermodynamically unstable with respect to Cu(0) and Cu²⁺ in water.

Transition metals have partially filled d orbitals whose energies lie close to one another and are also close to the (n+1)s orbital in energy. This means that a variable number of d electrons can participate in bonding or be removed upon ionization, giving rise to multiple stable oxidation states. For example, Mn can exhibit oxidation states from +2 to +7, corresponding to removal of its 4s and varying numbers of 3d electrons.

For Cu to dissolve: Cu(s) → Cu²⁺(aq) + 2e⁻ (oxidation, E° = −0.34 V) and 2H⁺ + 2e⁻ → H₂(g) (reduction, E° = 0.00 V). E°_cell = 0.00 − 0.34 = −0.34 V. A negative cell potential means ΔG° is positive, so the reaction is not spontaneous. Cu requires an oxidizing acid such as HNO₃ or hot concentrated H₂SO₄ to dissolve.

The Nernst equation is E = E° − (RT/nF) ln Q. For the reduction Mⁿ⁺ + ne⁻ → M(s), Q = 1/[Mⁿ⁺]. Increasing [Mⁿ⁺] decreases Q, which makes the ln Q term more negative, and thus E becomes more positive (more favourable for reduction). This is consistent with Le Chatelier's principle: increasing reactant concentration drives the equilibrium toward products.

An Ellingham diagram plots the standard Gibbs energy of formation (Δ_rG°) against temperature for oxide-forming reactions. A metal oxide can be reduced by carbon at temperatures where the C → CO line lies below the M → M_xO line, because the overall reaction (M_xO + C → M + CO) then has a negative Δ_rG°. This is the thermodynamic basis of carbothermic smelting used in metallurgy.

In a Frost diagram, the y-axis is νE° (the product of oxidation number and standard reduction potential), which is proportional to −Δ_rG°/F. The species at the lowest point is the most thermodynamically stable in aqueous solution. In acidic conditions, NH₄⁺ lies at the bottom of the nitrogen Frost diagram, indicating it is the most stable nitrogen species. This explains why nitrogen compounds tend to be reduced to ammonium in acidic aqueous environments.

In the Latimer diagram for Mn in acidic solution, MnO₄²⁻ (Mn +6) has a higher reduction potential on its right (the potential for the +6 → +4 couple) than on its left (the +7 → +6 couple). This means the reduction of Mn(VI) to Mn(IV) is thermodynamically more favourable than the reduction of Mn(VII) to Mn(VI), so MnO₄²⁻ will spontaneously disproportionate into MnO₄⁻ and MnO₂. This is why manganate(VI) is unstable in acidic solution.

In a Frost diagram, the slope of the line joining two adjacent points equals the standard reduction potential E° for the couple connecting those species. A steeper positive slope indicates a more positive E° (stronger oxidizing couple). This is because νE° = N × E°, so Δ(νE°)/ΔN = E°. Species that form a convex point (local maximum) are unstable with respect to disproportionation, while concave points (local minima) indicate thermodynamic stability.

At pH 7 and E = +0.5 V, the Pourbaix diagram for iron shows the stability field of Fe₂O₃ (or FeOOH), which is an insoluble iron(III) oxide or oxyhydroxide — in other words, rust. This region of the diagram is labelled the "passivation" zone because the insoluble oxide film protects the underlying metal. Metallic Fe is only stable at very negative potentials, and dissolved Fe²⁺ is stable only at low pH and moderate potentials.

Going down group 6, the d orbitals become more diffuse (3d < 4d < 5d in radial extent), which allows better overlap with ligand orbitals, particularly oxygen 2p. This produces stronger M–O bonds in the heavier congeners, thermodynamically stabilizing the +6 oxidation state. Consequently, WO₃ is very stable and W(VI) is not a good oxidizing agent, whereas CrO₃ (with its smaller, less effective 3d orbitals) is a strong oxidizer because Cr(VI) readily accepts electrons.