Redox Reactions And Electrochemistry

Almost every year NEET asks something from this pair of chapters — an oxidation-number puzzle, a balancing question, a Nernst equation calculation, or a numerical on Faraday's laws. The two halves are really one idea: redox chemistry describes electron transfer, and electrochemistry is what happens when we force those electrons to travel through a wire so we can measure or use them.

Oxidation, Reduction and Oxidation Number

The oldest definition tied oxidation to gaining oxygen and reduction to losing it. That is too narrow. The modern electronic view is general:

• Oxidation = loss of electrons = increase in oxidation number (O.N.)
• Reduction = gain of electrons = decrease in oxidation number
• The species that causes oxidation is the oxidising agent (it is itself reduced); the species that causes reduction is the reducing agent (it is itself oxidised).

A useful mental hook: the oxidising agent is the electron thief, the reducing agent is the electron donor. In Zn + Cu²⁺ → Zn²⁺ + Cu, zinc donates two electrons (oxidised, reducing agent) and Cu²⁺ accepts them (reduced, oxidising agent).

Oxidation number is a bookkeeping charge: the charge an atom would carry if every bond it forms were treated as fully ionic, with the shared pair assigned to the more electronegative partner. Rules for assigning it:

1. Free elements have O.N. = 0 (including O₂, P₄, S₈, graphite).
2. For a monatomic ion, O.N. = its charge (Na⁺ = +1, S²⁻ = −2).
3. Fluorine is always −1 in compounds. Other halogens are usually −1 but can be positive when bonded to oxygen or a lighter halogen.
4. Oxygen is normally −2; it is −1 in peroxides (H₂O₂, Na₂O₂), −½ in superoxides (KO₂), and +2 in OF₂, +1 in O₂F₂.
5. Hydrogen is +1 with non-metals, −1 in metal hydrides (NaH, CaH₂).
6. Group 1 metals are +1, Group 2 metals +2 in compounds.
7. The algebraic sum of oxidation numbers equals zero for a neutral molecule and equals the charge for a polyatomic ion.

O.N. need not be a whole number — it is an average. In Fe₃O₄ iron averages +8/3 (really a mixture of Fe²⁺ and Fe³⁺); in S₄O₆²⁻ (tetrathionate) sulphur averages +2.5. Also remember that an element's O.N. can never exceed its group-based maximum: nitrogen cannot go beyond +5, sulphur beyond +6, manganese beyond +7. This is why HNO₃, H₂SO₄, KMnO₄ can only act as oxidising agents, while H₂S or HI (S at −2, I at −1, already at minimum) can only act as reducing agents. Species with an intermediate O.N. — H₂O₂ (O = −1), SO₂ (S = +4), HNO₂ — can act either way.

Types of Redox Reactions

Four standard categories, each a favourite for one-mark recognition questions:

1. Combination — an element combines with another; at least one reactant must be a free element. Example: C + O₂ → CO₂.
2. Decomposition — a compound breaks into simpler substances with a change in O.N. Example: 2KClO₃ → 2KCl + 3O₂. (Note: CaCO₃ → CaO + CO₂ is not redox, since no O.N. changes.)
3. Displacement — one ion or atom is replaced by another. Metal displacement: CuSO₄ + Zn → ZnSO₄ + Cu. Non-metal displacement: 2Na + 2H₂O → 2NaOH + H₂, or Cl₂ + 2Br⁻ → 2Cl⁻ + Br₂.
4. Disproportionation — one element in a single substance is simultaneously oxidised and reduced; it must therefore start in an intermediate oxidation state. Examples:
   • 2H₂O₂ → 2H₂O + O₂ (O goes −1 → −2 and −1 → 0)
   • Cl₂ + 2OH⁻ → Cl⁻ + ClO⁻ + H₂O
   • 4KClO₃ → 3KClO₄ + KCl
   • 3MnO₄²⁻ + 4H⁺ → 2MnO₄⁻ + MnO₂ + 2H₂O

The reverse of disproportionation, where two different oxidation states of one element converge to a single intermediate state, is sometimes called comproportionation (e.g. IO₃⁻ + 5I⁻ + 6H⁺ → 3I₂ + 3H₂O).

Balancing Redox Equations

Oxidation-number method: write the skeletal equation, find the atoms whose O.N. changes, compute the total increase and total decrease, and multiply the species by suitable integers so that total increase = total decrease. Then balance the remaining atoms — O by adding H₂O, H by adding H⁺ (acidic medium).

Half-reaction (ion-electron) method — more reliable for ionic equations:

1. Split the reaction into an oxidation half and a reduction half in ionic form.
2. Balance all atoms except H and O.
3. Balance O by adding H₂O to the deficient side.
4. Balance H by adding H⁺.
5. Balance charge by adding electrons to the more positive side.
6. Multiply the halves so the electrons cancel, then add them.
7. If the medium is basic, add as many OH⁻ as there are H⁺ to both sides at the end, and combine H⁺ + OH⁻ into H₂O.

Worked skeleton: MnO₄⁻ + Fe²⁺ → Mn²⁺ + Fe³⁺ (acidic). Reduction: MnO₄⁻ + 8H⁺ + 5e⁻ → Mn²⁺ + 4H₂O. Oxidation: Fe²⁺ → Fe³⁺ + e⁻ (×5). Overall: MnO₄⁻ + 5Fe²⁺ + 8H⁺ → Mn²⁺ + 5Fe³⁺ + 4H₂O.

Remember the medium-dependent behaviour of permanganate: MnO₄⁻ gains 5e⁻ in acid (→ Mn²⁺), 3e⁻ in neutral/faintly alkaline medium (→ MnO₂), and 1e⁻ in strongly alkaline medium (→ MnO₄²⁻). Dichromate in acid: Cr₂O₇²⁻ + 14H⁺ + 6e⁻ → 2Cr³⁺ + 7H₂O.

Two related quantitative ideas: in a redox titration the equivalence point satisfies (equivalents of oxidant = equivalents of reductant), and the n-factor of a species is the number of electrons it gains or loses per formula unit (5 for KMnO₄ in acid, 6 for K₂Cr₂O₇, 2 for oxalic acid). Equivalent mass = molar mass / n-factor.

Galvanic Cells and Electrode Potentials

If zinc metal is dipped in copper sulphate, electrons pass directly from Zn to Cu²⁺ and the energy appears as heat. Separate the two half-reactions into two beakers joined by a salt bridge and connect the metals with a wire, and the same reaction drives a current: that is a galvanic (voltaic) cell — a device converting chemical energy to electrical energy.

Conventions you must not mix up:

• Anode = oxidation, and in a galvanic cell it is the negative terminal. Cathode = reduction, positive terminal.
• Electrons flow through the external wire from anode to cathode; conventional current flows the opposite way; in solution, anions migrate to the anode and cations to the cathode.
• In electrolytic cells the anode is connected to the positive terminal of the battery, so the anode is positive there. Oxidation-at-anode never changes.
• Cell notation: anode written on the left. Zn(s) | Zn²⁺(1 M) ‖ Cu²⁺(1 M) | Cu(s); single bar = phase boundary, double bar = salt bridge.
• The salt bridge (KCl or KNO₃ in agar) completes the circuit and prevents accumulation of charge (eliminates liquid-junction potential); it does not carry electrons.

Every half-cell has an electrode potential. Since only differences are measurable, potentials are quoted relative to the standard hydrogen electrode (Pt, H₂ at 1 bar, H⁺ = 1 M), assigned E° = 0.00 V at all temperatures. By IUPAC convention we tabulate standard reduction potentials. Then

E°cell = E°cathode − E°anode (both as reduction potentials)

A positive E°cell means ΔG° is negative and the cell reaction is spontaneous as written. In the electrochemical series, arranged by increasing E°, species at the top-left (F₂, MnO₄⁻, Cl₂) are strong oxidising agents; metals with very negative E° (Li, K, Ca, Na) are strong reducing agents. A metal displaces from solution any metal ion lying below it in reducing power — Zn (−0.76 V) displaces Cu²⁺ (+0.34 V), but not the reverse.

Nernst Equation, ΔG and Equilibrium

Electrode potential depends on concentration. For the half-reaction M^n⁺ + ne⁻ → M:

E = E° − (RT/nF) ln ([M]/[M^n⁺]) = E° − (0.0591/n) log (1/[M^n⁺]) at 298 K

For a general cell reaction aA + bB → cC + dD,

E_cell = E°_cell − (0.0591/n) log ( [C]^c[D]^d / [A]^a[B]^b )

Points to keep straight:

• Solids and pure liquids take activity 1; gases enter as partial pressures in bar.
• As the cell operates, products build up, the log term grows and E falls. At equilibrium E_cell = 0 and Q = K_c, giving E°cell = (0.0591/n) log K_c.
• ΔG = −nFE and ΔG° = −nFE°cell, with F = 96487 ≈ 96500 C mol⁻¹. Note E is an intensive property, so it does not change if you double the equation, but ΔG (extensive) does — because n doubles too.
• A concentration cell has E° = 0, and its entire EMF arises purely from the difference in concentration between the two half-cells (e.g. Zn(s) | Zn²⁺(c₁) ‖ Zn²⁺(c₂) | Zn(s), with c₂ > c₁): as current flows, dilute side loses metal and concentrated side deposits it, the two concentrations converge, and E falls steadily to zero once they become equal — at that point the cell can do no further work and is said to be run down.

Conductance, Molar Conductivity and Kohlrausch's Law

Electrolytic solutions conduct because ions, not electrons, carry the current. Conductivity (κ), the reciprocal of resistivity, measures how well a solution of given concentration conducts; molar conductivity (Λ_m) normalises this to a fixed amount of electrolyte:

Λ_m = κ / c (with c in mol m⁻³, so that Λ_m carries units of S m² mol⁻¹; the more common working unit is S cm² mol⁻¹ with c in mol L⁻¹ and an appropriate factor of 1000)

Both κ and Λ_m change with dilution, but in opposite directions and for different reasons. Conductivity always decreases on dilution, simply because there are fewer ions per unit volume to carry charge. Molar conductivity always increases on dilution, because it is normalised per mole of electrolyte, and dilution improves how effectively that fixed amount of electrolyte conducts:

• For a strong electrolyte, ions are already 100% dissociated even at moderate concentration; the rise in Λ_m on dilution comes only from reduced inter-ionic attraction letting ions move faster. Λ_m rises smoothly and, plotted against √c, extrapolates linearly to a finite value Λ_m° (limiting molar conductivity) at infinite dilution.
• For a weak electrolyte, the degree of dissociation itself increases sharply on dilution (Ostwald's dilution law again), so Λ_m rises steeply and without any linear trend; the plot cannot be extrapolated graphically to reach Λ_m°.

Kohlrausch's law of independent migration of ions solves exactly this problem: at infinite dilution, each ion contributes a fixed amount to the total molar conductivity, independent of the other ion it is paired with —

Λ_m°(electrolyte) = ν₊λ°₊ + ν₋λ°₋

where λ°₊ and λ°₋ are the limiting ionic conductivities and ν₊, ν₋ the number of cations/anions per formula unit. This lets us calculate Λ_m° for a weak electrolyte like acetic acid indirectly, by combining the (measurable, extrapolatable) Λ_m° values of strong electrolytes that share its ions:

Λ_m°(CH₃COOH) = Λ_m°(CH₃COONa) + Λ_m°(HCl) − Λ_m°(NaCl)

The degree of dissociation of a weak electrolyte at any concentration then follows as α = Λ_m(c) / Λ_m°, and since K_a = cα²/(1−α), this is also how conductivity measurements yield the dissociation constant of a weak acid experimentally.

Electrolytic cells, batteries and corrosion round out the practical side of the chapter. In electrolysis, Faraday's first law states that the mass deposited/liberated at an electrode is proportional to the charge passed (m = ZQ = ZIt, Z being the electrochemical equivalent), and the second law states that for a fixed charge, masses of different substances liberated are proportional to their equivalent masses. Common primary cells (non-rechargeable) include the dry (Leclanché) cell and mercury cell; the lead storage battery and nickel–cadmium cell are rechargeable secondary cells; fuel cells (H₂–O₂) convert chemical energy directly and continuously as reactants are fed in, without needing to store the reactants inside the cell itself. Corrosion (rusting of iron) is fundamentally an electrochemical process: an oxidation region (anode, bare metal) and a reduction region (cathode, where dissolved O₂ is reduced) exist on the same metal surface, connected by moisture acting as the electrolyte; galvanising (zinc coating) and connecting a more reactive metal (sacrificial anode) both work by ensuring the protected iron becomes the cathode instead.

Common Mistakes and Exam Traps

• Reversing the E°cell formula. The correct relation is E°cell = E°cathode − E°anode, using both as reduction potentials by IUPAC convention; swapping the subtraction order or mixing in an oxidation potential for one electrode is one of the most frequent sign errors in this chapter.
• Forgetting that ΔG is extensive but E is intensive. Doubling a cell reaction's stoichiometric coefficients leaves E° unchanged but doubles n and hence doubles ΔG° (since ΔG° = −nFE°) — students who assume both quantities scale the same way get half-marks numericals wrong.
• Assuming molar conductivity and conductivity always move the same way on dilution. Conductivity (κ) always falls with dilution because ion density drops, while molar conductivity (Λ_m) always rises with dilution because it is normalised per mole — treating them as moving together is a very common confusion.
• Trying to extrapolate a weak electrolyte's Λ_m vs √c graph to get Λ_m°. This graphical extrapolation only works for strong electrolytes, whose Λ_m vs √c plot is linear; a weak electrolyte's plot shoots up steeply near c = 0 and cannot be extrapolated, which is exactly why Kohlrausch's law of independent migration is needed instead.