Redox Reactions

1. Classical Idea: Oxidation & Reduction Reactions

Chemistry is essentially a study of the transformation of matter from one kind into another, and one of the most important classes of such transformations is the redox reaction. Redox processes are involved in combustion, metallurgical extraction, manufacturing of chemicals, batteries, and corrosion.

Classical (oxygen-based) definition: originally, oxidation meant the addition of oxygen (or an electronegative element) to a substance, e.g. $2\text{Mg(s)} + \text{O}_2\text{(g)} \rightarrow 2\text{MgO(s)}$. As chemists' understanding grew, the term was broadened to also include the removal of hydrogen from a substance, e.g. $2\text{H}_2\text{S(g)} + \text{O}_2\text{(g)} \rightarrow 2\text{S(s)} + 2\text{H}_2\text{O(l)}$ (sulphur is oxidised by loss of hydrogen). Correspondingly, reduction was originally the removal of oxygen from a compound, and was later broadened to also include the addition of hydrogen to a substance.

Combined classical definition: oxidation is the addition of oxygen/an electronegative element to a substance, or the removal of hydrogen/an electropositive element from a substance; reduction is the reverse.

Careful examination shows that oxidation and reduction always occur simultaneously — one substance cannot be oxidised unless another is reduced. This is why such reactions are called redox reactions (from reduction + oxidation).

2. Redox Reactions in Terms of Electron Transfer

Consider the reaction $2\text{Na(s)} + \text{Cl}_2\text{(g)} \rightarrow 2\text{NaCl(s)}$. Since sodium chloride is an ionic compound, better written as $\text{Na}^+\text{Cl}^-\text{(s)}$, this reaction can be split into two half reactions:

$$2\text{Na(s)} \rightarrow 2\text{Na}^+\text{(g)} + 2e^-$$

$$\text{Cl}_2\text{(g)} + 2e^- \rightarrow 2\text{Cl}^-\text{(g)}$$

The half reaction that involves loss of electrons is called the oxidation reaction; the half reaction that involves gain of electrons is called the reduction reaction. Their sum gives the overall redox reaction. To summarise:

• Oxidation: loss of electron(s) by any species.
• Reduction: gain of electron(s) by any species.
• Oxidising agent (oxidant): acceptor of electron(s) — itself gets reduced.
• Reducing agent (reductant): donor of electron(s) — itself gets oxidised.

3. Oxidation Number: Rules for Calculation

Many redox reactions (especially those forming covalent compounds, like $\text{H}_2\text{(g)} + \text{Cl}_2\text{(g)} \rightarrow 2\text{HCl(g)}$) do not involve a complete transfer of electrons, only a partial shift in electron density. To keep track of such shifts, the more general and practical method of oxidation number was developed, in which electron transfer is assumed to be complete (for book-keeping purposes only) from the less electronegative atom to the more electronegative atom.

Rules for assigning oxidation number:

1. In the free/uncombined elemental state, every atom has an oxidation number of zero (e.g. H₂, O₂, P₄, Na, Al).
2. For a monoatomic ion, the oxidation number equals the charge on the ion (Na⁺ is +1, Mg²⁺ is +2, Cl⁻ is −1). All alkali metals in their compounds are +1; all alkaline earth metals are +2; aluminium is +3.
3. The oxidation number of oxygen in most compounds is −2. Exceptions: in peroxides (e.g. H₂O₂, Na₂O₂), oxygen is −1; in superoxides (e.g. KO₂), oxygen is −(½); when bonded to fluorine (OF₂, O₂F₂), oxygen is assigned +2 and +1 respectively.
4. Hydrogen is +1 in most compounds, but −1 when bonded to a metal in a binary hydride (e.g. LiH, NaH, CaH₂).
5. Fluorine is always −1 in its compounds. Other halogens are −1 when they occur as halide ions, but can show positive oxidation numbers when combined with oxygen (in oxoacids and oxoanions).
6. The algebraic sum of the oxidation numbers of all atoms in a neutral compound must be zero; in a polyatomic ion, the sum must equal the charge on the ion.

If two or more atoms of the same element are present in a species (e.g. Na₂S₂O₃, Cr₂O₇²⁻), the calculated oxidation number is the average of the oxidation numbers of all such atoms — the true, structurally-revealed oxidation states of individual atoms of that element may differ from this average (a fractional oxidation number, like C in C₃O₂ being 4/3, is never the real state of any single atom — it is only an average).

Oxidation and reduction, redefined using oxidation number: oxidation is an increase in the oxidation number of an element; reduction is a decrease in the oxidation number of an element. An oxidising agent (oxidant) increases the oxidation number of another element; a reducing agent (reductant) decreases it.

4. Types of Redox Reactions

1. Combination reactions ($A + B \rightarrow C$): a redox reaction only if at least one of A or B is in the elemental form, e.g. $\text{C(s)} + \text{O}_2\text{(g)} \rightarrow \text{CO}_2\text{(g)}$. All combustion reactions are redox reactions.

2. Decomposition reactions (opposite of combination): a redox reaction only if at least one product is in the elemental state, e.g. $2\text{H}_2\text{O(l)} \rightarrow 2\text{H}_2\text{(g)} + \text{O}_2\text{(g)}$. Not all decomposition reactions are redox — e.g. $\text{CaCO}_3\text{(s)} \rightarrow \text{CaO(s)} + \text{CO}_2\text{(g)}$ involves no change in any oxidation number, so it is not a redox reaction.

3. Displacement reactions ($X + YZ \rightarrow XZ + Y$): an ion/atom in a compound is replaced by an ion/atom of another element.

• Metal displacement: a metal in a compound is displaced by another metal in the uncombined state, e.g. $\text{CuSO}_4\text{(aq)} + \text{Zn(s)} \rightarrow \text{Cu(s)} + \text{ZnSO}_4\text{(aq)}$. This underlies the activity/electrochemical series (Zn > Cu > Ag in electron-releasing tendency).
• Non-metal displacement (mainly hydrogen displacement): alkali metals and some alkaline earth metals (Ca, Sr, Ba) displace hydrogen from cold water; less active metals like Mg and Fe displace it only from steam; many metals displace hydrogen from acids. Very unreactive metals like Ag and Au do not react even with hydrochloric acid. A rarer case is halogen displacement: fluorine can displace Cl⁻, Br⁻ and I⁻ from solution, and chlorine can displace Br⁻ and I⁻ (this is the basis of the "layer test" for identifying Br⁻/I⁻) — the oxidising strength of halogens decreases down group 17: F₂ > Cl₂ > Br₂ > I₂.

4. Disproportionation reactions: a special type of redox reaction in which an element in ONE intermediate oxidation state is simultaneously oxidised and reduced, giving both a higher and a lower oxidation state of that element as products. A classic example is the decomposition of hydrogen peroxide:

$$2\text{H}_2\text{O}_2\text{(aq)} \rightarrow 2\text{H}_2\text{O(l)} + \text{O}_2\text{(g)}$$

Here oxygen goes from −1 in H₂O₂ to −2 in H₂O (reduced) and to 0 in O₂ (oxidised), simultaneously. Phosphorus, sulphur and chlorine also undergo disproportionation in alkaline medium (e.g. Cl₂ + 2OH⁻ → ClO⁻ + Cl⁻ + H₂O, the basis of household bleach). A species can disproportionate only if the element in it is NOT already in its highest or lowest possible oxidation state.

5. Balancing Redox Reactions

Two methods are used to balance redox equations; both are equally valid and the choice rests with the individual.

(a) Oxidation number method:

1. Write the correct skeletal formula for each reactant and product.
2. Assign oxidation numbers and identify the atoms undergoing a change.
3. Calculate the increase/decrease in oxidation number per atom (or per formula unit), and multiply by suitable numbers so that the total increase equals the total decrease.
4. If the reaction occurs in acidic solution, add H⁺ ions (or OH⁻ ions if basic) to balance the ionic charges on both sides.
5. Balance hydrogen atoms by adding H₂O molecules, then verify oxygen atoms balance automatically.

(b) Half reaction (ion-electron) method: the equation is split into an oxidation half-reaction and a reduction half-reaction, each is balanced separately for atoms and then for charge (by adding electrons), and the two half-reactions are then combined — after multiplying each by a suitable factor so the number of electrons lost equals the number gained — cancelling the electrons to give the final balanced net ionic equation. For a reaction in basic medium, atoms are first balanced as if in acidic medium, and then an equal number of OH⁻ ions are added to both sides to neutralise the H⁺ ions used (combining H⁺ and OH⁻ on the same side into H₂O).

6. Redox Reactions as the Basis for Titrations

Just as acid–base titrations use a pH-sensitive indicator, redox titrations use the oxidant/reductant's own colour or a redox-sensitive indicator to detect the equivalence point:

• Self-indicating titrant: KMnO₄ is so intensely coloured (purple) that it acts as its own indicator — the first permanent faint pink tinge signals the endpoint once all the reductant (e.g. Fe²⁺ or oxalate) is consumed.
• External indicator: with K₂Cr₂O₇ (not self-indicating), a substance like diphenylamine is oxidised right after the equivalence point, producing a sharp blue colour.
• Starch-iodine method: iodine gives an intense blue colour with starch; in iodometric titrations, I₂ liberated from an oxidant reacting with excess I⁻ is titrated against thiosulphate (S₂O₃²⁻), and the blue colour disappears exactly when all the iodine is consumed, marking a sharp endpoint.

7. Limitations of the Concept of Oxidation Number

The oxidation number method assumes a complete transfer of electrons even in covalent compounds, which is a book-keeping convenience, not a physical reality — in reactions like $\text{H}_2\text{(g)} + \text{Cl}_2\text{(g)} \rightarrow 2\text{HCl(g)}$, the charge transfer is only a partial shift in electron density, better described as an electron shift than a complete electron loss/gain. Modern understanding visualises the oxidation process as a decrease in electron density around an atom, and reduction as an increase in electron density, rather than literal electron transfer.

8. Redox Reactions & Electrode Processes

When zinc metal is placed in copper sulphate solution, electron transfer from Zn to Cu²⁺ happens directly (with heat evolved), but this transfer can also be made to happen indirectly by physically separating the two half-reactions into two beakers connected by a salt bridge and an external metallic wire — this setup is called a Daniell cell.

A redox couple is defined as having together the oxidised and reduced forms of a substance participating in a half-reaction (written as oxidised form/reduced form, e.g. Zn²⁺/Zn and Cu²⁺/Cu). The potential difference developed at each electrode is called the electrode potential; when the concentration of every species in the electrode reaction is unity (1 atm for any gas) at 298 K, it is called the standard electrode potential (E°). By convention, the standard electrode potential of the hydrogen electrode is taken as exactly 0.00 V, and all other standard electrode potentials are measured relative to it (as standard reduction potentials).

Reading the electrochemical series:

• A more negative E° means the reduced form (e.g. Li, K, Mg) is a stronger reducing agent than H₂ — it more readily loses electrons.
• A more positive E° means the oxidised form (e.g. F₂, MnO₄⁻, Cr₂O₇²⁻) is a stronger oxidising agent than H⁺ — it more readily gains electrons.
• This ordering predicts spontaneity: a species higher up (more positive E°, e.g. Cu²⁺/Cu at +0.34 V) can oxidise the reduced form of any couple below it (more negative E°, e.g. Zn²⁺/Zn at −0.76 V) — this is exactly why zinc displaces copper from copper sulphate solution, but not the reverse.