Reactivity 3.2.2 — Half-Equations in Redox Reactions

Redox (reduction–oxidation) reactions involve the transfer of electrons. To clearly analyze and balance redox reactions, chemists write them as two separate processes—called half-equations—representing the oxidation and the reduction steps individually.

A half-equation shows either:

• The loss of electrons (oxidation)
• The gain of electrons (reduction)

These equations explicitly include electrons as either reactants or products.

Rules for Writing Half-Equations:

1. Write the correct formula for the species being oxidized or reduced.
2. Balance atoms other than H and O first.
3. Balance oxygen atoms using \( \text{H}_2\text{O} \).
4. Balance hydrogen atoms using \( \text{H}^+ \) (if in acidic solution).
5. Balance charges by adding electrons \( \text{e}^- \).

Combining Half-Equations:

To obtain the full redox equation:

• Ensure the number of electrons lost in oxidation equals the number gained in reduction.
• Multiply each half-equation accordingly before adding.
• Cancel out identical species on both sides (e.g., electrons, water, \( \text{H}^+ \)).

Working in Different Media:

• Acidic solution: Use \( \text{H}_2\text{O} \), \( \text{H}^+ \), and \( \text{e}^- \).
• Neutral solution: Use the same method as acidic, but the presence of \( \text{H}^+ \) should reflect neutral conditions (may require balancing with \( \text{OH}^- \) in real scenarios—though not emphasized in the IBDP unless basic medium is specified).

Example Half-Equations (Acidic Medium):

• Oxidation (Fe²⁺ to Fe³⁺):
  \( \text{Fe}^{2+} \rightarrow \text{Fe}^{3+} + \text{e}^- \)
• Reduction (MnO₄^– to Mn²⁺):
  \( \text{MnO}_4^- + 8\text{H}^+ + 5\text{e}^- \rightarrow \text{Mn}^{2+} + 4\text{H}_2\text{O} \)

Full Redox Equation:

Multiply the iron half-equation by 5 and add:

\( 5\text{Fe}^{2+} + \text{MnO}_4^- + 8\text{H}^+ \rightarrow 5\text{Fe}^{3+} + \text{Mn}^{2+} + 4\text{H}_2\text{O} \)

Example Half-Equations (Neutral Solution):

Sometimes you are given a redox reaction occurring in neutral water without excess acid. The mechanism is the same, but be cautious not to oversupply \( \text{H}^+ \).

Example: Oxidation of zinc in water:

\( \text{Zn} \rightarrow \text{Zn}^{2+} + 2\text{e}^- \)

Common Oxidizing Agents (Reduced in reactions):

• \( \text{MnO}_4^- \rightarrow \text{Mn}^{2+} \)
• \( \text{Cr}_2\text{O}_7^{2-} \rightarrow \text{Cr}^{3+} \)
• \( \text{Cl}_2 \rightarrow \text{Cl}^- \)

Common Reducing Agents (Oxidized in reactions):

• \( \text{Fe}^{2+} \rightarrow \text{Fe}^{3+} \)
• \( \text{H}_2 \rightarrow 2\text{H}^+ \)
• \( \text{SO}_3^{2-} \rightarrow \text{SO}_4^{2-} \)