Half Equations for Electrode Reactions | Chemistry

📖 In-Depth Theory

What Are Half Equations?

A HALF EQUATION shows what happens at just ONE electrode during electrolysis — either the oxidation at the anode OR the reduction at the cathode.

Half equations must be:

ATOM BALANCED — same number of each atom on both sides.

CHARGE BALANCED — same total charge on both sides, using electrons (e⁻).

At the CATHODE (reduction — GAIN of electrons):

Positive ions gain electrons and become neutral atoms or molecules.

General form: positive ion + ne⁻ → neutral species

At the ANODE (oxidation — LOSS of electrons):

Negative ions lose electrons and become neutral atoms or molecules.

General form: negative ion → neutral species + ne⁻

Writing Half Equations — Key Examples

CATHODE EXAMPLES (reduction):

Copper deposition: Cu²⁺ + 2e⁻ → Cu

Aluminium deposition: Al³⁺ + 3e⁻ → Al

Hydrogen production: 2H⁺ + 2e⁻ → H₂

Sodium deposition (molten NaCl): Na⁺ + e⁻ → Na

ANODE EXAMPLES (oxidation):

Chlorine production: 2Cl⁻ → Cl₂ + 2e⁻

Oxygen production: 4OH⁻ → O₂ + 2H₂O + 4e⁻

Bromide oxidation: 2Br⁻ → Br₂ + 2e⁻

Copper dissolution (Cu anode): Cu → Cu²⁺ + 2e⁻

Oxide ion oxidation (Al extraction): 2O²⁻ → O₂ + 4e⁻

HOW TO BALANCE A HALF EQUATION:

1. Write the species on each side.

2. Balance atoms (add H₂O for oxygen, H⁺ for hydrogen if needed).

3. Count total charge on each side.

4. Add electrons to the MORE POSITIVE side to balance charge.

Combining Half Equations

The OVERALL equation for electrolysis = cathode half equation + anode half equation.

The electrons produced at the anode MUST equal the electrons consumed at the cathode.

If not, multiply one or both half equations by appropriate factors.

EXAMPLE — electrolysis of copper sulfate with copper electrodes:

Cathode: Cu²⁺ + 2e⁻ → Cu

Anode: Cu → Cu²⁺ + 2e⁻

Overall: Cu(anode) → Cu(cathode) [copper transferred from anode to cathode]

EXAMPLE — electrolysis of molten NaCl:

Cathode: Na⁺ + e⁻ → Na (×2)

Anode: 2Cl⁻ → Cl₂ + 2e⁻

Multiply cathode by 2: 2Na⁺ + 2e⁻ → 2Na

Overall: 2Na⁺ + 2Cl⁻ → 2Na + Cl₂

i.e. 2NaCl → 2Na + Cl₂ ✓

EXAMPLE — electrolysis of dilute H₂SO₄:

Cathode: 2H⁺ + 2e⁻ → H₂

Anode: 4OH⁻ → O₂ + 2H₂O + 4e⁻ (×1) and cathode ×2: 4H⁺ + 4e⁻ → 2H₂

Overall: 2H₂O → 2H₂ + O₂ ✓ (water is split)

⚠️ Common Mistake

Electrons are written on the LEFT of cathode half equations (gained) and on the RIGHT of anode half equations (lost). Also: the number of electrons in each half equation must match when you combine them to get the overall equation — multiply as needed.

📐 Key Equations

Cathode: Cu²⁺ + 2e⁻ → Cu

Cathode: 2H⁺ + 2e⁻ → H₂

Anode: 2Cl⁻ → Cl₂ + 2e⁻

Anode: 4OH⁻ → O₂ + 2H₂O + 4e⁻

Anode: Cu → Cu²⁺ + 2e⁻

📌 Key Note

Half equations: show one electrode reaction. Cathode: cation + ne⁻ → product (reduction). Anode: anion → product + ne⁻ (oxidation). Must be atom AND charge balanced. Combine cathode + anode (matching electrons) to get overall equation. OIL RIG — anode oxidises, cathode reduces.

🎯 Matching Activity — Match the Half Equation to its Electrode

Match each half equation to cathode (reduction) or anode (oxidation). — drag the symbols on the right to match the component names on the left.

Cathode

Drop here

Cathode

Drop here

Anode

Drop here

Anode

Drop here

Anode

Drop here

2Cl⁻ → Cl₂ + 2e⁻ — chloride ions lose electrons to form Cl₂

2O²⁻ → O₂ + 4e⁻ — oxide ions lose electrons to form O₂

2H⁺ + 2e⁻ → H₂ — hydrogen ions gain electrons to form H₂ gas

Cu → Cu²⁺ + 2e⁻ — copper atoms lose electrons (copper anode dissolves)

Al³⁺ + 3e⁻ → Al — aluminium ions gain 3 electrons

⚽ FIFA Worked Examples

Balancing a Half Equation

Balance the half equation for chloride ions forming chlorine at the anode: Cl⁻ → Cl₂.

F

Balance atoms first, then charges

I

2Cl⁻ → Cl₂ (2 Cl each side — atoms balanced). Left charge: 2×(−1) = −2. Right charge: 0.

F

Add 2e⁻ to the right to balance: 2Cl⁻ → Cl₂ + 2e⁻. Left: −2. Right: −2. ✓

A

2Cl⁻ → Cl₂ + 2e⁻

🎯 Test Yourself

Question 1 of 2

1. Which is the correct half equation for the reduction of copper ions at the cathode?

2. In electrolysis of molten NaCl, the cathode produces Na and the anode produces Cl₂. What is the overall balanced equation?

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🧪 Half Equations for Electrode Reactions

What Are Half Equations?

Writing Half Equations — Key Examples

Combining Half Equations

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