Gr 11 · Electrochemistry · Deep Study

Electrons in Motion

Electrochemistry is about one fundamental process: the transfer of electrons between substances. This guide builds from OIL RIG through oxidation numbers, half-reaction balancing, galvanic cells, standard potentials, and electrolysis — with the reasoning behind every step.

5 sections Worked examples with steps Checkpoint questions Intuition-first explanations
1
Oxidation & Reduction
OIL RIG and the language of electron transfer

Electrochemistry is built on one concept: electrons move from one species to another. The species that loses electrons is oxidized. The species that gains electrons is reduced. These two processes always happen together — electrons must go somewhere.

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OIL RIG: Oxidation Is Loss (of electrons)  —  Reduction Is Gain (of electrons)

Agents: The reducing agent donates electrons → it is itself oxidized. The oxidizing agent accepts electrons → it is itself reduced. This reversal trips up many students — the oxidizing agent gets reduced.
💭
Why can’t oxidation happen without reduction?
Electrons cannot float free in solution. For one species to lose electrons, those electrons must immediately be captured by another species. You can’t have a “half-redox” — both half-reactions are always happening simultaneously.
ProcessWhat happensOxidation stateSpecies is the…
OxidationLoses e&sup-;IncreasesReducing agent
ReductionGains e&sup-;DecreasesOxidizing agent
★ Easy
Identify oxidation and reduction in a reaction
In the reaction: Mg + CuSO⊂4; → MgSO⊂4; + Cu, identify what is oxidized, what is reduced, and the oxidizing and reducing agents.
Show solution
1
Assign oxidation states before and after
Mg: 0 → +2     (increases: oxidized) Cu: +2 → 0     (decreases: reduced) SO⊂4;: −2 unchanged (spectator)
2
Write half-reactions
Mg → Mg²+ + 2e&sup-;     (oxidation) Cu²+ + 2e&sup-; → Cu     (reduction)
3
Identify agents

Mg is oxidized → Mg is the reducing agent. Cu²+ is reduced → Cu²+ (CuSO⊂4;) is the oxidizing agent.

Answer: Mg is oxidized (reducing agent). Cu²+ is reduced (oxidizing agent).
✓ Checkpoint 1
a) In 2Al + 3Cl⊂2; → 2AlCl⊂3;: identify what is oxidized, what is reduced, and the two agents.
b) True or false: “A reducing agent gains electrons.” Explain.
c) Describe in one sentence why oxidation and reduction must always occur together.

a) Al: 0 → +3 (oxidized, reducing agent). Cl: 0 → −1 (reduced, oxidizing agent). AlCl⊂3; half-reactions: Al → Al³+ + 3e&sup-; (oxidation); Cl⊂2; + 2e&sup-; → 2Cl&sup-; (reduction).

b) False. A reducing agent donates electrons (loses them), so it is itself oxidized. It reduces another species by giving it electrons.

c) Electrons cannot exist freely in solution; every electron released by an oxidized species must immediately be captured by another species that is reduced.

2
Oxidation Numbers
Tracking electron distribution with assigned numbers

Oxidation numbers (oxidation states) are a bookkeeping tool that lets us track which atoms gained or lost electrons in a reaction. They are assigned, not measured — they represent a hypothetical charge if the compound were purely ionic.

The Rules (in priority order)

  • Rule 1: Pure element → oxidation number = 0. (Na, O⊂2;, P⊂4;, Fe are all 0.)
  • Rule 2: Monatomic ion → oxidation number = ionic charge. (Cl&sup-; = −1, Ca²+ = +2.)
  • Rule 3: Fluorine is always −1.
  • Rule 4: Oxygen is −2 in most compounds. Exceptions: peroxides (e.g. H⊂2;O⊂2;): −1; OF⊂2;: +2.
  • Rule 5: Hydrogen is +1 bonded to nonmetals; −1 in metal hydrides (NaH, CaH⊂2;).
  • Rule 6: Sum of all oxidation numbers = 0 (neutral compound) or = net charge (ion).
Strategy: Assign the known elements first (O = −2, H = +1), then use Rule 6 to find the unknown. This works for the majority of Grade 11 problems.
★ Easy
Find oxidation number of Cr in Cr⊂2;O⊂7;²−
What is the oxidation state of chromium in the dichromate ion Cr⊂2;O⊂7;²−?
Show solution
1
Assign O = −2
7 oxygen atoms × (−2) = −14
2
Use Rule 6: sum = overall charge (−2)
2Cr + (−14) = −2
2Cr = 12
Cr = +6
Answer: Cr = +6 in Cr⊂2;O⊂7;²−
★★ Medium
Identify the redox change in a reaction
Is this a redox reaction? Fe⊂2;O⊂3; + 3CO → 2Fe + 3CO⊂2;
Show solution
1
Assign OS to Fe
Fe⊂2;O⊂3;: 2Fe + 3(−2) = 0 → Fe = +3
Products: Fe(s) = 0
Change: +3 → 0 (decrease) → Fe is REDUCED
2
Assign OS to C in CO and CO⊂2;
CO: C + (−2) = 0 → C = +2
CO⊂2;: C + 2(−2) = 0 → C = +4
Change: +2 → +4 (increase) → C is OXIDIZED
3
Conclusion

Yes, it is redox. Fe is reduced (Fe⊂2;O⊂3; is the oxidizing agent). CO is oxidized (CO is the reducing agent).

Answer: Yes — Fe is reduced (+3→0), C is oxidized (+2→+4). This is the blast furnace reduction of iron ore.
✓ Checkpoint 2
a) Find the oxidation state of N in: (i) NO⊂2;, (ii) NO⊂3;&sup-;, (iii) N⊂2;H⊂4;
b) In the peroxide H⊂2;O⊂2;, what is the oxidation state of O? Why is it different from the usual −2?
c) Identify the OS change in: Cl⊂2; + 2KBr → 2KCl + Br⊂2;. What is oxidized and what is reduced?

a) (i) NO⊂2;: N + 2(−2) = 0 → N = +4. (ii) NO⊂3;&sup-;: N + 3(−2) = −1 → N = +5. (iii) N⊂2;H⊂4;: 2N + 4(+1) = 0 → 2N = −4 → N = −2.

b) O in H⊂2;O⊂2; = −1. In H⊂2;O⊂2;: 2(+1) + 2O = 0 → O = −1. The two oxygen atoms are bonded to each other (O–O bond) in addition to H, so they don’t draw a full 2 extra electrons as they would in a normal compound. The O–O bond shares electrons symmetrically between two identical atoms.

c) Cl⊂2;: Cl = 0 → KCl: Cl = −1 (decreases: Cl⊂2; is reduced, oxidizing agent). KBr: Br = −1 → Br⊂2;: Br = 0 (increases: Br&sup-; is oxidized, reducing agent).

3
Balancing Redox Equations
The half-reaction method in acidic solution

Redox equations must balance for both atoms and charge. The half-reaction method splits the reaction into two separate equations and balances them independently before combining.

Steps for Acidic Solution

  • Step 1: Write the unbalanced net ionic equation. Remove spectator ions.
  • Step 2: Split into oxidation half-reaction and reduction half-reaction.
  • Step 3: Balance atoms other than O and H in each half-reaction.
  • Step 4: Add H⊂2;O to balance oxygen atoms.
  • Step 5: Add H&sup+; to balance hydrogen atoms.
  • Step 6: Add e&sup-; to balance charge on each side of each half-reaction.
  • Step 7: Multiply each half-reaction by integers so electrons cancel exactly.
  • Step 8: Add the two half-reactions. Cancel electrons and any species appearing on both sides.
  • Step 9: Check: all atoms balanced, net charge balanced.
⚠️
Do NOT multiply E° values when you multiply half-reactions. E° is an intensive property (like temperature — it doesn’t double if you scale the reaction). Only coefficients and mole quantities are multiplied.
★★ Medium
Balance a redox equation — MnO⊂4;&sup-; + Fe²+
Balance: MnO⊂4;&sup-; + Fe²+ → Mn²+ + Fe³+ (acidic solution)
Show solution
1
OS check: identify the changes
Mn: +7 → +2 (reduced). Fe: +2 → +3 (oxidized).
2
Write half-reactions (unbalanced)
Reduction: MnO⊂4;&sup-; → Mn²+
Oxidation: Fe²+ → Fe³+
3
Balance reduction half: add 4H⊂2;O for 4 O, then 8H&sup+;
MnO⊂4;&sup-; + 8H&sup+; → Mn²+ + 4H⊂2;O
4
Balance charge in reduction: add 5e&sup-; to left
Left: −1 + 8 = +7. Right: +2. Need to add 5e&sup-; to left: MnO⊂4;&sup-; + 8H&sup+; + 5e&sup-; → Mn²+ + 4H⊂2;O ✓ (Left: −1+8−5=+2. Right: +2. ✓)
5
Balance oxidation half: add 1e&sup-; to right
Fe²+ → Fe³+ + e&sup-; ✓
6
Equalize electrons: multiply oxidation × 5
5Fe²+ → 5Fe³+ + 5e&sup-;
7
Add the two half-reactions (5e&sup-; cancel)
MnO⊂4;&sup-; + 8H&sup+; + 5Fe²+ → Mn²+ + 4H⊂2;O + 5Fe³+
Answer: MnO⊂4;&sup-; + 8H&sup+; + 5Fe²+ → Mn²+ + 5Fe³+ + 4H⊂2;O
✓ Checkpoint 3
a) Balance: Cr⊂2;O⊂7;²− + C⊂2;O⊂4;²− → Cr³+ + CO⊂2; (acidic). Identify what is oxidized and what is reduced.
b) How many electrons are transferred in total per formula unit of Cr⊂2;O⊂7;²− that reacts?

a) Cr: +6 → +3 (reduced −3 per Cr, −6 total for Cr⊂2;). C: +3 → +4 (oxidized +1 per C, +2 per C⊂2;O⊂4;²−).

Reduction: Cr⊂2;O⊂7;²− + 14H&sup+; + 6e&sup-; → 2Cr³+ + 7H⊂2;O

Oxidation: C⊂2;O⊂4;²− → 2CO⊂2; + 2e&sup-;

Multiply oxidation × 3: 3C⊂2;O⊂4;²− → 6CO⊂2; + 6e&sup-;

Cr⊂2;O⊂7;²− + 14H&sup+; + 3C⊂2;O⊂4;²− → 2Cr³+ + 7H⊂2;O + 6CO⊂2;

b) 6 electrons transferred per Cr⊂2;O⊂7;²− (3 per Cr, ×2 Cr).

4
Galvanic (Voltaic) Cells
Harnessing spontaneous redox as electrical energy

A galvanic cell separates the two half-reactions into different compartments. Electrons flow through an external wire from the anode to the cathode, producing an electric current. The spontaneous redox reaction drives the current.

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AN OX  —  RED CAT
AN­ode = OX­idation. RED­uction at CAT­hode.
In a galvanic cell: anode is the negative electrode (electrons leave here). Cathode is the positive electrode (electrons arrive here).
Electrons flow: anode → wire → cathode. Conventional current is opposite.
Zn Anode (−) Zn → Zn²++2e&sup-; ZnSO⊂4;(aq) Cu Cathode (+) Cu²++2e&sup-; → Cu CuSO⊂4;(aq) e&sup-; flow Salt Bridge (KNO⊂3;) NO⊂3;&sup-; → ← K&sup+; V Zn-Cu galvanic cell (Zn anode, Cu cathode, E°cell = +1.10 V)
Zn-Cu galvanic cell. Zinc oxidizes at the anode (negative), releasing e&sup-; through the wire. Cu²+ ions are reduced at the copper cathode (positive). The salt bridge maintains electrical neutrality: NO⊂3;&sup-; flows toward the anode half-cell; K&sup+; toward the cathode half-cell.

Standard Reduction Potentials and E°cell

Cell potential
E°cell = E°cathode − E°anode
Use reduction potential values for both. The anode value is subtracted (not negated separately).
★★ Medium
Calculate E°cell and determine spontaneity
A cell is constructed using Ni/Ni²+ (E° = −0.25 V) and Ag/Ag&sup+; (E° = +0.80 V). Which is the anode? Find E°cell.
Show solution
1
The species with lower E° is oxidized (anode)
Ni has lower E° (−0.25 V) → Ni is the anode (oxidized) Ag has higher E° (+0.80 V) → Ag&sup+; is cathode (reduced)
2
Calculate E°cell
E°cell = E°cathode − E°anode
E°cell = +0.80 − (−0.25) = +0.80 + 0.25 = +1.05 V
3
Spontaneity

E°cell = +1.05 V > 0 → the reaction is spontaneous ✓. This is a galvanic cell.

Answer: Anode = Ni (oxidized). E°cell = +1.05 V. Spontaneous.
✓ Checkpoint 4
a) Given E°(Fe²+/Fe) = −0.44 V and E°(Cu²+/Cu) = +0.34 V: which is anode, which is cathode? Calculate E°cell. Write the cell notation.
b) A cell has E°cell = −0.45 V. Is it spontaneous? What type of cell is it?
c) Why does a salt bridge contain ions rather than being a plain wire?

a) Fe has lower E° → Fe is the anode. Cu is the cathode. E°cell = +0.34 − (−0.44) = +0.78 V. Cell notation: Fe | Fe²+(aq) || Cu²+(aq) | Cu

b) E°cell < 0 → not spontaneous. It would require external electrical energy to run → it is an electrolytic cell.

c) As the cell operates, the anode half-cell builds up positive ions (e.g. Zn²+) and the cathode half-cell is depleted of positive ions. Without a salt bridge, charge imbalance would stop the current. The salt bridge allows ions to migrate between compartments to maintain electrical neutrality without mixing the solutions.

5
Electrolysis
Driving non-spontaneous redox with external electricity

Electrolysis uses an external electrical power source to force a non-spontaneous redox reaction to occur. The process is the reverse of a galvanic cell — we push electrons in the unfavored direction.

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Why is the anode positive in an electrolytic cell?
The external battery drives electrons away from the anode (connected to the positive terminal of the battery). This makes the anode electron-deficient and positive, which attracts anions from solution. At the cathode (connected to the negative terminal), electrons are pushed in, making it negative — it attracts cations which then gain those electrons and are reduced. The half-reaction identities (anode=oxidation, cathode=reduction) remain the same; only the battery polarity has changed.

Faraday’s Law of Electrolysis

The amount of substance deposited or released at an electrode is directly proportional to the amount of charge passed through the cell.

Charge
Q = I × t (C)
Faraday constant
F = 96 500 C/mol e&sup-;
Moles of e&sup-;
n(e&sup-;) = Q / F
Moles of product
Use half-reaction ratio
Strategy for Faraday problems: Q → mol e&sup-; → mol product (via half-reaction stoichiometry) → mass product (via molar mass). Always convert time to seconds if given in minutes.
★★ Medium
Mass of metal deposited by electrolysis
A current of 3.00 A is passed through a solution of AgNO⊂3; for 45.0 minutes. What mass of silver is deposited? (M(Ag) = 107.9 g/mol; half-reaction: Ag&sup+; + e&sup-; → Ag)
Show solution
1
Find charge Q
t = 45.0 min × 60 s/min = 2700 s
Q = I × t = 3.00 A × 2700 s = 8100 C
2
Find moles of electrons
n(e&sup-;) = Q / F = 8100 / 96 500 = 0.08394 mol e&sup-;
3
From half-reaction: 1 mol e&sup-; deposits 1 mol Ag
n(Ag) = 0.08394 mol
4
Find mass of Ag
m(Ag) = n × M = 0.08394 × 107.9 = 9.06 g
Answer: m(Ag) = 9.06 g
★★★ Hard
Electrolysis of water — volumes of gas produced
A 5.00 A current electrolyzes water for 30.0 min. (a) What volume of H⊂2; is produced at STP? (b) What volume of O⊂2;? Half-reactions: Cathode: 2H⊂2;O + 2e&sup-; → H⊂2; + 2OH&sup-;. Anode: 2H⊂2;O → O⊂2; + 4H&sup+; + 4e&sup-;.
Show solution
1
Find Q and mol e&sup-;
Q = 5.00 × (30.0 × 60) = 5.00 × 1800 = 9000 C
n(e&sup-;) = 9000 / 96500 = 0.09326 mol
2
H⊂2; at cathode: 2e&sup-; per mol H⊂2;
n(H⊂2;) = 0.09326 / 2 = 0.04663 mol
V(H⊂2;) = 0.04663 × 22.4 = 1.044 L
3
O⊂2; at anode: 4e&sup-; per mol O⊂2;
n(O⊂2;) = 0.09326 / 4 = 0.02331 mol
V(O⊂2;) = 0.02331 × 22.4 = 0.522 L
4
Verify volume ratio

H⊂2;:O⊂2; = 1.044:0.522 = 2:1 ✓ (as expected from the overall reaction 2H⊂2;O → 2H⊂2; + O⊂2;)

Answer: V(H⊂2;) = 1.04 L    V(O⊂2;) = 0.522 L (ratio 2:1 ✓)
✓ Checkpoint 5
a) A 2.50 A current is passed through molten CuCl⊂2; for 20.0 minutes. Find the mass of Cu deposited. (M(Cu) = 63.55 g/mol; Cu²+ + 2e&sup-; → Cu)
b) How long (in minutes) must a 1.50 A current flow through AlCl⊂3; to deposit 1.00 g of Al? (M(Al) = 26.98 g/mol; Al³+ + 3e&sup-; → Al)
c) In electrolysis of CuCl⊂2;, what happens at the anode? Write the half-reaction.

a) Q = 2.50 × (20.0×60) = 3000 C. n(e&sup-;) = 3000/96500 = 0.03109 mol. n(Cu) = 0.03109/2 = 0.01554 mol.

m(Cu) = 0.01554 × 63.55 = 0.988 g ≈ 0.99 g

b) n(Al) = 1.00/26.98 = 0.03706 mol. n(e&sup-;) = 0.03706 × 3 = 0.11118 mol. Q = 0.11118 × 96500 = 10729 C.

t = Q/I = 10729/1.50 = 7152 s = 119 min

c) At the anode, Cl&sup-; ions are oxidized: 2Cl&sup-; → Cl⊂2; + 2e&sup-;. Cl⊂2; gas is produced at the anode.