Electrochemistry

🟢 Lite — Quick Review (1h–1d)

Electrochemistry studies how chemical reactions produce or consume electrical energy. In galvanic cells (voltaic), a spontaneous redox reaction generates electricity; in electrolytic cells, electrical energy drives a non-spontaneous reaction.

Key formulas to memorise:

E°cell = E°cathode − E°anode (predicts if a reaction is spontaneous)
ΔG° = −nFE°cell (links free energy to cell potential; n = moles of electrons, F = 96,485 C mol⁻¹)
E = E° − (RT/nF)ln Q — the Nernst equation for non-standard conditions (use ln, not log₁₀)
m = (Q × M) / (n × F) — mass deposited by electrolysis (Faraday’s 1st law)

Quick pointers for the Makerere exam:

Anode = oxidation (loss of electrons), cathode = reduction (gain of electrons). Polarity reverses between galvanic and electrolytic cells — trap question.
Always multiply E° by n when building the overall reaction; do not multiply E°cell itself.
The sign of E°cell determines spontaneity: positive = spontaneous.
Salt bridges maintain charge neutrality; KNO₃ or NaNO₃ are common choices.

🟡 Standard — Regular Study (2d–2mo)

What Is an Electrochemical Cell?

An electrochemical cell contains two electrodes immersed in electrolytes. Galvanic cells convert chemical energy to electrical energy — the Daniell cell (Zn|Zn²⁺ || Cu²⁺|Cu) is the textbook example. Electrolytic cells do the reverse, using external power to drive a chemical change.

Anode and Cathode by Function

Electrode	Process	Mnemonic
Anode	Oxidation (loss of e⁻)	Anode = An oxidation
Cathode	Reduction (gain of e⁻)	Cathode = Catch electrons

A critical reversal: in galvanic cells the anode is negative (electrons build up), while in electrolytic cells the anode is positive (external source pulls electrons).

Standard Electrode Potentials

Standard potentials (E°) are measured at 298 K, 1 M, 1 atm. The more positive E°, the stronger the oxidising agent (more readily reduced). The cell potential:

$$E°{cell} = E°{cathode} - E°_{anode}$$

Example: Cu²⁺/Cu has E° = +0.34 V; Zn²⁺/Zn has E° = −0.76 V. For the Daniell cell: E°cell = (+0.34) − (−0.76) = +1.10 V (spontaneous).

Nernst Equation

For non-standard concentrations: $$E = E° - \frac{RT}{nF}\ln Q$$

At 298 K this simplifies to: E = E° − (0.0592/n)log₁₀ Q.

Electrolysis: Faraday’s Laws

First law: mass m deposited = (M × Q) / (n × F), where M = molar mass, Q = charge in coulombs.
Second law: same charge deposits equivalent moles of electrons from different substances.

Charge Q = I × t (current × time in seconds).

Predicting Redox Reactions

If E°cell > 0, the reaction proceeds as written (galvanic mode). If E°cell < 0, the reverse reaction is spontaneous.

🔴 Extended — Deep Study (3mo+)

Mechanism: Why Do Metals Have Different Potentials?

Standard electrode potentials arise from the tendency of a metal to lose electrons in aqueous solution. Metals with very negative E° (Na, Ca) are readily oxidised — they hold their electrons loosely. Metals with very positive E° (Au, Pt) resist oxidation. This behaviour underlies the galvanic series: a ranking of metals by reduction potential that predicts which metal will corrode in a given environment. Iron corrodes (Fe → Fe²⁺ + 2e⁻) when coupled to a more noble metal.

The Salt Bridge: Not Just a Conduit

A salt bridge (usually KNO₃ or NH₄NO₃ — ions that do not precipitate with cell electrolytes) completes the circuit by:

Allowing ion migration to maintain charge neutrality
Preventing direct mixing of half-cell solutions

Without it, charge builds up rapidly and the cell dies. In laboratory cells, a porous pot or membrane can substitute.

Common Exam Mistakes at This Level

Reversing E°cell polarity: Students calculate E°cell then flip the sign to get ΔG°, compounding error. Remember ΔG° = −nFE°cell directly — the sign is already handled.
Wrong n in Nernst: The n in the Nernst equation equals the total electrons transferred in the balanced cell reaction, not the electrons at a single electrode. For the reaction 2Fe³⁺ + Sn → 2Fe²⁺ + Sn²⁺, n = 2 (even though Fe³⁺/Fe²⁺ is a 1-electron couple).
Concentrating Q vs [ ]: In the Nernst equation Q is the reaction quotient — products raised to stoichiometric coefficients over reactants. Write the balanced equation first.

Worked Example

Calculate E for the cell Fe|Fe²⁺(0.01 M)||Cu²⁺(0.1 M)|Cu at 298 K.

E°cell = E°Cu²⁺/Cu − E°Fe²⁺/Fe = (+0.34) − (−0.44) = +0.78 V
Reaction: Fe(s) + Cu²⁺ → Fe²⁺ + Cu(s); n = 2
Q = [Fe²⁺]/[Cu²⁺] = 0.01/0.1 = 0.1
E = 0.78 − (0.0592/2)log(0.1) = 0.78 − (0.0296)(−1) = 0.81 V

Practice Prompts

A copper electrode in 0.5 M AgNO₃ deposits silver. Write the cell notation, calculate E°cell, and predict whether the reaction is spontaneous.
How many grams of aluminium are deposited by 5,000 C passing through molten Al₂O₃? (M_Al = 27 g mol⁻¹, n = 3)

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Electrochemistry