Physical · Electrochemistry

Electrochemistry — Cells, Nernst & Faraday

CSIR-NET Chemical Sciences revision note · 10 sections · about 602 words · free to read in full

Exam-focused revision notes on Electrochemistry — Cells, Nernst & Faraday for CSIR-NET Chemical Sciences, GATE Chemistry and IIT-JAM — the core concepts, the formulas worth memorising, the traps that cost marks, and a quick-recall table.

Two kinds of cell

  • Galvanic (voltaic) cell: a spontaneous redox reaction produces electricity. ΔG < 0, Ecell > 0.
  • Electrolytic cell: an external power source drives a non-spontaneous reaction. ΔG > 0, applied voltage needed.
  • In both: oxidation happens at the anode, reduction at the cathode — the definitions never change.

Anode / cathode signs (the trap)

  • Galvanic: anode is negative (−), cathode is positive (+).
  • Electrolytic: anode is positive (+), cathode is negative (−).
  • Oxidation/reduction assignment is fixed; only the charge sign flips between cell types.

Cell notation

anode | anode solution ‖ cathode solution | cathode
e.g. Zn(s) | Zn2+(aq) ‖ Cu2+(aq) | Cu(s)

Left = oxidation (anode), right = reduction (cathode). The double bar ‖ is the salt bridge.

Electrode potential & E°cell

  • Potentials are measured against the Standard Hydrogen Electrode (SHE), defined as E° = 0.00 V.
  • Standard reduction potentials are tabulated; more positive E° = stronger tendency to be reduced.
E°cell = E°cathode − E°anode (both as reduction potentials)

If E°cell > 0 the reaction is spontaneous (galvanic).

Nernst equation

E = E° − (RT/nF) ln Q

At 298 K, converting to log10:

E = E° − (0.0591/n) log Q  (V, at 25 °C)
  • Q = reaction quotient (use Q, not K, unless you are at equilibrium).
  • n = moles of electrons transferred; F = Faraday constant ≈ 96 485 C mol−1.
  • At equilibrium E = 0 and Q = K.

Thermodynamic links

ΔG° = −nF E°cell  and  ΔG° = −RT ln K

Combining gives the bridge between potential and equilibrium:

ln K = nF E°cell / RT
  • E°cell > 0 → ΔG° < 0 → K > 1 → products favoured.

Electrolysis & Faraday's laws

  • 1st law: mass deposited/liberated ∝ charge passed (m ∝ Q).
  • 2nd law: for the same charge, mass ∝ equivalent weight.
Q = I × t = n × F  →  moles of e− = Q / F ;   mass = (Q / F) × (M / z)

where z = electrons per ion, M = molar mass.

Conductance (quick note)

  • Molar conductivity Λm increases on dilution (more effective ionisation / less inter-ionic interaction).
  • Kohlrausch's law: at infinite dilution, Λ°m = ν+λ°+ + ν−λ°− — total is the sum of independent ion contributions.
  • Lets you get Λ°m of a weak electrolyte from strong-electrolyte data.

⚠️ Common traps students miss

  • Sign of E → spontaneity: E°cell > 0 means spontaneous (ΔG < 0). A negative E°cell is non-spontaneous.
  • Anode/cathode charge signs flip between galvanic and electrolytic cells — but oxidation is always at the anode.
  • In the Nernst equation use the reaction quotient Q, not K (K is only for equilibrium).
  • Use E°cell = E°cathode − E°anode with both as reduction potentials; don't flip a sign twice.
  • Watch n in ΔG° = −nFE° and in the Nernst term — it's electrons per balanced reaction.

Key equations at a glance

QuantityEquation
Cell EMF (std)E°cell = E°cathode − E°anode
Nernst (298 K)E = E° − (0.0591/n) log Q
Free energyΔG° = −nF E°cell
EquilibriumΔG° = −RT ln K
Faraday / electrolysisQ = I t = nF ; m = (Q/F)(M/z)

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