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Must-know facts
20 facts
- 1Galvanic cell: anode is negative, cathode positive. Electrolytic cell: anode is positive, cathode negative. Oxidation is always at the anode.
- 2E°cell = E°cathode − E°anode = E_right − E_left, using reduction potentials for both.
- 3SHE: Pt | H₂(1 bar) | H⁺(1 M), E° = 0 at all temperatures.
- 4E°: Cu²⁺/Cu 0.34, Zn²⁺/Zn −0.76, Ag⁺/Ag 0.80, Fe²⁺/Fe −0.44, O₂/H₂O 1.23, Cl₂/Cl⁻ 1.36, F₂/F⁻ 2.87, Li⁺/Li −3.05 V.
- 5F₂ is the strongest oxidant; Li the strongest reductant in water.
- 6Daniell cell E° = 1.10 V, ΔrG° = −212.27 kJ mol⁻¹, Kc ≈ 2 × 10³⁷.
- 7At 298 K: E = E° − (0.059/n) log Q and E° = (0.059/n) log K.
- 8E_cell is intensive; ΔrG is extensive. Never multiply E° when balancing half-equations.
- 91 F = 96487 C mol⁻¹ ≈ 96500 C mol⁻¹, the charge on one mole of electrons.
- 10Pure water κ = 3.5 × 10⁻⁵ S m⁻¹; 1 S cm⁻¹ = 100 S m⁻¹; 1 S cm² mol⁻¹ = 10⁻⁴ S m² mol⁻¹.
- 11Cell constant G* = l/A = Rκ, found with standard KCl.
- 12Dilution: κ falls, Λm rises, for both strong and weak electrolytes.
- 13Strong electrolytes: Λm = Λ°m − A√c; weak electrolytes: Λ°m only from Kohlrausch's law.
- 14λ°(H⁺) = 349.6 and λ°(OH⁻) = 199.1 S cm² mol⁻¹, far above other ions.
- 15Λ°m(HAc) = 390.5 S cm² mol⁻¹; α = Λm/Λ°m; Ka = cα²/(1 − α).
- 16Brine electrolysis gives H₂ at the cathode, Cl₂ at the anode (oxygen overpotential) and NaOH in solution.
- 17Dry cell ≈ 1.5 V; mercury cell 1.35 V, constant through its life.
- 18Lead storage battery: Pb anode, PbO₂ cathode, 38% H₂SO₄; PbSO₄ forms at both plates on discharge.
- 19H₂-O₂ fuel cell: about 70% efficient, versus about 40% for thermal plants.
- 20Rust is Fe₂O₃·xH₂O; zinc and magnesium protect iron as sacrificial anodes.
Common traps
Where marks are lost
Doubling E° when a half-equation is multiplied by 2 to balance electrons.
Calling the anode positive in every cell.
Writing Q upside down in the Daniell cell: log([Cu²⁺]/[Zn²⁺]).
Saying molar conductivity falls on dilution because conductivity does.
Finding Λ°m of acetic acid by extending its Λm-√c graph to c = 0.
Mixing units: κ in S cm⁻¹ with c in mol m⁻³.
Predicting O₂ at the anode in brine electrolysis because its E° (1.23 V) is lower than chlorine's (1.36 V).
Predicting sodium at the cathode in aqueous NaCl.
Using the atomic mass alone in Faraday's-law problems.
Thinking a sacrificial anode must be less reactive than iron.
Formulas
12 to know
Standard cell potential
E°cell = E°cathode − E°anode = E°right − E°left
Both as reduction potentials.
Nernst equation (electrode)
E(Mⁿ⁺/M) = E°(Mⁿ⁺/M) − (RT/nF) ln(1/[Mⁿ⁺])
R = 8.314 J K⁻¹ mol⁻¹, F = 96487 C mol⁻¹.
Nernst equation (cell, 298 K)
E_cell = E°cell − (0.059/n) log Q
Q = products/reactants, pure solids and liquids omitted.
E° and equilibrium constant
E°cell = (2.303RT/nF) log Kc = (0.059/n) log Kc
At 298 K.
Gibbs energy
ΔrG = −nFE_cell ; ΔrG° = −nFE°cell = −RT ln K
ΔrG is extensive, E is intensive.
Resistance and conductance
R = ρ l/A ; G = 1/R ; κ = 1/ρ
G in S; κ in S m⁻¹ or S cm⁻¹.
Cell constant
G* = l/A = R κ ; κ = G*/R
Calibrated with KCl solution of known κ.
Molar conductivity
Λm = κ/c ; Λm (S cm² mol⁻¹) = 1000 κ (S cm⁻¹)/M (mol L⁻¹)
1 S cm² mol⁻¹ = 10⁻⁴ S m² mol⁻¹.
Strong electrolyte dilution
Λm = Λ°m − A √c
A depends on electrolyte type (1-1, 2-1, 2-2), solvent and temperature.
Kohlrausch's law
Λ°m = ν₊λ°₊ + ν₋λ°₋
Sum of independent ionic contributions.
Weak electrolyte
α = Λm/Λ°m ; Ka = cα²/(1 − α)
Λ°m from Kohlrausch's law.
Faraday's laws
Q = I t ; moles deposited = Q/(nF) ; mass = M Q/(nF)
1 F = 96487 C mol⁻¹ ≈ 96500.
Key terms
16 terms
- Galvanic cell
- A cell that turns the Gibbs energy of a spontaneous redox reaction into electrical work.
- Electrolytic cell
- A cell in which an outside voltage drives a non-spontaneous redox reaction.
- Salt bridge
- An ionic link between two half-cell solutions that completes the circuit inside the cell.
- Electrode potential
- The potential difference between an electrode and its electrolyte; standard when every species is at unit concentration.
- Standard hydrogen electrode
- Platinised Pt in 1 M H⁺ with H₂ at 1 bar, the reference assigned 0 V.
- Emf
- The cell potential measured when no current is drawn.
- Inert electrode
- An electrode such as Pt or Au that carries electrons without taking part in the reaction.
- Conductivity (κ)
- The reciprocal of resistivity; the conductance of a unit cube of the material.
- Cell constant (G*)
- l/A of a conductivity cell, found from the resistance of a standard KCl solution.
- Molar conductivity (Λm)
- Conductivity divided by molar concentration: the conductance of all the solution holding one mole of electrolyte.
- Limiting molar conductivity (Λ°m)
- The value Λm approaches as concentration goes to zero.
- Kohlrausch's law
- At infinite dilution, each ion contributes a fixed amount to Λ°m, whatever its partner ion.
- Faraday (F)
- The charge on one mole of electrons, 96487 C mol⁻¹.
- Overpotential
- Extra voltage a slow electrode reaction needs beyond its equilibrium potential.
- Fuel cell
- A galvanic cell fed continuously with fuel and oxidant, turning combustion energy straight into electricity.
- Sacrificial electrode
- A more reactive metal joined to an object so that it corrodes instead of the object.