Electrochemistry: NEET notes

1. Galvanic and electrolytic cells

NCERT §2.1

• An electrochemical cell couples a redox reaction to an electric circuit. In a galvanic (voltaic) cell a spontaneous reaction produces electrical energy; in an electrolytic cell electrical energy from outside forces a non-spontaneous reaction.
• The Daniell cell runs Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s). With both ions at 1 mol dm⁻³ its potential is 1.1 V.
• Connect an external source that opposes the cell. While E_ext < 1.1 V, electrons still flow from the Zn rod to the Cu rod (current from Cu to Zn), zinc dissolves and copper deposits.
• At E_ext = 1.1 V exactly, no current flows and the reaction stops.
• When E_ext > 1.1 V the flow reverses: electrons go from Cu to Zn, zinc is deposited on the zinc rod and copper dissolves. The same hardware is now an electrolytic cell.
• Strictly, activities replace concentrations in these equations; in dilute solutions the two are equal.

2. Electrode potentials and the SHE

NCERT §2.2; §2.2.1

• A galvanic cell is two half-cells (redox couples). In the Daniell cell, Cu²⁺ + 2e⁻ → Cu is the reduction half on copper and Zn → Zn²⁺ + 2e⁻ the oxidation half on zinc. A salt bridge joins the two solutions; if both electrodes share one electrolyte, no bridge is needed.
• At each metal-solution interface, ions tend to deposit (charging the metal positive) while metal atoms tend to dissolve as ions (leaving electrons, charging it negative). The resulting potential difference is the electrode potential; with every species at unit concentration it is the standard electrode potential. By IUPAC convention, standard reduction potentials are called standard electrode potentials.
• Anode = oxidation, negative with respect to its solution in a galvanic cell. Cathode = reduction, positive. Electrons leave the anode through the wire; conventional current runs the opposite way.
• Cell notation writes the anode first, on the left, and the cathode last, on the right, with a single bar between metal and solution and a double bar for the salt bridge: Cu(s)|Cu²⁺(aq)||Ag⁺(aq)|Ag(s). Then E_cell = E_right − E_left = E_cathode − E_anode, and the emf is the value with no current drawn.
• A single electrode's potential cannot be measured alone. The standard hydrogen electrode, Pt(s)|H₂(g, 1 bar)|H⁺(aq, 1 M), made of platinum coated with platinum black in acid with H₂ bubbling, is assigned 0 V at all temperatures.
• Against the SHE (as anode), the Cu²⁺/Cu cell reads 0.34 V and the Zn²⁺/Zn cell −0.76 V, so E°(Daniell) = 0.34 − (−0.76) = 1.10 V. Positive E° for Cu means H⁺ cannot oxidise copper, so Cu does not dissolve in HCl (nitric acid attacks it through nitrate); negative E° for Zn means H⁺ does oxidise zinc.
• Platinum or gold serve as inert electrodes: they carry electrons and offer a surface but do not react, as in Pt(s)|H₂(g)|H⁺(aq) and Pt(s)|Br₂(aq)|Br⁻(aq).
• Down the table of standard potentials, from F₂/F⁻ (2.87 V) to Li⁺/Li (−3.05 V), oxidising power of the left-hand species falls and reducing power of the right-hand species rises. F₂ is the strongest oxidising agent and F⁻ the weakest reductant; Li is the strongest reducing agent in water and Li⁺ the weakest oxidant.
• Cell measurements also give pH, solubility products, equilibrium constants and other thermodynamic data, and are used in potentiometric titrations.

3. The Nernst equation

NCERT §2.3

• For Mⁿ⁺(aq) + ne⁻ → M(s), the potential at a general concentration is E = E° − (RT/nF) ln(1/[Mⁿ⁺]), since a pure solid is taken as unity. R = 8.314 J K⁻¹ mol⁻¹, F = 96487 C mol⁻¹, T in kelvin.
• For the Daniell cell, E_cell = E°_cell − (RT/2F) ln([Zn²⁺]/[Cu²⁺]). The cell voltage rises when [Cu²⁺] is raised or [Zn²⁺] lowered.
• At 298 K, with base-10 logs, RT/F × 2.303 = 0.059 V, so E_cell = E°_cell − (0.059/n) log Q.
• For aA + bB + ne⁻ → cC + dD, Q = [C]^c[D]^d/[A]^a[B]^b, with pure solids and liquids left out. Use the same n for both electrodes: for Ni(s) + 2Ag⁺ → Ni²⁺ + 2Ag(s), n = 2 and Q = [Ni²⁺]/[Ag⁺]².
• Worked: Mg|Mg²⁺(0.130 M)||Ag⁺(0.0001 M)|Ag with E° = 3.17 V gives E = 3.17 − (0.059/2) log(0.130/10⁻⁸) = 3.17 − 0.21 = 2.96 V.
• A hydrogen electrode in a solution of pH 10 (at 1 bar H₂): E = −0.059 × pH = −0.59 V.

4. Cell potential, Gibbs energy and K

NCERT §2.3.1; §2.3.2

• As a Daniell cell runs, [Zn²⁺] climbs, [Cu²⁺] falls and the voltmeter reading drops. When the reading reaches zero the concentrations stop changing: the reaction is at equilibrium.
• Putting E_cell = 0 and Q = Kc into Nernst gives E°_cell = (2.303RT/nF) log Kc, which at 298 K is E° = (0.059/n) log Kc.
• Daniell cell: log Kc = 2 × 1.1/0.059 = 37.288, so Kc ≈ 2 × 10³⁷. Cu + 2Ag⁺ → Cu²⁺ + 2Ag with E° = 0.46 V: log Kc = 15.6, Kc = 3.92 × 10¹⁵. Equilibrium constants too large to measure directly come from E°.
• The maximum (reversible) electrical work a cell can do equals the fall in its Gibbs energy: ΔrG = −nFE_cell; under standard conditions ΔrG° = −nFE°_cell.
• E_cell is intensive, ΔrG is extensive. Doubling the equation doubles n and ΔrG (−2FE becomes −4FE) but leaves E unchanged.
• Daniell cell: ΔrG° = −2 × 96487 × 1.1 = −212.27 kJ mol⁻¹. From ΔrG° = −RT ln K the equilibrium constant follows.
• Sign check: E° > 0 ⇔ ΔrG° < 0 ⇔ K > 1, a spontaneous reaction.

5. Conductivity of solutions

NCERT §2.4; §2.4.1

• Resistance R = ρ l/A, where ρ (resistivity) is in Ω m; 1 Ω m = 100 Ω cm. Conductance G = 1/R, in siemens (S = Ω⁻¹, also called mho).
• Conductivity κ = 1/ρ, in S m⁻¹ (1 S cm⁻¹ = 100 S m⁻¹): the conductance of a piece 1 m long with 1 m² cross-section. IUPAC prefers 'resistivity' and 'conductivity' over 'specific resistance' and 'specific conductance'.
• Values span a huge range (298.15 K): copper 5.9 × 10³, 0.1 M HCl 3.91, 0.01 M KCl 0.14, 0.1 M acetic acid 0.047 and pure water 3.5 × 10⁻⁵ S m⁻¹, glass 1.0 × 10⁻¹⁶ S m⁻¹. Superconductors have zero resistivity; some ceramics and mixed oxides superconduct at up to 150 K.
• Metallic (electronic) conduction is by electrons, depends on the metal's structure and number of valence electrons, falls as temperature rises, and leaves the metal unchanged.
• Electrolytic (ionic) conduction is by ions. It depends on the electrolyte, the size and solvation of its ions, the solvent and its viscosity, concentration and temperature (it rises with temperature). Pure water conducts slightly from its ~10⁻⁷ M H⁺ and OH⁻.
• Two problems in measuring a solution's resistance: direct current electrolyses it and changes its composition, and a liquid cannot be clamped into a bridge. The fixes are an AC source (audio frequency, 550 to 5000 Hz) and a conductivity cell with platinised platinum electrodes.
• The cell constant G* = l/A (unit m⁻¹ or cm⁻¹) is found by filling the cell with KCl of known κ and measuring R: G* = R κ. Then κ of any solution = G*/R.
• A Wheatstone bridge with a detector (headphone) balances when no current flows through it; today direct-reading conductivity meters are common.

6. Molar conductivity and dilution

NCERT §2.4.2

• Molar conductivity Λm = κ/c. With κ in S m⁻¹ and c in mol m⁻³, Λm is in S m² mol⁻¹; with κ in S cm⁻¹, Λm (S cm² mol⁻¹) = κ × 1000/molarity. 1 S cm² mol⁻¹ = 10⁻⁴ S m² mol⁻¹, and 1 mol L⁻¹ = 1000 mol m⁻³.
• Worked: a cell reads 100 Ω with 0.1 M KCl (κ = 1.29 S m⁻¹), so G* = 129 m⁻¹; with 0.02 M KCl it reads 520 Ω, so κ = 0.248 S m⁻¹ and Λm = 0.248/20 = 124 × 10⁻⁴ S m² mol⁻¹.
• On dilution κ always falls, for strong and weak electrolytes alike, because fewer ions are left in each unit volume.
• Λm rises on dilution. Λm is the conductance of the whole volume holding 1 mol of electrolyte, set between electrodes 1 unit apart; that volume grows faster than κ shrinks.
• The limit of Λm as c → 0 is the limiting molar conductivity, Λ°m.
• Strong electrolytes: Λm rises slowly and Λm = Λ°m − A c^½, a straight line against √c with intercept Λ°m and slope −A. A depends on the solvent, temperature and electrolyte type (NaCl 1-1, CaCl₂ 2-1, MgSO₄ 2-2), and is the same for all electrolytes of one type.
• Worked (KCl): the Λm–√c line gives Λ°m = 150.0 S cm² mol⁻¹ and A = 87.46 S cm² mol⁻¹ (mol L⁻¹)^−½.
• Weak electrolytes such as acetic acid: Λm stays low at ordinary concentrations and shoots up steeply near zero, because the degree of dissociation grows on dilution. The curve cannot be extrapolated to find Λ°m.

7. Kohlrausch's law

NCERT §2.4.2

• Kohlrausch noticed regularities among strong electrolytes at 298 K: Λ°m(KX) − Λ°m(NaX) ≈ 23.4 S cm² mol⁻¹ for X = Cl, Br, I, and Λ°m(MBr) − Λ°m(MCl) ≈ 1.8 S cm² mol⁻¹ for M = Na, K.
• Law of independent migration of ions: Λ°m of an electrolyte is the sum of the separate contributions of its cation and anion, Λ°m = ν₊λ°₊ + ν₋λ°₋, where ν₊ and ν₋ are the numbers of cations and anions per formula unit.
• Limiting ionic conductivities at 298 K (S cm² mol⁻¹): H⁺ 349.6, Na⁺ 50.1, K⁺ 73.5, Ca²⁺ 119.0, Mg²⁺ 106.0, OH⁻ 199.1, Cl⁻ 76.3, Br⁻ 78.1, CH₃COO⁻ 40.9, SO₄²⁻ 160.0.
• Λ°m(CaCl₂) = 119.0 + 2(76.3) = 271.6 and Λ°m(MgSO₄) = 106.0 + 160.0 = 266 S cm² mol⁻¹.
• A weak electrolyte's Λ°m is built from strong ones: Λ°m(HAc) = Λ°m(HCl) + Λ°m(NaAc) − Λ°m(NaCl) = 425.9 + 91.0 − 126.4 = 390.5 S cm² mol⁻¹.
• Degree of dissociation α ≈ Λm/Λ°m, and the dissociation constant Ka = cα²/(1 − α).
• Worked: 0.001028 M acetic acid has κ = 4.95 × 10⁻⁵ S cm⁻¹, so Λm = 48.15 S cm² mol⁻¹, α = 48.15/390.5 = 0.1233 and Ka = 1.78 × 10⁻⁵ mol L⁻¹.

8. Electrolysis and Faraday's laws

NCERT §2.5

• In an electrolytic cell an outside voltage drives the reaction. Two copper strips in CuSO₄ solution: Cu²⁺ + 2e⁻ → Cu deposits on the cathode (negative), and Cu → Cu²⁺ + 2e⁻ dissolves the anode.
• That is how copper is refined: impure copper is the anode, pure copper grows on the cathode.
• Metals with no suitable chemical reducing agent are won by electrolysis: sodium and magnesium from their fused chlorides, aluminium from Al₂O₃ dissolved with cryolite.
• Faraday's first law: how much substance reacts at an electrode is directly proportional to the charge that has flowed through the electrolyte, whether a solution or a melt.
• Faraday's second law: the same quantity of electricity liberates different substances in proportion to their chemical equivalent weights (atomic mass of the metal ÷ electrons needed to reduce its cation).
• Charge Q = I t (coulombs = amperes × seconds). One mole of electrons carries 1 F = 96487 C mol⁻¹, about 96500 C mol⁻¹ for rough work.
• Ag⁺ + e⁻ → Ag needs 1 F per mole; Mg²⁺ + 2e⁻ → Mg needs 2 F; Al³⁺ + 3e⁻ → Al needs 3 F. Industrial cells run up to 50,000 A, about 0.518 F each second.
• Worked: 1.5 A through CuSO₄ for 10 min passes 900 C; Cu needs 2F per mole, so mass = 63 × 900/(2 × 96487) = 0.2938 g of copper.

9. Products of electrolysis

NCERT §2.5.1

• The products depend on what is electrolysed and on the electrodes. An inert electrode (Pt, Au) only supplies or accepts electrons; a reactive one takes part in the reaction.
• Among competing reactions, standard potentials decide, but some reactions are so slow that they need extra voltage (overpotential) and lose out.
• Molten NaCl: only Na⁺ and Cl⁻ are present, so sodium metal forms at the cathode and Cl₂ at the anode.
• Aqueous NaCl, cathode: H⁺ + e⁻ → ½H₂ (E° = 0.00 V) beats Na⁺ + e⁻ → Na (−2.71 V). With water supplying the H⁺, the net cathode reaction is H₂O + e⁻ → ½H₂ + OH⁻.
• Aqueous NaCl, anode: water oxidation (E° = 1.23 V) should win over Cl⁻ → ½Cl₂ + e⁻ (1.36 V), but the overpotential of oxygen makes chlorine form instead.
• Net: NaCl(aq) + H₂O(l) → Na⁺(aq) + OH⁻(aq) + ½H₂(g) + ½Cl₂(g). The products are NaOH, H₂ and Cl₂.
• Concentrations shift the choice, since the Nernst potentials, not the standard ones, apply. H₂SO₄ at the anode: dilute acid gives O₂ from water (1.23 V); concentrated acid gives 2SO₄²⁻ → S₂O₈²⁻ + 2e⁻ (1.96 V).

10. Batteries

NCERT §2.6; §2.6.1; §2.6.2

• A battery is one galvanic cell or several in series. A useful one is light, compact and keeps a nearly steady voltage while in use.
• Primary cells react once and are then spent. The dry (Leclanché) cell has a zinc container as anode and a graphite rod in MnO₂ and carbon as cathode, with a moist paste of NH₄Cl and ZnCl₂ between them.
• Dry cell: anode Zn → Zn²⁺ + 2e⁻; cathode MnO₂ + NH₄⁺ + e⁻ → MnO(OH) + NH₃, reducing Mn from +4 to +3. The NH₃ binds Zn²⁺ as [Zn(NH₃)₄]²⁺. Potential about 1.5 V.
• The mercury cell, for low-current devices such as hearing aids and watches, has a Zn-Hg amalgam anode, a HgO + carbon paste cathode and a KOH-ZnO paste electrolyte: Zn(Hg) + 2OH⁻ → ZnO + H₂O + 2e⁻ and HgO + H₂O + 2e⁻ → Hg + 2OH⁻.
• Its overall reaction Zn(Hg) + HgO → ZnO + Hg involves no ion whose concentration changes, so its 1.35 V stays constant over its life.
• Secondary cells are recharged by driving current the opposite way, over many cycles. The lead storage battery (vehicles, inverters) has a lead anode, a lead grid packed with PbO₂ as cathode and 38% sulphuric acid.
• Lead storage, discharge: anode Pb + SO₄²⁻ → PbSO₄ + 2e⁻; cathode PbO₂ + SO₄²⁻ + 4H⁺ + 2e⁻ → PbSO₄ + 2H₂O; overall Pb + PbO₂ + 2H₂SO₄ → 2PbSO₄ + 2H₂O. Charging turns the PbSO₄ back into Pb and PbO₂.
• The nickel-cadmium cell lasts longer than the lead cell but costs more to make: Cd + 2Ni(OH)₃ → CdO + 2Ni(OH)₂ + H₂O on discharge.

11. Fuel cells and corrosion

NCERT §2.7; §2.8

• Thermal power plants burn fuel to make steam for turbines, which is inefficient and polluting. A fuel cell is a galvanic cell fed continuously with a fuel (hydrogen, methane, methanol) and oxidant, with products removed continuously.
• The H₂-O₂ cell (used in the Apollo space programme, where its water was drunk by the astronauts) bubbles both gases through porous carbon electrodes into concentrated aqueous NaOH, with finely divided Pt or Pd as catalyst.
• Cathode: O₂ + 2H₂O + 4e⁻ → 4OH⁻. Anode: 2H₂ + 4OH⁻ → 4H₂O + 4e⁻. Overall: 2H₂ + O₂ → 2H₂O. It runs as long as the gases are supplied.
• Fuel cells are about 70% efficient against about 40% for thermal plants, and do not pollute.
• Corrosion coats metals with oxides or other salts: rusting of iron, tarnishing of silver, the green coating on copper and bronze. It damages buildings, bridges and ships.
• Rusting is electrochemical. At an anodic spot 2Fe → 2Fe²⁺ + 4e⁻; electrons travel through the metal to a cathodic spot where O₂ + 4H⁺ + 4e⁻ → 2H₂O, with H⁺ from carbonic acid (dissolved CO₂) or other acidic oxides. Overall 2Fe + O₂ + 4H⁺ → 2Fe²⁺ + 2H₂O, E°cell = 1.23 − (−0.44) = 1.67 V.
• Air oxidises Fe²⁺ further to Fe³⁺, which deposits as rust, hydrated ferric oxide Fe₂O₃·xH₂O, releasing more H⁺.
• Prevention: keep air and water off the surface with paint or chemicals (such as bisphenol); coat it with another metal (Sn, Zn); or attach a sacrificial electrode of a more reactive metal (Mg, Zn) that corrodes instead of the object.
• Hydrogen economy: hydrogen burns to water only, so hydrogen made by splitting water with solar energy and used in fuel cells could replace fossil fuels; both steps rest on electrochemistry.

Must-know facts

1. Galvanic cell: anode is negative, cathode positive. Electrolytic cell: anode is positive, cathode negative. Oxidation is always at the anode.
2. E°cell = E°cathode − E°anode = E_right − E_left, using reduction potentials for both.
3. SHE: Pt | H₂(1 bar) | H⁺(1 M), E° = 0 at all temperatures.
4. E°: 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.
5. F₂ is the strongest oxidant; Li the strongest reductant in water.
6. Daniell cell E° = 1.10 V, ΔrG° = −212.27 kJ mol⁻¹, Kc ≈ 2 × 10³⁷.
7. At 298 K: E = E° − (0.059/n) log Q and E° = (0.059/n) log K.
8. E_cell is intensive; ΔrG is extensive. Never multiply E° when balancing half-equations.
9. 1 F = 96487 C mol⁻¹ ≈ 96500 C mol⁻¹, the charge on one mole of electrons.
10. Pure 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.
11. Cell constant G* = l/A = Rκ, found with standard KCl.
12. Dilution: κ falls, Λm rises, for both strong and weak electrolytes.
13. Strong electrolytes: Λm = Λ°m − A√c; weak electrolytes: Λ°m only from Kohlrausch's law.
14. λ°(H⁺) = 349.6 and λ°(OH⁻) = 199.1 S cm² mol⁻¹, far above other ions.
15. Λ°m(HAc) = 390.5 S cm² mol⁻¹; α = Λm/Λ°m; Ka = cα²/(1 − α).
16. Brine electrolysis gives H₂ at the cathode, Cl₂ at the anode (oxygen overpotential) and NaOH in solution.
17. Dry cell ≈ 1.5 V; mercury cell 1.35 V, constant through its life.
18. Lead storage battery: Pb anode, PbO₂ cathode, 38% H₂SO₄; PbSO₄ forms at both plates on discharge.
19. H₂-O₂ fuel cell: about 70% efficient, versus about 40% for thermal plants.
20. Rust is Fe₂O₃·xH₂O; zinc and magnesium protect iron as sacrificial anodes.

Common traps

Formulas

Key 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.