ELECTROCHEMISTRY | Chapter 3 | CHEMISTRY | Class XII

 

CHEMISTRY  |  Class XII

Chapter 3

ELECTROCHEMISTRY

Electrochemical Cells  ◆  Nernst Equation  ◆  Conductance  ◆  Electrolysis  ◆  Faraday's Laws

 

1. Introduction to Electrochemistry

Electrochemistry is the branch of chemistry that deals with the relationship between electrical energy and chemical reactions. It encompasses two fundamental processes: (1) spontaneous chemical reactions that generate electrical energy (as in batteries and fuel cells), and (2) the use of electrical energy to drive non-spontaneous chemical reactions (as in electroplating and extraction of metals).

Electrochemistry plays a pivotal role in modern civilisation — from the lithium-ion battery in your smartphone to the electrolytic refining of copper, from the corrosion of iron bridges to the electroplating of jewellery, and from hydrogen fuel cells to chlor-alkali industry. Understanding electrochemistry requires a grasp of thermodynamics, equilibrium, kinetics, and the physics of electric current.

Redox Reaction: All electrochemical processes are based on oxidation-reduction (redox) reactions. In a redox reaction, one species loses electrons (oxidation) and another gains electrons (reduction). The species that loses electrons is the reducing agent; the species that gains electrons is the oxidising agent.

 

2. Electrochemical Cells (Galvanic / Voltaic Cells)

An electrochemical cell (galvanic cell or voltaic cell) converts chemical energy from a spontaneous redox reaction into electrical energy. It consists of two half-cells — each containing an electrode dipped into its electrolyte solution. The two half-cells are connected by (a) an external metallic wire through which electrons flow, and (b) a salt bridge through which ions flow to maintain electrical neutrality.

2.1 The Daniell Cell — A Classic Example

The Daniell cell (1836) is the most studied galvanic cell. It consists of a zinc electrode dipped in zinc sulphate (ZnSO₄) solution (the anode half-cell) and a copper electrode dipped in copper sulphate (CuSO₄) solution (the cathode half-cell), connected by a salt bridge containing KCl or KNO₃.

Figure 1: Daniell Cell — Zinc (anode) is oxidised, releasing electrons that flow through the external circuit to the copper cathode where Cu²⁺ ions are reduced. EMF = 1.10 V.

Key Events in the Daniell Cell

ANODE (−): Zn(s) → Zn²⁺(aq) + 2e⁻   [Oxidation — zinc dissolves] CATHODE (+): Cu²⁺(aq) + 2e⁻ → Cu(s)   [Reduction — copper deposits] NET REACTION: Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s)   [Spontaneous; ΔG < 0] ELECTRONS flow through external wire from Zn (anode) to Cu (cathode). CATIONS in salt bridge flow from KCl solution toward the CuSO4 half-cell. ANIONS in salt bridge flow from KCl solution toward the ZnSO4 half-cell. EMF of Daniell cell under standard conditions = +1.10 V

 

2.2 Cell Notation (Cell Representation)

An electrochemical cell is represented by a standardised notation (cell diagram). By convention: the anode (oxidation half-cell) is written on the left, the cathode (reduction half-cell) on the right. A single vertical line ( | ) represents a phase boundary (solid/liquid interface). A double vertical line ( || ) represents the salt bridge.

Cell Notation for Daniell Cell

Zn(s) | Zn²⁺(aq) || Cu²⁺(aq) | Cu(s)

 

Reading left to right: zinc solid in contact with zinc ion solution | salt bridge | copper ion solution in contact with copper solid. The EMF is always calculated as E(cathode) − E(anode).

2.3 Standard Electrode Potential (E°)

The electrode potential is the tendency of an electrode to gain or lose electrons relative to a reference electrode. The Standard Hydrogen Electrode (SHE) is universally chosen as the reference and is assigned a standard electrode potential of exactly 0.00 V. The standard electrode potential of any other electrode is measured relative to SHE under standard conditions (1 M concentration, 1 atm gas pressure, 25°C = 298 K).

Standard Reduction Potential (E°red): The electrode potential measured when the electrode reaction is written as a reduction (gain of electrons). A positive E°red means the electrode is a better oxidising agent than SHE; a negative E°red means it is a better reducing agent.

 

Standard Cell EMF

E°cell  =  E°cathode  −  E°anode  =  E°reduction(cathode)  −  E°reduction(anode)

 

Spontaneity Criterion

E°cell > 0  →  Spontaneous (ΔG < 0);     E°cell < 0  →  Non-spontaneous (ΔG > 0)

 

Relation with Gibbs Energy

DeltaG°  =  −nFE°cell     [n = moles of electrons; F = 96500 C/mol]

 

Relation with Equilibrium Constant

DeltaG°  =  −RT ln Keq  →  E°cell  =  (RT/nF) ln Keq  =  (0.0592/n) log Keq  [at 298 K]

 

Figure 6: Standard Reduction Potential (SRP) Series — Electrodes with more negative E° are stronger reducing agents; more positive E° are stronger oxidising agents. E°cell = E°cathode − E°anode.

Electrode Reaction	E° (V)	Nature
Li⁺(aq) + e⁻ → Li(s)	−3.05	Strongest reducing agent (most active metal)
K⁺(aq) + e⁻ → K(s)	−2.93	Very strong reducing agent
Na⁺(aq) + e⁻ → Na(s)	−2.71	Very strong reducing agent
Mg²⁺(aq) + 2e⁻ → Mg(s)	−2.37	Strong reducing agent
Al³⁺(aq) + 3e⁻ → Al(s)	−1.66	Strong reducing agent
Zn²⁺(aq) + 2e⁻ → Zn(s)	−0.76	Moderate reducing agent
Fe²⁺(aq) + 2e⁻ → Fe(s)	−0.44	Moderate reducing agent
2H⁺(aq) + 2e⁻ → H₂(g)	0.00	Standard reference (SHE)
Cu²⁺(aq) + 2e⁻ → Cu(s)	+0.34	Moderate oxidising agent
Ag⁺(aq) + e⁻ → Ag(s)	+0.80	Strong oxidising agent (noble metal)
Cl₂(g) + 2e⁻ → 2Cl⁻(aq)	+1.36	Very strong oxidising agent
F₂(g) + 2e⁻ → 2F⁻(aq)	+2.87	Strongest oxidising agent

 

 

3. Nernst Equation

The standard electrode potential (E°) is measured at standard conditions (1 M, 298 K, 1 atm). In real situations, concentrations may differ from 1 M. The Nernst Equation gives the electrode potential (or cell EMF) at any concentration. It was derived by Walther Nernst from thermodynamic principles.

Nernst Equation (Cell EMF)

E_cell  =  E°_cell  −  (RT / nF) ln Q  =  E°_cell  −  (0.0592 / n) log Q  [at 298 K]

 

Reaction Quotient (Q)

Q  =  [Products] / [Reactants]     (same form as equilibrium constant K)

 

At Equilibrium (E_cell = 0)

E°_cell  =  (0.0592 / n) log Keq     →     log Keq  =  nE°_cell / 0.0592

 

At 298 K, RT/F = 0.02569 V ≈ 0.0257 V; and (RT ln 10)/F = 0.05916 V ≈ 0.0592 V (used with log base 10).

Figure 2: Nernst Equation Graph — As reaction proceeds (Q increases), E_cell decreases. At equilibrium, Q = Keq and E_cell = 0. The cell is 'dead'.

Physical Meaning: When reactant concentrations are high (Q < 1), the cell has a higher EMF than E°. As the reaction proceeds, reactant concentrations decrease and product concentrations increase (Q increases), causing the EMF to decrease. Eventually, when Q = Keq, the cell reaches equilibrium and E_cell = 0 — no more current flows (battery is 'dead').

 

Nernst Equation for Single Electrode: For a single reduction half-cell M^n+ + ne⁻ → M, the Nernst equation gives: E = E° − (0.0592/n) log(1/[M^n+]) = E° + (0.0592/n) log[M^n+]. The electrode potential increases when the ion concentration increases.

 

4. Conductance of Electrolytic Solutions

When an electrolyte is dissolved in water, it dissociates into ions that can carry electric current. The ability of an electrolytic solution to conduct electricity is described by conductance and related quantities. Understanding these terms is essential for studying ionic behaviour, determining degree of dissociation, and finding solubility products.

4.1 Definitions and Units

Resistance (R): Opposition to flow of current. Unit: ohm (Ω). For a conductor: R = ρ l/A  where ρ = resistivity, l = length, A = cross-sectional area.

Conductance (G): Reciprocal of resistance: G = 1/R. Unit: siemens (S) or mho (Ω⁻¹).

Specific Conductance (κ, kappa): The conductance of a solution of unit length (1 cm) and unit cross-section (1 cm²). κ = G × l/A = G × cell constant. Unit: S cm⁻¹.

Molar Conductance (Λm): The conductance of a solution containing 1 mole of electrolyte when placed between two electrodes of unit area separated by unit distance. Λm = κ/c (where c = concentration in mol/cm³) or Λm = (κ × 1000)/M (where M = molarity in mol/L). Unit: S cm² mol⁻¹.

 

Specific Conductance

kappa  =  G × (l/A)  =  G × cell constant   [S cm⁻¹]

 

Molar Conductance (from κ and M)

Lambda_m  =  (kappa × 1000) / M   [S cm² mol⁻¹;  M in mol/L]

 

4.2 Variation of Molar Conductance with Concentration

The molar conductance of both strong and weak electrolytes increases with decreasing concentration (dilution). However, the pattern of increase is very different for the two types — a distinction that is fundamental to understanding electrolyte behaviour.

Figure 3: Molar Conductance vs √c — Strong electrolytes show linear decrease with √c (Debye-Hückel); weak electrolytes show a sharp rise at low concentration due to increased dissociation.

Strong Electrolytes (e.g., KCl, NaCl, HCl, H₂SO₄): These are completely dissociated at all concentrations. The increase in Λm with dilution is because at high concentrations, interionic attractions slow down the ions (Debye-Hückel-Onsager effect). On plotting Λm vs √c, a straight line is obtained.

Debye-Hückel-Onsager Equation (Strong Electrolytes)

Lambda_m  =  Lambda°_m  −  b√c     (b = experimental constant)

 

Weak Electrolytes (e.g., CH₃COOH, NH₄OH): These are partially dissociated. At high concentrations, degree of dissociation (α) is very small. As concentration decreases (dilution), α increases dramatically — causing Λm to rise sharply. Λ°m cannot be determined by extrapolation and must be calculated using Kohlrausch's Law.

4.3 Kohlrausch's Law of Independent Migration of Ions

At infinite dilution, all ions are completely free of interionic interactions. Kohlrausch's Law states that the molar conductance at infinite dilution (Λ°m) of an electrolyte is the sum of the limiting molar conductivities of the individual ions (cation and anion), regardless of which other ion is present.

Kohlrausch's Law

Lambda°_m  =  v₊ × lambda°₊  +  v₋ × lambda°₋

 

Here v₊ and v₋ are the number of cations and anions per formula unit, and λ°₊ and λ°₋ are the limiting molar conductivities of cation and anion respectively.

Example: Λ°m of CH₃COOH

Lambda°_m(CH3COOH)  =  Lambda°_m(CH3COONa) + Lambda°_m(HCl) − Lambda°_m(NaCl)

 

Key Application — Degree of Dissociation: For a weak electrolyte, the degree of dissociation α = Λm / Λ°m. This allows calculation of Ka: Ka = cα² / (1−α) ≈ cα² for small α.

Degree of Dissociation (Weak Electrolyte)

alpha  =  Lambda_m / Lambda°_m

 

4.4 Important Limiting Molar Conductivities

Ion	λ° (S cm² mol⁻¹)	Ion	λ° (S cm² mol⁻¹)
H⁺ (hydronium)	349.6	OH⁻	198.0
K⁺	73.5	Cl⁻	76.3
Na⁺	50.1	NO₃⁻	71.5
Ca²⁺	119.0	SO₄²⁻	160.0
Mg²⁺	106.0	CH₃COO⁻	40.9
NH₄⁺	73.7	HCO₃⁻	44.5

 

Note: H⁺ and OH⁻ have anomalously high conductivities due to the Grotthuss (proton-hopping) mechanism — protons hop along a chain of hydrogen-bonded water molecules rather than physically migrating.

 

5. Electrolytic Cells and Electrolysis

An electrolytic cell is a device that uses electrical energy from an external source (battery or DC power supply) to drive a non-spontaneous chemical (redox) reaction. This process is called electrolysis. Unlike a galvanic cell (which generates electricity from chemistry), an electrolytic cell uses electricity to produce chemistry.

Figure 4: Electrolytic Cell — Electrolysis of acidulated water. At cathode (−): H⁺ ions are reduced to H₂ gas. At anode (+): water is oxidised to O₂ gas.

Feature	Galvanic / Voltaic Cell	Electrolytic Cell
Energy conversion	Chemical → Electrical energy	Electrical → Chemical energy
Reaction type	Spontaneous redox (ΔG < 0)	Non-spontaneous (ΔG > 0), driven by ext. power
External source	Not needed (cell is the source)	External battery/DC source required
Anode charge	Negative (−)	Positive (+)
Cathode charge	Positive (+)	Negative (−)
Anode reaction	Oxidation (metal dissolves)	Oxidation (ion discharge/oxidation)
Cathode reaction	Reduction (metal deposits)	Reduction (cation discharge)
Salt bridge	Required (to complete circuit)	Not required (both electrodes in same electrolyte)
Examples	Daniell cell, Dry cell, Lead storage battery	Electrolysis of water, brine; electroplating

 

5.1 Products of Electrolysis — Preferential Discharge

When multiple ions are present in an electrolytic cell, the ion that is discharged (reduced at cathode or oxidised at anode) preferentially depends on several factors: (1) Nature of electrode, (2) Concentration of ions, (3) Overpotential (extra voltage needed beyond theoretical, especially for gas evolution), and (4) Standard electrode potential (ions with higher SRP are preferentially reduced at cathode).

◆        At cathode: The cation with the highest (most positive) standard reduction potential is preferentially reduced. Exception: H₂ shows large overpotential on mercury, so metals like Zn are deposited even though E°(Zn) < E°(H₂).

◆        At anode: If the anode is active (Cu, Ag, Zn), it dissolves preferentially. If anode is inert (Pt, graphite/carbon), the anion with the lowest oxidation potential is discharged. OH⁻ is preferentially discharged over SO₄²⁻ in dilute solutions.

 

5.2 Important Industrial Electrolytic Processes

Process	Electrolyte	Cathode Product	Anode Product	Application
Electrolysis of water	Dil. H₂SO₄ or NaOH	H₂ gas	O₂ gas	Hydrogen production
Electrolysis of brine (NaCl)	Concentrated NaCl	H₂ gas	Cl₂ gas	Chlor-alkali industry (NaOH, Cl₂, H₂)
Electrolytic refining of Cu	CuSO₄ solution	Pure Cu (99.99%)	Impure Cu dissolves	Electronics, wiring
Electroplating with Ag	AgNO₃ solution	Ag deposits on object	Ag anode dissolves	Jewellery, tableware
Electroplating with Cr	Chromic acid	Cr deposits	Inert Pt anode; O₂	Automotive parts
Extraction of Al	Molten Al₂O₃ (Bayer process)	Al metal	O₂ gas; C anode burns	Hall-Héroult process

 

 

6. Faraday's Laws of Electrolysis

Michael Faraday (1833–34) formulated two quantitative laws relating the amount of substance deposited or liberated at an electrode to the quantity of electricity passed. These laws are valid for all electrolytic processes, regardless of the nature of the electrolyte, electrode, or conditions.

Figure 5: Faraday's Laws — First Law relates mass deposited to charge passed; Second Law relates masses deposited for different substances to their equivalent weights. F = 96500 C/mol.

6.1 First Law of Electrolysis

The mass of substance deposited or liberated at an electrode during electrolysis is directly proportional to the quantity of electricity (charge) passed through the electrolyte.

First Law

w  =  Z × Q  =  Z × I × t

 

Here w = mass deposited (grams), Z = electrochemical equivalent (g/C), Q = charge in coulombs, I = current in amperes, t = time in seconds. Z = E/F = M/(nF), where E = equivalent weight, F = Faraday constant = 96500 C/mol.

Faraday's First Law (Quantitative Form)

w  =  (M × I × t) / (n × F)  =  (M × Q) / (n × F)

 

Here M = molar mass (g/mol), n = number of electrons transferred per ion (n-factor), F = 96500 C/mol, I = current (A), t = time (s). The formula can be rearranged to find any one variable given the others.

6.2 Second Law of Electrolysis

When the same quantity of electricity passes through different electrolytes connected in series, the masses of different substances deposited or liberated are proportional to their equivalent weights (E = M/n, where n is the n-factor).

Second Law

w₁ / w₂  =  E₁ / E₂  =  (M₁/n₁) / (M₂/n₂)

 

6.3 Faraday Constant — Key Values

Faraday Constant (F)

F  =  N_A × e  =  6.022 × 10²³ × 1.6 × 10⁻¹⁹  =  96500 C/mol  ≈  96485 C/mol

 

Equivalents Deposited

Equivalents  =  Q / F  =  (I × t) / F

 

Volume of Gas at STP

V  =  (Q / nF) × 22400 mL  =  (I × t / nF) × 22.4 L

 

Step-by-Step Method for Faraday's Law Problems

Step 1: Find total charge Q = I × t (in coulombs). If current varies, use Q = ∫I dt. Step 2: Find moles of electrons = Q / F = Q / 96500. Step 3: Using stoichiometry of the electrode reaction, find moles of substance deposited.        (e.g., if Cu²⁺ + 2e⁻ → Cu, then 2 moles of electrons deposit 1 mole of Cu) Step 4: Multiply moles of substance by its molar mass to get mass in grams. Step 5: For gas volume (at STP), multiply moles by 22.4 L. Note: 1 Faraday = 96500 C = charge required to deposit 1 gram-equivalent of any substance.

 

 

7. Batteries — Commercial Electrochemical Cells

A battery is a combination of one or more galvanic cells connected in series (to increase voltage) or in parallel (to increase current capacity). Batteries are broadly classified into primary cells (non-rechargeable) and secondary cells (rechargeable).

7.1 Primary Cells (Non-rechargeable)

Battery	Anode	Cathode	Electrolyte	EMF	Application
Leclanché (Dry cell, 1866)	Zn	MnO₂ + C (graphite)	NH₄Cl + ZnCl₂ paste	~1.5 V	Torches, remotes, clocks
Mercury cell	Zn (in KOH)	HgO	KOH/ZnO paste	~1.35 V	Hearing aids, watches, cameras
Alkaline cell	Zn powder	MnO₂	KOH solution	~1.5 V	Higher capacity; longer life than dry cell
Lithium cell	Li	MnO₂ or SOCl₂	LiClO₄ in organic solvent	~3.0 V	Pacemakers, cameras, memory backup

 

7.2 Secondary Cells (Rechargeable)

Battery	Anode (discharge)	Cathode (discharge)	Electrolyte	EMF	Key Features
Lead Storage Battery (Car battery)	Pb (lead)	PbO₂	38% H₂SO₄ (aq)	~2.0 V/cell (12V for 6 cells)	Heavy; reliable; rechargeable; widely used in vehicles
Nickel-Cadmium (NiCd)	Cd	NiO(OH)	KOH solution	~1.2 V	Constant discharge; memory effect; toxic Cd
Nickel-Metal Hydride (NiMH)	Metal hydride (MH)	NiO(OH)	KOH solution	~1.2 V	Higher capacity than NiCd; no memory effect; used in hybrid cars
Lithium-Ion (Li-ion)	Graphite (Li intercalated)	LiCoO₂ / LiFePO₄	LiPF₆ in organic solvent	~3.6 V	High energy density; no memory effect; smartphones, laptops, EVs

 

7.3 Lead Storage Battery — Detailed Chemistry

The lead-acid battery (invented by Gaston Planté in 1859) is the oldest rechargeable battery and remains the most widely used for automotive applications due to its high power output, reliability, and low cost. Each cell generates about 2.0 V, so a standard 12 V car battery contains 6 cells in series.

Discharge — Anode Reaction

Pb(s) + SO₄²⁻(aq) → PbSO₄(s) + 2e⁻       [Oxidation]

 

Discharge — Cathode Reaction

PbO₂(s) + SO₄²⁻ + 4H⁺ + 2e⁻ → PbSO₄(s) + 2H₂O  [Reduction]

 

Overall Discharge Reaction

Pb + PbO₂ + 2H₂SO₄ → 2PbSO₄ + 2H₂O  (discharge)

 

During charging, the reactions are reversed — PbSO₄ is converted back to Pb and PbO₂, and H₂SO₄ is regenerated. The density of H₂SO₄ increases during charging and decreases during discharging — hydrometer measurement of H₂SO₄ density indicates the state of charge of the battery.

7.4 Fuel Cells

A fuel cell is a galvanic cell that generates electricity by the continuous electrochemical reaction of a fuel (hydrogen, methanol, hydrocarbons) with an oxidant (usually oxygen from air), as long as the reactants are supplied. Unlike a battery, a fuel cell does not 'run down' — it operates continuously like an engine. The only by-product of a hydrogen-oxygen fuel cell is water — making it extremely clean.

H₂–O₂ Fuel Cell — Cathode (with KOH electrolyte)

O₂(g) + 2H₂O(l) + 4e⁻ → 4OH⁻(aq)

 

H₂–O₂ Fuel Cell — Anode

H₂(g) + 2OH⁻(aq) → 2H₂O(l) + 2e⁻

 

Overall Reaction

2H₂(g) + O₂(g) → 2H₂O(l) + Electrical Energy

 

Fuel cells have efficiency of up to 70–80% (much higher than internal combustion engines at 25–35%). Applications include space shuttles (Apollo, Space Shuttle), backup power systems, electric buses (hydrogen fuel cell buses in many cities), and emerging passenger vehicles (Toyota Mirai, Hyundai Nexo).

 

8. Corrosion — An Electrochemical Process

Corrosion is the gradual deterioration of metals by chemical or electrochemical reaction with the environment — particularly with oxygen and moisture. Rusting of iron, tarnishing of silver, and the green patina on copper are all forms of corrosion. It is estimated that corrosion costs the global economy over USD 2.5 trillion per year.

Rusting of Iron — Electrochemical Mechanism: Rusting is an electrochemical process requiring both water and oxygen. The surface of iron acts like a galvanic cell — impurities or stress points on the iron surface become cathodic (more noble), while the main iron surface becomes anodic (corrodes). The overall reaction produces rust, which is hydrated iron(III) oxide: Fe₂O₃·xH₂O.

Rusting — Anode (Fe is oxidised)

Fe(s) → Fe²⁺(aq) + 2e⁻      E° = +0.44 V

 

Rusting — Cathode (O₂ is reduced)

O₂(g) + 2H₂O + 4e⁻ → 4OH⁻(aq)      E° = +0.40 V

 

Final Rust Formation

4Fe(OH)₂ + O₂ → 2Fe₂O₃.H₂O (rust) + 2H₂O

 

8.1 Prevention of Corrosion

◆        Barrier Protection: Painting, oiling, greasing, or coating with plastic prevents contact of iron with moisture and O₂.

◆        Galvanisation: Coating iron with zinc (a more reactive metal, E° = −0.76 V vs Fe = −0.44 V). Even if the zinc coating is scratched, zinc corrodes preferentially (sacrificial protection) because Zn has lower SRP than Fe.

◆        Cathodic Protection (Sacrificial Anode Method): A more reactive metal (Mg, Zn, Al) is connected to the iron structure. The sacrificial metal is oxidised instead of iron — protecting underground pipelines, ship hulls, and oil rigs.

◆        Alloying: Making stainless steel (Fe + Cr + Ni) creates a passive Cr₂O₃ layer that prevents further corrosion.

◆        Tin Plating: Used for food cans. Tin (Sn, E° = −0.14 V) is less reactive than Fe (E° = −0.44 V) — acts as barrier but NOT sacrificially (once scratched, Fe corrodes faster).

◆        Electroplating: Depositing noble metals (Cr, Ni, Au, Ag) on the surface by electrolysis — decorative and protective.

 

9. Master Formula Table — Electrochemistry

Formula / Concept	Expression	Key Notes
Standard Cell EMF	E°cell = E°cathode − E°anode	Both are standard reduction potentials
Gibbs Energy & EMF	ΔG° = −nFE°cell	n = moles of electrons; F = 96500 C/mol
EMF & Equilibrium K	E°cell = (0.0592/n) log Keq	At 298 K; log base 10
Nernst Equation	E = E° − (0.0592/n) log Q	Q = reaction quotient
Nernst (single electrode)	E = E° + (0.0592/n) log[M^n+]	For Mn+ + ne⁻ → M electrode
Spontaneity	E°cell > 0 → ΔG < 0 → spontaneous	E°cell < 0 → non-spontaneous
Conductance	G = 1/R    (S or Ω⁻¹)	Reciprocal of resistance
Specific Conductance	κ = G × (l/A) = G × cell constant	Unit: S cm⁻¹
Molar Conductance	Λm = (κ × 1000) / M	M in mol/L; unit: S cm² mol⁻¹
Kohlrausch's Law	Λ°m = v₊λ°₊ + v₋λ°₋	For strong & weak electrolytes
D-H-O Equation	Λm = Λ°m − b√c	Strong electrolytes only
Degree of Dissociation	α = Λm / Λ°m	For weak electrolytes
Faraday 1st Law	w = (M × I × t) / (n × F)	w in grams; I in A; t in s
Faraday 2nd Law	w₁/w₂ = E₁/E₂ = (M₁/n₁)/(M₂/n₂)	Same Q through electrolytes in series
Faraday Constant	F = 96500 C/mol	Charge per mole of electrons
Charge Quantity	Q = I × t    (coulombs)	1 coulomb = 1 ampere × 1 second
Moles of electrons	n_e = Q / F = It / 96500	Used in all Faraday calculations
Gas Volume at STP	V = (I×t / nF) × 22400 mL	n = electrons per molecule of gas
Electrochemical Eq.	Z = M / (n × F) = E / F	E = equivalent weight = M/n

 

 

10. Quick Revision — Key Points

Electrochemical Cells & EMF — Must Know

* Galvanic cell: spontaneous redox → electrical energy. Anode (−): oxidation. Cathode (+): reduction. * Cell notation: Anode | electrolyte || electrolyte | Cathode. Left = anode always. * E°cell = E°cathode − E°anode (both as standard REDUCTION potentials). * E°cell > 0 → ΔG < 0 → spontaneous.  ΔG° = −nFE°cell. * E°cell = (0.0592/n) log Keq at 298 K. Larger E°cell → larger Keq (more complete reaction). * Nernst: E = E° − (0.0592/n)logQ. At equilibrium: E = 0, Q = Keq. * Daniell cell: E° = E°(Cu²⁺/Cu) − E°(Zn²⁺/Zn) = 0.34−(−0.76) = +1.10 V.

 

Conductance — Must Know

* κ (specific conductance) = G × cell constant. Unit: S cm⁻¹. Increases with concentration. * Λm (molar conductance) = (κ × 1000)/M. Unit: S cm² mol⁻¹. Increases with dilution. * Strong electrolytes: Λm = Λ°m − b√c (linear). Λ°m by extrapolation. * Weak electrolytes: Λm rises sharply with dilution. Λ°m by Kohlrausch's Law. * Kohlrausch: Λ°m(CH₃COOH) = Λ°m(CH₃COONa) + Λ°m(HCl) − Λ°m(NaCl). * H⁺ has highest λ° (349.6) and OH⁻ next (198.0) due to Grotthuss proton-hopping mechanism. * Degree of dissociation α = Λm / Λ°m (for weak electrolytes). Then Ka = cα²/(1−α).

 

Electrolysis & Faraday's Laws — Must Know

* Electrolytic cell: electrical energy → chemical reaction (non-spontaneous). Anode = (+), Cathode = (−). * At cathode: cation with highest SRP is preferentially reduced. * At anode (inert): anion with lowest oxidation potential is preferentially oxidised. * Faraday 1st Law: w = MIt/(nF). Find Q = It → moles e⁻ = Q/F → moles substance → mass. * Faraday 2nd Law: w₁/w₂ = E₁/E₂. Masses ∝ equivalent weights (M/n). * F = 96500 C/mol. 1 Faraday deposits 1 gram-equivalent of any substance. * Gas volume at STP = (It/nF) × 22400 mL. e.g., 96500 C through water gives 11200 mL H₂ and 5600 mL O₂.

 

Batteries & Corrosion — Must Know

* Primary cell: non-rechargeable (dry cell 1.5V, mercury cell 1.35V, Li cell 3V). * Secondary cell: rechargeable. Lead acid: Pb/PbO₂/H₂SO₄, 2V/cell, 12V total. * During discharge of lead battery: both electrodes form PbSO₄; H₂SO₄ is consumed. * Li-ion cell: 3.6 V, highest energy density, no memory effect → smartphones, EVs. * H₂-O₂ fuel cell: continuous supply of H₂ and O₂; product = water only; 70-80% efficient. * Rusting: electrochemical process needing water + O₂. Fe acts as anode; impurity as cathode. * Galvanisation (Zn coating) → sacrificial protection. Tin plating → barrier only (not sacrificial). * Cathodic protection: connect Mg/Zn block to iron — Mg/Zn corrodes preferentially.

 

— End of Chapter 3: Electrochemistry (Chemistry) —