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Class 12 Chemistry Chapter 2 Electrochemistry — Formulas & Key Points

Electrochemistry commands 5-8 marks in the CBSE Class 12 Chemistry board paper and appears extensively in JEE and NEET. This formula sheet consolidates every NCERT Class 12 Chemistry Chapter 2 equation, constant, and definition into rapid-revision tables. Whether you are solving Nernst equation problems, calculating molar conductivity, or applying Faraday's laws, this page is your single-stop reference before the exam.

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Key takeaways

✓Nernst equation E_cell = E°_cell - (0.0591/n) log Q connects cell potential to concentration at 298 K; master it for half the numerical questions.
✓Kohlrausch law states limiting molar conductivity Λ°_m equals sum of ionic conductivities; crucial for weak electrolyte calculations.
✓Faraday's first law: mass deposited m = (Z × I × t) or (E × Q)/96500; second law uses equivalent weight ratios.
✓Standard electrode potential E° is measured versus standard hydrogen electrode (SHE) at 1 M, 1 bar, 298 K; cathode E° minus anode E° gives E°_cell.
✓Conductance G = 1/R; conductivity κ = G × (l/A); molar conductivity Λ_m = κ × 1000/M; all have distinct units and uses.
✓Sign convention: reduction potentials are tabulated; anode (oxidation) undergoes E reversal in cell EMF calculation.
✓CBSETUTOR.ai offers unlimited photo-based doubt solving for Electrochemistry numericals at ₹999/month, covering Classes 6-12 with a 3-day free trial.

Electrochemical Cell Formulas & Definitions

An electrochemical cell converts chemical energy into electrical energy (galvanic or voltaic cell) or vice versa (electrolytic cell). The electromotive force (EMF) or cell potential E_cell is the difference in electrode potentials between cathode and anode. Standard cell potential E°_cell is measured when all species are at unit activity (1 M for solutions, 1 bar for gases) at 298 K. The cell is represented using a conventional cell diagram: anode (oxidation half-cell) on the left, cathode (reduction half-cell) on the right, separated by a salt bridge (double vertical line) or a single vertical line for phase boundaries. The direction of electron flow is from anode to cathode in the external circuit, while cations migrate toward the cathode inside the cell.

Galvanic cell: spontaneous redox reaction, ΔG < 0, E_cell > 0
Electrolytic cell: non-spontaneous reaction driven by external voltage, ΔG > 0
Salt bridge: maintains electrical neutrality; commonly KCl or NH₄NO₃ in agar-agar
Anode: oxidation occurs; electrons are released
Cathode: reduction occurs; electrons are consumed

Standard & Cell Electrode Potential Formulas

Electrode potential is the tendency of an electrode to lose or gain electrons. It cannot be measured in isolation; we measure it relative to the Standard Hydrogen Electrode (SHE), assigned E° = 0.00 V. The standard reduction potential E° is tabulated for the half-reaction written as a reduction. To calculate standard cell potential, use E°_cell = E°_cathode - E°_anode. A positive E°_cell indicates a spontaneous reaction under standard conditions. The relationship between Gibbs free energy and cell potential is ΔG° = -nFE°_cell, where n is the number of moles of electrons transferred and F = 96500 C/mol is the Faraday constant. At equilibrium, E_cell = 0 and ΔG° = -RT ln K_eq, linking cell potential to the equilibrium constant.

E°_cell = E°_cathode - E°_anode (both as reduction potentials)
ΔG° = -nFE°_cell; if E°_cell > 0 then ΔG° < 0 (spontaneous)
At 298 K: ΔG° = -2.303 RT log K_eq = -0.0591 n log K_eq (in volts)
Higher (more positive) E° → stronger oxidizing agent when written as reduction
SHE: 2H⁺(1M) + 2e⁻ → H₂(1 bar), E° = 0.00 V by definition

Nernst Equation — The Core Formula Table

The Nernst equation relates cell potential under non-standard conditions to standard potential and the reaction quotient Q. At temperature T (Kelvin), E_cell = E°_cell - (RT/nF) ln Q. At 298 K, converting natural log to log₁₀, this simplifies to E_cell = E°_cell - (0.0591/n) log₁₀ Q. For a general reaction aA + bB → cC + dD, Q = [C]^c [D]^d / [A]^a [B]^b. Pure solids and liquids have unit activity and do not appear in Q. For concentration cells (same electrodes, different concentrations), E°_cell = 0, so E_cell depends solely on the logarithmic concentration ratio. The Nernst equation is also written for individual electrode potentials: E = E° - (0.0591/n) log([reduced]/[oxidized]) at 298 K.

General form: E_cell = E°_cell - (2.303 RT / nF) log Q
At 298 K: E_cell = E°_cell - (0.0591/n) log Q
For electrode: E = E° - (0.0591/n) log([Red]/[Ox]) at 298 K
Concentration cell: E_cell = (0.0591/n) log(C_cathode / C_anode) since E°_cell = 0
At equilibrium: E_cell = 0, so E°_cell = (0.0591/n) log K_eq

Conductance G is the reciprocal of resistance: G = 1/R, measured in siemens (S) or mho (℧). Conductivity (specific conductance) κ accounts for electrode geometry: κ = G × (l/A) = (1/R) × (l/A), where l is the distance between electrodes and A is the cross-sectional area; unit is S·m⁻¹ or S·cm⁻¹. The cell constant (l/A) is determined by calibrating with a solution of known κ, typically KCl. Molar conductivity Λ_m relates conductivity to concentration: Λ_m = κ / c, where c is molar concentration in mol/m³. In practical units (c in mol/L, κ in S·cm⁻¹), Λ_m = (κ × 1000) / M, giving units S·cm²·mol⁻¹. For strong electrolytes, Λ_m increases slightly with dilution and approaches a limiting value Λ°_m. For weak electrolytes, Λ_m rises sharply on dilution because the degree of dissociation α increases, and Λ°_m cannot be obtained by extrapolation.

Conductance G = 1/R; unit: siemens (S)
Conductivity κ = G × (cell constant) = (1/R) × (l/A); unit: S·cm⁻¹ or S·m⁻¹
Cell constant = l/A; determined using standard KCl solutions
Molar conductivity Λ_m = (κ × 1000) / M; unit: S·cm²·mol⁻¹
Limiting molar conductivity Λ°_m: value at infinite dilution (c → 0)

Kohlrausch Law of Independent Migration of Ions

Kohlrausch's law states that at infinite dilution, the limiting molar conductivity Λ°_m of an electrolyte is the sum of the limiting molar conductivities of its constituent ions: Λ°_m = ν₊λ°₊ + ν₋λ°₋, where ν are stoichiometric coefficients and λ° are ionic conductivities. For example, Λ°_m(NaCl) = λ°(Na⁺) + λ°(Cl⁻). This law allows calculation of Λ°_m for weak electrolytes (which cannot be measured directly by extrapolation) from strong electrolyte data. It also enables determination of degree of dissociation α for weak electrolytes: α = Λ_m / Λ°_m, and subsequently the dissociation constant K_a = (c α²) / (1 - α) for a weak acid or base at concentration c.

Λ°_m(electrolyte) = sum of ionic limiting conductivities
Example: Λ°_m(CH₃COONa) = λ°(CH₃COO⁻) + λ°(Na⁺)
For weak electrolyte: α = Λ_m / Λ°_m
Dissociation constant: K_a = (c α²)/(1 - α) or K_a ≈ c α² if α << 1
Used to find Λ°_m of weak acids/bases by adding/subtracting strong electrolyte values

Faraday's Laws of Electrolysis

Faraday's first law: The mass m of a substance deposited or liberated at an electrode is directly proportional to the quantity of electricity Q passed: m = Z × Q = Z × I × t, where Z is the electrochemical equivalent (mass deposited per coulomb), I is current in amperes, and t is time in seconds. Since Q = I × t and Z = E/F (E = equivalent weight, F = 96500 C/mol), we write m = (E × I × t) / 96500 or m = (E × Q) / 96500. Faraday's second law: When the same quantity of electricity is passed through different electrolytes, the masses deposited are proportional to their equivalent weights: m₁/m₂ = E₁/E₂. Equivalent weight E = Molar mass / n (n = number of electrons in the half-reaction). One Faraday (1 F = 96500 C) deposits one gram-equivalent of any substance.

First law: m = (E × I × t) / 96500, where E = equivalent weight (g/eq)
Equivalent weight E = Molar mass / valency (n-factor)
Q = I × t (charge in coulombs); 1 Faraday = 96500 C ≈ 96485 C (exact)
Second law: m₁/m₂ = E₁/E₂ for same Q through different electrolytes
Current efficiency η = (actual mass deposited / theoretical mass) × 100%

Batteries, Fuel Cells & Commercial Cell EMF

Primary cells (non-rechargeable) include the dry cell (Leclanché cell: Zn anode, MnO₂ cathode, NH₄Cl + ZnCl₂ electrolyte, ≈1.5 V) and mercury cell (Zn-Hg amalgam anode, HgO + carbon cathode, KOH electrolyte, 1.35 V constant voltage). Secondary (rechargeable) cells include the lead-acid battery (Pb anode, PbO₂ cathode, H₂SO₄ electrolyte, ~2 V per cell; six cells give 12 V automobile battery) and nickel-cadmium cell. Fuel cells convert chemical energy of fuels directly into electricity; the hydrogen-oxygen fuel cell operates with H₂ at anode (2H₂ + 4OH⁻ → 4H₂O + 4e⁻) and O₂ at cathode (O₂ + 2H₂O + 4e⁻ → 4OH⁻) in aqueous KOH, producing water and ~1.23 V per cell with 60-70% efficiency, far higher than thermal combustion engines.

Dry cell (Leclanché): 1.5 V, primary; anode Zn, cathode MnO₂
Mercury cell: 1.35 V, flat discharge, primary; Zn(Hg) | HgO
Lead-acid battery: 2 V per cell, secondary; Pb | PbO₂ in H₂SO₄
Nickel-cadmium (NiCd): rechargeable, 1.4 V
H₂-O₂ fuel cell: E°_cell ≈ 1.23 V, efficiency ~60-70%, produces H₂O

Key Terms & Definitions for Quick Revision

Oxidation: loss of electrons; increase in oxidation state. Reduction: gain of electrons; decrease in oxidation state. Oxidizing agent: the species that gets reduced (accepts electrons). Reducing agent: the species that gets oxidized (donates electrons). Electrode potential: voltage developed at an electrode relative to a reference. Standard electrode potential E°: measured at 1 M, 1 bar, 298 K versus SHE. Cell potential (EMF): potential difference between cathode and anode. Standard Hydrogen Electrode (SHE): Pt | H₂(1 bar) | H⁺(1M), E° = 0.00 V by convention. Salt bridge: a U-tube containing inert electrolyte that completes the circuit and prevents liquid junction potential. Electrochemical equivalent Z: mass deposited per coulomb (g/C). Molar conductivity Λ_m: conductivity per unit concentration. Limiting molar conductivity Λ°_m: Λ_m at infinite dilution. Degree of dissociation α: fraction of electrolyte dissociated into ions.

Anode → oxidation, loses electrons; cathode → reduction, gains electrons
SHE: reference electrode, E° = 0.00 V at all temperatures by definition
Galvanic cell: chemical → electrical (ΔG < 0); electrolytic cell: electrical → chemical (ΔG > 0)
Faraday constant F = 96500 C/mol (or 96485 C/mol exact)
Conductance unit: siemens (S); resistivity unit: Ω·m; conductivity unit: S·m⁻¹

Important Constants, Units & Sign Conventions

Faraday constant F = 96500 C/mol (approx) or 96485 C/mol (exact). Gas constant R = 8.314 J/(mol·K). Standard temperature = 298 K (25°C). At 298 K, (2.303 RT)/F = 0.0591 V (this appears in the Nernst equation). Units: conductance G in siemens (S); resistance R in ohms (Ω); conductivity κ in S·cm⁻¹ or S·m⁻¹; molar conductivity Λ_m in S·cm²·mol⁻¹; cell potential in volts (V); current in amperes (A); charge in coulombs (C). Sign convention for cell notation: anode (oxidation) is written on the left, cathode (reduction) on the right. All tabulated electrode potentials are reduction potentials. When calculating E°_cell, reverse the sign of the anode potential: E°_cell = E°_cathode - E°_anode. In the Nernst equation, Q uses concentrations of products over reactants; solids and pure liquids are omitted.

F = 96500 C/mol; R = 8.314 J/(mol·K); T = 298 K for standard conditions
0.0591 V factor at 298 K in Nernst equation (from 2.303 RT/F)
Cell notation: Anode | Anode solution || Cathode solution | Cathode
E°_cell = E°_cathode - E°_anode (both as reduction potentials)
Positive E_cell → spontaneous reaction; negative E_cell → non-spontaneous

Common Mistakes, Memory Tricks & Mnemonics

Sign errors in Nernst equation: remember Q = products/reactants by concentration, not mass. For concentration cells, E°_cell = 0, so E_cell is purely logarithmic. Unit confusion: when using Λ_m = (κ × 1000)/M, ensure κ is in S·cm⁻¹ and M in mol/L to get S·cm²·mol⁻¹. Forgetting to reverse anode sign: tabulated potentials are reductions; anode undergoes oxidation, so flip its sign when calculating E°_cell. Faraday's law: always check the n-factor (equivalents per mole); for Cu²⁺ it is 2, for Al³⁺ it is 3. Mnemonic for galvanic vs electrolytic: 'Galvanic Gives' energy (spontaneous), 'Electrolytic Eats' energy (requires external supply). Anode-cathode mnemonic: 'AnOx RedCat'—Anode Oxidation, Reduction Cathode. For Kohlrausch law, remember you can add/subtract whole electrolyte Λ°_m values just like Hess's law in thermochemistry. When writing cell reactions, always balance electrons first, then add half-reactions.

AnOx RedCat: Anode = Oxidation, Cathode = Reduction
Galvanic Gives (spontaneous); Electrolytic Eats (non-spontaneous, needs power)
Nernst at equilibrium: E_cell = 0 → E°_cell = (0.0591/n) log K
Unit check: Λ_m in S·cm²·mol⁻¹ needs κ in S·cm⁻¹ and M in mol/L, multiply by 1000
Always write both half-reactions, balance electrons, then add for net cell reaction

Three Solved Mini-Examples for Formula Practice

Example 1 (Nernst): Calculate E_cell for Zn | Zn²⁺(0.001M) || Ag⁺(0.1M) | Ag at 298 K. E°(Ag⁺/Ag) = +0.80 V, E°(Zn²⁺/Zn) = -0.76 V. Cell reaction: Zn + 2Ag⁺ → Zn²⁺ + 2Ag; n = 2. E°_cell = 0.80 - (-0.76) = 1.56 V. Q = [Zn²⁺]/[Ag⁺]² = 0.001/(0.1)² = 0.001/0.01 = 0.1. E_cell = 1.56 - (0.0591/2) log(0.1) = 1.56 - 0.02955×(-1) = 1.56 + 0.02955 = 1.59 V. Example 2 (Kohlrausch): Λ°_m(NaCl)=126.5, Λ°_m(HCl)=426.2, Λ°_m(CH₃COONa)=91.0 S·cm²·mol⁻¹. Find Λ°_m(CH₃COOH). Λ°_m(CH₃COOH) = Λ°(CH₃COONa) + Λ°(HCl) - Λ°(NaCl) = 91 + 426.2 - 126.5 = 390.7 S·cm²·mol⁻¹. Example 3 (Faraday): How long to deposit 1.0 g Ca from molten CaCl₂ using 2 A current? Ca²⁺ + 2e⁻ → Ca; E_Ca = 40/2 = 20 g/eq. m = (E I t)/96500 → t = (m × 96500)/(E I) = (1.0 × 96500)/(20 × 2) = 96500/40 = 2412.5 s ≈ 40.2 minutes.

Last-Minute One-Glance Revision Box & CBSETUTOR.ai

Core formulas: E_cell = E°_cell - (0.0591/n) log Q at 298 K; E°_cell = E°_cathode - E°_anode; ΔG° = -nFE°_cell; Λ_m = (κ×1000)/M; Λ°_m = Σ ionic λ°; α = Λ_m/Λ°_m; m = (EIt)/96500. Key constants: F = 96500 C/mol, R = 8.314 J/(mol·K), 0.0591 V factor at 298 K. Sign rules: reduction potentials are tabulated; anode undergoes oxidation so reverse sign; positive E_cell means spontaneous. Battery EMFs: dry cell 1.5 V, mercury 1.35 V, lead-acid 2 V/cell, H₂-O₂ fuel cell 1.23 V. Common errors: wrong Q (products/reactants), forgetting 1000 in Λ_m, incorrect n-factor in Faraday's law. For personalized doubt clearing on tricky Nernst or Kohlrausch numericals, CBSETUTOR.ai provides 24×7 AI tutoring with photo upload at just ₹999/month for all subjects across Classes 6-12, with a 3-day free trial to experience instant step-by-step solutions. Thousands of CBSE students rely on it during board season for quick formula recall and error correction. Revise this box 30 minutes before your exam for maximum retention.

E_cell = E°_cell - (0.0591/n) log Q; E°_cell = E°(cathode) - E°(anode); ΔG° = -nFE°_cell
Λ_m = (κ×1000)/M; Λ°_m = ν₊λ°₊ + ν₋λ°₋; α = Λ_m/Λ°_m; K_a = cα²/(1-α)
m = (E I t)/96500; E = Molar mass / n-factor; F = 96500 C/mol
AnOx RedCat; Galvanic spontaneous (E_cell>0), Electrolytic non-spontaneous
Dry 1.5V, Hg 1.35V, Pb-acid 2V, H₂-O₂ fuel 1.23V; check n-factor always

Frequently asked questions

What is the Nernst equation and when do I use it?+

The Nernst equation E_cell = E°_cell - (0.0591/n) log Q (at 298 K) calculates cell potential under non-standard concentrations. Use it whenever ion concentrations differ from 1 M or gas pressures differ from 1 bar.

How do I remember whether to add or subtract electrode potentials?+

Always subtract: E°_cell = E°_cathode - E°_anode. Both values are taken as reduction potentials from tables. The anode undergoes oxidation, so its reduction potential is subtracted.

Why can we not measure limiting molar conductivity of weak electrolytes directly?+

Weak electrolytes do not fully dissociate, so their conductivity remains low even at high dilution. Extrapolation to infinite dilution is unreliable. We calculate Λ°_m using Kohlrausch's law by combining strong electrolyte data.

What is the difference between conductance, conductivity, and molar conductivity?+

Conductance G = 1/R (unit: S) is a property of the solution between two electrodes. Conductivity κ = G×(l/A) (unit: S·cm⁻¹) accounts for geometry. Molar conductivity Λ_m = κ×1000/M (unit: S·cm²·mol⁻¹) normalizes for concentration.

How do I apply Faraday's laws to calculate mass deposited in electrolysis?+

Use m = (E I t)/96500, where E = molar mass/n-factor, I = current (A), t = time (s). First write the electrode reaction to find n (electrons transferred), then compute equivalent weight E.

What is the cell constant and how is it determined?+

Cell constant = l/A (cm⁻¹), the ratio of electrode separation to cross-sectional area. It is found by measuring resistance R of a standard KCl solution of known κ, then cell constant = κ × R.

Why is the Standard Hydrogen Electrode assigned E° = 0.00 V?+

By convention, SHE (Pt | H₂(1 bar) | H⁺(1M)) is the reference electrode. All other electrode potentials are measured relative to it, so it is defined as zero at all temperatures.

How does a concentration cell work if both electrodes are the same?+

A concentration cell has identical electrodes but different ion concentrations. E°_cell = 0, so E_cell arises solely from the Nernst term: E_cell = (0.0591/n) log(C_cathode/C_anode). Current flows until concentrations equalize.

What is Kohlrausch's law and how do I use it for weak acids?+

Kohlrausch's law: Λ°_m(electrolyte) = sum of ionic Λ°. For weak acid CH₃COOH, Λ°_m(CH₃COOH) = Λ°(CH₃COONa) + Λ°(HCl) - Λ°(NaCl). Then α = Λ_m/Λ°_m and K_a = cα²/(1-α).

Which cells are rechargeable and which are primary?+

Primary (non-rechargeable): dry cell (1.5 V), mercury cell (1.35 V). Secondary (rechargeable): lead-acid battery (2 V/cell), nickel-cadmium cell (1.4 V). Fuel cells continuously supply current as long as fuel is fed.

How is CBSETUTOR.ai useful for Electrochemistry numericals?+

CBSETUTOR.ai offers unlimited AI-powered doubt solving via photo upload. Upload your Nernst or Faraday problem, get instant step-by-step solutions with formula recall. ₹999/month flat for Classes 6-12, 3-day free trial available.

What are common sign errors in Electrochemistry?+

Reversing cathode and anode in E°_cell = E°_cathode - E°_anode; writing Q as reactants/products instead of products/reactants; forgetting to flip the sign when the half-reaction is reversed. Always write both half-reactions clearly.

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