CBSE Class 12 Electrochemistry — Complete Guide with Nernst Equation & Solved Numericals

In short: Electrochemistry (Chapter 3) is a numerically rich chapter in CBSE Class 12 Chemistry, carrying 5-6 marks out of 70. It covers galvanic cells, Nernst equation, conductance and conductivity, Kohlrausch's law, electrolysis, batteries, and corrosion. Expect at least 1 numerical (typically Nernst equation or conductance-based) and 1 theory question. The formulas are few but powerful — master the Nernst equation and conductance calculations, and this chapter becomes a guaranteed scoring zone.

Marks Distribution

For the complete chapter-wise breakdown, see CBSE Class 12 Chemistry chapter-wise marks weightage.

Galvanic Cell (Voltaic Cell)

A galvanic cell converts chemical energy into electrical energy through a spontaneous redox reaction.

Example — Daniell Cell: Zn-Cu cell

Cell representation: Zn(s) | Zn²⁺(aq) || Cu²⁺(aq) | Cu(s)

Salt bridge: Contains KCl or KNO₃ in agar-agar. It maintains electrical neutrality by allowing ion flow between the two half-cells.

EMF of cell: E°cell = E°cathode - E°anode

For Daniell cell: E° = +0.34 - (-0.76) = +1.10 V

Nernst Equation

This is the most important formula in the chapter. It relates EMF to concentration.

For a general reaction: aA + bB → cC + dD

Nernst Equation:

E_cell = E°_cell - (RT/nF) ln Q

At 25°C (298 K), converting to log₁₀:

E_cell = E°_cell - (0.0591/n) log₁₀ [Products]/[Reactants]

Where:

• E° = standard EMF
• n = number of electrons transferred
• Q = reaction quotient = [C]ᶜ[D]ᵈ / [A]ᵃ[B]ᵇ

At equilibrium: E_cell = 0, so E° = (0.0591/n) log K

Relationship Between ΔG° and E°

ΔG° = -nFE°

Where F = Faraday's constant = 96500 C/mol

Conductance and Conductivity

Key Terms and Formulas

Where M = molarity (mol/L).

Board exam tip: κ = conductivity, Λₘ = molar conductivity. Don't confuse them. κ decreases with dilution, but Λₘ increases with dilution (ions are further apart, less inter-ionic attraction).

Variation of Molar Conductivity with Dilution

• Strong electrolytes: Λₘ increases slightly with dilution (already fully dissociated). Λₘ = Λ°ₘ - A√c (Debye-Hückel-Onsager equation)
• Weak electrolytes: Λₘ increases sharply at high dilution (more dissociation occurs). Cannot extrapolate Λ°ₘ from graph.

Kohlrausch's Law

Statement: The limiting molar conductivity of an electrolyte equals the sum of the individual limiting ionic conductivities of its constituent ions.

Λ°ₘ(NaCl) = λ°(Na⁺) + λ°(Cl⁻)

Applications

1. Finding Λ°ₘ of weak electrolytes: Λ°ₘ(CH₃COOH) = Λ°ₘ(CH₃COONa) + Λ°ₘ(HCl) - Λ°ₘ(NaCl)

2. Finding degree of dissociation (α): α = Λₘ / Λ°ₘ

3. Finding dissociation constant (Kₐ): Kₐ = cα² / (1-α)

Electrolysis and Faraday's Laws

Faraday's First Law

The mass of substance deposited at an electrode is directly proportional to the quantity of charge passed.

m = ZIt = ZQ

Where Z = electrochemical equivalent, I = current, t = time, Q = charge.

Faraday's Second Law

When the same charge is passed through different electrolytes, masses deposited are proportional to their equivalent weights.

m₁/m₂ = E₁/E₂

1 Faraday (F) = 96500 C = charge on 1 mole of electrons

To deposit 1 mole of any monovalent ion: 1F needed To deposit 1 mole of divalent ion: 2F needed

Batteries and Corrosion

Primary Batteries (Non-rechargeable)

Secondary Batteries (Rechargeable)

Fuel Cells

• H₂-O₂ fuel cell: 2H₂ + O₂ → 2H₂O (E° ≈ 1.23 V)
• Continuous supply of fuel, no recharging needed
• High efficiency (40-70%), pollution-free

Corrosion

• Electrochemical process where metals are oxidized
• Iron rusting: Fe → Fe²⁺ + 2e⁻ (at anode); O₂ + 4H⁺ + 4e⁻ → 2H₂O (at cathode)
• Fe²⁺ further oxidizes to Fe₂O₃·xH₂O (rust)
• Prevention: Painting, galvanizing (Zn coating), cathodic protection, alloying

Solved Numericals

Numerical 1: Nernst Equation

Q: Calculate the EMF of the cell: Zn | Zn²⁺(0.001M) || Cu²⁺(0.1M) | Cu. Given E°Zn²⁺/Zn = -0.76V, E°Cu²⁺/Cu = +0.34V.

Solution: E° = E°cathode - E°anode = 0.34 - (-0.76) = 1.10 V n = 2 (two electrons transferred)

E = E° - (0.0591/n) log([Zn²⁺]/[Cu²⁺]) E = 1.10 - (0.0591/2) log(0.001/0.1) E = 1.10 - (0.02955) log(10⁻²) E = 1.10 - (0.02955)(-2) E = 1.10 + 0.0591 = 1.159 V

Numerical 2: Molar Conductivity

Q: The conductivity of 0.20 M KCl solution at 298 K is 0.0248 S/cm. Calculate its molar conductivity.

Solution: Λₘ = κ × 1000/M = 0.0248 × 1000/0.20 = 124 S cm² mol⁻¹

Numerical 3: Kohlrausch's Law

Q: Λ°ₘ of NaCl, HCl, and CH₃COONa are 126.4, 425.9, and 91.0 S cm² mol⁻¹ respectively. Find Λ°ₘ of CH₃COOH.

Solution: Λ°ₘ(CH₃COOH) = Λ°ₘ(CH₃COONa) + Λ°ₘ(HCl) - Λ°ₘ(NaCl) = 91.0 + 425.9 - 126.4 = 390.5 S cm² mol⁻¹

Numerical 4: Faraday's Law

Q: How long will it take to deposit 2.7 g of Al (atomic mass = 27) from Al₂(SO₄)₃ solution using a current of 5 A?

Solution: Al³⁺ + 3e⁻ → Al Moles of Al = 2.7/27 = 0.1 mol Charge needed = 0.1 × 3 × 96500 = 28950 C Time = Q/I = 28950/5 = 5790 seconds ≈ 96.5 minutes

Numerical 5: ΔG° Calculation

Q: The standard EMF of a cell is 1.5 V and 2 electrons are transferred. Calculate ΔG°.

Solution: ΔG° = -nFE° = -2 × 96500 × 1.5 = -289500 J = -289.5 kJ

Since ΔG° is negative, the reaction is spontaneous.

Board Exam Important Questions

1. Derive the Nernst equation for the cell Zn|Zn²⁺||Cu²⁺|Cu. Calculate EMF when [Zn²⁺] = 0.1M and [Cu²⁺] = 1M. (5 marks) — Very high frequency
2. Define conductivity and molar conductivity. How do they vary with dilution for strong and weak electrolytes? (3 marks)
3. State Kohlrausch's law. How can it be used to find Λ°ₘ of a weak electrolyte? (3 marks)
4. How much charge is required to reduce 1 mol of Cr₂O₇²⁻ to Cr³⁺? (2 marks)
5. What is a fuel cell? How does an H₂-O₂ fuel cell work? Write electrode reactions. (3 marks)
6. Explain the electrochemical theory of rusting of iron. How can it be prevented? (3 marks)
7. Calculate the EMF of a cell where ΔG° = -193 kJ/mol and n = 2. (2 marks)

Frequently Asked Questions

How many marks does Electrochemistry carry?

5-6 marks out of 70 in the theory paper. It is a moderate-weightage chapter but appears consistently with at least one numerical.

Is the Nernst equation numerical guaranteed?

Almost. It appears in about 80% of board papers either as a direct numerical or as part of a derivation question. Always practice with different concentration values.

What is the difference between conductivity and molar conductivity?

Conductivity (κ) measures the conductance of a solution between electrodes 1 cm apart — it decreases with dilution because fewer ions are present per unit volume. Molar conductivity (Λₘ) is conductivity per mole of electrolyte — it increases with dilution because inter-ionic interactions decrease.

How do I remember the Kohlrausch's law application formula?

Think of it as "addition and subtraction of salts." To get CH₃COOH, you need the CH₃COO⁻ ion (from CH₃COONa) and the H⁺ ion (from HCl), but you've added an extra Na⁺ and Cl⁻ — so subtract NaCl.

What is the cell constant and why does it matter?

Cell constant (G* = l/A) is a property of the conductivity cell — the ratio of the distance between electrodes to the area. κ = G × G*. You need the cell constant to convert measured conductance into conductivity.

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