Nernst Equation & Cell EMF: JEE Main Guide

Electrochemistry is one of the highest-yield chapters in JEE Main Chemistry, contributing two to four questions every session. The Nernst equation is its centrepiece — it connects standard cell potential to concentration, temperature, and equilibrium, threading through galvanic cells, concentration cells, and battery chemistry. This guide covers the Nernst equation systematically with every JEE Main question type explained.

Standard Electrode Potentials and Cell EMF

The standard hydrogen electrode (SHE) is the reference: E° = 0 V by convention. Standard reduction potentials E°_red are measured relative to SHE. Cell EMF: E°_cell = E°_cathode − E°_anode (always reduction potential of cathode minus reduction potential of anode). Positive E°_cell means the reaction is spontaneous. The species with higher reduction potential is reduced at the cathode; the species with lower reduction potential is oxidised at the anode.

Relation to Gibbs free energy: ΔG° = −nFE°_cell, where n is the number of electrons transferred and F = 96500 C/mol (Faraday's constant). Spontaneous (ΔG° < 0) ↔ E°_cell > 0. For the full electrochemistry chapter context, see our Electrochemistry Guide.

The Nernst Equation

The Nernst equation relates the EMF of a cell to the concentrations (or activities) of the species: E_cell = E°_cell − (RT/nF)·ln Q, where Q is the reaction quotient. At 25°C (298 K): E_cell = E°_cell − (0.0592/n)·log Q. JEE Main uses this form almost exclusively. For the reaction aA + bB → cC + dD: Q = [C]^c[D]^d / ([A]^a[B]^b). Note: solids, pure liquids, and gases at standard pressure (1 atm) are excluded from Q.

At equilibrium, E_cell = 0 and Q = K: 0 = E°_cell − (0.0592/n)·log K, giving log K = nE°_cell/0.0592. JEE Main tests this relationship: given E°_cell, find K; or given K, find E°_cell. Standard result to know: if E°_cell = 0.0592/n, then log K = 1 → K = 10. Take a free mock test on electrochemistry to practise Nernst equation calculations under exam conditions.

Concentration Cells

A concentration cell has identical electrodes but different concentrations of the same electrolyte in each half-cell. E°_cell = 0 (same electrodes), so: E_cell = −(0.0592/n)·log Q = (0.0592/n)·log (C_higher/C_lower). The electrode in contact with the more concentrated solution is the cathode (where reduction occurs). JEE Main tests: given concentrations in two half-cells, find the EMF, or identify which electrode is cathode.

Faraday's Laws of Electrolysis

First law: mass deposited m = ZQ = ZIt, where Z is the electrochemical equivalent and I is current in amperes for time t in seconds. Second law: masses of different substances deposited by the same quantity of electricity are proportional to their equivalent weights (M/n). Combined formula: m = (M/n) × (It/F). JEE Main calculation template: how long does it take to deposit 2.54 g of Cu (M=63.5, n=2) at 2 A current? t = m × n × F / (M × I) = 2.54 × 2 × 96500 / (63.5 × 2) = 3860 s ≈ 64.3 min.

Batteries: Primary and Secondary Cells

Daniel cell (Zn-Cu): Zn → Zn²⁺ + 2e⁻ (anode); Cu²⁺ + 2e⁻ → Cu (cathode); E° ≈ 1.1 V. Dry cell (Leclanché): Zn anode, MnO₂/NH₄Cl cathode, E ≈ 1.5 V — primary cell (non-rechargeable). Lead storage battery: Pb anode, PbO₂ cathode, H₂SO₄ electrolyte, E ≈ 2 V per cell (12 V car battery = 6 cells). Rechargeable — charging reverses the reaction. Mercury cell: Zn-Hg amalgam anode, HgO cathode, KOH electrolyte, E ≈ 1.35 V, constant EMF throughout discharge — used in hearing aids and medical devices.

Fuel cells: hydrogen-oxygen fuel cell — H₂ oxidised at anode, O₂ reduced at cathode, water formed. Highly efficient (no intermediate combustion). JEE Main tests the cell reactions of lead storage battery and fuel cells as product-identification questions.

Electrolytic Conductance

Conductance G = 1/R; specific conductivity κ = G × (l/A); molar conductivity Λ_m = κ/c (c in mol/m³). Kohlrausch's law of independent migration: Λ°_m = ν⁺λ°₊ + ν⁻λ°₋, where λ° are the limiting molar conductivities of individual ions. JEE Main uses Kohlrausch's law to find the molar conductivity of a weak electrolyte at infinite dilution from the data for strong electrolytes (using appropriate algebraic combinations). For the chemical equilibrium context that connects to this, see our Ionic Equilibrium Guide.

Exam Strategy

Nernst equation and Faraday's laws together cover 70% of electrochemistry JEE Main questions. For Nernst: identify n (electrons transferred in balanced equation), write Q from concentrations, substitute into E = E° − 0.0592/n × log Q. For Faraday: use m = MIt/(nF). For E°_cell: cathode E° minus anode E° — never get this order reversed. For standard cell potential from ΔG° or K, use the two bridge equations. Link with our Chemical Equilibrium Guide for the K relationship. Upgrade for ₹149/month for complete electrochemistry mock tests with Nernst and Faraday problems.