Nernst EquationJEE Main

Concept

Real cells rarely run at standard conditions. The Nernst equation corrects the standard potential $E°$ for the actual concentrations through the reaction quotient $Q$ — explaining why a battery's voltage drops as it discharges.

Key formula

Derivation

From thermodynamics, $\Delta G = \Delta G° + RT\ln Q$ and $\Delta G = -nFE$. Combining and converting $\ln$ to $\log_{10}$ at 298 K gives the $0.0591/n$ coefficient.

As products build up, $Q$ rises, $\log Q > 0$, and $E$ falls — until $E = 0$ at equilibrium ($Q = K$), when the cell is 'dead'.

Scenarios to explore

• Nernst Equation — Cell potential vs concentration & ΔG.
• Product-rich cell — Q = 1000 pushes the cell potential down by (0.059/n) log Q.
• Reactant-rich cell — A tiny Q raises the EMF above the standard value.

Real-world applications

• Battery and fuel-cell voltage prediction.
• pH meters and ion-selective electrodes.
• Corrosion and concentration cells.

JEE exam tips

• At equilibrium $E = 0$ and $\log K = nE°/0.0591$ — links potential to the equilibrium constant.
• A concentration cell has $E° = 0$, so its voltage comes entirely from the $\log Q$ term.

Common mistakes

• Writing $Q$ upside down — it is products over reactants.
• Using the $0.0591/n$ form at temperatures other than 298 K.
• Forgetting pure solids and liquids are omitted from $Q$.

Exam traps to avoid

• $E > 0 \Leftrightarrow \Delta G < 0$ — spontaneous; watch the sign relationship.
• Increasing reactant concentration lowers $Q$, which raises the cell voltage.