Molar ConductivityJEE Advanced

Concept

Molar conductivity $\Lambda_m$ measures how well one mole of electrolyte conducts. It rises on dilution — but very differently for strong vs weak electrolytes, which is how we tell them apart.

Key formula

Derivation

Strong electrolytes are fully dissociated; only ion–ion interactions limit them, so $\Lambda_m$ falls linearly with $\sqrt{c}$ (Debye–Hückel–Onsager) and extrapolates cleanly to $\Lambda_m^\circ$.

Weak electrolytes are barely dissociated when concentrated; diluting lets more dissociate, so $\Lambda_m$ rises steeply and $\Lambda_m^\circ$ must be found indirectly via Kohlrausch's law ($\Lambda_m^\circ = \lambda_+^\circ + \lambda_-^\circ$). Here $\alpha = \Lambda_m/\Lambda_m^\circ$.

Scenarios to explore

• Molar Conductivity — Kohlrausch's law for strong vs weak electrolytes.

Real-world applications

• Determining dissociation constants of weak acids.
• Water-purity testing via conductivity.
• Conductometric titrations.

JEE exam tips

• $\alpha = \Lambda_m/\Lambda_m^\circ$ gives the degree of dissociation for weak electrolytes.
• Kohlrausch's law lets you build $\Lambda_m^\circ$ of a weak acid from strong-electrolyte data.

Common mistakes

• Extrapolating a weak electrolyte's curve to get $\Lambda_m^\circ$ — it shoots up, so use Kohlrausch instead.
• Confusing conductivity $\kappa$ (per cm) with molar conductivity $\Lambda_m$.
• Forgetting the factor 1000 in the unit conversion.

Exam traps to avoid

• Both types increase $\Lambda_m$ on dilution, but only the strong one is linear in $\sqrt{c}$.
• Conductivity $\kappa$ decreases on dilution even as $\Lambda_m$ increases.