The correct expression and unit of molar conductivity ( Λ_m ) are:

The correct answer is Option (3) → \(Λ_m= κV; ohm^{-1}\,cm^{2}\,mol^{-1}\)

Molar conductivity is related to conductivity by:

    \( \displaystyle \Lambda_m = \kappa V \)

Since V is the volume that contains 1 mol, V = 1/c, so the same relation is also written \( \Lambda_m = \kappa / c \).

The unit follows from the units of the two factors:

    \( \displaystyle \kappa:\ \mathrm{ohm^{-1}\,cm^{-1}} \qquad V:\ \mathrm{cm^{3}\,mol^{-1}} \)

    \( \displaystyle \Lambda_m = \mathrm{ohm^{-1}\,cm^{-1}} \times \mathrm{cm^{3}\,mol^{-1}} = \mathrm{ohm^{-1}\,cm^{2}\,mol^{-1}} \)

So \( \Lambda_m = \kappa V \), with the unit ohm⁻¹ cm² mol⁻¹ (S cm² mol⁻¹).

Why the other options are incorrect

• Option (1) \(Λ_m= κc; ohm^{-1}\, mol\, L^{-1}\) — Incorrect. Molar conductivity is conductivity divided by concentration, not multiplied by it, and the unit is wrong too.

• Option (2) \(Λ_m= κV; ohm^{-1}\,cm^{2}\) — Incorrect. The expression is right, but the unit leaves out mol⁻¹, which comes from V being the volume per mole.

• Option (4) \(Λ_m= κc; ohm\, mol^{-1}\) — Incorrect. Both the expression and the unit are wrong; a conductance has the unit ohm⁻¹, not ohm.

NCERT (2026-27 edition):
Variation of Conductivity and Molar Conductivity with Concentration – …