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

$Λ_m= κV; ohm^{-1}\,cm^{2}\,mol^{-1}$

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

Molar conductivity is given by the formula:

$\Lambda_m = \kappa \times V$

where

• Conductivity ($\kappa$): $ohm^{-1} cm^{-1}$ (also known as $S \ cm^{-1}$).
• Volume ($V$): $cm^{3}$ per mol (or $cm^{3} \ mol^{-1}$).

Multiplying them together:

$\Lambda_{m} = (ohm^{-1} cm^{-1}) \times (cm^{3} mol^{-1})$

$\Lambda_{m} = ohm^{-1} cm^{2} mol^{-1}$