Write a note on molar conductivity $(\Lambda_{m})$ of a solution.

(N/A) The conductivity of solutions of different electrolytes in the same solvent and at a given temperature differs due to the charge and size of the ions in which they dissociate,the concentration of ions,or the ease with which the ions move under a potential gradient. It,therefore,becomes necessary to define a physically more meaningful quantity called molar conductivity. It is denoted by the symbol $\Lambda_{m}$ (Greek,lambda).
It is related to the conductivity of the solution by the equation:
$\Lambda_{m} = \frac{k}{c}$
Where,
$k =$ conductivity of the solution (unit: $S \ m^{-1}$)
$c =$ concentration of the solution (unit: $mol \ m^{-3}$)
$\Lambda_{m} =$ molar conductivity of the solution
Therefore,the unit of $\Lambda_{m}$ is $S \ m^{2} \ mol^{-1}$.
In practical units,if $k$ is in $S \ cm^{-1}$ and concentration $(c)$ is in $mol \ L^{-1}$ (molarity),the formula is:
$\Lambda_{m} = \frac{k \times 1000}{Molarity}$
The unit becomes $S \ cm^{2} \ mol^{-1}$ or $\Omega^{-1} \ cm^{2} \ mol^{-1}$.
Conversion factor:
$1 \ S \ m^{2} \ mol^{-1} = 10^{4} \ S \ cm^{2} \ mol^{-1}$