Write a note on Kohlrausch law of independent migration of ions and limiting molar conductivity $\Lambda_{m}^{o}$ of strong electrolyte.

(N/A) Kohlrausch examined $\Lambda_{m}^{o}$ values for several strong electrolytes and observed certain regularities. He noted that the difference in $\Lambda_{m}^{o}$ of the electrolytes $NaX$ and $KX$ for any $X$ is nearly constant. For example,at $298 \ K$ :
$[\Lambda_{m(KCl)}^{o} - \Lambda_{m(NaCl)}^{o}] = [\Lambda_{m(KBr)}^{o} - \Lambda_{m(NaBr)}^{o}] = [\Lambda_{m(KI)}^{o} - \Lambda_{m(NaI)}^{o}] = 23.4 \ S \ cm^{2} \ mol^{-1}$
Similarly,$[\Lambda_{m(NaBr)}^{o} - \Lambda_{m(NaCl)}^{o}] = [\Lambda_{m(KBr)}^{o} - \Lambda_{m(KCl)}^{o}] = 1.8 \ S \ cm^{2} \ mol^{-1}$
Kohlrausch Law: Based on the above observations,he enunciated the Kohlrausch law of independent migration of ions.
Law: The limiting molar conductivity of an electrolyte can be represented as the sum of the individual contributions of the anion and cation of the electrolyte.
If $\lambda_{Na^{+}}^{o}$ is the limiting molar conductivity of sodium ions and $\lambda_{Cl^{-}}^{o}$ is the limiting molar conductivity of chloride ions,then:
$\Lambda_{m(NaCl)}^{o} = \lambda_{Na^{+}}^{o} + \lambda_{Cl^{-}}^{o}$
In general,if an electrolyte on dissociation gives $\nu_{+}$ cations and $\nu_{-}$ anions,then its limiting molar conductivity is given by:
$\Lambda_{m}^{o} = \nu_{+} \lambda_{+}^{o} + \nu_{-} \lambda_{-}^{o}$
Here,$\lambda_{+}^{o}$ and $\lambda_{-}^{o}$ are the limiting molar conductivities of the cation and anion,respectively.