State Kohlrausch's law of independent migration of ions and explain its applications.

(N/A) Kohlrausch's law of independent migration of ions states that 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. Mathematically,$\Lambda_{m}^{\circ} = \nu_{+} \lambda_{+}^{\circ} + \nu_{-} \lambda_{-}^{\circ}$,where $\nu_{+}$ and $\nu_{-}$ are the number of cations and anions per formula unit of electrolyte,and $\lambda_{+}^{\circ}$ and $\lambda_{-}^{\circ}$ are the limiting molar conductivities of the individual ions.
Applications:
$1$. Calculation of limiting molar conductivity $(\Lambda_{m}^{\circ})$ for weak electrolytes: The law allows the determination of $\Lambda_{m}^{\circ}$ for weak electrolytes by using the limiting molar conductivities of strong electrolytes.
$2$. Calculation of degree of dissociation $(\alpha)$: For a weak electrolyte at a given concentration $c$,the degree of dissociation is given by $\alpha = \frac{\Lambda_{m}}{\Lambda_{m}^{\circ}}$,where $\Lambda_{m}$ is the molar conductivity at concentration $c$.
$3$. Calculation of dissociation constant $(K_{a})$: The dissociation constant is calculated using the formula $K_{a} = \frac{c \alpha^{2}}{1 - \alpha} = \frac{c \Lambda_{m}^{2}}{\Lambda_{m}^{\circ}(\Lambda_{m}^{\circ} - \Lambda_{m})}$.