Give a note on the measurement of limiting molar conductivity of a solution of a weak electrolyte.

(N/A) At infinite dilution (i.e.,concentration $c \rightarrow 0$),an electrolyte dissociates completely $(\alpha = 1)$. However,at such low concentrations,the conductivity of the solution is so low that it cannot be measured accurately.
Therefore,the value of $\Lambda_{m}^{\circ}$ cannot be determined by extrapolating the graph of $\Lambda_{m}$ versus $c^{1/2}$.
Instead,$\Lambda_{m}^{\circ}$ for weak electrolytes is obtained using Kohlrausch's law of independent migration of ions.
According to this law,$\Lambda_{m}^{\circ} = \nu_{+} \lambda_{+}^{\circ} + \nu_{-} \lambda_{-}^{\circ}$,where $\lambda^{\circ}$ represents the limiting molar conductivity of individual ions.
Furthermore,the dissociation constant $(K_{a})$ of a weak electrolyte like acetic acid can be calculated using the relation $K_{a} = \frac{c \alpha^{2}}{1 - \alpha}$,where $\alpha = \frac{\Lambda_{m}}{\Lambda_{m}^{\circ}}$.