If the molar conductivity ($\Lambda_m$) of a $0.050\ \text{mol L}^{-1}$ solution of a monobasic weak acid is $90\ \text{S cm}^2\,\text{mol}^{-1}$, its extent (degree) of dissociation will be [Assume $\lambda^\circ_+ = 349.6\ \text{S cm}^2\,\text{mol}^{-1}$ and $\lambda^\circ_- = 50.4\ \text{S cm}^2\,\text{mol}^{-1}$]

Solution & Explanation

\textbf{Answer:} (A) $\alpha = 0.225$ \textbf{Solution:} Limiting molar conductivity by Kohlrausch's law: $\Lambda_m^\circ = \lambda^\circ_+ + \lambda^\circ_- = 349.6 + 50.4 = 400\ \text{S cm}^2\,\text{mol}^{-1}$ Degree of dissociation: $\alpha = \dfrac{\Lambda_m}{\Lambda_m^\circ} = \dfrac{90}{400} = 0.225$