The conductivity of 0.001M acetic acid is $\displaystyle 7.8 \times 10^{-5} \mathrm{~S} \mathrm{~cm}^{-1}$. Calculate its degree of dissociation if $\displaystyle \mathbf{\Lambda}^{\circ} \mathrm{m}$ for acetic acid is $\displaystyle 390 \mathrm{~S} \mathrm{~cm}^{2} \mathrm{~mol}^{-1}$.

\[\begin{aligned} \mathbf{\Lambda}_{\mathrm{m}} & =\frac{\mathrm{k}}{C} \times 1000 \Omega^{-1} \mathrm{~cm}^{2} \mathrm{~mol}^{-1} \\ & =\frac{7 \cdot 8 \times 10^{-5}}{0.001} \times 1000 \Omega^{-1} \mathrm{~cm}^{2} \mathrm{~mol}^{-1} \\ & =78 \Omega^{-1} \mathrm{~cm}^{2} \mathrm{~mol}^{-1} \text { or } 78 \mathrm{~S} \mathrm{~cm}^{2} \mathrm{~mol}^{-1} \\ \alpha & =\frac{\mathbf{\Lambda}_{\mathrm{m}}}{\mathbf{\Lambda}_{\mathrm{m}}^{\circ}} \\ & =\frac{78}{390}=0.2 \end{aligned} \]