The conductivity of 0.001M acetic acid is 7.8 × 10^-5 S cm^-1. Calculate its degree of dissociation if Λ^° m for acetic acid is 390 S cm^2 mol^-1.

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