The conductivity of a weak acid HA of concentration 0.001 ~mol ~L^...

\Lambda_{\mathrm{m}}=1000 \times \frac{\mathrm{K}}{\mathrm{M}}$<br />$=1000 \times \frac{2 \times 10^{-5}}{0.001}=20 \mathrm{ S} \mathrm{ cm}^2 \mathrm{ mol}^{-1}$<br />$\Rightarrow \alpha=\frac{\Lambda_{\mathrm{m}}}{\Lambda_{\mathrm{m}^{{}^{\circ}}}=\frac{20}{190}= \left(\frac{2}{19}\right)
\underset{0.001(1-\alpha)}{\mathrm{HA}}\rightleftharpoons \underset{0.001 \alpha}{\mathrm{H}^{+}}+\underset{0.001 \alpha}{\mathrm{A}^{-}}<br />K_{\mathrm{a}}$=0.001\left(\frac{\alpha^2}{1-\alpha}\right)=\frac{0.001 \times\left(\frac{2}{19}\right)^2}{1-\left(\frac{2}{19}\right)}<br />$=12.3 $\times10^{-6}$