b
\(\wedge_{{m}}=1000 \times \frac{\kappa}{{M}}\)

\(=1000 \times \frac{2 \times 10^{-5}}{0.001}=20 {~S} {~cm}^{2} {~mol}^{-1}\)

\(\Rightarrow \alpha=\frac{\wedge_{{m}}}{\wedge_{{m}}^{\infty}}=\frac{20}{190}=\left(\frac{2}{19}\right)\)

\({HA} \rightleftharpoons {H}^{+}+{A}^{-}\)

\(0.001(1-\alpha) \,\,0.001 \alpha \,\,0.001 \alpha\)

\(\Rightarrow \quad {k}_{{a}}=0.001\left(\frac{\alpha^{2}}{1-\alpha}\right)=\frac{0.001 \times\left(\frac{2}{19}\right)^{2}}{1-\left(\frac{2}{19}\right)}\)

\(=12.3 \times 10^{-6}\)