Given: Concentration, $c = 0.007\text{ M}$ Molar conductivity, $\Lambda_m = 20\text{ S cm}^2\text{ mol}^{-1}$ Limiting molar conductivity of $H^+$, $\Lambda^{\circ}_{H^+} = 350\text{ S cm}^2\text{ mol}^{-1}$ Limiting molar conductivity of $CH_3COO^-$, $\Lambda^{\circ}_{CH_3COO^-} = 50\text{ S cm}^2\text{ mol}^{-1}$

According to Kohlrausch's law, limiting molar conductivity of acetic acid: $\Lambda^{\circ}_m(CH_3COOH) = \Lambda^{\circ}_{H^+} + \Lambda^{\circ}_{CH_3COO^-}$ $\Lambda^{\circ}_m = 350 + 50 = 400\text{ S cm}^2\text{ mol}^{-1}$

Degree of dissociation, $\alpha = \frac{\Lambda_m}{\Lambda^{\circ}_m} = \frac{20}{400} = 0.05$

Dissociation constant, $K_a = \frac{c\alpha^2}{1 - \alpha}$ Assuming $1 - \alpha \approx 1$ (since $\alpha$ is small): $K_a \approx c\alpha^2 = 0.007 \times (0.05)^2 = 0.007 \times 0.0025 = 1.75 \times 10^{-5}\text{ mol L}^{-1}$