Calculate Degree of Dissociation ($\alpha$): For a weak electrolyte, the degree of dissociation $\alpha$ is the ratio of molar conductivity at a specific concentration ($\Lambda_m$) to the limiting molar conductivity ($\Lambda_m^\circ$). $\alpha = \frac{\Lambda_m}{\Lambda_m^\circ}$ Given: $\Lambda_m = 8.0 \text{ S cm}^2 \text{ mol}^{-1}$ and $\Lambda_m^\circ = 400 \text{ S cm}^2 \text{ mol}^{-1}$. $\alpha = \frac{8.0}{400} = 0.02$

Calculate Dissociation Constant ($K_a$): The dissociation constant for a weak acid is given by: $K_a = \frac{c\alpha^2}{1 - \alpha}$ Given: Concentration $c = \text{M}/32 = 1/32 \text{ mol L}^{-1} \approx 0.03125 \text{ M}$. Since $\alpha (0.02)$ is very small compared to 1, we can approximate $1 - \alpha \approx 1$. $K_a \approx c\alpha^2$ $K_a = \frac{1}{32} \times (0.02)^2$ $K_a = \frac{1}{32} \times 4 \times 10^{-4}$ $K_a = \frac{1}{8} \times 10^{-4} = 0.125 \times 10^{-4}$ $K_a = 1.25 \times 10^{-5}$