Question #99918

An organic weak acid $\ce{HA}$ (Molar mass = $120 \text{ g mol}^{-1}$) is dissolved in benzene. At $298 \text{ K}$, the molarity of the solution is $0.80 \text{ M}$ and its density is $0.896 \text{ g mL}^{-1}$. In benzene, $\ce{HA}$ undergoes dimerization: $2\ce{HA} \rightleftharpoons \ce{(HA)2}$. The dimerization equilibrium constant on the molality scale at the freezing point of the solution is $K_m = 10.0 \text{ kg mol}^{-1}$. Given the freezing point of pure benzene is $278.50 \text{ K}$ and its cryoscopic constant $K_f = 5.12 \text{ K kg mol}^{-1}$, calculate the freezing point of the solution.