Question #44244

A solution is prepared by dissolving $12.2 \text{ g}$ of benzoic acid ($\ce{C6H5COOH}$) in $200 \text{ g}$ of benzene ($\ce{C6H6}$) at $280 \text{ K}$. Pure benzene freezes at $280 \text{ K}$ and its entropy of fusion at the freezing point is $34.86 \text{ J K}^{-1} \text{ mol}^{-1}$. The observed freezing point of the solution is $278.44 \text{ K}$. Assuming benzoic acid undergoes dimerization in benzene ($\ce{2C6H5COOH \rightleftharpoons (C6H5COOH)2}$), calculate the equilibrium constant for the dimerization process in terms of molality ($K_m$) at the freezing point.\n\n(Given: Universal gas constant $R = 8.3 \text{ J K}^{-1} \text{ mol}^{-1}$, Molar mass of $\ce{C6H6} = 78 \text{ g mol}^{-1}$, Molar mass of $\ce{C6H5COOH} = 122 \text{ g mol}^{-1}$)