Question #44060

An aqueous solution of a weak electrolyte \ce{X} (molar mass = $120 \text{ g mol}^{-1}$) has an initial concentration of $2.5 \text{ M}$ and a density of $1.10 \text{ g mL}^{-1}$ at $298 \text{ K}$. The electrolyte dissociates reversibly as: $\ce{X(aq) <=> Y(aq) + Z(aq)}$ The forward reaction rate depends only on $[\ce{X}]$, and the backward reaction rate depends symmetrically on $[\ce{Y}]$ and $[\ce{Z}]$. The rate constants are given as $k_f = 0.64 \text{ L mol}^{-1} \text{s}^{-1}$ and $k_b = 0.01 \text{ L}^3 \text{mol}^{-3} \text{s}^{-1}$.

Assuming \ce{Y} and \ce{Z} do not undergo any further reactions and the density of the solution remains constant, calculate the depression in freezing point ($\Delta T_f$) of the solution at equilibrium. (Given: $K_f$ for water = $1.86 \text{ K kg mol}^{-1}$)