Question #44562

A $2.665 \text{ g}$ sample of a hydrate isomer of chromium(III) chloride hexahydrate ($\ce{CrCl3 \cdot 6H2O}$) is dissolved in $100 \text{ g}$ of water. When an excess of aqueous $\ce{AgNO3}$ is added to this solution, it yields $2.870 \text{ g}$ of a white precipitate. Assuming complete ionization of the coordination complex and ideal behavior, what is the freezing point depression ($\Delta T_f$) of the original complex solution before the addition of $\ce{AgNO3}$?

(Given: Molar mass of $\ce{Cr} = 52 \text{ g mol}^{-1}$, $\ce{Cl} = 35.5 \text{ g mol}^{-1}$, $\ce{Ag} = 108 \text{ g mol}^{-1}$; $K_f$ for water = $1.86 \text{ K kg mol}^{-1}$. Assume the water of hydration released into the solution does not significantly change the total mass of the solvent.)