Question #44461

A $140 \text{ mmol}$ sample of propane ($\ce{CH3-CH2-CH3}$) undergoes photochemical monochlorination at $298 \text{ K}$. The relative reactivity of $1^{\circ}$ and $2^{\circ}$ C-H bonds towards chlorine radicals is $1 : 4$. The major monochlorinated product (A) is isolated based strictly on its theoretical kinetic yield. Compound (A) is then treated with $\ce{Mg}$ in dry ether, followed by bubbling $\ce{CO2(g)}$ and subsequent acidic workup ($\ce{H3O+}$) to yield compound (B). The entire quantity of (B) produced is dissolved in $1.0 \text{ kg}$ of a non-polar solvent (dielectric constant $\epsilon \approx 2.2$) having a cryoscopic constant $K_f = 5.0 \text{ K kg mol}^{-1}$. Assuming (B) undergoes complete dimerization in this solvent due to intermolecular hydrogen bonding, what is the freezing point depression ($\Delta T_f$) of the resulting solution?