To find the freezing point of an electrolyte solution like NaCl, we must include the van't Hoff factor ($i$) in the depression of freezing point formula: $\Delta T_f = i \times K_f \times m$.

1. Determine the van't Hoff factor ($i$): NaCl is a strong electrolyte that dissociates completely in water: $NaCl \rightarrow Na^+ + Cl^-$. Since it yields 2 ions per formula unit, $i = 2$.

2. Calculate Depression in Freezing Point ($\Delta T_f$): Given $K_f = 1.86 \, ^\circ\text{C}/m$ and $m = 0.1 \text{ m}$. $\Delta T_f = 2 \times 1.86 \times 0.1 = 0.372 \, ^\circ\text{C}$.

3. Calculate Freezing Point of Solution ($T_f$): $T_f = T_f^0 - \Delta T_f$ Freezing point of pure water ($T_f^0$) = $0^\circ\text{C}$.

• $T_f = 0 - 0.372 = -0.372 \, ^\circ\text{C}$.