The depression in freezing point observed for a formic acid solution of concentration $0.5 \mathrm{~mL} \mathrm{~L}^{-1}$ is $0.0405^{\circ} \mathrm{C}$. Density of formic acid is $1.05 \mathrm{~g} \mathrm{~mL}^{-1}$. The Van't Hoff factor of the formic acid solution is nearly : (Given for water $\mathrm{k}_{\mathrm{f}}=1.86\, \mathrm{k} \,\mathrm{kg}\,\mathrm{mol}^{-1}$ )

$\Delta \mathrm{T}_{\mathrm{f}}$ of formic acid $=0.0405^{\circ} \mathrm{C}$ <br/><br/> Concentration $=0.5 \mathrm{~mL} / \mathrm{L}$ <br/><br/> and density $=1.05 \mathrm{~g} / \mathrm{mL}$ <br/><br/> $\therefore$ Mass of formic acid in solution $=1.05 \times 0.5 \mathrm{~g}$ <br/><br/> $=0.525 \mathrm{~g}$ <br/><br/> $\therefore$ According to Van't Hoff equation, <br/><br/> $$ \begin{aligned} &\Delta \mathrm{T}_{\mathrm{f}}=\mathrm{i} \mathrm{k}_{\mathrm{f}} \cdot \mathrm{m} \\ &0.0405=\mathrm{i} \times 1.86 \times \frac{0.525}{46 \times 1} \end{aligned} $$ <br/><br/> (Assuming mass of $1 \mathrm{~L}$ water $=\mathrm{kg}$ ) <br/><br/> $\mathrm{i}=\frac{0.0405 \times 46}{1.86 \times 0.525}=1.89 \approx 1.9$