The van't Hoff factor of an aqueous solution of storage battery containing 49% ${\mathrm{H}}_2{\mathrm{SO}}_4$ by weight and a depression in freezing point of 27.9 K is approximately.

[Given: $K_f=1.86\mathrm{K}-\mathrm{kg}/\mathrm{mole}$]

Given, aqueous solution of storage battery contains 49% ${\mathrm{H}}_2{\mathrm{SO}}_4$ by weight. Freezing point = 27.9 K.

$K_f=1.86\mathrm{K}-\mathrm{kg}/\mathrm{mole}$

The van't Hoff factor can be calculated as,

$$\begin{gathered} \mathrm{\Delta }{T}_f=\mathit{i}\mathit{\times }{\mathit{k}}_{\mathit{f}}\times m \\ 27.9=i\times 1.86\times \frac{\frac{49}{98}}{100}\times 1000 \\ \Rightarrow i=3 \end{gathered}$$