Question

A storage battery contains a solution of $H_{2}S{O}_4$, 38% by weight. What will be the Van't Hoff factor if the $\Delta T_{fexperiment}is\mathrm{29.08.}[Given{K}_f=1.86mo{l}^{-1}Kg]$

• A. $i=1.25$
• B. $i=2.5$
• C. $i=3.$
• D. $i=3.5$

Answer 1

The correct option is B $i=2.5$

Freezing point depression is a colligative property observed in solutions that result from the introduction of solute molecules to a solvent. The freezing points of solutions are all lower than that of the pure solvent and is directly proportional to the molality of the solute.

$\Delta T_f={T_f}^0-T_f=i.K_b.m$.

$\Delta T_f$ is freezing point depression.

$T_f$ is freezing point of solution.

$K_b$ is depression constant.

Let the total mass be $100$ g.

Let the mass of sulphuric acid be $38$ g.

Molality $=m=\frac{\frac{38}{98}}{\frac{62}{1000}}=6.25$

$\Delta T_f=29.08K$

$K_f=1.86$

we get, $i=\frac{29.08}{6.25\times 1.86}=2.50$