Determine the expected value of $\Delta \mathrm{T}_{\mathrm{f}}$ for $1 \mathrm{~m}$ $\mathrm{CaCl}_2$ solution if 1 m urea solution has $\Delta \mathrm{T}_{\mathrm{f}}$ value ' $x$ ' K .

The freezing point depression $\Delta T_f$ is a colligative property given by $\Delta T_f = i \cdot K_f \cdot m$, where $i$ is the van't Hoff factor, $K_f$ is the cryoscopic constant, and $m$ is the molality.

For urea, a non-electrolyte with $i = 1$, the observed depression is $\Delta T_{f,\text{urea}} = x = 1 \cdot K_f \cdot 1$, so $K_f = x$.

Calcium chloride dissociates as $\mathrm{CaCl}_2 \rightarrow \mathrm{Ca}^{2+} + 2\mathrm{Cl}^-$, giving $i = 3$. Thus, for $1\ \mathrm{m}\ \mathrm{CaCl}_2$,
$\Delta T_{f,\mathrm{CaCl}_2} = 3 \cdot K_f \cdot 1 = 3x$.

The expected freezing point depression is $3x\ \mathrm{K}$.