For $1000 \ g$ of $1,4$-dioxane,the cryoscopic constant $K_f = 4.9 \ K \ kg \ mol^{-1}$. What will be the depression in freezing point for a $0.001 \ m$ solution prepared in dioxane?

Calculate $\Delta T_{f}$ of aqueous $0.01 \ m$ formic acid if the van't Hoff factor is $1.1$. $[K_{f} = 1.86 \ K \ kg \ mol^{-1}]$ (in $K$)

Freezing point of a $4 \%$ aqueous solution of $X$ is equal to the freezing point of a $12 \%$ aqueous solution of $Y$. If the molecular weight of $X$ is $A$,then the molecular weight of $Y$ is ............. $A$.

At $T$ $(K)$,$x \ g$ of a non-volatile solid (molar mass $78 \ g \ mol^{-1}$) when added to $0.5 \ kg$ water,lowered its freezing point by $1.0^{\circ} C$. What is $x$ (in $g$)? ($K_{f}$ of water at $T$ $(K)$ = $1.86 \ K \ kg \ mol^{-1}$)

$150 \ g$ of acetic acid was contaminated with $10.2 \ g$ ascorbic acid $(C_{6}H_{8}O_{6})$ to lower its freezing point by $(x \times 10^{-1})^{\circ} C$. The value of $x$ is (Nearest integer). [Given $K_{f} = 3.9 \ K \ kg \ mol^{-1}$; Molar mass of ascorbic acid $= 176 \ g \ mol^{-1}$]

Dissolution of $1.5 \ g$ of a non-volatile solute (mol. wt. $= 60$) in $250 \ g$ of a solvent reduces its freezing point by $0.01 \ ^{\circ}C$. Find the molal depression constant of the solvent.