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 ............. $A$.

The freezing point of a solution containing $4.8 \ g$ of a compound in $60 \ g$ of benzene is $4.48 ^\circ C$. What is the molar mass of the compound $(K_f = 5.1 \ K \ kg \ mol^{-1})$,(freezing point of benzene $= 5.5 ^\circ C$)?

$A$ solution of sucrose (molar mass $= 342 \, g \, mol^{-1}$) has been prepared by dissolving $68.5 \, g$ of sucrose in $1000 \, g$ of water. The freezing point of the solution obtained will be ......... $^oC$. ($K_f$ for water $= 1.86 \, K \, kg \, mol^{-1}$)

$A$ $5 \%$ solution (by mass) of cane sugar in water has a freezing point of $271 \, K$. Calculate the freezing point of a $5 \%$ glucose solution in water,given that the freezing point of pure water is $273.15 \, K$.

Calculate the molar mass of the solute when $1.5 \ g$ of a non-volatile solute is dissolved in $100 \ mL$ of a solvent having a density of $0.8 \ g \ mL^{-1}$,which lowers its freezing point by $0.75 \ K$. (Freezing point depression constant for the solvent is $5 \ K \ kg \ mol^{-1}$).

What is the molar mass (in $g \ mol^{-1}$) of a substance,which forms a $7 \%$ by mass solution in water,which freezes at $-0.93^{\circ} C$? ($K_{f}$ of $H_2O = 1.86 \ K \ kg \ mol^{-1}$)