Calculate the depression in freezing point of a solution when $4 \,g$ of a nonvolatile solute with a molar mass of $126 \,g \,mol^{-1}$ is dissolved in $80 \,mL$ of water. $[$Cryoscopic constant of water $K_f = 1.86 \,K \,kg \,mol^{-1}]$ (in $\,K$)

Ethylene glycol is used as an antifreeze in cold climates. To prevent $4 \ kg$ of water from freezing at $-6^{\circ}C$,how many grams of ethylene glycol must be added? (Given for water: $K_f = 1.86 \ K \ kg \ mol^{-1}$,Molar mass of ethylene glycol $= 62 \ g \ mol^{-1}$)

Given that $\Delta T_f$ is the depression in freezing point of the solvent in a solution of a non-volatile solute of molality $m$,the quantity $\lim_{m \to 0} \left( \frac{\Delta T_f}{m} \right)$ is equal to:

Two elements $A$ and $B$ form compounds with molecular formulas $AB_2$ and $AB_4$. When $1 \ g$ of $AB_2$ is dissolved in $20 \ g$ of $C_6H_6$,the freezing point decreases by $2.3 \ K$. When $1 \ g$ of $AB_4$ is dissolved in $20 \ g$ of $C_6H_6$,the freezing point decreases by $1.3 \ K$. The molal depression constant for benzene is $5.1 \ K \ kg \ mol^{-1}$. Calculate the atomic weights of $A$ and $B$.

Calculate the molality of the solution of a nonvolatile solute if it freezes at $-0.36 \ ^{\circ}C$. [Given: $K_{f}$ for solvent $= 1.86 \ K \ kg \ mol^{-1}$]

An aqueous solution contains $5\%$ by weight of urea and $10\%$ by weight of glucose. The freezing point of the solution is .......... $^oC$. [ $K_f$ for $H_2O$ is $1.86 \ K \ kg \ mol^{-1}$ ]