The freezing point depression of a solution containing $0.6 \ g$ of urea (molar mass $= 60 \ g \ mol^{-1}$) in $100 \ mL$ of benzene (in $K$) is ($K_f$ of benzene $= 4.0 \ K \ kg \ mol^{-1}$).

Calculate the cryoscopic constant $(K_f)$ of a solvent if the depression in freezing point of a $0.18 \ m$ solution of a non-volatile solute is $0.2 \ K$.

If the freezing point of an aqueous urea solution is $271.14 \ K$ at $1 \ \text{atm}$ pressure (given $K_f$ of water = $1.86 \ K \ kg/mol$),then what is the mole fraction of urea in this solution? (Freezing point of pure water is $273 \ K$)

Two solutions $A$ and $B$ are prepared by dissolving $1 \ g$ of non-volatile solutes $X$ and $Y$ respectively in $1 \ kg$ of water. The ratio of depression in freezing points for $A$ and $B$ is found to be $1: 4$. The ratio of molar masses of $X$ and $Y$ is.

When $36 \ g$ of a non-volatile,non-electrolytic solute having the empirical formula $CH_2O$ is dissolved in $1.2 \ kg$ of water,the solution freezes at $-0.93 \ ^\circ C$. The molecular formula of the solute is ($K_f$ of water $= 1.86 \ K \ kg \ mol^{-1}$)

If $6 \ g$ of solute dissolved in $100 \ g$ of water lowers the freezing point by $0.93 \ K$. What is the molar mass of the solute? $(K_{f} = 1.86 \ K \ kg \ mol^{-1})$