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:

$A$ solution containing $7.5 \ g$ of urea (molar mass $= 60 \ g \ mol^{-1}$) in $1 \ kg$ of water freezes at the same temperature as another solution containing $15 \ g$ of solute $X$,in the same amount of water. The molar mass of $X \ (g \ mol^{-1})$ is

What is the depression of freezing point,when mole fraction of non-electrolyte solute in aqueous solution is $0.01$ (in $K$)? ($K_f$ of $H_2O = 1.86 \ K \ kg \ mol^{-1}$)

Calculate the freezing point of a solution prepared by dissolving $1.8 \ g$ of glucose $(C_6H_{12}O_6)$ in $500 \ g$ of water. The $K_f$ value for water is $1.86 \ K \ kg \ mol^{-1}$. (in $K$)

$1.00 \ g$ of a non-electrolyte solute (molar mass $250 \ g \ mol^{-1}$) was dissolved in $51.2 \ g$ of benzene. If the freezing point depression constant,$K_f$ of benzene is $5.12 \ K \ kg \ mol^{-1},$ the freezing point of benzene will be lowered by .......... $K$.

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 $= 1.86 \ K \ kg \ mol^{-1}$)