Calculate the molality of a nonvolatile solution if the solution freezes at $-0.95^{\circ}C$ $[K_f \text{ for water} = 1.86 \ K \ kg \ mol^{-1}, \text{ freezing point of water} = 0^{\circ}C]$.

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 $B$.

$31 \ g$ of ethylene glycol $(C_2H_6O_2)$ is dissolved in $600 \ g$ of water. The freezing point depression of the solution is ($K_f$ for water is $1.86 \ K \ kg \ mol^{-1}$) (in $K$)

The amount of urea to be dissolved in $500 \ mL$ of water $(K_f = 18.6 \ K \ kg \ mol^{-1})$ to produce a depression of $0.186 \ ^oC$ in freezing point is $....... \ g$. (Assume density of water = $1 \ g/mL$)

$A$ solution of a nonvolatile solute is obtained by dissolving $15 \ g$ in $200 \ mL$ of water,which has a depression in freezing point of $0.75 \ K$. Calculate the molar mass of the solute if the cryoscopic constant of water is $1.86 \ K \ kg \ mol^{-1}$.

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 $0.2 \ K$.