If $0.072 \ g-atom$ of sulfur is dissolved in $100 \ g$ of solvent $(K_f = 7.00)$,the depression in freezing point is $0.84 \ ^\circ C$. The molecular formula of sulfur in the solution is .............

Calculate the molality of a solution of a non-volatile solute having a depression in freezing point of $0.93 \ K$ and a cryoscopic constant of the solvent of $1.86 \ K \ kg \ mol^{-1}$.

$A$ solution containing $8.0 \, g$ of nicotine in $92 \, g$ of water freezes $0.925 \, ^{\circ}C$ below the normal freezing point of water. If the molal freezing point depression constant,$k_f = 1.85 \, ^{\circ}C \, kg \, mol^{-1}$,then the molar mass of nicotine is $...$

The molal depression constant for water is $1.86\,^{\circ}C/m$. If $342\,g$ of sugar $(C_{12}H_{22}O_{11})$ is dissolved in $1000\,g$ of water,the freezing point of the solution will be ............. $^{\circ}C$.

The freezing point of a solution containing $10 \ mL$ of non-volatile and non-electrolyte liquid $A$ in $500 \ g$ of water is $-0.413^{\circ} C$. If $K_f$ of water is $1.86 \ K \ kg \ mol^{-1}$ and the molecular weight of $A = 60 \ g \ mol^{-1}$, what is the density of the solution in $g \ mL^{-1}$? (Assume $\Delta_{\text{mix}} V = 0$)

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 $273 \ K$)