$A$ 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 $1.86 \ K \ kg \ mol^{-1}$.

$C_{6}H_{6}$ freezes at $5.5^{\circ} C$. The temperature at which a solution of $10 \ g$ of $C_{4}H_{10}$ in $200 \ g$ of $C_{6}H_{6}$ freezes is $...... \ ^{\circ} C$. (The molal freezing point depression constant of $C_{6}H_{6}$ is $5.12 \ ^{\circ} C/m$.)

Pure water freezes at $273 \ K$ and $1 \ bar$. The addition of $34.5 \ g$ of ethanol to $500 \ g$ of water changes the freezing point of the solution. Use the freezing point depression constant of water as $2 \ K \ kg \ mol^{-1}$. The figures shown below represent plots of vapour pressure $(V.P.)$ versus temperature $(T)$. [molecular weight of ethanol is $46 \ g \ mol^{-1}$]. Among the following,the option representing the change in the freezing point is:

How many grams of urea must be dissolved in $500 \ g$ of water to produce a freezing point depression of $0.186^oC$? (Given $K_f = 1.86^oC \ kg \ mol^{-1}$)

For water,$K_f = 1.86 \ K \ kg \ mol^{-1}$. If your car radiator contains $1.0 \ kg$ of water,how many grams of ethylene glycol $(C_2H_6O_2)$ must be added to lower the freezing point of the solution to $-2.8 \ ^\circ C$?

$x$ moles of $CO(NH_2)_2$ are present in $1200 \ g$ of water. If the freezing point of the solution is $-4.02 \ ^oC$,calculate the value of $x$. Given $k_f \ (H_2O) = 1.86 \ K \ kg \ mol^{-1}$.