$A$ 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

Calculate the molar mass of the solute when $1.5 \ g$ of a non-volatile solute is dissolved in $100 \ mL$ of a solvent having a density of $0.8 \ g \ mL^{-1}$,which lowers its freezing point by $0.75 \ K$. (Freezing point depression constant for the solvent is $5 \ K \ kg \ mol^{-1}$).

What is the freezing point of a $1 \ molal$ aqueous solution of a non-volatile solute (in $^{\circ} C$)? $(K_{f} = 1.86 \ K \ kg \ mol^{-1}, T_{f}^{\circ} \text{ for water } = 0^{\circ} C)$

Calculate the molecular weight of a substance whose $7.0\%$ by mass solution in water freezes at $-0.93\,^{\circ}C$. The cryoscopic constant of water is $1.86\,^{\circ}C\,kg\,mol^{-1}$. .......... $g\,mol^{-1}$.

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 $273 \ K$)

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: