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 $46 \ g \ mol^{-1}$]. Which of the following plots correctly represents the change in the freezing point?

$83 \ g$ of ethylene glycol is dissolved in $625 \ g$ of water. The freezing point of the solution is $...... \ K$. (Nearest integer) [Use: Molal freezing point depression constant of water $= 1.86 \ K \ kg \ mol^{-1}$,Freezing point of water $= 273 \ K$,Atomic masses: $C = 12.0 \ u, O = 16.0 \ u, H = 1.0 \ u$]

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 $273 \ K$)

Which aqueous solution has the minimum freezing point?

Given below are two statements $:$
Statement $(I) :$ Molal depression constant $K_{f}$ is given by $\frac{M_1 R T_f^2}{1000 \Delta H_{\text {fus }}}$,where symbols have their usual meaning. (Note: The provided formula in the prompt was corrected to the standard thermodynamic expression $K_f = \frac{M_1 R T_f^2}{\Delta H_{\text {fus }}}$).
Statement $(II) :$ $K_{f}$ for benzene is less than the $K_{f}$ for water.
In the light of the above statements,choose the most appropriate answer from the options given below $:$

$A$ solution of sucrose (molar mass $= 342 \, g \, mol^{-1}$) has been prepared by dissolving $68.5 \, g$ of sucrose in $1000 \, g$ of water. The freezing point of the solution obtained will be ......... $^oC$. ($K_f$ for water $= 1.86 \, K \, kg \, mol^{-1}$)