An aqueous solution contains $6\%$ and $4\%$ by weight of a weak acid $(HA)$ and urea respectively. If the depression in freezing point is $\frac{13.6}{3} \, ^{\circ}C$,calculate the $K_a$ of $HA$. [Given: $K_f = 1.8 \, K \, kg/mol$,Molecular weight of $HA = 60$,$d_{solution} = 1 \, g/mL$]

$A$ cylinder containing an ideal gas ($0.1 \; mol$ in $1.0 \; dm^{3}$) is in thermal equilibrium with a large volume of $0.5 \; m$ (molal) aqueous solution of ethylene glycol at its freezing point. If the stoppers $S_{1}$ and $S_{2}$ (as shown in the figure) are suddenly withdrawn,the volume of the gas in litres after equilibrium is achieved will be ............ $litre$.
(Given: $K_{f}$ (water) $= 2.0 \; K \; kg \; mol^{-1}$,$R = 0.08 \; dm^{3} \; atm \; K^{-1} \; mol^{-1}$,freezing point of water $= 273 \; K$)

Which of the following statements are not correct?
$A$. For water, magnitude of $K_b$ is more than the magnitude of $K_f$.
$B$. The elevation in boiling point of water when a non-volatile solute is added to it is larger in magnitude than its depression in freezing point.
$C$. Osmotic pressure measurement is preferred over any other colligative property to determine molar mass of proteins and polymers.
$D$. The dimerised form of benzoic acid in benzene is $C_6H_5 - C(=O) - OH \cdots O = C(OH) - C_6H_5$. Choose the correct answer from the options given below:

At $80^o C$,the vapor pressure of pure liquid $A$ is $520 \ mm \ Hg$ and that of pure liquid $B$ is $1000 \ mm \ Hg$. If a mixture of $A$ and $B$ boils at $80^o C$ and $1 \ atm$ pressure,the mole percentage of $A$ in the mixture is ........... $(1 \ atm = 760 \ mm \ Hg)$.

The solution from the following with the highest depression in freezing point (lowest freezing point) is:

$2.5 \ g$ of a non-volatile,non-electrolyte is dissolved in $100 \ g$ of water at $25^{\circ} C$. The solution showed a boiling point elevation by $2^{\circ} C$. Assuming the solute concentration is negligible with respect to the solvent concentration,the vapour pressure of the resulting aqueous solution is . . . . . . $mm$ of $Hg$ (nearest integer).
[Given : Molal boiling point elevation constant of water $(K_b) = 0.52 \ K \ kg \ mol^{-1}$,
$1 \ atm$ pressure $= 760 \ mm$ of $Hg$,molar mass of water $= 18 \ g \ mol^{-1}]$