When a solute is added to a solvent,the freezing point of the solution decreases to $1.86 \ K$. What is the value of $\Delta T_b$? $[K_f = 1.86, K_b = 0.512]$

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 $HA = 60$,$d_{solution} = 1 \, g/mL$]

Which one of the following statements is false?

$2 \ \text{moles}$ each of ethylene glycol and glucose are dissolved in $500 \ \text{g}$ of water. The boiling point of the resulting solution is $:$ (Given $:$ Ebullioscopic constant of water $= 0.52 \ \text{K kg mol}^{-1}$) (in $\text{K}$)

Match List-$I$ with List-$II$

List-$I$	List-$II$
$A$. Solution of chloroform and acetone	$I$. Minimum boiling azeotrope
$B$. Solution of ethanol and water	$II$. Dimerizes
$C$. Solution of benzene and toluene	$III$. Maximum boiling azeotrope
$D$. Solution of acetic acid in benzene	$IV$. $\Delta V_{mix}=0$

Choose the correct answer from the options given below $:$

$A$ 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 If the stoppers $S_{1}$ and $S_{2}$ (as shown in the figure) are suddenly withdrawn,the volume of the gas in litres after equilibrium is achieved will be ............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 $= 273 \; K$)