Solid Lead nitrate is dissolved in $1 \, L$ of water. The solution was found to boil at $100.15^{\circ}C$. When $0.2 \, mol$ of $NaCl$ is added to the resulting solution,it was observed that the solution froze at $-0.8^{\circ}C$. The solubility product of $PbCl_2$ formed is $........... \times 10^{-6}$ at $298 \, K$. (Nearest integer) Given: $K_b = 0.5 \, K \, kg \, mol^{-1}$ and $K_f = 1.8 \, K \, kg \, mol^{-1}$. Assume molality to be equal to molarity in all cases.

The difference between the boiling point and freezing point of an aqueous solution of urea containing $10.0 \ kg$ of water is $100.2372 \ ^oC$. How many grams of urea are dissolved in the solution? (Given: $K_b = 0.513 \ K \ kg \ mol^{-1}$,$K_f = 1.86 \ K \ kg \ mol^{-1}$)

Which of the following aqueous solutions produce the same osmotic pressure?

$2.5 \ g$ 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 $= 18 \ g \ mol^{-1}]$

Which one of the following statements is false?

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 $:$