An aqueous solution of $NaCl$ shows the depression of freezing point of water equal to $0.372 \, K$. The boiling point of $BaCl_2$ solution of same molality will be .........$^oC$. $[K_f(H_2O) = 1.86 \, K \, kg \, mol^{-1}; K_b(H_2O) = 0.52 \, K \, kg \, mol^{-1}]$

Which of the following mixtures is known as Proof Spirit (by volume)?

Statement $1$: The cold pack used by athletes to treat injuries on the field works by dissolving a solute in water,which causes the temperature to decrease. Statement $2$: Adding a non-volatile solute to a solvent decreases its freezing point.

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

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 osmotic pressure of a solution of $NaCl$ is $0.10 \ atm$ and that of a glucose solution is $0.20 \ atm.$ The osmotic pressure of a solution formed by mixing $1 \ L$ of the sodium chloride solution with $2 \ L$ of the glucose solution is $x \times 10^{-3} \ atm.$ $x$ is.......... (nearest integer)