After adding a solute,the freezing point of the solution decreases to $-0.186 \ ^{\circ}C$. Calculate $\Delta T_b$ if $K_f = 1.86 \ K \ kg \ mol^{-1}$ and $K_b = 0.521 \ K \ kg \ mol^{-1}$. (Assume the freezing point of pure solvent is $0 \ ^{\circ}C$)

Boiling point of acetone is $.......$ $^{\circ}C$

Identify the false statement from the following.

$P$ and $Q$ combine to form two compounds $PQ_2$ and $PQ_3$. If $1 \ g$ of $PQ_2$ is dissolved in $51 \ g$ of benzene, the depression of freezing point is $0.8^{\circ} C$. If $1 \ g$ of $PQ_3$ is dissolved in $51 \ g$ of benzene, the depression of freezing point is $0.625^{\circ} C$. Given $K_f$ of benzene $= 5.1 \ K \ kg \ mol^{-1}$, calculate the atomic masses of $P$ and $Q$.

Which of the following statements concerning the properties of solutions describes a colligative effect?

The boiling point of water in a $0.1 \ m$ molal silver nitrate solution (solution $A$) is $x \ ^{\circ}C$. To this solution $A$,an equal volume of $0.1 \ m$ molal aqueous barium chloride solution is added to make a new solution $B$. The difference in the boiling points of water in the two solutions $A$ and $B$ is $y \times 10^{-2} \ ^{\circ}C$. (Assume: Densities of the solutions $A$ and $B$ are the same as that of water and the soluble salts dissociate completely. Use: Molal elevation constant,$K_b = 0.5 \ K \ kg \ mol^{-1}$; Boiling point of pure water as $100 \ ^{\circ}C$.) $(1)$ The value of $x$ is $(2)$ The value of $|y|$ is