$W \ g$ of a non-volatile electrolyte solid solute of molar mass $M \ g \ mol^{-1}$ when dissolved in $100 \ mL$ water, decreases vapor pressure of water from $640 \ mm \ Hg$ to $600 \ mm \ Hg$. If aqueous solution of the electrolyte boils at $375 \ K$ and $K_b$ for water is $0.52 \ K \ kg \ mol^{-1}$, then the mole fraction of the electrolyte solute $(X_2)$ in the solution can be expressed as (Given density of water $= 1 \ g/mL$ and boiling point of water $= 373 \ K$):

In the depression of freezing point experiment:
$A.$ Vapour pressure of the solution is less than that of pure solvent
$B.$ Vapour pressure of the solution is more than that of pure solvent
$C.$ Only solute molecules solidify at the freezing point
$D.$ Only solvent molecules solidify at the freezing point

$25 \ mL$ of an aqueous solution of $KCl$ was found to require $20 \ mL$ of $1 \ M \ AgNO_3$ solution when titrated using $K_2CrO_4$ as an indicator. What is the depression in freezing point of $KCl$ solution of the given concentration? (Nearest integer). Given: $K_f = 2.0 \ K \ kg \ mol^{-1}$. Assume: $(1)$ $100 \%$ ionization and $(2)$ density of the aqueous solution as $1 \ g \ mL^{-1}$.

For a dilute solution containing $2.5 \ g$ of a non-volatile non-electrolyte solute in $100 \ g$ of water,the elevation in boiling point at $1 \ atm$ pressure is $2^{\circ} C$. Assuming the concentration of solute is much lower than the concentration of solvent,the vapour pressure ($mm$ of $Hg$) of the solution is (take $K_{b}=0.76 \ K \ kg \ mol^{-1}$)

At $300 \ K$,an ideal solution is formed by mixing $460 \ g$ of toluene with $390 \ g$ of benzene. If the vapour pressure of pure toluene and pure benzene at $300 \ K$ are $32 \ mm$ and $40 \ mm$ respectively,the mole fraction of toluene in the vapour phase is:

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