The freezing point depression constant for water is $1.86 \, ^oC \, kg \, mol^{-1}.$ If $5.00 \, g$ of $Na_2SO_4$ is dissolved in $45.0 \, g$ of $H_2O,$ the freezing point is lowered by $3.82 \, ^oC.$ Calculate the van't Hoff factor for $Na_2SO_4.$

Which of the following aqueous solutions will have the highest freezing point?

The freezing point of equimolal aqueous solution will be highest for

If a compound $AB$ dissociates to the extent of $75\,\%$ in an aqueous solution,the molality of the solution which shows a $2.5\, K$ rise in the boiling point of the solution is $......$ molal.
(Rounded-off to the nearest integer) $[K_{b} = 0.52\, K\, kg\, mol^{-1}]$

An aqueous solution is prepared by dissolving $0.1 \ mol$ of an ionic salt in $1.8 \ kg$ of water at $35^{\circ} C$. The salt remains $90 \%$ dissociated in the solution. The vapour pressure of the solution is $59.724 \ mm \ Hg$. Vapor pressure of water at $35^{\circ} C$ is $60.000 \ mm \ Hg$. The number of ions present per formula unit of the ionic salt is . . . . . .

In which case is Raoult's law not applicable?