$0.5 \ m$ aqueous solution of a weak acid $(HX)$ is $20 \%$ ionized. If $K_{f}$ of water is $1.86 \ K \ kg \ mol^{-1}$,the lowering in freezing point of the solution is: (in $K$)

The freezing point depression constant for water is $1.86 \, ^\circ C \, m^{-1}$. If $5.00 \, g$ of $Na_2SO_4$ is dissolved in $45.0 \, g$ of $H_2O$,the freezing point is changed by $3.82 \, ^\circ C$. Calculate the van't Hoff factor $(i)$ for $Na_2SO_4$.

The Van't Hoff factor of the compound $K_3[Fe(CN)_6]$ is

Which of the following will have the lowest vapor pressure?

$5 \ g$ of $Na_2SO_4$ was dissolved in $x \ g$ of $H_2O$. The change in freezing point was found to be $3.82 \ ^oC$. If $Na_2SO_4$ is $81.5 \%$ ionised,the value of $x$ ($K_f$ for water $= 1.86 \ ^oC \ kg \ mol^{-1}$) is approximately .............. $g$ (molar mass of $S = 32 \ g \ mol^{-1}$ and that of $Na = 23 \ g \ mol^{-1}$)

$80$ mole percent of $MgCl_2$ is dissociated in aqueous solution. The vapour pressure of $1.0$ molal aqueous solution of $MgCl_2$ at $38^{\circ} C$ is $.........$ $mm$ $Hg$. (Nearest integer)
Given : Vapour pressure of water at $38^{\circ} C$ is $50$ $mm$ $Hg$.