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 $Na_2SO_4.$

Assuming $100\%$ ionization,the correct order of freezing point for the following solutions is:

$0.5 \text{ molal}$ aqueous solution of a weak acid $(HX)$ is $20\%$ ionised. If $K_f$ for water is $1.86 \ K \ kg \ mol^{-1}$,the depression in freezing point of the solution is $......... \ K$.

Consider the following solutions:
$I$. $1 \ M$ glucose $(aq.)$
$II$. $1 \ M$ sodium chloride $(aq.)$
$III$. $1 \ M$ acetic acid in benzene
$IV$. $1 \ M$ ammonium phosphate $(aq.)$

$A$ solution of $CaCl_2$ is prepared by dissolving $0.0112 \ g$ of $CaCl_2$ in $1 \ kg$ of distilled water. If the molal freezing point depression constant $(K_f)$ of water is $2 \ K \ kg \ mol^{-1}$,what is the depression in the freezing point of the solution? (Assume $100\%$ ionization of $CaCl_2$)

At a certain temperature,the vapour pressure of pure water is $76 \ mm$ of $Hg$. When $1 \ mol$ of $Na_2SO_4$ is dissolved in $36 \ mL$ of water,the vapour pressure of the solution becomes $38 \ mm$ of $Hg$. What is the percentage dissociation of $Na_2SO_4$ in the solution?