The experimentally determined molar mass of a non-volatile solute,$BaCl_2$,in water by Cottrell's method,is

At $300 \ K$,the osmotic pressure of a decinormal solution of sodium chloride is $4.82 \ atm$. The degree of dissociation of sodium chloride is $x \times 10^{-2}$. The value of $x$ is $\left(R=0.082 \ L \ atm \ K^{-1} \ mol^{-1}\right)$

In a solution with molality $m$,if the solute exists in the form of a dimer,which of the following cannot be the elevation in the boiling point of the solution?

$0.2$ molal aqueous solution of $KCl$ freezes at $-0.680^{\circ} C$. Calculate van't Hoff factor for this solution. $(K_{f} = 1.86 \ K \ kg \ mol^{-1})$

If a $0.01 \ m$ aqueous solution of an electrolyte freezes at $-0.056 \ ^{\circ}C$,calculate the van't Hoff factor $(i)$ for the electrolyte. (Cryoscopic constant of water $K_{f} = 1.86 \ K \ kg \ mol^{-1}$)

$2$ molal solution of a weak acid $HA$ has a freezing point of $-3.885^{\circ} C$. The degree of dissociation of this acid is ........ $\times 10^{-3}$. (Round off to the Nearest Integer).
[Given: Molal depression constant of water = $1.85 \ K \ kg \ mol^{-1}$,Freezing point of pure water = $0^{\circ} C$]