When $174.5 \ mg$ of octatomic sulfur $(S_8)$ is added to $78 \ g$ of bromine $(Br_2)$,the boiling point of bromine becomes ............. $K$. Given: $K_b$ for $Br_2 = 5.2 \ K \ kg \ mol^{-1}$ and the boiling point of pure $Br_2 = 332.15 \ K$.

Calculate the molal elevation constant $(K_b)$ of a solvent if the boiling point of a $0.12 \ m$ solution is $319.8 \ K$ (Boiling point of pure solvent = $319.5 \ K$).

Calculate the molality of the solution containing a nonvolatile solute if the boiling point elevation of the solution is $0.39 \ K$.
[$K_{b}$ of water $= 0.52 \ K \ kg \ mol^{-1}$]

$A$ solution of $6 \ g$ of solute in $100 \ g$ of water boils at $100.52^{\circ} C$. The molal elevation constant of water is $0.52 \ K \ kg \ mol^{-1}$. What is the molar mass of the solute?

If an aqueous solution contains $9 \%$ and $1 \%$ $(w/w)$ of two non-volatile non-electrolytes $X$ (molecular weight $180$) and $Y$ (molecular weight $50$) respectively,the boiling point of the solution in ${ }^{\circ} C$ is approximately $(K_b = 0.52 \ K \ kg \ mol^{-1})$

$A$ solution of $50 \text{ g}$ of solute '$X$' is dissolved in $150 \text{ g}$ of '$Y$' solvent boils at $357.27 \text{ K}$. What is the molar mass of solute (in $\text{ g/mol}$)? (Given $K_b$ and boiling point of pure solvent are $2.77 \text{ K kg/mol}$ and $350.06 \text{ K}$ respectively.)