JEE Main 2019 — Solutions Question with Solution

Since mole fraction of solvent is $0.8,$ it implies that $10\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{s}$ of aqueous solution will have $8$ moles of water and $2$ moles of solute.

$\therefore 2\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{s}$ of solute is present in $\to 8\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{s}$ of water

Or, $2\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{s}$ of solute is present in $\to \left(8\times 18\right)\mathrm{g}\mathrm{m}$ of water

$144\mathrm{ }\mathrm{g}\mathrm{m}$ of water has $2$ moles of solute
$1\mathrm{ }\mathrm{g}\mathrm{m}$ of water will have $\frac{2}{144}\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{s}$ of solute
$1\mathrm{ }\mathrm{k}\mathrm{g}$ of water will have $\frac{2}{144}\times 1000=13.88\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{s}$

$\therefore$ Molality = $13.88\mathrm{ }\mathrm{m}$