Chemistry - Concentration Terms Question with Solution | TestHub

Let molarity = molality $=\mathrm{m}$

∴ One litre solution contains on mole solute

∴ wt. of one litre solution $=1000\times 2=2000\mathrm{gm}$

∴ wt. of solvent $=2000-\mathrm{m}\times {\mathrm{M}}_{\text{solute }}$

∴ mole fraction of solute $=\frac{\mathrm{m}}{\mathrm{m}+\left(\frac{200-\mathrm{m}\times {\mathrm{M}}_{\text{solute }}}{{\mathrm{M}}_{\text{solvent }}}\right)}=0.1$

$\therefore \mathrm{m}=0.1\mathrm{m}+\frac{200-0.1\times \mathrm{m}\times {\mathrm{M}}_{\text{solute }}}{{\mathrm{M}}_{\text{solvent }}}$

$0.9\mathrm{m}\times {\mathrm{M}}_{\text{solvent }}=200-0.1\times \mathrm{m}\times {\mathrm{M}}_{\text{solute }}\dots \left(1\right)$

∴ molality $=\mathrm{m}=\frac{\mathrm{m}}{2000-\mathrm{m}\times {\mathrm{M}}_{\text{solute }}}\times 1000$

$2000-\mathrm{m}\times {\mathrm{M}}_{\text{solute }}=1000\dots \left(2\right)$

From (1) and (2)

$\mathrm{m}\times {\mathrm{M}}_{\text{solvent }}=\frac{1000}{9}\dots \left(3\right)$

From (2) $/(3):\frac{{\mathrm{M}}_{\text{solute }}}{{\mathrm{M}}_{\text{solvent }}}=9$