The mole fraction of a solute in a solution is 0.1. At 298 K, molarity of this solution is the same as its molality. Density of this solution at 298 K is 2.0 cc. The ratio of the molecular weights of the solute and solvent, $(\frac{M W_{s o l u t e}}{M W_{s o l v e n t}})$ , is ___

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Solution

$X_{A} = 0.1,$ M = m, D = 2gm/ml
0.1 mole 0.9 mole

m = M

$= \frac{0.1 \times 1000}{0.9 \times M W_{s o l v e n t}} = \frac{0.1 \times d \times 1000}{(0.1 M_{1} + 0.9 M_{2})}$

$= \frac{0.1 \times 1000}{0.9 \times M_{2}} = \frac{2}{(0.1 M_{1} + 0.9 M_{2})}$

$= \frac{0.1 M_{2} + 0.1 M_{1}}{0.9 M_{2}} = 2$
$1 + \frac{M_{1}}{0.9 M_{2}} = 2, \frac{M_{1}}{M_{2}} = 9$
$\frac{M_{1}}{9 M_{2}} = 1.$

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