Question

The mole fraction of a solute is $0.1$. At $298K$ molarity of this solution is the same as its molality. The density of this solution at $298K$ is $2.0gc{m}^{-3}$. The ratio of the molecular weights of the solute and solvent. $m_{solute}/m_{solvent}$ is:

Answer 1

Given-

1 mole solution has 0.1 mole solute and 0.9 mole solvent

Let $M_1$=molar mass solute

$M_2$=Molar mass solvent

Molality,$m=\frac{0.1}{0.9M_2}\times 1000$ ......(1)

Molarity,$M=\frac{0.1}{0.1M_1+0.9M_2}\times 2\times 1000$ ....(2)

Since $m=M$

$\frac{0.1\times 1000}{0.9M_2}=\frac{200}{0.1M_1+0.9M_2}$

$\frac{M_1}{M_2}=9$

Hence the ratio of molecular weights of solute and solvent is $\frac{9}{1}$.