Question

The mole fraction of a solute in a solution is $0.1$. At $298K$, morality of this solution is the same as its morality. Density of this solution at $298K$ is $2.0gc{m}^{-1}$. The ratio of the molecular weights of the solute and solvent, $\left(\frac{M{W}_{solute}}{M{W}_{solvent}}\right)$, is?

Answer 1

let $x_1$ and $x_2$ be the mole fractions of solute and solvent

we know that, $x_1+x_2=1$

$x_1=0.1$ (given)

therefore, $x_2=0.9$

$\frac{x_1}{x_2}=\frac{1}{9}$

now $x_1=\frac{n_1}{n_1+n_2}$

$n$ is the no of moles also $n=\frac{W}{M}$ where W and M are weight and molecular mass.

Therefore, $\frac{W_1}{W_2}\times \frac{M_2}{M_1}=\frac{1}{9}$ ....(1)

$W_1+W_2=density\times volume$

$W_1+W_2=2\times volume$

molarity=molality ....(given)

$\frac{n_1}{V_{solution}}=\frac{n_1}{W_1}$

$W_1=V_{soln}=\frac{W_1+W_2}{2}$

$2W_1=W_1+W_2$

$W_1=W_2$ .....(2)

therefore from (1) and (2)

$\frac{M_1}{M_2}=\frac{9}{1}$