The mole fraction of a solute in a solutions is `0.1`. At `298K` molarity of this solution is the same as its molality. Density of this solution at 298 K is `2.0 g cm^(-3)`. The ratio of the molecular weights of the solute and solvent, `(MW_("solute"))/(MW_("solvent"))` is

Explanation

Mole fractin of the solute `(X_(B))=0.1`
`X_(B)=n_(B)/(n_(B)+n_(A))=0.1/((0.1+0.9))=0.1`
According to availabel date, for the solution
`"Molality(m)"="Molarity (M),Density of solution"=2.0 cm^(-3)`
` "Density"=("Mass of solution")/("Volume of solution") or "Mass of solution"="Density"xx"Volume of solution"`
Mass of solute= 1000g: Mass of solvent =1000g
Now `X_(B)=n_(B)/(n_(B)+n_(A))or 0.1=(1000/M_(B))/((1000)/M_(B)+1000/M_(A))`
`100/M_(B)+100/M_(A)=1000/M_(B)or1/M_(B)+1/M_(A)=10/M_(B)`
`1/M_(A)=10/M_(B)-1/M_(B)=9/M_(B)or M_(B)/M_(A)=9`