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 fraction of solute = 0.1 means moles of solute = 0.1, moles of solvent = 0.9
`"Mass of solute "=0.1xxM_("solute")g,`
`"Mass of solvent "=0.9xxM_("solvent")g`
`=(0.1M_("solute")+0.9M_("solvent"))g`
Total volume of solution
`=("Mass")/("Density")=(0.1M_("solute")+0.9M_("solvent"))/(2xx1000)L`
Molarity of solution
`=(0.1xx2000)/(0.1M_("solute")+0.9M_("solvent"))"mol L"^(-1)`
`=(200)/(0.1M_("solute")+0.9M_("solvent"))`
`"Molality of solution"`
`=(0.1xx1000)/(0.9M_("solvent"))"mol kg"^(-1)=(100)/(0.9M_("solvent"))`
`"As molarity = molality"`
`(200)/(0.1M_("solute")+0.9M_("solvent"))=(100)/(0.9M_("solvent"))`
`"or "0.1M_("solute")+0.9M_("solvent")=2xx0.9M_("solvent")`
`"or "(0.1M_("solute"))/(M_("solvent"))+0.9=1.8`
`"or "(M_("solute"))/(M_("solvent"))=(0.9)/(0.1)=9`