JEE Main 2011 — Some Basic Concepts Of Chemistry Question with Solution

The formula between Mole fraction and Molality is $m = {{{X_{solute}}} \over {{X_{solvent}}}} \times {{1000} \over {{M_{solvent}}}}$
$$m$$ = molality, X_solute = Mole fraction of solute, X_solvent = Mole fraction of solvent, M_solvent = Molar mass of solvent

Here solute is methyl alcohol(CH₃OH) and solvent is water(H₂O). Here water is solvent because question says solution is aqueous.

Assume mole fraction of methyl alcohol = X

So mole fraction of water = 1 - X

and given molality (m) = 5.2

M_solvent = 18 (as molar mass of H₂O = 18)

$$\therefore$$ 5.2 = $$\frac{X}{1-X}\times \frac{1000}{18}$$

by solving this we get,

X = 0.086