<u>Answer:</u> The molality of the solution is 0.11 m
<u>Explanation:</u>
We are given:
Mole fraction of methanol = 0.135
This means that 0.135 moles of methanol is present in 1 mole of a solution
Moles of ethanol = 1 - 0.135 = 0.865 moles
To calculate the mass for given number of moles, we use the equation:

Moles of ethanol = 0.865 moles
Molar mass of ethanol = 46 g/mol

To calculate the molality of solution, we use the equation:

Where,
= Given mass of solute (methanol) = 0.135 g
= Molar mass of solute (methanol) = 32 g/mol
= Mass of solvent (ethanol) = 39.79 g
Putting values in above equation, we get:

Hence, the molality of the solution is 0.11 m