Answer :
Answer: The molality of the solution is 0.11 m
Explanation:
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:
[tex]\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}[/tex]
Moles of ethanol = 0.865 moles
Molar mass of ethanol = 46 g/mol
[tex]0.865mol=\frac{\text{Mass of ethanol}}{46g/mol}\\\\\text{Mass of ethanol}=(0.865mol\times 46g/mol}=39.79g[/tex]
To calculate the molality of solution, we use the equation:
[tex]Molality=\frac{m_{solute}\times 1000}{M_{solute}\times W_{solvent}\text{ (in grams)}}[/tex]
Where,
[tex]m_{solute}[/tex] = Given mass of solute (methanol) = 0.135 g
[tex]M_{solute}[/tex] = Molar mass of solute (methanol) = 32 g/mol
[tex]W_{solvent}[/tex] = Mass of solvent (ethanol) = 39.79 g
Putting values in above equation, we get:
[tex]\text{Molality of methanol}=\frac{0.135\times 1000}{32\times 39.79}\\\\\text{Molality of methanol}=0.106m\approx 0.11m[/tex]
Hence, the molality of the solution is 0.11 m