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  4. A 5.2 molal aqueous solution of methyl alcohol, CH 3 OH is supplied. What is the mole fraction of methyl alcohol in the solution?

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Q. A $5.2$ molal aqueous solution of methyl alcohol, $CH _{3} OH$ is supplied. What is the mole fraction of methyl alcohol in the solution?

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Solution:

Molality $=\frac{\text { Moles of solute }}{\text { Mass of solvent (in } kg \text { ) }}$
$=\frac{5.2\, mol\, CH _{3} OH }{1\, kg\, H _{2}O} \,\,[1\, kg =1000\, g ]$
$n_{1}\left( CH _{3} OH \right)=5.2, n_{2}\left( H _{2} O \right)=\frac{1000}{18}=55.56$
$\therefore n_{1}+n_{2}=5.20+55.56=60.76\, mol$
$\therefore x_{ CH _{3} OH }=\frac{n_{1}}{n_{1}+n_{2}}=\frac{5.2}{60.76}=0.086$