A 5.2 molal aqueous solution of methyl alcohol, CH₃OH, is supplied. What is the mole fraction of methyl alcohol in the solution?

0.100

0.190

0.086

0.050

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Solution

0.086

Molality space equals space fraction numerator Moles space of space solute over denominator Mass space of space solvent space left parenthesis in space kg right parenthesis end fraction space equals space fraction numerator 5.2 space mol space CH subscript 3 OH over denominator 1 space kg space left parenthesis equals space 1000 space straight g right parenthesis space straight H subscript 2 straight O end fraction straight n subscript 1 left parenthesis CH subscript 3 OH right parenthesis space equals space 5.2 straight n subscript 2 space left parenthesis straight H subscript 2 straight O right parenthesis space equals space 1000 over 18 space equals space 55.56 straight n subscript 1 plus straight n subscript 2 space equals space 5.20 space plus space 55.66 space equals space 60.76 space mol straight X subscript CH subscript 3 OH end subscript space space equals space Mole space fraction space of space CH subscript 3 OH space equals space fraction numerator straight n subscript 1 over denominator straight n subscript 1 plus straight n subscript 2 end fraction space equals space fraction numerator 52 over denominator 60.76 end fraction space equals space 0.086

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