Mole fraction

[anteater85]

Hi guys could u plz help me with this question:

The molecular weight of ethyl alcohol is 46, and MW of water is 18. How many grams of ethyl alcohol must be mixed with 100 mL of water for the mole fraction(X) of ethyl alcohol to be 0.2?

THe answer is 64.4g

Thank you

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[nze82]

Density of H2O = 1 g/ml
100ml H2O x (1g/1ml) x (1mole/18g) = 5.6 mole H2O

Mole fraction = n(alc)/n(total) = n(alc)/(5.6 + n(alc)) = 0.2

1.12 + 0.2n(alc) = n(alc)

0.8n(alc) = 1.12 --> n(alc) = 1.4 mole

1.4 mole x (46g/1mole) = 64.4g

 

[anteater85]

Density of H2O = 1 g/ml
100ml H2O x (1g/1ml) x (1mole/18g) = 5.6 mole H2O

Mole fraction = n(alc)/n(total) = n(alc)/(5.6 + n(alc)) = 0.2

1.12 + 0.2n(alc) = n(alc)

0.8n(alc) = 1.12 --> n(alc) = 1.4 mole

1.4 mole x (46g/1mole) = 64.4g

where did u get the 1.12 from?

 

[nze82]

where did u get the 1.12 from?

Little magic trick called "cross-multiplying."

5.6(0.2) = 1.12