Question

Calculate the mole fraction of ethanol and water in a sample of rectified spirit which contains 46% ethanol by mass

Answer 1

The question states that the solution has 46% ethanol by mass
so if the solution weighs 100gms, it contains 46gms of ethanol and 54gms of water
Number of moles of ethanol = weight of ethanol / molecular weight of ethanol
the molecular weight of ethanol is 46

The number of moles of ethanol is 46/46 i.e 1
The number of moles of water is 54/18 i.e 3

mole fraction of ethanol = no.of moles of ethanol / total number of moles

$Molefraction=\frac{n_1\left(numberofmolesofsolute\right)}{n_1+n_2(Numberofmolesofsolute+numberofmolesofsolvent)}$

$Now{n}_1\left(molesofethanol\right)$

$Molefractionofethanol=\frac{Numberofmolesofethanol}{Totalnumberofmoles}=\frac{1}{3}=0.33$

$Molefractionofwater=1-molefractionofethanol$

$=1-0.33=0.66$