Calculate mole fraction of ethanol and water in a sample of rectified spirit which contains 92% ethanol by mass.

Explanation

We are given that
The mass percentage of ethanol = 92 g
We are to find the mole fraction `(x_(A))` of ethanol and `(x_(B))` of water
We know that
Mass of solution = 100 g
Mass of ethanol `(w_(A))` = 92 g
Mass of water `(w_(B))` = 100-92 = 8 g
Mass of water `(n_(B))="Mass"/("Molar mass")=(8g)/(18"g mol"^(-1))=0.44"mol"`
Mass of ethanol `(n_(A))=(92g)/(46"g mol"^(-1))=2"mol"`
Using the relation , Mole fraction of ethanol `(x_(A))=n_(A)/(n_(A)+n_(B))=2/(0.44+2)=2/(2.44)=0.82`
Mole fraction of water `(x_(B))=1=0.82=0.18 [becausex_(A)+x_(B)=1]`