A solution of sucrose in water is labelled as `20%` w/w. What would be the mole fraction of each component in the solution ?

Explanation

`20%("W")/("w")` Sucrose in water solution means
20 gms of Sucrose and 80 gms of water.
Number of moles of sucrose `(n_(s))=(20)/(342)=0.0584`
Number of moles of water `(n_(0))=(80)/(18)=4.444`
Mole fraction of sucrose `X_(s)=(n_(s))/(n_(0)+n_(s))`
`=(0.0584)/(4.444+0.0584)=(0.0584)/(4.50284)=0.01296`
Mole fraction of water `X_(0)=(n_(0))/(n_(0)+n_(s))=(4.444)/(4.50284)=0.9869`
Or
`X_(s)+X_(0)=1`
`X_(0)=1-X_(S)=1-0.01296=0.987`