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

20%(w/w) sucrose solution means
20gms of sucrose present in 100gm of solution
$\therefore$wt. of sucrose(w) = 20gm
sucrose:
${\mathrm{w}}_1=20$
${\mathrm{n}}_1=\frac{{\mathrm{w}}_1}{{\mathrm{m}}_1}=\frac{20}{342}=0.05848$
water:
${\mathrm{w}}_2=80(100-20)$
${\mathrm{n}}_2=\frac{{\mathrm{w}}_2}{{\mathrm{m}}_2}=\frac{80}{18}=4.45$
Mole fraction sucrose
$\left({\mathrm{X}}_1\right)=\frac{{\mathrm{n}}_1}{{\mathrm{n}}_1+{\mathrm{n}}_2}=\frac{0.05848}{4.503}=0.013$
$\therefore$Mole fraction water
$\left({\mathrm{X}}_2\right)=1-{\mathrm{x}}_1=1-0.013=0.987$