The mole fraction of solvent in 0.1 molal aqueous solution is

Mole fraction of solute$=\frac{0.1}{0.1+{\displaystyle \frac{1000}{18}}}=\frac{0.1}{55.6}=0.0017$

Mole fraction of solvent = 1 -Mole fracti on of solute

Mole fraction of solvent = 100 -0.0017 =0.9982