The mole fraction of solvent in 0.1 molal aqueous solution is

 

 molality= moles of solute/ mass of solvent(kg) 

1 molal solution means 1 mole is present in 1000g of water 

mass of solvent= 1000g= 1kg moles of solvent=1000/18=55.56

${\mathrm{X}}_{\mathrm{solvent}}=\frac{{\mathrm{n}}_{\mathrm{solvent}}}{{\mathrm{n}}_{\mathrm{solute}}+{\mathrm{n}}_{\mathrm{solvent}}}=\frac{55.55}{1+55.55}=0.9982$