Mole fraction of the solute in a 1.00 molal aqueous solution is

1 molal solution means 1 mole of solute dissolved in 1000 gm solvent. 
$$\begin{gathered} {\text{∴n}}_{\mathrm{solute} }=1{\mathrm{w}}_{\mathrm{solvent} }=1000\mathrm{g} \\ \therefore {\mathrm{n}}_{\mathrm{solvent} }=\frac{1000}{18}=55.56 \\ {\mathrm{X}}_{\mathrm{solute} }=\frac{1}{1+55.56}=0.0177 \end{gathered}$$