The mole fraction of the solute in $1 \mathrm{molal}$ aqueous solution is :

Mole fraction of solute $x_{\text{solute }}=?$

Mole of solute$=1$; since the solution is one $\mathrm{molal}$, the

wt. of solvent water $=1 \mathrm{kg}=1000 \mathrm{g}$ 

Also $\text{ g. mol. }$wt. of  ${\mathrm{H}}_2\mathrm{O}=(2\times 1)+16=18 \mathrm{g}.\mathrm{So},\text{ no. of moles of }{\mathrm{H}}_2\mathrm{O}=\frac{1000}{18}=55.5$

Hence,              $x_{\text{solute }}=\frac{\mathrm{no}. \mathrm{of} \mathrm{moles}\text{ of solute }}{\mathrm{no}. \mathrm{of} \mathrm{moles}\text{ of solute }+\mathrm{no}. \mathrm{of} \mathrm{moles}\text{ of }{\mathrm{H}}_2\mathrm{O}}$

$=\frac{1}{1+55.5}=\frac{1}{56.5}=0.0177\simeq 0.018$