1.0 Molal solution as per definition of molality means 1 mole of solute is present in 1Kg (1000g) solvent
Here the solvent used is water as the solution is aqueous.
Water used = 1000g = 1000/18 moles = 55.56 moles
Number if moles of solute = 1 moles
Number if moles of solvent = 55.56 moles
As per the formula :-
Mole fraction of the solute
= Number if moles of solute/(Number if moles of solute+Number if moles of solvent)
= 1/(1+55.56)
= 1/56.56
= 0.01768
So Mole fraction of the solute in 1.0 molal aqueous solution is 0.01768 .
I hope that you would find this answer useful