The formula for mole fraction is:
-(1)
The solubility of oxygen gas = 1.0 mmol/L (given)
1.0 mmol/L means 1.0 mmol are present in 1 L.
Converting mmol to mol:

So, moles of oxygen = 0.001 mol
For moles of water:
1 L of water = 1000 mL of water
Since, the density of water is 1.0 g/mL.


So, the mass of water is 1000 g.
Molar mass of water = 18 g/mol.
Number of moles of water = 
Substituting the values in formula (1):


Hence, the mole fraction is
.