The partial pressure of a component of a mixture is equal to the product of the mole fraction (6.5e-6 in your case) and the total pressure. This is Dalton's Law (not really a law, but a definition).

But note that this merely gives the partial pressure of oxygen in the solution. The oxygen pressure in the atmosphere above the solution is a different matter; for this one needs Henry's Law.

At equilibrium the partial pressure in solution is the same as above the solution. Henry Law's constants for O2 at 25°C is 756.7 atm/(mol/litre) and Mw of oxygen is 32 g/mol. 6.5 ppm is 0.0065 g/Kg. From Henry' law you can calculate:

756.7*0,0065/32 = 0.15 atm.

Jukka, I am not quite sure of that. The fugacities are equal between equilibrium phases, but not the partial pressures. Henry's constant depends on the solvent. Mohammadh did not say which solvent he wants to use,