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Start with the molecular weight of oxygen, twice the atomic weight because it's O2.

So the molecular weight is 32.

Now at school you learn that a gram-mole of any gas occupies 22.4 litres.

A gram-mole of oxygen weighs 32 grams (1 gram times the molecular weight).

Therefore 32 grams of oxygen occupies 22.4 litres (at normal temperature and pressure).

22.4 litres of water (specific gravity = 1) weighs 22400 grams.

Therefore the specific gravity is 32/22400 = 0.00142857 . .

That's it!

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