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Air has an approximate molar mass of (28x.8 + 32x.2) = 28 + .2x4 = 28.8 g/mole

1 mole of gas at STP occupies 22.4 L = 22400 cm3 = 0.0224 m3

So 28.8 g/mole x 1 mole/.0224 m3 = 1286 grams per cubic meter at STP

If you take 'normal temperature' to be room temperature of about 20 degrees C then

1286 x (273/293) = 1198 grams per cubic meter at standard pressure and 20 C

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