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It would need around 4x1018 kg of air to raise Mars' atmosphere to earth's atmospheric pressure. The answer is formulated under general pressure-depth relation assuming ratio of atmosphere depth is very small to the planet's diameter.

P = m.g/A

P = pressure = 101300 Pascal at earth's sea level

m = mass of air [=] kg

g = Mars gravity = 3.7 m/s2

A = surface area of Mars [=] m2

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Q: How much air mass needed to raise Mars' atmosphere to Earth's atmospheric pressure?
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