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There are two problems with this question, one is that inert gas is more than one substance and the second is that so is air. Air is a mixture of nitrogen, oxygen, carbon dioxide, argon and other gases. The best way to determine its mass is to take an average between these components.

Next, what's an inert gas? Strictly speaking, the inert gases are the noble gases, which are the elements in group 0 of the Periodic Table. They are helium, neon, krypton, radon, xenon and argon. Hang on..., isn't argon in air?

Helium is the lightest inert gas and as anyone who has seen a helium balloon can testify, it is lighter than air. The further down group 0 you go, towards the likes of xenon and radon, the heavier they get. From krypton onwards, they are all heavier than air except....

... except that all of the noble gases, or the inert gases, can be found in air, in very small amounts. So in a weird way, if you're asking if inert gases are heavier than air, you're asking if they're heavier than themselves.

But to put it in the simplest terms, there is more than one inert gas. Helium can be considered an example of an inert gas that is lighter than air, whereas xenon can be considered an example of one that is heavier.

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11y ago
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Q: What is the inert gas that's lighter than air?
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