What occupies the spaces between particles in a gas?

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dioprem
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As you can see from the title, I'm puzzled as to what occupies the spaces in between the particles in a gas.

Take air for example. In Chemistry, I have learned that the particles in a gas are far apart. Hence the particles in the air around me are far apart. But if there are no particles in the spaces,it means no matter exists. So is it a vacuum? If so, why don't I experience it on a daily basis?

Sorry if the question is trivial, but it has been bugging me for some time.
 
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Yes, it is vacuum. You don't "see" it as you much larger than the air molecules.

Note that the space between atoms, regardless of the state of matter, or even inside atoms, is mostly vacuum as well.
 
So in other words the distances are insignificant when compared to our size?