What is the relationship betweeen the reactivity of an element and the likelihood of its existing as an uncombined element?

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There is a very real relationship between the two.  Elements that are not prone to combine with other elements to form compounds are usually very chemically unreactive.  The perfect example of this is a group of elements called the noble gasses.  They are located in group 18 on the far right side of the periodic table.  These elements exist only as monoatomic gasses and they do not readily form compounds with other elements.  This is because they are extremely stable, unreactive compounds.  They have an octet of electrons in their valence shells.  Other elements form ions and covalent bonds to try and achieve this stable octet of electrons.  Since the noble gasses already have a valence octet built in, they have no need to react with other elements to form chemical compounds.

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