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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Explain the relationship between the reactivity of an element and the likelihood of it existing as an uncombined element.

Reactivity is a measure of the reaction potential of an element. In other words, reactivity of an element tells us the likelihood of an element reacting with another element. For example, an element that has a high reactivity with oxygen, is likely to react with it, on exposure to oxygen or air. 

An element, that has a high reactivity, is more likely to exist in the combined form than uncombined form. For example, if an element has a high reactivity with oxygen, it is more likely to exist as oxide than as pure element, in nature. Nonreactive elements (such as noble gases), on the other hand, are more likely to occur in the pure form, since they are unable to combine with other elements. 

Thus, reactivity of an element is a deterrence to its existence in uncombined or pure form, in the nature.

Hope this helps. 

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