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Because the compounds produced are in a lower energy state (electrically) than the unreacted atoms.

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Energy has to be put into a compound to split it into its atomic components.

If you look at the "Noble Gasses" (Helium, Neon, Argon, Krypton etc) they do not react with other atoms to form compounds. This is because they have enough electrons orbiting their nuclei to "fill" or "complete" an entire electron shell - this is a very stable "low energy" position to be in.

Basically, when atoms form compounds, the atoms "share" their outermost electrons in an attempt to complete their electron shells (those with an extra electron sharing this with an atom that has too few).

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