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Is there any difference between hydroxide, hydroxyl, and hydroxy used in chemistry or are they all the same?

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Hydroxide - Hydroxide is a diatomic anion with chemical formula $\ce{OH-}$. It consists of a hydrogen and an oxygen atom held together by a covalent bond, and carries a negative electric charge.

Hydroxyl radical- {hydro- + oxy(gen) + -yl + radical} - The hydroxyl radical, •OH, is the neutral form of the hydroxide ion (OH-1). It is the monovalent group -OH which contains hydrogen and oxygen. The suffix -yl indicates it's a radical just like carbonyl.

Hydroxy or hydroxy group: A hydroxy or hydroxy group is the entity with the formula $\ce{-OH}$. It contains oxygen bonded to hydrogen. Hydroxy is also prefix which means containing hydroxyl group.

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