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Magnesium hydroxide is an ionic solid with the formula Mg(OH)2. It is considered an ionic compound since it is composed of the magnesium cation (Mg2+) and two hydroxide anions (OH-). There are no covalently shared electrons here. Magnesium hydroxide, although ionic, is not highly soluble in water. As such, it forms a suspension in water that resembles milk, thus the name "milk of magnesia". It is a common antacid since the dissolved hydroxide anions in solution readily quench excess stomach acid. The reaction of the hydroxide anions with acid causes more of the magnesium hydroxide to dissolve until all of the acid has been neutralized.
Magnesium hydroxide is an ionic or electrovalent compound. But it cannot be said that Milk of magnesia is aqueous Magnesium Hydroxide, since it is hardly soluble in water. Milk of magnesia is a suspension of Mg(OH)^2 in water.
It's ionic nature can be proved by the fact that it dissociates in aqueous solution (the small part of magnesium hydroxide which dissolves in water) to form Mg+ and hydroxyl ion (OH-):
Mg(OH)^2------> Mg+ + 2OH-
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