What is the difference between an aqueous solution and a hydrate?

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Every website I look at says something different and they seem to contradict the bits I think I’m understanding from other websites.

In: Chemistry
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In aqueous solution, the dissolved ions have a gang of water molecules tagging along because they’re attracted to the charge. There’s no real structure here, and waters come and go as they please.

A hydrate is more structured. The water molecules are trapped in a specific chemical lattice with the hydrated compound, and even if all the excess water evaporates away those water molecules will often remain interlaced in the solid. They’re an important part of the size, shape, and reactivity profile of the hydrate.

In a hydrate, the water is stoichiometrically bound in a crystal structure. A fixed amount of water related to the other ions. In a solution, the other ions float around in a random amount of water, with no fixed structure.