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One of the biggest factors in dissolving speed in the type of bonds its atoms have. The most soluble substances are ionic, meaning that a positive ion (usually an Alkali metal or Alkali Earth metal, like sodium) is attracted to a negative ion (always a non-metal or metaloid like chlorine). In the examples I gave, chlorine would bond with sodium to form salt.

Less soluble than ionic substances, covalant substances are formed when atoms share electrons in their outer (valant) electron shell in order to attain the stable electron configuration of a noble gas.

The least soluble is metallic bonding, which happens strictly between metals, and mostly in transition metals. This is when all the metal atoms band together in a group, with all the electrons on the outside.

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