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Let us say you have an ionic compound such as table salt, sodium chloride. The sodium atom donates a negatively charged electron to the chlorine atom, so that both atoms can achieve a more stable electron configuration. As a result, the sodium is now a positively charged ion and the chlorine is now a negatively charged ion. Opposite charges attract (as per Coulomb's Law) and so, the oppositely charged ions attract each other, and that's why the compound stays together.

Now, if it is a covalent compound such as, for example, water, then the process is different. The oxygen is sharing electrons with two hydrogen atoms. They stay together because they have to be together in order to share electrons. The stability of their electron configuration requires it.

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