It has to do with how many atoms the electrons are spread over. A localized lone pair stays near one atom in a molecule, whereas a delocalized lone pair is spread between two, or even more, atoms. An example of a localized lone pair would be an ammonia molecule, NH3, because the lone pair on the N cannot be spread over the hydrogen atoms. An example of a delocalized lone pair would be in acetic acid (CH3-COO), where the lone pair on the oxygen can be spread over the entire carboxyl group. You need to know about resonance structures in order for this to make sense. In a nutshell, if you can draw a resonance structure, the lone pair is delocalized. If you cannot, it is localized.
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