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I was reading on the Born-Haber cycle when I encountered a problem. The textbook seemed to suggest that since energy must be supplied to separate an ionic compound into it's composite ions, then the ions are more stable when they are bonded than when they are separate. My question is why?

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    $\begingroup$ It is consequence of the general rules of electrostatics. The opposite charges have lower energy when closer each other. Directly related is the lattice energy of ionic compounds, where are alternating ions with opposite charge, so energy decrease due closiness of the opposite charges is bigger than energy increase due closiness of the same charges, as the the formaer are in average closer each other. $\endgroup$ – Poutnik Jun 23 at 13:26
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What's meant by stability is whether the compound "wants" to be in current state. If it wants to change the state (separated ions want to bond) then the system is less stable.

In your example you can simply imagine 2 spherical magnets placed close to each other - they would rush towards one another. They had potential energy that turned into kinetic energy. And once they met - they don't have potential energy anymore, thus they are at lower energy state (more stable) and don't want to separate. Then you'd need to apply force to separate them.

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