Why exactly do smaller molecules have a stronger ionic attraction?

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It might be because they delocalize the charge less, as a result of the smaller molecule/atom.
 
Ionic molecules don't share electrons. ionic attraction is between positive charge and negative charge. The greater the positive and negative charges, the stronger the ionic attraction becomes. Smaller molecules have electrons closer to the nuclei ( more S character) , so the distribution of electrons doesn't spread over large space. Therefore, it allows the charge of the smaller molecules to be more "concentrated" , as a result, increase the charge effect, which leads to stronger ionic attraction.
 
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Consider coulomb's law: F = kQq/r^2

When molecules are smaller, the distance between them is reduced (they can get closer together before repulsion occurs).

Thus, smaller r values imply much larger force of ionic attraction. Using these physics equations can help avoid ambiguity when you're unsure of the concept!

Hope that helps!
 
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