The obvious reason is that electronegative atoms will pull electrons away from the oxygen atoms, delocalizing the negative charge in the carboxylate, hence stabilizing the molecule.
It turns out that this obvious reason is a minor one - the main reason is entropy.
You might guess that entropy increases when the acid disassociates, but this is only true in the gaseous phase. In a solvent such as water, charged species have a "shell" of solvent molecules, which is more ordered, hence total entropy change is negative.
When the charge is spread out over the carboxylate, there are more ways of arranging this shell of solvent molecules, so the entropy change is not as negative.
Diagram:
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