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So here's the thing... Ultimately, energy is not stored in a
bond. You can often, however, ADD energy, break that bond,
form a NEW bond, and end up with a NET release in energy.
That (extra) energy comes from the field between the original
atoms and NEW atoms in their vicinity... BUT... that 'field
energy' can only be accessed by breaking the original bonds.
Going back to ATP, you have to break those initial bonds,
absorbing energy, and THEN new, stronger bonds form releasing
more energy than was initially added.
Biology typically glosses over the intermediate steps and
leaves kids with a completely incorrect concept. As a
result, the topic of bonding in chemistry is one of the most
confusing they ever face.