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Energy is a conserved quantity that flows when there is a change.
In a chemical bond, the energy is at a local minimum. For a chemical
reaction to occur, an activation energy must be added. In some cases, the
electric field of another molecule in close proximity is enough to set the
reaction off spontaneously. The daughter products (at a new local minimum
of energy) are collectively at a lower energy than the parent
materials. This difference in energy between parent bonds and daughter
bonds is what is released. In the vernacular, it is referred to as energy
stored in the bonds. To be more precise, it is the energy in the electric
field between reactants that is released. The common usage of the energy
"stored in bonds" leads to many misconceptions, and should probably not be
used.
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