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In many reactions mechanisms, we study things like 'it forms explosive mixture and should be discarded off immediately'.

Now my question is 'If those compounds are that much unstable that it will explode, why they form at the first place?' For example, if an explosive is getting formed, atoms might have assembled together and its energy will be increasing. But if that much energy is stored that it will explode, why it gets stored then?

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Think of chemical changes as a heavy ball rolling down a hill. In some cases, there's a divot near the top of the hill, and the ball gets trapped (a metastable state). However, just beyond that divot is a steep drop-off.

As long as the ball stays in the depression (i.e., there's insufficient energy to activate it), all well and good. For example, the substance 2-methyl-1,3,5-trinitrobenzene is easily produced by the (step-wise) nitration of toluene. This product is quite stable under most conditions; in fact, it took 28 years from Wilbrand's synthesis in 1868 until Häußermann found it explosive!

Once the activation energy is reached, and the ball rolls downhill, it shakes the ground (i.e., causing vibration, and releasing heat), freeing enough energy to activate others that are trapped -- a chain reaction.

The only fly in the ointment is quantum mechanics. Depending how deep the activation well, occasionally, the ball can tunnel out of the divot. Bang! with no obvious activation. For example, nitrogen triiodide has a remarkably low activation energy, causing rapid unscheduled disassembly of the sample and related equipment while drying.

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