There are a lot of factors that go into this. Some chemicals are not stable because of their shape, like a three membered ring structure will have more strain on it than a 6 membered ring structure (imagine the shape and the angles they create). Some are not stable when exposed to air, because the water in the atmosphere reacts with the chemical, and hydrolyses it.
Well, ultimately it goes down to the lowest energy state of the structure of the chemical, If a chemical has a structure such that it will have strain, and requires higher energy to survive, it will try to change in such a manner, that a lowest possible energy state could be reached.
Many compounds we deem “stable” because under normal conditions (room temperature and in air) we can observe them and study them. But all compounds can be made to react if you give them enough energy (let’s say in the form of heat). This barrier varies in size. If the size is very small, ambient conditions may be enough force the compound apart, to react with other compounds like H2O or in extreme cases, catch fire.
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