To answer a couple of things more specifically:

1. Chlorine, cyanuric acid and around 12 species of chlorinated cyanurates remain in equilibria with each other. For most interactions, the reaction kinetics are VERY fast.

2. Chlorine is not volatile in a chemical or physical sense; only figuratively. Rather chlorine undergoes rapid hydrolysis in water, forming HOCl <=> -OCl, with both species subject to rapid photolysis when exposed to solar UV. Chlorinated cyanurate species are NOT subject to this photolysis, but remain in equilibria with those species. HOCl is the primary actor in most sanitation and oxidation; -OCl is not as active. But even though the presence of CYA greatly lowers the HOCl present, the chlorinated cyanurates form a LARGE reservoir of instantly available HOCl, so that stabilized chlorine appears more active in practice than the absolute level of HOCl present would suggest.

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