What's a "stability series" (or sequence) in chemistry?

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Answer:
stability series
A grouping of minerals arranged according to their persistence in nature; i.e., to their resistance to alteration or destruction by weathering, abrasion during transportation, and postdepositional solution; e.g., olivine (least stable), augite, hornblende, biotite (most stable). The most stable minerals are those that tend to be at equilibrium at the Earth's surface...
It is usualy a vertical list of elements. Each element is able to replace any of the elements below in their aqueous solutions.
The list goes like this: K, Ca, Na, Mg, Al, Zn, Fe, Sn, Pb, H, Cu, Hg, Ag, Au.
Obvoiusly, all metals are capable of replacing gold from its aqueous solution; meaning dissolving in gold salts solutions and causing gold to precipitate, i.e., reducing gold. Mg cannot do this to K, Ca & Na solutions, but can do it to the rest.
This is called electrochemical series.
There is a "stability series", but that is concerned with coordination chemistry, and I don't think you are asking about that.

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