Why Do Sodium and Potassium Form Peroxides and Superoxides When They Burn?

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Why do sodium and potassium form peroxides and superoxides when they burn?
 
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I'm not sure exactly what the issue is - what else could (reasonably) form given what is known about the chemistry of those metals and dioxygen? One will also form some amount of metal oxide in both reactions.

If you could share some more details about what is troubling you about these reactions, it might be helpful in satisfying your curiosity.
 
Well, why don't they form just the regular metal oxide? And why is superoxide superoxide more than peroxide with K?
 
Essentially, it's a matter of energetics - it's more favorable to produce the peroxides and superoxides for sodium and potassium. The following website -

http://www.chemguide.co.uk/inorganic/group1/reacto2.html

- does a nice, succinct job in describing what's going on in these reactions (and for the rest of the Group I elements).