I saw an interesting spectrum in my biology class the other day. On the left end was methane - the least oxidized form of carbon - and the most energetic form of carbon (at least relative to what else was on the slide). On the right end was carbon dioxide - the most oxidized form of carbon - and the form with the lowest energy.
Now, I do agree with the slide - we can combust methane but we can't combust carbon dioxide - at least I don't think we can.
However, is there an intuitive explanation of why increasing oxidation state correlates with lower potential energy, at least for carbon?
Does increasing oxidation state correlate with lower potential energy for all elements?
Why does it seem that oxygen forms rather strong bonds with other elements in many cases?